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Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

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actpd (On the action of nitric) on the esters of methyl-phenylaminoformic acid. 451.
— (On the nitration of orthochloro- and orthobromobenzoic). 462.
ADRIANI (J. H.). /Eutectie curves in systems of three substances of which two are
optical antipodes”. 463.
AGE of the Earth (The amount of the circulation of the carbonate of lime and the),
(1). 48. (IL). 116.
AGGLUTINATIVE substances. See SuBSTANCES.
AGONIADINE (Plumieride and its identity with). 35.
ALBERDA VAN EKENSTEIN (w.). See Lopry pz Bruyn (C. A).
ALPINIA malaccensis Rose. (On the essential oil from the leaves of). 451.
ANHARMONIC ratio. See Rario.
ANTIPODES (Hutectic curves in systems of three substances of which two are optical). 463.
Astronomy. E. I’. van pe Sanpe Bakauyzen: The motion of the Pole of the Earth
according to the observations of the last years”. 157.
— H. G. van pe Sanpe Bakuuyzen: /Report of the Committee for the organi-
zation of the observations of the solar eclipse on May 18th 1901”. 529.
— J. C, Kapreyn: On the luminosity of the fixed stars”. 658.
ATMOSPHERIC PRESSURE (Measurements on the magnetic rotation of the plane of pola
risation in liquefied gases under). (I). 70.
ATTRACTION (On the relation between radiation and molecular). 27.
Bacteriology. M. W. Berertnck: vOn different forms of hereditary variation of
microbes”. 352.
— M. W. Berertnex: On oligonitrophilous Bacteria”. 586.
BAKHUIS ROOZEBOOM (H. W.) presents a paper of Dr. Ernst Conen and H.
Rakxen: /The solubility of calciumearbonate in sea-water”. 63.
— The behaviour of mixtures of mercuric-iodide and silver-iodide, 84.
— presents a paper of Dr. A. Smits: 7A new method for the exact determination
of the boiling-point”. 86,
— presents a paper of Dr, Ernst Conen : Thermodynamics of standard-cells”. (Ll). 91.
(IID). 208.
— presents a paper of Dr, Ernst Conen : ”The Enantiotropy of ‘lin’. (V). 93. (VD. 469.
— presents a paper of Dr. C. van Eyx: /The formation of mixed crystals of
Thalliumnitrate and Thalliumiodide”. 98.
— presents a paper of Dr. A. Smits: On soap-solutions”. 138.
48
Proceedings Royal Acad. Amsterdam. Vol. III.

II CLOGNy DIEGN TE:

BAKHUIS ROOZEBOOM (H. W.) presents a paper of Dr. Erxst Conen: The
metastability of the Weston-Cadmiumeell and its insuitability as standard of
electromotive force”. 217.

— presents a paper of Dr. Ernsr Conen: /Experimental determination of the
limiting heat of solution”. 327.
— presents a paper of Dr. Ernst Conen: The Weston-Cadmiumeell”. 380.

— presents a paper of Dr. J. H. Aprranr: Eutectic curves in systems of three
substances of which two are optical antipodes”. 463.

— presents a paper of Dr. H. B. Hotssorr: On heats of solution in general,
that of Cd SO,, 8/; H,O in particular”. 467.

— presents a paper of Dr. A. Smits: /Determination of the decrease of vapour-
tension of a solution of NaCl at higher temperature”. 503.
— presents a paper of Dr. A. Smits: /Some observations on the results obtained
in the determination of the decrease in vapour-tension and of the lowering of
the freezing-point of solutions, which are not very dilute”. 507.
— presents a paper of Dr. Ernst Conen and E. H. Bucnner: /Etarp’s Law of
solubility”. 561.
—- presents a paper of Dr. C. H. Wryp: On the irregularities of the cadmium
standard cell”. 595.
— presents a paper of Dr. A. Smits: ”On the progressive change of the factor 7
as function of the concentration”. 717.
BAKHUYZEN (E. F. VAN DE SANDE). See SANDE Baknuyzen (I. F. van DE).
BAKHUYZEN (H. G. VAN DE SAND#). See SANDE Baknuyzen (H. G. van De).
BAKKER (G.). Contribution to the theory of elastic substances. 473.
BEMMELEN (J. F. VAN). Further results of an investigation of the Monotreme-
skull. 130. — 3r4 Note. 405.
BEMMELEN (J. M. VAN) presents a paper of Dr. F. A, H. ScurermeMaAKErs:
vOn the composition of the vapourphase in the system: Water-Phenol, with one
and with two liquid-phases”’. 1.
— presents a paper of Prof. Eve. Dunots: The amount of the circulation of the
Carbonate of Lime and the age of the earth’. (Q. 43. (IL). 116.
— On the system: Bi,O,—N,O,—H,0. 196.
— presents a paper of Dr. F. A. H. Scurernemakers: “Notes on Equilibria
in ternary systems”. 701.
BEIERINCK (mM. w.). Further researches on the formation of Indigo from the
Wond (Isatis tinctoria). LOI.
— On different forms of hereditary variation of microbes. 352.
— On the development of Buds and Bud-variations in Cytisus Adami. 365.
— On oligonitrophilous Bacteria. 586.
HEWERMAN (H. d,), Curious disturbances of the sensation of pain ina case of tabes
dorsalis. 253,
— On the influence upon respiration of the faradie stimulation of nerve tracts
passing through the internal eapsula, 689,

BILE (Researches on the secretion and e »mposition of) in living men, 584,

CONTENTS. Ii

BisMuTH (The Haut-effect and the increase of resistance of) in the magnetic-field at
very low temperatures. (IL). 177.

— (Crystals of). See Crystats.
BISMUTHNITRATE and Water (Qn the system). 196.
BLANKSMA (J. J.). Organic polysulfides and the polysulfides of sodium, 457.
BLooDcoRPUsCLES (On the resisting power of the red). 76.

— (On the permeability of the red) for NO,- and SO,-ions. 371.
BLOODsERUM (On the durability of the agglutinative substances of the). 41.
BOILING-PoINT (A new method for the exact determination of the). 86.
BOLTZMANN’s and Wren’s Laws of radiation. 607.

BONNEMA (J. H.). Leperditia baltica His. sp. their identity with Leperditia Eich-
waldi Fr. v. Schm. and their being found in Groningen diluvial erraties. 137.

— On the occurrence of remains of Leperditia grandis Schrenck sp. in the erratic
blocks of the Groningen diluvium. 545.

Botanics. M. W. Beterrscx: Further researches on the formation of Indigo from
the Woad (Isatis tinctoria)’’. 101.

—C. A. J. A. Ouprmans: Contributions to the knowledge of some undescribed
or imperfectly known fungi”. (L). 140. (IL). 230. (III). 332. (IV). 386.
— Hueco ve Vries: 7On the origin of new species of plants”. 245.
— W. Borck: Preservatives on the stigma against the germination of foreign
Pollen’. (Communicated by Prof. Hugo pE Vries). 264.
— M. W. Bewerrmck: On the development of Buds- and Bud-variations on
Cytisus Adami”. 365.
— F. A. F. C. Went: /On the influence of nutrition on the secretion of Enzymes
by Monilia sitophila (Mont.) Sace.” 489.
— S. L. Scnouren: A pure culture of Saprolegniaceae”. (Communicated by Prof.
F. A. F. C. Went). 60).
BOUDIN (m.). See KamprtincH Onnes (H.).
BRAND (J.). Researches on the secretion and composition of bile in living men. 584,
BRUYN (c. A. LOBRY D&#). See Lory DE Bruyn (C. A.).
BUCHNER (&, H.). See Conen (Ernst).
BuDs and Bud-variations (On the development of) in Cytisus Adami. 365.
BURCK (w.), Preservatives on the stigma against the germination of foreign Pollen. 264,
CADMIUMCELL (The metastability of the) and its insuitability as standard of electro-
motive force. 217.
— (The Weston). 380.
CADMIUM standard cell (On the irregularities of the). 595.
CALCIUMCARBONATE (The solubility of) in sea-water. 63.
— See also Carponate of Lime.
CARBONATE of lime (The amount of the circulation of the) and the age of the Earth.
(1). 48. (IT). 116.
— See also CALCIUMCARBONATE.
CHANGE (On the progressive) of the factor ¢ as function of the concentration. 717.

48*

re a ee Se

Iv COON YT EN Rs.

Chemistry. F. A. H. Scurervemakers: ,On the composition of the vapour-phase in
the system: Water-Phenol, with one and with two liquid-phases. (Communicated
by Prof. J. M. vAN BEMMELEN). 1.
— M. Gresnorr: ”Echinopsine, a new crystalline vegetable base”. (Communicated
by Prof. A. P. N. Francuront). 11.
— A. P. N. FrancurMont: /Plumieride and its identity with Agoniadine.” 35.

— P. van Rompurcu: On the crystallised constituent of the essential oil of
Kaempferia Galanga L.” 38.

— Ernst Cowen and H. Raken: The solubility of calcium carbonate in sea-water.”
(Communicated by Prof. H. W. Baxuurs Roozrgoom). 63.

— H. W. Baxkavis Roozesoom: The behaviour of mixtures of mercuric-iodide
and silver-iodide.” 84.

— A. Smits: vA new method for the exact determination of the Boiling-point”.
(Communicated by Prof. H. W. Baxuurs RoozEBoom), 36.

— Ernst ConEen: /Thermodynamics of standard cells”. (Communicated by Prof.
H. W. Baxuurs RoozEsoom). (If). 91. (I11). 208.

— Ernst Conen: The Enantiotropy of Tin”. (Communicated by Prof. H. W. Baxauts
Roozesoom). (V). 93 (VI). 469.

—- C. van Eyx: /The formation of mixed crystals of Thallium nitrate and Thallium *
iodide”. (Communicated by Prof. H. W. Baknurts RoozEsoom). 98.

— A. Smits: ”On soap-solutions”. (Communicated by Prof. H. W. Bakauts Rooze-
BOOM). 133.

— J. M. van Bemmeten: On the system: Bi,0,—N,0,—H,0”. 196.

— A. P. N. Francurmont presents the dissertation of Dr. L. van SCHERPENZEEL:
vYhe action of hydrogen nitrate (real nitric acid) and the three toluic acids and
some of their derivatives”. 203.

— Erysr Conen: The metastability of the Weston-cadmiumcell and its insuitability
as standard of electromotive force”. (Communicated by Prof. H. W. Bakuurs
Roozesoom). 217.

— fevst Conen: ”Experimental determination of the limiting heat of solution”.
(Communicated by Prof. H. W. Baknurs Roozesoom). 327.

— U. A, Losey br Bruyn: /Review of the results of a comparative study of the
three dinitrobenzenes”. 375.

— Enysr Courn: The Weston-cadmiumcell”, (Communicated by Prof. H. W.
Baknurs Roozenoom). 380,

— ©. A, Losey pe Bruyn and W. Atperpa van Mikenstein: 7A new kind of
formal- (methylene-) compounds of some oxy-acids”, 400.

— P. van Rompuron: /On the essential oil from the leaves of Alpinia malaccensis
Rose”. 451,

— P. van Rompuron: ,On the action of nitric acid on the esters of methyl-
phenylaminoformic acid’. 451,

— P. van Romiunai: »On the essential oil from Ocimum Basilicum L”. 454.

— J.J. Bianksma: Organic polysulfides and the polysulfides of sodium”, (Com-
munieated by Prof, ©, A. Loony pe Bruyn). 457,

CONTENTS. Vv

Chemistry. N. ScHoort: ,On urea derivatives of sugars”. (Communicated by Prof. C.
A. Lopry DE Bruyn). 459.
— A. F. Hotreman: On the nitration of orthochloro- and orthobromobenzoie acid”.
(Communicated by Prof. C. A. Lopry DE Bruyn). 462.
— J. H. Avrianr: Eutectic curves in systems of three substances of which two
are optical antipodes”. (Communicated by Prof. H. W. Bakuuis Roozezoom). 463.
— H. B. Hotsporr: On heats of solution in general, that of Cd SO,,°/, H,O in
particular”, (Communicated by Prof. H. W. Bakuurs RoozeBoom). 467.
— A. Smits: /Determination of the decrease of vapour-tension of a solution of NaCl
at higher temperature”. (Communicated by Prof. H. W. Baknuis RoozeBoom). 503,
— A. Smits: /Some observations on the results obtained in the determination of
the decrease in vapour-tension and of the lowering of the freezing-point of
solutions, which are not very dilute”. (Communicated by Prof. H. W. Bakuurs
Roozesoom). 507.
— Ernst Conen and E. H. Bucuner: /Etarp’s law of solubility”. (Communicated
by Prof. H. W. Bakutis Roozesoom). 561.
— ©. H. Winn: /On the irregularities of the cadmium standard cell”. (Communi-
eated by Prof. H. W. Baxaurs RoozEpoom). 595.
— Ff. A. H. Scureinemakers: /Notes on Equilibria in ternary systems’’, (Commu-
nicated by Prof. J. M. van BemMMELEN). 701.
— P. K, Lvnors: /Substitution velocity in the case of aromatic halogen-nitro-
derivatives’. (Communicated by Prof. C. A. Lopry DE Bruyn). 715.
— A. Smits: vOn the progressive change of the factor 7 as function of the con-
centration”. (Communicated by Prof. H. W. Baknurs RoozEBoom). 717.
crecLes (On the pedal) of the point-field in reference to a given triangle. 323.
COEFFICIENT of pressure variation of pure hydrogen between 0° and 1009. 299.
COHEN (£RNS1). Thermodynamics of standard cells, (IL). 91. (III). 208.
— The Enantiotropy of Tin. (V). 93. (VI). 469.
— The metastability of the Weston-cadmiumcell and its insuitability as standard
of electromotive force. 217.

— Experimental determination of the limiting heat of solution. 327.

— The Weston-cadmiumeell. 380.

— and E. H. Bocuner: Erarp’s Law of solubility. 561.

— and H. Raxen. The solubility of caleiumearbonate in sea-water. 63.
CONCENTRATION (On the progressive change of the factor 7 as function of the). 717.
CONDENSATION (On the phenomena of) in mixtures in the neighbourhood of the

critical state. 66.
CRITICAL STATE (On the phenomena of condensation in mixtures in the neighbourhood
of the). 66.
— (On pe Huen’s experiments about the). 628.

— (On differences of density in the neighbourhood of the) arising from differences
of temperature. 691.

crysTaLs (The formation of mixed) of Thalliumnitrate and Thalliumiodide. 98.

— of bismuth (On the Hall-effect and the resistance of) within and without the
magnetic field. 316. 407.

vi CONTENTS,

curvE (Involutions on a) of order four with triple point. 696.
curves 4" (On the spacial anharmonic ratio of) of order x in the system Sz with
n-dimensions. 235.

— (Eutectic) in systems of three substances of which two are optical antipodes. 463,
cyclic MotTIoN (The equation of state and the theory of). (I). 515. (II). 571. (II). 643.
cytTisus abAMI (On the development of Buds and Bud-variations in). 365,
pensity (On differences of) in the neighbourhood of the critical state arising from

differences of temperature. 691.
DILUVIAL erratics. See Errarics.
DINITROBENZENES (Review of the results of a comparative study of the three). 375.
DuUBOIs (EUG). The amount of the circulation of the Carbonate of Lime and the
age of the Earth. (I). 43. (ID. 116.
EARTH (The amount of the circulation of the Carbonate of Lime and the age of the).

(1). 48. (IL. 116.

— (The motion of the Pole of the) according to the observations of the last years. 157.
ECHINOPSINE, « new crystalline vegetable base. 11.

— (On the physiological action of). 23.

— (On the localisation of). 24.

ELASTIC substances. See SUBSTANCES.

ELECTROMOTIVE FORCE (The metastability of the Weston-cadmiumceell and its insuita-
bility as standard of). 217.

EMDEN (J. E. G. VAN). On the durability of the agglutinative substances of the
bloodserum, 41.

ENANTIOTROPY (The) of Tin. (V). 93. (VI). 469.

enzYMES (On the influence of nutrition on the secretion of) by Monilia sitophila
(Mont.) Sace. 489,

EQUATION of state (The) and the theory of eyclic motion, (D. 515. (IL). 571. (LID). 643.

EQUILIBRIA (Notes on) in ternary systems. 701.

eRkatics (Leperditia baltica His, sp. their identity with Leperditia Kichwaldi Fr. v.
Sechm. and their being found in Groningen diluvial). 137.

ERRATIC BLOCKS (On the occurrence of remains of Leperditia grandis Schrenck sp. in
the) of the Groningen diluvium. 545.

ERRATUM, 374,

ETARD’'s Law of solubility, 661.

EUTEOCTIC curves, See Curves.

EVERDINGEN JR. (E, VAN). The Hall-eflect and the increase of resistance of
bismuth in the magnetic field at very low temperatures. (IL). 177.

— On the Hall-effect and the resistance of erystals of bismuth within and without

the magnetic field. 316. 407,

ExPANsION of a function (On the) in a series of polynomials, 565.

ByYK (6, VAN), The formation of mixed erystals of Thalliumnitrate and Thallium-
iodide, 98,

vacton ¢ (On the progressive change of the) as function of the concentration, 717,

PAMADIO stimulation (On the influence upon respiration of the) of nerve tracts passing

through the internal capsula, 68%,

CONTENTS. vit

FoRMAL- (methylene-) compounds (A new kind of) of some oxy-acids. 400.

FRANCHIMONT (a. P. N.) presents a paper ‘of Dr. M. Gresuorr : /Echinopsine,
a new crystalline vegetable base”. 11.

— Plumieride and its identity with Agoniadine. 35.

— presents the dissertation of Dr. L. van ScuerPENzeeL: /The action of hydrogen
nitrate (real nitric acid) on the three toluic acids and some of their derivatives”. 203.

FREEZING-POINT of solutions (Some observations on the results obtained in the deter-
mination of the decrease in vapour-tension and of the lowering of the) which
are not very dilute. 507.

FouNcTION (On the expansion of a) in a series of polynomials. 565.

FuNGI (Contributions to the knowledge of some undescribed or imperfectly known).
(D. 140. (ID). 230. (ILD. 232. (IV). 386.

Gases (Isothermals of diatomic) and their binary mixtures. 621.

— (Measurements on the magnetic rotation of the plane of polarisation in liquefied)
under atmospheric pressure. (1). 70.

GEGENBAUER (t.). On the Mac Manon generalization of the Newron-GiraRD
formulae. 347.

Geodesy. J. A. C. OupEMans: ,On the contents of the 6 and last part of the Report
Die Triangulation yon Java’. 549.

Geology. Eva. Dusors: /The amount of the circulation of the Carbonate of Lime and
the age of the earth’. (Communicated by Prof. J. M. van BEMMELEN). (I). 43.
(IL). 116.

-— J. H. Bonnema: vLeperditia baltica His. sp. their identity with Leperditia
Eichwaldi Fr. y. Schm. and their being found in Groningen diluvial erratics”.
(Communicated by Prof. J. W. Mott). 137.

— J. L. C. ScuRoEDER VAN DER KoLk: The so-called opake minerals in trans
mitted light”. 254.

— J. H. Boynema: 7On the occurrence of remains of Leperditia grandis Schrenck
sp. in the erratic blocks of the Groningen diluvium”. (Communicated by Prof, J.
W. Motu). 545.

GERMINATION of foreign Pollen (Preservatives on the stigma against the). 264.

GLANDULA THYMUS (On the proteids of the). 383.

GRAPHICAL treatment of the transverse plait. 275.

GREsSuOFF (M.), Echinopsine, a new crystalline vegetable base. 11.

HALL-EFFECT (The) and the increase of resistance of bismuth in the magnetic field at
very low temperatures. (IL), 177.

— (On the) and the resistance of crystals of bismuth within and without the
magnetic field. 316. 407.

HAMBURGER (u. J.), On the resisting power of the red bloodcorpuseles. 76.

— On the permeability of the red bloodeorpuscles for NO,- and SO,-ions. 371.

HARTMAN (CH. M. A.), On the phenomena of condensation in mixtures in the
neighbourhood of the critical state. 66.

HEaT of solution (Experimental determination of the limiting). 327.

nEATs of solution (On) in general, that of Cd SO,, °/, H,O in particular, 467.

HEEN’s (DE) (On) experiments about the critical state. 628.

)
;
q
i]

VIIt GOR PEN TS:

HOFFMANN (c. K.) presents a paper of Dr. J. F. van BemMeven: /Further results
of an investigation of the Monotreme-skull”. 130.

HOLLEMAN (a. F.). On the nitration of orthoehloro- and orthobromobenzoic acid. 462.

HOLSBOER (H. B.). On heats of solution in general, that of Cd SQ,, */,; H,O in
particular. 467. i

HUBRECHT (A. A. W.) presents a paper of Dr. J. F. van BemMMeELeNn: Third note
concerning certain details of the Monotreme-skull”. 495.

HYDROGEN (Coefficient of pressure-variation of pure) between 0° and 100°. 299.

HYDROGEN NITRATE (real nitric acid) (The action of) on the three toluic acids and
some of their derivatives. 203.

HYNDMAN (H. H. FRANCIS). See KAMERLINGH OnnzEs (H. H.).

tnDIGO (Further researches on the formation of) from the Woad (Isatis tinctoria). 101.

INTERNAL CAPSULA (On the influence upon respiration of the faradic stimulation of
nerye tracts passing through the). 689.

TopivE (Lhe behaviour of mixtures of mercuric-iodide and silver-iodide). 84.

1oxs (On the permeability of the red bloodcorpuscles for NO,- and SO,-). 371.

ISATIS TINCTORIA. See Woap.

ISOTHERMALS of diatomic gases and their binary mixtures. 621.

— (Precise), 421. 481.

KAEMPFERIA Galanga L. (On the crystallised constituent of the essential oil of). 38.

KAMERLINGH ONNES (H.) presents a paper of Dr. Ca. M. A. Hartman: /On
the phenomena of condensation in mixtures in the neighbourhood of the critical
state”. 66.

— presents a paper of Dr. L, H. Stertsema : Measurements on the magnetic rotation
of the plane of polarisation in liquefied gases under atmospheric pressure”. (I). 70.

— presents a paper of Dr. E. van Everpincen Jr: /The Haxt-eftect and the
increase of resistance of bismuth in the magnetic field at very low temperatures”.
(Il), 177.

— Contributions to the knowledge of vaN per Waats’ p-surface. (I). Graphical
treatment of the transverse plait”, 275. (UL). The part of the transverse plait in
the neighbourhood of the plaitpoint in KUENEN’s experiments on retrograde con-
densation. 289.

— presents a paper of Dr. BE. van Everpincen Jr: »On the Haxt-eflect and the
resistance of crystals of bismuth within and without the magnetic field”. 316. 407.

— presents a paper of J, OC. ScuankwuK: /Precise isothermals. I. Measurements
and calculations on the corrections of the mercury meniscus with standard mano-
meters”, 421, 481.

— On ve Ileey’s experiments about the critical state. 628.

— On differences of density in the neighbourhood of the critical state arising from
differences of temperature. 61.

— and M, Bouprtx. On the measurement of very low temperatures. ILI. Coefficient
of pressure variation of pure hydrogen between 0° and 100°, 299.

—and H, HH, Paancis ttynpman, Isothermals of diatomic gases and their binary
mixtures, 1, Piezometers of variable volume for low temperatures. 621,

KAPTEYN (J, ©). On the luminosity of the fixed stars. 658.

CONTENTS. 1x

KLUYVER (J. c.). On the expansion of a function in a series of polynomials. 565.
KOBERT (k.). On the physiological action of Echinopsine. 23.
KOLK (J, L. C. SCHROEDER VAN DER). See SCHROEDER VAN DER KOLK (J. L.C.).
KUENEN’s experiments (The part of the transverse-plait in the neighbourhood of
the plaitpoint in) on retrograde condensation. 289.
LANGELAAN (js, w.). On muscle-tone. 248.
— On the determination of sensory spinal skinfields in healthy individuals. 251.
LEPERDITIA baltica His. sp. their identity with Leperditia Eichwaldi Fr. vy. Schm.
and their being found in Groningen diluvial erraties. 137.
— grandis Schrenek sp. (On the occurrence of remains of) in the erratic blocks of
the Groningen diluvinm. 545. .
LIQUID-PHAsEs (On the composition of the vapour-phase in the system : Water-Phenol,
with one and with two). 1.
LOBRY DE BRUYN (ce. A.). Review of the results of a comparative study of the
three dinitrobenzenes. 375.
— presents a paper of Dr. J J. Branxsma: vOrganic polysulfides and the poly-
sulfides of sodium”. 457.
— presents a paper of N. Scuoori: On urea derivatives of sugars”. 459.
— presents a paper of Prof. A, F. Hotneman: On the nitration of orthochloro-
and orthobromobenzoic acid”. 462.
— presents a paper of Dr. P. Kk. Lunors: Substitution velocity in the case of
aromatic halogen-nitroderivatives”. 715.
— and W. Auserpa vaN Exenstets: ”A new kind of formal- (methylene-) com-
pounds of some oxy-acids”. 400.
LORENTZ (H. A.). The theory of radiation and the second taw of Thermodynamics. 436.
— Bourzmann’s and Wren’s Laws of radiation. 607.
LULOFs (P. K.). Substitution velocity in the case of aromatic halogen-nitroderi-
vatives. 715.
MAC GILLAVRY (TH. H.) presents a paper of Dr. J. E. G. van Empen: »On the
durability of the agglutinative substances of the bloodserum”’. 41.
MAC MAHON generalization (On the) of the Newron-Grrarp formulae. 347.
MAGNETIC FIELD (The Hatt-effect and the increase of resistance of bismuth in the)
at very low temperatures, ([L). 177.
— (On the Hatt-effect and the resistance of erystals of bismuth within and without
the). 316. 407.
MAGNETIC ROTATION (Measurements on the) of the plane of polarisation in liquefied
gases under atmospheric pressure. (I). 70.
MANOMETERS (Measurements and calculations on the corrections of the mercury meniscus
with standard). 421. 481.
Mathematics. P. H. Scuourr: On the spacial anharmonic ratio of curves 6" of order
n in the space Sx with n-dimensions”. 255.

— Jan ve Vrigs: vOn the pedal-circles of the point-field in reference to a given
triangle”. 323.

— L. Grcensaver: On the Mac Manon generalization of the Newron-Grrarp
formulae”. (Communicated by Prof. JAN pe Vriks). 347.

x €ONTENTS.

Mathematics. J. C. Kuvyver: /On the expansion of a function in a series of
polynomials”. 565.
— Jan ve Vates: /Involutions on a curve of order four with triple point”. 696.
MEASUREMENT (On the) of very low temperatures. 299.
MEASUREMENTS and calculations on the corrections of the mercury meniscus with
standard manometers. 42]. 481.
— on the magnetic rotation of the plane of polarisation in liquefied gases under
atmospheric pressure. (I). 70.
MENIScUs (Measurements and calculations on the corrections of the mercury) with
standard manometers. 421. 481.
MERCURIC-iodide. See [ODIDE.
METASTABILITY § (The) of the Weston-cadmiumcell and its insuitability as standard of
electromotive force. 217.
METHOD (A new) for the exact determination of the boiling-point. 86.
METHYL-PHENYLAMINOFORMiC ACID, See ACID.
METHYLENE-compounds, See Formau- (methylene-) compounds,
MICROBES (On different forms of hereditary variation of). 352.
MINERALS (The so-called opake) in transmitted light. 254.
— (On hardness in) in connection with cleavage. 645.
Mineralogy. J. LL. C. ScHrorDER VAN DER KoLk: On hardness in minerals in connection
with cleavage”. 655.
MIXTURES (lsothermals of diatomic gases and their binary). 621.

— (On the phenomena of condensation in) in the neighbourhood of the critical
state. 66,

— (The properties of the pressure-curves for co-existing phases of). 163.
— of mercuric-iodide and silver-iodide (The behaviour of). 84.

MOLECULAR attraction. See ATTRACTION.

MOLL (J. w.) presents a paper of J. H. Bonnema: /Leperditia baltica His. sp. their
identity with Leperditia Kichwaldi Fr. vy. Schm. and their being found in Groningen
diluvial erraties”. 137.

— presents a paper of J. H. Bonnema: /On the occurrence of remains of Leperditia
grandis Schrenck sp. in the erratic blocks of the Groningen diluvium”. 545.
MONILIA siTOPHILA (Mont.) Sacc. (On the influence of nutrition on the secretion of

enzymes by). 489.

MONOTREME-SKULL (Hurther results of an investigation of the). 180. 3™4 Note, 405.

MUSCLE-TONE (On). 248.

NeRVE tracts (On the influence upon respiration of the faradic stimulation of) passing
through the internal capsula. 689.

NEWTON-GIRARD formulae (On the Mac Manon genelarization of the). 347.

NITRIC ACID. See ACID.
— See HybDkOGEN NITRATE.

NITRATION (On the) of orthochloro- and orthobromobenzoic acid. 462.

NITRODERIVATIVES (Substitution velocity in the case of aromatic halogen-). 716.

NUTRITION (On the influence of) on the secretion of enzymes by Monilia sitophila
(Mont.) Sace. 489.

CONTENTS. XT

OcimMUM BastLicum L. (On the essential oil from), 454.
ort (On the essential) from the leaves of Alpinia Malaccensis Rose. 451.
— (On the essential) from Ocimum Basilicum L. 454.
— of Kaempferia Galanga L, (On the crystallised constituent of the essential). 38.
OLIGONITROPHILOUS Bacteria (On). 586.
ONNES (A. KAMERLINGH). See Kamersinen Onnes (H.).
ORTHOCHLORO- and orthobromobenzoic acid. See Acrp.
OUDEMANS (C. A. J. A.). Contributions to the knowledge of some undescribed or
imperfectly known fungi. (1). 140. (II). 230. (ILL). 332. (LV). 386.
OUDEMANS (J. A. c.). On the contents of the 6th and last part of the Report:
w\ie Triangulation von Java’. 549.
oxy-acips (A new kind of formal- (methylene-) compounds of some). 400.

PAIN (Curious disturbances of the sensation of) in a case of tabes dorsalis. 253.
Pathology. J. E. G. van Emprn: 7On the durability of the agglutinative substances
of the bloodserum’’. (Communicated by Prof. Tu. H. Mac Ginpavry). 41.

— H. D. Bererman: /Curious disturbances of the sensation of pain in a case of
tabes dorsalis”, (Communicated by Prof. C. WINKLER). 253.

PEKELHAR1NG (Ee. a.). On the proteids of the glandula thymus. 383.

PERMEABILITY (On the) of the red bloodcorpuscles for NO,- and SO,-ions. 371.

PHASES of mixtures (The properties of the pressure-curves for co-existing). 163.

PHENOL (On the composition of the vapour-phase in the system Water-), with one
and with two liquid-phases. 1.

Physics. J. D. van per Waaus Jr: /On the relation between radiation and molecular
attraction”. 27.

— Ch. M. A. Hartman: On the phenomena of condensation in mixtures in the
neighbourhood of the critical state”. (Communicated by Prof. H. Kamertineu
Onnzs). 66.

— L. H. Stertsrma: Measurements on the magnetic rotation of the plane of
polarisation in liquefied gases under atmospheric pressure”. (I). (Communicated by
Prof. H. Kamertineu Onnzs). 70.

— J. D. van per Waats: The properties of the pressure-curves for co-existing
phases of mixtures”. 163.

— E. van Everpincen Jr: The Haut-effect and the increase of resistance of
bismuth in the magnetic-field at very low temperatures’. (II). (Communicated by
Prof. H. KamertineH Onnes). 177.

— H. Kameriinen Onnes: /Contributions to the knowledge of van DER WAALS’
J-surface. I. Graphical treatment of the transverse plait”. 275. I. The part of
the transverse-plait in the neighbourhood of the plaitpoint in KUENEN’s experi-
ments on retrograde condensation”, 289.

— H. Kameriincao Onnes and M. Boupiy: On the measurement of very low
temperatures. ILI. Coefficient of pressure variation of pure hydrogen between 0°
and 100°”. 299.

— E. van Everprncen Jr: 7On the Hall-effect and the resistance of crystals of
bismuth within and without the magnetic field”. (Communicated by Prof. H.

KamerbineH Onnzs). 316. 407.

XII CONTENTS,

Physics. J. C. Scuatkwwuk: Precise Isothermals. I. Measurements and calculations on
the corrections of the mercury meniscus with standard manometers’’. (Communi-
cated by Prof. H. Kameriincn Onnes). 421. 481.

—H. A. Lorenz: The theory of radiation and the second law of Thermody-
namics”. 436,

— G. Bakker: /Contributions to the theory of elastic substances”. 473.

— J. D. van perk Waais: ,Lhe equation of state and the theory of cyclic
motion”. (1). 515. (fH). 571. (III). 643.

— H, A. Lorentz: /BoLtzMann’s and Wren’s Laws of radiation”. 607.

— H. Kamertinen Onnes and H. H. Francis Hynpman: Isothermals of diatomic
gases and their binary mixtures, I. Piezometers of variable volume for low tem-
peratures”. 621.

— H, Kameruincn Onnus: On pr Heen’s experiments about the critical state”. 628.

— H. KamertincH Onnes: 7On differences of density in the neighbourhood of
the critical state arising from differences of temperature”. 691.

Physiology. H. J. Hampurcer: /On the resisting power of the red bloodcorpuscles”. 76.
— J. W. Lanceraan: On muscle-tone”. (Communicated by Prof. T. Pace). 248.
— J. W. Lancrtaan: vOn the determination of sensory spinal skinfields in healthy

individuals”. (Communicated by Prof. C. Wixxkurr). 251.

— H. J. Hampurcer: On the permeability of the red bloodcorpuscles for NO,-
and SO,-ions”. 371.

— C. A. Prexennarine: vOn the proteids of the glandula thymus”. 383.

— J. Branp: /Researches on the secretion and composition of bile in living men’’.
(Communicated by Prof. B. J. Srokvis). 584.

— H. D. Beterman: On the influence upon respiration of the faradic stimula-
tion of nerve tracts passing through the internal capsula”. (Communicated by
Prof. C. WiNKLER). 689.

PIEZOMETERS of variable volume for low temperatures. 621.

PLACE (t.) presents a paper of Dr. J. W. Lancetaan: /On muscle-tone”. 248.

pLaiTpoint (The part of the transverse-plait in the neighbourhood of the) in KUENEN’s

experiments on retrograde condensation. 289.

PLANTS (On the origin of new species of). 245.

PLUMIERIDE and its identity with Agoniadine. 35.

POINT-FIELD (On the pedal circles of the) in reference to a given triangle. 323.

POLARISATION (Measurements on the magnetic rotation of the plane of) in liquefied
gases under atmospheric pressure. (I). 70.

pote of the Earth (The motion of the) according to the observations of the last years, 157.

POLLEN (Preservatives on the stigma against the germination of foreign). 264.

POLYNOMIALS (On the expansion of a function in a series of), 565.

POLYSULFIDES (Organic) and the polysulfides of sodium. 457.

POWER (On the resisting) of the red bloodcorpuscles. 76.

PRESSURE-CURVES (Ihe properties of the) for co-existing phases of mixtures. 163.

PRESSURE-VARIATION (Coefficient of) of pure hydrogen between 0° and 100° 299.

proterps (On the) of the glandula thymus. 383.

CONTENTS. XIII

RADIATION (On the relation between) and molecular attraction. 27.
— (The theory of) and the second law of Thermodynamics. 436,
— (Boirzmann’s and WIeEN’s Laws of). 607.
RAKEN (H.). See ConENn (Ernst).
RATIo (On the spacial anharmonic) of curves £" of order x in the space Sx with
n—dimensions. 255.
REINGANUM (m.) and H. Kamerttnen Onnes. The part of the transverse-plait
in the neighbourhood of the plaitpoint in KUENEN’s experiments on retrograde
condensation. 289.

RESEARCHES on the secretion and composition of bile in living men. 584,
RESISTANCE (The Hatt-effect and the increase of) of bismuth in the magnetic field at
very low temperatures. (II). 177.
— of crystals of bismuth (On the Hatt-effect and the) within and without the
magnetic field. 316. 407.

RESISTING Power. See POWER.

RESPIRATION (On the influence upon) of the faradic stimulation of nerve tracts passing
through the internal capsula. 689.
RETROGRADE condensation (The part of the transverse-plait in the neighbourhood of
the plaitpoint in KUENEN’s experiments on). 259.
ROMBURGH (P. VAN). On the crystallised constituent of the essential oil of
Kaempferia Galanga L. 38.
— On the essential oil from the leaves of Alpinia malaccensis Rose. 451,
— On the action of nitric acid on the esters of methyl-phenylaminoformic acid. 451.
— On the essential oil from Ocimum Basilicum L. 454.
ROOZEBOOM (H. W. BAKUUTIS). See Baxuurs Roozesoom (H. W.).
SANDE BAKHUYZEN (E. F. VAN DE). The motion of the Pole of the Earth
according to the observations of the last years. 157.
SANDE BAKHUYZEN (H. G. VAN DE). Report of the committee for the
organization of the observations of the solar eclipse on May 18th 1901. 529.
SAPROLEGNIACEAE (A pure culture of). 601.
SCHALKWIJK (J. c.). Precise isothermals. I. Measurements and calculations on the
corrections of the mercury meniscus with standard manometers. 421. 481.
SCHERPENZEEL (ut. VAN). The action of hydrogen nitrate (real nitric acid) on
the three toluic acids and some of their derivatives. 203.
SCHOORL (N.). On urea derivatives of sugars. 459.
SCHOUTEN (s. L.). A pure culture of Saprolegniaceae. 601.
SCHREINEMAKERS (fF, a. H.). On the composition of the vapour-phase in the
system: Water-Phenol, with one and with two liquid-phases. 1.
— Notes on Equilibria in ternary systems. 701,
SCHROEDER VAN DER KOLK (J. L. c.). The so-called opake minerals in
transmitted light. 254.
— On hardness in minerals in connection with cleavage. 655.
SCHOUTE (P. H.). On the spacial anharmonic ratio of curves 6" of order x in the
space Sv with v-dimensions. 255.

XIV CONTENTS,

SEA-waTer (The solubility of calciumearbonate in). 63.
SIERTSEMA (L. H.). Measurements on the magnetic rotation of the plane of pola-
risation in liquefied gases under atmospheric pressure. (I). 70.
SILVER-iodide. See [op1pE.
SKINFIELDS (On the determination of sensory spinal) in healthy individuals. 251.
smits (a.). A new method for the exact determination of the boiling-point. 86.
— On soap-solutions. 133,
— Determination of the decrease of vapour-tension of a solution of Na Cl.at higher
temperature. 503.
— Some observations on the results obtained in the determination of the decrease
in vapour-tension and of the lowering of the freezing-point of solutions, which
are not very dilute. 507.
— On the progressive change of the factor 7 as function of the concentration, 717.
soaP-solutions (On). 123.
sopium (Organic polysulfides and the polysulfides of). 457.
SOLAR ECLIPSE (Report of the committee for the organization of the observations of
the) on May 18th 1901. 529.
SOLUBILITY (Erarb’s Law of). 561.
soLuTION (Experimental determination of the limiting heat of). 327.
— of NaCl (Determination of the decrease of vapour-tension of a) at higher tem-
perature. 503.
— (Heats of). See Heats.
soLuTIONs (Some observations on the results obtained in the determination of the
decrease in vapour-tension and of the lowering of the freezing-pomt of) which
are not very dilute. 507.
spacE Sn with n-dimensions (On the spacial anharmonic ratio of curves 6" of order x
in the), 255.
STANDARD-CELLS (Thermodynamics of). (IL). 91. (III), 208.
stars (On the luminosity of the fixed). 658.
sTIGMA (Preservatives on the) against the germination of foreign Pollen. 264.
sTOKVIS (8. J.) presents a paper of Dr. J. Branp: /Researches on the secretion
and composition of bile in living men”. 584.
suBSTANCES (On the durability of the agglutinative) of the bloodserum. 41.
— (Contribution to the theory of elastic). 473.
suGARS (On urea derivatives of). 459.
y-surFacE (Contributions to the knowledge of vAN per Waals’). 275.
sysTEM (Bi,O,—N.,O;—H;0) (On the). 196.
systeMs (Notes on equilibria in ternary). 701.
papus dorsalis (Curious disturbances of the sensation of pain in a case of). 253.
TEMPERATURE (Determination of the decrease of vapour-tension of a solution of Nal
at higher). 503.
— (On differences of density in the neighbourhood of the critical state arising
from differences of). 691.
Temperatures (‘The Hatt-effect and the increase of resistance of bismuth in the
magnetic field at very low). (IL), 177.

OVOoN= TB oN DS. XIV

TEMPERATURES (On the measurement of very low). 299.

— (Piezometers of variable volume for low). 621.
TERNARY systems. See SysTEMs.
THALLIUMNITRATE and Thalliumiodide (The formation of mixed crystals of). 98.
THEORY of radiation (The) and the second law of Thermodynamics. 436.

— of elastic substances (Contribution to the). 473.

— of cyclic motion (The equation of state and the). (D. 515. ({1). 571. (ID). 643,
THERMODYNAMICS of standard-cells. (II). 91. (IIT). 208.

— (The theory of radiation and the second law of). 436.
TIN (The Enantiotropy of). (V). 93. (VI). 469.

ToLuic acrps (The action of hydrogen nitrate (real nitric acid) on the three) and
some of their derivatives. 203.

TRANSVERSE-PLAIT (Graphical treatment of the). 275.

— (The part of the) in the neighbourhood of the plaitpoint in KUENEN’s experiments
on retrograde condensation. 289.

TRIANGLE (On the pedal circles of the point-field in reference to a given). 523.

TRIANGULATION (Die) von Java (On the contents of the 6th and last part of the
Report). 549.

TRIPLE POINT (Involutions on a curve of order four with). 696.°

UREA derivatives (On) of sugars. 459.

VAPOUR-PHASE (On the composition of the) in the system: Water-Phenol, with one and
with two liquid-phases. 1.

VAPOUR-TENSION (Determination of the decrease of) of a solution of NaCl at higher
temperature. 503.

— (Some observations on the results obtained in the determination of the decrease
in) and of the lowering of the freezing-point of solutions, which are not very
dilute. 507.

VARIATION (On different forms of hereditary) of microbes. 352.

veELocitTy (Substitution) in the case of aromatic halogen-nitroderivatives. 715.
VERSCHAFFELT (E.). On the localisation of Echinopsine. 24.

VRIES (HUGO DB). On the origin of new species of plants. 245.

— presents a paper of Dr. W. Burck: /Preservatives on the stigma against the
germination of foreign Pollen”. 264.

VRIES (JAN DE). On the pedal circles of the point-field in reference to a given
triangle. 323.

— presents a paper of Prof. L. GrcenBaurr: ”On the Mac Manon generalization
of the Newron-Grirarp formulae”. 347.

— Involutions on a curve of order four with triple point. 696.

WAALS (VAN DER) w surface (Contributions to the knowledge of). 275.
WAALS (J. D. VAN DER). The properties of the pressure-curves for co-existing
phases of mixtures. 163,
— The equation of state and the theory of cyclic motion. (1). 515. (IT). 571. ({1]). 643,
WAALS JR (J. D. VAN DER). On the relation between radiation and molecular
attraction. 27.

XVI CONTENT &

WATER (On the system: bismuthnitrate and). 196,
WATER-PHENOL (On the composition of the vapour-phase in the system), with one and
with two liquid-phases. 1.
WENT (fF. A. F. C.). On the influence of nutrition on the secretion of Enzymes by
Monilia sitophila (Mont.) Sacc. 489.
— presents a paper of S. L. Scnouren: 7A pure culture of Saprolegniaceae”. 601.
weEsTon-Cadmiumeell. See CaDMIUMCELL.
— (The). 380.
WIEN’s Laws of Radiation (BoutTzMaNnn’s and). 607.
WIND (c. u.). On the irregularities of the cadmium standard cell. 595.
WINKLER (c.) presents a paper of Dr. J. W. Lanceraan: On the determination
of sensory spinal skinfields in healthy individuals”. 251.
— presents a paper of H. D. Brryerman: Curious disturbances of the sensation
of pain in a case of tabes dorsalis”. 253.
— presents a paper of H. D. BeryermaN: On the influence upon respiration ot
the faradic stimulation of nerve tracts passing through the internal capsula’’. 689.
woab (Isatis tinctoria) (Further researches on the formation of Indigo from the). 161.
Zoology. J. F. van BemMe en: /Further results of an investigation of the Monotreme-
skull”. (Communicated by Prof. C. K. Horratany). 139.
— J. F. van BemMe en: Third note concerning certain details of the Monotreme-
skull”. (Communicated by Prof. A. A. W. Husrecut). 405.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday May 26, 1900.

DOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 26 Mei 1900 Dl. IX).

Contents: “On the composition of the vapour-phase in the system: Water-Phenol, with one or
with two liquidphases.” By Dr. F. A. H. Scurrinemakers (Communicated by
Prof. J. M. van BemMeven), p. 2. —“Echinopsine, a new crystalline vegetable base.”
By Dr. M. Gresnorr (Communicated by Prof. A. P. N. Francuimonr), p. 11. —
“On the relation between radiation and molecular attraction”. By J. D. van DER
Waats Jr. (Communicated by Prof. J. D. vax per WaAAts), p. 27. — “Plumieride
and its identity with Agoniadine”. By Prof. A. P. N.@rancurmonr, p.35. — “On the
crystallised constituent of the essential oil of Kaempferia Galanga L.”. By Dr. P. van
Romeureu, p. 38.—“On the durability of the agglutinative substances of the bloodserum”.
By Dr. J. E. G.van EmpEn (Communicated by Prof. Tu. H. Mac Giiiavry), p. 41. —“The
amount of the circulation of the carbonate of lime and the age of the Earth”. I. By
Prof. Eve. Dusois (Communicated by Prof. J. M. vAN BemMELEN), p. 43. —‘“The solu-
bility of Caleium Carbonate in Sea-water”. By Dr. Ernst Comen and H. RakEN
(Communicated by Prof. H. W. Bakauis Roozesoom), p. 63. — “On the pheno-
mena of condensation in mixtures in the neighbourhood of the critical state”. By
Dr. Cu. M. A. Harrman (Communicated by Prof. H. KameRLInGH Onnes), p. 66.—
“Measurements on the magnetic rotation of the plane of polarisation in liquefied
gases under atmospheric pressure’. By Dr. L. H. Srertsema (Communicated by

Prof. H. Kameriinca Onnes), p. 70. (With one plate). — “A new method for the
exact determination of the elevation of the Boiling-point”. By Dr. A. Smirs (Com-
municated by Prof. H. W. Bakuurs Roozesoom), p. 74. — “Thermodynamics of

Standard Cells” (2nd part). By Dr. Ernst Consen (Communicated by Prof. H. W.
Bakuuis RoozEsoom), p. 74. — “On the Enantiotropy of Tin”. V. By Dr. Ernst Conen
(Communicated by Prof. H. W. Bakuuris Roozesoom), p. 74. — “The formation of
mixture-crystals of Thalliumnitrate and Thalliumiodide”. By Dr. C. vax Eyk (Coin-
municated by Prof. H. W. Bakuurs RoozEBoom), p. 74.

The following papers were read:

Chemistry. — ‘On the composition of the vapour-phase in the
system Water-Phenol, with one and with two liquid-phases”.
By Dr. F. A. H. Scuremnemakers (Communicated by Prof.
J. M. vAN BEMMELEN).

(Read April 21, 1900.)

1. The apparatus.

To determine the composition of the vapour phases the apparatus

shown in fig. 1 was used. The flash A into which the mixture to
1
Proceedings Royal Acad. Amsterdam. Vol. III.

(2)

be investigated was introduced is closed by means of a ground
in tube B containing a little mercury in which the thermometer
was placed.

Sig I.

The tube C is connected by means of a ground joint with the
condenser and through this with a space of about 18 litres capac-
ity, in which the pressure can be altered as desired by means of a
pump; the pressure in this space was determined by means of an
open mercury-manometer.

The flash A is further connected by means of the tube D with
the little flask # which is connected by a ground joint with D. This
flask may further be connected by means of / with the outer air,
or with the space with which A is always connected or with another
space in which the pressure may be regulated at will. In order to
determine the vapour tension at a certain temperature, the bath was
raised a few degrees above the desired temperature and the pressure
in the space which is connected with A, afterwards altered, until the
liquid contained in A began to boil. By a further slow change of
the pressure, the boiling point of the liquid was brought to the
desired temperature and read off on the thermometer placed in B.

The vapour evolved in 4A ascends through C into the condenser,

(3)

where it is condensed and returned to A; it cannot pass into the
space , because the tube P contains a little mercury between the
two small bulbs, and the space Z is connected with the same space as 4.

To determine the composition of the vapour phase, some vapour
from A was transferred to the flask 2, which was placed in a
freezing mixture in order to completely condense the vapour. In order
to transfer the vapour from A to £ the latter was connected, by
means of the tube F, with a space in which the pressure was a
little less than that in the space connected with A. The vapour
evolved in A now bubbles through the mercury in the tube D; the
rapidity with which this takes place may be regulated at will by
making the difference in pressure between A and /’ greater or smal-
ler. By means of this arrangement, it is not only possible to regu-
late the rate at which the vapour is conveyed from A to £, but also
to stop or to restart the transference at will, the temperature and
pressure in A remaining unchanged. Because the bath has alwaysa
higher temperature than the liquid and vapour in 4, no condensation
can take place in that part of the tube Y which is immersed in the
bath, but condensation may occur in the part of the tube which is
outside the bath. To prevent condensation at @ this part of the
tube was maintained at a higher temperature by means of a small
flame; the vapour which condensed in the further end of D, was
transferred to £ by heating after the distillation was ended.

The composition of the liquid remaining in 4A was, of course,
altered by the removal of vapour; as, however a quantity of 100—
200 grams was introduced into A and only 5—10 grams of liquid
condensed in £, the change in A was as arule comparatively smal),
unless the vapour- and liquid-phases differed very much in compo-
sition. In such cases I give the composition of the liquid-phase both
at the beginning and the end.

During the transfer of vapour from 4 to Z, vapour was continually
rising into the condenser where it was condensed. ‘This condensed
liquid, the composition of which was, of course, in general different
from that of the liquid in A, gave off a different vapour when flowing
down the sides and so caused an error. As a rule, however, this
error will doubtless be small. Some determinations have been repeated
without admitting any vapour into the condenser during the transfer
from 4 to £. For this purpose a little apparatus was used by means
of which the tube C could be closed and reopened below the level
of the bath. The use of this apparatus, however, gave rise to many
difficulties and it was therefore only used a few times.

As experience showed, the determinations of the vapour tension
1*

Cs)

are not quite correct but may be wrong to the extent of a few m.m.;
this was found by repeating several times the determination of the
vapour-tension of pure water or of a three-phase system in the same
apparatus at the same temperature and with the same thermometer,
when the determinations sometimes differed among themselves to the
extent of 2 or 3 m.m. The liquid collected in the flask EH was at
the end of the operation weighed and analysed. In the system Water-
Phenol, the phenol was estimated by the method of KoppEscHAaR,
i. e. by titration with a solution of K Br and K Br Og.

Il. The three-phase system.

In the system: Water-Phenol, three phases can be in equilibrium
with each other between the transition-temperature (about 1°5) and
the critical temperature (about 68°), namely two liquid-phases and
the vapour. The composition of the two liquid-phases, which may
be in equilibrium with each other at the different temperatures,
has already been investigated several times, among others, by
ALEXEJEFF ') and V. Rotnumunp’); I have now determined the
composition of the vapour-phase in the way described.

In table I 7 stands for temperature; P for the pressure of the
three-phase system in m.m.; Z, Ly and Z, for the composition of
the three phases, L,; and Ly for those of the two liquids and L, for
that of the vapour. The composition is expressed in percentage by
weight of phenol in the mixture of phenol and water.

TABLE I.

iE P Di Ts io.
29.°8 29 8 70 5.96
38.°2 48 9.5 67 6.98
42.°4 62 10 66 6.91
50.°3 94 12 63 7.28
56.°5 126 14.5 60 7.83
60.°1 150 17 57 8.06
64.°4 182 22.5 48 8.66

The composition of the three phases is shown graphically in
figure 2; the temperature is measured along the horizontal axis,
the pressure along the vertical axis. The lines Z, and ZL, represent

1) Wied. Ann. 28. 305.
*) Zeitschr. f. Ph. Ch. 26. 488,

(5)

the two liquid-phases, the line Z, the vapour-phase. It will be seen
from the figure, that the two liquid-phases 2, and ZL, gradually
approach the same composition as the temperature rises, and that at
68° they become identical at a point & which indicates about 34 pCt.
of phenol. The line Z,, which shows the vapour phases, which may
be in equilibrium with both the liquid-phases, lies entirely below
the line Z,. The vapour-phase, therefore contains less phenol than
occurs in either of the other liquid-phases.

If we call Z,, which contains the most water, the aqueous, and
ZI, which contains the most phenol, the phenol-layer, then the vapour
contains still less phenol than the aqueous layer.

If a mixture of two liquid-phases of water and phenol is distilled
at a constant temperature, say 56°.5, then according to the preceding
table the vapour pressure is 126 m.m.; the aqueous layer then
contains 14,5 pCt. of phenol, the phenol-layer on the other hand
60 pCt., whilst the vapour only contains 7,83 pCt. of phenol. The
aqueous layer has, therefore, a composition between that of the
vapour and the phenol-layer; on distillation the aqueous layer will
be resolved into the phenol-layer and the vapour, its volume decreas-
ing continually until finally only the phenol-layer remains in the
retort. If now the distillation is pushed further at constant 7, the
pressure cannot longer remain constant, but it must fall as there
are now only two phases remaining instead of three. I will revert
to this matter presently.

The vapour-curve J, has in this system, a position owtside the
two liquid-curves L, and L,. In other systems it may, however,
be situated between them; this is for instance the case with the
system Water-Aniline which I will mention later on.

It is plain that the different position of branch L, may give rise
to other phenomena during the distillation of two liquid phases. This
will be discussed subsequently.

In Figure 2, the pressure
has not been included ; this
might be done by introducing

1004

a third axis perpendicular on
é the plane of the drawing and
% marking on this the pressure.

The lines LZ, Lg and L, then
no longer lies in the plane of
the drawing, but in space, in
such a way that their three
projections on the plane P—'l’ form a curved line,

(Te
Sig. IL.

(6)

This line on the plane P—T shows the relation between the
temperature and the pressure of the threesphase system. It is,
according to table 1, a line which rises with the temperature.

Ill. The two-phase system.

The different two-phase systems which may appear in a binary
system, leaving solid phases out of account, are:

1st The system of two liquid-phases.

2nd The system of a liquid with vapour.

The first system has been investigated by VAN DER LEE!); he
determined the influence of the increase in pressure on the lines
I, and Lz, and found it to be very small.

I have now examined the second systein, mainly in order to
discover the connection between the composition of the liquid and
the vapour. This may be done in two widely different ways; first
the boiling-points and the compositions of the vapours of liquids
of different composition may be determined at a constant pressure ;
secondly the vapour-pressure and composition may be determined
at a constant temperature. I have chosen the last method at the
temperatures 56°3, 75° and 90°. The first temperature is situated
below the critical point; two liquid phases therefore make their
appearance; at the two other temperatures this is not the case.

The following table contains the determinations at 56°.3.

TABLE 2.

No, L D P

1 0 pCt. 0 p(t. 125 mm.
2 2.0 2.55 125
i) 5.58 5.49 127
4 7.42 6.57 126.5
5 10.88 7.42 127
6 14.5—60 7.83 126
7 69.2 { 9.98 124
7e 76.7 yes 122
Bb 80 34 { 11.98 118
8e 88.06 le sem 102

hh . . . . .

The percentage of phenol in the liquid is given under L; the
composition of the vapour under D, and the vapour pressure under P.

Determination N°. 6 relates to the ¢wo liquid-phases which may

') Dissertation. Amsterdam.

(7)

be in equilibrium with each other at 56°.3, one of which contains
14.5 pCt., the other 60 pCt. of phenol.

Determination N°. 7 is entered under 7> and 7° ; 7> gives the
initial, 7° the final concentration of the liquid. As will be seen,
these differ by 7.5 pCt., whilst the vapour differs immensely in
composition from the liquid.

The same applies to determination 8.

As will be seen from the table, a liquid containing about 5.5 pCt.
op phenol yields a same composition. Liquids containing less than

5 pCt. of phenol yield a vapour containing more phenol than the
ae liquids containing more phenol, BOwercr) yield a vapour con-
taining less phenol.

Table 3 gives the determination at 75°.

TABLE 3.
No. ih D P
1 0 0 299
2 2.43 3.44 293
3 4.15 5.21 293
4 7.51 7.41 294
5 16.82 9.11 294
6b 22.53 294
Ge 24,18 asl 294
7b 44.44 eo 294
7° 49.2 jee 294

gb 60.47 | 292-293

ge baer os? e289
gb 76.7 280

i

ge 82.4 yteeRo 259
10> 88.06 | 218
10° Gi, =p ane 177

In determination N° 4, the vapour and liquid have again about
the same composition; with a percentage of 7.2 of phenol they
are identical.

If therefore a liquid containing less than 7.2 pCt. of phenol is
distilled at 75°, the vapour contains more phenol than the liquid;
the reverse is the case if the liquid contains more than 7.2 pCt.
of phenol.

The determinations at 90° are given in table 4.

(8)

TABLE 4.
N°, L D P
1 0 0 525 mM.
2 2.36 3.64 528
5 7.00 7.69 531
4 8.29 8.30 531
5 9.74 8.96 530
6b 172. { 530
6: Tipe wei ee 530
7 ube woe 530
Ze Alipay ate 530
gb 42.2 | 530
se figy pba 530
b KES ns
9 pad \ 11.24 530
ge 58.0 | 530

As shown in this table, the liquid which at this temperature is
in equilibrium with a vapour of the same composition contains about
8.29 pCt. of phenol.

The results shown in the first three tables may be represented
graphically in different ways.

I will here, however, make use of only one of these, namely that
showing the composition of the vapour-phase as a function of the
liquid. The vapour-pressure is thus not considered.

Figure 3 is a graphical repre- —
100722. 8 sentation of this kind; the
concentration of the liquid is
measured along the horizontal
axis, that of the vapour (in
percentage of phenol) along the
vertical axis.

If we draw the line AB
through the square, the points

or on it represent liquids whose
A 0% aE Zoxe,. Vapour has the same composi-
Sig ADS tion. If a point is situated to

the left of 4B, the vapour con-

tains more phenol than the liquid; if to the right it contains less phenol.

From the drawing it is seen that at each of the three temperatures,

a liquid containing a small quantity of phenol yields a vapour con-

taining more, and one containing much phenol yields a vapour con-
taining less phenol than itself.

(9)

The point of intersection of a curve with AB represents a liquid
which is in equilibrium with a vapour of its own composition. The
proportion of phenol in this liquid increases with the temperature.
This liquid must have a maximum or a minimum vapour pressure ;
in our case a maximum one.

In our ease, according to table 2, the maximum must be at N°. 3
namely 127 m.m.; in No. 4 the vapour-pressure is certainly not
quite accurate, as N°. 5 again indicates 127 m.m. The deviation is,
however, far within the experimental error which may amount to
several mm. That, in figure 3, the line of 56.3° ends, at least
experimentally, in the points Z, and Z, is clear, because L; and Lg
indicate the composition of the two liquid-phases which are in
equilibrium with the vapour. If, therefore, water and phenol are
brought together in such a proportion, that the mixture is represented
by a point situated between 2, and Ly, this will break up at 56°3
into the two liquid-phases £, and Zy and vapour, the concentration
of which is indicated by the ordinate of one of these points.

In the two other curves the straight line Ly 2, does not occur;
they belong to temperatures above the critical point. They, however,
present the peculiarity, that they are almost horizontal for a con-
siderable distance; or in other words —as may also be seen from the
tables 3 and 4—-when the liquid has reached a certain percentage
of phenol the composition of the vapour is but little affected even
by considerable variations in the amount of phenol in the liquid.
According to table 3, the vapour at 75°0 only changes from 9.11
to 10.43 pCt. of phenol, when the liquid changes from 16.82 to
65.75 pCt. With a still larger percentage of phenol in the liquid
the amount of phenol in the vapour increases more rapidly, finally
increasing very fast indeed, since all the lines in figure 3 must
terminate at B.

Not only the amount of phenol contained in the vapour, but also
the vapour-pressure alters but little, when the composition of the
liquid varies between very wide limits.

In table 3 the maximum of vapour-pressure must lie between the
two determinations 3 and 4 and very close to N°. 4. In determi-
nations 4, 5, 6 and 7, the vapour pressure is constant at 294 m.m. ;
theoretically this is, of course, impossible, but experimentally the
differences may fall quite within the limits of experimental errors.

Van DER Lee has also measured the vapour pressure at 75°; he
also finds a vapour-pressure of 294 mm. when working with a liquid
of widely varying concentration. His other determinations agree
fairly well with my own; only liquids containing a very large amount

( 10 )

of phenol show differences. As I have now determined the compo-
sition of liquid and vapour, it is possible to test the observations
by means of the approximately accurate formula of VAN DER WAALS:

dP _ P («a— 2)
dq ta(l — aa) ~

The best way would be to take the values of zg and P from the
dP ‘
determinations as also the values of rae and then to caiculate a
rd
by means of the formula and compare this value with the experi-

cannot accurately be de-

d
mental result. In our case, however, a
axd

duced from the experiments, as / does not change or very little
between very wide limits.

dP
I have therefore, followed a different plan and calculated as

by means of the experimental values of P, xq and «a, from the
formula. For this purpose let us take the determinations at 75°
(table 3) and recalculate everything in molecules; let us then take
the mean of the initial and final compositions and pressures in exper-
iments 7, 8, 9 and 10. We then obtain :

TABLE 5.
dP

No x1 Ld xg—al

dad
1 0 0 0 289
2 0.0047 0.0067 +0.0020 293 + 88
3 0.0082 0.0104 +0.0022 293 + 62
4 OL015 3 mem OLOilte —0.0002 294 — 3
5 0.0372 0.0188 —0.0184 294 — 294
6 0.0551 0.0193 —0.0358 294 — 556
7 0.1446 0.0204 —0.1242 294 —1825
8 0.2477 0.0218 —0.2259 291 —3083
9 0.4296 0.0269 —0.4027 270 —4154
10 0.6322 0.0493 —0.5829 197 —2449

From the values of in the preceding table I have calculated

akd
the values of A P for each pair of successive observations.
iad pa ; dP
Considering for example observations 2 and 3, the value of aes
wd

may be regarded as the mean of the values found in the two exper-

(11 )
88 + 62
i

“

iments, 1. €. =75; the value of A P between observations

2 and 3 is therefore,

AP=A 2a = = (0.0104—0.0067) X 75 = 0.35.
Ld

dP :
The values of a and A P thus obtained are given in table 6;
avd

also, for comparison, the values of A P obtained by direct experiment.

TABLE 6.
, dP
Between observations aes A P ealeulated A FP found
No. 2 and No. 3 75 0.3 m.M. 0 m.M.
3 > 4 30 0.1 1
ARE SUD — 149 — 0.5 0
be6 — 425 — 0.2 0
6.2% 1190 — 1:3 : 0
fis — 2454 — 3.4 — 3
Ses 9 — 3618 — 18.5 — 21
9 »10 — 3302 — 73.9 — 73

As may be seen from the table, AP calculated and A P found
agree satisfactorily; the difference are smaller than the experimental
errors which may amount to several m.ms.

Chemistry. — ‘“Kchinopsine, a new crystalline vegetable base’’.
By Dr. M. GresHorr (Communicated by Prof. A. P. N.

FRANCHIMONT).
(Read April 21, 1900).

Of late years alkaloids have been discovered in plantfamilies which,
previously, had been made but little the subject of phyto-chemical
studies, and in which, at any rate, no vegetable bases had been
found or even suspected. So, for instance, in the large family of
the Compositae, which comprises about one-tenth part of all the
phanerogamia, with more than 800 genera.

The writer has been engaged for many years in the systematic
study of alkaloidal distribution in plants, also in this family,!) and

1) Compare: On the distribution of alkaloids in the family of the Compositae. Ned.
Tijdschr. vy. Pharm., Mei 1990, blz. 137. In this article 50 alkaloid-containing
genera are summarised, mostly the result of my own investigations.

(12)

has now the opportunity to present the meeting with at least one
of his new compositae-alkaloids in a pure condition, and to give a

description of the same.
First of all, some particulars about the botanical origin.

The genus Echinops L. (= Echinanthus Nucx., Echinopus Tourn., Sphaero
cephalus 1.) belongs to the division Twbuliflorae-Cynareae of the Compositae.
These Cynareae are divided into four groups: Echinops, Carlina, Carduus and
Centaurea, all plants popularly known as thistles; some are characterised,
from a chemical standpoint, by containing alkaloids, glucosides, bitter principles
and pigments; a few yield hydrocyanic acid.

The group Echinops only contains this genus itself, and Acantholepis orien-
talis Luss., a plant from the steppes of Central-Asia. Echinops numbers about
60 species, also mostly Central-Asiatic herbs with alternate, frequently
thorned leaves, and all species characterised by having capitula. To the West,
the Echinops territory extents over the whole of the South of Europe and the
coasts of the Mediterranean, to the East as far as Japan; some species are
also natives of tropical Africa. In Germany, &. sphaerocephalus L. grows
wild; no species is found wild in Holland. In that country various kinds are,
however, cultivated as ornamental plants, on account of the robust stature
and the beautiful large flower heads from which the genus derives its name
of “ballthistle’” (the latin name is composed of echinus, hedgehog and ops,
eye or appearance). The flowers are sometimes light blue #. Ritro L., or
dark blue £. bannaticus Rocu. The genus is divided by botanists into 7
sections; compare ENGLER u. PrantL, Natiirliche Pflanzenfamilien IV, 5, p. 313.
The species are mostly described in Borsster’s Flora orientalis and also
by Bunes, Bull. de l' Académie de St. Pétersbourg VI, 390. My investigation
extents over 15 species from different sections 1) which all were found to
contain echinopsine, so that there is reason to believe that the presence of
this alkaloid is a general characteristic of the Echinops-species.

On the use of Echinops in popular medicine and in toxicology, a question
revived by the discovery of the powerful Echinopsine, not much information
is at my disposal. Different species, such as #. Ritro L., dahuricus Fiscu.,

1) This is perhaps the proper place to state the source of the important material
of my investigation and to thank those who provided me with the same. From the botan-
ical garden at Leiden, I received through the care of Mr. E. Tu. Wirre, hortulanus,
EL. Ritro L. and #. niveus Wau. Of the first plant, the firm Haace u. Scumopr at
Erfurt provided me with the 10 kilograms fruits, which have served for the preparation
of a larger quantity of echinopsine, than the supply from the botanical garden allowed.
I also got from the sume source JZ. sphaerocephalus L., E. ewaltatus Scuran.,
EB. paniculatus Jacg. and £. syriacus Borss. On a holiday tour in Sweden in Aug.
1899 I noticed in the excellently kept botanical garden of Lund and Upsala some
other varieties cultivated there. In Lund, I collected leaves of EH. dahuricus Fiscu.,
EB. bannaticus Rocu., L. platylepis Travrv. and EL. microcephalus Supru.; afterwards
I received from there seed of #. globifer Janka and of another species which accor-
ding to Dr. Sv. Murpeck was, probably, ¥. commutatus Jur. From Lund, the hortulanus
Mr. Fr. Perrerson forwarded me beautiful material from 2. viscosus DC., FE. humilis
Bres. and L, elatus Bune.

(13 )

sphaerocephalus L., are used in East-Russia and Siberia as diaphoretica and
diuretica, are also applied in skin diseases. In olden times, the “Herba
echinopsidis’ was also used in Europe for treating gravel and stone.
To Dr. G. van Vuoren of Leiden I am indebted for a note on the
use of this genus by the Arabs. Ipny Wauscuia states in his treatise:
De Venenis (cod. Leiden) the following particulars about a plant which he
calls “Djirdama’’:

“Djirdama grows at Djukha and at Schafiatha (in Babylonia), and is a
powerful poison which kills quickly. It is a tall plant with small leaves, its
stem attains the height of a meter. It has a white roselike flower and
its taste is even more pungent than that of mustard. A person who has
had 2—2,5 drachms of the pulverized plant administred in his food feels
a violent itching on the surface of his body and a twisting and pains in
the throat and the stomach and a violent burning, so that he often undresses
and sits down naked. A weight of two “daniq’s” administred in a beverage
to pregnant women causes abortion, and a little of the powder rubbed on
the skin causes burning and inflammation.”

It is questionable whether this plant is really meant for an Echinops, as
the description corresponds more with that of a pungent crucifer. The
name, however, agrees with that of Forskani, Flora aegyptiaco-arabica; but
it must not be forgotten that ForSKAHL’s names are of modern times, whilst
those of Ipy WauscuyA date from about 800—900. It is, however,
true that Echinops has indeed been proved to contain a rapidly killing
poison, while if the last line of Isy Wauscuia is intended for the pappus,
this is also in complete accordance with the facts that it burns on the skin
exactly like itchpowder. (Mucuna.)

A notice in the Pharmacographia Indica seems important, that Echi-
nops echinatus DC. is an Indian medicinal plant, called in sanskrit “Utati”
and sold in the bazaars as “Utkatara”. The root is bitter and serves as a
tonic and diuretic. I may not, however, omit to state that Prof. Dr. H. Kern
of Leiden does not believe Utati to be a sanskrit word and said that Echinops
is not to be found in literature on ancient Indian medicine. Messrs. D. Hooper
and G. Warr of Calcutta, coeditors of the said Pharmacographia, could not
as yet give me further particulars on the subject of Utati, but they have
promised to order material of this drug for me from Mysore, to ascertain
whether the action is due to echinopsine.

For the preparation of Kchinopsine chiefly use has been made of
the above mentioned fruits of Hchinops Ritro L., collected for this
purpose by Mess's. HaaGe and Scumipt of Erfurt. The first difficulty
experienced with this material was its unusual bulk, which excluded
the use of extraction-apparatus of ordinary size. Fully two-thirds of
it was a straw-like chaff, a stiff tile-like involuerum, which could
only be separated with very great difficulty from the fruit proper.
A great deal of trouble was caused by the sharp hairs on the fruit,
acting on the skin like itchpowder; by rubbing the fingers with oil
this could be somewhat guarded against. The fruits yield */3 of
seed and '/; of chaff, but the commercial article consists to the extent

(14)

of one-half of empty fruits. The hard exterior (yielding 5,4 pCt. of
ash) does not contain alkaloid, but yields a dark colored extract
which impedes the purification of the alkaloid contained in the fruits.
An aqueous decoction of the fruits tastes bitter yet at 1 : 3000—4000,
but that of the involucrum is tasteless. It is, therefore, advisable to
remove the involucra in order to obtain a cleaner and less bulky
material, but this end cannot be attained either by crushing and grind-
ing, or by sifting; the only way is by peeling the fruits by hand,
but this is very tedious work. Under those circumstances, I have
called in the aid of the governor of the penitentiary at Haarlem
where this labour of separating the chaff has been performed by
convicts. One kilogram crude material contains 36000 fruits and
measures 10 dM°.

The /pvrified material (32 pCt. by weight of the original) was
passed through a sieve, to remove the hairs, ground next and again
sifted to retain pieces of the fruit-shell. The powdered seed boiled
with 10 times its weight of alcohol of 95 pCt. yielded at the first
extraction 19,2 and at the second 4 pCt. of extract, total 23,2 pCt.
which high percentage is caused by the fatty oil from the seeds
‘which has dissolved in the aleohol. The material was, therefore,
first deprived of its oil by extraction with below 50° rectified
petroleum ether, which does not dissolve any alkaloid. The powder
may also be moistened with an equal weight of ether and then
strongly pressed; nearly all the oil is thus removed with the ether.
This seedeake was then dried, again pulverized and now percolated
to exhaustion with alcohol of 95 pCt. mixed with 3 pCt. of acetic
acid. A good yield is also obtained by boiling a few times with
alcohol containing acetic acid and pressing warm each time. Of
the straw-yellow tincture the alcohol was distilled off. The remnants
of this extraction were only bitter at 1 : 150, being "a9 to Moy
of the original bitterness. The alcoholic extract had a peculiar
ozonelike odour; it was taken up with water and filtered; remained
on the filter a little of a not-bitter resin, but the filtrate was inten-
sely bitter. This was once more shaken out with petroleum ether,
a large quantity of chloroform added, the acid nearly neutralized
with sodium carbonate and the whole thoroughly shaken, after the
addition of an aqueous solution of caustic potash, slightly in excess.
The extraction with chloroform was repeated three times; all the
alkaloid goes into the solvents; after distilling off the chloroform, it
remains as a light-yellow crystalline mass which dissolves readily
in alcohol; the solution is strongly green fluorescent. This solution is
decolorized by animal charcoal, but it retains its fluorescence, which

(15 )

property is shared by the crystals. There is, however, a liquid
extremely well adapted to complete the purification of the crystalline
vegetable base present in this complex; it is pure benzene. This
readily dissolves the alkaloid by warming, but on cooling off separates
practically all out, leaving the fluorescent admixture in solution.

In this manner, by repeated crystallisation until a substance of
constant melting point is obtained and also by the judicious use of
animal charcoal, a pure and unmixed chemical body is obtained,
Echinopsine. This substance may also be obtained in an equally
pure state by a repeated crystallisation from boiling water.

In this way 0,5 pCt. of Echinopsine was obtained from the
chaff-deprived fruits of E. Ritro; about equally large is the yield
of KEchinopsine, from the fruits of other species, analysed by me,
such as FH. bannaticus, exaltatus, globifer, niveus, paniculatus ,
sphaerocephalus, syriacus, viscosus; the yield of Echinopsine from
select material of EH. humilis and elongatus was considerably
higher; from the first named species it amounted to 1,20 pCt. (!),
the other yielded 0,84 pCt. Material received from Erfurt in
February 1900 also yielded quite 0,8 pCt. of Echinopsine and
in addition 0,1 pCt. of Echinops-fluorescine and 0,15 pCt. of
Echinopseine. The amount of alkaloid in the leaves of E. ban-
naticus, dahuricus, nivalis, platylepis, which like those of EF. Ritro
hardly taste bitter, does not exceed 0,01 pCt. in the fresh or
0,04 pCt. in the dry material. It is considerably higher in the
leaves of E. microcephalus, viscosus and globifer, which are all per-
ceptibly bitter. From the fresh roots of EZ. Ritro about 0,1 pCt. of
Echinopsine may be prepared.

Echinopsine obtained by this process erystallises in thin colourless
needles of several cM. in length, forming feathery groups. As has
already been shown, it possesses the general properties of an alkaloid ;
it contains nitrogen, and leaves no ash. It isa weak base; the crystals
when pressed between moist red litmus paper do not colour this
blue. The melting point is exactly 152° C. When heated higher
Echinopsine remains unaltered for a long time, then decomposes
and burns with a sooty flame.

Kchinopsine dissolves 1:60 in water at 15°; in boiling water it
dissolves very readily 1 : 6. The alkaloid practically all separates
from the saturated solution on cooling, first anhydrous; the fluid
then solidifies to a snow-white mass liquifying again upon the
addition of hydrochloric acid. Kehinopsine dissolved in water shows
very beautifully the phenomenon of supersaturation; the introduction
of a minute crystal into the solution soon causes an abundant

(16)

separation of the alkaloid. On slow evaporation, Echinopsine may
be obtained in large transparent hydrated crystals; these become
opaque when heated with water, tefore dissolving, owing to loss of
water of crystallisation.

Echinopsine is easily soluble in methyl-, ethyl- and amyl-alcohol,
not so easily in carbon disulphide, insoluble in petroleum ether.
The base is soluble in ethyl ether when freshly precipitated, but
when crystallised it requires about 600 parts of that solvent at 15°;
this is the reason why ethyl ether is not suitable as an extraction
liquid for Echinopsine. Chloroform is a very suitable fluid, which
dissolves the alkaloid at the ordinary temperature in all proportions
and leaves it in a unaltered state on evaporation. Benzene dissolves
it but sparingly in the cold (15°), but easily at 80°, about 1 in 10;
this fluid is, therefore, well adapted for the purification of Echinopsine.
The hydrated base is soluble in benzene with much more difficulty
than the anhydrous compound; addition of water to the cold solution
of the latter therefore causes a further separation of alkaloid.

The solutions of Echinopsine are all colourless and do not show
fluorescence, neither when acidified with sulphuric acid.

Echinopsine is optically inactive (a 2,5 pCt. alcoholic solution
examined in a 10 eM. tube showed no polarisation at 15°.)

An aqueous solution of echinopsine faintly acidified with hydro-
chlorie acid is a bitter-tasting liquid; a hypodermatical injection of
10 milligrams in a mouse proved fatal. Prof. Dr. R. Kopert of
Rostock has, at my request, closely studied the poisonous action
(see Addendum I).

Echinopsine gives precipitates with phospho-molybdie acid, solution
of iodine, Mayer’s reagent, picric acid, tannin, mercuric chloride,
gold- and platinic chloride, potassium thiocyanate, potassium ferro-
cyanide and potassium chromate. The delicacy of these general
alkaloid-reagents is but moderately great; one drop of a solution of
echinopsine 1/15), gives precipitates with a drop of all the said
‘reagents; solutions of '/j999) only with the first five, of '/joo009 only
with the first two. Solutions of 1/95990—"/so000 are to me hardly
bitter; this is also the limit of the picrie acid and mercuric-
potassium iodide test. (Mayer’s reagent).

The latter reagents are well adapted for micro-chemical reactions
but an aqueous or alcoholic solution of iodine is so in a still higher
degree (limit 1: 100000); the crystalline precipitates obtained with
mercuric chloride, potassium thiocyanate, potassium ferrocyanide and
potassium chromate are also very useful.

The localisation of Echinopsine in the tissues may be very plainly

ely

traced by the aid of iodine solution which yields a beautiful crystalline
precipitate in the cell. This study has been undertaken by
Prof. Dr. Ep. VERSCHAFFELT at Amsterdam, who will communicate
his preliminary results in Addendum IT.

Both the anhydrous and hydrated Echinopsine excel by erystall-
ising unusually easily; from every solvent even traces of alkaloid
leave a beautiful crystalline spot. The hydrated crystals belong to
the rhombic system.

Echinopsine, although a weak base, is very stable.

Echinopsine does not decompose, when melted, until 350°, when
it gradually chars, but even after having been heated for an hour
at 450°, the liquified mass yield yet about one-third of unaltered
alkaloid. Melted with potassium hydroxide it gradually forms a
redlead-coloured resin, whilst ammonia is being evolved and an odour
of pyridine is perceptable. Kchinopsine dissolves almost colourless
in mineral acids, also in sulphuric acid on adding weak or strong
oxidising agents. It also yields, under circumstances to be investigated
later on, particularly by the action of acids by a high temperature,
a decomposition product, which may be recrystallised from water
and then appears as brown hard nitrogenous crystals which still
give alkaloidal reactions, may be extracted from an acid fluid, by
means of chloroform, and melt at 198°.

Echinopsine has a special reaction which should not be overlooked.
Moistened with a dilute solution of ferric chloride it gives a fine
blood-red colour; other colour reactions have not yet been observed.

This base forms a number of salts eminently crystalline but of
a loose combination; the amount of water of crystallisation is not
constant.

The first combustions of the Echinops-alkaloid did not give con-
curring figures for carbon. The melting point was not only raised,
(at first it was 140°), when the total alkaloid, however colourless,
was still further purified, but the percentage of carbon (at first
73 pCt.) 1) increased owing to the previous admixture of accom-
panying alkaloid closely related to Echinopsine. But even the analysis
of chemically pure Echinopsine presents difficulties; this substance
is extraordinarily troublesome to ignite and gives easily a too low
carbon figure unless it is ignited in a current of oxygen. I will

) Analyses of the total alkaloid :
0,1760 gr. gave 0,4734 gr. of CO, and 0,0950 gr. of H,O, therefore C. 75,4 pCt. and H 6,0 pt.
0,1366 a , 0,3650 v ” 4 0,0818 ” a wv r 72,9 a ” ” 6,6 a

0,1522 #« y» 12,3 c.c. of N. at 18° and 765 mm. therefore N. 9,5 pCt.
9
Proceedings Royal Acad. Amsterdam, Vol, III.

( 18 )

only mention here those elementary analyses, which have been used
as the base of the formula. A part of the analyses was done by
Mr. J. Sack, assistant in this laboratory.

Estimation of carbon and hydrogen.

J. 0,1758 gr. of Echinopsine gave 0,0950 gr. of HO and... .. gr. CO,.
Il. 0,1522 w« , uv 0,0844 woe vw 0,4290 4 w
TI. 0,2208 , ” v 0,1194 u ” ” 0,6186 ” yw
IV. 0,1196 ~» w v 0,0606 e » « 0,3868 7 ~%
therefore :
I. ke IIL. Ie
H. 6,0 pCt. 6,2 pCt. 6,0 pCt. 5,6 pCt.
C. 76,9 » 76,4 76,8 ou

Estimation of nitrogen.

0,2100 gr. of echinopsine analysed by the Kjeldahl-method con-
sumed 11,6 cc. of N./;, sulphuric acid, corresponding with 7,7 pCt.

of nitrogen.
0,2410 gr. consumed 12,8 ce. N./;, acid, corresponding with 7,4 pCt.
of nitrogen.

Determination of the molecular weight.

Mol. Weight.
0,0820 gr. of echinopsine in 17,5 gr. of benzene gives an increase of 0,07° 157
0.5063 4 » ” » 11,9 » » alcohol 7 ¢ ” v 0,28° 175
0.5740 » » Y » 17,5 « , benzene » wW y n 0,46° 185
0,8310 » » u v 17,5 4 « » you ” w 0,70° 177
0,9890 »# » a » 17,5 0 « ’ sou u y 0,79° 186
0,1990 “ou 7 ” 17,5 you 7 ” 7] 7 “ 0,16° 185
0.5020 wv wu y u Vio oy 2 5 uw ” wv 0,43° 174

The elementary composition may be expressed by the formula
C,, Hy NO. The analytical figures also agree well with (Cj; Hi9 NO),
but this formula must be rejected on account of the results of the
determination of the molecular weight.

Found. Calculated for C,, H, NO.
iT: I. nS elves Vie Vile
He 60; 69/060" 95.6 5,3
Cc — 769 764 768 —- — 77,2

N. (40 ET 8,2
Op = _ SS

The calculated molecular weight of this formula is 171; the
average of the found molecular weight is 177.

Estimation of water in hydrated echinopsine.

Found. Calculated for C,, H, NO, aq.
10,3 pCt. 10,0 pCt. 10,0 pOt. 9,8 pCt. 9,5 pCt.

(19 )

Analysis of some salts of echinopsine.

Echinopsine hydrochloride. Is a gritty crystalline powder, easily
soluble in warm water, and even in the cold more freely soluble
than the free base. If a crystal of hydrated Echinopsine is added to
a drop of dilute hydrochloric acid, it changes into a white crystalline
powder, which disappears on warming. On slow evaporation the
salt is deposited in fine, large rhombohedra, on rapid evaporation in
microscopic six-sided plates. The hydrochloride is well adapted
for physiological experiments; at first it tastes acid, afterwards per-
sistently bitter. It loses hydrochloric acid already at 105°. The
air-dried salt, pressed between blotting-paper, retains from 6,9—14,4 pCt.
of water (2 mols. of water = 14,8 pCt.), which it soon loses when placed
in a dessiccator over sulphuric acid.

Amount of hydrochloric acid (of the anhydrous salt).
1) 0,2080 gr. takes 0,972 cc. N./potash or 0,0352 gr. or 16.9 pet. of H Cl.

)) CRISKYA G5) aye = DMR ADE, 35 LORS aes sh O;Onest a te tgs
3) 0,2147 ” oy 1,025 2 »”» ” 0,0374 » ”» 17.4 ” 3 ”
Found. q Calculated for C,, H, NO, HCl
16,9 pet. 16,9 pct. 17,4 pet. 17,7 pet.

Echinopsine sulphate. Crystallises very beautifully in elongated colour-
less needles, which dissolve slowly in cold but easily in warm water.

The sulphates prepared by me contained respectively 26,0 pet.
(8 mols. = 24,6 pet) and 8,2 pet. (2 mols. = 7,6 pet.) of water.
Amount of sulphuric acid (calculated on the anhydrous sulphate).
1) 0,1777 gr. of anhydr. sulph. takes 0,840 cc. of N. potash or 0,0412 gr. or 23,2 pet. of H, SO,
B30 2, culph Sng. ., 0,490, , » > 0,090,999. 5

Found Caleulated for (C,, H, NO),, H, SO,
23,2 pet. 22,9 pet. 22,3 pet.

Echinopsine nitrate. Is also crystalline and not easily soluble in

cold, easily soluble in warm water.

Amount of nitric acid (of the anhydrous salt).
1) 0,1462 gr. takes 0,640 cc. N.potash or 0,0403 gr. or 27,5 pCt. of HNO,
2) 0,0521 » » 0,230 » z S OLOTSa a pe e78i zs, >
Found Calculated for C,, H, NO, HNO,
27,5 pCt. 27,8 pCt. 26,9 pCt.
Echinopsine oxalate. A beautifully crystallised salt which, when
air-dried, contained 18,1 pCt. of water (4 mols. = 14,3 pCt.).

Amount of oxalic acid (in the anhydrous salt).
0,1777 gr. takes 0,830 ce. N.potash or 0,0373 gr. or 20,9 pCt. of C,; O,H,
Found Calculated for (C,, H, NO),, C, O, H,
20,9 pCt. 20,8 pCt.
Kchinopsine picrate. A yellow crystalline salt very slightly solu-
ble in water, of varying composition and melting at about 215°, decom-
posing hereby. The picric acid, present in the alkaloidal salt and
O*

=

( 20 )

obtained by shaking with petroleumether after decomposition with
sulphuric acid, amounted to 81,1 pCt.

On combustion 0,1040 gr. of the same picrate gave 0,0380 gr.
of H,O and 0,1598 gr. of COs.

Found Calculated
C. 41,9 pCt. 40,0 pCt.
Her A0r 3,6 »

Echinopsine mercuric chloride. Is beautifuily crystalline and
melts exactly at 204°. It dissolves easily in boiling water, but
requires 120 parts of water at 15°.

Kchinopsine mercuric iodide. The precipitate caused in a solution
of echinopsine containing a slight excess of hydrochloric acid by
Mayer’s reagent is a yellowish-white, sticky, substance, which becomes
coarsely crystalline when recrystallised from alcohol of 50 pCt. and
melts at 178°. 0,150 gram of echinopsine yielded 0,455 gram of
this bi-iodide, dried at 100°.

Found Calculated for (C,, H, NO, HJ), + Hg Jy.

33,0 pCt. of alkaloid. 32,6 pCt.

Echinopsine acetate. Is also crystalline and readily soluble, even
in cold water, to a bitter fluid; the salt is very unstable and loses
its acetic acid completely at 100°.

Todo-echinopsine. The crystalline precipitate produced by a solution
of iodine in a liquid containing echinopsine differs in colour and
composition according to the concentration and excess of the iodine
employed; it also readily loses some of the iodine. It is somewhat
soluble in boiling water and separates on cooling with a light-choco-
late colour. When carefully dried, washed with carbon disulphide
and recrystallised from alcohol, it forms a coffee-coloured crystalline
powder, which melts at about 135°, but gets already sticky before
that temperature is reached.

As regards the nature of Echinopsine, the following should be
observed. It cannot escape notice that this substance behaves chemic-
ally more like an amide than an amine, namely like a cyclical
amide, while the physiological action is strychnine-like similar to
piperidone, pyrrolidone ete. To this may be added that the colour-
ation with ferric chloride and the empirical composition also seem to
point to a substance as phenylpyridone. I made some reduction
and oxidation experiments‘) to learn the structure of Echinopsine,

) Reduction of echinopsine. Ueated in a combustion tube with zine dust in a
slow current of hydrogen, echinopsine yields a distillate consisting of a yellowish-
brown oily liquid having the odour of pyridine; it is heavier than water and insoluble
therein but is readily dissolved on adding hydrochloric acid. This solution was

( 21 )

but the greater portion of my material had already been exhausted
by the general study of this new substance. I can only say, that
Echinopsine, although not identical with the phenylpyridone described
in the Berl. Ber. XXIX, 1697 is probably related to the same.

The analysis of Hcehinops is not completed with the investigation
of crystalline Echinopsine.

There are, namely, indications that other special substances occur
in this material. In the first place it must be observed that the
erystalline Echinopsine possesses only a part of the bitterness of the
raw material; a decoction of the fruits is still bitter in the pro-
portion of 1: 3000—4000, Echinopsine hardly any more at 1 : 30.000 ;
there must, therefore, exist some other active components which
cause or increase this bitterness.

The precipitate from Mayer’s reagent in the acidulated aqueous
solution of alcoholic extract of echinops is much more considerable
than can be accounted for by the quantity of echinopsine which
might be prepared from it, and it even amounts to 0,2 gram for
1 gram of seed, being of a different nature than the precipitate
obtained by Mayers reagent in an acidulated watery solution of pure
Echinopsine; it has for instance a much higher melting-point.

I have devoted no small amount of labour to the study of these
-other constituents, but for the present I can only offer the Echin-
opsine in a pure condition and venture some information about the
accompanying alkaloids, without wishing to pretend that the following
alone account for the missing echinops-alkaloid-complex.

It has already been mentioned that the purified total-alkaloid, when
repeatedly recrystallised from benzene, gradually acquires a higher
melting-point. There is present a crystalline accompanying alkaloid

repeatedly washed with ether, the base was liberated with aqueous caustic potash,
distilled in a current of steam and removed from the milky distillate by means of
ether. It was thus obtained as a colourless liquid of the same main properties as the
crude distillate, namely heavier than water and insoluble in the same. With hydrochloric
acid it forms a compound soluble in water of a burning taste giving crystalline precip-
itates with picric acid (yellowish-white), platinum and gold chlorides (first yellow,
afterwards pale-red) which all melt and decompose at 200°; also a compound with
mercuric chloride consisting of velvet-like white needles melting at 159°. These data
do not admit of any identification with one of the known phenylpyridines,

Oxidation of echinopsine. Echinopsine was oxidised in the cold with 6 times its
weight of a neutral 4 pCt. solution of potassium permanganate, the filtrate was treated
with carbon dioxide, evaporated to dryness and the residue extracted with alcohol
containing hydrochloric acid; this left undissolved a nitrogenous, hygroscopic substance
soluble in water but insoluble'in ether. It begins to melt at about 120° and yields
on stronger heating an oily distillate having the odour of pyridine and diphenylamine,

(3-Echinopsine), which behaves in most respects like Echinopsine, but
passes readily from the acid solution into chloroform, gives no colour
reaction with ferrie chloride, contains less carbon than Echinopsine,
is a still more weak base and melts at 135°.

Mention has also already been made of the substance soluble in
water, alcohol, amyl alcohol and benzene, which causes the green
fluorescence of the solutions of the crude alkaloid, Eehinops-fluores-
cine. The benzene motherliquor obtained in the preparation of
Echinopsine, leaves on evaporation a dark brown mass; this was
dissolved in dilute acetic acid, washed with petroleumether and
ethylether and then again shaken out with chloroform ; the fluorescine
passes from the acid, but more readily from the alkaline solution, |
into that solvent. It was dissolved in acidulated water and precipi-
tated with picric acid. The picrate, after being washed with water
and dried between blotting paper, formed a sulphur-yellow crystalline
cake melting at 210°. This picrate was decomposed with an aque-
ous caustie potash of 10 pCt. and the base thus liberated was taken
up with chloroform ; it seemed to be admixed with much Echinopsine.
After this had crystallised out, the fluorescine remained as a brown
resinous substance of alkaloidal nature, melting at 105°, not bitter,
and with an extraordinarily large fluorescing power. The green
fluorescence of the light brown solution is not changed by alka-
hes; addition of acids renders it colourless but on exposure to
the air it soon regains its colour and fluorescence. The yield of
fluorescine is small, the fruits of E. exaltatus containing a larger
quantity of it than any other species, examined yet. To judge from
the picrate precipitate, the purified material of H. Ritro contains
about 0,10 pCt.

There is also in the motherliquor a non-fluorescent amorphous alka-
loidal constituent, Hehinopseine, present. It is a brown mass decom-
posing on the waterbath and turning cherry-red thereby ; this change
of colour is also caused by alkalis. From an acid, but more readily
from an alkaline solution, it passes into chloroform. The solution
in very dilute sulphuric acid is bitter-adstringent, has a flavour of
benzylaldehyde and gives with picric acid an abundant yellowish-
green precipitate, also melting above 200°, decomposing thereby.
This picrate was also decomposed’ by aqueous caustic potash and
the base dissolved in chloroform; the chloroform residu, which was
cherry-red, still contained much Echinopsine; the Echinopseine being
obtainable only as a resinous mass, melting at 125°; I therefore,
had to give up further research in this direction.

Both Echinopseine and Echinops-fluorescine obstinately adhere to

( 23 )

Echinopsine, causing this to exhibit for a long time a green fluores-
cence and to turn occasionally pink, when moistened with distilled
water. This colourreaction is caused by a trace of alkali, presents
in the distilled water, from the glass vessel.

Finally a few words on Echinops oil, which is met with when
extracting the alkaloid. When quantitatively estimating the oil by
extraction with ether, 27,5 pCt. was found in the seed of HL. Ritro,
It is a pale yellow sweet thick oil, of 0,930 sp. gr. at 15°, slowly drying.
It has the striking property to dissolve on warming in an equal volume
of absolute alcohol; on cooling an emulsion is formed and then
the oil separates almost completely; at 15° the oil requires about
25 parts of alcohol for solution. Methylalcohol does not possess
this remarkable property '). The oil is soluble in all proportions in
kerosene, ether, carbon disulphide and benzene, also in an equal
volume of warm glacial acetic acid. The saponification number of the
oil is 194°, the melting point of the solid fatty acids 41° and the
solidifying point 39°.

M. GRESHOFF
Laboratory, Colonial Museum, Haarlem.

eho DU Nee
On the physiological action of echinopsine.
By Professor Dr. R. Kopert.

In October 1899, I received from Dr. M. Gresnorr of Haarlem
half a gram of crystallised Echinopsine hydrochloride.

With this small quantity only 3 experiments could be made with
frogs and 2 with guinea-pigs.

These, however, sufficed to establish the following facts:

1. Echinopsine hydrochloride is a poison for cold-blooded and
warm-blooded animals (frogs and guinea-pigs).

2. With both classes of animals the actions are similar and
consist of an irritation of the motor-centres of the nervous system.

3. Both brain and spinal chord are taking part in this irrita-
tion. The irritation of the brain is only noticed in the case of
warm-blooded animals and then shows itself as trismus and most
violent spasmodic contraction of the masseteres. The irritation of

‘) Other fatty oils from the seeds of the Compositae are also more soluble in
boiling alcohol than is usually the case, but not to such an extent as Echinops oil.
-Madia oil for instance, requires 6 parts of boiling and 30 parts of cold alcohol.

( 24 )

the spinal chord which, in the case of the frog, is not stopped
by severing the brain, is apparent from the convulsion of all the
four extremities. In the case of warm-blooded animals these may
appear as klonus and tonus occasionally even as opisthotonus.

4. When a very large dose is administred to a frog, the irrita-
tion instantly passes into paralysis, whilst with a smaller dose the
irritation symptoms may continue for 4—5 hours.

5. When a dose is administred to cold-blooded animals in suffi-
cient quantity to cause irritation, it will be noticed that before the
first convulsions set in and during the intervals, there exists a state
of torpor, dotage and reflex-debility.

6. In the experiments on frogs the heart is decidedly weakened

and such by doses which do not yet paralyse the spinal chord.
7. The complete action of echinopsine reminds of that of a mix-
ture of strychnine and brucine but is not identical with the same,
as the ophisthotonus and the reflex-irritation are not so marked as
with minimal doses of strychnine and also because the heart is more
affected than is the case with strychnine.

8. Doses: A subcutane dose of 0,02 gr. does not affect esculentae
of ordinary size (winter frogs); 0,05 gr. causes an irrition lasting,
with intervals, for several hours; 0,08 gr. paralyses the nervous
system without previous irritation and also paralyses the heart at
the same time.

A dose of 0,10 gr. has no visible effect on a guinea-pig weighing
325 gr., but 0,25 gr. kills the animal after suffering violent spasms
for several hours.

9. Antidotes for echinopsine are to be looked for among those
narcotics which do not weaken the heart.

10. It is not probable that anatomical changes oceur in echinop-
sine poisoning cases, but I will pay attention to this matter when
making experiments with the fresh material recently received from
Haarlem.

Institute for pharmacology and physiological
chemistry, University, Rostock.

AD DE N Dsus ie
On the localisation of echinopsine.
By Professor Dr. E. VERSCIAFFELT.

The research on the microchemical localisation of echinopsine in
the tissues will form the subject of an elaborate paper in which

( 25 )

it will also be attempted to trace the relation between this localisation
and the physiological signification of the alkaloid. Provisionally,
attention will only be called to a few particulars respecting the
distribution of echinopsine in the fruit of Echinops Ritro. For this
purpose the method originally proposed by ERRERA was employed }),
which is based on the precipitation of the alkaloid in the cells by
means of iodine dissolved in potassium iodide or alcohol. With
some plants mistakes may be made when using this method on
account of the presence of other substances which also give preci-
pitates with iodine such as amines, glucosides, albuminoids ; but when
dealing with Hchinops no fear need be entertained as the iodo-echi-
nopsine precipitate is not like the others *) in the form of a minute
granular brownish-red precipitate but in large exceedingly character-
istie crystals. The crystals formed in the tissues will be found
under the microscope to be similar in appearance to the iodo-com-
pound of pure echinopsine. As solutions of iodine were so eminently
satisfactory it was not thought necessary to use other reagents on
an extensive scale. The manner these behave towards the alkaloid
in the tissues will be mentioned later on.

The scales of the involucrum which surround the ripe fruit
in a dry condition, are free from alkaloid just like the dry fruit
walls and their toothed hairs. The cells of the embryo, on the
contrary, are mostly rich in alkaloid. This fleshy straight embryo
practically occupies the space of the coalesced fruit-wall and seed-
coat as far as the latter is developed. The embryo is surrounded
with a double layer of thick-walled cells which like the cells of the
embryo itself are filled with reserve material.

The morphological nature of this membrane which easily detaches
either way from the embryo, as well as from the fruit-wall, cannot
be explained witb certainty without watching the course of development.
It may be a rudimentary endosperm, also a seed integument. The cells.
of the embryo contain fatty oil and albuminoids as reserve materials.
The fatty oil may be rendered visible in the ordinary way by killing the
cells, for instance, by heating or by means of an acid which causes
the oil to be liberated and collect in large drops. The cells are
closely filled with aleuron-granules, which are present in such large
numbers that they are only separated from each other by a network

1) Errera, MaisTr1au et Craustriau. Ann. Soc. Belge de Microsc. 12, 1889, ERRERA
thid. 13, Mémoires.

2) Compare the researches of pE Whyre, DE WitpEMaN, Anema, Motte, Lorsy,
Bart and others.

( 26°)

of thin plates consisting of amorphous oil-containing protoplasm and
often flatten one another (see Fig.). These aleuron-granules are
small, their diameter being at the most ore third of the size of those
of Ricinus and Linum, but they are fairly equal in size. Their
further structure may be silently passed over.

The cells of the already mentioned double layer present around
the embryo also contain granules of an albuminous nature but these
are much smaller than the aleuron-granules of the embryo.

Annexed figure gives a representation of
a group of cells from the cotyledons of
Echinops Ritro after treating a section with
glycerol mixed with tincture of iodine until
the mixture assumed a mahogany-brown colour.
I have made frequent use of this mixture as
well as of iodine dissolved in potassium iodide.
After the sections had stayed for a while in
the mixture, they were preserved and mounted
in pure glycerol.

The figure does not, however, show what
is seen the moment the objects are treated with
the reagent, then large crystals are not for-
med at once. In the beginning a minute brown-

Eh ish-red granular precipitate is obtained which,
a. borders of the aleuron- however, unites after a few minutes to the
granules. larger aggregations of dark coloured needles,

4. most nu us needle- yiate :
oe Most numerous nee as shown. It is interesting to watch under the
shaped aggregations of the :

iodo-echinopsine compound, Microscope the first formation of the precipitate ;
ce. less numerous brown it then appears to form in the aleuron-granules
Bite which instantly turn brownish-red and show
afterwards inside their mass darker and larger crystals. The
amorphous protoplasm between the aleuron-granules turns at once
pale yellow and remains so. Echinopsine occurs, therefore, only in
the aleuron-granules and was in consequence formed within the
vacuolae of the unripe seed, which is as might be expected.

The crystals which are visible in the cells after some time belong
to two very plainly different forms. The more numerous are dark
coloured manifuldly-grouped needles 6. These agree, as regards appea-
rance, very well with the precipitate caused in a solution of pure
echinopsine of which Dr. GresHorr was kind enough to present me
with a certain quantity. Between these needles are noticed a smaller
number of light brown, more plate-like crystals of a peculiar feathery
appearance c, which I have not been able to observe in the iedine-

( 27)

precipitate of the pure alkaloid, at least under the conditions in
which I worked, so that I feel inclined to suspect the presence of
the iodo-compound of an accompanying alkaloid. The double peripheric
layer of the seed contains alkaloid. In the cotyledons, a beginning of
differentiation is observable in palisade and spongy parenchyma, a
phenomenon occurring in different plants the cotyledons of which
afterwards turn green and assimilate (for instance, Brassica, Linum).
There is, apparently, no difference in the amount of alkaloid contained
in the tissues. The epidermis of the cotyledons also contains much
alkaloid. The procambium bundles which traverse the seed lobes are,
on the other hand, perfectly free from alkaloid and the same is true
of those of the root. The bark of the latter is quite as rich in
echinopsine as the tissue of the cotyledons.

The centre of the root which is surrounded by the procambium
bundles is poor in alkaloid, so that here, a cylinder poor in alkaloid
is separated from the bark rich in alkaloid by a layer free from
alkaloid.

This want of alkaloid in the procambium of the embryo is
interesting because, as will be more fully demonstrated later on,
tolerably much alkaloid is actually found in the bast (phloem)
in the further course of the development.

Botanical Laboratory, University, Amsterdam.

Physics. — ‘On the relation between Radiation and Molecular
Attraction”. By J. D. vAN DER WaAats Jr. (Communicated
by Prof. J. D. van DER WAALS).

At the end of a paper in the Proceedings of the Royal Acad. of
Sciences of March 1900 I expressed my intention of investigating
whether the ponderomotoric action of radiation could give an expla-
nation of molecular attraction. The course which I would take, was
the solution of the equations of motion of a number of vibrators
which act on each other and are subjected to no other forces. If
we could solve these equations, and if this action proved sufficient
to explain the molecular attraction, we might be able to deduce from
this whether ithe quantity a of the equation of state is a function of
the temperature, and if so, what function, and whether the attraction
is really proportional! to the square of the density, or if it is so
only by approximation.

I have however, not succeeded in finding the function solution
of this. problem, not even for the case that there are only two

( 28 )

vibrators. Nor is the general solution, to be used. The
action of the molecular force is only felt if the distance of the

r
molecules is very small. Then ae ee t'—t is very small and we

should have to take into account a great many terms.

The following considerations may however serve for a preliminary
investigation as to whether the order of the quantity of the forces of
radiation is the same as that of the molecular forces, or whether they
are so small that we are forced to assume that there acts besides
the forces of radiation, another kind of foree between the molecules.

For this purpose we examine how much smaller the quantity of
energy is, which a set of vibrators has, when they are influenced
by one another, than the sum of the energy which every vibrator
would have separately, if it were alone in space with its own am-
plitude. The difference of these two quantities of energy may be
considered as the energy which the vibrators would lose if they
were brought from an infinite distance to the places they now
occupy, provided care be taken, that they had the same amplitude
during the whole process (i. e. that the process was carried out
isothermically).

An exact solution of this problem would be very intricate and
the energy of the field would certainly have to be taken into con-
sideration. I shall, however, assume that the energy to be found is
by approximation represented by:

$24nV*(far+ga,+ha,).

This comes to the same thing as if we put the moment of a
vibrator o at a given moment and then seek the difference of the
following two quantities of energy:

1st The energy necessary for giving the moment a to the molecule
when it is not subjected to any action of other molecules.

2nd The energy necessary for giving the moment to the molecule,
When it is in a region, where the electrical displacement has the
components /, g, h.

If we take the sum of these quantities of energy for all molecules,
we have taken both the energy which molecule I has with respect
to molecule II and that which molecule II has with respect to
molecule I. We have therefore to divide the result by 2.

If the quantities a, and f were independent of each other, faz
added for all the molecules, would yield o. In consequence, however,
of the partial regulation of the vibrations of the molecules with
respect to the electric forces, f and az will not be independent,

( 29)

(Compare “Entropy of Radiation II,” Proc. Roy, Acad., Febr. 1900).
The same holds of course also good for ga, and haz.

I shall assume that every molecule on an average has absorbed
the amplitude ob} from the field. If we knew o as function of the
temperature and of the density for every substance we had a com-
plete solution of the problem. We do not know o however, and
can only compute how great o must be in order that the forces of
radiation account for molecular attraction. We must find a fraction
and we may expect that the fraction will not be very small.

For f I shall take the value as it is calculated in “Entropy of
Radiation J,’’ (Proc. Roy. Acad., Dec. 1899). In doing so we are
guilty of the inconsistency of taking a value for /, calculated on
the supposition, that the motion is perfectly irregular, while the
energy which we are seeking, is the very consequence of the partial
regulation. We cannot, however, calculate another value for /, if
the way of regulation is not known and the mistake which we make
in doing so, is probably slight.

The mean value of ga, and ha. being equal to that of faz, we
may write for the energy:

3
B=] 24aV* fas

and we need only take those terms of az which are caused by the
forces of the field; so:

2nt 20t
B=62 V2 = (feos = + fo sin 7 ) x

2Qat 2at
& cos if + bre sin a)

E
where
bi =p fit dhs bz = —QGfitPhe
4 7? f
V22 S15) rene ;
Ee an GA 58 f \2 2\2 e& 1 /2n6
Ge ela = aes)
2 e 1 /2n\3
V2e 3B m V =)
g=—4a se :

m 7472 f \2 2\2e% 1 /2 26
( is +)+(~) (=)
T? m 3/7 mV2\ T

') See note at the end of this paper,

( 30 )

’ 2 at PRT AG wt
On an average the terms containing sin Sar will become

zero and also {hose containing the product f,f. As the mean of

2 nt 2nt . 2
both sin? = and cos? 7 8 4, and the mean of ie equal to that

of ap we find:
E=61V*op =f?

For S fi we may write }7«°, in which » represents the number
of molecules per unity of volume and « the quantity, defined at
pag. 322 (Proc. Roy. Acad., Dec. 1899). For ¢ we may, however,
not take the approximated value calculated there, which holds only
for points at some distance from the source.

Let us represent a volume-element by r? dr sin@d0 dp and let us
call the shortest distance, to which two molecules can approach ¢, then:

sae 1 e 2a
e& —2n a aout J f 7? dr sin 0 dO dep e—2¥r
p 0 0

Wolietee: te Ses 1\2. /3a2 1 \24n?
(Ce gue ya

rt ried

a} x 2a
—— 1
&=—2n a wal SS r° dr sin 0 dO dp . e—2r
p 0-10

A 1? Ir hie 0 eet well as 2 1 1 3
(== 2 sin + aay oy (5 cos a— ) -|- ai (8 cos 0 -+- 1)| .
If we take into consideration that:

7

2 4 e 2
if sin® Od0 = — and il sin O cos? 0 db = —
3 3

0

0

this becomes:

Roars Te 1 af. [(? PN? A~ © Alpe Ved
=i =a)¥45 sncehen —2ur
87 Bi .) "3 tga eee ‘al Be:

(31 )

The first term may be at once integrated and furnishes :

1 ( 47? i 4
aE | | eee — ¢—2EP ,
2u A? 3

The two other terms cannot be integrated; if however we omit

the factor e—2“", the last term becomes predominant, viz 12

v
The terms with small r appear to have most influence, even if
e-2er ig omitted. This is a fortiori true if the factor e~?” is pre-
served. For terms with very small r the factor e—2" is nearly 1,

1 : -
so that 12 =a) is really an approximated value of the integral of
g

Lee ; ] 4 1?\2
the third term. Further —— is great compared with —— es , 80
v3 2a\-

that we may write by approximation :
= i

SS a0

a ri g3

In order to determine the quantity «? we take into consideration

that for one vibration the quantity of energy, emitted per second is
1 2 8 y2 n* Py aa roe 1
equal to Ts apes AS

I represents the mean quantity of energy emitted by a molecule.
KE. Wiedemann!) calculates that 1 molecule platinum at a temp. of
1000° emits 3,3.10-16 Gr. cal. = 1,4.10—® erg. per second.

_ If we accept the law of STEPHAN, we find for Z at about 0” the
value:

1,4
2a 10=* ers. ==32)2 10-1,

For the quantity of energy sought we find therefore:

") Wied. Ann. XXXVIL, 2, Bl. 203.

( 32)

We shall use the following approximated values as given:

n= 5.101 Ree OTS)
m

V= 3.101 < = 2,5.10-5 })
m

Sass!

Taking these values into account we can give p a simpler form.
To that purpose we determine & from the equation:

2k pee eo
+=o(a a= )

We bave to use the positive root of this equation, which has a
value of about 107, Now we see that 2 is small compared with
472

ae and may be neglected, so that we may write approximatively

h 2 9
te et pee,
m V
The term with %*° may be neglected, and we find:

ut ee ee
T2 m - 4 \mV T2

This quantity is of the order 10!*, The square of it occurs in
the denominator of p and is of the order 1075. This term may
therefore be neglected, as the other term of the denominator

E € zy ik is of the order 10%. So we find for p:
m
3 ( e y' (ai
V2e 4 \mV aE
7

m eye aN ee 3
G mV T?

1) Lorentz, Versl. Kon. Akad. vy. Wetensch., Maart 1898.
*) Proc. Royal Acad. of Se. Amsterdam, Febr. 1909, p. 417.

(33)

or
27 1 e

~ 16 2m

P Ree

If we substitute this value for p in 2, we find:

So we see that / depends in a high degree on 4, and that the
value which we find, is quite determined by the value for 4 which
we assume. Now the quantity Z is determined for a continuous spec-
trum, and it is not at once to be seen what value for 4 we have
to take. I shall therefore have to confine myself to calculate, what
value 4 must have, to make / equal to the energy of the molecular
attraction. o is however also unknown and in order to calculate A,
we have to assume a value for o. If we put o=1, we know
that we take a too great value for o. The value of 4, which we
calculate from it, is therefore the minimum-value which 4 must have
in order to make / equal to the energy of the molecular attraction.

The energy of the molecular force, is, as we know, represented by
= . For 1 c.c.M. air under normal circumstances this is 2700 erg.
For Z we have however taken the quantity of energy emitted by
one molecule platinum. Therefore we have to take also the quantity

a e . .
— for platinum. As substances with great molecular weight have
v

also a great value for a, we shall take a for platinum ten times as
great as it is for air, and put therefore:

That platinum under these cireumstances forms a phasis of little
stability or perhaps even an instable phasis, is of no consequence.

. 7 . . a . “ *
If we replace £ by this value of — and further all quantities

v
by their numerical values, we get:
243. 1 6 2,5. 10-18
Te as toe et 2,2.10-1
512 7 3.10!° 27.10—24
or
9.512

an 10
137,5.10.2

Proceedings Royal Acad. Amsterdam, Vol, III.

( 34 )
So we find by approximation:

fi BEI WO

At 0° the wave-length of radiation emitted in a sensible quantity
is certainly greater than 10~*, while the greatest wave-lengths
measured amount to + 22.10—*. It is therefore no unsatisfactory
result that we have to take for 4 as minimum 3,16 . 10+.

Though the numerical result may not have much value on account
of the great uncertainty of the numbers used, yet it pleads rather
in favour of the supposition that the cause of the molecular attraction
must be looked for in radiation, than against it. The-more so, as
this supposition is supported by its simplicity. It is true that an
accurate calculation of the molecular attraction from the forces of
radiation would be pretty intricate, but we cannot doubt of the
existence of the forces of radiation and the question is only: “are
they the only forces, or does there exist another kind of force
acting between the molecules and giving an explanation of the
molecular attraction?’ And certainly the assumption of the first
alternative is simpler than that of the second. In the meantime it
will have to appear from later investigations whether this suppo-
sition will be able to explain the action of the molecular forces
more in particulars.

Nolte. The values for p and g used here are not quite the same as those which
I found for them on pag. 417 Proc. Roy. Acad., Febr. 1900.

Two mistakes occur namely in the values given there. First the two quantities
must have the opposite sign. Secondly Prof. Lorentz has pointed out to me that
the formula, from which I start, and which is borrowed from formula 111 of his
treatise in the Arch. Néerl. XXV, 5, is not quite correct. The two terms of 111
have both to be multiplied with ?/,.

To demonstrate this, we continue the series of calculations on pag. 486, which is
there without good reason stopped at x, for two terms more, and replace the quantity
occurring there :

u J «ie
by
: is rl. pane
x — V x aE; y2 x —6V3 x

For x, we get then the following terms in addition to those which Loreniz took

into aecount:
1 : a) 24, 1 Fe eee
8a V# X J Gordr + 24n Vi xa lomcidce

: dx d*®x é r
If we neglect the terms with er and WE? as they are of the order ( _

a “ is 2 , : : xy ;
with respect to x and x and if we notice that integrals like | fo ——@r’ are zero,

a

because of the symmetry, these terms of x, contribute only the following terms for /:

1 S 02 ” : t 1 soe 02 af F ; ;
a Bey ee eS oe = ee cet
Sa V2. ay Baa VS Fey SF

Now:
and

The two new parts of f are together:

il ze ( 1 (#—2')?) NY, e =
— — —_ — =~ x.
ek ee Oe re poe 12” V3

We have to multiply this with 42% V2p,dzr, in order to get the corresponding
parts of the force acting on the ion in the direction of the z-axis, and then to
integrate over the whole ion. This gives:

sft ( LL @=2'?} er
Tx |) Qpdt ¥ Oo ete a | dt — PBT

The value of the second term remains the same when we substitute (y—y')® or
(z—2'f for (r—2')*, and is therefore one third of what we should get, if we substituted
ry? for (e—a')*. The foree which is to be added, becomes then:

te 22 0 Geos 4 aed -~ @&
3 «fe arf Sar ana yer ae ves Ree POR y

and if this is added to the terms of 111, only */, of this last value remains.

Chemistry. — ,Plumieride and its identity with Agoniadine”’. by
Prof. A. P. N. FrRancuimont.

The name Plumieride has been given in 1894 by Dr. Boorsma
of Buitenzorg to a substance which he had isolated from the bark of
Plumiera acutifolia. Dr. Boorsma states i.a, that Plumieride does not

3*

(36)

melt, that it is not a glucoside, that its composition is C,H )O)s-4+-H,0
and he concludes that it is a substance quite different from the one
prepared in 1870 by Dr. Tu. PecKoxt, of Rio de Janeiro, from the
bark of Plumiera lancifolia and called by him <Agoniadine. This
substance was analysed and investigated in Jena by Prof. A. GEUTHER
who gave it the formula C,,H),0,; it melted at 155° and yielded
on boiling with dilute sulphuric acid a sugar and a brown, amor-
phous substance and consequently was a glucoside.

In his review of 1895, it is stated by E. Merckx that he had
obtained from the root of Plumiera acutifolia, a substance different
from that of Boorsma, melting at 157—158° with evolution of gas.
He gives as its composition C;7H72 Oz; + 2 H,0 and for its mole-
cular weight 1074—1080, although the given formula requires 1280.

On the occasion of his last visit to Holland, our fellow member
Dr. TREUB requested me to re-investigate the plumieride which I
agreed to do. .

Preliminary experiments made me see at once that plumieride is
a polyhydrie alcohol, optically active and fairly strong laevogyrate
in aqueous solutions; also that it decidedly deserves the name of
glucoside and that the sugar obtained in its hydrolysis is birotatory
and dextrogyrate and also gives a phenylosazone which is identical
with that of glucose, as shown by its melting point and rotatory
power. I also noticed that the substance of Merck behaves in
every respect, except in its fusibility, like Boorsma’s plumieride
and could show with great probability that the difference is caused
by a variation in the amount of water.

When rendered anhydrous, properly purified and crystallised from
dry ethylacetate, both appeared to be identical; they do not melt
and have the same rotatory power and crystalline form. When
recrystallised from water they were again identical, had the same
melting point and contained the same amount of water.

Still a difference might have been caused by the fact that BoorsMA
had repeatedly boiled his substance with amylaleohol and that it
was possible that this is not an inert solvent. I had, therefore,
the substance prepared from the bark which had been forwarded to
me from Buitenzorg, avoiding the use of amylaleohol and also a
high temperature; this preparation after being recrystailised from dry
ethylacetate was also identical with the other.

That plumieride yields fairly much glucose on boiling with dilute
hydrochloric acid was proved afterwards by isolating the glucose
in a pure, crystallised anhydrous state and identifying it by its
melting point and rotatory power. At the same time the absence of

C Je)

mannose and pentoses was shown. Then if plumieride is boiled with
hydrochloric acid of 10—12 pCt. strength, only insignificant traces
of furfuraldehyde are formed, while the glucose is decomposed into
formic and laevulinic acids, which were both identified, in the com-
pany of a humus-like substance which is mixed with the second
product of the hydrolysis of plumieride, a brown amorphous substance
the weight of which amounts in this case to more than half the
weight of the plumieride. On boiling with hydrochloric acid of 5 pCt.
strength, glucose may be obtained one-fourth part of the weigth of
the used plumieride although Jaevulinie acid is also formed here, by
destruction of a part of the glucose; the weight of the amorphous
substance is then about one-half of that of the plumieride. On
boiling with hydrochloric acid of half a pCt. strength, the hy-
drolysis of plumieride also takes place, although much slower, and
a part of the glucose may also be decomposed of which I have con-
vineed myself by actual experiment. The brown substance now
certainly weighs less than half the weight of the used plumieride,
but still always contains a humus-like decompositionproduct of
glucose. It is, therefore, plain that the exact quantity of glucose
which plumieride is capable of yielding cannot, apparently, be deter-
mined in this manner and that the second product from the plumie-
ride is not to be got in a pure state in this way.

I hope to communicate later on, at the close of the investigation,
about this brown substance and the hydrolysis of plumieride by
enzymes.

After plumieride had been undoubtedly characterised as a glucoside,
it was desirable to study agoniadine which is also known as such
and also gives a brown amorphous substance on hydrolysis, and to
explain the difference between both substances, should a difference
exist. The difference in melting point goes for nothing.

As bark from Plumiera lancifolia was not obtainable, I have made
use of about 5 grams of agoniadine sent by Dr. PEckoLr. This pre-
paration, which was not pure, gave after being repeatedly crystallised
from dry ethylacetate a beautifully crystallised substance perfectly
resembling anhydrous plumieride in shape as well as in chemical
and physical properties. It was not fusible without decomposition
and had the same laevorotatory power etc. Our fellow member
Prof. Beurens had the kindness to compare microscopically different
preparations of plumieride with each other and with those obtained
from PrcKoLtT’s agoniadine; on account of the fact that they have
the same form, polarisation and index of refraction, he thinks he
may safely conclude that they are identical. I, then, do not hesitate

( 38 )

to declare that the substance, isolated from PEcKOLY’s agoniadine, is
identical with plumieride.

Although it is customary in such cases to retain the name given
by the first discoverer, it seems to me that the name ,plumieride” is
preferable. It reminds of both plants from which it is obtained and
by its termination it is more suited for a glucoside. 1, therefore,
obliterate the name ,agoniadine”’, which on account of its termina-
tion reminds more of an alkaloid, from the chemical literature and
in future will call plumieride the substance discovered by PECKOLT
in 1870 in the bark of Plumiera lancifolia, which substance has
afterwards been found by Boorsma and also by Merck in the bark
of Plumiera acutifolia.

Plumieride is a methyl-ester (a methoxyl containing substance)
then it yields methyliodide with hydroiodic acid of a certain con-
centration. It yields, by the action of dilute alkalis or barytawater
at the ordinary temperature, or by water alone at a higher temper-
ature, an acid which I have provisionally called plumieridic acid ').
This does not contain methoxyl but is a glucoside which on boiling
with dilute acids yields a brown amorphous substance and a sugar, the
osazone of which has the same melting point as that of glucose.

If plumieride is now simply a methyl-ester of plumieridic acid as
nearly everything found as yet seems to bear out, the easy decom-
position (saponification) by alkalis and even by water and the con-
sequent difficulty to obtain a pure preparation by recrystallisation
from water becomes apparent.

I, finally, wish to add that the solution of Peckort’s preparation
in cold water was of a very brown colour and strongly reduced .
FeaLtna’s solution; when first extracted with ethylacetate it left
a good deal of a brown amorphous substance behind and it was
only by repeated crystallisation from ethylacetate, which operation
was attended with great loss, that it was obtained pure. The impure
fractions contained glucose.

Chemistry. — ‘On the crystallised constituent of the essential oil
of Kaempferia Galanga L.” By Dr. P. van Rompuren.

When the rhizomes of Kaempferia Galanga L., a plant belonging
to the family of the Zingiberaceae, which is cultivated on a small
seale by the natives in Java for medicinal and culinary use and

') The name plumierie acid has already been given by our deceased fellow member

Prof, A, ©. Oupemans Jr. to another acid obtained from the milky juice of
Plumiera acutifolia.

( 39 )

known under the name of “kentjoer” or ‘tjekoer”, are distilled
with water, the first fractions contain a small quantity of an essential
oil lighter than water. Afterwards an oil heavier than water distils
which deposits abundant crystals, whilst towards the end a erystal-
line substance is almost exclusively obtained. The distillation must
be continued for a long time as this substance is but little volatile.
The yield and also the relation between the solid and liquid product
differ very much with different samples; most likely this depends
on the age of the rhizomes, which matter [ am now making the
subject of practical investigation.

The crystals deposited from the oil may assume very large di-
mensions; they are very shining and transparent, melt at 50° and
may be obtained in a beautiful form by reerystallisation from alcohol.
A 20 percent alcoholic solution appeared to be optically inactive.

The elementary analysis gave numbers, which lead to the formula
Cj, Hy, 03, while the molecular weight, determined in acetone by
LANDSBERGER’s method, came to 197, 206 being calculated.

On heating with alcoholic potash this substance yielded almost
at once a mass of beautiful little crystals of a potassium salt, from
which sulphuric acid liberates an acid crystallismg im colourless
needles. This acid is not easily soluble in water but easily soluble
in ether and it may be very satisfactorily recrystallised from dilute
methyl alcohol.

The melting point is 169°; at that temperature it melts to an
opalescent liquid which does not become. transparent till 185°.

The elementary analysis gaye results corresponding with the com-
position Cy) Hyp Os.

The originai substance differing from this by Cy Hy must, there-
fore, be an ethyl-ester. To further prove this, 30 gram of the crystals
were saponified with aqueous caustic potash and the resulting alcohol
was distilled off. After treatment with dry potassium carbonate and
rectification over anhydrous copper sulphate a liquid was obtained
which boiled at 78° and showed all the properties of ethyl alcohol.

The potassium and silver salts of the acid were prepared and
analysed. The potassium estimation gave 17.7 pCt. of K (theory
requiring 17.6), the silver estimation gave 38.06 pCt. Ag., (theory
requiring 37.9).

Tf a solution of the acid in ethyl alcohol is treated with hydrogen
chloride, a product is obtained which melts at 50° and is identica!
with the original ester. The methyl ester prepared in an analogous
manner melts at 90°.

( 40 )

The solution of the acid or its ester in chloroform absorbs two
atoms of bromine forming an addition product.

The acid does not show either aldehydic, alcoholic or phenolic
properties. Heated with hydriodie acid it yields alkyl iodide. A
quantitative estimation according to ZeISEL gave an amount of silver
iodide corresponding with 16.85 pCt. of methoxyl, theory requiring
17.4 pCt.

On oxidation with potassium permanganate in neutral solution,
the ester gives off an agreeable odour resembling hawthorn, while
an acid is also produced which proved to be identical with anisie
acid. The oxidation of the acid in an alkaline solution proceeds more
quickly; the odour of anisie aldehyde is also noticed here and a
good yield of anisic acid is obtained. From this it follows that in
regard to the side-chain the group OC Hz is situated in the para-
position and in connection with the additive power the formula is

Ya
therefore, most probably 1.4 Cg Ha ee CH — COOH » conse-
quently that of p. methoxycinnamie acid.

The properties do indeed correspond with those recorded of this
acid '). The only thing which is not mentioned is the peculiar
behaviour on melting, so that I thought it necessary to prepare the
synthetical acid for comparison purposes.

According to KNOEVENAGEL 2) it is obtained by condensation of
anisic aldehyde with malonic acid under the influence of alcoholic
ammonia. The acid prepared by this method also melted at 169°
to an opalescent liquid which did not get clear till 185°.

VoRLANDER ®) obtained the ethyl ester of p. methoxylcinnamie
acid by condensation of anisic aldehyde with ethyl acetate. This
I also prepared and found it to be identical with the product
obtained from “Kentjoer”, whilst the acid obtained from it by sapon-
ification again showed the properties mentioned above.

I dare not, as yet, decide what may be the cause of this peculiar
behaviour. Perhaps a polymeric body is formed, or else the acid
exists in two liquid isomeric modifications *). By heating above the
melting poimt, the acid is gradually decomposed with evolution of
carbon dioxide, but if the decomposition already exercised some

‘) In Beilstein’s Handbuch it is erroneously stated that p. methoxyeinnamie agid
cristallises in yellow needles.

2) Berl. Ber. 31 S. 2606.

5) Ann. der Chemie. 294, S. 295.

*) Compare: Rupo.e Scnenck, Untersuchungen iiber die krystallinischen Fliissig-
keiten. Zeitschr. f. phys. Chemie XXV, 8. 837, XXVIIS. 167.

( 41 )

influence during the determination of the melting point, this would
be found lower on repeating the experiment, but this is, however,
not the case.

By treating the alcoholic solution of the acid obtained from
kentjoer with sodium amalgam p. methoxyphenylpropionic acid is
formed, which melts at 102° and has already been described by
Witt!). The methyl ester of methyl naringeninic acid *) prepared
by the same chemist, which is identical with the methyl ester of
p- methoxyeinnamic acid, melts at 90° just like the methyl ester
obtained by myself, whilst its bromine-addition product showed the
melting point of the methyl ester of dibromomethylparacumaric acid.

There cannot, therefore, be any further doubt that the crystallized
substance which forms the chief constituent of the essential oil from
Kaempferia Galanga L., is the ethyl ester of p. methoxycinnamic
acid, a substance which had not yet been met with in nature and
which now goes to increase the comparitively small number of
known ethyl esters from the vegetable kingdom.

From the liquid portion of the oil I could separate in ad-
dition to the above mentioned ester a small quantity of a terpene
boiling at 160°—170° and a bluishgreen liquid boiling at 150° in
vacuo (probably a sesquiterpene). There is also present an acid of
a lower melting point which I am still investigating.

Pathology. — ‘On the durability of the agglutinative substances
of the bloodserum.” By Dr. J. EK. G. VAN EmpeEn. (Commu-
nicated by Prof. Th. H. Mac Ginuayry.)

Wipat and Srcarp*) and also AcHARD and Bensaupg*) have
communicated that the bloodserum of patients suffering from febris
typhoidea and that of animals, that had been rendered immune
against the bacille of Esertu, keeps its agglutinative power undi-
minished for many months; the agglutinines are so resistant that
they do not perish even in mouldy and putrefying serum.

On the contrary I found that serum after some six weeks indeed

1) Berl. Ber. XX S. 2530.

*) Berl. Ber. XX S. 301.

*) Annales de I’ Instit. Pasteur XI p. 353.

4) Bensaupe: Le Phénoméne de VAgelutination des Mierobes, (Paris 1897).

( 42)

had lost a great deal of its agglutinative action: this at least was the case
with sera from typhoid patients and from rabbits immunised against
the bacillus aérogenes.

Also VAN DE VeELDE!) had observed an important decrease of the
agelutinative titre of serum that had been put away.

Stimulated by my”) communication van Hourum®) investigated
two sera that had been kept five and eleven months in sealed glass
tubes in the dark and at the temperature of the room: the agglutinative
power had not diminished.

The disagreement in the results mentioned above must in my
opinion be caused by differences in the ways in which the sera had
been kept.

The tubes of vAN Hourum had been sealed, but iy tubes — from
which repeatedly a small quantity of serum was taken for testing pur-
poses — were closed by cottonwool stoppers covered by pieces of
paper or tinfoil.

Now the next experiment showed that the way of closing had a
decisive influence on the fact whether the agelutinative power keeps
constant or diminishes.

Serum of a known titre was kept in:

i tubes closed by cottonwool

9 ale

AN Bs - cork

Di lois 5 » sealing

4, filled with hydrogen and sealed
Sees yy» earbon dioxide and sealed

Four months afterwards the agglutinative titre was determined
again.

The agelutinative power of the serum in a// the sealed and corked
tubes had remained wnchanged.

On the other hand in all the tubes closed with cotton wool the
agelutinative power of the serum had strongly dimimished, notwith-
standing the ciearly visible condensation — except in the case of
one. This exception regards a soiled tube, in which the serum was
covered by a layer of mould; this serum had also kept its power
unchanged.

Conclusion. When the circulation of the air is hindered or suffi-

') Semaine médie, 1898 p. 379.
*) Nederl. Tijdschr. van Geneesk. 1898 II p. $42. Zeitschr. f. Hyg. und Infect. XXX p.19.
4). sce mn a a 1898 II p, 841,

ciently limited, the bloodserum keeps its agglutinative power longer
than when the access of air is free.

It lies at hand to think here of the influence of the oxygen in
the air and in fact, experiments not yet terminated, support this opinion.

Now it is important to investigate whether the unstability of the
other specific substances occurring in the blood, especially the anti-
toxines must also be ascribed to the influence of the air. Perhaps
that the efficiency of various medicinal sera will prove to be more
durable, when they are kept in vacuo or in a neutral gas.

Geology. — “The Amount of the Circulation of the Carbonate of
Lime and the Age of the Earth”. I. By Prof. Eva. Dunots.
(Communicated by Prof. J. M. van BemMMELEn.)

In a similar way as water is continually passing into the atmos-
phere, to return again to the earth, we find the carbonate of lime
perform a circulation, as this matter is solved from limestone, and
after having been carried to the ocean by the rivers, is there, through
the agency of organic beings, again given back in solid state.

Even an approximative estimate of the amount of this circulation
would be of considerable importance for geology, because we may
regard it in connection with questions about the formation of that
carbonate by decomposition of silicate rocks, and about the time
required for its formation.

The results of an estimate as referred to, and some conclusions
based on these results, are given in this paper, and in another
paper I propose to present on the next occasion.

In investigating the amount of this circulation let us start from
the carbonate of lime in the ocean.

The ocean contains in the deposits over its floor and floating
about in the water such a vast amount of solid carbonate of lime,
as remains of shells and skeletons of organisms, that, considering
the perpetual movement, and the consequent mixing of the ocean
“water, we may take it for granted that, under the existing pressure
of carbonic acid and the actual temperature of the atmosphere, it
contains carbonate and bicarbonate of lime in saturated solutions.

From experiments kindly made at my request by Dr. Ernst ConEn
in collaboration with Mr. Raken, and the results of which, are
communicated to the Academy at the same time as this paper, this

( 43)

proved really to be the case. According to W. Dirrmar!) 0.345 pCt. of
all the salts of average ocean-water are carbonate of lime. The relative
quantity of salts being 0.035, which may be considered as the average
salinity of the ocean®), 1 litre of ocean-water would then contain 120.7
merms. Ca COs, of which 53.1 mgrms. CO, of normal calcium carbonate.
From the average of 26 samples of water, taken from different parts of
the ocean and at different depth, we may calculate 54.9 mgrms. CO;
of normal calcium carbonate, and moreover 43.6 mgrms. of loose earbonic
acid forming bicarbonate *). ToRNbE came to nearly the same results,
as he found in the North Sea 53 mgrms. forming normal carbonate
and 43 merms. of loose carbonic acid, forming bicarbonate *), per litre
of water. With these the results of other analysts coincide. On
account of the great uniformity of the chemical composition of the
water of the ocean it may therefore be taken for granted, that in
one litre of ocean water there are in solution on an average from
120 to 125 mgrms. carbonate of lime and of these about 100 mgrms. as
bicarbonate. The investigation of Dr. Congn shows that in artifi-
cial ocean-water, containing all the salts in the average quantity,
as stated by Dirrmar, but no carbonate of lime, in a litre 125 mgrms,
calcium carbonate could be dissolved from a surplus of suspended
solid calcium carbonate by passing during a sufficient time a current
of air, containing 0.00045 carbonic acid (a relative quantity in ac-
cordance with the average).

We may say, therefore, that in the ocean-water the aforenamed
matter exists as a saturated solution under the given pressure of
carbonic acid in our atmosphere, and therefore we must take it that
all the carbonate of lime which the rivers carry incessantly to the
ocean is a surplus.

A considerable amount of carbonate of lime is often to be found
in the matter carried in suspension by large rivers to the ocean.
Some analyses relating to this and extending over longer periods of
time may be mentioned here. C. Scumipv.®) found in twelve monthly
determinations for the relative quantity of calcium carbonate in the
suspended matter of the Amu-Darja from 17.0 to 19.6, on an average

1) Neport on researches into the composition of ocean water collected by H. M.S.
Challenger. Challenger Reports, Physics and Chemistry. Vol. £. London 1884, p. 204.

*) Dirrmar |. c. p. 201.

SVE Cy pep Pal

*) Berichte der Norwegischen Nordmeer-Expedition. Abt. Chemie, referred to by
JoausLAWsKI, Handbuch der Ozeanographie. Stuttgart 1884. Bd. L, p. 139.

5) ©. Scumipr und I, Dorranpr, Wassermenge und Suspensionsschlamm des Amu-
Darja, Mémoires Acad. imp, St. Pétersboure (7). Tome 25. n°. 3. 1878, p. 31.

( 45 )

18.3 pCt., from which may be calculated an average quantity of
41.7 mgrms. of that salt per litre of water. BALto!) found that from
the 300 mgrms. suspended matter contained in a litre of Danube-water,
5.53 pCt. is lime combined with carbonic acid, being 9 pCt. or 27 mgrms.
CaCO, per litre of water. The water from the Blue Nile near
Khartoum, as the river was low or high, contained per litre 16.9
to 62.1 mgrms. solid calcium carbonate in suspension.”) The clay which
the Nile deposits in its delta, according to different analysts contains
3.72 pCt. of this salt *), so, that taking into account the average
quantity of solids in suspension of 458 mgrms. per litre *), the water of
the Nile would have contained at the delta an average of 17 mgrms.
calcium carbonate in suspension.

Where thus in many of the large rivers there is always a surplus of cal-
cium carbonate, which may easily be acted upon by the dissolving
agents, it is obvious that in these river waters too the solution must
be saturated. Whereas however in the ocean-water this salt, as
regards its absolute quantity, is of very little account in comparison
with the other salts, in the water of such like rivers it constitutes
nearly the half ofall the salts which here form a much weaker solution.

According to a combination by Sir Jonn Murray °) of the analyses
of 19 large rivers one litre of river water contains on an average
186 mgrms. of total sslids in solution, of which 79.6 mgrms. are
calcium carbonate.

From the experiments of ScHL@siNG °), so highly important for
geology, made in a similar way on pure water, as the recent expe-
riment of Dr. Ernst CoHEN on ocean-water, by bringing a large
quantity of calcium carbonate in suspension in long contact with
air, containing a constant relative quantity of carbonic acid, it follows 7)
that in one litre of pure water by common air, the pressure of
carbonic acid being 0.0005, and 16° C temperature, 74.6 mgrms. car-
bonate of lime are soluble. The solution takes place for about 13.1 mgrms.

1) Chemische Untersuchung des Wassers des Donaustromes bei Budapest. Berichte
der Deutschen Chemischen Gesellschaft. 1878, p. 444.

*) A. Cutxu, Le Nil, le Soudan, Egypte. Paris 1891, p. 25.

8) C. Scumupr, |. ¢., p. 40.

4) CHELU, |. c., p. 203.

®) On the total annual rainfall on the land of the globe, and the relation of rainfall
to the annual discharge of rivers. Scottish Geographical Magazine. Vol. 3. Edinburgh
1887, p. 76.

6) Tu. ScuiesinG, Sur la dissolution du carbonate de chaux par lacide carbonique.
Comptes rendus de l’Académie des Sciences. Paris. Tome 74. (1872), p. 1552—1556,
and Tome 75 (1872), p- 70—73.

*) L.¢., p. 1555.

( 46 )

as normal carbonate, independent of the pressure of carbonic acid
and very little dependent on temperature, for a greater part however,
namely 61.2 mgrms. as bicarbonate, the lime being combined witha
double quantity of COs. The quantity of the bicarbonate thus formed
depends, for a given temperature, on the pressure of carbonic acid.
The value of the pressure of carbonic acid and of the quantity of
carbonate forms two geometrical series, but the ratio of the former
is greater than that of the latter series. If the pressure of carbonic
acid were’ 0.0008, i. e. more than one and a half the actual
pressure, the quantity of bicarbonate formed would be 73.2 mgrms. per
litre of water. At a pressure of 0.05, i.e. the hundredfold of the
pressure of carbonic acid in the atmosphere, the quantity of bi-
carbonate only increases to 349,3 mgrms. per litre of water, that is
a little more than five times and a half (5.7). Generally stated
the quantity of bicarbonate formed depends in such a way on the
tension of carbonic acid, that, if that tension is called 2, the quantity

; : 7p 0;37866
of the bicarbonate y Se Cer

So if the pressure of carbonic acid rose to 700 times that in the
atmosphere the quantity of carbonate of lime dissolved in the state
of bicarbonate would be only about twelve times as great as at the
actual pressure of carbonic acid in the atmosphere, and that of the
carbonate dissolved in both states, as normal carbonate and as bicar-
bonate, only about ten times as great as under the actual condition
of carbonic acid pressure.

Scun@sinc found moreover, that with every degree of variation
in the temperature, the quantity of the bicarbonate dissolved varies
about 1 pCt., viz: it rises as the temperature falls, and it diminishes
as the latter rises.

The figures given by Scuiasine@ for the quantity of the carbonate
of lime dissolved at the pressure of carbonic acid in the atmosphere
and 16°C. temperature come so near the average quoted quantity of
that matter in river water, which on an average has about the same
temperature (the mean temperature at the surface of the earth being

5° C), that it may be taken for granted, that those large rivers keep
the carbonate of lime in solution in similar way as in pure water,
partly as carbonate, for the greater part however as bicarbonate,
and that the quantity of that double salt in it is depending on the
pressure of carbonic acid in the atmosphere.

The number of analyses, from which Murray drew the above
mentioned averages seems to be sufficiently large for the purpose, never-
theless, when the existing reliable analyses of river water are compared

(a7)

with one another, it appears that these deviate rather strongly, and
that the average has only this value, that on the whole the relative
quantity of dissolved carbonate of lime oscillates about saturation
with that salt in pure water under the pressure of carbonic acid
in the atmosphere. In some cases the relative quantity observed
remains below it, but mostly it rises higher.

In one and the same place the relative quantity of carbonate of
lime dissolved in river water varies according to the water mark.
If the river rises the quantity of suspended matter per litre of water
increases, but the quantity of dissolved matter, and among these of
carbonate of lime diminishes. A few examples may explain this.

According to the determinations of Voni') the quantity of
carbonate of lime in the water of the Rhine, taken from the same
place, a little above Cologne, varied from 52.37 mgrms. per liter at
high water mark, to 109.37 mgrms. at low water mark, thus in the
ratio 1 to 2. This diminution of the relative quantity of dissolved
matter in general and of carbonate of lime in particular, when the
discharge of water is greater than usual, is a fact generally observed,
which, among others, has been sufficiently proved from long and
reliable observations made on the water of the Danube by Bato?)
and WoLFBAUER®*) and from the water of the Meuse by Spring
and Prost. WoOLFBAUER found‘) that the relative quantity of suspen-
ded matter in 23 determinations, made during a year with intervals
of, on an average, 16 days, proved to vary from 9.6 mgrms. as a
minimum to 331.3 mgrms. as a maximum per litre of water, which
two numbers stand to each other in the ratio as 1 to 35, whilst at
the same time with the given minimum of the quantity of suspended
matter a maximum of dissolved matter of 207 mgrms. was obtained,
and at the same time with the quoted maximum of the quantity of
suspended matter a minimum of dissolved matter of 130 mgrms. per
litre, which two numbers stand to each other as 1.6 to 1. Whereas
during low water the Blue Nile near Khartoum, according to Cust *)
earries only 156.3 mgrms. and during high water 1673.4 mgrms. of sus-
pended matter per litre of water, so in the ratio 1 to 10.7, the

1) H. Vout, Ueber die Be:tandtheile des Rheinwassers bei Céln. Dincurr’s Poly-
technisches Journal. Bd. 199. 1871. p. 311 sqq. ;

*) M. Bauto, lic. p. 441—445.

*) J. F. Worrsaver, Die chemisthe Zusammensetzung des Wassers der Donan vor
Wien im Jahre 1878. Sitzungsberichte der Math. Naturw. Classe d. Kais, Akad. Wiss.
Wien. Bd. 87. (1887), p. 404—424.

4) lc. p. 414.

2) pleiG-\p-2o—

( 48 )

quantity of dissolved matter during high water was at the same
time even a little higher than during low water, it rose namely from
201.4 merms. to 232 mgrms. per litre. The total solids in solution
in the water of the Meuse at Liege attained during a year a maximum
at low water mark of 279 mgrms. and a minimum at high water of
86.2 mgrms. per litre, giving a ratio of a little more than 3 to 1).
For the matter in solution in the Arve the maximum is to the
minimum in the ratio 2.5: 1, whilst for the suspended matter this
ratio was 5000: 1. *).

However those extremes are only attained on one single day.
Comparing longer periods of time we find the differences far smaller.
For the Elbe in Bohemia the minimum quantity observed in 22
determinations, made during a year, amounted to 20.3 mgrms. CaO,
the maximum quantity to 45 mgrms. per litre of water, and the
quantities of the other substances showed similar unimportant varia-
tions, °) whilst those of the suspended matter*) varied from 1.13 to
756.01 mgrms. per litre. WOLFBAUER corroborated moreover the fact,
which had already repeatedly been noticed, that, no matter how
much the absolute quantities of the dissolved substances may vary,
the mutual ratio of the components remains almost unchanged °).
Something similar is also known of the substances in suspension in
the river water, and appears clearly from the twelve monthly
analyses of the suspended matter in the Amu-Darja, published by
Scumipt “). Silicates and quartz for instance varied in it only from
76.2 to 79.86 pCt. Hence follows, which is important for the
following considerations, that the results of a single analysis may
be applied to determinations of the absolute quantities of the
same river.

Besides those variations of the relative quantity of suspended
matter depending on variations of the water mark in connection
with time, and which, as is generally observed, can in large rivers

') W. Serine et EK. Prosr, Etude sur les eaux de la Meuse. Annales de la Société
géologique de Belgique. Tome 11 (1S83—1884). Liége 1883. p. 175.

*) B. Bakrr, Les eaux de Arve. These. Genéve 1891, p- 59.

3’) PF. Unirx, Beobachtungen iiber die Bestimmung der wihrend eines Jahres im
Profile von ‘Tetschen sich ergebenden Quantititsschwankungen der Bestandtheile des
Hlbewassers und der yon letzterem ausgefiihrten loslichen und unléslichen Stoffe.
Abhand. kon. bohmischen Gesellschaft der Wissenschaften. VI. Folge, 10 Band. Math.
Naturw. Classe. N°, 6. Prag 1880, p. 31.

‘) Ibid. p. 28.

5) lic. p. 415.

6) icp ol.

(49)

at most amount to the ratio 1: 3, and this very transitorily, varia-
tions have been stated of the relative quantity of carbonate of lime
in solution in the rivers according to space. Some rivers have a
lower average quantity of carbonate of lime than others, though
with most large rivers those differences are not great, at most amount
to about the same ratio as the temporary variations, which are of
very short duration.

But also in the same river, and even over small distances, the
quantity may be a little different. That was apparent again from
the observations of Vout. The water taken on the same day, but
from three different points, namely above, in and below Cologne,
as well during high as low water mark, proved to grow richer in
carbonate of lime in its course through the town.

The quantity of carbonate of lime, in milligrammes, contained in
one litre of water from the Rhine was,

during very low watermark, during high watermark,
on Oct. 21st 1870, on Nov. Sth 1870,
above Cologne 109.37 52.37
: in Cologne 115.78 68.92
below Cologne 123.44 108.68

This increase is evidently to be accounted for by the influence
of organic matter, combinations of carbon, which pollute the water
and are consequently oxydized in it, and which, as long as they
remain there, keep more carbonate of lime, in the state of bicarbonate,
in solution than the carbonic acid of the atmosphere, absorbed in the
water, would alone be able to do. That really the organic substances
in the river water are soon oxydized is evident from the fact, stated
by Utuix, that those substances soon diminish in water samples
kept standing for some time. From the observations made by him ')
is to be derived that on an average in 24 hours 3.5 pCt. (from
1.7 to 5.4 pCt.) of the organic matter is decomposed. Bacteria and
algae are the principal agents and contribute mostly to the so called
self-purifying of the rivers.

Very instructive in this respect are the analyses of the water of
lakes as they have been stated principally by DeLtysecque. From
these it has been made evident, that the water of lakes fed by rivers
and rivulets in a region rich enough in limestone, takes in general
the more carbonate of lime in solution in proportion to the surface

es peabe

Proceedings Royal Acad, Amsterdam, Vol. ILI.

(50 )

of the lake being smaller. 'The increase of the circumference indeed
is less than that of the surface, it increases in general as the square
root of the surface. A lake, whose surface for instance is the ninth
part of that of another lake, has, if the two are uniform, still the
third part of its surface. Moreover the depth also often decreases
with the length and breadth, though by no means in the same propor-
tion, so that the volume of water of a small lake in comparison
with its circumference is a good deal less. Now as organic matter
principally enters the Jakes from the circumference, it is clear that
by the continually flowing source of carbonic acid, which this matter
produces by its decomposition, the quantity of carbonate of lime, in
the state of bicarbonate, in the water of these lakes under otherwise
similar circumstances is greater in proportion to the lakes being
smaller. Foret!) had already pointed out that in the mud at the
bottom of a lake the quantity of organic débris is the greater in
proportion to the lake being smaller. In the following lakes, inves-
tigated especially by DELEBECQUE?), all draining the same limestone
regions, the influence of size is clearly to be recognized.

Surface, in K.M2. Volume, in M’. CaCo,, in mgrms. per L,
Lake of Geneva *) 582.40 88920000000.0 72.3
Lac du Bourget 44.62 3620.0 96.0
> d’Annecy 27.00 1123.5 123.7
>» d’Aiguebelette 5.43 166.6 126.4
> de Paladru 3.90 97.2 150.9
» de Nantua 1.41 40.1 154.5
> de Sylans 0.50 4.8 152.6

Something similar is to be observed concerning rivers. At the same
length a large river is less liable to pollution than a smaller one.
The distance from Geneva to Lyons is less than that from lake
Ontario to Vaudreuil (above Montreal), yet the Rhone to Lyons
having the same length of bank and containing only !/,; of the water
of the St. Lawrence river, takes more organic matter and in consequence
of this the Rhone at Lyons*) held in winter 150, and in summer
100 mgrms. CaCOs per litre in solution, the St. Lawrence (March 30th)

1) F. A. Foren, Le Léman. Etude limnologique, Lausanne 1895. Tome II, p. 134.

*) Archives des sciences physiques et naturelles. (3). Tome 27, Geneve 1892, p
569—570 and p. 134. — Tome 28, p. 502.

*) From Foren and DeLesrcgue (quoted afterwards).

*) According to Boussincauur and Pasaurer, quoted by G. Biscuor, Lehrbuch der
chemischen und physikalischen Geologie, 2 Aufl. Bd. I, Bonn 1863, p. 272.

(51 )

only 80.3 mgrms. '), whereas in the Jarge lakes, whose outlets they
are, there is only about as much Ca CO, dissolved as in pure water.

Freshwater lakes with an outlet are of great importance in consid-
ering these questions, on account of the rather constant composition
of their waters, which is a consequence of their volume being very
large in comparison with that of the discharge of the affluents and
of the outlet. The lake of Geneva contains about 11 times as
much water as the yearly discharge of the Rhone at Geneva, lake
Ontario 10 times as much water as is flowing every year through
St. Lawrence river; the water of the lake of Annecy is on an average
renewed in 3.3 years, and that of the lake of Paladru in 4 years *).
So one single analysis of their waters has already a great value.
The quantity of carbonate of lime in the water of some lakes must
therefore been spoken of somewhat more in extenso.

Very large lakes, in the drainage area of which much limestone
occurs, receive relatively to the bulk of their waters so little
organic matter, and their relative quantity of carbonate of lime
is therefore so greatly influenced by the pressure of the carbonic
acid in the atmosphere alone, that it agrees nearly with that which
ScuLa@sinG stated for pure water. From 11 reliable analyses of the
water of the lake of Geneva, which varies only a little in composition
in consequence of the mixture being temporarily and locally less
perfect, or by variations of the temperature and the pressure
of the air, contains per litre in 175 mgrms. dissolved solid matter
74.9 mgrms. calcium carbonate *). In the opinion of DELEBECQUE *) the
first named number is not right; as average of 33 determinations,
quoted by him, we find 169 mgrms. dissolved solid matter per litre of
lake-water, in which, therefore, 72.3 mgrms. calcium carbonate are
contained. The volume of the water in the lake of Geneva being
89 K.M®., at an average yearly discharge of the Rhone at Geneva
of 8 K.M*., the water remains in the lake, as has been already
stated, for about 11 years. Therefore organic matter which the
rivers carry into the lake and which enters it from the shore can
hardly have any noticeable influence on the quantity of the calcium

1) According to T. S. Hunt in: Geology of Canada. Geological Survey of Canada.
Reports of progress from its commencement to 1863. Montreal 1863, p. 567. Also in
Philos. Magazine (4). vol. 13, p. 239. The sample was taken at the Point des Casea-
des near Vaudreuil, on the 30th of March 1863.

>) Foret, |.c. Tome I, p. 446, and DeLesecaue |. c.

5) Foret, Le Léman II, p. 587.

4) A, DELEBECQUE, Les lacs francais. Paris 1898, p. LYL and 197-198.

4*

( 52)

carbonate. In fact the water of the lake of Geneva contains
only little organic matter, on an average 5.5 mgrms. per litre '),
whereas rivers according to MurRay’s statement contain on an
average 19 mgrms. In the water of the Danube WoLFsauer found, it
is true, only 5.6 mgrms., there is however still suspended organic mat-
ier, according to BALLo 20 mgrms. per litre, of which hardly any is
to be found in the lake of Geneva. ULLik ®) stated during one year’s
observations, that the organic matter in the water of the Elbe got
below 6 mgrms. per litre on three days only, he found for the mini-
mum 5 mgrms., and for the maximum 22.6 mgrms. per litre.

The lake of Geneva, therefore, contains, in distinction from other
lakes, which are smaller, but also situated in a limestone region, hardly
more carbonate of lime in solution than that corresponding to the
tension of carbonic acid in the atmosphere. If with DELEBECQUE
we take that the latter contains 0.00029 of its volume carbonic
acid, the average pressure of the air on the lake of Geneva being
730 mm., we find for the tension of carbonic acid 0.000424, and
from the formula of ScHL@sING we calculate that 70.5 mgrms. carbonate
of lime can be dissolved, as normal salt and as bicarbonate, in 1
litre of pure water at 16° C temperature, therefore at the average
temperature at the surface of the lake of Geneva of 9.6° C.,
75 mgrms.

At the mean relative quantity of carbonic acid of the atmosphere
on the northern hemisphere of 0.000282 Vol. pCt.*) and the mean
pressure of the air, where the rivers flow into the ocean, of 762 mm.
we find that 70.8 mgrms. calcium carbonate (in both states) are
soluble in 1 litre of water. *)

The great North American lakes, whose waters flow to the ocean
through the St. Lawrence river, have 425 times the surface of the
lake of Geneva and about 500 times its volume, and lake Ontario,
the water of which flows directly into the St. Lawrence river, has
34 times the surface and 40 times the volume of the lake of Geneva.
The St. Lawrence river discharging yearly 364 K.M®. of water,
lake Ontario would empty in about 10 years, if the water were
rot continually renewed. Under these circumstances, even on account
of one single analysis it may be taken that the water of the St.

1) Foret, Le Léman, IL p. 615.

2) Tisie:, -p: Sl.

‘) A. Minrz et E. Austy, Recherches sur Vacide carbonique de Vair. Mission
scient. du Cap Horn 1§82-1883. Tome ILI. Paris 1886, p. A. 82.

') DELEBEcQuE (Les lacs frangais, p. 218) arrives at different results by erroneously
substituting the relative volume for the relative pressure.

(be)

Lawrence above Montreal, to where only one single insignificant
little river joined, and has only been in contact with cambrian and
cambrio-silurian crystalline rocks, can only be very little richer in
carbonate of lime than the water of the lake itself. Near Vaudreuil
it contained in a litre, according to the modus of calculation, from
80.3 to 80.8 mgerms. carbonate of lime!). The relative quantity of that
salt in the lake-water will therefore not differ greatly from that
of Geneva.

The water of lake Peipus in Russia, another large fresh water
basin (having 6238 KM. in surface and 12 M. as its greatest
depth) contains, according to the analysis of C. Scumipt*), in summer
67 mgrms. CaCO; per litre.

The water of the lake of Gmunden or Traunsee in Upper Austria
(having a volume of 2.3 K.M*., and through which flows the Traun
keeps in solution 64 mgrms. calcium carbonate per litre °).

In the drainage area of all the above named lakes limestone
is largely represented. Moreover in the mud on their bottoms
there is much carbonate of lime, and the waters of the affluent
rivers carry on an average more of that salt in solution with
.them than the waters of the lakes contain*). In the mud of the
lake of Geneva °) there is found a mean percentage of 27.8,a mini-
mum of 14.9 carbonate of lime, that of the lake of Bourget*) contains
55.5 pCt., of Annecy 28 to 79 pCt.; of Aiguebelette 29.7 pCt., of Paladru
84.7 pCt., of Nantua 56.3 pCt., of Sylans 73 pCt. °).

It is therefore evident that those waters must be satured with Ca COs.

In regard to the analyses of river water I refer to Brscnor and
Rotu in the first place’). Some reliable and especially important
analyses may still be quoted here.

According to two analyses of Von *), one during high and one

1) T. S. Honr in: Geology of Canada. Montreal 1863, p. 566.

2) Bulletin de Académie impér. des Sciences St. Pétersbourg, T. 16. 1871. p. 192.

5) R. Goperrroy, Ref. in Jahresbericht iiber die Fortschritte der Chemie ftir L882,
p- 1623.

*) According to Durarc (le Lae d’Annecy, Archives des sciences physiques et
naturelles (3), Tome 31. Gentve 1894, p. 197) the water flowing through 13 rivulets
into the lake of Annecy contains on an average 199.1 mgrms, CaCO, per litre, that from
the lake itself 50 mgrms. less. The surplus is consumed by algae, whilst calcareous,
tufa is formed.

5) Caleu'ated according to 15 analyses mentioned by Foren (Le Léman, L. p. 122 - 128).

*) Archives, Genéve. Tome 27. p. 573 and Tome 31. p. 197.

7) G, Biscnor, 1. ec. — J. Rorn, Allgemeine und chemische Geologie. Berlin 1879,
Ba. Lv, 457 saq.

) Le,

( 54 j

during low water mark, of the water from the Rhine, taken above
Cologne (in and below Cologne a temporary increase of the quan-
tity of carbonate of lime takes place) it contains a mean of 80.8 mgrms.
CaCO, per litre. BiscHor found during low water at Bonn 94.6 mgrms.,
GuwninG !) in February 1862 at Arnhem 87.5 mgrms. Some other
analyses of water from the Rhine yielded figures slighly higher, for
instance those of FreyraG (above Cologne in 1853 and 1855)
132.3 and 134.1 mgrms. and of Sainte Cratre Devine (1848 at
Strassbourg) 135.6 mgrms. per litre (these analyses all quoted by Vout).

The determinations of the matter in solution in the Meuse at
Liege, daily made during a year by Sprine and Prost, and the
analyses of those, collected in 13 periods differing according to the
water mark, show that the Meuse contains on an average 90 mgrms.
Ca CO; per litre of water *).

According to the analyses by WoLFBAUER of 23 samples of water
taken during a year with intervals of about 16 days, the water of
the Danube above Vienna contains on an average 97.9 mgrms.,
according to one analysis of Batno at Budapest (in the middle of
November) 88.7 mgrms. carbonate of lime per litre.

The Embach above Dorpat and the Welikaja at Pskow, which-
both flow into lake Peipus, contain in summer, during low water,
88 resp. 82.5 mgrms. dissolved carbonate of lime per litre of water %).

The Syr-Darja (May 1878°, according to an analysis by C. Scumipr *)
contains 86.4 mgrms. Ca COs per litre water.

The Blue Nile near Khartoum has on an average, from an obser-
vation at high and another at low water, 77.5 mgrms. carbonate of
lime in a litre of water *).

From the analyses of water of the Nile near Cairo published by
Cutitu") it appears, that on an average (from twelve, monthly
repeated, observations) among the dissolved matter 42.5 merms. Ca O

1) J. W. Guanine, Onderzoek naar den oorsprong en de scheikundige natuur van
eenige Nederlandsche wateren. Utrecht 1853, p. 66. Also in Jcurnal fiir praktische
Chemie, Bd. 61 (1854), p. 139.

*) Calculated from the statements (I. c. p. 208 and 212) of the solid matter in solu-
tion carried during a year and the yearly discharge of water. — Four analyses of
water from the Meuse by CaanpELon (quoted by Brscnor) yield a mean of 86,3 mgrms.,
one of Gunnine (l.¢.) at Grave 72 merms. per litre.

*) C. Scumrpr in Bulletin de l’Académie imp. des Sciences St. Pétersbourg 1875,
Tome 20, p. 134.

*) Mémoires de l’Académie imp. des Seiences St. Pétersbourg. (7). Tome 29,
1881, p. 25.

*) Cni&nu, |. c. p. 25,

©) Thier: 277,

(55 )
are found, which would correspond to 96.6 calcium carbonate pér
litre. Part of this lime, however, is combined with sulphuric acid,
in what quantity cannot be stated from the other results of the
analyses, which seem to be stated wrongly.

From the water of the Mississippi, which, being a very large
river, with a drainage area equal to 16 times that of the Rhine,
would be of great importance, I am acquainted only with two
analyses, one by AveQquin!) and another by Jones?). According
to Avequin, in August 1856, 1 gallon of water from the
Mississippi above New Orleans (at Carrolton) contained 7.307 grains
of carbonate of lime and carbonate of magnesia; according to JONES
near New Orleans 1 litre contained 92.8 mgrms. carbonate of lime
and no magnesia. If now according to the usual ratio we reckon
that one United States gallon is equal to 57750 grains it would
follow from the analysis of the first named chemist that one litre of
Mississippi-water then contained 126.5 mgrms. Ca CO; + Mg CO,
in solution. If taking however with Metnuarp ReapDeE that one
gallon is equal to 56000 grains then the number for the dis-
solved carbonates would be 130.4 mgrms. Carbonate of magnesia being
in every case only present in small quantities, the two latter num-
bers for the carbonates appear to agree pretty well with the result
of the analysis of AVEquin. According to the values for the yearly
discharge of carbonate of lime and the yearly discharge of water
of the Mississippi, quoted by Russet, a quantity of 75.5 mgrms. per
litre is to be calculated °).

The average quantity of carbonate of lime of twenty rivers in
North America, nearly all of which, however, are of very small size,
and many draining regions poor in or even deficient of limestone,
is according to RussELL 56.4 mgrms. per litre *).

Among the smaller rivers there are many, flowing over limestone
or taking up the water of sources situated in limestone, which are
very rich in dissolved calcium carbonate, partly because they contain
spring water, not yet sufficiently ventilated, which has taken up
carbonic acid under a higher pressure, and partly on account of

1) A. Avequin, Journ, Pharm. (3). Vol. 37 p. 258. (1857). Qnoted by T. Mentarp
Reape in American Journal of Science, (3). Vol. 29. (1885), p. 251.

2) W. J. Jones, Report La, St. Board of Health 1882, p. 370, qnoted by J. ©.
Russet in: Geological History of Lake Lahontan, Monograph of the US, Geological
Survey, Vol. Xl. (1885), p. 176, Table A.

3) Le. p. 175.
le, p. 174,

( 56}

their being more polluted by organic matter. In their farther course
they Jose much of their dissolved carbonates.

Here may still be remembered the 9 analyses of Thames water,
quoted by Brscnor'), which all show a high quantity of calcium
carbonate, namely from 115.6 mgrms. to 205.4 mgrms. per litre, and
also those of the water of the Seine at Paris, according to Pog-
GIALE*) by whom during a year an average of 115 mgrms. was
found, and according to Sv. Charge Devinie, who found 163.5 ngrms.
per litre in the water of the Seine below Paris. These results
indicate again the increase of the quantity of carbonates of lime in
consequence of pollution of the water by organic matter °).

Some rivers, which flow for the greater part of their course over
erystalline silicate rocks, and of which only few are of-large size,
are on the contrary poor in calcium carbonate.

From the water of the Rio de la Plata, a river which, as to the
size of its drainage area, is only little inferior to the Mississippi,
and which discharges more water, there exists according to MELLARD
ReaDE*) “a very exhaustive series of observations and analyses,” |
made by Juan J. J. Kyus, during 1872 and 1873 and the results |
of which he has published in a pamphlet of 11 pages in 1873 at |
juenos Ayres, which to my great regret I have neither been able
to procure, nor to read. As average quantity of solid matter in

solution of fourteen analyses of water taken at different times, from .
April to June, in the neigbourhood and above the city of Buenos Ayres,

MeELLARD ReaveE gives !/g.43, and from two analyses in September
Y/si95- If we take the sixteen analyses to be of equal value we geta |

mean of 1/g93 or 166 mgrms. per litre of water, figures which agree
very well with those observed in most of the other large rivers.
Starting from the last stated mean we may compute from the results
of analyses of Rio de la Plata water, published by Kyzz elsewhere ®*), |
that it keeps in solution only 23 mgrms. carbonate of lime per litre.

The Amazone, according to the analysis of one sample by P. S.

1) J. c. p. 273 and 274.
2) Jahresber. der Chemie, 1855. p. 521.

*) H. M. Wirt, On the variation in the chemical composition of the Thames water.
Philos. Magaz. (4). Vol. 12. London 1856 p. 114—122, published a number of analyses
of the water of the Thames at Kingston and at Chelsea, according to which e.g. with
a relative quantity of 137.3 mgrms. calcium carbonate, 23.3 merms, of organie matter
were determined.

‘1 ic. p. 292,

®) Chemieal News, Vol, 38 (1878), p. 28,

(89
FRANKLAND!), keeps as little carbonate of lime in solution, 27.5 mgrms.
per litre.

The Dwina above Archangel has, according to one analysis by
©. Scumipt, only 20.2 mgrms carbonate of lime ina litre of water °).

As to smaller rivers, for instance the water of the Hudson, cal-
culated from an analysis by C. F. CHANDLER *) keep 42 mgrms. calcium
carbonate per litre in solutions, and that of the Delaware, according
to an analysis by H. Wurtz of a sample taken from the reservoir at
Trenton *), 25 mgrms. calcium carbonate per litre. Such rivers poor
in dissolved calcium carbonate are mostly of minor importance as
to their discharge of water.

In regard to the rivers, in whose drainage areas limestone rocks
abound, it appears from the above stated facts and considerations,
that in the water which they discharge into the ocean, dissolved
carbonate of Jime is found in a ratio which on the whole is some-
what higher than that which would exist, if it were under the influ-
ence of the carbonic acid of the atmosphere only and it contained a
surplus of solid carbonate of lime. In fact limestone being spread
all over the earth, we may take for granted that the greater part
of the river water flowing into the ocean has had an opportunity
to get saturated with carbonates of lime. Those rivers in general
contain during low water mark rather more carbonate of lime,
whereas during high water mark the quantity of this matter may fall
somewhat below the saturation-point of pure water. On the other hand
some large and many small rivers, draining areas which are poor
in or deficient of limestone, keep considerably less carbonates of lime
in solution.

It appears, therefore, that we cannot be far from the truth if we
assume that the water which the rivers carry to the ocean keeps on
an average as much carbonates of lime in solution as pure water
ean contain, thus taking that the influence of the carbonic acid de-
veloped by the decomposing organic matter is counteracted by that
of the temporary diluting during high water mark, and that of the
river waters flowing directly into the ocean, which are poorer in
carbonate of lime. The surplus which the organic matter gradually
develops in the river-water can never cause the pressure of carbonic

1) Quoted by MeExtarp Reape, |. c, p. 295.

*) Bull. Acad. imp. St. Pétersbourg. Tome 20 (1875), p. 152.

4) Report of the American Public Health Association. Vol. I, p. 542=543 (quoted
by I. C. Russevt, l.c. p. 176, Table A).

*) Also quoted by Russe, ibid,

( 58 )

acid to rise high, as is already evident from the fact that in summer
the quantity of calcium carbonates dissolved is by no means always
greatest, the greater absorbing power at lower temperature is pre-
valent as a rule. The highest surplus is found in such profusely
polluted waters as those of the Thames.

The total quantity of the water, which the rivers discharge yearly
into the ocean has repeatedly been estimated, by K. Ritcius ') at
28000 K.M, by A. Woerrkorr’) at 18800 K.M.%), by Sir Jonn
Mcrray*), from the most reliable data, at 27000 K.M%. and
DE LAPPARENT and Penck agree with Murray.

According to Murray’s figures, if at the same time we take that
the water which the rivers discharge into the ocean contains on an
average 74 mgrms. of carbonate of lime per litre, we may calculate
that two billion (i. e. 2 x 10!) KG. of carbonate of lime, which
as solid rock would have a volume of about three fourths K.M%,
forming a cube with more than 900 M. side, are yearly carried
to the ocean in dissolved state.

Considering now that the ocean water is saturated with carbonate
of lime, that the quantity of ocean water does not undergo percept-
ible changes, and that moreover it is wholly inadmissable that this
yearly surplus should serve only or for a large part to increase the
calcium sulphate of the ocean, the latter salt being found in it only
in about the tenfold quantity of the carbonate of lime, and therefore
only in 800.000 times as great a quantity as that of the aforesaid
yearly surplus itself; these two billion KG. of carbonate of lime must
pass every year from the liquid into the solid state. That this hap-
pens entirely, or at least principally, by the agency of organisms
and as we now know for the greater part indirectly through calcium
sulphate, is of no account here. That on the other hand this carbon-
ate of lime, which in the ocean became svlid again, will once be
elevated by the endogene forces of our planet and changed into
land, brought again into solution to take the same way, is to be
concluded as well from the fact that we find already mighty strata
of limestone in the archean formations and in all later formations,
as from the fact that all rivers and lakes in whose drainage areas
no limestone reeks are found, contain only little carbonate of lime

") La Terre. Vol. I. 4me Edition, p. 514—517,
*) Die Klimate der Erde, Jena 1887. p. 50.
a) RAC upand

*) A. De Larparent, Traité de Géologie, 4me Edition, Paris 1900, p. 232. ~ A, Pexek,
Morphologie der Erde. Theil I, p. 273,

(59)

in solution. The instances already quoted by Biscnor of the Dee at Aber-
deen, whose sources are situated in crystalline silicate rocks (granite)
and which contained only 12.2 mgrms. calcium carbonate per litre of
water and of the glacier-rivulet Méll at Heiligenblut and Oetz at
Vent, which, flowing over crystalline shists, proved to contain only 8.4
and 4.5 mgrms. per litre resp. of that salt in solution, whereas on the
contrary the Lutschine at Grindelwald, having limestone for its
bed, contained even close at the glacier as much as 40.5 mgrms. ')
may here be mentioned as a proof that by far the greater part of
the calcium carbonate, which the rivers carry to the ocean originates
from limestone mountains, which have been formed from calcium
carbonate made already solid in the ocean in former times.

The Croton River (supplying water to the City of New-York),
draining a region of archean rocks, has only 87.2 mgrms. of dissolved
matter and 28.5 mgrms. calcium carbonate in a litre of water !).

The Ottawa, receiving the greater part of its waters, flowing through
many small lakes, from a region of crystalline rocks, and also draining
great areas of forest and marsh, contains in solution 24.8 mgrms. calcium
carbonate and 16.4 mgrms. of organic matter per litre of water *).

The water from the Upper Bann in Ireland, before reaching Lough
Neagh has been flowing over 50 KM. of granite, and contains only
17.7 mgrms. CaCOs per litre °).

The water of the Elbe, on reaching Tetschen, near the northern
frontier of Bohemia, has been in contact chiefly with crystalline
silicate rocks and sandstones, and only in the silurian basin of
Prague and in the Cretaceous rocks of the northern part of Bohemia
also with some limestones. It contains, according to the deter-
minations, made by ULuiK in 22 periods during a year, only
67.5 mgrms. matter in solutien per litre (besides the organic substances),
of which 50 mgrms. are calcium carbonate. That is not more than
about a half of what a river so profusely polluted with organic
matter as the Elbe at Tetschen would be able to take, if its waters

1) Ii. ce, p: 275.

2) J. D. Dana, Manual of Geology. Fourth Edition. New-York 1896, p. 121, quoted
from E. Water, water supply of New-York City, 1881 and C. VF. CHanpier
in Johnson’s Cyclopedia. Vol. 1V. The water was taken from the reservoir supplying
New-York City, itself supplied from the upper part of the drainage area of this small
river.

8) T. S. Hur in Geology of Canada. Geological Survey of Canada. Report of Progress
from its commencement to 1863. Montreal 1863, p. 566. “The water was taken on
the 9th of March at the head of St. Anne’s Lock, and was remarkably free from any
sediment or mechanical impurity.”

‘) HopcEs, Chemical News, Vol. 30 (1874), p. 102.

( 60 )
eame so largely in contact with limestone as is the case with most
of the large rivers. And so in the suspended matter there are hardly
any traces of solid carbonate of lime, indeed less than 1 mgrms
per litre of water ').

The contact with limestone rocks of the waters of the Moldau, a
large tributary to the Elbe, having been still less above Prague,
they contain even less than half the calcium carbonate of the Elbe
at Tetschen 2).

According to an analysis of water from the Uruguay River at
Salto by Kyue (l.c.) it kept in solution per litre 10 mgrms., according
to another analysis by R. ScuorLLer®) of the water from the same
river below Fray Bentos 16.2 mgrms. calcium carbonate. The
drainage area is almost entirely taken by sandstone rocks, which
are very poor in lime.

In six little lakes of the granite region of the Plateau Central
of France DELEBECQUE found only 18 to 77 mgrms. solid matter in
solution in a litre, on an average 37 mgrms.*), whereas 14 lakes, equally
small, in the département du Jura, where limestone rocks abound, held
108.6 to 195.6, on an average 147 mgrms. solid matter in solution 5).

The lakes of Gérardmer, in the département des Vosges, and Issarlés,
in the département Ardéche, whose drainage areas are situated in
granite, hold per litre of water 5.9 and 10 merms. carbonate of lime
in solution; those of Chauvet, Godivelle-d’en-Haut and Pavin (in
Puy-de Dome), situated in basalt, 6.8, 5 and 15.7 mgrms., whereas
for the total of the solid matter in solution these lakes were found
to keep 21.1, 27, 21, 18.3 and 79 mgrms. per litre of water °).

The Rachel-See, a little mountain lake, situated in the Bavarian
Forest in cordierite-gneiss, and having an outlet, contains, according
to the analysis of H. L. Jonnson’) only 2.22 mgrms. calcium carbonate
per litre of water.

') Caleulated from the total of the solid matter in solution and in suspension yearly
carried (1. ¢, p. 53) and the yearly discharge of water (l. e., p. 51). On its further
course the Elbe has so much opportunity to dissolve different substances, especially
carbonate of lime, that its water above Hamburg contains per litre 237 mgrmns. of total
solids in solution (PENck, Morphologie der Erdoberfliche, Stuttgart 1894. I Theil, p. 309.)

*) According to 7 analyses by A. BELonousek (Untersuchungen des Moldauwassers)
in Sitzungsberichte der K. Bohmischern Gesellschaft der Wissenschaften in Prag.
1876, p. 37.

*) Berichte des Deutschen chemischen Gesellschaft. 1887, p. 1786.

*) Archives etc. Gentve 1892, (3) T. 28 p. 504.

°) Ibid. p. 503.

*) Calculated from the results of analyses, published by Detesrcqur, Les laes fran-
gais, p. 202—203. See also, Carte Géologique de France aw 1/g 999, feuilles Epinal, Le
Puy et Brioude,

7) Livpie’s Annalen der Chemie, Bd, 95 (1855), p. 230,

(61)

The large lake Onega!), which is almost entirely surrounded by
Finland granites and diorites, contains only 10.8 mgrms. calcium
carbonate per litre of water.

The water of Lake Superior, whose drainage basin is composed
of ancient sandstones, conglomerates and crystalline rocks, with very
little limestone *), keeps only 30.8 mgrms. calcium carbonate, 45.7
mgrms. of total solids in solution per litre *).

Reindeer Lake, lying in the great archean area of Central Canada,
north of Lake Winipeg, has only 29 mgrms. dissolved solid matter, of
which only a slight trace of lime, in a litre of water *).

Lake Tahoe, amid the granitic and shistose peaks of the Sierra
Nevada and ‘overflowing in the Truckee River, has 72.3 mgrms. of
dissolved solid matter, of which 23.2 mgrms. are carbonate of lime,
in a litre of water >).

Other lakes, which receive their water entirely or for the greater
part, from areas of glacial deposits, which consists, mostly of the
débris of crystalline silicate rocks, diluvial regions, are equally poor in
calcium carbonate. So the lake of Starnberg or Wiirmsee in Bavaria °),
which holds in solution only 4.8 mgrms. calcium carbonate per litre of
water, and Loch Katrine in Scotland, which according to the analyses
of WALLACE’), contains in a litre of water only 2.7 mgrms. CaO, for
the greater part still bound to SO;, and of which the drainage area,
according to the description of Sir Jonn Murray and F. P. Put-
LAR ‘) consists almost entirely of drift (clay, sand and gravel), by the
side of shistose grit with some mica-shists and very little diorite,
rocks, which do not contain carbonate of lime. The latter is also
wanting in the mud on the bottom of that little lake®). Lake Wener
has only 36.2 mgrms. and lake Wetter 51.7 mgrms. matter in solution
per litre of water!) In the drainage area of both these Swedish

') C. Scumipr, in Bulletin de Académie imp. des sciences. St. Pétersbourg. T, 28
(1888), p. 248.

*) R. D. Twine, The copper-bearing rocks of Lake Superior. Monographs of the
Vj. S. Geological Survey. Vol. V. Washington 1883, p. 340.

*) Analysis in Geological on Natural History Survey of Minesota. Eleventh annual
Report, p. 175, quoted by Warren Upham, The Glacial Lake Agassiz. Washington
1895. Monographs of the U. S. Geol. Survey. Vol. 25, p. 444.

‘) From analysis by F. W. Cuarke, quoted by I. C. Russet, History of Lake
Lahontan, p. 42.

*) Geology and Natural History Survey of Canada. Report of Progress for 1880 —
1882, p. 6. H.

®) Menpivs, in Jahresber, der Chemie fiir 1856 p. 765.

7) Report of the meeting of the British Association for the Advancement of Science,
held at Manchester 1861. London 1862, p. 94.

8) Geographical Magazine. Vol. 25. 1900. Plate II.

nt Te SPEE

*”) A, ALMEN in; Berichte d. Deutschen chemischen Gesellsch, Berlin 1871, p. 751.

( 62 )

lakes by the side of crystalline rocks only diluvial soil oceurs.

All the last named lakes are, in respect to their having an outlet
and concerning their nearly constant composition, which is dependent
on the chemical character of their drainage area, to be compared with
the lake of Geneva and the other beforenamed lakes which are
all rich in lime. Likewise the very large lake Baikal, through
which flow the Upper Angara and the Selenga and which moreover
receives some two hundred small rivers, and rivulets, and over-
flows in the tumultuous Lower Angara. As far as that region
has been geologically explored, there are found in the draining area of
lake Baikal, besides of some pleistocence formations, principally archean
rocks, also, however, to relatively small extent, palaeozoit limestone.
Calculated according to the’ analyses of Scumipr !) its water (taken
in April 1877 from under the ice) keeps per litre not more than
40.1 mgrms. carbonate of lime in solution. Lake Tschaldyr in
Armenia, another, much smaller lake, of about 150 KM? surface
and likewise having an outlet, containing only lixiviation water
from trachytes, kept in solution (28 July 1879) per litre 42.5 mgrms.
calcium carbonate. This relatively high figure for a basin situated
in silicate rocks may be explained by the continual movement of
the shallow water of the lake by violent gusts of wind, which keep
it troubled and of a milky colour*). In consequence of this the
suspended detritus of the rocks can more easily be decomposed by
water and carbonic acid.

According to the estimate of TrLLo *), the crystalline silicate rocks
occupy about '/, of the land surface of the earth, surely a much
larger surface than that which is occupied by the limestone rocks.
As nevertheless the river-waters take their carbonate of lime by far
the greater part from the limestone mountains, it follows that the
making of calcium carbonate from calcium silicate is a much slower
process than the solving of previously formed limestone, and. that
therefore the above calculated quantity of two billion KG. of calcium
carbonate performs for much the greater part a real circulation, of
which only very little is newly added carbonate, though all the
calcium carbonate of the earth must gradually have originated from
the decomposition of silicates.

1) C. Scumrpr in Bulletin de VAcadémie imp, de St. Pétersbourg, Tome 24 (1878),
p- 420.

) ©. Scumrpr in Mémoires de Académie imp. de St. Pétersbourg (7). Tome 29.
(1881), p. 46 and 48.

8) Comptes Rendus, Académie des Sciences, Paris 1892, p. 5.

( 63 )

Chemistry. — “The solubility of calcium carbonate in sea-water”
By Dr. Ernst Conren and Mr. H. Raken (Communicated
by Prof. H. W. Banus Roozrsoon).

Whilst engaged in forming a theory on the age of the earth, it
was of importance to Professor Kuaine Dusois to possess further
data as regards the solubility of calcium carbonate in sea-water
under the usual conditions of temperature and pressure.

It is at his request that we undertook a research in order to
obtain those data.

The modus operandi was, that sea-water in contact with the
atmosphere (having the normal amount of carbon dioxide) was
saturated with calcium carbonate and that after this point was
reached, the amount of CaCO, dissolved in an aliquot part of the
liquid was estimated by analytical means.

Arrangement of the Experiments.

We prepared some litres of sea-water accepting as its po aaants
that found by Dirrmar }).
He finds the total percentage of salts to be 3.5 consisting of:

NaCl = 77.758
MgCl, 10.878
MgSO, 4.737
CaSO, 3.600
K,SO4 2.465
MeBr, 0.217

100.000

The calcium carbonate was precipitated CaCO, previously tested
for the absence of other carbonates. As the solubility is dependent
on the temperature this had to be carefully regulated. The experi-
ments were made at 15°, which temperature was kept constant
within 0.03—0.05° for some montis. For this purpose we employed
a thermostat with a toluene regulator also a spiral of composition
tube through which streamed the water from the mains. This tube
was placed in the water of the thermostat. The cooling thus caused

1) Report on the scientific results of the voyage of H. M. S. Challenger 1873~’76
1884, pag. 204.
2) The CaCO, was only added afterwards when determining the solubility,

( 64 )

was automatically compensated for by means of a gas flame con-
nected with the regulator.

In the thermostat in which a few puddle- boards were kept in
motion by a Henricr hot-air motor, were placed two bottles con-
taining the sea-water with a large excess of CaCO;. The bottles
were closed by trebly-perforated corks. Through the first hole
passed a glass tube down to the bottom of the flasks, through the
second one a glass tube ending immediately below the cork. Through
the third hole passed a thermometer. A current of air was passed
through the tubes reaching to the bottom of the flasks; this current
was always strong enough to thoroughly stir up the aden car-
bonate. The air entered the room through a glass tube which was
pushed through an opening of the window ee passed through a
meter in which its volume was measured and was then conducted
through a spiral of composition tube 10 meter in length which was
placed in the thermostat. In this manner it was heated to 15°
before entering the sea-water.

The tubes which ended underneath the corks of the flasks were
connected with a water-suction airpump which drew the current of
air through the water.

A slight evaporation of the sea-water takes place which is but
irifling as the air takes up water from the meter, but we have still
taken notice of this and carefully marked the level of the liquids
so as to be able to keep this regularly constant.

The time of saturation was varied in order to be sure that equi-
librium had indeed set in. Therefore, an analysis was made after
passing the air for 8 days and nights and another after the lapse
of 17 days and nights; these gave the same results so that it may
be taken for granted that 8 days and nights are already sufficient
to reach a state of equilibrium.

From time to time the CO, of the air which had passed through
was estimated. To do this, we interposed in the arrangement a large
flask holding about 5 litres through which the air passed before
reaching the meter. After 1—1'/, hour the CO, was estimated by
shaking with standard barium hydroxide and titrating the excess
with succinic acid. In calculating, due regard was paid to the tem-
perature and pressure.

When the experiment was finished, the current of air was stopped
and the CaCO; was allowed to deposit. Then the liquid was filtered
at 15°,

( 657)
Analyse.

Under the circumstances described, there existed in the water ')
after the experiment :

1. Carbon dioxide in the free state.

2. Neutral calcium carbonate.

3. Acid calcium carbonate.

Through the clear solution was now conducted a current of air
which was completely freed from CO, by passing it through a 2 meter
long tube filled with soda-lime and some washbottles containing
aqueous caustic potash. On passing a neutral gas such as air, both
the free carbonic acid and that of the acid calcium carbonate are
expelled whilst neutral calcium carbonate is precipitated.

Specially conducted experiments, one of which lasted 4'/, and the
other 100 hours, proved that after 41/2 hours the decomposition of
the acid calcium carbonate and the expulsion of the carbon dioxide
is complete.

The solution thus treated was now examined as to its amount of
combined carbon dioxide (CaCO;) by decomposing this with hydro-
chlorie acid and weighing the expelled CO, in soda-lime tubes, according
to the method of Konps-FResENrIUS 7) which was carefully followed
in every particular. i

Results.

300 ce. of sea-water were used for each analysis.

a. Solution of Ca CO; through which was first passed a current
of atmospheric air for 8 days and nights and then a current of air
free from CO, and saturated with water vapour, for 4'/. hours.

According to the indication of the meter, 41100 litres of air had
passed through the solution in 8 days and nights which is about
108 litres per hour.

Three estimations of carbon dioxide made during this time on
different days gave as result 0,0371, 0,0323 and 0,0290 per cent
of CO, by volume.

_ Found 16,2 milligrs of CO, in 300 ce. of solution saturated at
15°, or 53.94 milligrs per litre.

b. Solution of Ca CO; through which was first passed a current
of atmospheric air for 17 days and nights and then a current of air
free from CO, and saturated with watervapour for 100 hours.

Found 17.2 milligrs in 300 ce. or 57.27 milligrs per litre. We,
therefore, find that. sea-water saturated at 15° with calcium carbonate

') Compare GueLin-Kravr, Handbuch Anorg. Chemie, Part 1, 358.

*) Fresenius, Anleitung zur quant. Chem. Analyse, Bd. I (1875) § 449.
5

Proceedings Royal Acad. Amsterdam, Vol. II,

( 66 )

contains an amount of 55.6 milligrs of neutral-combined COg per litre.
It now appears from the researches of JACOBSEN !), TORN¢E *) and
Dirrmar®) (CHALLENGER Expedition) that the amount of neutral
combined GO. in sea-water varies from 52.8—55 milligrs. per litre.
Our research, therefore, leads to the result that sea-water is satu-
rated with calcium carbonate.
Amsterdam, Chemical University Laboratory, March 1900.

Physics. — “On the phenomena of condensation in mixtures in the
neighbourhood of the critical state”. By Dr. Cu. M. A. HARTMAN
(Communication N°. 56 from the Physical Laboratory at
Leiden by Prof. H. KAMERLINGH ONNES).

In a communication of DunEm*) the hypothesis is laid down that
in a mixture of two entirely miscible substances the experimental
and the theoretical isothermals for one and the same temperature,
situated between the temperature of the plaitpoint and that of the eritical
point of contact, intersect twice in the area of the unstable conditions.

On p. 31 and in
thesis I of my disserta-
tion for the doctorate *)
I have drawn attention
to the fact that this hy-
pothesis is at variance
with VAN DER WAALS’
..» theory of mixtures ®).
= The following may
serve as a nearer ex-
planation.

The actual condition
may be seen from the
annexed figure, derived
from my dissertation in
which the lines of equal
pressure on the a-sur-
face in the neighbour-

') Liesie’s Ann. 167. 8. 1 (1878); Jahresbericht der Commission zur wissenschaft-
lichen Untersuchung der deutschen Meere in Kiel. 1872, 8. 43,

*) Den Norske Nordhays-Expedition 1876-78.

4) lee.

') Procés-Verbaux des séances de la Soc. des Se. phys. et nat. de Bordeaux, 1899.

5) Metingen omtrent de dwarsplooi op het -vlak van VAN ber WAALS bij mengsels
van Chloormethyl en Koolzuur. Leiden, Juni 1899.

5) vAN pur Waats, Arch, Néerl. XXIV, p. 1—56, 1889.

(68)

hood of the area of the retrograde condensation are drawn projected
upon the «V-plane.

That the course of the lines of pressure must be so, follows from
VAN DER WaAALs’ formula, concerning all points of the connodal
line in the w-surface:

oy d’y ow \2
fk eM (OU by GP 2 5 2? (ra)
fizz 2 ale taal ey ')

ave

as has been explained on p. 30 of the dissertation.

As the second member of this equation is always positive (at the
2

: ; dP :
plaitpoint P it becomes zero, at the same time as eae) the two factors
av
of the first member have always the same sign.
ie ; METS ean nate
In the critical point of contact 2, where —— is infinitely great,
ar '
the tangent-chord will touch the projection of the line of pressure.
g pro) I
Therefore in each point between P and F, where, as follows from

dP . i se ae

the figure, —— is negative, =) wili be greater than —_——.,, or
dz On p 2—z

in words: there the line of pressure will be steeper with regard to

the z-axis than the chord.

At the other end of the chord, where —
;

dP . -—

18 positive, the slope
of the line of pressure will be less steep,

For pressures between Pp and Pr the lines of pressure in the
unstable part lie therefore in projection between the chord and
the connodal line, so that the projections of the chord and the
pressure line for one and the same pressure between Pand R cannot
intersect.

For pressures lower then Pr the chord and the line of pressure
will intersect in projection only in one point S. The line in which
these points of intersection are situated extends over the whole breadth
of the plait and terminates in the critical point of contact R.

If now we follow a line x=, with decreasing volume, we shall

‘) van per Waats, l.c. p. 15; in this formula a difference has been made between
P the two-phase-pressure, and p the pressure in any point of the y-surface. 7, 2 and
F', x' then refer to the co-existing phases,

2) VAN DER Waals, l.c. p. 56.

( 68 )

be able to deduce the phenomena of condensation from the figure.

In the beginning of the condensation we shall for one and the
same pressure first meet the line of pressure at a, then the chord
at 6, beyond S on the contrary, we first meet the chord at ¢ and
then the line of pressure at d.

If now we map the connection between V and p on a Vp-dia-
gram, we shall refind the above-mentioned point of intersection for
all mixtures, which show condensation, as the intersection of the
experimental and theoretical isothermals, and this will be their
only intersection. In the same way at the beginning of the
condensation the first-mentioned isotherm will always be situated
below and afterwards beyond the point of intersection always above
the second.

2. Dunem has arrived at his hypothesis in the following way :

First he traces how the total volume 1 of a complex of two
phases varies with the two-phase-pressure P, if the temperature
remains constant.

Let x, VY and m be the composition, molecular volume and quantity
of the first phase (liquid), 2’, V' and 1—m those of the second
phase (vapour), and 2, the mean composition of the complex, then is

i) =n) 3 ©, Sve. (CEE

}

dm

+l gee

Now Dwunem considers what this relation becomes at the plait-
point. Then

cram rats G=G)m GQ).

Te Le"
Moreover he assumes, that here also —— = —— and so concludes
dP dP
hat (25). (SE) ana (2) ly great at the plaitpoi
Ab = , = € md are ‘ y oreat at t Alb ¥
tha es 1 >), ap sift equally great at the plaitpoint.

dx
He overlooks however that at the plaitpoint ae is infinitely great
j ,

so that these quantities are not equal.

( 69 )

In the plaitpoint therefore the experimental and theoretical iso-
thermals in the Vp-diagram have not the same tangent, as has been
wrongly drawn by Dunem. Hence his further conclusions may be
neglected.

3. Prof. VAN DER WAALS was so kind as to inform me that
the mutual relation of the theoretical and experimental isotherms,
and hence also the error of DuHEM’s theorem, can be directly de-
duced from the sections of the w-surface and of the loeus of the
tangents-chords by a plane x = const.

Fig, 2a. Fig. 20.

For this Prof. van DER WAALs remarks: 1%. that — see fig. 2¢
and 2°1) where w has been taken as ordinate and V as abscissa —
for a definite mixture the experimental y-line ASD must lie below
the theoretical line AS'D.

2nd. that at the beginning and end of the condensation, at A and D,
the experimental and theoretical y-lines have the same slope, and
touch at those points.

3°¢. that hence for a volume B in the beginning of the conden-
sation the theoretical w-line has a greater slope than the experi-
mental, or Per.< ptheor. An equality of pressure for one and the
same volume will again be attained where the tangents to the two
w-lines become parallel, at S and S’ in the figures. Again for a
volume C near the end of the condensation the experimental w-line
has a greater slope than the theoretical, or Pezp. > Ptheor.

1) Fig, 2a relates to the case where the critical temperature of the mixture, sup-
posed to remain of constant composition, lies below, and fig. 24 where it lies above
the temperature, for which the -surface is constructed; or: fig. 2a refers to yalues
of x on one side, fig. 24 on other side of the straight line parallel to the V-axis
and passing through X, the theoretical critical point on the p-surface, see Dissertation
Pl. I fig. 5. K does not necessarily coincide with the intersection of tangent-chord
and line of pressure.

( 70 )

The points S and S’ agree with the intersection of the two iso-
thermals in the Vp-diagram, fig. 3¢ and 34, and with the inter-

f
at Sg

“

=v

~ |
v

<—

Fig. 3a. Fig. 30.

section of the chord and the line of pressure in fig. 1. As no other
eases than fig. 2¢ and 2° are possible there is only one such point.

4. With respect to the course of the condensation in the case
of mixtures the following remarks may be added.

In the Vp-diagram the experimental isothermal can be either
convex or concave towards the V-axis. The first is the case for a
mixture which contains only a small proportion of the more volatile
component, as occurs in VERSCHAFFELT’s experiments ') — see
fig. 3¢ —. The second is the case for mixtures which consist prin-
cipally of the more volatile substance, as occurs in KUENEN’s expe-
riments*) — see fig. 3° —.

The experimental y-line will have its greatest curvature near D
in the first case, near A in the second (comp. fig. 27% with fig. 3¢
and fig. 2 with fig. 3°).

Physics. — ‘“Weasurements on the magnetic rotation of the plane
of polarisation in liquefied gases under atmospheric pressure’. I.
By Dr. L. H. Srertsema (Communication N°. 57 from the
Phys. Labor. of Leiden by Prof. H. KaMERLINGH ONNES).

1. The continuity of the optical properties of substances under dif-
ferent circumstances of pressure and temperature, especially during
changes in the state of aggregation is an important point of invest-
igation on which light can be thrown by measurements of the mag-
netic rotation of the plane of polarisation. If we calculate from the

») Versl. Kon. Akad, v. Wetensch. Amsterdam 24 Dec. 1898, p. 281; Proc. id.
I, p. 288 and 323; Comm. Phys. Lab. Leiden, N°. 45.

2) Proc. R. Soe. Edinb. 21, p. 483, April 1897. Zeitschr. f. phys. Chem. 24.
pag. 672, 1897.

-

n®(n°— 1)

CP)

observations the molecular rotatory constant @p,'), this quantity
will generally depend on pressure and temperature, and we can
consider the manner in which it changes during the transition from
the gaseous to the liquid state.

Measurements on this subject have been made by Brcqueret and
by Bicuat*) with Carbon disulphide and Sulphur dioxide as liquid and
vapour. From these observations, in which no determinations of
dispersion have been made, it follows that during the transition into
the gaseous state the magnetic rotation of Carbon disulphide decreases
much more rapidly than the density; and that Becqueren’s formula
ua = Const. holds during the change of the state of aggregation.

My measurements on the magnetic rotation in gases °) led me into
an investigation in this direction, which also was furthered by the
ample means offered by the Leiden laboratory for experiments with
liquid gases.

2. For the measurements of the magnetic rotation in liquefied gases
under atmospheric pressure some special difficulties have to be
surmounted. In the first place care must be taken that the cylinder
containmg the liquid, which must let through the pencil of light,
shall be free from bubbles of gas which may easily be generated
on the walls when they are not properly protected against the en-
trance of heat by conduction. Moreover this cylinder should be
closed by plane parallel plates of glass of very good quality, as for these
measurements it is difficult to place the nicols 7 the experimental-tube
and thus within the closing-plates as could occur in the measure-
ments on gases. These plates must also be protected against the
entrance of heat but especially against moisture, as the least for-
mation of ice on these plates hinders the measurements. This renders
it necessary to place more than one set of glass-plates between the
nicols, which latter circumstance again makes it necessary to use
greater rotations than was required for the investigation with gases,
as the glass-plates, good as they may be, render the adjustments
less accurate.

8. The difficulties mentioned have been taken into account in

1) Comp. Proc. Royal Acad. Amsterdam. Vol. I, p. 299.
BecqvereE., J. de Ph. (I) 8; p. 198. Bicnar. J. de Ph. (1) 8 p. 204; 9 p, 275.
(t) 8, p I

%) Proc. Royal Acad. Amsterdam. Vol. I, p. 296. Arch. Néerl. (2) 2 p.291. Comm.
Phys. Lab. Leiden, Suppl. 1.

( 72 )

constructing the apparatus shown in figs 1 to 3, which consists of
glass and ebonite only.

The experimental tube which is filled with the liquefied gas,
consists of a glass tube a, closed by the glass-plates b, fastened to
the tube by means of fishglue. By means of some brass collars ¢,
acting as springs, a loose glass tube d lies in the experimental tube
of the same length as the latter. The spaces within and round the
tube are connected by means of the two obliquely ground ends at EH.
Through this tube d the pencil is directed during the measurements.
The experimental tube is filled with the liquefied gas to a
little above this loose tube, which thereby is filled with the liquid
and entirely surrounded by it. Even supposing that a few bubbles
of vapour arise on the walls of the experimental tube, they cannot
get into the liquid contained in the loose tube and will not disturb
our field of view.

The experimental tube is moreover surrounded by two glass tubes
f and g. Through the openings 4 and 7 the cold vapour of the
liquid in the ex perimental tube can stream successively through the
two spaces formed by these glasses, and then escape through the
india-rubber tube &, fastened to an ebonite ring / round the last
named tube. The tube / conducts the vapour to a caoutchouc bag,
in which it is collected provisionally, to be afterwards condensed.
The liquid is admitted through an opening in the ebonite nuts m,
which also serve to connect the various glass tubes.

To fill the tube we use the steel capillary @ (fig. 3) which is put
through the opening in the nuts m (fig. 1) so as to reach into the
experimental tube, to which it is fastened by means of the cap 6
(fig. 2). When the tube is filled we remove this capillary and close
the opening by means of a small stopper.

The two glass tubes f and g are closed by the ebonite caps 2,
in which caoutchouc rings o serve as washers. The caps are
mutually connected by six brass tightening rods. The closing plates
6 of the experimental tube are kept in their places by means of the
ebonite rings p in the caps ». These closing plates are shut off from
the atmosphere by means of the glass-plates g, enclosed by the
nuts 7 together with a leather packing s. These latter glasses are
again protected against the formation of ice by spaces formed by
them and the plates t, which spaces can be filled with dry air by
means of the ebonite tubes u, or by placing some Phosphorous
pentoxide into them!). The spaces between the glass-plates 4 and q

1) Comp. the Cryostate, Proc. Roy. Acad. Amsterdam, Sept. 1899.

Ji) : ’

ma . sie
-
ee be ph) oil

a eh de lies) yy pel

VN OV Oe uv vi "4 lee j
PTO Cy bald» Wt
SPOT) he fe vn 4 ith
en
‘ Hae aii : j !

0 Hipitiiieg me Dio win) Lad uirtity ae ‘
y Bisa finn. bail! Mi ‘eyo at PL ke at Ue inet al Se ee

Hel Wyl p a)! nor oevel” gh zu bed
Se ee r .

ie

i } ivi Hii HO }
P ayy we wt " Fri uet 2 fp BOR) Maou i a nn
a A Sari ee ein E ma mw
= ae ‘ : “4 Ad
Fines Ale } et iol * AhAa halge 4) ibd Ai 1 Ay vl
igh ee te Li. may : ea ” iD hee ¥ 7 [a
7 Y itirte cat i ai oft; fit MSY WT 7
- ee te ii. fee yrcin a
‘ A u i? r 7
d sui “oe avi st Dated voy wo “1 mii a >
fi rr
Ly ei ne a rn! + = Le
A mae ih AU > , ri =
ed iis cia, wlth vey Dain ’
Nei,
ri ringer rringet — —
es Pi \ ; { a : 7
i aA
a e AS 4 =

OO Oe MiGente e
mT Dy * Saal" js oo, | :

eee. fij jak ir

wiles We rt ALdt Gags! Jie dennd ris NO dai ooi PALIT
ful roar) yinlit i tad ayen Ee DAM oot.

'

ig ale ony piel Sant. pe Meph'e OO a ty i ul

ae ny Pe Avs aapaliemurty Ba? te wn | é [Aan

ae sy Bist vu coll D jie Sarto sinitisott Ao eiie adregoy % Atv
, ui? Wis Fe id on de Oia) felin WIGEs: Fulah H ful? |
ot r oom a i SY ie jny THR nisl ye esta, od? Die une

bei Ra pioaley: rr Ne ee keiela, ». wid) if efueyii 2

fit
yey Pp

i aig Honea wiate BAT: (CL i ig) dhitkotiney

ae f _
Eteltoih tg y PY as inn? sible ilies) aoe) 4
-

ie
‘

oat

C1)

In this table w/@p stands for the proportion of the rotation to that
for sodium light.

A (w/wp) CH, Cl (a/wp) gases

0.631 0.90 0.87
0.546 1.17 1.17
0.480 1 58 1.53
0.449 1.76 1.76
0.435 1.90 1.90
Chemistry. — “A new method for the exact determination of the

Boiling-point”?. By Dr. A. Sirs (Communicated by Prof.
H. W. Bakuurs Roozesoom).

(Will be published in the Proceedings of the next meeting).
Chemistry. — “ Thermodynamics of Standard Cells” (2"¢ part). By

Dr. Ernst Coen (Communicated by Prof. H. W. Baknurs
ROOZEBOOM).

(Will be published in the Proceedings of the next meeting).
Chemistry. — “On the Enantiotropy of Tin” (VN). By Dr. Ernst
Conen (Communicated by Prof. H. W. Baknurs RoozeBoom).

(Will be published in the Proceedings of the next meeting.)
Chemistry. — ‘The formation of mixture-crystals of Thalliwm-

nitrate and Thalliumiodide”, By Dr. C. vAN Eyk (Commu-
nicated by Prof. H. W. Bakuurts Roozesoom).

(Will be published in the Proceedings of the next meeting.)

(June 30, 1900.)

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday June 30, 1900.

———26G

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Juni 1900 DI. IX).

Contents: “On the resisting power of the red bloodcorpuscles”. By Dr. H. J. Hampurcer,
p- 76. — “The behaviour of mixtures of mercuric-iodide and silver-iodide”. By
Prof. H. W. Bakunurs Roozeroom, p. 84. — “A new method for the exact deter-
mination of the Boiling-point”. By Dr. A. Smirs (Communicated by Prof. H. W.
Bakuuis Roozesoom), p. 86. — “Thermodynamics of Standard-Cells” (2nd part). By
Dr. Erxst Conen (Communicated by Prof. H. W. Baxiurs RoozeBoom), p. 91. —
“On the Enantiotropy of Tin”. V. By Dr. Ernst Conen (Communicated by Prof.
H. W. Bakuuis Roozesoom), p. 93. — “The formation of mixed-crystals of
Thalliumnitrate and Thalliumiodide”. By Dr. C. vax Eyx (Coinmunicated by Prof.
H. W. Baxuuis RoozEesoom), p. 98. “Further researches on the formation of Indigo
from the Woad (Isatis tinctoria)”. By Prof. M. W. Brtserincx, p. 101. — “The
amount of the circulation of the carbonate of lime and the age of the Earth”. IT.
By Prof. Ece. Dusors (Communicated by Prof. J. M. van BemMeten), p. 116. —
“Further results of an investigation of the Monotreme-skull”. By Dr. J. F. van
Bemmeten (Communicated by Prof. C. K. Horrmany), p. 130 (With one plate). —
“On soap solutions’. By Dr. A. Smirs (Communicated by Prof. H. W. Baxutis
RoozEBoom), p. 1338. — “Leperditia baltica His. sp., their identity with Leperditia
Eichwaldi Fr. v. Schm. and their being found in Groningen diluyial erratics”. By
J. H. Bonnema (Communicated by Prof. J. W. Mott), p. 137. — “Contributions
to the knowledge of some undescribed or imperfectly known fungi”. (Ist. Part). By Prof.
C. A. J. A. OupEmans, p. 140 (With 3 plates). — “The motion of the Pole of the
Earth according to the observations of the last years”. By Dr. E. F. van pe SanpE
Bakuvyzen, p. 157. — “The properties of the pressure-curves for co-existing phases
of mixtures”. By Prof. J. D. van peR Waats”, p. 163. — “The Haut-effect and
the increase of resistance of bismuth in the magnetic-field at very low temperatures”. IT.
By Dr. E. van Everpincen Jr. (Communicated by Prof. H. Kamerztincu Onnes),
p- 177. — “On the system: Bi, O;—N.Os—IO0”. By Prof. J. M. van BemMeren,
p- 196. — Prof. A. P. N. Francuimonr presents the dissertation of Dr. L. van
ScHerPenzeEL: “The action of hydrogen nitrate (real nitric acid) on the three toluic
acids and some of their derivatives”, p. 203. — “Thermodynamics of Standard
Cells’ (8rd Part). By Dr. Ernst Conen (Communicated by H. W. Bakuvis
Roozenoom), p. 208. — ,,The metastability of the Weston-cadmiumeell and _ its
insuitability as standard of electromotive force’. By Dr. Exxsr Courn (Commu-
nicated by Prof. H. W. Bakuvis RoozeBoom), p, 217.

The following papers were read:

Proceedings Royal Acad, Amsterdam, Vol. III.

( 76 )

Physiology. — ‘On the resisting power of the red blood cor-
puscles”. By Dr. H. J. HamBurcer.

(Read March 31, 1900).

Since Duncan!) had in 1867 called attention to the fact that in
chlorosis the red bloodcorpuscles lose colouring matter in a solution
of salt, in which this does not take place under normal circum-
stances, MALAsSEZ 2) as a consequence of his study on the counting
of the red bloodcorpuscles determined the so-called resistance of these
cells, by mixing blood with a strongly diluted salt-solution and by
examining at regular intervals how many bloodcorpuscles were left.
The sooner the bloodcorpuscles were destroyed, the less the resistance.

Later on determinations of resistance were given by CHANEL °) equally
by counting, although in a different way. Both methods are rarely
cited even in French literature and still less put into practice. This
is also the case with reference to the method of Lanpors, LAkEN
and also of others, who determined the power of resistance in regard
to electric discharges, desiccation and other influences.

A more favourable reception was accorded to a method of in-
vestigation, originally only intended for the study of the laws of
isotony in the bloodcorpuscles *) but which was first applied in
1890 by von Limpeck *) to investigate the resistance of the blood-
corpuscles during disease. It consists in the determination of the
particular NaCl-solution, in which the first bloodcorpuscles are about
to lose colouring matter. If this happens for instance in a NaCl-
solution of 50 pCt., then 0.50 pCt. is called “the resisting power
of the least resistant bloodcorpuseles”’.

If the dilution of the salt-solution is continued, a certain number
of the more resistant bloodcorpuscles also lose their coloured con-
tents, and finally all the bloodcells, even the most resistant, have
lost these. In a salt-solution, somewhat stronger than the last one
mentioned, the most resistant can thus still exist. It is this salt-
solution which then represents the “maximum resistance” (Mosso °),

1) Duncan, Sitzungsber. d. Wiener Akad. d. Wissensch. 11 April 1867.

2) Manassez, Mém. de la Soc. de Biol. 1873, p. 134; Compt. rend. de la Soc. de
Biol. 1895, p. 2.

3) CuaneL, Sur la résistance des globules rouges. Thése. Lyon 1886.

4) Hampurcer, Kon. Akad. v, Wetensch. Proces-Verbaal der Zitting van 29 Dec.
1883. Archiv. f. (Anat. u) Physiol. 1886.

5) von Limpeck, Prager med. Wochensch. 1890, No. 28 u. 29.

®) A. Mosso, Archives Italiennes de Biol. 1887. T. VIII, p. 257.

( 77)

Vioua !)). With the methods here mentioned (HamBuRGER-Mosso-
Vioua) a relatively large number of resistance-determinations have
been made, but whether they have increased our knowledge of the
physiological and pathological conditions, to the study of which
they were applied, is very doubtful.

To a certain extent an exception might be made for cyanosis
and feverish conditions. The observation that in cyanosis “decrease
of resistance” is observed can at least be referred to the fact, that
the same is seen in bloodcorpuscles treated with CO, *), and for
this last symptom we have a good explanation °).

That the resistance must diminish in feverish conditions is evident
when it is taken into consideration that in fever the proportion of
alkali in the serum is lowered, which decrease also involves that
the bloodeorpuscles belonging to it already begin to lose colouring
matter in a higher concentration of salt than those which have
sojourned in normal serum *).

The reason why the resistance-determinations referred to, have
thus far had little success may be sought in the circumstance that
it was not duly taken into account what was indeed obtained by
determination of the resistance, and what was the physiological
meaning to be attached to it. Even in 1895 one could read in the
conclusions of the dissertation of Urcenay: “Sur la résistance de
globules rouges”, Thése de Paris: “La cause de la résistance des
globules rouges nous est inconnue’”’, and this at a time, when most
of the resistance-determinations thus far known had been performed
and Urcetay had contributed some himself.

As regards myself, I never felt induced to use my method of
investigation otherwise than for more circumscribed aims, and on
purpose I have thus far avoided to use the 7 casw unfit word
“resistance’’ when colouring matter disappeared under the influence
of certain salt-solutions and other mixtures.

Being invited to read a paper on this subject in the International
Medical Congress to be held in Paris next August, I find a wel-
come opportunity to study the question at the present time, the

1) Viona, Gazette degli Ospedali 1894, p. 115; Archives de Physiol. et de Pathol,
générale 1895, p. 37.

2) Hampurcer, Versl. en Meded. Kon, Akad. v. Wet. 3e Reeks. Vol. IX. 1891,
p. 197. Zeitschr. f. Biol. B. 28. 1592, S. 105.

3) Hampurcer, Zittingsverslag Kon. Akad. v. Wet. 28 Nov., 1896 ; 24 Febr. 1897.
Zeitschr. f. Biol. 1897. S. 252.

4) Hampurcer, Versl. en Meded. Kon. Akad. v. Wet. 3e Reeks. Vol. IX, 1892,
p- 354; Archiv f. (Anat. u.) Physiol. 1892, p. 513.

6*

( 78 )

more so because this affords a means of controlling the investigations
lately made on the volume-determination of the protoplasmic retic-
ulum of the bloodcorpuscles.

I shall try to analyse the term “resistance” of the bloodcorpuscles
in regard to salt-solutions and must in the first place inquire which
are the factors on which depends the loss of colouring matter in
the bloodcorpuscles by means of salt-solutions. My particular view is,
that the bloodcorpuscle consists of a protoplasmatic reticulum, the
interstices or meshes of which, closed or unclosed, contain the intra-
globular liquid; it is this liquid which solely represents the power
of the cell to attract water; the protoplasmatic reticulum has no
share in this.

If one now imagines a bloodcell being immersed in a hypisotonic
solution, then only the contents of the meshes will swell. The
amount of this swelling will be more considerable in a certain
hypisotonic solution, the greater the amount of the osmotic pressure of
the intracellular liquid and aiso the greater the quantity of the intra-
cellular liquid in a given cell-volume.

The more considerable the increase in volume is, which the intra-
cellular liquid can be made to undergo without colouring-matter being
extruded from the protoplasmatic network, the more resistant the pro-
toplasm may be considered to be.

Taking these matters into consideration, we conclude that when
‘different salt-solutions are allowed to act upon the red bloodcorpuseles,
three or perhaps two forms of resistance come forward.

1. The resistance of the bloodcorpuscle against loss of colouring
matter, under the influence of diluted solutions.

It is this form of resistance, which has been determined until
now. It is of a complicated nature.

2. The relative resistance of the protoplasm against the extrusion
of colouring matter during expansion.

3. The absolute resistance of the protoplasm against extrusion of
colouring matier during expansion.

Ad I. Resistance of the bloodcorpuscle against loss of colouring
matter in diluted salt-solutions.

As it was observed above, it is this form of resistance which has
hitherto been determined by the so-called method of the bloodcorpuseles.
Yo salt-solutions of gradually diminishing concentration a few

(79 )

drops of the same blood are added and it will be observed that in
a Na-Cl-solution of 0.49 pCt. some colouring matter has been
extruded, which is not the case in a NaCl-solution of 0.50 pCt.
This is called the minimum resistance. It would be more correct
anyhow to express it by aN as the resistance is inversely pro-
portional to the limit of concentration referred to; therefore in general

Laie : set
Ri loodcorpuscles) = pee ea which C represents the limit of concentra-

tion, in which the first bloodcorpuscles are about to lose colouring
matter. With regard to the application of this method we take the
liberty to propose a modification. It seems to us to be recommend-
able, also in connexion with the determination of the other forms
of resistance to perform the determinations in small funnelshaped
tubes of which the capillary part is calibrated and closed with a
little ebony stop. They have the same shape as described formerly’),
but in view of their being used for human blood they are smaller.
With a capillary pipette a determined quantity of defibrinated or
oxalate blood is measured for the different tubes which contain an equal
volume of the different salt-solutions and the mixtures allowed to
stand for half an hour; they are then centrifugalized. After a quarter
of an hour’s moderate rotatory velocity the bloodeorpuscles have
already subsided and it can be seen by comparison where colouring
matter begins to extrude and where not. This way of experimenting
has a threefold advantage.

1. As the relative quantity of blood and salt-soluticn has been
fixed and also the shape and measures of the little funnel-tubes are
equal, we can compare the results of different investigators better
than could be done hitherto and uniformity is thus enhanced.

2. As the full subsidence need not be waited for, the time for
the determination of the resistance will be shortened.

3. Those tubes of which it is desirable, can further be used
for the determination of both the other forms of resistance; but
later on more of this.

To find the maximum-resistance the same method is followed as
for the minimum resistance: the salt-solution is determined, which,
mixed with the blood, gives a perfectly pure transparent liquid.

The solution, which yet retains a trace of opacity is the sought
for C’5.

—_—

1) Verslag Kon. Akad. vy. Wetensch. 21 April, 1897.

( 80 )

1
The maximum-resistance is then 2’, = C.:

1 1 1
The average resistance }(& + Ry) = ale + coy, J» Whereas we
i l
‘ ' 1 1 '
shall call the difference &', — Ry = Faure resistance - breadth.
l i
The determination of this value seems important to me.
It ought to be kept in mind, however, that quantities of a com-
plicated nature are here determined, which it can however be im-

portant to be acquainted with in certain circumstances.

Ad, 2. Relative resistance of the protoplasm [,,.

It is measured by the proportion of the volume V; which the
intraglobular liquid may attain in maximo before it is exuded by
the protoplasm, as compared to the volume (V,), which it possesses
in normal conditions.

=
This proportion = can be found by means of three methods.

n

Method a.

This method consists in attempting to determine the limit-
concentration of the NaCl-solution, in which the bloodcorpuscele
swells at its maximum (Cy), and is thus about to lose its colouring
matter, and also the concentration of the Na Cl-solution, in which
its volume remains unchanged, that is: a NaCl-solution Cy , isotonic
with the serum. As the attraction exercised by the intracellular
liquid towards water, agrees with that of its environment under

ig a , at least when the disso-
l

different circumstances, so
Un

ciation of the contents of the bloodcorpuscles and the surrounding
Na Cl-solution are left out of consideration !).

For the determination of C, the freezing-puint-method can be
used, or if only very little blood is available the method of Grigns-
EYKMAN ”).

Method b.

According to this method the quantity of water is determined
with which the respective blood-serum can be diluted, without the

') This is permissible here, as will be explained elsewhere. Here this explanation
would lead us too far. FE

*) C. Eykman, Annual report of the Laboratory for Patholog. Anat. and Bacteriol.
at Weltevreden for the year 1894.

( 319

blood losing any colouring matter. Let « be the percentage of the

v 100 +2
water added, then cy at
Un 100

The quantity of serum required can be considerably limited, by centrifu-
galizing each time blood has been added to the diluted serum and after
having waited for half an hour. When by this time the red colour has
not yet «wppeared a known quantity of water is dropped into this serum,
it is mixed with the serum, and the serum thus diluted is brought into
close contact with the underlying bloodcorpuseles. This is repeated until
colouring matter is seen to be extruded. At the utmost 8 ce. of blood
is needed for this method.

Method c.

According to a method formerly indicated by me, the volume of
the protoplasmatie reticulum of a given quantity of bloodcorpuscles
is first determined !). Let this be wz. If further the volume of the
bloodcorpuscles in their own serum be V;,, then the volume of the
intra-globular liquid in the normal condition is Va—a and in the
condition of maximum swelling Vi—z, and therefore the relative

ist R JalVirge
resistance Rp,= ee

With this method c the average relative resistance of the proto-
plasm is immediately fixed, the three values of Vj, Vn and a having
reference to all bloodcorpuscles together.

For the two other methods mentioned sub 2 the resistance must
be fixed separately, for the least resistant and for the most resistant.

If for method @ the NaCl-concentration, in which the most resistant
bloodcorpuscles are about to lose the colouring matter, be C';, then

. . G,
the maximum resistance is 2',, = ——, and the average
P G ’] fo}

yy

Cr C,,
4 (Rp, + R m= (ster)
If for method b, 2’ be the percentage of water that must be added
in order to extract colouring matter even from the most resistant
100 + 2’
bloodcorpuscles, then R'p,= paar

The average resistance will then be:

100+ 2 A y= 1 (ete ain

|
4 Bar + Bin) = 5 ( 100 100

1) Reports of the Roy Acad. of Sciences. Amsterdam May 28, 1898.

(82)
The relative resistance breadth of the protoplasm we indicate by
RES sey

This value seems important from a physiological and pathological
point of view.

Ad. 3. Absolute resistance of the protoplasm against the extrusion
of colouring matter during expansion Rya.

Superficially it might be supposed that the relation of the intra-
cellular contents of the bloodcorpuscles in the condition of maximal
swelling and in the normal condition, expresses the degree of resist-
ance in an absolute sense. This however is not the case. Imagine
two bloodcorpuscles of. equal size in their own serum, both have
intraglobular contents of equal osmotic pressure, but the volume of
the intraglobular liquid is greater in the first bloodeorpuscle than in
the second. If it is proved that, nevertheless, both bloodcorpuscles
lose colouring matter in the same saltsolution (C;), in which case
the osmotic pressure of the intraglobular contents must necessarily
be equal, then the conclusion is inevitable that the protoplasm of
the first bloodeorpuscle is more resistant than that of the second,
for the absolute increase of volume of the first bloodcorpuscle was
more considerable than of the second. With equal C, and C; it is
therefore not necessary that the resistance should be equal. In order
to be able to compare the absolute resistance of the protoplasm of

two bloodcorpuscles, the quotient - which was therefore called rela-

tive resistance, must be multiplied by a factor which expresses the

percentage of the volume of the intraglobular liquid, a factor which

we calculate from 2.

V,—1
V,

— 100.

As we do not kuow whether this factor may be used separately with
the minimum-resistance, or with the maximum-resistance because
we do not know whether the relative volume of the protoplasmatic
reticulum is the same in all bloodeorpuscles of the same blood, it
is undoubtedly safer to use the factor only where it is in all cases
applicable, viz. with the average resistance.

Thus in this third method the average absolute resistance of the
protoplasm against the transmission of colouring matter when expanded
: (of method 2a).

: , i—
is determined, so that Rpa =f ee
n

(83 )
SIMULTANEOUS DETERMINATION OF THE THREE FORMS OF RESISTANCE.

Suppose the three forms of resistance have to be determined during
an illness and little blood is thus at our disposal. 1 cc. of blood is
taken, defibrinated and strained or made to flow in 0.2 ee. sodium-
oxalate of 1.5 pCt. Of this blood equal quantities (measured with a
capillary pipette) are transferred to little funnel-tubes, which contain
NaCl-solution of 0.30, 0.32, 0.34, 0.36, 0.38, 0.40, 0.42, 0.44, 0.46
0.48, 0.50, 0.52, 0.54, 0.56 pCt. 4).

These liquids are mixed, allowed to stand for half an hour and
then centrifugalized. After this it is determined in which tube
colouring begins to show itself. The tube following upon this
containing a more concentrated liquid, represents C;. By determining
where the mixture has become transparent, the maximum-resistance
C", is found. Thus 2) = and «R= a (Method 1).

Now five tubes are prepared with equal quantities of blood.

Tube (1), undiluted defibrinated blood.

» (2) blood + NaCl 0.9 pCt. | to investigate in which Na Cl-so-

PAL) a vue Cale we. 1408S rosin lution the volume of the bloodcor-

td) tS ie et: S6 . puscles becomes like that in tube (1).

» (5) , + the NaCl-solution just found, viz. the limit
solution C; in which the bloodcorpuscles are on
the point of emitting colouring matter.

» (6) , + NaCl 1.5 pCt., also for the determination of the
protoplasmatic reticulum.

The whole mass is centrifugalized to a constant volume.

Ch ae
We can now calculate the relative resistance aA by dividing the
l

concentration of the NaCl-solution (2), (3) or (4) by that of the

NaCl-solution (5) (Method :2a), or also by calculating the proto-

plasmatic reticulum a from the NaCl-solution (2), (3) or (4) and

the NaCl-solution (6). Tube (1) gives V,, tube (5) gives V,, and
(ee

therefore relative resistance 2), is also = — (Method 2c).

All the values are now also known for the calculation of the ab-

1) If so many tubes are not to hand, the same could preliminarily be performed
by increasing with 0.4 pCt. NaCl and seeking whereabout the limits lie for
‘minimum~ and maximumresistance and then fix these more accurately later on.

( 84 )
solute resistance, of which only the average can be determined. It is
V,—% :
V, (Method 3).

If there is reason to believe, in comparing the resistance of two
samples of blood, that under normal circumstances the volume of the
protoplasmatic reticulum, or, what comes to the same, of the intra-
- cellular liquid, does not differ, then the determinations become sim-
pler and the results of 2a, 2b or 2c mnay prove to be sufficient.
If moreover the osmotie pressure of the serum is the same, then
the first method suflices.

100 Rp,

Chemistry. — ‘The behaviour of mixtures of mercuric iodide and
silver iodide’. By Prof. H. W. Baknuis Roozeboom.

(Read May 26, 1900.)

The double iodide HgI,2AgI is known as one of the finest
examples of a solid substance which undergoes a change at a defi-
nite temperature, because this substance changes, when heated to
45°, from the pure yellow to orange red.

There was, however, a difference of opinion as to the change
which takes place here; some attributed it to the change of the
compound itself into another modification; others thought that, at
45° it broke up into the two component iodides,

At my request Dr. STEGER has made a further investigation of
the matter and has come to the conclusion that the two iodides
mixed in varying proportions and at different temperatures are of
a very varying nature. If we start from fused mixtures, it appears
firstly that the melting point of HgI, is lowered from 257° to
242° by an admixture of 14 mol. pCt. of AgI. On the other hand
the melting point of AgI is lowered from 526° to 242° by an
admixture of 86 mol. pCt. of HgI,.

By means of an accurate determination of the temperature-interval
in which solidification of a certain mixture takes place, it may be
found out what happens during the solidification. To do this with
accuracy, a bath was used of melted NaNO,;+K NO; which was
stirred and which by judicious heating enabled us to maintain any
constant temperature between 200°—500°, or to slowly vary it.
The course of solidification of the different mixtures shows that two
kinds of mixed crystals are formed; on the HgI, side with 0—4
mol, pCt. of AgI, on the other side with 18—100 pCt. of Ag I.
The first series has the type of the rhombie HgI,, the other

( 85 )

that of the regular AgI which exist from their melting points
down to 127° and 147° respectively.

After the solidification, there is therefore a hiatus in the mixing-
series from 4 to 18 pCt. All intermediate mixtures consist, there-
fore, after solidifying of a conglomerate of the two limiting mixed
erystals. Those of 4 pCt. undergo a change near 127° because the
HgI, changes from the rhombic into the tetragonal form. The
mixed crystals of 18 pCt. or more of AgI behave in a more
remarkable way. Firstly, on cooling below 157° the mixed crystals
having the composition HgI,2AgI are suddenly changed into a
compound of the same composition which is accompanied by a change
in colour from pink to red.

This point of 157° is perfectly comparable with the solidifying
point of a chemical compound deposited from a liquid mixture. But
the analogy goes further. If a chemical combination can deposit
from a liquid solution of the same composition, it can also do so
from solutions whose compositions deviate in both directions, and
the deposition then takes place at temperatures which are situated
below the solidifying point of the liquid of the same composition.
This also happens here. From mixed crystals which contain less
AgI, the formation of the compound HgI,2AgI occurs at tem-
peratures which fall from 157°—118°; from those containing more
AglI at temperatures from 157°—135°.

A further fall is impossible because at 118° and 135° two points
appear, which present a perfect analogy with the eutectic points
which are encountered when mixtures of liquids, which deposit only
a single chemical compound, solidify. Just as in such points, the
remaining liquid totaily solidifies to a conglomerate of the com-
pound with one or the other of its components, the remaining mixed
erystals in this case form a conglomerate of the compound Hg I,2 Ag I
with either HgI, or AgI.

In the case of liquid solutions the situation of the eutectic point
is determined by the intersection of the line for the compound with
that of the one or the other component.

The last mentioned lines then run as far as the melting points
of the components.

Instead of these we have here the transition temperatures of Hg I,
(127°) and Agl (157°). The line for the transformation of mixed
crystals into compound, therefore, meets on both sides:

1. The line for the transformation of regular AgI into the
hexagonal form, which is lowered by admixture of HgI, from
147°—135°, the junction takes place here at 90 mol. pCt. of Ag I.

( 86 )

2. The line for the transformation of Hel, rhombic into the tetra-
gonal form, which is lowered by admixture of Ag I from 127°—118°.
This last line is, however, broken off because the mixing is not
continual from 4—10 pCt. The exact composition of the mixed
erystals at the eutectic point on this side is not yet known.

Below 118° and 135° all solidified mixtures are therefore trans-
formed either into conglomerates of double salt with HgI, or
with AgI. Whether a small admixture of the other iodide in both
iodides is possible is not yet quite certain.

When those conglomerates, on further cooling, arrive at 45°,
the compound changes into another condition (from red to yellow),
whether it is pure or mixed with Hel, or AgI.

In agreement with this view it was found that the temperature
at which this change took place was quite independent of the total
amount of both iodides.

The most important result of the research is not however the
correct interpretation of the last mentioned change which it affords,
but the transformations which the mixed erystals, which are formed
on solidifying, undergo between 157° and 118°.

We have here the second instance of mixed crystals changing
into a chemical compound, the first instance having been observed
by ADRIANI in the case of racemic campheroxim. We have, however,
here the first instance of that change being connected with the
change of both the components, which gives rise to a complete
analogy with generally known phenomena of liquid solutions.

The discovery is particularly importart because it concerns a
connection between phenomena which I fancy also arise during
the formation of mixed crystals from iron and carbon, but could
not thus far be ascertained with certainty on account of the very
high temperatures at which these changes occur.

Chemistry. —- “A new method for the exact determination of the
Beiling-point”. By Dr. A. Sirs (Communicated by Prof.
H. W. Bakuuis Roozesoom).

(Read May 26, 1900).

Some time ago I described a very delicate method for the deter-
mination of the increase of the boiling point, in which the boiling
took place in a silver apparatus the pressure being maintained con-
stant. In many cases it is however an advantage to be able to

( 87 )

use glass apparatus as we may then continually observe what is
taking place.

I have, therefore, tried once more to satisfy the conditions required
to obtain trustworthy results with a glass boiling vessel. The first
condition is the removal of the danger of superheating and the
second the prevention of perceptible radiation.

The easiest device fer boiling a solvent or a solution without
danger of superheating is undoubtedly to pass the solvent in the
form of vapour through the solvent or the solution instead of heating
directly with a flame.

This method has already been applied by LANDsBERGER !) to the
determination of molecular weights. I have mentioned, previously,
that I had already applied this method, but that the accuracy of
the results was not satisfactory. As I noticed that one of the reasons
of the less satisfactory results was a perceptible radiation of heat
from the boiling liquid, I have had a piece of apparatus constructed
by means of which this radiation can be reduced to a minimum
in the simplest manner.

Description of the Apparatus.

A is the boiling vessel, 180 m.m.
long and 30 m.m. wide which is
furnished at the bottom with a nar-
row tube @ about 3 m.m. which is
bent upwards and at the top with a
wider side-tube b. This boiling-vessel
is placed in a flask B with a long
neck about 50 m.m. wide. The neck
of this flask is furnished above with
a side-tube C. The boiling vessel A
may be fitted airtight into the neck
of the flask B by means of a perfo-
rated cork cut in two halves.

After the flask B has been partially
filled with water the boiling vessel A
is filled with about 25 gr. of water and
fitted airtight into the flask B by
means of two half corks. The appa-
ratus is now placed on a piece of cop-
per-gauze and heated by means of an
Argand-burner. The side tube Cremains
open until the water boils. When it

1) Zeitschr, f. anorg. Chem. 17 422 1889.

( 88)

is closed, the water-vapour escapes through the tube @ and after
having passed through the water in the boiling vessel it leaves the
apparatus through the tube 6. So long as the temperature of the
water in the boiling vessel lies below the boiling temperature, a per-
ceptible condensation of water vapour will take place which contin-
ually decreases until the water in the vessel A also boils. After
1 or 2 minutes, the water has reached a constant boiling point.
Neither a reinforcement of the current of water vapour, nor a dis-
placement of the thermometer has now any influence on the indi-
cation of the thermometer provided a strong current of vapour pas-
ses through the boiling liquid. From the latter it, therefore, appears
that the mixing in this case neutralizes the difference in temperature
of the different aqueous layers.

The result was somewhat different when I experimented with a
solution. I noticed in this case that the indication of the thermo-
meter was affected by an increase or decrease of the current of
water vapour. The peculiar thing was that the stronger the current
of water vapour became, the lower the indication of the thermometer.
Tt struck me that this phenomenon must be explained as follows:

Water vapour may heat a solution, the boiling point of which lies
above 100°, to its boiling point in consequence of the latent heat
of evaporation set free during the condensation of the water vapour ;
as however the vapour bubbles have the temperature of 100°, these
when in contact with the thermometer will tend to cool it to 100°.
The more water vapour comes in contact with the thermometer,
the greater will be the cooling and this is the very thing I
observed.

To eliminate this error I introduced into the boiling vessel a
cylinder of platinum gauze which was closed below. The diameter
of this platinum gauze tube was rather less than that of the boiling
vessel in order to render the passage of the current an easy one.
The height of this platinum gauze tube amounted to about 5 c. m.
so that the mercury reservoir of the thermometer was completely
surrounded by it.

This arrangement produced the desired result; it was now a mat-
ter of complete indifference whether the current passed slowly or
rapidly through the solution. The thermometer placed in the solu-
tion did not seem to be affected thereby. The mixing was now also
complete as no difference in temperature could be noticed when the
thermometer was displaced.

Whilst nothing special is noticed in determining the boiling point
of water, and the duration of the experiment has no influence on

( 89:)

the reading of the thermometer, this is not the case with solutions,
because the concentration is continually changing owing to the con-
densation which takes place.

The largest quantity of water-vapour is condensed in unit time
during the heating to the boiling temperature. Once the boiling tem-
perature is reached, the condensation is at its lowest, and amounts
to so little in the apparatus just described that the boiling point
remains constant within 0.001° for about 3 minutes. The effects
of the dilution then become perceptible and the boiling point slowly
falls as is apparent from the graphical representation.

It is clear that the concentration of the liquid at the time when
the boiling point has been
Be constant for the half of 3
1,490 minutes, or one minute and
L cry a half, is nearest the con-
centration which corresponds

= if 4 to the recorded maximum
5 temperature.

= _o Peo

= 1,480 ais After the temperature has

ir a 2
Cp therefore remained constant

—— a
t+ for 1/2 minute, the exper-
H +} iment must be stopped and
| +-| the concentration deter-
1,470 mined. As each experiment
eee Og aed t50e) 6 ed) BiG). 10 :
res a re only takes a few minutes,
Fig. 2. the manostat need not be

used in these observations. If two of the apparatus described are
employed, and water is boiled in one of them, the slight error
which might be caused by small variations in the atmospheric pres-
sure during the short duration of the experiment may be eliminated.
If the highest attainable accuracy is not desired, a single apparatus
is sufficient, but then it is necessary to determine the boiling point
of the pure solvent before taking in hand a fresh solution.

When the boiling point of the water (solvent) has been read off,
the side tube C is opened and after the thermometer has been taken
out of the bath, a weighed quantity of the substance is introduced
into the boiling vessel. After putting back the thermometer, the
flask B is heated and the side tube C is closed when boiling has
set in. When the maximum boiling temperature of the liquid has
been read off, the side tube C is quickly opened, the tube B is
closed with an india-rubber cork, the boiling vessel is taken out of
the flask and after a slight cooling it is attached with its thermo-

( 90 )

meter to a balance showing accurately 0.01 gram and then weighed.
No vapour can escape during the cooling as air bubbles are con-
stantly entering from outside through the tube A. After every ad-
dition the same manipulation is performed.

If the boiling vessel and thermometer has been weighed when
empty, the concentrations of the different solutions will be known.

I have determined the increase in boiling points of solutions of
NaCl using a single apparatus and consequently working under the
least favourable conditions and have found the following.

Na Cl.
Increase Molecular Increase
Concentration. i.
of Boiling point. of Boiling point.

0,0617 0,065 10,5 2
0,1277 0,119 9,40 1,81
0,5590 0,520 9,30 1,79
1,1180 1,122 10,04 1,931

From this table it follows that the accuracy which may be obtained
with a single boiling apparatus is great enough to demonstrate the
peculiar progressive change of the molecular elevation of boiling
point and of ¢ with solution of NaCl. The minimum of ¢ lies here
also between 0.1 and 0.5 gram molecule as was found with the
silver boiling apparatus. As I have already stated, the accuracy is
greater when two boiling vessels are used, one of which is always
filled with water so as to eliminate the error caused by small changes
in the atmospheric pressure.

It appears to me that when used in this manner, the apparatus
gives more accurate results than that of Beckmann which moreover
has the disadvantage of being very complicated.

The new apparatus will be very suitable for collecting data for
dilute solutions. It is less suited for the determination of the molec-
ular weights of substances in non-aqueous solutions because the
condition of its accurate action is the use of a perfectly pure solvent,
as this, if impure does not have a constant boiling point when
continuously boiled.

After I had already made a few preliminary experiments with
the new apparatus, an almost identical arrangement was described

‘

(91 )

in the “American Chemical Journal” April 1900 by H. N. Me. Coy.
The resemblance is striking, the only difference is that the tube a
through which the vapour passes into the solution has been placed
by Mc. Coy inside the vessel 4, whilst in my apparatus it is
situated outside it. Mc. Coy, has not however taken the precaution
to prevent the vapour coming into contact with the thermometer
and this, as we have seen, is very essential, if great accuracy is to
be attained, as only then the boiling temperature is independent
of the degree of heating of the flask B.

Amsterdam, University Chem. Lab. May 1900.

Chemistry. — ‘ Thermodynamics of Standard Cells” (24 part). By
Dr. Ernst Conen (Communicated by Prof. H. W. Bakuuis
RoozEBOON).

(Read May 26, 1900).

1. In the first paper on this subject!) I have shown that the
ideas prevailing on the reactions which take place in the standard
cells are incorrect and ought to be replaced by others.

With the CLark-normal cell, a very satisfactory agreement was
found between the theory and the measurements.

Before subjecting the existing data of the Wesvon-normal cell
to calculation in an analogous way, a calculation which as will
appear later on, is more complicated than for the Crark-cell, |
would like to further explain a few points about the latter.

2. In the theory and in the calculation in the previous paper
it was assumed that the cell was built up as follows:

He—Heg.SO, — saturated solution of zincsulphate — Zn

whilst for the caleulation measurements made with cells of the
following construction were used ;

o — Ho — saturated solution of zine sulphate — zine amaleam
Hg — Hg, SO, — saturated solution of Ipl lgam,

about which it may be observed that the amalgam was composed
of 1 part of zine to 9 parts of mercury ®).

We may now inquire whether such cells may be theoretically
treated as if the negative poie consisted of pure zinc. It has already

1) Proc. Roy. Acad. Amsterdam. 1900, pag. 719.
*) Compare Kauue, Wiepemanns Annalen, 5). 205 (1894).

~I

Proceedings Royal Acad. Amsterdam Vol. LI.

(92 )

been shown by Linpeck *) in 1888 that zine and zine amalgam
show, towards solution of zine sulphate, the same potential difference
when a certain minimum of about 2 per cent of zinc in the amalgam
is exceeded.

The zinc amalgam used in the CLArk-cells, therefore, behaves
like pure zinc. That the presence of mercury exercises no influence
is shown, moreover:

a. from the observations of KanuLe who showed that cells con-
structed with an amalgamated zinc rod instead of a 10 per cent
amalgam showed an E.M.F. which differed by less than 0.2 millivoit
from that of the amalgam cells; it may be observed that in these
cases the amalgamation had taken place but very superficially.

b. From the communications of CALLENDAR and Barnes !), who
have always worked with an amalgamated zine rod instead of the
amalgam and have still obtained results perfectly identical with
those of KAHLE.

3. In the amalgam-cells, a new link enters into the mechanism,
because on the passing of 2 96540 coulombs, the zine must be
first abstracted from the amalgam before it can unite with SO, to
ZnSO, which then undergoes the hydration which has been discussed
in the previous paper.

That the evolution of heat involved in the abstraction of zine
from the amalgam is of no importance, is showa from the fact that
the E.M.F. and the temperature coefficient are exactly the same for
the amalgam cells and for those where a superficially amalgamated
zine rod is employed

4. It appeared to me of importance to lay stress on the foregoing,
as in contrast to the zinc amalgams, the cadmium amalgams behave
quite differently and this becomes important in the application of
my theory on the Wesron-standard cells in which the negative
electrode happens to be formed by cadmium amalgam.

I hope to make more extensive communications on the theory of
these standards as soon as I have experimentally determined the
required data.

Amsterdam, University Chem. Lab. May 1900.

3) Wiep. Ann. 35, 311 (1888).

‘) About the diluted amalgams, compare Linpveck, |. c. 324. Also Rrciarps
and Lewis, Proc. American Acad. of Arts and Sciences. Vol. XXXIV 87 (Dec. 1898).
Zeitschrift fiir phys. Chemie 28. | (1899).

1) Compare my first paper.

*) Compare Wiep. Annalen 65, (1898) 926. Crova, Ann. de chim. et de physique
(3) 69, 458 (1863) had already found that if in a Danre.t~cell the zine is replaced
by zine amalgam, the properties of the cell thereby undergo no change.

(93 )

Chemistry. — ‘On the Enantiotropy of Tin” (V). By Dr. Ernst
CoHeN (Communicated by Prof. H. W. Bakuurs Roozesoom),

(Read May 26, 1900,)

1. In the second and third communications on the peculiar conduct
of tin, mention was made of the velocities with which the reactions
white tin — grey tin
and grey tin — white tin
occur at different temperatures.

It was then established that the change of the white modification
into the grey one shows a maximum velocity at about — 48°, while
above the transitiontemperature there was, as might be expected,
no question of the appearance of a maximum.

I have now studied more in detail the velocity of change at diffe-
rent temperatures which has brought to light a number of interesting
points which I will discuss in this paper.

2. I had filled a large dilatometer with about half a kilo of white
tin filings which were inoculated with grey tin and in contact with
a 10 per cent solution of pink-salt in absolute aleohol. This dilato-
meter was kept for three months in brine, the temperature of which
varied from — 4° to — 7°.

After the lapse of this time small quantities of white tin were
still observable between the grey mass in the dilatometer. I now
proposed to keep the dilatometer at — 45° until, at that temper-
ature, no change should take place in the level of the liquid in the
eapillary tube; I could then be certain that all the white tin had
changed into the grey modification. A very narrow capillary was

selected. By weighing out with mercury, the volume of 1 mm. in

length was found to be 0.00037e.m. so that a displacement of 1 mm.
showed the change of 10 milligrams of white tin into the grey
modification if we still accept provisionally 7.3 and 5.8 as the re-
spective sp. gr. of those modifications.

In order to maintain the temperature at — 45° for a long time,
I made use of liquefied ammonia which may be strongly recom-
mended for such purposes. A wide mouthed stoppered bottle, holding
one litre, was nearly filled with the liquefied gas and introduced
into a somewhat wider battery glass, on the bottom of which some
corks were placed; the air surrounding the bottle forms a first-rate
isolation. The whole was now placed in a box filled with bran,

The bottle was closed by means of a trebly-perforated cork; one
T*

( 94 )

hole served to admit the dilatometer-capillary, through the other
passed a thermometer and through the third a glass tube, ending
just underneath the cork, the other end of which passed through the
window outside the room.

When the surrounding temperature was about 15°C., I only needed
to add about 50 grams of liquefied gas every 24 hours to keep the
dilatometer quite immersed. It very soon became apparent that the
yate of change at — 45° was extremely small which seemed to me
to contradict the results previously obtained. (Compare Proc. Roy.
Acad. Amsterdam. 1899 102 also Zeitschr. fir phys. Chemie 80, 616).
The research in this direction was consequently undertaken on a
more extensive scale.

3. The large dilatometer was opened, the tin was carefully washed
with dilute hydrochloric acid (the temperature was continually kept
lower than the transition point), then with alcohol and ether and
finally dried in vacuo over sulphuric acid ').

4. In order to be able to investigate afresh the velocity of the
change, white tin—grey tin, I filled a dilatometer (A) with 43,9334
erams of the preparation, the purification of which has just been
described and in which a certain amount of white tin was still
present; 1 mm. increase in the capillary represented a change of
14 milligrams of white tin into the grey modification. As measuring
liquid a 10 per cent solution of pink-salt in absolute alcohol was
employed. The observations were now made in the following manner:
to study the velocity at a very low temperature, I first placed the
dilatometer in a bath of melting ice and water, which was vigorously
stirred by means of a Wirt’s stirrer connected with a tLErNnrict’s
hot air motor, and then read off the level of the liquid in the eapil- .
lary. The dilatometer was then placed in the cooling bath (solid
CO, and alcohol, liquefied NHs, different cryohydrates) and left there
for definite periods. It was then again put back into the ice-bath
and the level of the liquid read off. By this method of working we
become independent of small variations in the temperature of the
low-temperature bath, which is very necessary, as the dilatometer
acts also as an extremely delicate thermometer.

5. Working in this way, the results with dilatometer A were:

1) The pink-salt was entirely removed in this manner; on shaking with water no
chlorine reaction could be got with silver nitrate.

ail

(95 )

TA TE 1.

See acer stare) T99P20 ctciaage: "toa in bows

0° 14 mm. 2 | —45° 0.4 mm. 6°/,
—45° 0.16 mm. 152°, | 0° 0.48 mm. 167/,

oe 12 mm. 45! | —15° 0.43 mm. 7!
any 3 mm. 2'/, 0° 0.45 mm. 17'/,

0° 12 mm. 4), ee 0.00 mm. 4

oe 5 mm. 172/, 0° 0.50 mm. 177/,

0° 1.5 mm. 29 0° 0.31 mm. 47),

0° 0.5 mm. 10'/,, 0° 0.21 mm. 14);

From this we plainly see that the velocity is greatest at 0° whilst
formerly we have found a maximum velocity at — 48°. On the
other hand we see once more that at — 85° the velocity is smaller
than at — 48°.

6. In order to ascertain whether the presence of pink-salt exer-
cised any influence on the position of the maximum of the velocity
of change, a certain quantity from the same mass which originally
filled the dilatometer A was introduced into a dilatometer (B) with
addition of absolute alcohol but without pink-salt. The following
results were obtained: —

PAB LE I.

Temperature. Velocity of change. Time of observation in hours.
—45° 1.6 5
0° 0.0 17
—15° 0.36 6
0° 0.06 10
—85° 0.0 37),
—45° 0.17 201/,,

The maximum velocity now lies near — 45°.

From these results, taken in connection with those in Table [, it
appears that the position of the temperature at which the change
proceeds most rapidly, is changed by the addition of pink-salt.

In the experiments described previously (compare Proc. Roy. Acad.
Amsterdam, 1899. 102 also Zeitschr. f. phys. Chem. 1899. 30, 616) the

( 96 )

: ‘ ; 6 > ’
maximum was also found at — 45° in the presence of pink-salt,
but at that time a tin was used which had already undergone the
change of white tin 2 grey tin in both directions.

From this we see what enormous influence is exercised on these
phenomena by the “previous history’? of the white tin.

GpRNEZ') has noticed quite analogous phenomena with sulphur;
the velocity of the change, melted sulphur — rhombic sulphur, is
there dependent on 7, the temperature at which the sulphur was
melted, the time during which it remained fused, ¢ the temperature
at which it remained superfused, t’ the time during which it was
superfused, 9 the temperature at which the change takes place after
contact with a crystal of rhombic sulphur.

GERNEZ has published no observations showing a displacement of
temperature of the maximum velocity such as has been found here.
It would be of interest to investigate whether a similar phenomenon
may also occur there.

7. With substances like sulphur it is not possible to do more
then acknowledge the existence of these mysterious phenomena.

Now that similar phenomena are met with in a substance like
tin which is electrically well-defined, there is a prospect of learning
something more about these changes which are coupled with a change
in free energy.

I hope soon to undertake a research in that direction.

8. In the first communication on the enantiotropy of tin 2), it
was casually remarked that the velocity of change increases when
the change has occurred a few times in both directions. This is
correct, but it is now evident that the transition point need not be
passed, that is to say that on exposing white tin to low tem-
peratures, the velocity of change constantly increases (at the same
temperature).

The behaviour of a dilatometer *) which was filled with 20.370 grams
of grey tin and 19.040 grams of white tin which had originated
from the grey tin by warming may serve as an example.

*) Journal de physique 2nd series. 1885. 349.

*) Proc. Roy. Acad. Amsterdam. 1899. 38.

5) Filled with aleohol with pink-salt. 1 mm. displacement of the liquid column in
the capillary corresponds to a conyersion of 10 milligrams of white tin into the
grey modification,

(97 )

PRAM Bela ar.

Temperature. Velocity of change. Time of observation in hours.
—45° 2.33 6
0° 0.47 15*/,
—45° 2-3 rile
ge 0.7 17
—15° 3 4p
oe 0.86 171/,
—85° ee. 3?/,
—45° 4.0 1)

Although the active mass of the white tin has considerably
decreased, the velocity at 0° has still increased from 0.47 to 0.86
that at —45° from 2.33 to 4.0.

9. From the experiments described here, it appears clearly that
only those results are comparable which have been obtained with
tin which has the same (preferably, known) “previous history”.

I have, therefore, examined the curves of the velocity of change
of the reaction

grey tin = white tin

which in the previous communication 1) were determined with samples
having different “previous history”, by means cf one and the same
sample.

T ALB tik IV,

Temperature. Velocity of change.
—85° 3358.
—45° 4.0
—16° 3.0
oe 1.06
20° — 0.09
25° — 2.0
30° — 20.0
35° — 132.0
40° —2700

It is difficult to unite these data into a clear graphical figure on
a small scale and I, therefore omit this.

') Proce, Roy. Acad. Amsterdam. 1899. 103, 286,

( 98 )
Summary of Results.

1. The addition of pink-salt does not only influence the velocity
of the change

=>

— white tin

grey tin
but also the temperature of the maximum velocity.

2. The “previous history” of the tin exercises a great influence on
the velocity with which the above reaction takes place.

The mysterious phenomena observed by GERNEZ in the case of
sulphur are also met with here. As however, we possess in tin a
substance with well-defined electrical properties, there is a prospect
of getting some insight, by electrical means, into the changes which
this metal undergoes, since those changes must be accompanied by
a change in the free energy.

3. Comparable results are only obtainable with samples having
the same “previous history”.

Amsterdam, University Chem. Lab, May 1900.

Chemistry. — ‘The formation of mixed-crystals of Thallium-
nitrale and Thalliumiodide’. By Dr. C. van Eyx (Commu-
nicated by Prof. H. W. Baxaurs RoozEBoom).

(Read May 26, 1900.)

j. No instance is known of the formation of mixed crystals of
nitrates with iodides. Preliminary experiments showed me that a
mixing in the solid state probably takes place with several nitrates
and iodides. The system Thalliumnitrate—Thalliumiodide has now
been closely investigated. In the first place the relation between the
composition of the fused mixtures of salis and that of the mixed
crystals deposited on cooling has been examined.

2. The commencement and progress of the solidification of mixtures
of 100 pCt. of T1 NO; to 100 pCt. of T1I was observed.

mol. °/y TIT Commencement of End of
Solidification. Solidification.
0 206° 205°.4
1.6 207° 206°
4.1 208°.6 207°

6.7 211° 208°.4

(99 )
mol, %/, TII Commencement of End of
Solidification. Solidification.
9.9 2AD- 209°.5
15 238° 210°
18 264°.5 215 s.D
23.7 288° >
31.4 SiileoD >
36 3217.5 >
| 50 346°.5 >
. 54.5 354° a
| 60.2 363° =
| 69.9 378°.5 290°
80.5 393° 335°
; 90.1 408° syd’
| 94.7 415° 7
100 422° =
A clear view is given by the graphic representation in which the
: line ACB represents the first
solidifying points. The crystals

10 20 30 40 50 60 70 80 90 100
TINO, TI

which deposit on solidification of
0 to 9.9 mol. pCt. TIT are white,
with a higher percentage of TII
they are red.

3. From the course of the
melting point line (type IV of
Bakuuis Roozesoom, Zeitschr.
fiir phys. Chem. 80. 399), which
commences to rise immediately
from the solidifying point of
TINO,, it follows that mixed
crystals, and not the single salts,
are deposited from the melt, and
that the mixed crystals are of
two kinds corresponding to the
solidifying point lines AC and
CB. This may, further, be deduced
from the following: 1. the crystals
which are deposited from mixtures
of 0 to 9.9 mol. pCt. TIT are
white and contain TI, the colour
of which becomes visible at lower

( 100 )

temperatures on account of the change then undergone by the mixed
erystals ; 2. admixture of TI1I with TINO, as well as of TI NO, with
TIL loweis the transition point of both TINO, (142°) and TII
(169° red —» yellow).

4. The connection between the concentration of the mixed crystals
and that of the melt has been determined in the case of mixtures,
which begin to solidify below 300°, by isolating the crystals from
the melt and subjecting them to analysis (compare Zeitschr. fiir
phys. Chem. 80. 432); in the case of mixtures showing a higher
solidifying point it has been derived from the course of the solidification.

mol. pet. of T1I mol, pet. of TII
in the melt. in the mixed erystals.
4.7 8
6.7 11.5
9.2 16.4
13.3 63
20 67
24.7 77

In this way are obtained the lines AD and EB which show the
composition of the white and red mixed crystals obtained from
mixtures cf 0O—10 and 10—100 mol. pCt. of TII. The second line
EB is not so reliable as the first, as the method used for the sepa-
ration of melt and crystals causes a small quantity of the melt to
adhere to the drained crystals.

With melted mixtures containing more than 10 mol. pCt. of TIT
this may cause a rather large divergence in the analysis of the
mixed crystals, as with these mixtures the concentrations of melt
- and crystals differ by more than 50 pCt.

It is, therefore, quite possible that the real values are situated
a trifle more towards the right than has been found by analysis.

From the lines it follows that the white mixed crystals may
contain from 0—18 mol. pCt. of TII and the red ones from about
65—100 pCt., so that there is here a hiatus in the series of mix-
tures between 18 - 65 pCt. Accordingly, all mixtures between these
concentrations solidify at 215°.5 to a conglomerate of the crystais
D and £.

5. Thalliumnitrate, rhombic at the ordinary temperature, is
rhombohedrie above 142°, whilst the yellow Thalliumiodide is de-
scribed in the manuals as regular. Prof. ScoHROEDER VAN DER KOLK

¢ 1017

had the kindness to determine the erystalline form which these salts,
assume on solidifying.

The red TII appeared to be regular, the yellow on the other
hand biaxial. Thalliumnitrate also seems capable of crystallyzing
from the melt in the regular system. This corresponds with the
fact that the white as well as the red mixed crystals are regular.

Breda, Chem. Lab. Royal Milit. Acad.

Botanics. — “Hurther researches on the Formation of Indigo from
the Woad (Isatis tinctoria)”. By Prof. M. W. Betertcx.

Since my first communication on the chromogene of the woad ') I
have found that the indoxyl does not exist in it in a free condition,
as I then thought, but in a loose compound which I will call
isatan, and which, by an enzyme, simultaneously present, the isatase,
is easily decomposed with production of indoxyl.

1. The research of Scnuunck.

As soon as I had come to this conclusion, the question arose,
whether the matter prepared by Scuunck from the woad in 1855,
and described *) under the name of “indican’”’, can be either or not
identic with isatan. That in many of his experiments he has indeed
had isatan before him I consider as certain. But in carefully reading
his essay I met with number of contradictions, which are only to be
explained by Scuunck’s working with two other substances besides,
which he continually interchanges with each other and with isatan ;
these are indoxyl and a chromogene which colours intensely yellow
by alkalies, occurs abundantly in the woad, precipitates, just like
isatan, with basic lead acetate, but has nothing to do with indigo.
If I well understand him he calls this substance ,changed indican”’
and considers that it differs from it by containing one or two H°O
more, but this is a wholly unproved hypothesis.

Indoxyl was not known to Scuunck at all, but his second
preparation method of the “indican” reposes on ether extraction of
the dried plant. As isatan is not soluble in ether I suppose that

1) On the Formation of Indigo from the Woad (satis tinctoria). Kon. Akad. van
Wetenschappen, Amsterdam ; Proceedings of the Meeting of 30th September 1899.

2) E, Scuuncx. On the Formation of Indigo-blue. Part I. Philosophical Magazine
(4) Vol. 10, pag. 74, 1855. For the indiglucine: Ibid. Vol. 15, pag. 127, 1858,

( 102 )

during the preparation small quantities of indoxyl originated from
the isatan, which easily occurs under various influences, and for which
ether is an excellent solvent.

However strange it may be, it was the matter colouring
yellow by alkalies, and not the indigo-chromogene itself, which
Scuunck subjected to the three analyses on which reposes the well-
known formula of the “woad-indican”. Quite clear he is not, but
so far as I conceive his meaning, the first and the third prepar-
ations, which he analyzed, contain no indican at all, yet he calls
them the purest; the second he considers as less pure, and he seems
to have subjected it to the analysis after having convinced himself
that by precipitating it with alcohol, lead acetate and ammonia ‘it
contained no longer unchanged indican”, which consequently means,
that he had before him the said matter turnmg yellow by alkalies
and thus containing no more indigo chromogene.

Word for word he says the following, first concerning his analyses
in general (1. c. Part I, pag. 89): “I have hitherto been unable, I
regret to say, to ascertain the exact composition of indican by direct
experiment. On account of the deliquescent nature, and its so readily
undergoing change when heated, it was impossible to subject it to
analysis in a free state and I was therefore obliged to have recourse
to the lead-compound.” Then follows the description of the three
analyses themselves. Of the first he says (1. c. pag. 90): “Notwith-
standing the care, however, which I took in the preparation of the
specimen, I found that it did not contain unchanged indican, as
a little of it, when tested with sulphuric acid, gave no indigo-blue.
It is nevertheless the purest specimen of the lead-compound which
1 have analysed”. Then he says of the second and third: “The
next analysis which I shall give, places in a striking light the effect
which alkalies exert on indican. I took some of the same solution
of indican which I had employed for the preceding analysis, and
which I found to give, when a little of it was boiled with acid, very
pure indigo-blue; but instead of evaporating it, I added a large
quantity of alcohol to it, and then precipitated with acetate of lead
and ammonia. The precipitate no longer contained unchanged indican”’...
“The third analysis was performed with a lead-compound made in
the same way as that of the first analysis.” 1)

') Three analyses of such doubtful substances are the sole foundation upon which
the well-known indican formula of Scuunck
C*° H! NOM -+-2 H'O = C8 H® NO + 3 (C8 H? 0°),
Indican Indigo-blue Indiglucine

( 103 )

All this is not quite clear, but I read from it that these analyses
have nothing tv do with the indigo chromogene itself, that is to say,
with isatan, and I think that they relate to a mixture of the chromo-
gene from the woad, which colours yellow by alkalies, and plant-
slime (“indiglucine’’). The explanation of this enormous fact should,
I think, be ‘sought in the following circumstances. SCHUNCK prepared
the “indican” by alcohol extraction from carefully dried woad-leaves,
which in itself is quite rational, because in this way relatively con-
eentrated and rather pure solutions are obtained. But if the dried
leaves are kept a little too long, for instance two days at 28° to
30° C., or if they grow a little moisty, the isatan vanishes completely
from them. Though Scuunck evidently knew that the chromogene
can easily disappear from the dry leaves, he does not mention the
short time after which this occurs already, so that 1 think it very well
possible that the chromogene has disappeared during his preparation
without his having observed it. For it is to be kept in view that
his method of demonstrating the indigo-blue qualitatively is highly
deficient and consisted in decomvosing the chromogene by ‘strong
mineral acids’, the very worst method to be followed, as strong
acids are pernicious as well to isatan as to indoxyl. {

My opinion that ScHunck at the moments when it was particularly
important, had not to do with the indigo chromogene itself, but with
another substance, is also based on several observations which he
makes about the properties of the “pure indican”’. So we read on pag. 85
(l.c. Part I): “With caustic alkalies, baryta and lime-water the watery
solution turns of a bright yellow.” This reaction holds only good for
the impurity which remains in the dried leaves after the isatan
is destroyed in them. Jf in the preparations any isatan had been
present the yellow colouring would have been immediately followed
by the formation of indigo-blue, which then becomes much more dis-
tinctly visible than if the same preparation is decomposed by acids.
Evidently he has examined different samples with acids and alkalies,
and samples, free from isatan, only with the latter, else he would
certainly have found that those preparations, which by acids produce
indigo-blue, yield much more indigo if they are treated with an

is based and which, since 1855, has been accepted, without criticism, in all great
chemical manuals. Formerly I was inclined to write the formula thus:
C** H 27 NO + 2 H?O = C* H? NO +3 (C® Hs 0°)
Indoxyl Glukoron
but now, having carefully studied Scuunck’s essay, I think this interpretation also
worthless.

( 104 )

alkali. Likewise the following statement of his preliminary researches
is for the greater part unintelligible if it is admitted that Scnunck
speaks of isatan. He says (1. c. pag. 81): “I was enabled to
infer, with positive certainty, that the Jsatis tinctoria contains a
substance easily soluble in heat and cold water, alcohol and ether,
which, by the action of strong mineral acids, yields indigo-
blue; that the formation of the colouring matter from it can be
effected without the intervention of oxygen or of alkalies; and that
the latter, indeed, if allowed to act on it before the application of
acid, entirely prevent the formation of colouring matter.” In opposi-
tion to this, the fact must be stated, that the best method for demon-
strating with certainty and quickness isatan or indoxyl in woad-sap,
just consists in adding alkali to it, by which the isatan is decomposed
and the indoxyl is quickly oxidized to indigo at the air; after this,
the addition of acid may be desirable to decolour the yellow pigment
formed by the alkali, by which the indigo-blue appears with greater
purity.

The uncertainty of the whole research explains how it is possible,
that Scuunck, when later becoming acquainted ') with Polygonum
tinctorium, could think that the indican therein occurring, the com-
position of which, C!! H' NO*% + 3 H?O, has recently been deter-
mined by Messrs. HooGkwerRrr and TER MEULEN ”), and which is
entirely different from isatan, could be identie with his , woad-indican.”

Consequently I believe that ScuuncK cannot be considered as the
discoverer of the isatan, though it is not to be doubted, that in his
experiments, he has sometimes had this substance before him, and,
basing on the above exposition I take his indican formula for not
apphable to isatan.

2, Preparation and properties of isatan.

Indoxyl and isatan are very unstable and siill at present most
imperfectly known substances, which only in acid solutions can easily
be distinguished from each other, in neutral solutions, without the
use of isatase, with much more trouble, in alkaline solutions not at
all, because in these isatan produces indoxyl.

The reason why at first I thought that the woad must contain free
indoxyl and no compound of it, is the fact that in the extracts obtained

) On Indigo-blue from Polygonum tinctorium. The Chemical News, Vol. 39, pag.
119, 1879.
2) Kon. Akad. van Wetensch, te Amsterdam, 31 Maart 1900, pag. 598.

( 105 )

from young woad-leaves, rich in isatan, as well by decoction as by
cold extraction, the isatan is decomposed and an indoxyl solution is
obtained. New I admitted in the beginning, that if in the woad, as
was my leading theory, a glucoside was present, which, in analogy
to the indican, must be decomposed by an enzyme, at the decoction
no indoxyl but exclusively this glucoside would be obtained, because
by boiling the enzyme is suddenly destroyed. In this view I was
supported by the fact, that this indeed takes place with Indigofera
and Polygonum, which by decoction yield indican, by cold extraction
indoxyl.

But I began to doubt of the generality of this theory, when observing,
that Phajus grandiflorus, which belongs to the indican plants, never-
theless ') produces indoxyl at decoction. So this seemed also possible
with the woad, though it was clear that the properties of the ,gluco-
side” ought in this case to be quite different from those of indican.

But I was only put on the right way, by the experience, that it is
possible to obtain from the leaves of the woad, by the extraction
with dilute acids a solution, which remains unchanged at the air,
although it yields with alkalies much indigo-blue, while an equally
acid indoxyl solution slowly oxidizes at the air to indigo. I then
clearly saw why I had before obtained indoxyl from the woad. My
experiments had been performed on a small scale; I had been able
with care to select growing leaves and buds only; but they contain
much isatan and so little acid, that the enzyme isatase can become
active, so that by decoction, as well as by cold extraction with
water, and even with alcohol, they produce indoxyl, though at the
decoction and alcohol extraction mixed with much isatan, which
fact I only observed later, If I had used older leaves which contain
more acid, I should have found at once isatan quite free from indoxyl.

The relative constancy of isatan in feebly acid solutions, even at
boiling temperature, can be utilized for its preparation.

Though the acidity during the extracting must be feeble yet it must
be strong enough to prevent the decomposition of the isatan by the
isatase. To this end an acidity of 1.6 to 3.2 ce. of normal oxalic acid
per 100 cc. of the extraction liquid, (0.1 to 0.2 weight percentage)
suffices, for the acidity of the older leaves themselves amounts to
about 1,5 ec. normal per 109 ec. of the juice, and this is the very
limit of acidity above which the isatan becomes inactive. If the
extraction is effected by boiling, this degree of acidity should be

1) Indigofermentation. Kon. Akad. van Wetensch, Amsterdam, Proceedings of the
Meeting of Mar 1900 pag, 573.

( 106 )

exactly observed. In cold extraction, with oxalic acid, the isatan is
much less subject to decomposition, so that, below 50° C. solutions
of 1 to 3 pCt. oxalic acid can safely be employed. But at these low
temperatures the acid penetrates with less rapidity into the cells,
in whieh accordingly the enzyme can become more or less active
producing some indoxyl. Hence, in the acid extraction at low temper-
ature, it is advisable to rub the leaves down in a mortar, immersed
in the acid liquid.

In particular at boiling temperature and when using an extraction
liquid of an acidity of 2 to 3 ce. of normal oxalic acid, it is easy
to obtain a quite undecomposed isatan solution from the growing
woad-leaves, even of the youngest still neutrally reacting meristemes.
In consequence of the boiling temperature, aided by the perfect sur-
rounding of the cells with the dilute acid, the isatase is destroyed
simultaneously with the dying of the protoplasm, by which decom-
position of isatan is quite excluded. As the extraction continues,
there is an interchange between the feabler acidity within (0.5 ce.
normal pCt.), and ithe stronger acidity without the young cell, and
at the end of the experiment, a solution of isatan of 0.5 to 2 ce. of
normal acid per 100 ce. of juice in obtained, when the weight of
the leaves used, equals that of the extraction liquid.

More acid used in the boiling than the said percentage causes
isatan decomposition, by which not only indoxyl but also brown
products of decomposition originate,

Oxalic acid can be replaced by other acids and by acid salts.
Thus I obtained good results with dilute sulphuric acid and phos-
phoric acid, and with a saturated solution of boric acid, at room
temperature. Acetic acid causes a feebler decomposition than oxalic
acid. When the appearance of brown products cf decomposition during
the boiling is taken as a criterion for the decomposition, I found
that 12 ce. of normal acetic acid added to 100 ce. of juice (ea 0.8
weight percentage), is about proportioned to 5 ce. of normal oxalic
acid (= 0.3 weight percentage). Acid salts act like acids. Kalium-
bioxalate and biphosphate can only b2 used in strongly diluted
solutions. With a cold saturated solution of kalium bitartrate the
extracting may be operated at boiling temperature without deecompo-
sition; only by prolonged boiling a little indigo-blue is produeed.
I prefer, however, the extraction with oxalic acid. Therewith the
solutions remain clear and of a light yellow and can very easily
be filtered '); after Altering, the remaining leaf-matter is soft, but

*) If the woad-leaves are boiled with more acid than 2 to 3 ec. normal per 100
cc. of the juice, the decoction grows slimy and gives trouble in filtering.

uf

( 107 )

by no means slimy, and can quite well be pressed dry, so that, in
consequence of the high water percentage of the leaves, a quantity
of extract is obtained nearly twice as much as the original volume
of the oxalic-acid solution.

If with the thus obtained isatan solution enzyme experiments are
to be performed, the acid must be removed, which is best done by
boiling with chalk !). As the reaction of the chalk is slightly
alkaline it should be very finely divided, as larger particles form a
little indigo on their surface. After filtering off the oxalate and the
superfluous chalk, a liquid results, somewhat brownish indeed, but
not so much as to be hurtful to the enzyme experiments.

This liquid cannot be evaporated to dryness without being decom-
posed, even not at room temperature, because during the concen-
tration the acidity increases. To neutralize the syrupic matter is
troublesome.

The extraction of the isatan can also be effected with feebly acid aleo-
hol, both in the cold and at boiling temperature. Fresh leaves are then
to be preferred to dried ones, because in drying there always gets
lost some, at last all isatan. The alcohol extract must be evaporated
at low temperature and finally be neutralized. with chalk. After
boiling a brownish, almost neutral and very rich isatan solution
is obtained, which can be purified with neutral lead acetate.

For further concentration the isatan can be precipitated with basic
leal acetate, and the yellow precipitate be decomposed in the cold
with oxalic acid. The lead oxalate separates freely from the isatan
solution, and the excess of oxalic acid can be removed with chalk,
the lead with sulphurated hydrogen. This solution can be kept
without decomposition for some time, but after a few weeks the isatan
vanishes.

In the decoction method with oxalic acid, followed by lead
precipitation, the chlorophyll is removed from the very first and
evaporation is excluded. More plant slime will then precipitate with
the lead than by alcohol extraction, but on further purifying,
this slime can be precipitated with ether-alcohol. I have as yet not
been able to prepare dry isatan, as a powder, from these extracts, such
as I before prepared the indican.

The most characteristic difference between indican and isatan consists
in their behaviour to alkalies: indican is constant in concentrated
alkaline solutions, isatan is decomposed by very feeble alkalies, even

1) Neutralizing without endangering the subsequent enzyme action, can also be
done with lead-, mangan-, magnesia-, or baryta-carbonate, but I prefer chalk,

8
Proceedings Royal Acad, Amsterdam, Vol, IL.

( 108 )

in the cold. Concentrated solutions of dinatrium phosphate, phosphoric
salt and ammonium earbonate produce indoxyl from isatan, already
at room temperature. By acids, both indican and isatan are decom-
posed, but indican with much more difficulty, which is especially
evident when using acid salts. So, isatan is already decomposed by
boiling with dilute kalium bioxalate, in which indican is constant.

Both substances precipitate with basic lead acetate, producing
yellow precipitates, which colour is probably proper to the substances
themselves, and not to impurities.

Tsatase, the specific enzyme from woad, does not act on indican;
isatan on the other hand is not decomposed by the indigo-enzymes.

Isatan is not direetly splitted by the common microbes; indirectly
it may, of course, be decomposed by the alkali produced by microbes.
Indican, on the other hand, as I have formerly shown, is directly
decomposed by many microbes, either by ferment action of the
protoplasm (katabolism), or by specific enzymes, proper to the
microbes. This difference between isatan and indican is probably
related to the nature cf the substances set free in the decom-
position beside the indoxyl. So the glucose, from the indican,
is an excellent nutrient for many bacteria, whilst the very stability
of the isatan in relation to microbes, seems to indicate that the
matter, which besides indoxyl originates from it, is no glucose,
perhaps no sugar at all.

3. The isatase.

The preparation of the woad-enzyme is effected in the same
way as that of the indigo-enzymes. The related parts of the plant are
rubbed down in living state under alcohol, and the alcohol is so
often renewed until all the chlorophyll pigment is removed. After
filtering and drying the crude isatase is obtained as a_ white,
feebly acid powder in which, of course, all substances not soluble in
alcohol are present, hence, all the other enzymes of the woad too.
As the enzyme is quite insoluble in water it can be purified by
extraction with destilled water, by which the other enzymes, at
least those that are soluble, disappear. Solvents for the isatase itself
I have not yet found.

As the woad, like the cabbages, is very rich in gypsum, the
crude isatase contains so much of it that to remove it with destilled
water is troublesome. I have therefore, in order to answer the
question, whether in the action of isatase on isatan perhaps a sul-
phate is produced, as in the splitting of kalium myronate by

( 109 )

myrosine, prepared in the following way isatase free from gypsum.
Woad leaves cut fine were rubbed down in destilled water, then
pressed out, and the remaining matter extracted with water
until the filtrate proved free from sulphuric acid. Then the chloro-
phyll pigment was removed by alcohol and the remaining matter
dried and powdered.

Though the thus obtained preparation is poor in enzyme, because
this is localized in the chlorophyll granules, which during the pressing
of the leaves are for the greater part also pressed out, it is still
sufficient to bring about a strong isatan decomposition. As was to
be expected, sulphates were not thereby set free.

The isatase is spread through the whole woad-plant; it occurs
as well in the growing parts as in full-grown roots, stems, leaves,
and flowers. So the distribution is another than that of the isatan,
which is wanting in all full-grown parts, and is the more accumu-
lated in growing roots, stems, and leaves, the younger they are.
Another distribution also than that of the indigo-enzymes in the
indican plants, which are only found in the parts rich in indican.

On the other hand the distribution of the isatase within the cell
itself, corresponds with that of the indigo-enzymes: both are local-
ized in the chromatophores. The isatan has also, in the cell, a locali-
sation corresponding with that of the indican, for in as much as can be
inferred from micro-chemical experiments, both are found in the
living protoplasm of epidermis, mesophyll and other parenchymatous
tissues. For establishing the localisation of isatan and isatase in the
cell, the same way can be followed which I formerly pointed out
for detecting the indican and the indigo enzymes !).

As regards the isatan, for this end, not too thin microscopic sections of
young, vigorously growing stems or leaves are put in a boiling mixture of
hydrochloric acid and isatine; by the acid indoxy] is separated, which
produces, with the isatine, red crystal needles of indigo-red, localized
in the protoplasm. More difficult to observe, but still, I think, quite
convincing is the precipitation of indigo-blue, as small granules, in the
living protoplasm, when the sections, in a living state, are put in a
mixture of boiling hydrochloric acid and ferrichlorid. Remarkable
is the strong accumulation of isatan in the epidermis cells, and
especially in the hairs found on the young leaves.

The localisation of isatase in the chromatophores can be demon-
strated in two ways. Either little bits of the easily loosening epidermis
of woad-leaves, or microscopic sections of stems or leaves, all in a

1) Indigofermentation p. 579,

Co
*

( 110 )

living state, can be put in a neutrally reacting woad-decoction, rich
in isatan, and heated to ca. 45° C, After some minutes already
the chromatophores begin to colour blue; the intensity of colour
increases some time, to reach its limit in an hour or so.

The blue-colouring of the colourless chromatophores of epidermis
and stem-pith, is here distinctly to be observed, so that, particularly
the fragments of the first, become very interesting preparations.

The localisation of the isatan in the protoplasm, of the isatase in
the chromatophores, renders their inter-action in the living cell pos-
sible without any influence of the acid cell-sap. At the death of the
cell, this state will suddenly change and the acidity of the cell-sap
determines whether the isatase can act or not on the isatan.

In no other plant but the woad I have hitherto been able to
detect isatase. I had expected its presence in some short-valved
Cruciferae. So in Capsella bursa pastoris, where, in case the root-
neck is muck hurt, a trace of indoxyl can be pointed out, but here
also the enzyme is wanting. Likewise it wants in the indican plants.
Also all microbes examined are devoid of isatase.

4. Action of isatase on isatan.

The action of isatase on isatan is, as observed before, only pos-
sible in neutral or amphoteric and very feebly acid solutions. In
alkaline solutions the observation becomes uncertain, because the
alkali itself splits off indoxyl. If the acidity amounts to 1.5 ec. of
normal acid per 100 ce. of the isatan solution, the action is much
weakened, and at ca. 1.8 ec. of normal acid, there is no more decomposi-
tion of isatan at all, which is noteworthy as this percentage of acidity
is reached in the cell-sap of older woad-leaves. This does not however
exclude isatan-decomposition by the enzyme in the living cell, as
the process can be limited to the protoplasm, in accordance with
the localisation described

As the action of the isatan is judged after the formation of indigo-
blue, two chemical processes are involved in it, isatan-splitting and
indoxyl-oxidation. If the experiment is performed with free access
of air, for instance in a thin layer of the isatan solution, with the
enzyme floating on it, the indoxyl changes directly into indigo; but
if the isatan is decomposed with imperfeet access of air, for
instance, in the depth of an experiment tube, then it is necessary,
during the experiment itself, to render the oxidation of the indoxyl
as complete as possible by agitation with air, which does not
however always succeed with sufficient quickness, and so limits

( 411)

the accuracy of the experiment. Of course the liquid cannot be
alkalized, because then net only the indoxyl formed by the isatase
would become visible, but also the indoxyl set free by the alkali
from the isatan not decomposed by the isatase. If the object is to
observe the isatase action at a determined temperature, then the
enzyme cannot be destroyed at the end of the experiment by heating, but
this must be effected by some enzyme poison, as for instance sublimate.

Addition of acid to render the colour of the indigo-blue more pure
must likewise be avoided, in order not to decompose isatan.

Accordingly it is necessary to perform the reaction in a very
feebly acid solution, and to judge of the results without other
precautions than a thorough aeration. I have not been able hitherto
to answer the question after the nature of the matter, which at the
isatan-splitting, most probably is set free beside the indoxyl. Pressed
yeast, produces in woad-extract, heated with crude isatase at 30° C.,
more aleohol and carbonic acid, than in the same extract without
isatase (in the proportion of 8:5), so that in the first there must
certainly be formation of sugar capable of fermentation. But this
sugar results, probably not from the isatan, but from the action of
other enzymes, present in the crude isatase, on glucosides or carbohy-
drates, present in the isatan-solution, such as myrosine on myronates,
and diastase on granulose.

The process of the decomposition cannot be studied with Fratina’s
cupric solution, as the isatan is decomposed by the alkali. —

That to Sciuncx’s “indiglucine” no value can be attached follows
from § 1.

In order to state the influence of heating on the isatase action,
the experiments were arranged as described elsewhere for the
indigo-enzymes !), with the difference, that for the above reasons,
alkalisation and subsequent acidification are here omitted. The
very finely powdered enzyme is shaken in an experiment tube
with the isatan solution, and in a water bath, at determined tempe-
rature, heated a determined number of minutes. There are always
performed two experiments at the same time, so that a colorimetrical
comparison of the produced indigo is possible, e.g. at 48° C. and
50° C., or at 40° and 60°, 45° and 55°, ete. ‘Ihe best results were
obtained with dilute isatan-solutions, which are brought, as exactly as
possible, to an acidity of 0.5 ec. normal per 100 ec. of liquid, and
with so little enzyme, that the complete conversion was very slowly
accomplished and took about half an hour.

—————

') Indigofermentation pag. 586,

(112 )

The optimum for the action was
found at 48° to 50° C., but could not
be determined more accurately as differ-
ences of two 2°C. produce no distinct
colorimetrical difference. At 70° C. the
enzyme is completely destroyed. The
minimumlimit is low, far below 0° C.,
as is seen in the figure. Noteworthy

: is the slowness with which the inten-
lu 20 gu 40 50 60 70° C. > S
Weta yaaa ten aatan sity of action decreases at decrease of
temperature, and the quickness with which it takes place when the
temperature rises. So the action at 10° and at 0° C. respectively
is as strong as at 60° and 60.5° C.

On other substances but isatan isatase seems not to act; it has
certainly no action on indican, neither could I decompose with
isatase the potassium indoxyl-sulphate in horse urine.

When judging of these experiments it must be kept in view that
other enzymes are present in the crude isatase, which may produce
substances not indifferent for the isatase action. So, mention was
made above of the presence of myrosine and diastase in the erude
isatase preparations, and below I will refer to the presence of peroxydase.

5. Extraction of indoxyl from the woad-leaves.

Once acquainted with the chief proporties of isatase and isatan, it is
possible at will to extract isatan or indoxyl from the woad. Though
in my former communication [ spoke already of the indoxyl extraction,
my being unacquainted with isatase prevented me from doing this
with perfect clearness.

As alkalies produce indoxyl from isatan the extraction of woad-
leaves therewith will at every temperature produce indoxyl. But by
the presence of alkalies the indoxyl becomes so very oxidisable and
then passes at the air so quickly into indigo, that the air, ever
present in the leaves, causes a great portion of the indoxyl to get
lost. On the other hand, neutral, or feebly acid solutions oxidize
much more slowly; it is true that also in these finally all the
indoxyl passes into indigo, but such solutions keep unchanged for
hours at room temperature and are fit for studying the properties
of the indoxyl.

The chief point for obtaining such neutral or feebly acid indoxy]
solutions from woad-leayes, is during the extraction to further the
isatase-action, consequently to do the very thing which I formerly

( 113 )

indicated as essential for the indoxyl extraction from indican plants,
where all depends on the action of the indigo-enzymes. With woad
this can best be effected by keeping the extraction temperature
between 45° and 50° ©, and by addition of chalk or of a salt of
feebly alkaline reaction, partly to neutralize the acid of the leaves.
Thus a good result is obtained by entirely filling a wide-mouthed
stoppered bottle with young woad-leaves, and pouring over them a
'/, pCt. dinatrium-phosphate solution (Na? Hl PO + 12 H? 0), heated
at about 50° C., removing the air as much as possible, closing the
bottle and allow it to stand at 40° C. for 24 hours. By decantation
and pressing the leaf matter, boiling and filtering, all the indoxylis
obtained in an amphoteric solution, which is somewhat brownish, but
is excellent for indoxyl experiments. The presence or absence of unde-
composed isatan is observed by precipitation with lead acetate, whereby
the indoxyl remains dissolved. The indoxyl can also be shaken out
with ether and in the remaining liquid sought with isatase for isatan.
Not decomposed isaian remains also in the filtrate, when the indoxy]
is allowed to oxidize at the air and the indigo-blue is filtered off.

The ether solution of the indoxyl, obtained by shaking it out of
the extract, can be evaporated at low temperature at the air, by
which the indoxyl is left behind as a liquid soluble in water, which
can be coloured by different impurities. Though the watery solu-
tion of this “purified indoxyl” is inconstant at the air, its oxidation
to indigo-blue proceeds slowly enough for studying the influence
which different substances exert on this process.

Various circumstances have induced me to put anew the question,
whether in this oxidation an oxidizing enzyme is active '). After
much doubt I have finally, as before, come to. the conelusion
that such is not the case. My primitive uncertainty was caused by
the very unequal acceleration of the oxidation of indoxyl solutions
by different powde:s spread on the surface. So the oxidation is
somewhat furthered by the erude enzyme of woad, and very
strongly, by that of Indigofera leptostachya, but by boiling, the
erude enzymes are by no means deprived of this property. By a
minute comparison of the behaviour ef crude indoxy] solutions pre-
pared from isatan and indican, with “purified” ones *), [ascertained

1) Mr. Briaupar erroneously asserts (Compt. rendus T. 127, p. 769, 1893: and

T. 128, p. 1478, 1898) that in the extracts of Isatis indigo-white occurs, W vhic h, by an
oxydase is turned into indigo-blue,

*) Besides from woad I prepared indoxyl by decomposing in a closed bottle a4 pure
indiean solution with indigo enzyme at “60° C. Moreover Mr, H. ER Meunen had
the kindness to prepare for me in the Chemical Laboratory of the Polytechnical School
indoxyl solutions in chemical way. The “purified” indoxyl was always obtained by
ether extraction.

(114)

that, both in the erude enzymes and in the erude indoxyl solutions,
there are present soluble and insoluble chemical compounds, which
influence the quickness of the indoxyl oxidation, but which are not
destroyed by enzyme poisons and by heating, and which accordingly
have not the nature of enzymes.

Crude isatase has neither an oxidizing action on pyrogallol,
hydrochinon, and guajac emulsion.

Though thus oxydase is wanting in the crude isatase, there is
present in it, as in all such like powders, prepared at random from
higher plants, peroxydase (“leptomine” of Racreorsk1) !), that is the
enzyme which, in the presence of hydrogen peroxyd, colours guajac
emulsion blue. But indoxyl is by no means oxidized by it to indigo.

6. Nekrosis and Nekrobiosis.

Living tissues can die off in two ways: by necrosis, that is the
dying of the protoplasm with simultaneous destruction of the enzymes,
and by necrobiosis, in which the protoplasm dies, but the enzymes
remain active. The phenomenon, formerly described by me as the
“blue stripe” in partly killed woad-leaves, on the confine of the living
and the dead portions, which both retain their green colour, reposes
accordingly on necrobiosis. The action of isatase on isatan explains
this phenomenon satisfactorily and renders my former hypothesis of
alkali formation at the dying of the protoplasm superfluous.

The simplest way to perform the experiment is to kill the tip
of a young woad-leaf in a Bunsen flame, or in the vapour of
boiling water, then to allow the leaf to remain at ordinary temperature,
by which in the said part alone indigo precipitates. If the chlorophyll
pigment is extracted with alcohol, then both the “living” and the
“dead” parts become colourless, the portion between them blue. The
phenomenon is best distinguished in young woad-leaves; in older
leaves, with a higher acid percentage, it is hardly to be observed
because the acid renders the isatase inactive.

In various other plants, too, nekrobiosis causes formation of pigments.
If these pigments are brown or black, and if the experiment is
performed in the usual way with the leaves of these plants, then
the coloured stripe may become still much more marked than in the
woad. Particularly fit for this demonstration are the leaves of Pyrus —
communis, Trollius, Aconitum, Asarum., Salix purpurea, Populus
nigra and several other species, which at necrobiosis turn of a jet

') Berichte der Deutsch, Botan, Gesellschaft. Bd. 16, pag. 52, 119, 1893,

Gils y

black and at necrosis remain green. Pear-leaves especially are
recommendable for the experiment; the enzyme in them is tyrosinase,
the nature of the chromogene is unknown, tyrosine it is not. Hence,
when preparing a herbarium, the chief thing to keep such plants
uncoloured, is to prevent necrobiosis. This frequently happens of
itself, as the acid cellsap is so much concentrated in drying, that
enzyme action cannot occur; so in the drying of woad-leaves, where
the highly sensitive isatase remains inactive. In other cases, to
obtain this end, it will be necessary to destroy the enzyme, either by
boiling water, or by poisonous vapours.

Sometimes necrobiosis gives rise to aromatic or stimulant matters,
which are present in the plant itself as glucosides, from which they
are set free by specific enzymes at the dying of the cells. This
fact is well-known regarding the myronates and the myrosine of
the Cruciferae, the amygdaline and emulsine of the Amygdaleae,
the spiraeine, gaultherine and gaultherase of Spiraca. But it holds
good, too, for the cumarine of Asperula oderata, which appears not
in it as such, but as a glucoside, which by necrosis continues unchanged
and henee can be removed from the plant by boiling, while there
is besides in this plant a specific enzyme, which by necrobiosis
produces from the glucoside cumarine. This enzyme is not identic
with emulsine and differs likewise from gaultherase. In a quite
corresponding way the aromas originate from the fruit of the
vanilla and the rovts of Geum urbanum.

The comparative study of necrosis and necrobiosis in plants shows
the way for the detection of a number of new chromogenes or
glucosides and specific enzymes,

3 Conclusions.

Indoxyl eceurs not, as I formerly thought, in a free state in the
woad but as a loose compound, called by me isatan.

Isatan is only constant in feevly acid solutions, and is obtained
by extracting the woad therewith. It is decomposed, under format-
ion of indoxyl, by alkalies and stronger acids, and in solutions, less
acid than 1.5 ce. of normal acid per 100 ce., by an enzyme, isatase,
which acts the most vigorously at 50°C., and occurs in all parts of
the woad-plant.

Isatan is not decomposed by the indigo-enzymes nor by microbes
in as much as the latter do not form alkali. Isatase does not act
on indican.

Jsatase is localized in the chromatophores, isatan in the protoplasm,

( 116 j

which is in accordance with the formerly described localisation of
the indige-enzymes and of indican.

If woad is extracted without acid, so that the isatase can act, or
with dilute alkalies, e.g. !/. pCt. solution of dinatrium phosphate,
indoxyl is produced.

The necrobiotic stripe in partly killed woad-leaves results from
the action of isatase on isatan.

Geology. — “The Amount of the Circulation of the Carbonate of
Lime and the Age of the Earth”. 11. By Prof. Eve. Dusots.
(Communicated by Prof. J. M. van BEMMELEN.)

In my first communication on this subject I have quoted a num-
ber of reliable data from which it follows that the waters of those
rivers in whose drainage areas much limestone occurs, as is mostly
the case with the larger rivers, are more than saturated with carbon-
ate of lime, when reaching the ocean.

In consequence of their being polluted, to an extraordinary high
degree, with organic matter, the quantity of carbonate of lime in
the waters of many rivers of that kind, whose drainage areas are
very thickly populated, in Europe and partly too in other parts of
the world, is larger than in the primitive condition, before man
existed in large number, thus during almost the whole past of the
earth. In this respect I draw attention to the relatively higher quantity of
carbonate of lime in such rivers as the Thames and the Seine, and
also of the difference in that quantity between small and large rivers
and lakes, as well as of some other facts showing the influence of
the pollution of the water by organic matter on the relative quantity
of dissolved carbonate of lime. ‘Ihe drainage water of soils, rich in
humus, holds, for instance, considerably more carbonate of lime in
solution than would correspond with saturation under the only
influence of the atmospheric carbonic acid. But down the course of
the rivers the last influence becomes by far the more preponderant.

Taking into consideration that in general the quantity of carbonie acid,
produced by the decomposition of organic matter, increases somewhat
at the mouths of the rivers, where much of that matter settles, and
starting from the existing analyses, it seems to me that an average
quantity of 95 mgrms. carbonate of lime per litre of water would
represent, on the whole, with approximative accuracy, the primitive
condition at the mouths of those rivers which have been so largely

in contact with limestone that their waters could be saturated with
‘arbonate of lime.

ene),

This ample contact of flowing waters with limestone seems to
exist in almost every case, where true sedimentary formations pre-
dominate in their drainage area. Where, on the contrary, crystalline
silicate rocks prevail in the drainage area, the quantity of carbonate
of lime in solution decreases in the river-waters to a more or less
lower amount.

According to the analyses by Kyle, quoted in my first paper, the
Rio de la Plata keeps, 8 KM. above Buenos-Aires, per litre of
water only 23 mgrms. carbonate of lime in solution. he drainage
area of this large river consists for the larger part, by the side of
Pampas-formation, of sandstones, Archean crystalline rocks and only
little Palaeozoic rocks. The Amazonas, which, between the narrows
and Santarem, keeps, according to the quoted analysis by Frankland,
27.5 and at Obidos, somewhat up the river, according to two other
analyses, by Katzer, 11.4 to 14.6 mgrms. carbonate of lime in solu-
tion per litre of water !), drains principally regions of gneiss, sand-
stones and clays. The same is the case with the Rio Paré (Tocantins),
which, according to the analysis of a sample of the water from the
harbour of Paré, taken during very low tide, keeps in solution
12.4 mgrms. carbonate of lime per litre of water ').

The waters of most of the rivers and river-lakes mentioned in this
and in my first communication, as examples of the kind keeping
fewer dissolved carbonate of lime in solution than the quantity cor-
responding to saturation, have, however, not been exclusively in
contact with silicate rocks, but also with some limestone.

The waters of some other, mostly small, river-lakes on the contrary,
have not been in contact with limestone and derive the calcium
carbonate they keep in solution entirely from the decomposition of
silicate rocks or the desintegration products of silicate rocks. Such
are those from the Lake of Starnberg, with 4.8 mgrms., Loch Katrine,
with even much less than 4.8 mgrms., Reindeer Lake, with only :
slight trace, and the Rachel-See, with 2.22 merms. calcium carbonate
per litre of water; further the five named small French Jakes with
outlet, surrounded by granite and basalt, having a mean quantity of
8.9 mgrms. calcium carbonate in solution per litre of water.

For a comparison of the relative quantity of calcium carbonate in
the five latter small river-lakes, draining regions of silicate rocks,
with that of five equally small French river-lakes, in whose drainage

1) F. Kagzer, Das Wasser des unteren Amazonas. Sitzungsberichte der Kin. Bélimi-
schen Gesellsch. d. Wissensch. Math, naturw. Classe. Jahre. 1897. Prag L898, N°XVL,
p- 3—6 and 8.

-

( 118 )

areas limestone abounds, and which are likewise situated on a high
level, I have dressed the subjoined table !).

Height above sca- Volume, CaCO,, in mgrms.
Lakes of level, in M. inmillionsof M*. — per litre.

Issarlés 997 60.0 10.9
Pavin 1197 23.0 13.7
Gérardmer *) 660 TON 7.5
Chauvet 1166 17.3 6.5
Gov ivelle-d’en-Haut 1225 rei 5.0

Mean 8.9
Paladru 501 97,2 150.9
Chalain 500 46.6 136.4
Nantua 475 40.1 155.5
Remoray 851 12.1 182.0
Sylans 5S4 4.8 152.6

Mean 155.5

The mean relative quantity of CaCO, in solution in the latter
group is 17.5 times as high as that of the first group of river-lakes.

Concerning the waters of the rivers and river-lakes, which have
a higher relative quantity of calcium carbonate than those of the just
mentioned lakes in granite and basalt, we can trace in most cases
that, although they flow over crystalline rocks, they also have had
an opportunity to dissolve some calcite.

So in the cases of the Rio de la Plata, which contains 23 and
the Amazonas, which contains 11.4 to 27.5, of the Rio Para, which
keeps 124 mgrms. CaCO; in solution per litre of water, of the
Dwina with 20.2, the Delaware with 25, the Croton River with
28.5, the Ottawa with 24.8, the Moldau with 19.4, the Uruguay
with 16.2, Lake Superior with 30.8, Lake Tahoe with 23.2, Lake
Baikal with 40.1 mgrms. CaCO, in solution per litre of water.
The Hudson River, with 42 mgrms., is moreover connected through

1, The figures here quoted are also taken or caleulated from the statements in
DeLepegue’s Laes francais. The reader will have noticed, that in the small table on
p- 8 (51) of my first communication the volumes should be in médlions of MA’

2) The gnantity of CaCO, given here, which is also taken from DeLEBrqur’s Lacs
francnis, concerns the water of the surface, the formerly given the bottom water,

(119 )

a channel with Lake Ontario, which is rich in dissolved carbon-
ate of lime. For Lake Tschaldyr there is not sufficient infor-
mation available to judge whether we have to think of the same
mixtion with dissolved CaCOs or that the relatively high quantity ot
this matter is indeed to be interpreted by a particularly quick decom-
position of silicates, as supposed in my first paper.

From all the available data it is evident that the quantity of
calcium carbonate in solution in river waters is determined by the
nature of the rocks with which they have been in contact. Indeed
a great contrast is to be observed between the waters containing only
the lixiviation products of erystalline silicate rocks and those flowing
to some extent over true sedimentary formations. In the latter case
the contaet of the waters with limestone proves almost always sufli-
cient to bring about a saturate] solution of calcium carbonates.

If we estimate that in regions consisting entirely of crystalline silicate
rocks —— all other circumstances being equal — on an average a
tenth part carbonate of lime is annually carried in solution by the flowing
waters as in regions where limestone abounds, this estimate certainly
remains rather below the real proportion.

Assuming moreover that the regions of the earth consisting of
erystalline silicate rocks are on the whole in contact with as much
flowing water as those where only true sedimentary formations are

found — an assumption we may make with safety, as appears
from . the comparison of pluvial with geological maps — and

taking, further, according to the figures given by Tillo, that the
erystalline silicate rocks cover the fourth part of the land area of
the globe, we find that the latter produce 9.5 parts carbonate of
lime in solution at the same time as the remaining area of the land
3X 95 or 285 parts. According to this calculation the river-
waters which are discharged into the ocean contain on an average
74 megrms. carbonate of lime per litre and carry every year 2
billions (or 2 X 10!?) K.G. carbonate of lime into the ocean, a value
already mentioned in my first paper, though not yet explained.

According to this estimate the quantity of the calcium carbonate
newly formed every year amounts only to a thirticth (more exactly
'/3)) part of the total quantity which the ocean receives every year.
Annually there are thus formed from silicates 64.5 milliards (or
64.5 X 10°) K.G. of calcium carbonate, containing 28.4 milliards (or
28.4 < 10°) K.G. of CO, in stable combination.

‘jhe earth having been evolved from a white hot liquid state, by
cooling, and consequent envelopment with a solid crust, to its
present state, we must assume that all the carbonate of lime arose

( 120 )

from the silicates of that crust. Silicie acid, being present in very
great surplus in the erust of the earth, would, as is well known, al-
ready at boiling temperature of water have decomposed eventually
extant carbonates. The formation of the crust, however, must
have begun about 1000° C., for the melting-points of most silica-
tes are between 900° and 1500° C.!). The carbonates, therefore, can
only have come into existence after the formation of a solid crust of al-
ready considerable thickness. As shewn by Lord Ketyin, rather soon
after beginning solidification the temperature at the surface of the
earth must have been almost exclusively under the influence of the
radiation of the sun. At the end of 100 years this temperature may
have been about 8° C. higher, and at the end of 100 centuries 0.8° C.
higher than without underground heat *). We therefore may take
it for granted that, considered from a geological point of view, the
formation of the carbonates from silicates was initiated at the same time
with the beginning of the condition of temperature, which made the
earth an abode fitted for life.

If, therefore, we did know the average progress of this formation
process as well as the total quantity of carbonates now extant, we should
also know the time which has elapsed since the earth became fitted as
an abode for life. As concerns the quantity of carbonates, besides
the caleium carbonate, only the magnesium carbonate has to be taken
into consideration; the other carbonates exist in relatively so small
quantities, that in the very approximative calculations, concerned
here, they may be neglected.

The proportion of the quantities of CO, in combination, as Ca COs
and as MgCOs, is for the water of the Rhine at Mayence%) probably
about 3.3, for that of the Meuse at Liege 5.08, of the Danube at
Vienna 2.36, of Thames *) at Kingston 8.33, of the Seine °) at Paris
5.17, of the Loire ®) at Orleans 6.62, of the Spree’) above Berlin

1) J. Joly, The Melting Points of Minerals. Proceedings R. Irish Academy
1891, If., p. 44.

2) On the Secular cooling of the Earth. Transactions of the Royal Society of
Edinburgh, Vol. 23. Compare also Lord Kexvin’s latest paper on the subject:
On the Age of the Earth. Annual Address for 1897 of the Victoria Institute
of London, p. 21.

5) According to the analyses during a year by E, Eaeer (Chemisches Centralblatt
1888, p. 1131 and Ref. in Jahresber, iiber die Fortschritte der Chemie. 1888, p. 2762.)

A) Winal kc: poellG:

5) PocerAre, ref. in Jahresber. iiber die Fortschritte der Chemie fiir 1855, p. 833.

®) Brsscnor, l.c., p. 273.

7) Roru, l.c., p. 457.

(121 )

7.09 of fhe Vistula’) at Culm 5.28 of the Nile at Cairo probably
about 3.00, of the Blue Nile at Khartoum 1.97, of the Syr-Darja
0.96, of the Rio Negro*) at Mercedes in Uruguay 5.44, of Lake
Peipus 3.68, of the Lake of Geneva 3.08, of the Lake of Zurich *)
3.92, of the Lake of Bourget 4.42, of the Lake of Annecy 5.69 of
St. Lawrence River 2.66, of the Lake of Gmunden 2.97, of the
Take of Saint-Point *) 11.55. The mean proportion in these twenty
waters, which flow over true sedimentary formations, and are satu-
rated with calcium carbonate, is 4.63. If this proportion, in which
both carbonates are redissolved from sedimentary strata, also indicates
the proportion in which they formerly originated in silicates, about
1, of the CO, consumed in the evolution of the carbonates would
have been taken by MgO.

It appears to me that the following considerations may lead to an
approximative estimate of the quantity of the carbonic acid consumed
and fastened in these carbonates.

It is most probable that all the oxygen, which now partakes of
the composition of the atmosphere, and even more, has entirely or-
ginated in carbonic acid gas through the assimilation process of the
plants. In the rocks composing the earth’s crust there is a great
deficiency of chemically fixed oxygen, which would not be the case
if in the former, hot, state of the earth there had been a sufficient
quantity of oxygen available. According to CLARKE’s analyses ®)
the rocks which compose the earth’s crust consist on an average of
3.44 pCt. of FeO, thus an incompletely oxydized combination of iron.
From the analyses of 83 basalts and diabases, published by ZrrkeEx ©)
and RosENBusCH ’), a mean percentage of 6 FeO is to be caleu-
lated, from the analyses of 29 granites a mean of 1.5 pCt., of 47
gneisses a mean of 3.8 pCt. Starting from the proportion given by
CLARKE we may estimate, that all the O of the atmosphere would

1) Bisscuor, |. ¢., p. 275.

2) ScHOELLER, I. c., p. 1787.

3) Rotu, lee. p. 457.

4) The Lake of Saint-Point, through which the Doubs flows, and whose water,
having a volume of 81,6 millions of M%., is renewec in 205 days, contains, according
to DELEBECQUE (Les Lacs francais, p. 202) 136.4 mgrms. CaCO, per litre of water.

5) BF. W. Crarke, The relative Abundance of the Chemical Elements. Bulletin 78,
United States Geol. Survey. Washington 1891, p. 37 and Thid. No. 148. 1897, p.12.

6) FB. Zrrket, Lehrbuch der Petrographie. Zweite Auflage, Leipzig 1893. Band II,
p- 29 and p. 901; Band III, p. 80 and 223,

7) H. Rosensuscu, Elemente der Gesteinslehre, Stuttgart 1898, p. 78, 308-309
and 468—471.

only be sufficient to oxydize the FeO that is contained in the
earth’s crust to a depth of less than '/9 K.M. All the parts of the
crust, which are no true sedimentary formations, up to the surface,
are, however, rich in Fe O.

In the reduction of carbonic acid through the plants there having
been made free an equal volume of oxygen, and the oxygen in the
atmosphere having a volume 700 times as large as that of the carbonic
acid therein, there must have been in or passed through the atmos-
phere at least 700 times as much carbonic acid as it contains at
present. Another quantity of the oxygen made free through the
agency of the plants, which quantity it is impossible to estimate,
was certainly consumed for the oxydation of FeO and other consti-
tuents of the crust which are poor in oxygen.

It appears, therefore, that when the earth was in the white hot
fluid state there could not exist any free oxygen. That which was not
combined with carbon or hydrogen would have been taken by FeO,
and as there is still much FeO, certainly to a depth of many K.M., in
the earth’s crust, apparently at the beginning formation of that crust
no free O can have been in the atmosphere. The quantity now in the
atmosphere must be rather less than that formed from the consump-
tion of free CO, reduced through the agency of the plants, for younger
sediments are certainly poorer in FeO, and must therefore have consu-
med O. There has, however, at the same time with that oxydation,
taken place reduction of combinations of iron by organic matter. The
clay deposited by the Rhine in the Delta of the Lake of Constance
contains, besides 1.66 pCt. organic matter, 3.23 pCt. FeO; slates from
the carbonic formation, besides 0.7 pCt. organic matter, 4.73 pCt. FeO).
In consequence of this reduction again CO, is coming into the atmo-
sphere, from which again O is set free through the agency of the plants.
So from 1 volume of COg, which originally was in the atmosphere, there
may be formed 2 or more volumes of O*). That reduction of Fe: 0; com-
binations takes place on a grand scale is proven by the existence of
the blue mud, which covers an area 37.6 millions of K.M.? or more than
‘yo of the floor of the ocean, and which owes its colour to organic
matter and FeS:. Also the slates contain much FeO; as the mean
percentage of 16 slates, of which the analyses are given by CLARKE,
3.25 is to be computed. In the waters of the larger rivers and

1) Rosenbuscu, 1. ¢., p. 413.

2) Of course only a superior limit for the amount of coal and other carbonaceous
remains of organie origin in the earth’s crust may be deduced from the 700 a parts
of COs, which have passed through the atmosphere, as the C of these has, in such a
manrer, been made use cf several times,

¢ 123 )

lakes, on the contrary, are to be found in solution combinations of
Fe,O, only.

But whatever may be the source of the CO, from which the O of
the atmosphere has been set free through the assimilation process of
the plants — for another process, which can produce O on a large
seale in nature we cannot imagine — we must take it for granted,
that an equal volume, that is at least 700 times the quantity of free
CO, now extant in the atmosphere, has been in it, and most probably
has gradually passed through it. Now too the supply of carbonic
acid, through the volcanic activity of the earth (which certainly is
the chief source) and the consumption, through the fossilisation of
carbonaceous organic remains, and in still much higher degree that
through the formation of carbonates, which according to the above

1 ; ;
made estimate now annually requires aaah of the quantity of carbonic
fo

acid in the atmosphere!), take place gradually. In all past times that
consumption, as is shewn by the immense carbonaceous formations
of organic origin and mighty strata of carbonate rocks, has been so
large that we hardly can imagine but that this consumption and the
supply from the interior of the earth have been equipoising processes.

Now Scuiam@sine*?) has shewn, that for water which keeps in
solution other salts (of natrium, magnesium, calcium) the quantity of
the bicarbonate formed may be different from that formed in pure
water, but that nevertheless, as in the latter case, it increases with
the tension of the carbonic acid gas, so that there arises again a
state of equilibrium between it and the tension of the carbonic acid
gas. ScHL@sING, further, pointed out that in the water of the ocean,
which since many thousands of centuries has been in contact with
the atmosphere and with the calcium carbonate of its floor, its shore
and the supply of the rivers, there is a continual tendency to acquire
this equilibrium. Variations in the quantity of the carbonic acid
of the atmosphere will cause emission of carbonic acid from the
ocean-water and severing of solid carbonate, if the variation is a
decrease, or absorption of carbonic acid and dissolving of carbonate,
if the variation is an increase. SCHL@sING then calculated the quan-
tities of carbonic acid contained in free state in the atmosphere, and in

1) The amount of the carbonic acid in the atmosphere is taken in this caleulation at
2140 billions KG. (which value is equal to 75400 x 28.4 milliard) from the averages
stated below for the percentage of carbonic acid and the atmospheric pressure.

2) Tu. Scuie@stnc, Sur la constance de Ja proportion d’acide carbonique dans
Yair. Comptes rendus des séances de l’Académie des Sciences. 1880. Tome 90, p.
1410—1413.

9

Proceedings Royal Acad. Amsterdam. Vol. LUT.

( 124 )

loose chemical combination in bicarbonate in the ocean. He found
that the ocean keeps in reserve, and at disposal for exchange with
the air, a quantity of carbonic acid ten times as large as the total
quantity which the atmosphere contains, and concluded therefrom
that the ocean exercises a regulating influence on the quantity of
the carbonic acid of the air, acting as a reservoir which holds a
quantity of carbonic acid at disposal very much larger than the quan-
tity which constitutes the variation in the air.

The volume of the water of the ocean is, however, much larger
than ScuLta@stmne had assumed. Computed from the most recent and
reliable data for the area and the mean depth of the ocean it
comes to 1300 million K.M*. If we accept the mean quantity of
loose carbonic acid of 43.6 mgrms. per litre of ocean-water, accor-
ding to Dirrmar, the mean atmospheric pressure at the surface of
the earth of 740 mM. and the mean percentage of carbonic acid in
the air, in volume, for both hemispheres, according to Mtnrtz and
Austin '), of 0.027385, we find that in the ocean there is, in com-
bination as bicarbonate, 26,5 times as much loose carbonic acid and
also 26.5 times as much carbonic acid in stable combination as in
the air in free state. Starting from the whole quantity of 55 mgrms.
carbonic acid in stable chemical combination per litre of ocean-
water, stated by Dirrmar, or from that of 53 mgrms., according to
other statements, we further find, that in the water of the ocean
33.4 or 32.2, say 33 times, as much carbonic acid is in solution,
in stable combination in calcium carbonate and bicarbonate, as the
quantity of the free carbonic acid contained in the atmosphere. The
quantity of the bicarbonate, however, alone is dependent on the
pressure of the carbonic acid.

There being in the ocean 26.5 times as much loose carbonic acid
as contained in free state in the atmosphere, the ocean has of every
variation in the total quantity of carbonic acid by far the largest
share. Of 27.5 parts carbonic acid which are to be disposed of or which
are consumed, it always takes or gives 26.5 parts, and it has done so
as long as its volume, its composition and its mean temperature and
the pressure of carbonic acid did not differ much from the present
state. Slight modifications of the pressure of carbonic acid, such as most
probably have only taken place, can neither have had any noticeable
influence. If, in fact, the quantity of the free carbonic acid in the
atmosphere even changed with 60 pCt., the quantity of the carbonic
acid taken up by the ocean in loose combination, according to the

A Lecpepr A See

law of ScHLa@sinc, would only vary with 16 pCt. or about 1).
Calling the quantity of the loose CO, in the ocean 0, that of the free CO,

0 5
in the atmosphere a, we find that — would come to 19.23 instead of
a

26.5. To 1 part of free CO, in the atmosphere, the ocean would
then only contain 19.23 parts of loose CO, in combination as bicar-
bonates, i.e. 0.725 of the actual proportion. In order, however, to
cause this variation of 60 pCt. in the pressure of the carbonic acid
in the atmosphere, the production or the consumption should undergo
a variation of 0.6 X 19.23 or more than 11.5 times the quantity
of carbonic acid at present in the atmosphere. Variations of the
quantity of carbonic acid in the atmosphere of so great an amount, that

5 : 0
they might have considerable influence on the value > ue therefore

indeed highly improbable, as it appears that the consumption of
carbonic acid regulates itself after the production.

As pointed out by Hoepém ') production of carbonic acid chiefly takes
place by voleanic exhalations and geological phenomena connected there-
with, and consumption by the formation of carbonates from silicates on
weathering. “As the enormous quantities of carbonic acid, represen:
ting a pressure of many atmospheres, that are now fixed in the
limestone of the earth’s crust cannot be conceived to have existed
in the air but as an insignificant fraction of the whole at any time
since organic life appeared on the globe” the consumption through
formation of carbonates and the storing up in sedimentary formations
of carbonaceous remains of organisms must have been compensated
by means of continuous supply, that is. to say the two processes must
always have nearly counterbalanced each other. May it be that the
mentioned source of carbonic acid has not flowed regularly, but, just
as single volecanous, has had its periods of relative rest and intense
activity, and has produced now less, then again more carbonic acid,
on the other hand also an increase of the supply surely causes an
increase of the consumption. But even the relatively slight alterations
of the quantity of carbonic acid in the air, which according to
Hoarém may still be allowed, are entirely prevented by the vege-
table world. The decomposition of CO, through the green plants
varies with the tension of that gas in so high a degree, and the
absolute quantity of CO, which annually is decomposed by the vegeta-

") Quoted by S. Arruenius, On the Influence of Carbonic acid in the Air upon
the Temperature of the Ground. Philosoph. Magazine. Vol. 41, (1896) 5th. Series,

p. 272.

g*

( 126 )

tion is so large (namely about 1/5) of the whole quantity in the
atmosphere) that soon the former percentage of CO, in the air, on
which plant life is regulated, would be restored.

On account of the facts discussed in this and in my first paper
we may assume, that certainly not more than one thirtieth part of
the carbonate of lime, which the rivers now discharge into the ocean
is newly formed from silicates. In the past, when still more silicate
rocks lay uncovered at the surface of the earth, this quantity must
have been larger. At the time the earth’s crust consisted still enti-
rely of them, the carrying of newly formed carbonate of lime would,
under otherwise similar circumstances, certainly not have been more
than one eighth part of the quantity of the carbonate of lime now
carried by the rivers to the ocean, and which is by far the greater
part only circulating (redissolved) carbonate of lime. As the silicate
rocks have gradually been covered with sedimentary strata that pro-
portion must gradually have got smaller. If we take the most simple
and most probable case, that this decrease took place proportionable
to the time, then on an average 0.08 of the present annual carrying
of calcium carbonate by the rivers would every year have been newly
formed, thus 160 milliards (or 160 x 10°) K.G., containing 70.4
milliard (or 70.4 & 10°) K.G. of CO, in stable combination.

In the long run the consumption of CO, for the formation of
carbonates from silicates and that for the formation of oxygen are to be
considered as two processes, parallel in their magnitude, which, if other
circumstances do not vary, are dependent on the pressure of the
carbonic acid in the atmosphere. It is clear that the oxygen which
only circulates through the plants is not concerned here. the cir-
culating oxygen again serving for the oxydation of organic matter,
just as the circulating calcium carbonate does not consume any
sarbonic acid, there being used tor the formation of bicarbonate as
much as is set free again when it returns into the solid state.
However, to 700 a parts of free carbonic acid, consumed for the
storing up of oxygen, in the atmosphere, 26.5 x 700 or 18550 a
parts must have been liberated from bicarbonates in the ocean,
and thus at least 18550 @ parts of carbonic acid in loose, and an
equal quantity in stable chemical combimation haye been in bicar-
bonates redissolved from solid carbonates.

When thus at least 700 a parts of free carbonic acid in the atmosphere
have been turned into oxygen, there must have been consumed in the
waters of the rivers and the ocean at least 26.5 & 700 x 0.03 or 1484
a parts carbonic acid for the carbonates newly formed from silicates.
Thus we find that, from the time the globe, by cooling, has been sur-

(127)

rounded by a solid crust, at least 7.22 trillion (or 7.22 x 1018) K.G.
calcium carbonate have been formed which, equally spread over the
whole area of the land of the globe, would be able to form a
layer of limestone everywhere about 20 M. thick!). Of course this
is only a minimum, as the value 700a@ also is a minimum. Accord-
ing to the estimates of MELLARD Reape”) and Dana *) the mean
thickness of the limestone under the land area of the globe would
be 28 to 52 times as large. Assuming that the rivers carry to the
sea on an average 450 mgrms. per litre or 6 times as much matter
in suspension and in solution as they do carbonate of lime in solu-
tion, this proportion would lead us to impute to the sedimentary
rocks under the continental areas an average thickness of about
3000 to 6000 M., certainly no too high estimates.

The time required for the evolution of that minimum amount of
carbonate of lime from silicates it is, after these considerations, very
easy to estimate.

In the same way as the quantity of the bicarbonates in the ocean,
the average quantity of the bicarbonates in the river-waters is depen-
dent on the pressure of the carbonic acid in the atmosphere. So the
ratio between the average quantities of the bicarbonates, which the
rivers have annually carried into the ocean, and the total of those
which were in solution in the ocean is independent of the pressure
of the carbonic acid in the atmosphere. Whatever variations the
pressure of that gas in the atmosphere may have undergone, at any
time in the past history of the earth the ratio between the quantities
of those salts in solution in the ocean-water and the river-waters
was not changed thereby. Further there must exist between
the total quantities of the redissolved and the newly formed
bicarbonates, which in the ocean have ever passed from the
dissolyed into the solid state, the same ratio as in the river-
waters, for the ocean-water owes its provision of those salts
to the rivers. As now the rivers carry annually two billion K.G.

calcium carbonate in solution, containing a carbonic acid, a

2432
total amount of 18550 2432 or 45 million times that quantity,
in combination in calcium carbonate, has in the ocean passed from
the dissolved into the solid state.

1) Reckoned on a basis of 8 pCt. impurity.

2) Limestone as an index of Geological Time. Proc, Royal Soc. Vol. 28. London,
1879, p. 281.

©) ab.

( 128 )

Therefore the formation of the whole estimated minimum amount
of carbonate of lime on the earth would require about forly-five
millions of years, that of the real amount, however, a very much
larger lapse of time.

It appears, furthermore, that —

1
2.770.000. of the total quantity of

the carbonate of lime of the earth participates annually in the present
circulation.

The amount of carbonic acid corresponding to the limestone rocks
and carbonaceous formations in the earth’s crust has been estimated
very differently, namely between 12.000 and 15.0000 times the quantity
of free carbonic acid contained in the atmosphere. The newest
estimates differ somewhat less from one another. HéGBom !) considers
it as probably underestimated, if we take that 25000 as much
carbonic acid is fixed in the limestone of the sedimentary formations
as exists in free state in the atmosphere. Dana *) calculates the
quantity of carbonic azid, corresponding to the limestone and to the
coal, mineral oils and gasses in the earth’s crust on 45 atmospheres,
that is 100.000 times the quantity of free carbonic acid in the atmos-
phere. CHAMBERLIN *) estimates, without indicating his method, that
quantity on 20.000 to 30.000 a. At all events these geological
estimates all differ too much from the minimum of 1484 a, ealcu-
lated above by indirect way, that the presumption should not
been raised — if indeed the bases of these estimates are in some
degree reliable — that the value 700 a, from which the present
calculation started, is only a minimum, and that indeed very much
oxygen from the atmosphere has been taken away by oxydation of
substances in the earth’s crust which are poor in oxygen.

On the calculated number of 45 millions of years some corrections
are to be made. Firstly this number should be diminished with at
least a sixth part, because the carrying of carbonate of magnesia
through the rivers has not been taken into account. Secondly the
eroding agency of the ocean has not been considered; the ocean too
assailing, at its border, silicate rocks and the forming of carbonates
taking place there too. But thereby the number can decrease only
little, as the eroding influence of the ocean is but slight compared
to the agency of the waters on the land. Dp Lapparent*) estimates

1) 1. c. p, 271.

*) J. D. Dana, Manual of Geology. Fourth Edition. New-York 1896, p. 485.

4) T. J. CiamBrruin, Journal of Geology, Chicago 1897, p. 656.
‘) A, DE Lapparent, Traité de Géologie. 4me Edition. Paris 1906, Tome I, p. 242.

oe oh

( 129 )

the proportion on less than 1 : 10 and Jony*) even on Ly. sual Gs
Thirdly the rivers may have discharged more water during the
prevailing of warmer climates, thus during the longest time of the
past of the earth. Neither can this influence, by which the stated
number would get smaller, have been considerable, for, according
to figures given by Murray ”) the rivers under the present condi-
tions discharge — at equal drainage area — in the area of the land
between 30° North and 50° South of the equator on an average
only 1.55 times as much water as outside of the 30° North and
South. It therefore would certainly be too high an estimate assuming
that, at the time when over the whole earth a tropical climate pre-
vailed, the discharge of water, and therefore too the carrying of
calcium carbonate (which at higher temperature of the water is even
somewhat less soluble) had been one and a half time as high as at
present. Fourthly the weathering of silicates and the formation of
carbonates may have been more rapid on account of the temperature
having been on the whole higher, of a more abundant supply of
carbonic acid or of more rapid changes in orographic and hydrogra-
phic conditions. These factors too would diminish the stated number,
but probably not considerably. Fifthly the ocean has originally been
less salt; though already in such old formations as the cambrian
mighty beds of rock-salt occur, a proof that in this factor is not to
be sought the cause of important changes in the absorbing power
of the ocean for carbonic acid, and therefore, by modifying the pro-
portion 0: a, of the time required for the formation of the limestone
rocks, a modification that would also diminish the stated number.
Sixthly a higher average temperature of the ocean-water would decrease
the proportion 0:a; at a homogeneous tropical climate of the earth
probably about 20 pCt., with which amount the estimated time also
would have to be diminished. Seventhly the volume of the ocean-water
could haye decreased; but the analyses of the rocks show that in
such a manner at most a decrease of a few hundredths parts could
have taken place. On the contrary much water is produced in
yoleanie exhalations and connected geological phenomena.

All those influences, hewever, which would decrease the result
of this time estimate, apparently do not counterbalance together the
one influence of the loss of oxygen from the atmosphere by the
oxydizing of FeO and similar substances poor in oxygen, so that

1) An Estimate of the Geological Age of the Earth. Scientific Transactions Roy.
Dublin Society. Vol. VII (Series IL). Dublin 1899, p. 63.
2) 1. «, p. 70.

( 130 )

it appears, that we may assume, that the formation of the carbonates
from silicate rocks has required at least some decuples of millions
of years, and this the earth’s crust also exists at least the same
length of time. But this is a minimum; the real lapse of time
since the formation of a solid crust and the appearance ef life upon
the globe may be more than a thousand million of years.

This final result of the investigation, however little claim it may
make to exactness, might nevertheless interest geologists and biologists,
who generally demand such a vast space of time. Moreover this
result would be of some importance, if it should suggest nearer trial
of the so called physical methods of estimating the age of the earth,
by which Lord Krnvin has acquired unperishable merit for geology
and biology, a trial which in many other respects too is desirable and
promises important results. In his already quoted latest paper on this
subject !) Lord Krnvrin estimates the age of the earth’s crust, on the
basis of these methods, at about 24 millions of years, and the sun he
estimates about as old. It seems possible to modify some factors in
the calculations of Lord Krtyin in such a way that higher results
are obtained. The here sketched geological method appears to con-
firm that opinion. May it therefore be further worked out and lead
to a more exact estimate of the age of the earth as an abode fitted
for living beings than the estimates hitherto obtained.

Zoology. — “further results of an investigation of the Monotreme-
skull’. By J. F. vaN BemMeten, The Hague (Communicated
by Prof. C. K. Horrmann).

I. Palate.

In a former note *) the curious fact was mentioned, that in the
Echidna-skull the pterygoids form part of the floor of the cerebral
cavity, fillmg up a gap between the body of the sphenoid bone and
its posterior or temporal wings (alisphenoids), so as to be visible on
the inner side of the skull-bottom. To this we may now add,
that the same is the case with the palatine bones. In a skull, in
which the majority of the sutures could still be distinetly traced, a
slender porterior process of the palatine was seen running down on

1) On the Age of the Earth, p. 11 and 25.
*) These Proceedings. October 25% 1899. p. 81.

(131 )

either side of the sphenoid body, separating it from the pterygoid.
Both palatine and pterygoid took part in the formation of the median
border of the oval foramen, the palatine forming the anterior, the
pterygoid the posterior part of this border. Only at a very advanced
stage of growth, the lateral border of the foramen in question also
gets closed up by bone, i.e. by that thin bony plate, which in my
opinion must be considered as representing the alisphenoid (l.c. p. 82).
The antero-median angle of this ossification reaches the posterior
border of the curious temporal wing of the palatine, likewise men-
tioned in my first note.

Of course only that part of the palatine is visible at the inner
side of the skull-bottom, which is not overlapped by the body of the
sphenoid. This part amounts to about the lateral third of the pos-
terior palatine processus (situated behind the temporal wing). The
middle strip is covered by the side-border of the corpus sphenoidei,
while the inner or medial third-part projects as far as the middle
line of the skull forming the floor of the nasal canals. It is well-
known, that in Kchidna this floor is incomplete, the palatine plates
diverging posteriorly, so as to leave open between them a deep fis-
sure which however, in Proéchidna, is reduced to a mere concavity
of the transverse hind-border.

It needs hardly to be specially mentioned, that the participation
of membrane-bones of the roof of the buccal cavity, such as the pala-
tines and pterygoids, to the formation of the floor of the cerebral
skull, can only be explained by the supposition that the primary
cartilaginous skull-floor has suffered complete reduction within the
limits of these bones. At the same time this hypothesis gives an
explanation of the fact, that the ali-sphenoids do not reach the cor-
pus sphenoidei: the cartilage, that was to bring about this connec-
tion having disappeared early instead of ossifying. The same phe-
nomenon must have occurred on the outer side of the region of ptery-
goids and palatines, leading to the formation of the great gap or
fontanella in the temporal area of the skull-wall, which is so cha-
racteristic for young Echidna-skulls. The alisphenoidal ossification,
which finally closes up this gap, must thus develop in membrane,
and must permanently remain separated from the corpus sphenoidei.

The probability of this supposition receives a firm support by
the comparison with the skull of the Echidna-pouch-suckling. This
‘shows the primordial cartilage still in situ under the osseous ptery-
goids and palatines, though it is totally absent in the region of the
above-mentioned temporal fontanella. The final disappearance of this
cartilage, leading to the entrance of pterygoids and palatine-processes

®

( 182 )

into the composition of the skull-floor, must therefore oceur ai a
relatively advanced stage, at all events after birth.

Il. Sguamosal.
q

In a recent publication’), Prof. V. Sixra, has made a comparison
between the skulls of the Monotremes and that of Psammosaurus
griseus, and has come to the conclusion, that the former agree with
the latter in most respects, notably in the possession of a quadrate
bone. In Ornithorhynchus this bone is said to bear the glenoid
surface for the under-jaw, in Echidna, on the contrary, it is said to
form a bony bridge on the ventral side of the stylo-mastoid foramen.

In order to verify the correctness of this assertion, | once more
looked over my material of young and adult Monotreme skulls, but
I was not able to find any trace whatever of a separate quadrate
bone, not even in the skulls of newly-born (or still unborn) suck-
lings. Moreover the osseous bridging over of the stylo-mastoid-foramen
mentioned above is no peculiarity of Echidna alone, but occurs as
well and in the very same spot in Ornithorhynchus, with only this
restriction, that it does not completely surround the ventral side of
the foramen, but leaves open a small gap at the medial side.

If therefore this bone-bridge did really represent the Reptilian
quadrate, the same designation could never be applied to a far more
laterally-situated part of the Ornithorhynchus-skull. In my opinion
however we have no right at all to consider either part of the Mono-
treme skull as a quadrate: the glenoid fossa of Ornithorhynchus
simply forming the ventral face of the squamosal, whereas the bony
bridge under the facialis-foramen of both genera is a part of the
mastoid, and must be called the processus mastoideus. SIXTA, in
Ornithorhynchus, calls it the processus paramastoideus, which name,
according to my views, is wrongly applied as it must be retained
for an outgrowth of the exoccipital (pieuro-occipitale or occip.
laterale) occurring in many mammals, and not be given to a part
of the mastoid.

1) Sixra, V. Vergleichend-osteologische Untersuchung iiber den Bau des Schiidels
yon Monotremen und Reptilién. Zoologischer Anzeiger. Bd XXIII N°. 613. 23 April 1900.

J, F. VAN BEMMELEN. Further results of an investigation of the Monotreme-skull.

~--- ----nasale.
Ai

- - - frontale.

. for. ovale.
,” palatinum.

. . pterygoideum.

syiamosim + - --

_.corpus sphenoidei
(sella turcica).

petrosum --~ é ene me ---- - for. caroticum.
.. meatus acustic. int.

basioceeipitum.

mastoideum - - - =- --- for. pro nervo IX, X, XIen XT.
_ . fenestra occipitalis.

otcipitale laterale «- —— -

Echidna hystrix. Floor of the cerebral cavity, left side, inner aspect *)).

roceedings Royal Acad. Amsterdam. Vol. ITI.

C133 4

Chemistry. — “On Soap Solutions.” By Dr. A. Surrs (Commu-
nicated by Prof. H. W. Bakuurs Roozesoown).

Determinations of the boiling point of concentatred solutions of soap,
made by E. Krarrr!) in Breckman’s apparatus, have lead to the
surprising result that the boiling point of a concentrated solution of
soap is identical with that of pure water.

On account of this phenomenon, Krarrr has proposed to clas-
sify soaps among the colloids, which induced L. KanLenBerG and
O. ScHREINER *) to investigate aqueous solutions of soap in a physico-
chemical direction.

They first of all applied the method of boiling, but they found
in agreement with the experiments of Krarrr, that, when using
BECKMAN’s apparatus, a concentrated solution of soap boils at the
same temperature as pure water. If they did not apply a direct
flame but heated by means of a paraffin bath at 125°, the boiling
point was 0.191° lower than that of pure water.

From these observations they came to the result, that they were
not dealing here with a simple boiling phenomenon and called the
boiling of a soap solution ,Pseudo-Boiling”’.

Abandoning the method of boiling, they have determined the
electrical conductive power of dilute solutions of soap at 25° and
have found that these solutions are all good conductors of the
electric current, from which they have rightly concluded, that these
soap solutions cannot be classed among the colloids. In my opinion
they have, however, overlooked the significance of the dilution. The
greatest concentration mentioned in the tables amounts to !/, gram
mol. per litre in the case of sodium oleate, whilst it amounts to
'/s, gram mol. for potassium stearate and '/;, gram mol. per litre
for potassium palmitate.

Greater concentrations could not be investigated at 25° on account
of gelatinizing setting in. They state to have convinced themselves
that solutions of soap containing more than !/, gram mol. per litre
are good conductors of the electric current at temperatures at which
they are liquid but they do not say how great those concentrations
have been.

KAHLENBERG en SCHREINER have also determined the lowering

‘) Ber. d. d. chem. Ges. 27, 1747 (1894).
Ber, d. d. chem. Ges. 28, 2566 (1895).
Ber. d. d. chem. Ges. 29, 1328 (1896),

*) Zeitschr, f, Phys. chem, 27, 552 (1898).

( 134 )

of the freezing point of dilute solutions of sodium oleate. The
greatest concentration was 1/, gram mol. per litre. The results
ovtained indicate that the investigated solutions contained double-
molecules.

In a subsequent treatise entitled: ,Ueber das Sieden wiisseriger
colloidaler Salzlésungen”') in which Kra¥Frr says nothing about
the researches of KaHLENBERG and ScuReINER except that they
are ,héchst unzweckmissig ausgefiihrte Versuche’’, he communicates
a series of boiling point determinations of different more or less
concentrated solutions. The general result is that concentrated solu-
tions of soap have the same boiling point as pure water. In order
to prove that the boiling of the soap solutions proceeded normally,
a small quantity of sodium chloride was added to the boiling solu-
tion after which a normal elevation of the boiling point was
generally noticed.

As Krarrr, to prevent burning, was obliged to introduce into
his boiling vessel large glass beads at a height of only 12—15mM.
instead of a 5 cM. layer of “shot”, the boiling water must have
been considerably superheated. To avoid this error I have made
some boiling point determinations of solution of sodium palmitate
with my recently described boiling apparatus *). Superheating or
burning is completely avoided when using this apparatus.

The sodium palmitate used by me was prepared from very pure
palmitic acid according to Krarrt’s method. The soap contained
8.26 per cent of Na, theory requiring 8.27 per cent.

It was to be expected that, with the new method of boiling, the
soap solution would froth dreadfully. By various devices I have
tried to limit this frothing so as to prevent the lather from leaving
the boiling vessel but I have not been able to find satisfactory means
and so I finally did not trouble about the lather.

After the maximum temperature had been read off, a few were
pipetted out of the boiling vessel and weighed. The concentration
of this weighed solution was determined by warming with an excess
of standard sulphuric acid, until the palmitic acid had completely
melted and separated on the surface of the liquid. When cold, the
solution was filtered and the excess of sulphuric acid titrated with
standard potassium hydroxide.

I experienced all the same that the frothing of the soap solutions,
when experimenting in this manner, was a great nuisance particularly

') Ber. d. d. chem. Ges. 32, 1584 (1899).
2) Proc, Royal Acad. Amsterdam, May 26, 1900 p. 31.

( 135 )

when dealing with concentrated solutions, because the frothing is
then so excessive that, unless the steam is passed exceedingly slowly
through the solution, hardly any will be left in the boiling flask. I
have, therefore, heen obliged to pass an extremely slow current of
steam particularly when dealing with more concentrated solutions.
The result is consequently less accurate than I desired.

In this way. I found:

SopiuM PALMITATE.

Concentration
c Elevation of the Boiling} Mol. elevation of the Boiling
in
point. point.
gr. mols. per 1000 gr. of H,0.} |
0.0282 0.024 8.6
=e
0.1128 0.045 40 re
a
0.2941 0.050 Wey FA
o
0.5721 0.060 1.0 a

From this it is seen that the molecular elevation of the boiling
point ccntinually lowers with the increase of the concentration.

The annexed graphic representation shows that the curve of the
mol, elevation of the boiling point approaches the concentration axis.

Fig. 1.

Mol. elevation of the Boiling point
Cor Me FR aN wo
= +
: im

0,1 0,2 0,3 0,4 05 0,6
concentration
To trace the point where this curve practically meets the con-
centration axis. I ought to have determined the boiling point of
still more concentrated solution, but when doing this in the manner
described the intense frothing is such a nuisance that T was obliged
to abandon the plan.

(136 )

In order to study the behaviour of more concentrated soap solutions,
I have applied the method of vapour tension. For that purpose one
of the bulbs of a Bremer oil-tensimeter was filled with sodium fal-
mitate and water and the other with pure water. After the instru-
ment had been evacuated by means of an automatic mercury air-
pump it was sealed, furnished with a glass scale and placed in a
waterbath the temperature of which was kept constant at 80°. In
this manner the decrease in vapour tension of three different con-
centrations was determined.

The results were as follows:

SopiuM PALMITATE.

Concentration | Decrease of Vapour tension
in in
er. mol. per 1000 gr. of H,O. m.m. Hg at 0°
1.00 0.00
0.75 0.50
0.50 1.30

Whilst therefore the soap solution of 1 gram mol. concentration
appeared to have the same vapour tension as pure water, the de-
crease of the vapour tension became larger when the concentration
became smaller. It is plain that with a continuous decrease of the
concentration it will reach a maximum and then finally fail again
to zero.

We now have sufficient data to state the probable progressive
change of the molecular elevation of the boiling point.

The curve representing the change will have about the following

Fig. IL. form and, therefore, have a in-
flection-point.

=) >

oz 8 é

ed As regards the explanation of
SP 5 this progressive change, I think
me lan 9 .

S33 +| this must be found in the strong
Wey : fatale a ae fhe p . .
AS} Peopoee | diminution of the hydrolytie dis-

0.1 0,2 03 04 05 06 0,7 08 09 10 Sociation of the soap when the
eee concentration increases.

The hydrolytic dissociation at the concentration of 1 gram mol.

is practically né/ which is also proved by the exceedingly small

( 137 )

alkalinity of this concentrated soap solution. At this concentration
we, therefore, have only a solution of the normal salt which does
not seem to cause an elevation of the boiling point or a decrease
of the vapour tension.

Summary of the Results.

It has been demonstrated by a combination of the methods of
boiling point and vapour tension that solutions of sodium palmitate
below the concentration of 1 gram mol. per 1000 grams of H,O
cause an elevation of the boiling point and a decrease in the vapour
tension, which starting from the concentration 0 must reach a
maximum to again become 0 at about a concentration of | gr. mol.

This progressive change which hitherto had not been carefully
studied may be explained by the appearing and again disappearing
of the hydrolytic dissociation.

As a concentrated solution of sodium palmitate has the boiling
point and vapour tersion of pure water, it may be rightly concluded
with Krarrt that this concentrated solution is colloidal.

KAHLENBERG and ScHREINER found that both dilute and concen-
trated solutions are good conductors of the electric current. From
the foregoing it is plain that dilute solutions should beso. Concen-
trated soap solutions will probably be bad conductors of electricity.
It will, however, be very difficult to prove this fact as for this
purpose an absolutely pure material is required.

Amsterdam, Chem, Lab. University, June 1900.

Geology. — ‘“eperditia baltica His. sp., their Identity with
Leperditia Kichwaldi Fr. v. Schm. and their being found in
Groningen diluvial erratics. By Mr. J. HW. Bonnema (Commu-
nicated by Prof. J. W. Mott).

In his Miscellanea Silurica I (Mém. Acad. St. Pétersbourg, VIT
Série, Tome XXI, N°. 2) and Miscellanea silurica III (Mém. Acad.
St. Pétersbourg, VIL Série, Tome XXXI, N°. 5) Mr. von Scumipr
describes i.a. Leperditia baltica His. sp., which then had not yet
been found in the Russian Baltic provinces, but are frequently met
with in Gotland in stones, whose age corresponds with that of the
Lower Oesel Zone. He also enumerates the characteristics of a new
species, viz. Leperditia Kichwaldi, which are declared to occur in

( 138 )

dolomites of the Northern coast of Oesel, belonging to the Lower
Oesel Zone.

Now, when in the collection of sedimentary erratics from ,Honds-
rug”, that are found in the Geological Museum at Groningen, I
gathered, in accordance with this description, the remains of Leper-
ditia Wichwaldi Fr. v. Scumipr, it struck me, that they were repre-
sented by right valves only.

Attentive reading proved to me, that other persons had arrived
at the same conclusion and seen the same phenomenon. I found
that in the ,Zeitschrift der Deutschen geologischen Gesellschaft” year
1891, pag. 489, Mr. Krause makes mention of a few right valves
belonging to his collection, which valves he classes with Leperditia
Eichwaldi. Mr. Kizsow too, in the ,Jahrbuch der Kénigl. Preuss.
geologischen Landesanstalt fiir 1889” describes on page 91 only a
right valve of this species.

At the same time I observed, that of the species Leperditia baltica
His. sp. many left valves (which may directly be known by the
transverse striae on the outer part of their inverted ventral plate)
are found in the above-named collection, but that right valves were
very rare.

It seemed most improbable to me, that all this should have to be
ascribed only to Chance; the more so as in a few erratics, in which
both left and right valves are found, the former were said to be
Leperditia baltica and the latter Leperditia Eichwaldi.

I supposed, therefore, that Leperditia Eichwaldi Fr. v. ScammDT
and Leperditia baltica His. sp. had better be united. The cireum-
stance, that they are of the same age, was entirely in accordance
with this.

The very first thing I did was to try to explain, why transverse
striae should be wanting on the ventral plate of the left valves of
Lep. Eichw., by which the latter, according to Mr. von ScuMIDT,
are distinguished from the left valves of Lep. baltica. An explana-
tion was soon found in the circumstance, that the chief material of
Mr. von Scumipt consisted of stone-kernels (casts) of Kiddemetz:
for when I made a longitudinal section on the transverse striae of
the ventral plate of a left valve of Lep. baltica, I found that the
elevations on the lower side are not answered by corresponding
evooves on the upper side. Consequently, no trace of strokes will be
present on the cast.

After this, I traced the difference between the right valves of
these two Leperditia-species. According to Mr. von Scamipr this
difference consists in the right valves of Leperd. Eichw. being penta-

ee ——————~ST

13s)

gonal, as it has an obtuse projection in the midst of its belly-side.
I found, that Mr. von Scumipr had afterwards changed his opinion
with regard to this. In ,Einige Bemerkungen iiber das Baltische
Obersilur in Veranlassung der Arbeit des Prof. W. Dames iiber die
Schichtenfolge der Silurbildungen Gotlands (Mélanges géologiques et
paléontologiques tirés du Bulletin de l’Académie impériale des sciences
de St. Pétersbourg, Tome I Livraison 1) he writes on pag. 124 the
words, whose translation into English runs as follows: ,The right
valve of the pectinata (Lep. baltica) shows a more or less distinct
projection in the centre of the belly-side.” In accordance with this
was the fact, that at Kiro (southward of the country-seat Tagamois)
in Oesel, which place is also mentioned by von ScHMIpT on page
123 of the same essay Lep. baltica had been found there — I had
come across a right valve with a clearly visible projection.

Consequently I arrived at the conclusion, that Lep. Eichwaldi
Fr. v. Scum. had to be united with Lep. baltica His. sp.

Not without satisfaction I now percieve, that Mr. von ScHMIDT
already shares my opinion, in part at least. In the above-named essay
he tells the reader on page 133, that some of the specimens of
KIDDEMETZ, at first described by him as being Lep. Eichw. belong
to the Lep. baltica.

As far as the form of the carapace is concerned, Lep. baltica
(Lep. Eichwaldi included) often resembles Lep. arctica Jones, sketched
and pictured in Ann. and Mag. Nat. Hist. Serie III, Vol. 7, page 87,
Pl. VII figs. 1—5. The eye-tubercle of this latter species is however,
surrounded by a rhombic blot. The valves of Lep. baltica are thick
and the sides are usually but slightly arched. They frequently run
up regularly towards the centre, and consequently they become flat-
conic. They show rather distinct points, which are put into a net-
work of grooves, running out of the middle blot. The anterior and
posterior margin run up rather steep. A flat marginal rim on the
anterior and posterior borders is usually not to be seen; it is clearly
perceptible only in large right valves, and the most clearly on the
anterior margin.

As was already said before, the right valves possess in the middle
of their ventral border a more or less strong projection, in consequence
of which they become rather pentagonal in form. In those places,
where the right valves of Leperditia grandis Schrenck has a round
aperture, we find here several slit-like ones, the number of which
is not easily fixed. In one case I count ten in front, in another I
find six on the back-side.

The left valve may immediately be known by the transverse slit-

10

Proceedings Royal Acad, Amsterdam, Vol, UI.

( 140 )

like elevations, that are found on the outer part of the lower side
of the inverted ventral plate.

The Groningen erraties, containing remains of Leperditia baltica,
are limestones, varying between yellowish-grey and yellowish-brown.
In these stones, or in others of exactly the same nature, are also
found remains of Encrinurus punctatus Wahlenb. sp., Proetus con-
cinnus Dalm. sp., var Osiliensis Fr. v. Schm., Calymene tuberculata
Briinn., Cyphaspis elegantula Loy. sp., Bumastes barriensis Murch.,
Beyrichia spinigera Boll, Primitia seminulum Jones, Primitia mun-
dula Jones, Strophomena rhomboidalis Wilk. sp., Strophomena imbrex
Vern. (non Pander), Atrypa reticularis L. sp., Zaphrentis conulus
Lindstr., Halysites sp. and Tentaculites sp. This proves sufficiently,
that these erratics are of the same age with the Lower Oesel Zone.
The comparing-material at my disposal does not enable me to come
to a positive conclusion with regard to their origin.

Botanics. — “Contributions to the knowledge of some undescribed
or imperfectly known Fungi” (1st Part). By Prof. C. A.J. A.
OUDEMANS.

On entering upon the task which I have undertaken, 1 wish to
express my kind thanks to Mess's, C, J. J. van Hatt, Candidate
in Botanics and Zoology at the Amsterdam University and Assistant
to Professor Dr. J. Rirzema Bos; Mr. C. J. Konine, Chemist at
Bussum, one of my former disciples and author of an essay published
by vaN Huereren (Amsterdam) and ENGELMANN (Leipzig), and en-
titled: “Der Tabak. Studien iiber seine Kultur und Biologie”,
dedicated to Prof. Dr. J. Forster, Straatsburg, and to Mr. C. A. G.
Bers, private person at Nunspeet, who in different ways have helped
me to facilitate that task, as well by the collecting and sending of
objects, and the yielding of their observations there about, as, and
this regards Mess"s. vaN Hann and Konine@ by their putting at my
disposal their drawing-pen and pencil, where I wanted these to elucidate
here and there the text of my contribution. I highly value that
help and am fully confident that in future it will not be denied me.

( 141.)

§ ASCOMYCETAE,
PYRENOMYCETAE.
Sphaeriaceae.

a. Phaeodidymae.
‘DIDYMOSPHAERIA Fuckel.

1. DipymospHaERIA RHopopENDRI Oud. n. sp. — On branches
of a cultivated exotie Rhododendron: Wassenaar, 1894.

Perithecia fere destructa. Asci perfecte cylindracei, subsessiles,
116 X Ty, paraphysibus quam plurimis filiformibus obvallati. Sporidia
oblique monosticha, umbrina (Sace. Chromotaxia, n°. 9), bilocularia,
cylindrica, ad polos rotundata, vix constricta, 14% 4—95 yu.

b. Phaeophragmiae.
LEPTOSPHAERIA Cesati et de Notaris.

2. LEPTOSPHAERIA GENISTAE Oud n. sp. On the pods of Genista
anglica. — Nunspeet, 2 Jan. 1899; Mr. Berns.

Perithecia innato-erumpentia, in maculis pallescentibus vulgo
aggregata, nigra, 1/; mill. in diam., vertice p.m. depresso perforato ;
asci cylindracei, breve pedicellati, 8-spori; sporae distichae, amoene
fuscae, 2-septatae (3-loculares), ad polos rotundatae, absque appen-
diculis, 14—18?/s 4°/s 4, loculo intermedio leniter incrassato.

Sporulis 2-septatis a pluribus affinibus descissit.

3. LEPTOSPHAERIA PHLoGIS Oud. n. sp. — On the leaves of
Phlox decussata, cultivated at Dedemsvaart, 10 Nov. 1898. — Sent
by Prof. Dr. Rirzema Bos.

Perithecia parva, sparsa. Asci cylindraceo-clavati, curvuli, sessiles,
46 X< 91/, uw. Sporidia disticha, cylindracea, curvula, ad_ polos
obtusa, 3-septata, loculo penultimo antico ceteris ampliore, fuscidula,
23—25 x 4—5 uw. (Pl. IV fig. 1).

4. LEPTOSPHAERIA VAGABUNDA Sacc. Fgi Ven. Ser. II, 318;
Sace. Mycol. Ven. p. 97 et tab. IX f. 37—46, sub titulo erroneo
»sphaeria fuscella’”; Sace. Syll. II, 31; Fabre Ann. Se. nat. 6, IX,
89; Berlese Icones Fung. I, Fase. II, tab. XLV f. 1; Penzig,
Funghi Agrumicoli p. 30 et tab 1144 B; Winter Kr. Fl. II, 465;
Oud. Ned. Kr. Arch. 2, V, 482 et 2, VI, 33; Oud. Rév. II, 288.
(Pl. I fig. 1).

Ramicola. Perithecia corticola, sparsa vel aggregata, nigra,
';—/2 mill. in diam., depresso-sphaeroidea, ostiolo parum vel nequa-

10*

( 142 )

quam prominulo, primitus peridermate tecta, postremo exposita, Asci
eylindraceo-clavati ( d ), breve stipitati, vertice rotundati, paraphy-
sibus filiformibus copiosis obvallati, 8-spori, 132—15422 #. Sporidia
disticha, primitus continua, hyalina, fusiformia, 4-guttulata; denique
aeque hyalina, 2-locularia, ex partibus dimidiis conoideis conformata,
singulis biguttulatis, basi sua sibi invicem arete applicatis et coare-
tatis, infra apicem obtusum paullo collapsis; postremo cylindraceo-
fusiformia, fuseescentia, quadrilocularia, ad septa constricta, recta
vel curvula, nune eguttulata, tune vero loculo uno alterove gnttula
pracdito, ad polos obtusata; sporidia hyalina 1313, colorata 221/5
longa, ultima praeterea 41/, 4“ lata; utriusque generis in iisdem
ascis mixta, quum varia evolutionis stadia representent. Sporidia
immatura mire simulant ea plurium specierum Diaporthes.

On branches of Tilia. Bussum and elsewhere in “het Goov’.
March, 1900. Mr. C. J. Konine.

Though this fungus has long been known already, we have yet
reserved a place to LL. vagabunda in this essay, 1st because we
have to give some particularities from the life of the fungus itself;
2nd as we wished to sketch the changes which its presence brings
about in the more profound tissues of T%lia, and 3*¢ because we
wanted to draw attention to the result of some experiments per-
formed by Mr. Konrye@ about the nature and virulence of the poison
secreted by the mycelium of the fungus.

The infection of branches of limetrees by the spores of Lepto-
sphaeria vagabunda manifests itself by small black spots on the sur-
face of the green, or brown-red, glossy young branches, of which
the youngest internodes are first attacked. They are shorter- or
longer-oval, a half to one and a half centim. long, and some millim.
wide, and in the middle they always show one or two white dots.
By-and-by the black colour changes into a dark brown and the
spots take the appearance of solid, brittle scales, which after shorter
or longer time isolate themselves from the surrounding parts to
resemble little isles which are separated from the rest by a cirele-
shaped groove, and finally also let loose the tissue underneath and
fall off. Microscopic examination points out that they consist of flat
table-shaped, brown air-bearing cells, and that their colour is due
as well to a change of the cell-walls, as to a modification of their
contents which is condensated to a shriveiled mass. The white dots
are lacunae, filled with colourless, loosely contiguous globose cells,
ie. lenticels which, as in many other trees and shrubs, take the
place originally occupied by a stoma.

The result of this research, combined with the appearance of the

|

( 143 j

black spots, can lead to no other view but that the stomata or
lenticels are the localities where the spores of a former generation
came down and germinated, and that the germinal tubes secrete a
poisonous substance which caused the above described changes.

It was obvious that these germinal tubes and the thence proceed-
ing mycelium-filaments ought to be found out. On the very first
prepared transverse sections of the black spots and. the tissue under-
neath, it seemed, however, that this end could not be gained. Very
rarely a mycelium filament came into sight, so that the impression
arose that a destruction, as figured on our plate, was not in the
least propertioned to the number of germinal tubes or mycelium-
branches wanted to bring about so much mischief. Meanwhile,
however, after the knife had been introduced in other directions,
and in particular in a tangential one through the spots, and more
inwardly, more and more filaments were discovered, so that the
proportion between the damage occasioned, and the cause of it,
appeared in a quite different light from what had been supposed
at the beginning of the research.

Before coming to this result, rather much time had however got
lost, apparently uselessly, and that in consequence of the trouble
which it gives to recognise the mycelium filaments. They go creep-
ing in the intercellular canals, but are so extremely thin and
quite colourless, so that they are not to be distinguished from the
healthy ceil-walls between which they make their way. Only after
having got acquainted with the finely granulous contents of the
mycclium filaments, by the use of stronger lenses, the task becomes
lighter, and when, finally, the cell-walls of the surrounding bark
tissue have begun to change colour under the action of the poison,
it may be said that the research affords no more difficulty.

Here attention should be drawn to an accidental particularity
which, previous to the examination of the diseased Tilia-branches,
might well have disappointed our expectations. This, namely, con-
eerned an investigation of diseased branches of Negundo fraxinifolia
— an ash-tree frequent in gardens — which, by the thickness of
the mycelium filaments, the brown tint of their walls, as well as
by the presence of transverse partitions, combined with the accom-
panying nodated appearance in some places, had much more quickly
carried us to our end. Under the impression of these observations
our research of Tilia had begun, and so it was not to be wondered
at that at first we thought it much more troublesome to get on,
than jater it proved in reality to be.

There can be no doubt but the changes, which are observed as

( 144 )

well in the tissues situated nearer to as in those farther from the
mycelium-filaments, and to which belong 1st the decoloration of the
bark- and bast-parenchyma-cells, of the phioem-layers, of the medul-
lary rays, and of the wood-parenchyma, and 2"¢ the killing or
liquefaction of those tissues, are caused by the more and more
inwardly penetrating mycelium-branches and this in such a sense
that by them a substance is secreted — an enzyme — which, as
a poison for living plant-cells, exerts a deadly influence upon them.
The original contents of the cell grow unrecognisable, and are replaced
by a brown-red shapeless precipitate, which proves indifferent to
number of reagents (alcohol, ether, kalium chromate, ferrichlorid,
caustic kali, ammonia, nitric- and sulphuric acid) and can but be
decoloured by a few oxidising substances, as a mixture of kalium
bichromate and sulphuric acid, or chromic acid. The poison leaves
the bast fibres uncoloured and, in as much as can be ascertained
by microscopic observation, unchanged.

In order experimentally to demonstrate the presence of a poisonous
substance, Mr. Konine proceeded as follows:

He cut out some hundreds of black spots from young Tilia-bark,
erushed them fine under addition of 20 cM®. of sterilised water and
filtered the viscous liquid through a Chamberland-Pasteur-candle.
The filtrate amounted to 7 cM*. and was of a light yellow colour.

With it branches and sections of branches of a healthy Tilia
were treated; the former by longitudinal incisions with a flamed
knife plunged in the liquid, or by injections, the latter by submerging
with the liquid in a watch-glass or an experiment tube.

Experiments in both directions with sterilised water and bark sap
of healthy Tilia-branches served for control. The resuit of these
proceedings was after 8 days for the incised and injected branches
and of 2 24 hours for the sections:

“that what had been treated with sterilised water or with healthy
bark sap, hid remained uncoloured, but that the wound edges of
the incised or injected branches on one hand, and the flat sides
of the sections on the other, had suffered a brown, albeit light,
colouring”.

Another, later performed experiment, quite corresponded with the
above described. It concerned some healthy Tilia-branches, eut off
with the necessary precautions and of which some were placed in
the filtrate of healthy, some in that of diseased Tilia-bark. After
3 < 24 hours the poison proved, as might be expected, to have most
positively exerted its influence, as the original colour of the branches
piaced in pure liquid, had remained unchanged, whilst that of the

(145 )

branches which had been plunged into the infected sap had changed
from light brown-red into dark brown.

The perithecia of Leptosphaeria vagabunda develop in the bark
parenchyma, but gradually they make their way to the surface of
the branches where, accordingly, they are then found, like the pyenidia.

The former are much more numerous than the latter and appear
either at the surface of the scales, or at the wound edges, or in
grooves and cavities. They have solid, black walls and a small
ostium, with or without papilla, and contain numerous narrow club-
shaped 8 sporedasci. Their width or diameter averages from 1/5
to 1/. mill. The spores are 132 to 154 w long and 22 w& wide and
show so much difference in appearance, according to their age, that
one might often be inclined to believe in the existence of two different
Pyrenomycetes. By this characteristic Leptosphaeria vagabunda is
easily recognised among the numerous species of the genus.

In the very youngest period of development the spores are spindle-
shaped, colourless and one-celled ; somewhat later there appears in
their middle a transverse partition; still later the two halves take
the form of a very obtuse cone, but which, at a third of its height,
appears constricted and then consists of a pulvinate under- and a
knob-shaped upperportion; moreover in each of the two portions
appear two superposed drops of oil.

Between each two drops now a new partition makes its appear-
ance and accordingly 4, instead of 2 loculaments, are observed. Then
the spores again assume their original form, the drops disappear,
the deeper constrictions are replaced by superficial ones and the
spindle-shape shows itself again. Now, however, the spores have be-
come 4 celled and have got a light olive tint, which both charac-
teristics secure the Fungus its place among the species of Lepto-
Sphaeria (ibid. g).

Notwithstanding the virulence of the poison produced by the
mycelium of Leptosphacria vagabunda, which brings about the
destruction of an infected branch, nursery-men are not afraid of
this parasite, because, according to their experience, the diseased
parts are pushed off, and, as they say, the tree outgrows the evil.
The justness of this observation is supported by the fact that 7'i/ia
belongs to the trees which regularly, first in the depth of the bark
tissue, afterwards in that of the bast, produce cork-layers which
exclude all beyond from the supply of water and thus abandon it
to dessication. The thus killed tissue, in which the fungus had
nestled, is sooner or later pushed off, or at least rendered harmless,
and the absence of stomata and lenticels at the surface of the now

( 146.)

exposed parts, deprives the spores of every opportunity again to
infect the branches.

Besides a few perithicia cut through our figure shows at the
outside of the section a pyenidium cut through, i.e. a spore-fruit,
in which only free spores are to be seen but none enclosed in
asci. This fruit has all the properties of the genus Phoma, but
was not hitherto distinguished as a species. I call it therefore Phoma
Tiliae and assign to it the following properties:

PuHoma TILIAn n. sp. Perithecia primo peridermate velata, denique

hoe rupto semilibera, subsphacrica, nigra, tandem vertice perforata,
154—225 w in diam.; sporulae ellipticae, continuae, hyalinae, ad
polos rotundatae, 4.5 < 2.7 4. Differt a Ph. velata Sace. et Phoma
communi Rob. sporulis enucleatis et multo minoribus (4.5 % 2.7 4
contra 10—12 * 2.5 w et 6—T X 1.5).
» This Phoma belongs most probably to the eyclus of development
of Leptosphaeria vagabunda, i.e. is most probably produced by the
same mycelium filaments as the ascus-bearing form, but earlier. The
proof for this supposition would be procured if from one and the same
mycelium both forms of spore-fruits were seen to come forth ; or, if
from the spores of either form the second was seen to originate, or,
lastly, if none of either forms were ever met with separately (unless
by high exception), but constantly in company of the other. Hitherto
these phenomena could not be stated, so, the last word is not yet
said about the relation between the two mentioned forms.

In the course of this paper we have already inferred that the
nursery-man does not care for the infection of his lime-trees by
Leptosphacria vagabunda, as the diseased parts are thrown off and are
not replaced by new ones. Meanwhile it remains advisable to render
the infected branches harmless as the ripe spores of both the peri-
thecia and the pyenidia, might afterwards again show their destructive’
power, and as it cannot be determined beforehand whether the in-
fectious matter might not spread further, than has been observed
till now. As to myself, among the thin branchlets, I sometimes
met with much thicker ones, which had not a little suffered of the
Leptosphaeria-disease.

HX PLANATION OF THE FIGURES:

Plate I. Fig. 1. — Part of transverse section of a one year’s lime-tree
branch, infected by Leptosphaeria vagabunda Sace.
The colourless spaces « represent the bast-bundles; 6 brown, in radial’

(147)

direction extending medullary rays, of which some upwards fan-shaped
elated; y a fan-shaped elated portion of a medullary ray with a colourless
mycelium filament and destroyed tissue.

a. Two perithecia with asci and paraphyses.

b. A perithecium with asci and paraphyses separately.

ec. Young ascus.

d. Ripe asci with spores and paraphyses.

e. f. g. Spores of different ages; e. and /f. 2-celled, uncoloured; g. 4-celled,
coloured.

h. Pyenidium of Phoma Tiliae Oud.

i. Branchlet at the beginning of the disease. The black spots with white

dot in the middle are distinctly seen.

j. Branchlet in a later period of the disease. Instead of the black spots a
scale is seen (the highest) and a wound after the scale is fallen off.

k. Older, knotty branch, upon which some closed perithecia (/).

m. Lenticel, out of which a mycelium filament has penetrated more
deeply and has occasioned decolouring of the bark-parenchyma cells
and destruction of tissue.

Fig. 3. Piece of lime-tree bark cut transversely to show the detaching
of a diseased part (a) from the still healthy, more profoundly situated (0)
portion. At ¢ the cork layer is seen which has brought about the separation
between diseased and healthy tissue.

ec Hyalophragmiae.

5. Meraspuarrta Taxt Oud. n. sp. On the leaves of Taxus
baccata. — Nunspeet, 18 Sept. 1898; Mr. Berns. — Perithecia
epigena, valde numerosa, gregaria, '/s—1/g mill. in diam., continuo
sub epidermide abscondita, tardem prominentia, vertice perforata,
nigra, carbonisata, applanato-globulosa; asci claviformes, saepe cur-
vati, 65 —70><9—10 w, paraphysibus filiformibus obvallati; sporae
8, distichae, colore destitutae, lanceolatae vel obovato-lanceolatae,
3-septatae, ad septa non constrictae, 18 —23 x 4°/;—5!/. «.

d. Dictyosporae.

6. Preospora Necunpints Oud. — On the one- to three years’
branches of Negundo fraxinifolia and californica, often in company
of Phoma Negundinis Oud. — March, 1900. Bussum, and elsewhere
in ,het Gooi”. — Mr. C. J. Konina.

Ramicola. Perithecia gregaria, primo epidermate vel peridermate
tumidulo velata, postea papilla apicali, postremo toto corpore expo-
sita, globoso-depressa, '/;—1/, mill. in diam., papillata, nigra, glabra,
contextu parenchymatico, fuligineo. Asci cylindracei vel cylindraceo-
clavati, subsessiles, vertice rotundati, 120—17622—23 «, para-
physibus paullo longioribus obvallati, octospori. Sporidia disticha,
oblonga, medio leniter constricta, utrimque rotundata, 25 — 35 <

(148 )

12—16 «, primo hyalina, 1-septata, mox flavescentia, 3- et 5-,
postremo mellea, 7-septata, atque, loculamentis interseptalibus fere
omnibus septis 1 vel 2 longitudinaliter denuo divisis, muriformia.
A Pleospora Gilletiana Sacc. (Fgi ital. del. tab. 330 et Berlese
Teon. Fung. vol. II, fase. 1, tab. XX f. 2) differt ascis latioribus
(23 « contra 14—15 w), sporidiis distichis neque monostichis, rectis
neque curvatis; absentia hypharum basilarium expositarum.

The above described fungus causes much damage to the plants
which it attacks and destroys, and loss to the cultivator. According
to informations obligingly afforded to Mr. Konine by Mr. Jac.
Smits, nursery-man at Naarden, the phenomena of the disease
manifested themselves for the first time in 1898, on plants, cultivated
on soil, deprived of sand. On argillaceous and sandy soils they
were not observed as yet. In most cases, the variegated specimens
of Negundo have much to suffer, though, as an exception to the
rule, it is worth mentioning that in the nursery of Mr. VERSTEGEN
at Naarden, p.m. 500 M. distant from that of Mr. Smirs, specimens
of Negundo californica, with purely green leaves, were attacked by
our Pleospora. On the var. Kosteriana of N. fraxinifolia, and on
the aurated variety of the latter, the disease was not seen hitherto.

On branches, older than three years, the Pleospora does not occur.
The nusery-man is usually not aware of the disease before St. John
(21st June), which does not prevent, however, that in September
ensuing many may be dead already.

Pleospora Negundinis Oud. and Phoma Negunndinis Oud. seem
genetically to belong to each other. Usually they are found on the
same branch (Pl. I, Fig. 2 d and @ and Fig. &, 2 and m) and in
each other’s vicinity, in which case the perithecia of the former are
recognised by their larger dimensions and looser dispersion, those of
the latter by their smaller dimensions and more compact crowding.

The perithecia of Pleospora Negundinis are concealed in the bark-
parenchyma, but with dried twigs, by the shrinking of the softer
parts, they seem to repose on the bast-bundles. At their foot, hidden
in the parenchyma, are seen numerous brownish mycelium filaments
which spread around and ramificate (d). In our figures is seen under
the same circumstances a Phoma-pyenidium (a) and a bundle of
brown, upright filaments (4) of a black mould, all supported by
hidden mycelium-hyphae, which cannot be distinguished from those
of the //leospora-perithecia. These filaments, like those of Lepto-
sphaeria, secrete a poison, and cause a modification, though appar-
ently not equally important, of the contents of the parenchymacells
of the bark and of those, situated in the direction of the medullary

(149 )

rays. The diseased spots (4) grow, at the surface of the branches, from
green to red-brown, over larger or smaller extents, in accordance with
the bark-parenchyma, situated under the epidermis which, however,
though likewise red-brown, keeps a lighter tint. If a branchlet,
spotted by the disease, dies (/), the red-brown colour turns of a
gray one, though the tint of the mycelium continues unchanged,
and on the sharply marked spots the perithecia, often preceded by
pyenidia, are seen to appear. On the drawing, the red-brown tint
is not represented, for the very reason that it was borrowed from
a dead branchlet. Some cells — those containing chlorophyll —
have till now escaped the influence of the poison.

Tissue-elements of an abnormal colour frequently appear in
Negundo at places where no myceliumfilaments are found. Bast-
and phloem-bundles seem to resist the influence of the poison.

The largest Pleopospora-perithecia are found at the oldest inter-
nodes, so that it seems not doubtful but these organisms require
much time for their complete development. In accordance with this
is the fact, that the larger perithecia may quite have thrown off the
periderma above them, while with the smaller and younger ones
this protecting layer is still extant and is only perforated by the
papilla perithecii.

Of destructions in the shape of resorption of tissues and the appear-
ance of caverns, quite differently from Leptosphaeria vagabunda
on Tilia, nothing is observed. Notwithstanding this the poisonous
power of the Negundo-fungus is much more vigorous than that of
the Tilia-fungus, as is proved by the fact, that, according to the
experience of nursery-men, the once infected Negundines are vowed
to death, while the Tilias, as they say, overgrow the evil and
persist.

The disease of the Negundo-branches is, as in Tilia, announced
by local decolorations of the cork-tissue, upon which first red-
brown, and later paled, black-encircled dots become visible.
By-and-by the said dots begin to wrinkle and to detach from the
lower bark parenchyma. Meanwhile tiny, black, corpuseulae appear
through the peridermis and gradually increase so much in height as
to attain this membrane. By the pression which they exert on it
the surface of the branchlet grows somewhat uneven, until the
papillae of the perithecia perforate the periderma. In this state the
ascl and spores, which had been introduced into the inside of the
perithecia, have not yet attained their full growth. Only when their
diameter is increased to about '/, mill. these organs are not sought
in vain, so that then a commencement ean be made with their de-

( 150 )

scription and measurement. As we formerly inferred already, the
ripe spores sometimes are oblong-elliptical, sometimes club-shaped,
and have a yellow or yellow-brown colour. In well-developed
specimens are found 7 partitions and a superficial constriction on a
third of their height. Usually the foremost half, i.e. the one turned
to the summit of the ascus, is a little wider than the backpart.
Each loculament is divided by one or two longitudinal partitions,
into smaller ones, so that the whole bears some resemblance to a
brick wall, whence the expressions: “Sperae muriformes”, “Spores
muriformes’’, “Spores murées’’, “muriform spores’. There are spores
whose longitudinal paititions lic in each other’s direction and together
form a straight line, but there are others where 1 and 2 partitions
alternate in the successive loculaments.

The infection in Negundo does not occur through interference of
stomata, but probably through that of wounds, found near the foot
of the leaf-buds, and without doubt caused by tensions during the
growth. There at least are commonly found the first abnormally coloured
spots. Other places are not excluded, probably, however, wounds will
there, too, have given access to the spores.

If we survey the results to which have led the investigation of the
Tilia- and Negundo-diseases, we find that they agree in so far as:
Ist. they are caused by Pyrenomycetes: the Tilia-disease by Lep-
tosphaeria vagabunda, the Neguudo-disease by Pleospora
Negundinis ;
2nd, in both often lower frnit-forms, such as one or more kinds
of pyenidia and Dematieac, precede the perithecia;
in both, not the fruits (perithecia or pycnidia), but the myce-
lium-filaments are the producers of the evil;
4h. in both by these filaments a poison is secreted, which in
Tilia — and most probably also in Negundo — persists in
its action, even after filtering through a Chamberland-Pasteur-
candle, so, deprived of all solid components, and that conse-
quently in both cases the nearest cause of the disease of the
plantcells must be ascribed to the action of an enzyme;
5h. in both cases the same portion of the bark (the parenchyma)
is affected, and the phloem-fasciculae seem beyond the noxious
influence of the mycclium-filaments.

2
3rd 4

Both diseases, on the other hand, differ from each other, in as
much as;

1st. the mycelium-filaments of the J'i/ia-disease are colourless,
devoid of partitions, very thin and delicate and so not easily
perceived, while those of the Negundo-disease unite a brownish
tint with the possession of partitions and a great solidity,
and accordingly attract more the attention ;

2nd. the volume of all the mycelium filaments jointly, when com-
pared to the space in which they are spread, is much smaller
for Tilia than for Negundo;

3. the enzyme of the Tvlia-disease acts more locally, that of
Negundo also at a distance; the former can give rise to lique-
faction of tissue, the latter not.

EXPLANATION OF THE FIGURES.

Plate I, fig. 2. — Portion of a transverse section of a one year’s branch
of Negundo fraxinifolia (Acer Negundo), attacked by Pleospora Negundinis Oud.

a. Pyenidium with Phoma Negundinis Oud.

w. ‘The same, separately.

b. <A bundle of unripe hyphae of a Dematiea.

c. Coloured mycelium.

d. Perithecium.

d'. The same, magnified.

e. Ripe asci.

f. Paraphyses.

g. Mycelium.

f'. Spores.

h. <A dying more-years’ branchlet.

i. Dying brown fragment of bark.

j. Dead colourless fragment of bark.

k. Dead branchlet.

1. Perithecia with asci.

m. Pyenidia of Phoma.

SCLEROPLEA n. g.

Genus Pyrenomycetum e familia Sphaeriacearum et e sectione
Dictyosporarum, generi ,Pleospora’” proximum, tamen ab eo distinctum
perithecio duplici: uno nempe interiore (spurio) tenuiore, incompleto
(i.e. sursum hiante), e cellulis rotundatis composito, ascos sporigeros
et paraphyses fovente; altero exteriore (vero) crassiore, magis resis-
tente, vigro, carbonaceo, strato parenchymatoso hyalino, satis volu-
minoso, a priore distincto.

7. ScLEROPLEA CLIVIAE un. sp. — Perithecia innato-erumpentia,
subgregaria, sphaerico-depressa, calva, 0.5 mill. in diam., summo
apice tantum supra epidermidem prominentia et coriaceo-carbonacea ;
asei cylindraceo-subclavati, in pedicellum brevem et crassum abrupte

( 152 )

desinentia, octospora, LOO—140 & 15—35 w, paraphysibus longiori-
bus articulatis obvallati; sporae distichae, fulvo-flavescentes, elliptico-
obevatae, utrimque obtusissime rotundatae, muriformes, 7-, rarius
6-septatae, loculis interseptalibus omnibus, ultimis tantum vulgo
exceptis, septis 1 vel 2 longitudinaliter divisae, ad septum medium
constrictae, parte dimidia anteriore parum tumidiore, 3510 — 12 w;
paraphyses ascis paullo longiores, articulatae.

On the leaves of cultivated specimens of Clivia nobilis. December
1899. Hees near Nijmegen.

In the Meeting of the section of 28 November 1896, a paper
was presented by me, entitled: “Notice sur quelques “Champignons
nouveaux’’, which was published the 9ttDecember of the same year
in the Proceedings of the Meeting. To the still unknown Fungi,
discussed in this paper, belonged also Chaetostroma Cliviae, of which
on pag. 226 of the said Proceedings an accurate description is found.

The plant, attacked by Chaetostroma was the well known Clivia
nobilis, and the diseased specimen, sent me by Professor Dr, J. RITsEMA
Bos, grown in the garden of Mr. GERRITSEN, at Hees, near Nijmegen.

Having after the 28 of November 1896 heard nothing more of
diseased Clivia-leaves, I received, on the 27 December 1899, accompa-
nied by a letter from Mr. C. J.J. van Haut, Candidate in Botanies
and Zoology and assistant to Prof. Rirsema Bos, in Amsterdam, some
Clivia-leaves from the same garden, again diseased by Chaetostroma
Cliviae, but moreover provided with perithecia with ripe asci and
spores, which latter, by reason of their well-known characteristic
structure, were recognized by Mr. van Hatt as Pleospora-spores.

The diseased leaves looked like fig. 4 on Plate II. At their upper
face, markedly separated by a dark line, could continually be dis-
tinguished two portions, of which only the smaller foremost one was
beset with groups of perithecia, the larger back portion, on the
contrary, was wholly devoid of these black points. The purely green
colour of before was no more to be observed at the back portion,
but it was replaced by a yellow or yellowish dingy one, whose
equality had come forth from the confluence of primitively smaller,
later more increased spots. At the foremost, perithecium-bearing
portion, the change of green into yellow had never been observed,
but instead a decrease in freshness of the green, combined with
the appearance of a brown tint, and corresponding with that a
drying and withering, so that it might be said that quite ripe pe-
rithecia were observed exclusively at the withered summits of the
leaves. As afore mentioned, the Cheatostroma-pustulae occurred in-
deed on the yellow portions of the leaf, but then the withered

( 153 )

portions were wanting there and the dark line proved to be the
demarcation, not between gray-brown, withered perithecium-bearing,
and green or stained unfertile parts, but between yellow, perithecium-
bearing and green unfertile parts.

A vertical section of Chaetostroma Cliviae (Pl. IL fig. 2) gives an
idea of the structure of this fungus of which in our former paper
only a conidium, supported by its basidium, was figured (PI. IT,
fig. 3). The intact fungus, 25 times magnified, is seen on PI. IT,
fig. 1.

The fungus allied to the genus Pleospora as regards its spores
is, 25 times magnified, represented on Pl. ILI, fig. 2. In the leaf-»
parenchyma, arrived at its full growth, it tries to perforate the
epidermis of the leaf, in which it sueceeds at last. As is seen, this
protective layer is hereby pushed asunder, sometimes into 3 lip-
shaped slips.

A vertical section of the perithecium and its environment is figured
on Pl. II, fig. 5. Here the remarkable fact presents itself that the
true perithecium (a) does not directly surround the so-called nucleus
(asci and paraphyses) but is separated from it by a wide layer of
parenchyma-tissue (c), and besides, by a pseudo-perithecium wall.
The question whether this special condition of which no other in-
stance was known to us among the singular dictyosporic Pyrenomy-
cetes, had perhaps been observed by other mycologues, called forth
a nearer investigation, and so we found that already Saccarpo had
in some way alluded to it on p., 277 of Vol. IL of his Sylloge, where
the 3*¢ sub-division of the genus Pleospora, named “Scleroplea’”,
is being discussed.

SAccARDO, namely, divided the numerous species of Pleospora
into three categories:

I. Hu-Pleospora.
Il. Catharinia.
Ill. Scleroplea.

Of these the 1st (p. 241) embraces the species with thin-walled,
membranous perithecia and coloured spores ;

the 2"¢ (p. 275) the species with thin-walled (membranous) peri-
thecia and colourless spores, and finally;

the 3 (p. 277) the species with thick-walled perithecia, and
coloured spores.

Eu-Pleospora embraces the most numerous, and long since known,
species, always indicated by the simple name of Pleospora; whilst
to Catharinia are assigned no more than eight, and to Scleroplea
only two species. Nevertheless Catharinia was in 1896 by SaccaRDo

( 154 )

in Vol. XI of his Sylloge, and in 1897, independently of Saccarpo,
by myself in Vol. IT of my “Révision des Champignons des Pays-
Bas”, raised from a sub-genus to an independent one.

With a view to the above diagnoses there was no doubt but the
Pleospora produced by Clivia must belong to Scleroplea, as both
characteristics: a thick, as carbonised wall, and coloured spores,
were present.

The question now presented itself whether, now that Catharinia
had been raised to an independent genus, the same measure should
not be applied to Scleroplea too. It appeared to us that no motivated
doubt could thereabout exist for the following reason: not only
because a thick, as carbonised, opaque perithecium-wall might be
called as great an exception among the Jeospora-species as the
colourless spores of Catharinia, but also as the structure of the
perithecia, as we have seen, is of a much more complicated nature
than that found in the species of Eu-Pleospora and Catharinia.

Cause of astonishment might be found in Saccarpo’s not recording
among the characteristics of his sub-genus the by us observed spe-
cial structure of the perithecia of Scleroplea, yet the reason of this
lies at hand. The two species of Pleospora which are noted in the
Sylloge under the afore-mentioned sub-genus, having selected for
their dwelling-place the organs of exotic plants, flourishing in New-
Zealand and Argentinia, were not, or only in dried state examined
by him, so that he had to depend on the descriptions of others,
who had, perhaps, likewise, worked under unfavorable circumstances,
or whose attention had not by preference been directed to the in-
ternal structure of the perithecia.

Only for Pleospora nuda (Sac. Syll. I, 277 = Pyrenophora nuda
Cooke, Grevillea VIII, 68) — called by Cooke ‘nuda’, because he
was of opinion that in this fungus no perithecium had come to
development, Saccarpo alludes to the phenomenon observed by us,
using the following expressions: “Secundum Cooke stratum perithecii
exterius brunneo-cellulosum a perithecio vero interiore separabile est.”

Meanwhile it should be borne in mind that Cooke who wrote in
English, did not use the terms attributed to him by Saccarpo, but
simply asserted: “These are no true perithecia. The cells surrounding
the perithecial cavity are brown, globose and readily separable”.
Saccarpo has consequently wrongly understood Cookn’s words, but
still, at least as regards Scleroplea Cliviae, has come very near the
truth. How much, however, the views of both mycologues diverge, is
obvious to any-one who pays attention to the fact that Cooke disowns
the existence of a true perithecium, whilst SaccaRDo, on the con-

( 155 )

trary, infers the presense of two perithecia, and that the English
mycologue does not recognise our layer (@) as a perithecium-wall,
whilst the Italian savant applies to it the name of “perithecium
interius’’.

But let us leave to both authors the responsibility for their
respective judgments and exclusively consider the resuits of our
microscopic investigation most successfully reproduced by Mr. VAN
Hatt in Fig. 5 on Plate II, we then come to the conclusion that
the perithecia of Scleroplea Cliviae are built up of:

1st a thick, solid, as carbonised black layer of cells (a) (the

“stratum perithecii externum” of Saccarpo; probably the
continuation downward and inward of the “cuticula nigrefacta”
of COOKE;

2nd a many cells thick layer of thin-walled parenchyma built up

of polyhedral elements (c);
3™ an imperfect, i.e. at the upperside not closed layer of light
brown globose cells (d) surrounding the nucleus perithecii,
that is to say the asci and paraphyses (“the brown and
easily separable cells, surrounding the perithecial cavity” of
CookE; “perithecium interius’” of SaccaRDo);
and that the raising of the sub-genus Scleroplea, to a genus chiefly
reposes with us on the presence of an external and internal perithe-
cium, separated from each other by a rather vigorously developed
interpushed parenchyma which, at a later period, probably passes
into decay and in doing so breaks up the connection between the
said two layers.

If we admit, — which however ought to be determined by a
nearer research, —- that Pleospora nuda Sacc. (= Pyrenophora nuda
Cooke) and Pleospora sclerotioides correspond with Scleroplea Cliviae
in the structure of their perithecium, then the latter genus, to be
interposed between Pleospora and Pyrenophora, would for the present
moment consist of 3 species, all bound to exotic plants.

By the addition of iodium the ascus-wall of Scleroplea Cliviae
assumes a red-brown (presence of glycogene), the spore-wall a blue-
green, and the contents of the spores a blue colour.

The germination of the spores, tried by Mr. van Hat in a
decoction of Clivia-leaves, was satisfactory. After the separate spores
were strongly swollen, many began to send out germinai tubes.

(Plate III, fig. 5.)

The question whether Chaetostroma Cliviae and Scleroplea Cliviae
are to be considered either as parasites or as saphrophytes, should,
we think, be answered in the latter sense, because in the tissue of

11

Proceedings Royal Acad. Amsterdam. Vol. ILI.

( 156 )

the faded yellow leaves or parts of leaves, where no black spots
appear, no trace of mycelium filaments is to be found'). The
decoloration, the cause of which remained unknown to us, precedes
accordingly the appearance of the fungus.

An effort was made by Mr. van Haut to infect a dying Clivia-
leaf with ascospores of Scleroplea in state of germination. The result
of the experiment was vot favorable. Small black points developed
indeed in the environment of the inflicted wound, but they soon
ceased growing, so that it remains undecided whether they belonged
or not to Chaetostroma.

EXPLANATION OF THE FIGURES.

Plate II, fig. 4. A leaf infected by Scleroplea Cliviae. The foremost brown
portion bears small groups of perithecia, of which the summits are only
visible. The hindmost: yellow portion bears neither of the two fungi and
contains no mycelium filaments.

Fig. 2. Vertical section of a pustula of Chaetostroma Cliviae Oud., de-
scribed more in details on pag. 226 of the Proceedings of the Meeting of
28 Noy. 1896.

Fig. 1. Some Chaetostroma pustulae 25 times magnified. The chaetae to
which the genus owes its name, can be distinctly seen.

Fig. 3. A conidium of Chaetosiroma Cliviae, reposing on its basidium,
500 times magnified.

Fig. 5. Vertical section of a perithecium of Scleroplea Cliviae (216 times
magnified).

a. exterior or primary perithecium.

d. interior or secundary perithecium.

c. parenchyma tissue between the primary and secundary perithecium.

ie ERCE

Plate Ill, fig. 1. Older and younger perithecia of Scleroplea Cliviae (8
times magnified).

Fig. 2. Some perithecia of the same, which have torn asunder the epi-
dermis (25 times magnified).

Fig. 5. Spore of the same in state of germination.
Fig. 3. Spore-bearng ascus with its paraphyses (800 times magnified).
Hig. 4. Four spores of different ages and sizes of the same (800 times

magnified); a.a@.a. moistened spores, ). spores soaked in water.

1) At our request Prof. P. Magnus in Berlin had the kindness to test the accuracy
of our research with some leaves sent to him; he fully confirmed it.

- Contributions to the Inowledge of some undescribed ar imperfectly

known fungi.

TBYtea bth PI Muldenipor Leider

i . > by 7 ay.) ae 4 4 -
a ae a , e % ‘, re J '
© ah Sth eaae ;
.
‘
:
4 '
¢
Ms a
i
, :
> :- 5 «
-
*

JEytel hth PI Mulderiryer Leiden.

- AMSTERDAM. VOL TL.

- bg f y Dts e
_
. a vr “
yy" Sa) z )
A ‘se | A » es 7
'
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—
«

( 157 )

Astronomy. — “The motion of the Pole of the Earth according
to the observations of the last years”. By Dr. EK, F. van pu

SANDE BAKHUYZEN.

In a postscript to my last paper on the motion of the pole of
the earth in “Archives Neérlandaises. Série II, Tome II” 1 briefly
mentioned in how far the results from the latest observations deduced
by ALBRECHT in his “Bericht am Schlusse des Jahres 1898”, agreed
with my formulae.

Since that time Prof. ALBRECHT has again published in a following
paper!) his summaries and calculations including one year more.
This closes in a certain sense a period in the researches of our
problem. Up to 1899 the results obtained were due to the free
co-operation of a certain number of observatories. At the close of
1899 however, the new international organisation has come into
force, according to which observations after the Horrebow-method
are made in exactly the same way in six stations which all are
situated on 39°8' northern latitude, and have heen especially arranged
for this purpose.

Therefore this seemed to me the proper moment for making a
new comparison between my formulae and the results deduced by
ALBRECHT from the combined observations of the last 10 years.

2. ALBRECHT takes the results obtained in his “Bericht im
December 1897” to be definitive for the period 1890—1895.0. In
his last “Bericht” therefore he considers only the period from
1895.0—1899.8, for which he had at his disposal the results of
on the whole the same observatories as before.

For the intended comparison I chose for the 14-monthly motion
my elements II of Archiv. Neérl. T. II, p. 481 (35), for the
yearly motion my results derived from the period 1890—96 (Proc.
Royal Academy of Amsterdam, June 1898).

Here follow the results of this comparison. The differences between
the observation and the computation are expressed in thousandths
of seconds.

1) Tu. Atsrecur, Bericht iiber den Stand der Erforschung der Breitenvariation am
Schlusse des Jahres 1899. Berlin 1900.

iil

( 158 )

x ALBRECHT — & computed.

113|4 130/4+ 95/4 59|— 15|— s9l— 103|— 72|—
14 81+ 130-1 150+ 123-4 20|— 69)— 109|—
|

y ALBRECHT — y computed.

ra
poate fig Weal Pa fa fcc Pla |
| SS ent
——
| |
1890 |— 26+ 53\f 90-4 70+ 24+ 4}— 25 27\—
| | %, eal
91 954)—) 18° 23+ 74\1- 41)— 38)— 100}— 195|—
| | | }
92 Le vole onl 33i\— 29 75j= 914 36-45
got sit ght gate iqnenigg@e aops em eta ee
| |
9% |— 13)— 124 16+ 4+ iit 6 4i— 46
|
95 | Wi 7|— 20-— 33 265— SIE 41+ BOLE
96 — 5— gi 43\— 364 5 56+ 644 58|—
o7 |— @— asi 4at sil agate 714 ae7L at

98 + sot 26— 36) ssl— 93 601+ + 56/1
99 |4 724+ 23/— 14|— 52}— Siva 64{— 23, 3LE

From this we find as mean value of the deviations:

( 159 )

or if we omit the results for 1899.0—1899.8 as being probably
less accurate as yet:

SAF Say
zZ ee + 0'.047 pate Pe BEG:

n n

Formerly the mean deviation was found to be +0".040 and
+ 0."045, and we see that the agreement has not improved during
the last years.

The fact, that this time I did not use for the 14-monthly motion
the results obtained from the period under consideration only, may
have slightly increased the deviations, but at any rate its influence
cannot have been great.

3. First of all we had now to investigate whether the agreement
might be improved by deducing for the whole period new elements
for the yearly motion, although it was improbable that this would
have much influence.

For this deduction, we have started from the above-mentioned
differences, obs.—comp. and have derived from them the corrections
of the elements formerly assumed. The values since 1899.0 were
not considered and the results of the 9 years 1890.0—1898.9 were
combined to 10 mean values in the same way as before.

In this way we found for the components of the yearly motion
the following revised values:

270 t—-148

t—z
x= + 0.100 cos 2 7 Pacer y = + .0'.054 cos 2 a Bae

and hence again:
Position-angle Maj. axis ellipse 19° east of merid. of Greenw.
Components of the motion in the direction of the principal axes:

t— Oct. 5 Oras
zw’ = + 0".104 cos 2a —- —- v= £210! 044 sin 2 5 === —
2 oa 365 y "365

and so the results are but slightly different from those found formerly.

The variations, which the computed co-ordinates (on the original
axes) for the 10 starting-points have undergone, together with the
differences, obs.—comp., follow here:

( 160 )

A x comp. O-C. | Aycomp. | SOC fs
++ 0018 — 0003 + 0007 — 0007
> 2M ue 06 |. | apa
a get= 0). 25 SAO eas
Be 08) | 08, |) ea aE
= 06 | — 10 — 13 — 06
21 lig spt-pan, an | be 1 pga eae ane
LEMS | “iil 92) OME ae Gran ane,
RT a ema A TM hae Te) big key
2 s08 dc 8 + 4] + 06
= ame06 | — 08 + 13 00

If now again we derive the mean values of the residual differences
O.—C. for ALBRECHT’s original co-ordinates, we find:

from the 99 values from 1890.0--1899.8

ZAx’ ZzAy
eae == 55 (I) 050 We Ay = + 0",048
n

nu

from the 90 values from 1890.0—1898.9

SA Sage
VA Peers V 24¥ = + on049
n

nt

As will be seen, the mean value of the deviations still remains
greater than that formerly found for the years 1890 —1897, and the
deviations for the last years still show a very distinct systematic
character. Therefore, although the possibility remains that the
systematic errors have a greater influence than might be anticipated,
it becomes probable that the true motion of the pole deviates even
now perceptibly from my simple formula.

If this is the case, we can make 3 suppositions :
the yearly motion is more complicate than was assumed ;

2 the elements of the 14-monthly motion are not constant;

3 there are still other partial motions besides the two mentioned.

Any observed motion may be explained mathematically in any
of the three suppositions, aid then it remains only to be seen
which of these will lead to the physically simplest explanation.

—

( i6i )

Probably a long series of accurate observations will still have to
be made before a decision on this matter can be taken. Yet, in order
to prepare later researches in this direction, I have considered to
which conclusions the material in hand would lead in the first two
suppositions.

4. In the first place I have supposed that the assumed 14-
monthly motion is correct, and that its elements are constant.
Assuming this I have investigated which yearly motion would be
found for the three periods: 1890—1892, 1893—1895 and 1896—
1898 successively.

The following results were obtained :

1890—1892.

a= +0118 cos 20 = aa as =
18931895.

r= + 0".113 cos 22 = Yi cise GAiche are ae
1896—1898.

x= + 0".090 cos 22 = seep hanane a2 —s

and hence I derived:

Position-angles with respect to the merid. of Greenwich:

1890—1892 Major axis ellipse 34° east.
1893—1895 o a =; pil9® east.
1896—1898 ‘ 3 4° west.

Components of the motion in the direction of the principal axes:

1890—1892.
t — Sept. 21 — Sept, 21
zt as + 0".135 COs 2 vA ee ad dBc y! ——s 0'.063 ade 2 ies ep
365 365
1893—1895.
a = 0" 119 9 t— Oct. 5 ; 0” 05S ey i— Oct. 5
7 WE Eh y = — 0°.055 sin 2 mw — Bs
tke 365 y 365
' 1896—184¢8.
§— Oe 27 Fa Obie

y = — 0".047 sin 2 t ———

eee 000 cs
bam ie hay 2052 aineen 365

( 162.)

If the differences between these results are not to be ascribed to
perturbing influences during the observations (for instance local refract-
ions), our first supposition would lead us to the conclusion that the
elements of the yearly motion have varied gradually. The pole would
have remained behind in its motion, or actually would have de-
scribed its orbit in more than a year, while the orbit itself would
have become smaller, and the apses of the ellipse would have moved
in a direction opposite to that of the pole itself +).

5. After this I have started from the second supposition. The yearly
motion was taken to be constant, and first I assumed for it the
elements, which had been derived sub 3. Assuming this the 14-
monthly motion was derived separately for the same 3-yearly periods
as have been considered sub 4.

The results obtained were:

Amplitude. | Corr. Epoch.
| from x | from y from x from y
|
1890-1892 | o"188 | 0"175 4 AD dg) = lens
1893—1895 0.131 0.138 — 2 — 2
1896—1898 0.119 0.182 + 24 + 28

Secondiy I assumed the yearly motion to be as it had been
derived formerly from the observations 1890—1896, and then made
the computation again in the same way.

This time the results were:

hE

Amplitude, Corr. Epoch.
from & | from y from x from
1890—1892 | 0173 | 0''168 — 9d. — 8d.
1893—1895 0.146 0.146 — 4 — 4
1896—1898 0.105 0.126 + 29 + 32
|

differing but slightly from those of the first computation.

1) Compare also: CuannLer, Astr. Jown, Vol, XIX, N° 446 1898,

( 163 )

Consequently, assuming the yearly motion to be constant, we find for
the 14-monthly motion, both from the # and they, values of the am-
plitude that decrease pretty regularly and pretty rapidly '). For the
epoch we find from the first and the second period a fairly good agree-
ment *), whereas from the third we find a decidedly deviating value.

The reality of this last deviation is not very probable, and this
tends to diminish the force of the arguments which are in favour of the
acceptation of a decrease of the amplitude, which might be explained
by frictional influences *).

Physics. — “The properties of the pressure curves for co-existing
phases of mixtures”. By Prof. J. D. vAN DER WAALS.

In the “Verslagen en Mededeelingen der Akademie voor 1891”
I have deduced an explicite expression for the pressure in the case
that one of the phases of a mixture may be considered as a
rarefied gas.

Since that time the course of the value of the pressure for diffe-
rent mixtures has been determined experimentally in different ways,
so that we are enabled to test the given formula at the results of
the experiments.

In the given formula an auxiliary quantity ws occurs, which

a, Se
represents: pu — [pdv or pp—MRTlog(v—b:)——- , while the diffe-
; v

. F f A : du
rential coefficient of this quantity with respect to «, viz. =)
& Sy T

may be approximately equated to — ae

As examples I draw attention to two shapes of these curves,
which have been communicated in the Proceedings of this Academy :
1st. by Mr. Harrman for mixtures of CH;Cl and CO, and 24 by
Mr. Cunagus for mixtures of Acetone and Ether. The curve traced
by Mr. Hartman is remarkable on account of the simple shape of
p=f (x), which is almost a straight line, and that of Mr. Cunarus

1) See also Archiv. Neéerl. T. Il, p. 475 (29).

2) See also Archiv. Néerl. T. 11, p. 469 (28).

8) CHANDLER finds by his empirical theory that the amplitude varies periodically
and decreases in the years considered. It seems to me however that the foundation
of his formula is not yet sufliciently certain.

( 164 )

on account of the fact, that in the curve p = / (#9) a distinet inflection
point occurs.

The investigation in how far these curves agree with the given
formula, will show that in one respect these two shapes may be
considered as two limiting cases. For simplicity’s sake [ shall write

: , bez
henceforth “#z instead of WET In the same way I shall represent
(due
\ du ie ee. : bret ,
—— by wz, and a similar expression for the second differential
MRT

coefficient by wr. The value of these quantities for = 0 and «=
will be: fg» oy feo and “4, “’; and w";. Then p may be repre-
sented by the formula:

p = MRI (1—ay) #1 1H) A MRT 2, ots (Ine, 1
or

f ‘
P= Do (1—2}) ett — Hy — 1 Hay = Pt e ¥xy—F, F(1—2)) 4a,

In general we cannot express p explicitely as function of 2. But
for the same value of p we have the following relation between 2,
; 5 : d
and «g which may be derived from the equality of (=) for the

dx/ yP
two phases :

Eat " rT
ee SS

1—2, 1—ay

If we take into consideration, that for very low temperatures,
ar
ee

. . a . .

the value of w's is approximately equal to — qe We may indi-
v

Seas) ono Ge
cate a few limiting cases for the course of the quantities Fe and
zc

the shapes which the pressure curves will assume in these limiting
shapes. I have already assumed in my: “Théorie Moléculaire” that
ar
gece

bx

by approximation y', may be equated to — and the deductions

av
which have there been obtained from this assumption, have since
been confirmed to such an extent by the properties of the plaitpoint
curves for mixtures, which show a minimum critical temperature,

( 165 )

that I feel justified in deriving further results from this approxi-
mation. I shall, however, first derive other equations which are
independent of this approximation from the given values for p.

If we write p= MRTe * Cat fl—2x, + 2, fry then follows:

(e* 1 — 1) + 2 eM uz,

“
= — es, +

p dx ,
— 1 — 2+ ajehe

_ @f—)E +40 —9) 8)

ul
l—v+ ae

This latter value agrees peifectly with that which is found by
starting from the rigorously correct equation:

if compared with v,, the volume of a molecule in the vapour phasis,
MRT

dv
we neglect the value of v, and (>) and equate vy to
dity/ oT a Pp

We may namely put w-+ pe tor ¢; we find then:

7 2 ‘d
(2)= MRE tog) =)
t)/ pT La de\/ pT
and
‘ sire RR, wy (ae
dx, pT x, (1 — 2) at)

After elimination of 2, we find:

fee tee LE Pe see)

ld To—2] |
eae oe 1 re eet
pd (1—2)) (1 — 2) + 2 eft

The following wellknown facts may be deduced from this equation:
d, : ’ d :
it, 2 = 0 if = 1 or fait 0- or ts =loyy and) 2nd ? =0 if
dixy day
@
14 2, (1—a) wh, = 0 oF (75) =i.
re dvy*/yT

( 166 )
From

dp (e*—1) [1+ (Va) 75, ]

dry a
— ry + 7 e™

we deduce

Pp

aap a uw’ " “ut “

day 1 dp (e ™—1)+ a7, 6 *14'y, CE) Shes.

dp = p day a “! ais re re "4

i l—at+aje % oe a I

day

(122) ey ae
ry \
a
1+ (l—m) a

or

dp

wees hes

day” a enn (1 — 2 2x,) )
== ee —— ———————————— SSS

dp SEA lie wa, eS far

day

a(l—2z
si He i( 1) =
7] + a, (1 — 2) (es
Let us put some special cases:
Put
e '=1 or a's 0, 1S 0S
then :
dp
dr,2

=pe tlt —a)enj

as ve Gan ape meee :
If «, is positive “? is also positive; so in this case there is
Zz ) dx? ?

a minimum pressure. But from the assumption that MRT yw may
be equated with __——"“ follows: MRT” =———— .
x ay

conclude therefore, that at very low 7 there is a minimum pressure

We

cal

P . ay c :
for that mixture, for which i has a maximum value. A mixture
@

. - Ae
with a maximum value for — has, however, not been found as
x

yet, and it is even doubted whether this will ever occur for normal
substances.

e 167}

o
Ts ; Din. c ”
If &,, 1S negative, then de is negative, when 1 + 2, (1 — 2%) ey

is positive. So there is for » 2 maximum value for that mixture

; it. Qa : ;
which shows a minimum for ine Aud numerous instances of this
(a

have been found. If #, has so great a negative value, that
1 + x, (1 — 7) “, is also negative, then p has again a minimum

value. That 1 + 2, (1 — x) a is negative, implies however, that

d? \ é ;
73). 18 negative, and can therefore only occur for unstable phases.
% vy~ pr

And for this too we may say that it is very doubtful, whether this
can ever be the case for mixtures of normal substances.

If

we find:
d*p ) Wo
= Gey al
( dina) = Pi to (Be )
ug : &p
If the pressure is increasing at «= 0, then (4) has the same
LAC

sion as w”,. If the pressure should also increase on the side where
a,=1, and if there should therefore be a maximum pressure for a
dz

certain value of x,, then the quantity = has all over the curve
aan)”

p=f(%) the sign «", which is necessarily negative. The supposition

a
ah
aad td b ° a "
that we may put MTR «) = — ae makes the sign of «” depen-
r dun 7
dent on:
G b
Cy He 29 “2
2 2
2) b2 Doz db by by be

or = 3
[ by (1—z) +bha i :

“if : b) -+ bg
at least if we may replace J). by the approximate value ae a

But even though this should not be quite accurate, yet it is not to

be expected that the value of a should deviate much from the

given formula. The given formula makes the sign of «' dependent

( 168 )

ay dg 9 a9 ° .
on +——2 , so that all over the curve the sign remains
b,? by” db, by

invariable.
If on one of the sides the pressure should decrease, and if we
put on that side 2;=0, then the value of e*» is smailer than 1.

2 ; 2
We get then was <1. But not before iyi the sign of (2
x Ly 2 \dx,?/ 9
will differ from that of «5.
If we have the exceptional case that there is a maximum
pressure just on one of the sides then e*»=1, and _ therefore

ad : :
€ z) =p, “'. This is almost, if not quite the case for the mixtures
C e~

of acetone and ether investigated by Mr. Cunarus. On the ether-
side the pressure is maximum, and the simple shape of the curve

: ad
p=f(«), for which the curvature is always such that a
5 la

follows immediately from this supposition.

In this curve of CuNAEUs we have the case that one of the mix-
tures has a minimum critical temperature, though it is one of the
components, but on the other hand in the curve of HARTMAN we
have almost, if not quite the case, that «': is constant for all values
of «, and that there is therefore no question of a minimum critical
temperature — not even if we should take « far beyond the limits
of «=0 and e=1. It is not to be expected that this will ever
be rigorously the case. Only if we put for 4. the approximate
value b; (l—a) + by 2, = would be a linear function of x, in case

z
ea a5 Aare ols equal to zero. But even if we do not introduce
by? | bg? «By
this approximate value of 6,, we may at least imagine as limiting

a ees : : :
ease such a value of —, that it differs little from a straight line

x
between 0 and 1. As limiting ease we may therefore put “¢’; = constant.
Then we get “:, —@, u's, = uy and fry+ (l—2) «e's, = 4, and
cohol te teer AE Ho \ \

p = MRT (1—2)) eo—! + MRT ex, e:—1
or
p= po (1—2) + pi)

Consequently p =f (#)) is exactly a straight line, which HarTMAN
has found for mixtures of CO, and CH; Cl by approximation.
Moreover, it follows immediately from the value which we have

( 169 )

&p os A Ge
found for —~, that if we always put «7 and so also «7 , as equal
div}* : :

to zero, the value of this quantity is always equai to zero, and the
pressure must be represented by a straight line.

In this special case it is also possible to give p=/ («:) explici-
citely. We have namely as relation between 7 and 29:

x r , @ v Dp
Bas. u eat os bai Pa PL
1—2, 1—2x, l—2r, 1—2z Po
or
, 1—wzy
l—vr), SS Sao SSS
1—2, +- Po Wo
PL
and
Po
—= To
= P\
2) =
pe
1—zr, 4. Po Fo
P

Substituting these values we find:

p= Po Pi
Pi (1— a) + 7% 72

The curve p =f (#2) traced by Hartman, resembles a hyperbola,
but it deviates too much from it for the deviations to be ascribed
to experimental errors. But in reality, these observations have been
made at a too high temperature for considering the vapour phasis
as a rarefied gasphasis. Specially for carbonic acid, where the pres-
sure was even greater than 45 atmospheres, the deviations, caused
by it, must have been considerable. It would be interesting to
investigate whether at a lower temperature (HaRTMAN observed at
9°,5) the vapourbranch would approach closer to a hyperbola.

We may in this case write for p == / (9):

1 1—2y Lo

——? ’

Po P)
from which, as we are here concerned with gasphases, follows:
v= vp (l—ay) + 2 ay.

If we take therefore an arbitrary quantity of the saturated vapour

( 170 )

of the first substance, and also an arbitrary quantity of the saturated
vapour of the second, and if they mix in a volume which is the
sum of the two volumes, the mixture is again saturated vapour.
This result deviates altogether from the law of Dauroy applied
to saturated vapour. But this law of Darron will only hold
good as an approximation, if the liquid, which would be formed
through condensation, may be considered as unmixed liquid.

It is well-known that Dante Bertngnor has put «9? = aya. I
have refuted this opinion some time ago, first because the ground
which was alleged for concluding to this relation, seémed incorrect
to me, as it does still, but secondiy because the great variety, which
the critical phenomena of mixtures show, seemed to me to clash
with the assumption of such a simple relation between a)., a) and ag.
Since I have learned to ascribe many complications, which mixtures
show, to the anomaly of the components themselves, a great many
objections, which I had against the relation a2 ={/ a, ag, have lost
their weight, and any rate I think it desirable to keep in view at
every phenomenon the possibility, that this relation should be ful-

: 5 dnc ag
filled. If we do so also in this case, the condition that oa be a
xz

linear function of ;, becomes at least by approximation the following:

Vay ve) = 0
( by by ae

or the critical expressions of the components are the same. Now it
is indeed remarkable, that in the mixture of Harrman, for which
the critical temperatures are almost in the proportion of 3 to 4,
the critical expressions differ comparatively little — that of CO,
being equal to 73 and that of CH, Cl to 65 or 66 atmospheres.
The condition that the critical expressions must be the same for

the components, is fulfilled if 7-, = 7, cat so if the critical tem-
1

peratures are proportional to the volumes of the molecules. And
though this condition is not quite fulfilled for CO, and CH, Cl, yet it is
fulfilled in an incomparably greater degree than for the other examined
mixtures, for which the substance with the smallest molecule pos-
sesses the highest critical temperature. So is in a mixture of acetone
and ether the critical temperature of ether lower than that of acetone,
whereas the volume of the molecules of ether exceeds that of acetone.

‘O Va

For acetone and ether the condition mn = - is certainly not ful-

1 2

G@1718)

filled and in close connection with this is the great difference in the
curve determined by CuNAgEUs as compared with that of Harrman !).

In what precedes we have been specially oceupied with the dif-
ference in the course of p=//(,) for these mixtures. Let us also
pay attention to p= / (#2). As the elimination of x; from the equation:

is not possible, when w'sz, depends on 2), p can generally not be

uv : dj
expressed explicitely in 2. Yet we may deduce formulae for ah
ni)
dp : : ha larg ;
~, which are of importance for the determination of the dif-
@o~
ferent shapes of these curves.
From the two strictly accurate equations:

and

Cg
% dp = (#2—2) (es) diy
aX, pr
and
ae
Vi9 dp = (a1 —29) = x dity
@y pr
follows, in case the second phasis is a rarefied vapour-phasis, and
we may consequently put v2) =v, and vy, = — vg:
as aC
Ga) day = (- :) dity
diy? / pT ditg?/ »T
or
diay \ day

ee Sl He : Lh Ge
# (a)t 1 + 2 (1—2)) fey ae

% (1—2p) k
When the second phasis follows the gas laws sufficiently, the
second term is simplified to the form given here,

By means of this relation between dz, and dx, and of the relation
XQ Cal

iy
= e “1, we find:
2 1s,

1) The value of a; caleulated by Mr. Quine for mixtures of C1H and C,

»» how-
ever, does not fulfil the relation a3 = Vaya.

12
Proceedings Royal Acad, Amsterdam. Vol. ILL,

( 172 )

1 dp 1 dp dz, es (1a \(1s, a ee fn)

Pp di, P day ditg

or

d a j
Ei =p (1—e Me \ ay a ay)
diy

It appears from this formula that p as function of 2, presents a

maximum or a minimum only when e*:=1. In the case, that a
longitudinal plait exists, there are two more values of «,, for which
p as function of 7; might become maximum or minimum in the
unstable region, but this is not the case for p as function of «9.
The curve p=f(#9) presents two cusps for the values of 29,
which are conjugated to those values of x), for which 1 +-2,(1—2) fe

should be zero. This I have already pointed out in the Théor. Mol.
ey é ne :
In order to determine oe we differentiate the logarithm of the

ary
last equation, which yields:

d*p
diy? dey(ldp . (eo "—1)4+a ef a ne oda
dp ~ dite l p de, (eine “en eee oe j
diy
or
1, p lp dx ON aed aa , Ee ed 1
Dae eae po tens | +
4 a 1 Sey + a; en x 1— 2,+-2,e°" Pee |
Special cases are:
d*p dx.
ay Bel zr, (1 — 2) un’ =0 then WO, is | =
(2) Sate dé xi ’ dig? » as re ice)

in this case. We have already pointed out, that the curve p= f(g)
presents cusps in the points conjugated to these values of 2.
Pp "x
b) Be «a's, =0, then — = ——t . If we com-
) rh ee 2 pes ae

: we GH | :
pare this value with ae it appears, that at the point of contact
ary

the two curves p =f (2,) and p= /f (a2) lie on the same side of the
tangent. he curvatures however are unequal, except in the case,
that for such a point 2;=0. For the mixture of acetone and ether

(173 )

this exception occurs at least approximately on the side of the ether.

dy 2 (eo — 1)? + we
7, — 0 (+) — eae Ee .
(ec) Be 2 , then ize), Po Gor
‘ Pp
This equation shows, that (<5) will be negative only by
dz*/ , :

exception; only when wz”, is negative and has a numeric value,
greater than (e“«—1)*. It may however occur, and that on both
sides for mixtures with maximum-pressure. It the following three
figures the curves p=/(«)) and p=/(), which may then occur,
are drawn.

Fig. 1. Fig. 2. Fig. 3.

In fig. 1 a curve has been drawn, for which the maximum-
?
pressure is not much greater than the pressures on both sides, and
for which therefore e“— 1 has a small value, even on the sides.
J
As in the case of a maximum-pressure the quantity w” is negative,
@p : .
may be negative on both sides.
dz,” te)
0

In fig. 2 this is the case only on one side, while in fig. 3 the

9 : &p
value of (e“»— 1} is supposed to be great enough, to cause — to
LQ~

be positive on both sides.

The curve, traced by Mr. Cunagus relating to his investigation
on acetone and ether is therefore to be considered as either the
lefthand or the righthand half of fig. 3, and the point of inflection,
which he has found, was to be expected, as on the side of acetone

vg —

v
o\. Sey
) is rather great, viz. 3,5.
“a 0
From the value of «,; and x,, at which the point of inflection has

been found, we may derive the value of «” with the aid of the

xy

the value of e“o—1= (

12*

(174)

dp

y 2°
dry”

formula we haye found for To that purpose we have to equate

2 1— 2,

dp dx
the factor of eee to zero. If we _ substitute for

Ak Akg — & a

we may write this factor as follows:

(e’
é “ly

1 lg — 2) "
pbeidin.dtign. Th ay st ae [2 oe ee C= )| t

From this we deduce for the point of inflection:
(2 — %)?
; a (1 — 2)
= Le —— ;
2 (9 — a)? + x, (1— 2)

In the experiments of Mr. CuNAEUS, we are not perfectly sure
of the values of ; and «xy for the point of inflection '), The numerie
value of «” cannot therefore be found with accuracy. Put

*1

" 8
, then the value of — w, = Zz put 2 = 0,45

1
=. and 23

‘

ce| bo

and #2 = 0,65, then the value of — wu", will be found slightly tess

than unity.

We can predict the course of the critical curves for mixtures of
acetone and ether, from the properties of the pressure-curves for
these mixtures at low temperatures. Let us imagine the critical
curve, either the plaitpoint-curve or the curve of the critical points
of contact of Cl H and Cy Hg, and let us take the upper half of it,
ie. that part, that lies above the minimum-temperature. That mini-
mum temperature, the critical point of ether, will be the starting
point. We have therefore reason to expect that mixtures of ether
in which a little quantity of acetone has been solved, will present
r.c. II. But for these critical curves also it is to be expected that
they will deviate so slightly from one another, that it will be
difficult to observe the retrograde condensation *).

1) In the determination of the vapour-phasis by means of the refractive power, the
circumstance, that the glass plates are covered with a condensed layer has an influence,
which is probably large enough, to vitiate noticeably the values found fur ay.

2) Let us avail ourselves of this occasion to point out that the rule, given by Prof.
KuenEN, to find 7¢ IL is not quite correct. Prof. KuENEN thought that 7¢ LIL is to
be looked for in mixtures of substances, of which that one, which has the highest
critical temperature, has at equal temperatures also the highest vapour tensions. If
we consider a plaitpoint curve, beginning exactly at the minimum critical temperature
and therefore just beginning with 7e II, the vapour tension of the component with
the highest 7; will be lower than that of the other component; and the more so,
when the difference between 7, and 7%, is large.

nt \

(175 )

: nas ;
Let us write the value of ae also under the following form:

aLg
Cp 2 E sae al (72—2)) [ tex, |
dag? a (1—ag)! ¢ La, (1—2y) (oe Sarees

a
This form enables us to conclude to the curvature of the vapour-
branch, if it has an unstable part !), in consequence of the presence of
a longitudinal plait, which intersects the liquid branch. For this unstable
part we have 1 + 2,(1 — 2) ae <0, and ue and pata a tee

has the same sign. For this unstable part of the vapour branch
we get therefore >. Let us imagine two values of 2, dif-
fering very little from that which makes 1 + 2, (1 — 2) fe =O, and
chosen on either side of it, then 1+ 2, (1 — 7) 2" has either a
very small positive value or a very small negative att and therefore

x on =
7a very great positive or a very great negative

1+ x (1— 2) x

: : P
value. This makes us conclude that the sign of 4 changes for
ok)
those values of 22, which are conjugated to these, at which the
liquid branch enters or leaves the unstable region. At the extremities
of the unstable part of the vapour branch we find therefore cusps.
Consequently the two stable parts of the vapour-branch end with a
a

negative value of As a rule the vapour-branch at «= 0 and

Ary”
ae d*p
«=1 has a positive value of ae therefore there are also as arule
Lo

2
two points, where = will be equal to zero. Probably these points
2
always lie near the cusps. The following figure gives a shape of
the vapour branch fulfilling these conditions.
If before its end the vapour branch should possess a maximum,
the second inflection point is unnecessary and its shape will be
represented by fig. 5.

1) We use here the term “unstable part” to indicate that the phases, represented
by it, could only co-exist with unstable phases, Considered in themselves these
phases are stable.

( 1%6 )

Fig. 4. Fig. 5.
This latter figure represents the vapour branch of mixtures of
phenol and water below the critical temperature of complete mixture.

If the second phasis is a rarefied gasphasis, the pressure of which
is p, p(l1—«) represents the partial pressure of the first component
and pz that of the second component. The value of these quantities
is given by

Fy. —2*) H -1
p(l—a) = MRT(1—2)e'
and
& H(1~ 4) H _
pty= MRT x e€”
and
tr etme Bay
p (I=) =p) (I—m)
and

| a HHH) ae
Po — Pi 7) é

We conclude from this:

dp (1—ag) 1— 2, (
EE Ss 1 (1—
dry se ( sane 3) M4
dp tg ts v |
——s = 4p) = 1 2, (1—zx)) “.
day LZ ry ( + 1 ( 1) h af
And
d*p (1—2p) 1—ay \ ” ”
ee ES ES LL pe ea ay ee eeeH |) 1 x, (l—ay, 2 =
dr’ P Ty ae a ates ras

d [3 + a (1-2) |

pat dx,

(177 )

=p sed }a—n) fe, [! + x, (l—2,) | -+
ie :

d [3 ome (aay) «| |

t dey j

By adding the two last conditions, we find:

BF ut (re ny (AO 4 oma}
Pp dx,? 1-2, (l—2)) u “1 (x, (1—a,) 2, (L—2))
d M1 vy (1 — 2) oe)
Lg—2y i a4
rT (1—2)) dry ’

a form to which we may also reduce the form given before. From
the value for the first differential coefficients we deduce, that for
substances, which are perfectly miscible, the partial pressure of one
component decreases, when the second component is substituted for
a part of it. From this follows that the total pressure must be
smaller than the sum of the tensions of the separate components.
If 1+2,(1—2) wz, should be negative, the partial pressure of a
component increases on the other hand on substitution by the second
component. Then it will be the question whether the partial pressure
cannot rise so high, that it exceeds the initial value.

This question, however, cannot be soived without the knowledge
of the properties of the function yw.

Physics. — Dr. E. van Everpincen Jr.: “The Hatt-effect and
the increase of resistance of bismuth in the magnetic field at
very low temperatures.” II. (Communication N°. 58 from the
Physical Laboratory at Leiden, by Prof. H. Kameriinen
ONNES).

1. From the measurements of the Hatu-effect in bismuth at the
boiling-point of liquid nitrous oxide and liquid oxygen, described in
the Proceedings of 29 October 1899, p. 22i and 30 December 1899,
p- 380, it appeared that the Haxt-coefficient increased considerably
with falling temperatures; it hence seemed desirable to determine
this increase with greater accuracy. The measurements in liquid
nitrous oxide had shown that the strength of the magnetic field had

(178 )

a considerable influence on the temperature-coefficient. Hence also
the measurements in liquid oxygen ought to be taken with different
strengths of the field. For the theory of the phenomenon it is
necessary to know the resistance of the bismuth in the magnetic
field at the same temperatures, in order to be able to calculate the
angle through which the equipotential lines are turned. So I at
first decided to measure, in say five different fields, Haxt-effect,
resistance and increase of resistance at the temperature of the room
and at the boiling points of liquid nitrous oxide and oxygen. After- —
wards a series of measurements at the boiling point of methyl chloride
was added, and finally I completed the research by repeating the
same measurements at the boiling point of water. As_ earlier
researches!) have shown, that at still higher temperatures both HALL-
effect and increase of resistance become very small, it might be
considered superfluous to further raise the limit of temperatures.

Hence the temperatures range from — 182° C. te + 100° C. or
from 91° to 373° on the absolute scale.

2. Experimental arrangements. In all the experiments except
those at 100° C. the experimental plate of bismuth was mounted in
the apparatus, described in §6 of the communication of 30 December
1899). The only change made in this since then is that the streng-
thening-rim at*the lower end of ss (see fig. 2 of that communication)
has been omitted, and replaced by two glass tubes, fixed at both
sides of the vessel > and over which the thin paper of s3 is stretched.

In the modified section of the apparatus, fig. 1%, these tubes are
indicated by the letters « ‘This enabled me to adjust the vessel
between the pole-pieces and to take it out again without altering
the distance of the pole-pieces. In this manner 1* the apparatus
remained quite closed at t,, 2"¢ during the whole research the
distance between the poles, and hence the strength of field for a
given magnetising current, remained unaltered, and 3" the repair
of small faults in the various leads during the experiments was
facilitated.

The apparatus continued to give satisfactory results and was at
the end of the whole research still in good condition.

For the experiments at 100° C. the plate was placed in a copper

1) See for instance Lesret, Versl. der Verg. Kon. Ak. vy. Wetensch. van 28 Sept.
1895, p. 103, Comm. Phys. Lab. Leiden N°. 19, p. 26; Henperson, Wied. Anv. 53,
p- 912, 1894.

*) Versi. der Verg. van 80 December 1899, p. 380, Comm, N°. 53, p. 10.

Fig. 14% Fig. 1.

vessel, coated with asbestos and packed in wool, which was closed
at the upper end by means of cork and through which steam
was led.

Whilst therefore the baths of constant temperature presented no
special difficulties, we had to bestow great care to secure good
contact at the Hatt- and resistance electrodes. In earlier experi-
ments, soldering was deemed unsuitable, on account of the danger
of spoiling the purity of the bismuth So here we had to use
clamp-electrodes. It soon appeared that, for the contacts to resist
the intense cooling, they ought to be made elastic. Steel springs
could not be used, because of the disturbance they would have
caused in the magnetic field; brass springs, which were tried first,
appeared to lack sufficient elasticity, so that the contacts were
nevertheless spoiled on cooling. These difficulties were overcome, for
the most part at least, by using springs made of an alloy of Platinum
with 30 pCt. of Iridium.

With reference to fig. 1 we will now describe how the plate of
bismuth was fixed in the carrier in its fina! form.

For this purpose we first direct our attention to the perspective
drawing on the right. There we see the plate of bismuth P stuck
through the vertical slit of the frame R& to which the Platinum-
Iridium springs V, and V, are fixed by means of screws S, and 89.
To the extremities of these springs little Platinum pens are attached,
which go through cylindrical holes in & and end on the horizontal
line in the middle of the plate P. These constitute the resistance
electrodes, and are about 10 mm. apart. The springs Vy and V, are
placed in slits of the frame in order not to increase the total

( 180 )

breadth and are thus at the same time protected against damage.
To make sure that the liquefied gases reach the plate the central
portion of the vertical slit is widened and moreover large holes are
made in the sides of the frame.

In the middle of the upper and lower planes there is a small
hole 0. Through this enter the secondary electrodes of the plate-
carrier /, drawn in section in the figure. The primary-electrode 2,
has been screwed through the brass strip A, and through the frame
! and is therefore not elastic. £, on the contrary has been screwed
only through the brass plate A, and goes freely through /, whilst
Ag is elastically attached to /. The secondary electrodes 2; and Ey
are also elastically attached; they go freely through the brass plates
A; and Ay, but are screwed through the nuts 4, and M,, which
are pressed imwards by spirals of Piatinum-Iridium, whilst a pin
prevents them from turning together with the screws. The plate
A, is connected by a thin insulated wire to the copper wire D4.
To the wires D,...D4 the thin copper wires m, mg, mj, ng (see
fig. 1 Comm. N°. 53) are fixed by means of screw-connexions, From
the screws S, and S, copper wires of 0,1 mm. diameter go out of
the apparatus through the same glass tubes as m, and mg for the
measurement of the resistance.

In the experiments at 100° C. the plate-carrier / was made of
wood and the frame & of ivory; in the other experiments both
were made of ebonite.

3. Measurements of the Hawt-effect. The plate of bismuth which
served in all experiments was not the same as that used in the
preliminary experiments of Communication N°. 53, as the latter
was broken, when further observations had already been made at
some temperatures. The new plate was however obtained in the same
manner by electrolysis; the current for this was chosen somewhat
smaller than on the former occasion. The resistivity of this plate
appeared to be a little smaller than that of the other, while the
Tauu-effect and the increase of resistance were somewhat larger;
this indicates that this bismuth is a little purer. That however com-
plete purity is not yet attained follows from the most sensitive eri-
terion: the resistance out of the magnetic field at low temperatures,
to which we will draw attention once more further on.

The dimensions of the plate were: length 21 mm., breadth 9,1
mm., thickness 0,795 mm.

Of the method of observation nothing new need be mentioned }).

» Verslag d. Vergadering van 30 Mei 1896, p. 47. Comm. N° 26, p. 3.

-

( 181 )

As with the last measurements of Comm. N°. 53 the resistance in
the secondary circuit was measured for both directions of the mag-
netic field immediately after the determination of the resistance
required in the compensative-circuit. In order to be able to quickly
perform this measurement I proceeded in the following way: As a
commencement I observed the deflection of the galvanometer caused
in the secondary circuit by a WesTon-element when a resistance
of 50.000 Ohms was inserted and the poles of the element
were connected to two of the mercury-cups of the commutator
of this circuit), the other two mercury-cups being connected by a
short copper wire. As this deflection remained constant during a
series of observations, it need be observed only once. For the mea-
surement of the resistance the deflection was observed again after
a shunt had been made between the two first mentioned mercury-
cups with a known resistance about equal to that of the secondary
circuit, so that the deflection was reduced to about one half of its
former value. If we call a the total deflection, 6 the reduced deflec-

tion and w the resistance of the shunt, then the resistance of the
a—b

secondary circuit is w

First we give the results for the HALt-coefficient R in various
magnetic fields (in C.G.S. units).

Hatt-coefficient R.

Temperature in degrees Centigrade.

+ 100° | + = 11°5 | — 238° | — 90°

mM |R | MT R | mu | R | mM | R

1090 | 7.23 | 1050 13.24 1060 |16.90 | 1020 |27.88 } 1050 61.8
2200 | 7.16 | 2100 |12.69 | 2120 115.83 2140 |24.80*} 2100 54.5
3920 | 6.99 | 3100 |12.06 | 3110 {14.98 | 3070 22.87 | 3830 46.2*
4800 | 6.87 | 4440 (11.42 | 3770 [14.55 | 3730 |21.85 | 6050 39.8
4870 | 6.82 | 6010 |10.61 | 4320 |14.13 | 4370 /21.10

5970 | 6.75 4440 [13.94 | 5180 |19.97
5260 13.39 | 6050 |18.68*

6010 |12.90

') See my thesis, plate LIL.

( 182 )

These results are represented graphically in fig. 2, where the
little crosses indicate observed points.

When a series of observations was finished usually one or more
of the determinations were repeated; on the one hand this gave a
means of testing the accuracy of the measurements, on the other
hand of testing the constancy of the temperatures. With + 100° C.
the two measurements in a field of about 4800 may serve for a
test; with — 23°C. those in a field of about 4400; with the tempe-
ratures — 90° and — 182° an asterisk in the table indicates that
the measurement was repeated and gave the same result; the value
46.2 in the field 3830 at —182° C. is the result of three meas-
urements in complete agreement !).

Usually before or after a series of measurements a determination
at ordinary temperature was made; these too agreed always well,
so that, at least during the three months occupied by the research,
no traces of a variation with time are to be detected.

With the experiments in methylchloride and nitrous-oxide no
trouble was experienced in keeping the vessel filled with liquid for
about 5 hours, so that there was abundant time for observations.

') The results, obtained with the plate afterwards broken, usually also agree with
those above mentioned.

ee eee

~

( 183 )

With the experiments in liquid oxygen however the vessel was
usually nearly empty before a new quantity of liquid could be
admitted, hence in this case the number of measurements was
somewhat reduced.

During the experiments at 11°,5 C. air was sucked through the
apparatus in order to ensure equilibrium of temperature with the
surroundings.

The results wholly confirm the rule formulated before!): that
the variation of the Hatt-coefficient with the magnetic field is
larger the lower the temperature, or: that the influence of temper-
ature on the Hawt-coefficient is largest in weak fields.

The value @4,8 of the Hatt-coefficient in the weakest field at
— 182° C., is again considerably larger than the highest value
obtained before *) (in the magnetic field 4400).

By means of the curves drawn through or between the observed
points the Hatt-coefficients in the fields 1000, 2000... 6000 were
interpolated, and multiplied by the corresponding magnetic fields.
The values of the thus obtained product R’/, which may be consi-
dered as a measure of the total transverse difference of potential,
are represented in the same figure. The scale value of these ordinates
is indicated on the right hand side.

Finally in fig. 3 the variation with temperature of the Han-

7

| 200 aso T 300

Fig. 3.
coefficient for given values of the field was represented for the fields

) Versl. 30 Mei ’96, p. &9. Comm. N° 26, p. 20.
*) w» 30 Dec. 799, p. 382. Comm. N° 53, p. 13,

( 184 )

1009 to 6000. The data for this figure are also given in the
table below.

Hatt-coefficient R.

Magnetic field in C, G. S. units.

obs

' | |
1000 | 2000 | 3000 | 4000 | 5000 | 6000

|

91 62.2 55. 49.7 | 45.8 42.6 40.1
|
183 28.0 22.9 21.5 20.2 18.9
|
|

250 17.0 16. 15.1 14.3 | 13.6 12.9
2

2845 13.3 1 12.1 115% EOS 10.6

a a a er,

373 7.28 (hel 7.06 6.95 6.84 6.72

It appears that in all fields the increase of the Hatt-coefficient
with falling temperature is approximately proportional to 7—@ ,
where a@ is greater than unity.

4. Measurements of resistivity and increase of resistivity. For
the method of observation reference may be made to Comm. N°. 48 }).
(The resistance in the circuit containing the resistance-electrodes
was measured in the same manner as that of the secondary circuit for
the Hau effect).

In the experiments before a determination of the resistance of the
bismuth in the magnetic field a determination without magnetic field
was always made, and the increase of resistance caused by the
magnetic field was calculated by a direct comparison of these resistances.

Hence we obtained for the resistance out of the magnetic field as many
values as there were measurements. ‘The agreement between these
values was always very satisfactory, once more confirming that the
temperature remained constant during the experiments. For, these
observations were made at the same time with those for the Hatt-effect.

For the calculation of the resistivity we further want the dimensions
of the plate in the transverse section, which were known accurately,
and the distance of the resistance-electrodes, which could not be
obtained with the same accuracy, were it only because the planes
of contact were rather large as compared with their distance. In

———

1) Versi. 25 Maart 99, p. 486. Comm, N°. 48, p. 6.

(185 )

order’ to get nevertheless at the various temperatures a good cor-
respondance in the values of the resistivity, immediately before or
after a series of measurements a determination of the resistance of
the bismuth at ordinary temperature was made. In this manner we
got an accurate determination of the ratio between this resistance
and that at the lower or higher temperature. Finally for the resist-
ivity at 11°5C. a value was accepted as right and from this the
values at other temperatures were calculated. The difference between
the value calculated in this manner and that obtained directly was
in the most unfavourable case only 2 pCt.

A correction for contraction of the plate of bismuth and the plate-
earrier by cooling would be too small to be worth considering.

We first communicate the results for the percentage increase of
the resistivity in the magnetic field.

Percentage increase of resistivity Avr.

Temperature iu degrees Centigrade.

+. 100°

+ 115 | — 93° | — 90° | —

M Ar M Ar M Ar M AY

2200 | 9.9 1050 | 0.9 | 1060 |} 1.5 | 1020 | 3.5 | 2050 | 35.9
3950 | 2.6 | 2060 | 3.0] 2140 | 5.2 | 2140 | 12.5 | 38730 | 90.2
4830 | 4.0 | 3060 | 5.8 | 3110 | 9.7 | 38100 | 22.4 | 4740 |127.1
6100 | £.8 | 4450 | 10.4 | 3790 | 13.2 | 3760 | 29.9 | 6000 |175.7
6030 | 16.6 | 4410 | 16.6 | 4150 | 34.6 |
5250 | 21.5 | 5200 | 47.7

6050 | 26.5 | 6110 | 59.6 |

It appeared that the formula for the increase of resistance given
in Comm. n°. 48
C, M?
Selo
1+ ym
represents very satisfactorily the determinations at all the temperatures
of observation. For brevity I shall not mention here the caleulated

‘) Versl. 25 Maart ’99, p. 485. Comm, N® 48, p. 4.

q

( 186 )

values and communicate only the values of C, and Cy, and the largest
deviations between calculation and observation.

| Largest
Taps m1 | Cy deviation.
91 0.312 14.027 3.7
183 0.285 4,381 0.69
250 0.219 1.681 0.34
284° 0.187 0.968 0.29
373 0.069 0.220 0.12

In fig. 4 the curves are drawn through the calculated points, the
crosses indicating the observations. They also show a good agreement,
while the deviations are not systematically distributed.

arene

OO ae ae

100

Vig. 4.

By means of the values of the percentage increase calculated from
this formula and the results for the resistivity out of the magnetic

( 187 )

field (second column) the following values for the resistivity in the
magnetic field have been found,

Resistivity 7 (multiplied by 10-‘),

Magnetic field in C. G. S. units.
Tens:

2000 4000

5000 | 6000

91 | 1.721 | 1.894 | 2.316 | 2.826 | 3.418 | 4.054 | 4.718
183 [1.526 | 1.578 | 1.701 | 1.853 | 2.023 | 2.219 | 2.493
250 | 1.600 | 1.623 | 1.683 | 1.744 | 1.828 | 1.920 | 2.020
284° | 1.690 | 1.703 | 1.738 | 1.783 | 1.839 | 1.904 | 1.967

373 | 2.094 | 2.098 | 2.111 | 2.129 | 2.152 | 2.180 | 2.219

These results are represented graphically in fig. 5.
If we compare them with those of FLemine and Dewar}, it

AR, ee ae
Cg PFS Pe A Oe

>

EB RSS1(REeSe

§

ne

\OLVA

as SelB II EVA al ala
LESS aN ees)

tll ea az!
COLE AA
SEE Aart
Bie
Stee Seis es |
Eh, a
EDaGlaeh Ven
fl a,
iD ERRSSeniciien

PZ ESSE
CSE AS Ge

g
ES
2
§

Fig. De

1) Proc. Roy. Soc. 60, p. 425, 1896.
13
Proceedings Royal Acad, Amsterdam, Vol. III,

( 188 )

appears that the general character of the curves is the same. The
resistivity out of the magnetic field however does not continuously
decrease here, as with the electrolytic bismuth from HarTMANN and
Braun, but reaches a minimum and then rises again to about the
value it showed at ordinary temperature. FLEMING and Dewar ')
found a similar behaviour with some samples of bismuth carefully
prepared by chemical means; my curve happens to coincide prac-
tically with the one they found with ,Marruey’s Bismuth (B)”.
Hence yery likely the bismuth of my plate also contains only a
very slight impurity; for the present research this impurity is of
no consequence.

5. Angle of rotation of the equipotential lines. A combination
of the results of § 3 and 4 enables us to calculate the angle, through
which the equipotential lines are turned in the magnetic field. Thus
if the product RM is devided by the resistivity 7, the quotient
is equal to the tangent of that angle. Again the quotient of
R and r is equal to that same tangent for a magnetic field 1, a
quantity first introduced by Lepuc*) and which we shall call D as
he did. From what follows it will appear that this quantity has a
simpler theoretical meaning than the Hatt-coefficient 2.

The results of the calculation of D are found in the following
table and in fig. 6.

Rotational coefficient DY (multiplied by 10°).

Maguetic field in C. G. S. units.

Deas a = =
1000 2000 3000 4000 5000 | 6000
91 32.9 23.8 17.6 13.4 10.5 8.5
183 | 17.7° 14.7 12.3° 10.6 9.1 7.8
250 | 10.48 10.45 9.50 8.66 7.82 6.39

2845 7.81 7.31 6.79 6.28 5.80 5.39

373 3.47 3.40 3.32 3.23 3.14 3.04

In order to facilitate a survey of the influence of temperature

1) Proc. Roy. Inst. June 5, 1896, p. T6.
2) La Lumiére Electrique 29, p. 280, 1888.

Fig. 6.

and of magnetic field on D, I tried to represent the results for
each of the five temperatures by a formula of the same form, and
succeeded very well with the formula

Dis

D

0
1+ DY M2 + .D, Me

As in the case with the increase of resistance I shall give here only
the constants, and the largest deviations from the calculated values.
M was expressed here in the umt 1000 C.G.8., D in the unit

10-> C.G:S.

284°

47.48
21.13
11.50
8.40
3.53

D

0.3708
0.1850
0.0885
0.0663
0.0155

dD,

0.06603
0.01714
0.00736
0.00451
0.00188

| Largest

deviation.

0.14
0.18
0.03
0.03
0.002

126
(227)

Fig. 7 contains the curves drawn to represent these formulae.

13*

Fig. 7.

D, is evidently the limit to which 2 approaches in very weak
fields; this quantity is best adapted to form a judgment of the influence
of temperature alone, as the influence of the magnetic field on the
resistivity of bismuth may be neglected in such weak fields.

The coefficients 2) and D, show a somewhat parallel course, as

D :
appears from the column headed ae Only the ratio at 7= 373°
1
differs considerably; but here the line is almost straight and the

whole variation with J small, so that the interpolation and with
this the deduction of the coefficients becomes a little arbitrary. If
we put Dy= 0 for 7 = 373°, then the results for that temperature
are represented to within differences of at most 0,03 by a formula
with D, = 3,56 and D, = 0,0266, and hence with —° = 134.
1

All coefficients are approximately proportional to 7’—¢, where ais
greater than 1, especially for Dg.

Whilst, as we saw before, even at the lowest temperature the
product &M increases throughout with 47, we see here in fig. 6 that

(191)

the product DM (drawn on a scale 1000 time. smaller than D)
shows a maximum at —182°C.'). This peculiarity also is borne
out by the formula, in which above a definite value of M the term
D,M* dominates; one might even deduce from it that in strong
magnetic fields (17.000 to 20.000) the product would have its highest
value at the highest temperature, which does not seem very probable.
But it is possible that with the very high values which the trans-
verse difference of potential reaches in this plate a disturbance is
caused by the electrodes for the primary current, which are 3,5 mM.
thick and hence can certainly not be considered as mere points, so
that we do not measure the full Haut-effect. Von ErrinGsausENn
and Nernst?) found that the full Hatt-effect was almost reached
when the ratio of breadth to length was as 2 to 3, and the primary
electrodes fully covered the sides. In their research however they
did not obtain nearly such high values of R. If therefore my pre-
sumption is justified, one might suppose that the true effect is repre-
sented by the same formula with D,; = 0. DM approaches then for

ae) D6
all temperatures to a common limit so
1

6. Remarks on the theory of the phenomenon.

These results may contribute to the determination of the temper-
ature-functions @' and Q; in Vorat’s thermo-dynamical theory *).

The theory of the HaLu-phenomenon, based upon the recent theo-
ries of the conduction of electricity in metals, such as that of Lorentz *)
or as a part of the “Electron-theory of metals”, after DrupgE°), is
at this moment still in the nascent state. Yet I think it possible
even now to draw from the foregoing some conclusions with respect
to that theory and to indicate how far this theory is able to give
an explanation of the influence of temperature and of magnetic field
on the constants which represent the Haut-effect.

As yet the only completely elaborated theory on this basis is that
of RrecKE ®). This gives the following formula’) for the HALL-coefiicient:

1) This maximum 0,536 is smaller than the value 0,740, given in Communication
N°. 53. There however a preliminary value for the resistance was assumed which
now appears to have been too low.

*) Wien. Sitz. Ber. 94, p. 568, 1887.

8) Wied. Ann. 67, p. 717, 1899.

4) Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten
Korpern. Leiden, 1895.

®) Ann. der Physik. 1, p. 566, 1900.

®) Wied. Ann. 66, p. 345 en 545, 1895S,

) ib. p. 563,

( 192 )

1 u? gn—v* gp

¥Y Ugn+? Ip

(y = conductivity, «~andv velocities of the charged particles
caused by a potential gradient 1, y, and gy, velocities caused by a
temperature gradient 1).

Hence for D we find:

p) 2
U- In—V* Jp

u gn+v Ip

According to Rigcke’s theory u and »v, and likewise g, and gn,
are to be multiplied by the same factor for variations of temperature.
From this it follows immediately that with change of temperature
D is multiplied by the same factor as u or v.

Precisely the same result is deduced from the formula for the
Hatu-phenomenon in electrolytes, given in my thesis for the doctorate
and in Comm. N® 417), which wholly agrees with a formula deduced
by Wrinp*) for the Hatt-effect in metals. This reads:

R =r (u—v) hence D = (u—v).

If « and » undergo proportional variations with temperature 2
here also is multiplied with the same factor. The same would
apply if w were many times greater than v, or the reverse. Therefore
we shall assume for simplicity that the temperature-variation of D
is controlled by that of u. According to the deductions in my thesis
and to the theories of Riecke and Drupr

ert
u= K — !)
Vv

where K is independent of the temperature, 7 is the mean free path
and v the mean velocity of the charged particles.
The suppositions made regarding the variations of 7 and v with
temperature will hence determine the temperature factor of wu.
RIECKE assumes:

i=) —/2)
v=ce//T(1+ 0%

') Thesis p. 107. In Comm. n° 41 (Versl. d. Verg. 28 Mei 1898, p. 53, Comm. n°, 41
p. 9.) the formula for D contains another numerical factor.

2) Verh. Kon. Ak. v. Wet. Deel V N°, 3, § 17.

8) Thesis p. 104, Rigcke 1. c, p. 277, Drupe |, ¢. p. 575,

( 193 )
hence the temperature factor of D becomes

1—(B+d)t
V3 ag

where ¢ means the temperature in centigrade degrees, and T the
absolute temperature. The shape of this formula remains the same
even if we should assume that v is strictly proportional to y 7,
as then only 3 becomes zero.

If this formula is applied to the values of 2,, these appear to
be reconcilable with it if (?--0) (or ? in the limit) is positive. Tn
the latter case this means that the mean free path decreases with
Tising temperatures, which is according to Rrecker’s assumptions.

“When the range of temperature from 373 to 91 (abs.) is sub-
divided into three parts, we find as mean values for (?+-0) or 7?

: 373 —2845 0,00549
2845183 0,00898
183 —91 0,01481

RIEcKE himself calculates!) @ and 6 from the variation of the
conductivities for heat and electricity in bismuth between 0° en 100° C.,
however using a relation between 0 and another temperature-coef-
ficient which is perhaps not unobjectionable ; he finds /? to be 0,00205,

3d — 0,0000103, hence

2 +5 =0,00204

a result of the same order of magnitude. Also considered apart
the results deduced above need not be called improbable.

Calculating however the values for the same temperature coefhi-
cient in the magnetic field 6000, we find

373 —2845 0,00382
2845183 0,00159
183 —91 —0,00207

It seems impossible that the value of ? could be so different in
the magnetic field.

) Le. p. 573,

(194)

An explanation of this apparent contradiction can be obtained by
means of the hypothesis, that in the magnetic field the number of
free charged particles is diminished, the same hypothesis, which leads
to an explanation of the increase of the resistance in the magnetie
field, and of the proportionality between longitudinal-effect and increase
of resistance 1).

Indeed in my thesis I ventured the supposition ®), that this
decrease is caused in the following way, that the particles with
velocities smaller than a certain amount (say smaller than a critical
velocity z) are caused to move in closed orbits in the magnetic field
and cease to partake in the transference of the current. It is evident
that the mean velocity of the remaining, free particles will be greater
than the mean velocity of all particles. Hence in our formula we
ought to insert for v the mean velocity of all particles, multiplied
by a factor q. In a magnetic field of definite strength the critical
velocity « has a definite value which in my thesis I assumed pro-
portional to “, The lower the temperature, the larger the number
of particles with velocities below the critical. If now for a
moment we assume MAXWELL’s law for the distribution of the veloc-
ities of the free particles, then it appears that the rate of increase
of q is greater, the larger the ratio of the critical velocity to the mean
velocity of all particles, or, that the rate of increase of g itself increases
with falling temperatures.

For a constant value of the magnetic field and hence of 2, this
result may be introduced easily into the formula by giving to 0 a
rather large negative value for a magnetic field of 6000; in this
manner the negative sign of (/ -+ 0) would be explained.

.We have not yet the data to enquire whether our hypothesis
gives a quantitative explanation of the phenomena. But we may
notice that the hypothesis is sufficient to also explain other partic-
ularities in the variation of the quantity D, as may be seen by
reference to fig. 6 and 7.

The decrease of D with increasing magnetic forces at constant
temperature (fig. 6) is explained immediately by the increase of 2;
for the mean velocity of all particles remains constant, and g con-
sequently increases. This decrease of D is most rapid at the lowest
temperature; this also is explainable, as then the critical velocity

') See Versl. Kon. Akad. y. Wetensch. 25 Maart 1899, p. 496. Comm. N°, 48 p. 23
*) See p. 112.

(195 )

is greatest as compared with the mean velocity and the rate of
increase of gq is larger. If the critical velocity happened to become
much larger than the mean velocity, v would become approximately
independent of temperature; hence this might be the explanation of
the small influence of the temperature in strong fields, and render
it probable that in a very strong field would become independent
of the temperature. A maximum of the quantity ”M at — 182°C.
would not be explained, but one might expect an approach to a
constant value, as the critical velocity and hence the mean value
of v for the free particles increases proportionately to 47, so that
D would decrease nearly proportionately to the inverse of 7, which
is completely in agreement with our formula, if we put in it Dg = 0,

Our hypothesis throws also some light upon the reason why the
increase of the resistance in the magnetic field for small strengths
is proportional to a power of M higher than first. For if we assume
MAXWELL’s Jaw, then the probability that a particle has a velocity

smaller than x is proportional to if ae— #2 dx; for very small values
of z we may take e—*° equal to unity, and find then that the number
of particles with velocities smaller than 2 would be proportional to
the third power of z, which means to the third power of M. The large
increase of the resistance at low temperatures can be explained by
the decrease of the mean velocity as compared with the critical
velocity. Finally we remark, that, as at — 182° C. the resistance is
increased nearly in the ratio of 1 to 3 in a magnetic field of
6000, it hence seems that about °/; of the free particles lose their
freedom in that case. At 100° C. on the contrary this number is
very small, so that between these temperatures g should undergo a
considerable change. This is in agreement with the large variation

of the value of (7+ 0).

This survey is of course only superficial and leaves several questions
undiscussed. I think however that it affords sufficient reason to
assume, that with the introduction of this hypothesis in the electron-
theory of metals a step has been made in the right direction,

( 196 )

Chemistry. — “On the system: |BtgOz,—N:0;—H,0|”. By Prof.
J. M. van BEMMELEN.

Dr. G. M. Rurren has occupied himself in the Inorganic chemical
Laboratory of the University of Leiden with the investigation of the
system

[Beg O; — No O; — H,O]

according to the phase rule. He also has, when studying the solid
phases, subjected the observations of former investigators (HEINTZ,
GLADSTONE, Becker, JANSSEN, RuGce, Yvon, Lipprecke, Dirre and
others) on the basic nitrates and the so-called “Magisterium Bis-
muthi” to a critical investigation.

His results were as follows:

A. The solid phases.

1. The neutral salt Br, Os.3 Ng 05.10 H,O (in future called
briefly Zj)1)). This formula accepted of late years has been found
correct. The salt does not possess a true melting point as formerly
stated (72°), but it decomposes at 75°,5 into a liquid and the basie
salt Bey Os. No OF H.0 (By—1—1).

The prismatic, triclinic crystals exhibit an angle of extinction of 26°.

Two further hydrates of the neutral salt were discovered: Zy
and Zs.

Il. The neutral salt Z; (with 3 Mols. of H,O). It was obtained
at the ordinary temperature from Z;,, or from Bz, O3 by addition
of anhydrous nitrie acid, in regular crystals as beautifully formed
rhombic dodecahedrons. It should be mentioned that its composition
eould not be determined directly, because it was not possible to
separate the erystals completely from the syrupy mother liquor. The
composition was deduced by means of SCHREINEMAKERS’ method of
calculating, from the graphical construction in an equilateral tri-
angle of the compositions: 1st of two different mother liquors which
were in equilibrium with erystals of Z3, and 2°¢ of the crystals
themselves with some of the mother liquor still adhering. The same
applies to the salts presently to be described Z, and Bi—s—1, which
also could not be separated from the adhering mother liquor.

Ill. The neutral salt Z, (with 4 mols. of H,O). A definite mode

1) In future the salts which contain 1 mol. of B,,O;, 3 Mol. NO; and 10 or 4
or 38 Mol. H,O will be briefly called Zj, Zs, Z,; similarly the basic salts will be
written Bnj—n,—n, if they contain n, Mol, of Bs: Os, ng Mol, Nz Os and n, Mol, H,O

(197 )

of preparing this cannot yet be given. The salt was accidentally
discovered when making efforts to realize points of a quadruple line
in the system [Zjo,Z,,L,G]'). The erystals differ from Zs; and Z),
as they are not regular and have an angle of extinction of 90°.

IV. Hydrate of Z in a colloidal state. This was discovered
when anhydrous nitric acid was dropped into a mixture of Z,, with
a strong solution of Bismuth nitrate. A salt was deposited in the
form of transparent jelly which enclosed all the mother liquor. The
colloidal state lasted, however, but a short time. Very soon small
erystals were deposited which made the impression of octahedrons,
perhaps Z:; or another hydrate. They have not yet been investigated.

V. The basic salt By-2~. In one experiment Z,) was decom-
posed at 75° (which gave rise to the formation of Bj—:—1), then
mixed with Zs, heated to 80° and cooled down to 68°. A crystalline
salt was produced which differed in form from Zj) and Zs, had an
angle of extinction of 40°, and the composition B,~2~2. More ana-
lyses are however desirable.

VI. The basic salt By1~2. The investigation and the analysis
confirmed the fact that this salt is the first product of the action
of cold water on Zj,; also of cold dilute nitric acid containing less
than 6 pCt. of N,O; on Zjo; or of cold water on a not too acid
solution of bismuth nitrate. It forms small scales, exceedingly thin
erystalline plates without a definite shape and showing double
refraction. They are not permanent when they remain in contact
with the mother liquor but gradually become converted into another
basic salt. It cannot even be dried over sulphuric acid without de-
composition. No nitric acid is expelled but it loses water until
0.7 mol. of this is left. This behaviour is not yet explained since
Bi_1_1 does not lose water over sulphuric acid. The velocity ot
change and the composition of the basic salt both depend on the
concentration of the mother liquor and the temperature. As such basic
salts have been found: By:-1, Bio—9—7, Be—s—a). It has not yet
been ascertained at what dilution and temperature between 20° and
75° the formation of B;;~». by the action of water on Zo ceases
and Byy—1 is formed (or Bio—9—7 or Be—s—s).

VII. ‘he basic salt By;—;. This salt is formed from Bi-1~2,

2} L=Solution, G = Vapour,

(198 )

when this remains in contact with a solution containing more than
1 pCt. N,O;. If the nitric acid amounted to a few percent only
the change required some months at the ordinary temperature.
When a few more percent were present the time was reduced to a
few weeks. ‘lhe more the strength of the acid approaches the point
where the existence of Z\, becomes possible, namely 24.83 pCt. of N,O,
with 32.9 pCt. of Bz.O; at 20°, the more quickly the change will
take place. For instance, if it contains 21 pCt. (with 27.15 pCt. of
Be,03) the change only takes a few hours at 20°1). At higher
temperatures — between the limits 9° and 75° — the change
proceeds proportionally more rapidly.

The crystals thus formed are probably monoclinic and have an
angle of extinction of 10°—15°. Their composition was determined
by analysis, which had not been done as yet.

When Zj,. decomposes at 75.5°, the same salt is formed, but
it then has another erystalline form. It forms hexagonal thin
prisms which are apparently isotropic but extinguish to the
right if they lie on a side plane (salt /?). Analysis gave the com-
position By-1:-1. It is also formed, together with the first form
(salt @), at lower temperatures, such as 65°, from Z, and a solution.
The salt # seems to be more stable than the salt @; since in a
solution from which the salt @ had first deposited, this was after
some time converted into the salt /, the liquid having undergone
no perceptible change in composition *).

VIII. The basic salt Be-s_ys. This salt is formed (as shown
by very concordant analyses) at the ordinary temperature from
B,_1~2, when this remains for some months in contact with a very
dilute solution (<1 pCt. of N,O; and < 0.33 pCt. of Beg Os).

It also erystallises out when Zj) is decomposed by water, and the
solid salt which is formed is dissolved in much water. This solution
after a short time deposits Bg—s—ss). Even when the scales (Bi—1~»)
are left for a long time over water so that they attract moisture
and become covered with a layer of liquid, this salt is gradually
formed. In one experiment, they were completely converted after

the lapse of one year *).
The crystals are bi-axial, optically negative and belong to the

1) The erystals of Bi—1—2 were shaken in a shaking-apparatus with the solutions
for 5 hours.
*) Some difference must exist, though a very small one,

8) For instance, a dilution obtained by adding 1 part of Zy) to 24 parts of H,0,

(199 )

rhombic system and consequently extinguish to the right. Placed
over sulphuric acid they behave like B;-;—: losing neither nitric
acid nor water.

They are also formed at higher temperatures from Bj—;~2 or
Bi-1-1, even when the solution is still more concentrated, but they
then appear as small right — angled rhombic crystals. They are very
stable, for they may be boiled for a considerable time with water
without losing their transparency. A portion, however, dissolves but
again deposits on cooling as Bs—s—os). Larger crystals of the same
composition are also formed. When heated for some hours on the
boiling waterbath, the crystals become opaque; they have then
disaggregated to a minute crystalline powder of Bo—)-1.

The number of mols. of water in the salt Bg—s—o(g) is not yet
quite fixed. It varies from 8—9 and it remains possible that there
exist two hydrates with 8 and 9 mols. of H,O respectively, and
that this may account for the small difference in the crystalline
form noticed in different preparations. A further investigation must
decide.

IX. The basic salt By—9—;. This compound is nearer to By—1—1
than the preceding one. By treating Zo with water a salt answer-
ing to this composition was obtained occasionally. The crystals
extinguish to the right like Be—s—s, but still they make another
impression; they also exhibit a weaker double-refraction.

On treating Z1) with warm water, not only Be—s—9s) but also
By-1-1 and Bio»; made their appearance and this appeared to
depend on the quantity of water present.

By-1-1 with a quantity of 1—about Sparts of water to Ipart of Z))
Bio=9—7 | > » % abouto—) >| ORs = 30" > ~ SU) sce 5 >

Be—s—s9) >» > >» » >» 20—25o0rmore » » » » » FZ

An investigation was instituted to see whether Bjo—9—7 represented
merely a state of transition between B,;—;—; and Bg—5—s, and whether
erystals were obtainable which stood nearer to By; 1; or to Bg—s—s,
but this investigation has not as yet given any positive results.

X. The basic salt By,—-1. As already stated above this salt was
obtained in a crystalline condition as the final product of the action
of boiling water on the neutral salt. This is in agreement with the
experience of former investigators. The crystals were too small to
permit their shape to be properly observed.

( 200 )

SG: The basic salt Bs-4-9, Bes "5; Bs_s—8, Bs_3—6 described
by Janssen, Becker, Durios and HERBERGER do not exist.
Following their methods of preparation no other salt than Be—5—s a);
could be obtained as shown by the crystalline form and the analysis.
As the analytical process used by these investigators was faulty
as regards the nitric acid, we may assume that they have found
too little nitric acid. By a too prolonged washing with hot water
(DurLos and HERBERGER) ‘they may have had to deal with mix-
tures of Beg—s—9 and Bo; ;. The said basic salts must therefore
be rejected as long as there is no better proof of their actual
existence.

XI. Magisterium Bismuthi. The preparation of this pharma-
ceutical preparation is differently described in the pharmacopaea and
chemical manuals and its composition is given wrongly. As all the
pharmacopaea direct the decomposition of Zj) with about 20 parts
of hot or boiling water, it cannot consist of B,j~;~2 or Bj 1-4, but
must contain Bg—s—9 (g) or Bio9_7, or a mixture of both, sometimes
even By_;—;. An investigation showed that different Dutch pharma-
ceutical preparations answered to the composition Bg—s—» s) and
others to a mixture of this salt with Byip—9—7.

B. EQuimLiBRIUMS IN THE sysTEM [Beg O;—N, O;—H,0]
WITH SOLID AND LIQUID PHASEs.

The vapour phase has been altogether left out of consideration so
that all results relate to the ordinary atmospheric pressure.

The course of the Isotherms, which indicate the composition of
the liquid phases which were in equilibrium with the different solid
phases, was totally or partially determined for three temperatures:
20°—30°—65°. Some few points were also determined at 9°, 11°
and temperatures between 65° and 80°.

These isotherms ware graphically represented in the well-known
manner in equilateral triangles ; with the aid of these a regular prism was
constructed, the length of which answers to the temperature axis }).

In this way a figure in space was formed of which I now present
to the meeting a plaster cast, with the followmg perspective drawing
of the same.

The triangle in the front surface of the figure corresponds to a

1) The points at the angles of each equilateral triangle (therefore the long sides of
the prism) answer to the compositions 100 parts of H,O, 100 parts of N,O;, 100 parts
of By. Os. (See figure.)

( 201 )

temperature of 9°. The point d which lies furthest-back is situated
in the triangle of 75°.5. The equilibria of the system which are
possible at these temperatures in the most dilute and the most
concentrated solutions, and also the equilibria at temperatures below
9° and above 76° are as yet entirely wanting.

100 Bi,0,

On the isotherm at 20°, the course of the branches was deter-
mined where the salts Bg—s—s, Bi—i—2, Zio and Z; occur as solid
phases in the system. In the figure it is shown by a dotted line.
The branch with Zo is determined at 30°, the branches with
Bi-1-1, Zo and Z; as solid phases are determined at 65°. The
courses of two quadruple lines ') were also determined.

1. The one (4 bc in the figure) which has the solid phases
Byi1 and Z,) has been determined between the temperatures
9° (a) and 75°5 (b) and further back to 72°(c). This line shows a tem-
perature maximum at 75°5, where Z)) is decomposed into By;—\—1
and liquid (p. 198). It then rebends itself. Its backward course has
been examined up to 72° (¢ in the fig.).

2. The quadruple line which has the solid phases Zi) and Z,

1) The quadruple lines separate the triple surfaces formed by the different isothermal
curves of diflerent temperatures,

( 202 )

has been determined between 9° and 65° (points d and e in the
fig.). The region of B,-;-; (A in the fig.) between 9° and 75°5
has been to a great extent explored, but its boundary with the
region By, ,;~2 and of Bs—5—9s) is not yet known. The regions of
Bi-1-2 and of Beg—s—s gs) are situated near the low concentrations,
They partly cover or practically comecide with the region of Bj4—1
or with each other, because B;-;~2, which is the more labile phase,
can change in presence of the same liquid into the more stable phases
B,-1-1 or Bg—s—s, which causes but very little change in the liquid
phase.

The region of Zi), as a solid phase (8 in the fig.), has been
explored between 9° and 75°5; except a small portion at the right
of the figure between 65° and 72°, where the region is probably
bounded by that of Bij.» and that of Z,. The missing part lies
between c and e as indicated in the figure by a right angle.

Of the region of Zs as a solid phase (C’ in the fig.) only a portion
is known: 1st. because the quadruple line with Z; and Z, as solid
phases, which must bound it on one side, has not yet been determined
Qnd because it has not been determined how far the isotherms with
Zz extend to the right. These have not been continued further than
the point, where the hquid phase reaches the strength of 1 mol. of
NO; on 1 mol. of H,O. It remains possible that with solutions,
which contain less water still, Zs is not capable of existence, but
that a neutral salt with less than 3 mols. of H,O, or an anhydrous
salt or a salt with more than 3 mols. of N.O; takes its place. In
each case the region of Z; must end and pass into another one
before the system is reached which consists entirely of Bz, O;
and N,O; }).

From this it is evident that the solubility of B;:—; increases
pretty regularly between the said temperatures with the amount of
nitric acid in the liquid phase, but that it again slightly decreases
after the temperature maximum of 75°.5, The solutions which are
in equilibrium with B,—:—1 differ (as above mentioned) very little
from those which belong to Bg—s—is), at least at 20°. The solubility
of Zo between 9° and 75° first decreases rapidly with the increase
of nitric acid in the liquid phase, then passes through a minimum
and then again inereases until Z; becomes the solid phase. The
solubility of Z,4 decreases rapidly with the increase of the strength
of the nitric acid. It is not known whether it also passes through
a minimum.

!) These systems lie in the graphic representation on the right side plane of the
regular triangular prism.

( 203 )

The graphic representation of the experimentally found triple-
planes and quadruple-lines in an equilateral triangle (in the well-
known manner) allows of the prediction of quite a series of cases
of equilibrium. So for example it may be concluded what will happen
when a certain quantity of Zo is treated at a certain temperature
(within the observed limits) with increasing quantities of water, i.e.
which solid phases are formed and what composition the liquid phase
possesses. Also what will happen when a certain quantity of the basic
salt B;_,—1 (with or without motherliquor) is treated with increasing
quantities of nitric acid of a certain strength, or when the strength
of the acid is increased. If may also be concluded which mixtures of
Be,Os, N.O; and H,0 may lead at a certain temperature to the for-
mation of one of two above mentioned solid phases, and which
changes that mixture will undergo at increasing or decreasing tem-
peratures. And so on,

The isothermal curves at temperatures above 75.5° are not yet
determined. This determination will present great difficulties in
its execution, particularly in the separation of the solid phases.

The agreement in form of the triple-lines in this system with
those of [Hg0—SO;—H,O] as determined by C. Horrsrema (Zeitschr.
physik. Chem. 1895, 17, 651) is worthy of notice.

Chemistry. — Prof. A. P. N. Francuront presents to the library
of the Academy the dissertation of Dr. L. VAN SCHERPENZEEL
entitled: “The action of hydrogen nitrate (real nitric acid)
on the three toluic acids and some of their derivatives”, the
contents of which he explains as follows:

The research of Dr. VAN SCHERPENZEEL is connected with that
of Dr. Montagne about which I reported Jast January and was under-
taken at the same time. It required the knowledge of a twenty new
eompounds which have been prepared by Dr. VAN SCHERPENZEEL
and are described in his dissertation.

Following up the researches of vAN RoMBURGH in 1885 and of
TAVERNE in 1897 and 1898 on the action of nitric acid on benzoic
acid and some of its derivatives, such as the methyl ester, the amide
and both the methylamides, the question arose what influence would
be excercised on the action of the nitric acid by the introduction
of an atomic group in different positions into the benzene nucleus.
Whilst Montagne had chosen the monochlorinederivatives and thus

Proceedings Royal Acad. Amsterdam, Vol. ILI. af

( 204 )

introduced the negative element chlorine into the nucleus, VAN
SCHERPENZEEL did the reverse and chose the monomethylderivatives
with the positive group CH;, which are isomeric with phenylacetic
acid and its derivatives already investigated by TAVERNE.

It has been known since long that the temperature plays an
important part in the action of nitric acid. VAN SCHERPENZEEL also
found that at zero mononitrocompounds are always formed, whilst
at the ordinary temperature dinitroderivatives are mostly produced,
although the longer duration of ihe action in the second case also
has a share in the result. Taverne had also obtained dinitro-
substances with phenylacetic acid and its derivatives, whilst with
benzoic acid only mononitroderivatives were formed, which according
to MonvTaGNE is also the case with the three monochloro-benzoic
acids.

The suitability of real nitric acid as a nitrating agent was also
again demonstrated here by the easy formation of the dinitrocom-
pounds without any oxidation.

The influence of the groups OH, OCH;, NHz, NHCHs; and N
(CHs). on the nitration of the benzene residue was shown to be the
strongest in the ease of those containing nitrogen. With ortho- and
meta toluic acid and their derivatives, where two isomeric nitro-com-
pounds are generated, the amount of that which is obtained as a bye-
product is much increased. In not a single case, however, was the
influence of the different groups of such a nature that the nitro-group
took up a position other than in the case of the free acid.

It deserves attention that in the case of the dimethylamides of
the three toluic acids no second nitro-group entered the benzene
nucleus even if they were exposed for 24 hours at the ordinary
temperature to the action of the nitric acid, whilst those of phenyl-
acetic acid and phenylpropionic acid yielded, according to TAVERNE,
dinitro-acid.

The following facts were noticed as regards the influence of the

itrated acid-residues on the nitrogen-containing groups. At zero,
neither the amides nor the methyl derivatives were decomposed.
At the ordinary temperature only the amides and monomethylamides
but not the dimethylamides were decomposed; the latter yielded
the dimethylamides of the mononitro-acids whilst the others were
decomposed and yielded dinitro-acids.

Stable methylnitramides were not obtained. There exist, therefore,
great differences between the derivatives of benzoic acid, of the three
chlorobenzoic acids, of phenylacetic and phenylpropionic acid and those
of the toluic acids; these differences may be reduced to their true dimens-

( 205 )

ions by means of more accurate determinations keeping account of the
temperature and time of action. If the present results are accepted, the
nitrotoluic acids which are mentioned now ought to be comparable with
trichloracetic acid. This is, however, an extraordinarily strong acid,
according to the affinity constant, which is not to be expected of
the nitrotoluic acids, the constant of which does not seem to have
been determined as yet. Again, according to the affinity constant,
benzoic acid is a weak acid which, excepting one case, becomes
still weaker by the introduction of a methyl group; para- and meta-
toluic acid, also phenylacetic acid are weaker, but for orthotoluic
acid an affinity constant twice as great as that of benzoic acid is
recorded. Although by the introduction of the nitrogroup, particularly
in orthoposition to the carboxyl group, the strength of the acid
is much increased — the affinity constant of orthonitrobenzoic acid
is more than a hundred times larger ihan that of benzoic acid —
this cannot cause the strength of the nitro-acids to equal that of
trichloracetic acid. There remains further the strange fact that no
difference has been noticed between the isomeric nitrotoluic acids
although great differences were to be expected.

From all this appears that the observed facts cannot be explained
simply by the negativeness of the acid-residue, but that other
causes take part in the matter as has been found repeatedly
former similar cases.

VAN SCHERPENZEEL regards the nitro-o-toluie acid melting at
145°, prepared by JAcoBsoN and WIeRss as a mixture and attributes
the same composition, namely 6 nitro-o-toluie acid (C Hs at 1), to
the acid which he has isolated from this mixture by converting it
into the methylesters, selecting their crystals and saponifying them;
it melts at 184°—184°.5.

The reasons for his opinion are as follows:

It is formed together with the acid which has the nitrogroup at
4 and it not only differs from this but also from those where the
nitrogroup stands at 3 and 5. The position 6 is after 4 the most
favorable for the introduction of the nitrogroup, namely meta to the
earbony! group, and ortho to the C Hs. On further nitration the same
dinitro-acid is produced which is formed from the 4 mononitro-acid.

The as yet unknown dinitro-m-toluic acid now obtained by van
SCHERPENZEEL has been given by him the formula 4.2 (C Hg at 1)
because the two preceding mononitro-acids are 4 and 2 and also

14*

( 206 )

because it is the most probable, since the nitrogroup does not readily
take up the paraposition in regard to carboxyl during nitration.

This acid gives a violet coloration with alkalis, the colour changing
gradually into dark red, a phenomenon observed also in other
nitro-compounds and described by V. Mryer, Losey pe Bruyn,
HANtzscu and others. Tt is remarkable that 2.6 dinitro-p-toluic
acid and 4.6 dinitro-o-toluic acid did not give this reaction although
from the position of the nitro-groups they might have been expected
to do so.

Van SCHERPENZEEL finally noticed a very peculiar property of
the dimethylamide of 4 nitro-metatoluic acid prepared by means of
dimethylamine from the chloride of that acid. The colourless thick
crystals on being exposed to light, more rapidly in direct sunlight,
assumed a red colour which is not superficial as may be proved by
rubbing them to powder and examining the fine particles under the
microscope. The colour does not disappear when the substance is
kept in the dark at the ordinary temperature, but on being repeat-
edly recrystallized colourless crystals are always obtained which again
turn red on exposure to light. This phenomenon somewhat resem-
bles that to which Marckwatp has given the name “Phototropy”.
It is remarkable, however, that when the same compound is pre-
pared in another way, namely by nitrating the dimethylamide of
m-toluic acid it does not show this phenomenon; this would indicate
the presence of an unremovable impurity, but no proof could be
given of its existence.

He, therefore, prepared the chloride of o nitrobenzoic acid and
from this the as yet unknown dimethylamide melting at 78°. This
also turned red on exposure to light although not so strongly.

After remarking that the dimethylamides used in his experiments
were more soluble in water than the monomethylamides and that
the latter were again more soluble than the amides, he gives in
the annexed table the melting points of the substances mentioned.
They exhibit few deviations from the ordinary regularities. It is a
peculiar fact that whilst the melting points of nearly all the deriva-
tives of 4 nitro-o-toluie acid are situated higher than those of their
isomers, the acid itself and its chloride have lower melting points:

( 207 )

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( 208 )

Chemistry. — ‘Thermodynamics of Standard-Cells” (3° Part). By |
Dr. Ernst Conren (Communicated by Prof. H. W. Baxuuts
RoozEBOOM).

1, It is my intention, in this communication, to apply the
previously developed theory to the Wursron-cadmiumstandard-cell
and to show that it is also here in perfect agreement with experi-
ment. In the first place the mechanism of the reaction will be more
closely considered.

The cell is constructed !) as follows:

Hg—Hg,SO,— saturated solution of cadmium sulphate—cadmium amalgam (14,3 pCt. of Cd.).

We must notice here, as I have already said in my second com-
munication, that cadmium amalgam does not behave in the same
way as pure cadmium. The measurements of Hockrn and Taytor 2)
and those of JAGrR*) have plainly proved this. The following
table taken from JAGER’s communication shows this:

TA 3B 36 a1,

Composition of the amalgam.
E.M.F. against the 14.5 percent

Dede Cd: Hg. Cdamalgam (Volt.)
|
1 It Bate) — 0.021
2 2, LOO — 0.013
5 5.3 ; 100 nearly 0 °
10 1).1 : 100 0
11.4 12.9 : 100 0 up to 2/15) millivolt
13.0 15.0 = 400 0
14.3 16.7 : 100 0
15.4 18.2 : 100 0 up to + 0.001
20.0 25.0 : 100 + 0.001 up to + 0.01] )
gradually rising.
Cd. amalga- 0 to about -+ 0.044 §
mated.
Cd. pure. + 0.051

') JAcer and Wacusmuty, Wieprmanns Annalen 59, 575 (1896).
1) Journal of the Society of Telegraph-Engineers, VIII p. 282 (1879).
*) Wiepewanns Annalen, 65, 106 (1898).

( 209 )

When 2 96540 Coulombs pass through the cell, then

a. 1 gram atom of Ca will be withdrawn from the cadmium
amalgam (Heat effect WW)

b. the liberated Cd will combine with the SO, of the Hg SO,
to CdSO, (Heat effect 1V,),

ec. which will then abstract water from the saturated solution of
cadmium sulphate and form Cd S0,.‘%/; H, O (Heat effect W;). This
salt will deposit in the saturated solution.

The said abstraction of water will take place according to the
equation :

A

CaSO, + —*— Ca80,. AHO = —

as dS | QV. « «
7 i, Cd80O,. §/, H2O (1)

ig
in which A represents the number of mols. of water associated with
1 mol. of Cd SQ, in the saturated solution at the temperature of
the cell.

2. The total heat effect in the cell on the passage of 2 x 96540
Coulombs is now:

W,+ W,-+ Ws calories.

The heat of formation of Cd SO, and Hg, SO, are known and
amount to respectively 219900 and 175000 calories.

The heat evolved when 1 gram atora of Cd is withdrawn from
the amalgam (Wj) has been experimentally determined by me (see
below) whilst the quantity of heat (Ws) evolved by the process
represented in equation (1) may be deduced from the thermochemical
determinations of THOMSEN, taken together with those of Mr. H. B.
Hoxssorr which he has kindly placed at my disposal.

a. Experimental determination of the Heat evolution (W,) which
takes place on the withdrawal of 1 gram atom of cadmium
from the 14.3 pCt. Cd amalgam.

3. I have not determined this heat effect by thermochemical, but
by electrochemical means by a method which in a case like this
deserves the preference on account of its very great accuracy ').

For this purpose I constructed a cell according to the following
scheme :

Cd - dilute solution of cadmium sulphate of arbitrary concentration= 14.3pCt. Cd amalgam.

1) Compare Ricuarps and Lewis, Proc. Americ. Acad. of Arts and Sciences. Vol.
AXXVI, 87. Dec. 1898. Zeitschr. fiir phys, Chemie 28.1 (1899).

( 210 )

When in such a cell the current is closed, Cd will pass from
the cadmium electrode to the amalgam.

If we apply to this cell the well-known equation of Gipps and
von HELMHOLTZ.

Fi ge

i SS TE SIR al

Ep
we can find £, by the determination of the K.M.F. of the cell
and its temperature coefficient and this quantity is simply the amount
of heat evolved when 1 gram atom of cadmium is added to the amal-
gam, in other words, the quantity of heat which we wish to deter-
mine but with the opposite sign.

P, P, 4. The cell used had
i : | the form indicated. The
capillaries /’, and F are
sealed to the arms 4 and
C of the vessel ABC, The
capillary 4, communica-
tes with A but /, on the
other hand is closed at
the spot where it is sealed
to C and admits a plati-
num wire which in C is
wound up to a spiral §
and projects into /’, about
1 cm.

Into A is poured the
amalgam (14.3 pCt. of
cadmium) which is in
direct contact with the
platinum wire 4,, which
runs into A,

Into C is introduced
F, metallic crystalline cad-
mium so as to quite sur-
round the platinum spiral
S. Into Fy mercury is
poured which forms the
contact between S and the
platinum wire Hg.

H,

(201 )

5. The metallic crystalline cadmium was prepared as follows !):
200 grams of erystallized cadmium sulphate were dissolved in warm
water precipitated with ammonia and redissolved in a slight excess
of the same. After diluting to 600 ec., the liquid was electrolyzed
between two platinum electrodes of 55 em*. surface at a tension of
6—8 volts and with a current of 4—5 ampéres. Splendid dendritic
erystals of Cd are deposited at the negative electrode which are left
in the liquid until enough of the metal has separated.

The crystalline metal is first washed a large number of times
with very dilute sulphuric acid, then with the same solution of
cadmium sulphate which serves afterwards in the cell Cd -—CdSO,
Cd-amalgam. The solution, the concentration of which may _ be
chosen at will, was prepared by dissolving 200 grams of crystallized
cadmium sulphate in 500 cc. of water ®).

The metallic cadmium after being well washed (reaction with
congo-red) was kept in this solution; the electrodes thus prepared
are electrically well-defined and different preparations only showed
a mutual potential difference of 0.00001 volt.

6. The cadmium amalgam of 14.3 pCt. was prepared by weighing
the respective quantities of the components. In the metallic cadmium
from Merck no impurities could be detected by analytical means
and the test recommended by Mynius and Funk *) which shows
0.01 pCt. of zine with certainty also gave a negative result.

The mercury was purified with mercurous nitrate and then dis-
tilled twice in vacuo.

7. After the electrodes in the cell fig. 1 were put in their place,
the above mentioned solution of cadmium sulphate (which was far
from saturation even at 0°) was poured in and the cell closed by
means of an india-rubber stopper, g.

The length of the capillaries renders it possible to completely
immerse the whole cell in a thermostat.

The E.M.F. of this cell of which I first constructed 2 specimens
for contro! (I and III) was determined at 0°.0 C. and 25°.0 C.

The cells were kept at zero in a thermostat consisting of a copper
eylinder isolated with cotton-wool and containing a mixture of finely

1) Compare Ricuarps and Lewis, Proc. Amer. Acad. Arts and Se., Vol. XXXIV,
p- 87, Dec. 1898. Zeltschr. phys. Chem. 28, 1 (1899).

*) The water was the same as used for determinations of the electrical conductivity
and consequently very pure.

8) Zeitschr. anorg. Chem. 13, 157 (1897).

( 212 )

crushed ice and water. Only by vigorously stirring. with three screw
propellers fixed at different heights in the cylinder and kept in
rotation by a Hernrici hot-air motor, was it found possible to
maintain in every part of the thermostat an equal temperature !) of 0°.

The thermometer used was divided in '/}9° and compared with a
standard instrument from the Physikalisch-Technische Reichsanstalt
at Charlottenburg.

At 25°,0 C. the temperature was regulated with a toluene-regulator
within 0°,03 C.

The E.M.F.’s were measured, by means of PoGGENDORFE’s com-
pensation method. A THOMSON’s mirror galvanometer was used as
the zero instrument, a small accumulator as the working cell and
a Weston-cell and two Cuark-cells as standards.

The Weston and the Cxuark-cells stood in the thermostat at
25°,0 C. (also in the experiments at 0°)?). After each measurement
the accumulator was tested by means of the Wesron-cell.

8. In the first place, I determined the relation between the
E.M.F. of the Waston-cell and of both the Cuarxs 4 and B.

CLARK Ag50 __ 1.3942 CLARK Bg;0

WESTON 95° WESTON 9;0 ae

2/,0°
If we take as the E.M.F. of the Crarx-cell at 25°,0 1.4202 Volt

then that of the Westron-cell at 25°,0 = 1.0185 Volt whilst in the

Reichsanstalt 1.0184 Volt has been found at this temperature.

9, The E.M.F.’s of the cells I and IfI were then determined
at 25°0 C. and 0°,0 C.

Tate be ae

Electromotive force at 25°.0 C. of the cell!
Cd—CdSO, solution — Cd-amalgam 14.3 °/) Cd. in Volts.

Date No. I. Date No. 1.
2/,0° 4.00 p.m. 0.04998 9/,°° 3.45 p.m. 0.04989
4.30 0.04995
5.10 0.04999
4/,°° 12.25 p.m. 0.04995
averge 0.04997 averge 0.04989

1) The method so frequently used for the testing of thermometers of placing these
instruments in a funnel with crushed ice, seemed to me to be untrustworthy as dif-
ferences in temperature up to 0°.38 C> were observed.

*) Proc. Nov. 25, 1899, p. 290.

( 213 )
At 0°,0 C. the following was found :
GAB ty; A.

Electromotive force at 0°.0 C. of the cell
Cd—CdSO, solution — Cd. amalgam 14.3%, Cd. in Volts.

Date No. I. Date No III.
2/,0° 1h.50 p.m. 0.05571 51602 «= 4h.50 p.m. 0.05571
2h.25 0.05571 5h.24 0.05581
2h.50 0.05571
4,00 1h.15 am. 0.05591
11h.50 0.05591
average 0.05579 average 0.05576

We, therefore, find as the mean of the observations with both
the cells:

E.M.F. at 25°0, C. = 0,04993 Volt.
E.M.F. at 0°,0 C. = 0,05577

”
The temperature co(fficient of the E.M.F. is therefore on the average

0,04993—0,0
wees = — — 0.000233 Volt.

10. On this result I had a check '), which was very welcome
to me. JAGER®*) has determined the E.M.F. of a similar cell and
has found 0,051 volt, but he has not given the temperature at
which his determination was made. I have now calculated from my
determinations the temperature at which EL would be 0,051 volt
according to my observations. I find from

FE, = Ey; + (25—t) 0,000233
(== PATOL

In reply to my inquiry, Prof. JAGER was kind enough to state
that he had indeed made his observations at about 20° C.

‘) Subsequent experiments proved to me the correctness of the supposition that the
temperature coefficient between 0° and 25° does not alter with the temperature.
*) Wiepemanns Annalen, 65, 106 (1895).

( 214 )

dE
dT
the equation 2 on page 210 and calculate Z, for 18° C., we find:

11. If we now introduce the values of Z and found, into

di
(£59, = 0,0515; Pr 0,00023838 ; T = 291)

¢ = 2(0,0515 4+ 291 x 0,000233) 22782 calories = + 5436 calories.

The heat effect of the withdrawal of 1 gram atom of Cd from
the 14.3 pCt. Cd amalgam is therefore,

W, = — 5436 calories !).
(2. Determination of the Heat effect Ws.

12. We have still to determine the heat effect which accompanies
the change:

8/3 A or
CdSO, + 2a CdSO,. AH,O — A—8/5_ CdSO,. 8/5 H,0.
The factor A (see page 209) may be taken from the solubility
determinations of Myiius and Funk*) and KonnstTamM and CoHEN®),
who have found quite identical figures.

1) In my second communication on the thermodynamics of the standard-cells (these
Proceedings 26 May 1900 pag. 36) it was concluded from older and newer statements
in the literature that the abstraction of 1 gram atom of zine from the zinc-amalgam
of the Cxark-cells took place without any heat effect. That such is really the case
is taught by the following experiment:

{ constructed a cell according to the scheme:

Zn amalgam — ZnSO, solution — Zn
(hs 8) dilute

just in the same manner as described above for the Cd-cells. Of this cell the E.M.F.
was determined at 0°,0 C. and 25°,0 C. There was found at:

0°,0 C. 0,000488 Volt.

25°,0 C. 0.000570 »

_ ah E
therefore 77, = + 0,00000328 Volt.

From this follows: He = 2 (0,00048 — 278 X 0,00000828) 22782 calories
Ee = — 9 calories.

The quantity of heat required, is therefore + 9 calories or practically nil.
2) B. B. 80, 824 (1897).
3) Wreprmanns Annalen 65, 344 (1898).

Oe

( 215 )

ALS Ol eek SS) Se:

The equation representing the change therefore becomes at this
temperature :
CdSO, + 0,212 (CdSO,. 15,17 H,O) = 1,212 CdSO,. 8/; HO. . (3)

If the systems to the left and the right of the sign of the equality
are dissolved in so much water, that both have the concentration
CdSO,—-400 H.O, we can find the quantity of heat Ws (p. 209)
from the heat effects so obtained.

I now reproduce the following from the data put at my disposal
by Mr. Horsporr:

Heat of dilution CdS0,.13,6 H,0 to CdSO,. 30 H,0 = + 1034 calories.

‘ CdS80,. 15,6 HO , CdS0,. 20,6 HO =+ 405

: CdS0,. 20,6 HO , CdS0,.30,6 HO=+ 28 ,
. CdSO,.30,6H,0 , CdS0,.50,8HO=+ 231 ,
‘ CdS0,.50 H,O , CdSO,. 100 H,O=+ 220 ,
y Cd80;- 100H,O , CdS0, 200H,O=+ 171 ,
Z OdSO,. 200H,O , CdS0,. 400H,O=+ 103,

From this I calculate:

405
H. o. d. CdSO,. 15,17 H,O—CdS0,. 20,6 H,0 ice 0,43 -+ 405 = + 440 calories.

, CdS0,. 20,6 H,0O—CdS0,. 30,6 4,0 = = 41 985-9,
, CdS0,. 30,6H,0—Cd80,. 50H,0 = =+4 992
, CdS0, 50H,0O—CdS0,. 400 H,0 = Semon:

Heat of dilution CdS0,. 15,17 H,O — CaS0,. 400H,0 = +1446

The heat of solution of CdSO,—CdSO,. 400 H,O = + 10740 eca-
lories (THomsEN, Thermochem. Untersuchungen III, 8.201), and the
the heat of solution of CdSO,. °/3 H,0—CdSO,. 400 H,O = + 2660

calories.

The heat effect (Ws) which accompanies the change represented
in equation (3) is therefore:

W, = 10740 + 0,212 X 1446 — 1.212 X 2660 = + 78232 calories.

13. The heat evolved at 18° C. in the Waston-cell at a pas-
sage of 2 X 96540 Coulombs may now be calculated:

E, = W, + Wz + Wz = — 5436 + (219900 — 175000) +
-++ 7822 = + £9286 calories.

14. This quantity must now be compared with that obtained

( 216 )

from the direct observations of the E.M.F. of the Wasron-cell by
JAGER and Wacusmutu !):

From their measurements it fullows that the E.M.F. at ¢ is
represented by the equation :

E, = 1,0186 — 0,000038 (¢—20) — 0,00000065 (¢—20)? Volt.

therefore : E\s0 = 1.0186 Volt.
My
(=) = — 0,0000354 Volt.
al Sts 18 C iO,

or EL, = -+ £6880 calories
whilst the thermodynamic calculation gave “, = + 49286 calories.

The agreement between theory and experiment is, therefore, very
satisfactory.

15. I will not neglect to point out that the idea hitherto pre-
vailing on the mechanism of the change and which was represented
by the equation:

Cd + Hg, 80, 2 Hg 4+ CdSO,
would here a'so lead to quite wrong results.

From the. above it appears that we may represent the mechanism
of the change which occurs in the Wesron-cell by

Cd amalgam 2 Cd + He’)
and
A
Cd + ——— a (CdS0, AH,O) + Hg.SO, = 2Hg + uaa 7, CdSO,. §/, H,0

liquid . solid

Amsterdam, University Chem. Lab.
June 1900.

') Wiepemanns Annalen 59. 575 (1896).

2) This provisional equation only represents the change of the amalgam qualitatively.
The exact quantitative equation can only be given when the behaviour of the cadmium
amalgam has been more exactly studied. (See my next paper on the metastability of
the Wesron-cell).

( 217 )

Chemistry. — ‘The metastability of the Weston-Cadmiumcell and
its insuitability as Standard of electromotive force’. By Dr.
Ernst CoHEN (Communicated by Prof. H. W. Bakuuts
RoOozEBOON).

1. As is well known the Crark-cell is inconvenient for accurate
measurements on account of its great temperature coefficient (1 mil-
livolt degree). For a number of years JAGER and Wacusmura of
the Physikalisch-Technische Reichsanstalt have been engaged with
the study of a cell which does not suffer from this drawback. As
is known, the result of their investigations has been?) that in 1896
they proposed to employ the cadmium cell of Wesron in a some-
what modified form as a standard.

This cell, constructed according to the scheme:

Cadmium amalgam (14.3 pCt. of Cd) — saturated solution of cadmium sulphate — Hg,SO,—Hg

possesses, according to their communications, all the good qualities
of the CLark-cel! as regards constancy and ease of construction, but its
temperature coefficient is 25 times smaller than that of the CLark-cell.

The change of the E.M.F. amounts to only */i999 pCt. per degree
centigrade whilst that of the Crark-cell is 1/}) pCt.

Thermostats become superfluous even when very accurate measure-
ments are required, which is a fact of some importance when it is
considered that standard cells are much used for industrial purposes.

2. The connection between the E.M.F. and the temperature was
determined by JAGeR and Wacusmutu. They found (between 0°
and 26°).

E, = Foy) — 3.8 X 10-5 (t—20) — 0.065 X 10-5 (t—20)?,

but they observed at the same time that some cells did not follow
this curve but showed certain irregularities at low temperatures ;
these cells had a much greater E.M.F. (about 1 millivolt) than the others.

In view of these deviations, Mr. Kounsramm and I, in 1898,
made a closer study of the behaviour of cadmium sulphate and
found?) that the temperature coefficient of the svulubility of
Cd SO, . °/3 H2O undergoes a sudden change at 15°.

Solubility determinations which were executed with many precautions
gave the following result.

*) Wiepemann’s Annalen, 59. 575 (1896).
*) WiEDEMANN’s Annalen, 65, 344 1598).

( 218 )
PAB EE a!

Grams of CdSO, dissolved in 100 grams of water.
I ————

Temperature. Ie IL. Ii. Average.
0°0 75.52 — — 75.52
5°0 75.69 75.61 = 75.65
7°0 75.73 = = 75.73
9°0 75. 84 75.87 = 75.85

11°5 75.98 75.90 _— 75.94
13°0 76.00 76.07 = 76.04
15°0 76°11 76.14 76.09 76.11
16°0 76.16 = = 76.16
17°0 76.14 76.12 _ 76.13
18°0 76.18 76.15 -- 76.14
19°0 76.18 76.18 — 76.18
25°0 76.82 76.78 76.84 76.79

The accuracy could be controlled by determinations which Mytius
and Funk had made in the Reichsanstalt at the same time. The
following table contains a comparison of the results.

fT AWB bak ie

In 100 grams of water dissolve grams of CdSQ,.
re

Temperature. Mytivs and Punk. KouHNsTAMM and Conen.
0° 75.47 75.52
10° 76.00 75.90
15° 76.06 76.11

Figure I represents the progressive change of the solubility.

0°75.52 3° 5? 7 99 11.59 189 159 169 17918919"200 250

( 219 )-

At about 15° C. the CdSO,.*/; H,0 must, therefore, undergo a
change. This change has been already proved by means of the
dilatometer ').

The deviations found by Jager en WacHsMuTH in the E.M.F.
were explained by assuming that CdSO,.‘/;H,0, the solubility of
which is represented by the curve SCD remains, as a rule, some-
what obstinately in the metastable condition. A smaller E.M.F.
of the Weston-cells then corresponds to the greater solubility of
the metastable phase (curve P,S). If the salt passes into the stable
modification (curve APBS), the solubility is lowered and the E.M.F.
of the cells in which that modification exists is raised.

No objections to this view have been raised since the appearance
of our paper; on the contrary in his publication on deviations
noticed by himself in the behaviour of cadmium-cells, Barnes 2)
accepts our view. J will however, not neglect to point out that it
always astonished me that such a small difference in solubility as
represented by the points P and P, should lead to such an impor-
tant difference in E M.F.

At the end of our paper we concluded that the Wesron-vell in
the form used at the Reichsanstalt, i.e. containing the solid salt
Cd 504. 8/3 H,0, should not be used below 15°, if the risk of having
a cell which considerably deviates from the temperature formula
given by JAGER and WacusMuTH is to be avoided.

3. My investigations on the thermodynamics of the standard
cells made me return to the Wexsron-cell which was now extensi-
vely studied in another direction.

In the following lines, I wish to give a summary of this
investigation.

4. In order to find the heat-effect caused by the withdrawal of
1 gram-atom of Cd from the 14.3 pCt. cadmium amalgam used in
the Weston-cells, I constructed (see previous paper pg. 208) a number
of cells of the type: Cd—dilute solution of cadmium sulphate —
Cd-amalgam 14.3 pCt. The solution of cadmium sulphate was not
saturated at 0°,0C., so that no crystals could be deposited at that
temperature. The details of the construction of the cells together
with the precautions taken in view of impurities contained in the

alc.
*) Journ. of physical Chemistry, May 1900.

Proceedings Royal Acad. Amsterdam. Vol. ILL.

( 220 )

materials have been fully described by me in my third communi-
cation on the thermodynamics of the standard cells (see commu-
nication (p. 208).

The E.M.F.’s of cells I, If and TIT at 0°,0 C. and 25°,0 C. were
determined by Poce@rnporrr’s method as described in the paper
already referred to.

The Weston-cell and the Cuark cells which served as standards
were always kept in a thermostat at 25°,0 C. In this way I found:

TAY Bala bie eile
At 25°.0 C.
No. I. No. II. No. 1II.
Date E.M.F. in Volt. Date E.M.F. in Volt. Date E.M.F. in Volt.

2/00 4h. p.m. 0.04998 27,09 4h.0 p.m, 0.04999 5/,°°3h45p.m. 0.04989

4 30 0.04995 4 30 0.04992
5 10 0.04999 5 10 0.04992
4/,2°19 25pm. 0.04995 4/,°°12 95 0.04995
average (0.04997 Volt. average 0.04992 Volt. average 0.04989 Volt.
At 02.0 C.
No. I. No. II. No. JI.

Date E.M.F. in Volt. Date E.M.F. in Volt. Date E.M.F. in Volt.
4,°° 1h50 pm. 0.05571 7/,°° 1h.50 p.m. 0.05520 9/,0° 4n50 p.m, 0.05571
2 25 0.05571 2 25 0.05408 5 24 0.05581
2 50 0.05571 2 50 0.05347
4/,°°11 15pm. 0.05591 /,°°11 15pm. 0.05082
11 50 0.05591 1l 50pm. 0.05092
average 0.05579 Volt. hod average 0.05576 Volt.

As regards this table it must be observed that the cells I and II

were kept in ice from */,° to /,°°. They were then measured at
4/,°°, first at 0°,0 and then at 25°,0 C.

The result of these measurements is therefore, that whilst I, IL
and III have exactly the same E.M.F. at 25°,0 C. namely
I, = 0,04997 Volt.
II, = 0,04992 Volt.
= 0,04989 Volt.

i
—
=
iS

( 221 )

an important difference exists at 0°,0 C. between I and III on the
one hand and II on the other.

I. = 0,05579 Volt.
Il. = 0,05092 Volt.
Ili. = 0,05576 Volt.

It is moreover of importance to point out that I and III after
they were cooled from 25°,0 C. to 0°,0 C. very soon reached their
end-value whilst with If this was only the case after a few days.

5. The observations described immediately gave rise to the sus-
picion that the Cd-amalgam used in the cell is a metastable sub-
stance!). This, it is true, appeared to be in contradiction with the
investigation of JAGER*) who states that amalgams with 5— 15 pCt.
of Cd are unchangeable to 1/jo9 millivolt but there were so many
indications which appeared to contradict this, that I continued the
investigation in the original direction. In what follows it will be
seen that JAGER’s view is incorrect; the reason why he was unable
to prove the instability of the 14.3 pCt. cadmium amalgam used
will also appear.

6. I tried in the first place to find the temperature at which
the difference between the cells I (and III) and II first appears.

For this purpose the E.M.F. of I and II was determined at dif-
ferent temperatures between 0°,0 C. and 25°,0 C.

The temperatures 5°, 10°, 15° and 20° were kept constant for a
long time by allowing ice-water to flow from an elevated reservoir
into a bath provided with stirring apparatus and toluene regulator,
the supply being regulated by means of a tap. The heat given off
by the flame is compensated for by the refrigeration caused by the
iced water and in this manner the temperature may be kept con-
stant all day long within 0°,03 C.

) It might be thought that metallic cadmium, which formed the negative electrode of
the cells, might be metastable like tin. A special investigation, however, gave indi-
cations that such is xo¢ the case and J, therefore, occupied myself in the first place
with the cadmium amalgam.

*) WigpEMANN, Annalen 65, 107 (1898).

( 222 )
7 ABLE Wy.

Crit I. Ceri. I.
Temperature. Time. E.M.F. in Volt. Temperature. Time. E.MF. in Volt.
0°0 gh. 0.0559 4) 0°0 9b.10 0.0509
10 30 0 0559 10 40 0.0509
5°0 11 7 0.0549 5°0 11 12 0.0515
11 30 0.0549 11 35 0.0515
10°0 12 0 0.0536 10°0 12 10 0.0517
12) 17 0.0536 12 22 0.0517
15°0 12 47 0.0524 15°0 12 52 0.0517
2 20 0.0524 2 30 0.0517
20°0 3 10 0.0513 20°0 3.15 0.0510
3 45 0.0515 3 50 0.0510
2500 5 15 0.0501 4) 25°0 5 20 0.0501 1)
5 50 0.0501 6 0 0.0501

If with these data we construct a curve which has the tempera-
tures as abscissae and the electromotive forces as ordinates fig. 2
is obtained,

—

Volt

0° 5° 10° 15° 20° 25°

The two curves intersect at about 23°.
From this it is seen that the cadmium amalgam (14.3 pCt. of Cd.)
contained in cell I and IIT is metastable below 23°.

') These measurements took place 6 days after the cell had been constructed. It
will be seen that in that time the E.M.F. has been raised about 0,0002 Volts. This corre-
sponds with the observations of Rrcuarp and Lewis, Zeitschr. fiir phys. Chemie 28,
1. (1899) on Cd-electrodes of this kind.

( 223 )

7. As these observations as we will see later on, are of great
importance when judging of the suitability or otherwise of the
Weston-cells as standards, I have convinced myself of the correctness
of these conclusions by the dilatometric process.

For this purpose the cadmium-amalgam which had served for the
construction of the electrodes was introduced into a dilatometer filled
with petroleum as measuring liquid.

That the amalgam is not in equilibrium at 0° is seen from the
following observations :

Ay Bullet), Ve

Height of the level

Time in hours. in the dilatometer.
0 107
Qi/5 99
4 96 4
43/4 94
534 92
6°/, 9]
24 71
48 55
72 40

8. It now becomes more plain from the electric measurements
(fig. 2) why JiceR !), who according to his communication, made his
measurements at about 20°, did not notice the metastability, for that
temperature is so close to 23° that under these circumstances any
change in the amalgam could only be observed after the lapse of an
exceedingly long time.

9. Apparently the amalgam electrodes of the cells 1 (and IIT)
and II had been treated in the same manner and yet that of IL
had changed into the stable modification whilst I and II continu-
ally remained metastable. That the change may often occur is

1) See my previous communication p. 213.

( 224 )

shown by the fact that of the three cells which I had made, one
contained stable cadmiumamalgam !),

Provisionally we will call the amalgam contained in the cells I
and III (the metastable modification below 23°) the /-amalgam
whilst that in cell II will be given the name of @-amalgam.

From table IV we see that cells with the ?-amalgam have at
0° an E. M. F. which is not less than 5 millivolt larger than those
of the cells in which the «amalgam forms the positive electrode.

10. The question now at once arises: Do the observations made
by Jicer and WacusmMuTH with the Wesron-cell relate to cells
in which stable amalgam is present, or have they been made with
cells which have the metastable body as negative electrode?

The fact that with some cells at 0° they found a higher E. M. F.
than with others would indicate that they have mostly worked with
the metastable modification This cannot, however, be stated with
certainty, because it follows from the results of our investigation on
the behaviour of cadmium sulphate that the presence of the stable
form of this salt may have increased the E.M.F. at O°.

I, therefore, have studied this point more closely. For this pur-
pose the cells I, II and III were transformed into Weston-cells
(cells Ie, JI* and III?) except that they were filled with a clear
solution of Cd SO,. §/; H,O (stable modification) at 0° without any
erystals at the bottom.

The dilute solution of Cd SO, was poured out of ABC (previous
communication fig. 1), the arm A provided with a layer of cotton-
wool, and the metallic Cd removed from C and replaced by mercurous
sulphate.

The solution of Cd SO,.*/3 H,O (stable modification) saturated at
0° was prepared by mixing the anhydrous salt with water at 0°,
care being taken to cool the liquid so as to prevent the temperature
from rising over 15°.

The bottles containing the salt and the water were shaken for
4 hours at 0°.0C. and the solution was filtered. The saturated
solution thus obtained was introduced into I, IL and III and the
cells which previously had been rinsed with this solution were closed
and brought, in the thermostat, to 0° C. The E.M.F. of the cells
(Ie, Ife, IlI*) was then determined.

In this way the following values were found:

1) Compare Barnes |. c.

( 225 )
Ae As Bs VE

Temperature 0°.0 C.

Weston-Cell Ta 1.0198 Volt.
Weston-Cell IIa 1.0231 Volt. 1)
Weston-Cell Illa 1.0197 Volt.

We, therefore, see that all the measurements of JAGER and
W AcHSMUTH have been made with Weston: cells which are metastable*).

11. The formula given by the Reichsanstalt for the connection
between the E.M.F. of Weston-cells and the temperature and which
should be used between 5° and 26° C., therefore loses its value on
account of these facts and, considering the metastability of the cad-
mium amalgam, is only true for temperatures between 23° C. and
26° C., whiist the metastability of cadmium sulphate as we have
previously demonstrated is a second reason of its insuitability.

12. Since 1592, a standard-cell has been sold by Weston at
Newark (obtainable in Europe from the “European Weston Electrical
Instrument Co.”, Berlin) which is constructed in accordance with the
scheme :

Cd-amalgam 14.3 pCt. — solution of cadmium sulphate — Hg,SO,—Heg.
(Saturated at +- 4° C.) without solid phase.

It was thought, even after our investigation on the change which
Cd SO,.°/; H:G undergoes at 15° C., that this cell constituted a
perfectly trustworthy standard, since above 4° C., uo solid phase
is present.

But since it has been proved that cadmium amalgam below 23° C.
may occur in two modifications, it follows that even this standard
may show a different E.M.F. below that temperature according to
which of the two modifications of the amalgam is present.

13. Owing to the fact that both in the Wesron-cell of the Reichs-
anstalt and in that of the Weston Co. there exists cadmium amal-

) It will be noticed that whilst at 0°.0 C. the difference in E.M.F. of the cells I
(or If) and IL amounted to 5 millivolt, the Wrston-cells showed a difference of
3,4 miivolt at that temperature. I will afterwards return to this matter.

*) Between 0°C. and 23°C,

( 226 )

gam which readily remains in the metastable form (it must be
remembered that all the measurements of the R. A. have been made
with metastable cells) and that this amalgam may spontaneously pass
into its stable form which change is accompanied by a change in
the E.M.F. (up to 5 millivolt at 0°)] we must come to the con-
clusion that both forms!) are unsuitable as standards of electro-
motoric force.

A cell which at the time of its construction is compared with
another standard and found to possess the E.M.F. indicated by the
Reichsanstalt at the given temperature, may subsequently come to
have some totally different E.M.F.

What is required of a standard cell is that, when constructed in
a definite way, its E.M.F. shall be positively defined at a stated tem-
perature; it will be seen from the foregoing that the Wesron-cells
do not by any means conform to this specification.

14. Above 23° C. all the WeEsron-cells, as seen from the foregoing,
possess a sharply defined E.M.F. which follows the temperature
fermula given by the Reichsanstalt (to 26°). Only by making use
of a thermostat in which the cell is placed when in use (and for
some times beforehand in order to convert any metastable amalgam
into the stable form) can these drawbacks be avoided. But then
the great advantages which this standard seemed to possess compared
with others with a larger temperature coefficient are lost. More-
over, working with thermostats is far too tedious for technical

purposes.

15. After reading the above, the question naturally arises; do
such complications arise with the CuarK-cell?

The amalgam which is used there as negative electrode has the
composition Zn: Hg = 1:9.

Although my investigations in this direction are not yet quite
finished, I think that it is very probable that we shall meet with
similar phenomena. J mention, therefore, briefly the investigations
of WitLows?) on the changes in the electrical conductivity of dif-
ferent amalgams at a constant temperature, when those amalgams
have been exposed to changes in temperature.

For the sake of brevity I will here bring forward only one case

1) The first named is moreover often metastable owing to the presence of the solid
salt Cd SO, . °/, H,0.
*) Plulos. Magazine, November 1899, 433.

a

( 227 )

from the large number studied by WitLows and choose as an
example, the zinc amalgam containing 9,5 pCt. of zinc and having
therefore, about the same composition as the amalgam used in the
Criark-cells.

In fig. 3 the resistance of the amalgam as a function of the

Fig. 3.

temperature is shown. The arrows indicate whether the temperature
was rising or falling. The curve A was obtained immediately after
the amalgam had beer heated several times, whilst B represents the
results which were found after the amalgam had been kept for some
weeks at the temperature of the room.

It is plainly visible from this figure that the amalgam can have
very different resistances at the same temperature, a good proof that
even after a long time a condition of equilibrium in the amalgam
is not reached.

Wittows has found similar curves for cadmium amalgam, but
the amalgam which interests us here most (1:6) has not been
investigated by him.

The former observations on cadmium sulphate and also those
which have been communicated in this paper on cadmium amalgam
may be summarised as follows:

Results of the Investigation.

1. Cadmium sulphate (Cd SO,. °/; H,O) can exist below 15° C. in
two modifications.

2. Cadmium amalgam (14.3 pCt. of Cd) can appear in two

modifications !) below 23°C.

‘) The word “modifications” is here only preliminary. A further investigation will
have to show what changes take place in the amalgam.

( 228 )

3. At O0°C. a potential difference of 5 millivolt exists between
those modifications of the cadmium amalgam.

4. The Wrston-Cadmium-cells, both the form studied and recom-
mended by the Physikalisch-technische Reichsanstalt, and that sold by
the European Weston Electrical Instrument Co. are metastable systems
(below 23°) which may pass quite spontaneously into the stable con-
dition. As this change is coupled with a great change in the E.M.F.
these cells are unsuitable for standard of electromotive force.

5. The researches at the Reichsanstalt are made with metastable
Weston-cells and the temperature-formula -given by JAGreR and
WaAcuHsMuTH therefore relates to metastable cells.

When a better insight into the behaviour of cadmium amalgams
has been obtained a proposal may, perhaps, be made for the con-
struction of a standard-cell which possesses all the advantages and
none of the drawbacks of the Wrsron-cell.

Mr. H. C. Bist has already made a beginning with the investi-
gation of these amalgams in this laboratory.

Amsterdam, University Chem. Lab., June 1900.

(August 28, 1900.)

KONINKLUKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday September 29, 1900.

aE

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 29 September 1900 Dl. IX),

Contents: “Contributions to the knowledge of some undescribed or imperfectly known fungi”
(2nd Part). By Prof. C. A. J. A. OupEMans, p. 230. — “On the origin of new spe-
cies of plants”. By Prof. Hugo pg Vrigs, p. 245. — “On muscle-tone” (abstract).
By Dr. J. W. Lanceraan (Communicated by Prof. T. Pracg), p. 248. — “On the
determination of sensory spinal skinfields in healthy individuals”. By Dr. J. W.
Lanceraan (Communicated by Prof. C. Winker), p. 251 (with one plate). —
“Curious disturbances of the sensation of pain in a case of tabes dorsalis”. By
D. H. Beiszerman (Communicated by Prof. C. W1NKLER), p. 253 (with one plate). —
“The so-called opake minerals in transmitted light”, By Prof. J. L. C. ScoRoEDER
VAN DER Kok, p. 254. — “On the spacial anharmonic ratio of curves p” of order n
in the space Sn with x dimensions”. By Prof. P. H. Scnours, p. 255. — “Presery-
atives on the stigma against the germination of foreign Pollen”. By Dr. W. Burck
(Communicated by Prof. Huco br Vries), p. 264. — “Contributions to the know-
ledge of vaN DER Waats’ -surface, I. Graphical treatment of the transverse-
plait’. By Prof. H. Kameriincu Onnes, p. 275 (with 2 plates). — “Contributions
to the knowledge of van DER WAAts’ -surface. II. The part of the transverse-plait in
the neighbourhood of the plaitpoint in Kurnen’s experiments on retrograde conden-
sation”. By Prof. H. Kameriineu Onnes and Dr. M. Rereanum, p. 289 (with 2
plates). — “On the measurement of very low temperatures. III. Coefficient of pres-
sure variation of pure hydrogen between 0° and 100°". By Prof. H. KaAMERLINGH
Onnes and M. Boupry, p. 299 (with one plate). — “On the Hatt-effect and the
resistance of crystals of bismuth within and without the magnetic field”. By Dr.
E. vAN EverDINGEN JR. (Communicated by Prof. H. KameruincH OnnEs), p.316.—

The following papers were read:

16
Proceedings Royal Acad. Amsterdam, Vol. III.

( 230 )

Botanics. — ‘Contributions to the knowledge of some undescribed
or imperfectly known Fungi” (2™4 Part) !). By Prof. C. A. J. A.
OUDEMANS.

HE. FUNGE SECUNDARITE sive
INFERIORES.

7; SPHAEROPSIDEAE.
a. Sphaeroideae.

a. Hyalosporae.

PHYLLOSTICTA ~ Persoon.

6. PHYLLOSTICTA AESCULANA Oud. n.sp. On the leaves of Aescu-
lus Hippocastanum. Nunspeet. Oct. 2, 1899; Mr. Bens.

Perithecia primo sub epidermide occultata, postea exposita, sparsa,
subglobosa, nigra; sporulae ellipticae, hyalinae, ad polos late rotun-
datae, nitide biocellatae, 6—T X 31/,—4*/; «. Differt ab omnibus
affinibus (Phyll. aesculina Sace., Phyll. sphaeropsidea Ell. et Kyv.,
Phyll. Aesculi Ell. et Mart. et Phoma aesculina Sacc.) dimensione
sporularum majore vel minore, seu mutata ratione longitudinem
sporularum inter et latitudinem (Pl. IV, fig. 2).

7. PHYLLOSTICTA ALNEA. Oud. n. sp. On the leaves of Alnus-
glutinosa. Nunspeet, Oct. 13, 1899; Mr. Bets. — Maculae am-
phigenae, utrimque fertiles, 2—10 mill. in diam., pallide ferrugi-
neae, tandem a partibus sanis viridibus vicinis descissentes. Perithe-
cia minima, fuliginea, sphaerica, prominentia. Sporulae hyalinae,
rectae vel subcurvatae, 4!/3 — 7><2!/3 «. — Differt a Phyll. alnicola
Cooke et Massee (Contrib. Mycol. Vér. 18; Sace., Syll. IX, 117)
sporulis manifeste majoribus (4°/;—7 X 21/3 w contra 2.38 X0.7 4).

8. PHYLLOSTICTA BRACTEARUM Oud. n. sp. — On the bracts
of the female inflorescences of Humulus Lupulus. — Nunspeet, 8
Dec. 1898; Mr. Berns. — Maculae nullae. Perithecia sparsa, nigra,

coriacea, !/jo—!/; mill. in diam., poro apicali destituta. Sporulae ba-
cillares, rectae, hyalinae, eguttulatae, parvae (4—4?/; 11/2), ad polos
rotundatae.

When applying stronger lenses it appears that in both poles a
small, drop-shaped body is hidden.

9. Paynnosticra Buronu Oud. n. sp. (Phoma Bufonii Oud. in

1) Hor 1st Part see these Proceedings p. 140.

(231)

Hedw. XXXVI (1898) p. 313). On the leaves of Juncus bufonius.
— Nunspeet, March 1898; Mr. Berns. — Perithecia sparsa, primo
tecta, postremo exposita, !/);—1/; mill. in diam., nigerrima, membra-
nacea, centro poro pertusa; sporulae achromae, continuae, ellipticae,
eguttulatae, 9X4 w.

10. Psyxuosticra Fact Oud. n. sp. — On the leaves of Fagus
silvatica. — Nunspeet, Oct. 30,1899; Mr. Berns. — Maculae am-
phigenae, fertiles tantum in pagina superiore, dilutissime fuligineae,
My circa cent. in diam., sed saepe confluentes. Perithecia epiphylla,
maculicola, exilissima, +/}.—1/;) mill. in diam., dense distributa, or-
bicularia, opaca. Sporulae minutisimae, bacillares, 47/3 X 11/6 “#, im-
mixtis paucis 7 «., hyalinae, continuae, guttulis expertes, ad polos
rotundatae, basidiis filiformibus longiusculis suffultae.

11. PHyntosticra HOLOSTEICOLA Oud. n. sp. — On the leaves
of Stellaria Holostea. — Nunspeet, April 17, 1900; Mr. Bers. —
Perithecia amphigena, vulgo autem epigena, in maculis pallide griseis
foliorum siccatorum subprominentia, vulgo numerosa et conferta, sub-
micantia, }/s—!/, mill. in diam., tenera, subfuliginosa. Sporulae cylin-
dricae, rectae vel subcurvatae, ad polos late-rotundatae, 16—20
42/,—51/, uw, biocellatae, guitulis, volumine sporularum in rationem
inducto, pusillis.

12. Puytuosticra Inicis Oud. n. sp. — On the leaves of Ilez:
Aquifolium. — Nunspeet, May 28, 1899; Mr. Berns. — Maculae
valde extensae, ad ambitum multo pallidiores, irregulariter limitatae,
hypogenae. Perithecia hypogena, rarissime epigena, gregaria, atra,
micantia, prominula, primo occultata, postea exposita, centro per-
forata, 1/s—1/, in diam. — Sporulae ellipticae vel breviter-oblongae,
-utrimque rotundatae, hyalinae, protoplasmate aequali repletae,
5-7 X 2—3 wu.

13. Pusyuiosticra Laspurni Oud. n. sp. — On the leaves of
Cytisus Laburnum. — Nunspeet, Oct. 25, 1899; Mr. Beis. —
Maculis arescendo albidae, diversiformes, 1—1?/, cent. in diam.,
non marginatae; perithecia irregulariter distributa, atra, semigloboso-
depressa, opaca, 1/,—/, mill. in diam., tandem poro pertusa; spo-
rulae hyalinae, oblongae vel ovato-oblongae, ad polos rotundatae,
9—12 3 w, biguttatae, guttulis majoribus saepe minoribus paucis
concomitatis. — Differt a Ph. laburnicola Sacc. Mich. I, 152 et
Syll. III, 10, macularum praesentia, et peritheciis sporulisque majo-
ribus (166—250 contra 60—T70 yw, et 9—12 X 3 contra 3—5 X 1 w).

16*

( 232 )

14. Parytiosticra Narcisst Oud. n. sp. — On the leaves of
a cultivated species of Narcissus. —- Noordwijk, June 18, 1898. —

In company of Heterospora gracilis and Septoria Narcissi. — Peri-
thecia amphigena, numerosissima, conferta, tamen inaequaliter distri-
buta, innata, 40 mw in diam., membrana valde subtili praedita;
cirrhi, ubi adsunt, sphaerici, dilutissime rosei. Sporulae ellipticae
aut oblongae, rectae vel curvatae, hyalinae, continuae, biocellatae,
42/, 14 X 2!/,— 31, w, guttulis valde distinctis.

*PHYLLOSTICTA PERSICICOLA Oud. n. sp. — On the blown-up por-
tions of Peach-leaves attacked by Exoascus deformans. — Apeldoorn,
June 1898; O. — Hedw. XXXVII (1898) p. 313.

15. Pnryziosticra PopAaGRARIAE Oud. n. sp. — On the leaves
of Aegopodium Podagraria, in company of Discosia Artocreas and
Septoria Podagrariae. — Nunspeet, Oct. 14, 1899; Mr. Bens.
— Maculae amphigenae, pallide ferrugineae, valde extensae, irre-
gulariter limitatae, utrimque fertiles. Perithecia sparsa, sub epider-
mide occultata, !/),—'/15 mill. in diam., fuliginosa, depressa, tandem
centro perforata. Sporulae ellipticae vel ovatae, ad polos rotundatae,
continuae, hyalinae, guttula nitida in quovis polo praeditae,
7—T.2 21/;—4?/, w. — Species nostra toto coelo differt a Phoma
Podagrariae West. (Not. III, Bull. Acad. r. de Belg. XIX, 1852,
p- 116 et Sace. Syll. III, 169) cujus synonyma sunt: Sphaeria Poda-
grariae Roth, Dothidea Podagrariae Fr. et Septoria Podagrariae
Lasch.

*PHYLLOSTICTA QUERCICOLA Oud. n. sp. — At the under face
of the leaves of Quercus Robur. cf. Hedw. XXXVII (1898) p. 175.

16. Payxuosticra Trappentt Oud. n. sp. — On the leaves
of Fraxinus juglandifolia. — Naaldwijk 1864; the late Dr. J. E.
VAN DER TRAPPEN. — Maculae amphigenae, vulgo valde extensae
(ad 3 dec. in diam.), obscure limitatae. Perithecia nigra, numerosa,
aequaliter distributa, adulta !/, mill. in diam., prominentia. Sporulae
oblongae vel elongato-ellipticae, ad polos rotundatae, hyalinae,
TX 24/5 fe

17. Puyiiosricra vincicota Oud. n. sp. — On the leaves of
Vinca major. Nunspeet, July 9, 1899; Mr. Bremys. — Maculae
amphigenae, nigrae, quoad formam et dimensiones valde diversae,
irregulariter limitatae, utrimque fertiles. Perithecia minima, in paren-
chymate foliorum abscondita, vertice perforata, Sporulae initio in

( 233 )

globulum albidum, perithecii orificium obstruentem coalitae, singulae
ellipticae, ad polos obtusissimae, hyalinae, biocellatae, basidiis fili-
formibus, sporulis multo longioribus suffultae, 3!/)—4?/3 X 1°/,—2«. —
Differt a Phyll. Vineae Thiim., Phyll. Vincae majoris Allescher,
Macrophoma Vincae Berl. et Vogl. et Macrophoma cylindrospora
Berl. et Vogl., nunc praesentia guttularum, tune iterum dimensionibus
sporularum reductis.

PHOMA Fries.

18. PHoma AmyepaLi Oud. n. sp. — On the leaves of Amyg-
dalus communis. Nunspeet, April 27, 1899; Mr. Berrys. — Peri-
thecia parva (?/;) mill.), centro perforata. Sporulae breve-ellipticae,
4—5X3 w, hyalinae, continuac, guttulis destitutae.

19. PHoma cotcnicar Oud. n. sp. — On the petioles of Sta-
phylea colchica. — Nunspeet, March 1898; Mr. Berns.

Perithecia numerosa, !/,—1/y mill. in diam., per totam petiolorum
superficiem irregulariter dispersa, epidermide perpetuo tecta, promi-
nentia, vertice exposito perforata, cirea ostiolum epidermidis portiun-
eula annulari nigrefacta ornata. Sporulae angustius vel latius oblongae,
rectae, perfecte hyalinae, ad polos obtusiusculae, continuae, nitide
2-, 3-vel 4-guttalatae, S—10X3—4 wu.

Maculae stromaticae nigrescentes, linea atra subinde distinctissime
cinctae, quarum mentio facta est a mycologis Berlese et Voglino in
deseriptione Phomae Brunaudi (Sace. Syll. UI, 150), in ramulis
nostris certe non defecerunt; relationem attamen has inter et peri-
thecia supra descripta revera existere, nobis non licuit.

Phoma colchicae ab affinibus Ph. Robergeana, Ph. Staphyleae et
Ph. Brunaudi, omnibus ramorum Staphyleae colchicae incolis, lucu-
lenter differt guttularum valde conspicuarum, nitidissimarum in spo-
rulis praesentia, nec non peritheciornm volumine.

20. PuHoma cornicona Oud. n. sp. — On the branches of Cornus
alba. — Naaldwijk, 1866; the late Dr. J. KE. van Der TRappen.

Maculae nullae. Perithecia numerosissima, conferta, perpetuo sub
epidermide occultata, prominentia, vertice exposito perforata, ,/, mill.
in diam. Sporulae ellipticae, 5 X 21/, w, rectae, hyalinae, continuae,
biocellatae.

Differt nostra species a Phoma Corni sporulis suis minoribus
(5X2!/, « contra 8—102—3 w), rectis, ellipticis (neutiquam oblongo-
eylindricis); a Phoma thallina absentia macularum linea purpurina
limitatarum; a Phoma Corni suecicae peritheciis confertis, nec nou

( 234 )

sporulis suis ellipticis (neque cylindricis); a Phoma candidula peri-
theciis confertis, nec non sporulis suis ellipticis, rectis (nec eylindri-
cis, rectis et curvatis commixtis).

* PHoMA DESCISCENS Oud. n. sp. — On branchlets of Vites vinifera.
ef. Hedwigia XX XVII (1898) p. 314.

* Puoma Dovciasi Oud. n. sp. — On the cone-scales of Abies
Douglas. cf. Hedwigia XX XVII (1898) p. 314.

21. PHoma Cosmr Oud n. sp. — On the stems of Cosmus bipin-
natus. — Nunspeet, Sept. 5, 1899; Mr. Berns.

Perithecia caespitosa, nigra, globuloso-depressa, sub epidermate
abscondita, '/;>—1/g mill. in diam., minute papillata, vertice perforata;
sporulae oblongae, continuae, hyalinae, ad polos rotundatae, egutta-
latae, 91/3 X 2"/o ue.

22. PHOMA EUPHORBIPHILA Oud. n. sp. — On the stems of
Euphorbia Lathyris. — Naaldwijk, Dec. 1866; the late Dr. J. E.
VAN DER TRAPPEN.

Perithecia numerosissima, conferta totamque internodiorum super-
ficiem occupantia, perpetuo sub epidermide occultata, parum promi-
nentia, tandem vertice exposito perforata et circa ostiolum portiun-
cula epidermidis annulari nigricante ornata, !/, mill. sine, mill. 1 cum
zona nigricante in diam. metientia. Sporulae oblongae vel subclavatae,
rectae vel curvatae, 7—9 > 2!/, , 1- ad 4-guttulatae, hyalinae, continuae.

*PHoMA FRANGULAE Oud. n.sp. — On thin branches of Rhamnus
Frangula. cf. Hedw. XXXIV (1898) p. 314.

23. PuHoma Hamametipis Oud. N. K. A. 3, I, 487. — This should
be Phoma Halesiae Oud. n. sp. On branches of Halesia tetraptera.
Nunspeet, March 7, 1898; Mr. Beins.

The name of the plant was first given me wrongly, later correctly.

24. Puoma Iparr Oud. n. sp. — On the branches of Rubus
idaeus. — Nunspeet, Febr. 3, 1899; Mr. Berns.

Perithecia orbiculari-depressa, 1/;—-!/, mill. in diam., vertice per-
forata, membrana justo crassiore praedita, perpetuo sub epidermidis
portiunculo scutiformi, elliptico vel oblongo, nigro et paullo micante,
ad polos acutato, 1—2>1 millim., occultata. Sporulae ellipticae vel
oblongae, ad polos rotundatae, hyalinae, biocellatae, 7 — 81/, x
2'/,—3'/s a, basidiis sporularum longitudinem attingentibus suffultae.

( 235 )

* PHOMA INEXPECTATA Oud. n. sp. — On the leaves of Adres
pectinata. Cf. Hedw. XXXVITI (1898), p. 176.
* PHOMA INOPINATA Oud. n. sp. — On the leaves of Pinus Stro-

bus. Cf. Hedw. XX XVII (1898), p. 177.

25. Puoma Laricis Oud. n. sp. — On the twigs of Larix de-
cidua. Scheveningen, May 1894.

Perithecia caespitose aggregata, subglobosa, primo sub_ perider-
mate abscondita, postea exposita, atra, 100—250 4 in diametro.
Sporulae ellipticae, hyalinae, continuae, eguttalatae, 7X2" wu.

26. PxHoma Necunpinis Oud. n. sp. — On the branches of
Negundo fraxinifolia.

Perithecia numerosissima, primitus sub peridermate abscondita,
tandem exposita, 140 « in diam., ochracea, vertice perforata. Spo-
rulae ellipticae, continuae, hyalinae, 4°/;31/2 w.

27. PHOMA OENOTHERICOLA Oud. n. sp. — On the leaves of
Oenothera biennis. Nunspeet, March 13, 1898; Mr. Berns.

Perithecia inordinate distributa, sub epidermate latentia, lenti-
formia, vertice perforata, 3/j) mill. in diam. Cellulae epidermales
ostiolo perithecii contiguae saturatius tinctae quam aliae magis
distantes. Sporulae breviter oblongae, 7 21/, w, eguttulatae, hyalinae.

Differt haec nostra species a Phoma oenotherella Sace. sporulis
angustioribus (7X2!'y @ contra 74.) et colore cellularum perithecii
ostiolum circumdantium ; a Phoma Oexotherae Sace. et Phoma Ona-
grarearum Cooke guttularum in sporulis absentia; a Phoma Onogra-
rearum insuper sporularum latitudine minore (7 X 2!/3 « contra
.6—8 X31/.—4 wu).

*PHOMA QUERNEA Oud. n. sp. On branches of Quercus Robur. —
Nunspeet, March 7, 1898; Mr. Bers. Cf. Ned. Kr. Arch. 3, I, 489.

28. PHoma Saccarpor Oud. — On branches without bark of Sam-
bucus nigra. Naaidwijk, 1864; the late Dr. J. E. van per TRAPPEN.

When on p. 491 of the 1st volume of the 3" series of the “Ne-
derlandsech Kruidkundig Archief’ (1898) I mentioned Phoma vicina
Desm. as a new indigena for our country, I pronounced the sup-
position that my specimens would not differ from those described
by Mr. Saccarpo in Syll. III, 71, notwithstanding the measurements
(5 X 2) of the spores examined by the Italian mycologist, did not
correspond with those of Desmazibres and of myself (7—5<1.9 «).
At that time I had not however, had an opportunity of getting
acguainted with Phoma vicina Saceardo, which is bound to branches

deprived of bark of Sambucus nigra. Now, however, that I have
come into possession of such objects, I have been enabled to con-
vince myself that such an identity between both Phomas, as to which
I referred above, does not exist, and that consequently, they cannot
be indicated by one and the same name. For this reason I supplied
Phoma vicina Sace. by Phoma Saccardoit.

To be sure, it cannot be denied that in both species the base of
the perithecia dives down to a slight depth into the wood of the
branches, but this does not prevent the perithecia of Phoma vicina
Desm. from having a much more robust appearance, and thicker
walls, and from its never occurring but on the branches of the elder
covered with bark, whilst those of Phoma Saccardoi Oud. are much
more delicate and small, have a transparent membranaceous wall,
and prefer branches devoid of bark.

*PHOMA SALICELLA Oud. n. sp. — On the branches of Salix
cinerea. — Nunspeet, March 7, 1898; Mr. Beins. — Cf. N. Kr.
Arch. 3, Lp. 490:

29. PHoma SaLisBURYAE Oud. n. sp. — On the branches of
Salisburya adianthifolia. — Botanical Garden Leiden, Aug. 1893.

Perithecia numerosa, inordinate distributa, orbicularia, nigra,
/4—1/, mill. in diam., primo sub peridermate latentia, postea in
fissuris corticis exposita, vertice perforata. Sporulae fusiformes, ad
polos anguste rotundatae, hyalinae, continae, eguttulatae, 9X2 «.

*PHOMA SEMPERVIRENTIS Oud. n.sp. — On the still green branches
of Lonicera sempervirens. — Nunspeet, April 15, 1898; Mr. BErns.
— Cf. Hedw. XXXVI (1898) p. 315.

30. PHOMA SOLANIeNILA Oud. n.sp.— On the stems of Solanum
nigrum. — Nunspeet, Dec. 19, 1899; Mr. Berns.

Perithecia laxe caespitosa, sub epidermide latentia, postremo exposita,
sphaeroideo-depressa, 140—160 in diam., nigra, vertice perforata.
Sporulae ellipticae, hyalinae, continuae, eguttulatae, ad polos rotun-
datae, 4°/;—7T X 2°/3,—3 uw.

Differt a S. dulcamarina, pampeana, Dulcamarae et solanicola,

absentia guttularum, et a P. ewropaea et Solani sporularum dimen-
sionibus desciscentibus.

*PHOMA SUBTILISSIMA Oud. n. sp. — On the dried peduncles of
Cytisus Laburnum. — Cf. Hedw. XXXVIT (1898) p. 315.

( 237 )

31. PHoMA TATARICOLAE Oud. n. sp. — On the branches of
Lonicera tatarica not yet deprived of their bark. — Nunspeet,
March 5, 1899.

Perithecia numerossima, nunc totam internodiorum superficiem occu-
pantia, tune vero gregatim conferta limitesque macularum_palles-
centium valde extensarum non excedentia, sub peridermate occultata,
postea autem vertice suo perforato, intra zonulam nigrescentem incluso,
exposita. Sporulae nunc ellipticae, tune vero paullo elongatae, ad
polos rotundatae, biocellatae, hyalinae, T—8 X 31/.—4 w.

Species neutiquam confundenda neque cum Ph. oblongata Briard et
Henrich (Sace. Syll. X, 145), nee cum Ph. Mariae, quae ambae lignicolae;
neque cum Ph. cryptica Sace. (Syll. II, 69), cujus sporulae forma
recedunt; neque cum Ph. minutula Sace. (Syll. IL, 70), cujus spo-
rulae voluminosiores; neque cum Ph. tatarica Allescher (Wint. Kr.
Fl. VI, 221), cujus sporulae non tantum voluminosiores sed insuper
forma recedunt; neque cum Ph. xrylostei Cooke et Harkness (Sace.
Syll. III, 70) et Ph. viventis Cooke (Sacc. Syll. X, 145), quarum
sporulae voluminosiores.

32. PHOMA THYRSIFLORAE Oud. n. sp. — On the stems of Lysi-
machia thyrsiflora, in company with Ascochyta Lysimachiae Oud.
Nunspeet, April 15, 1898; Mr. Berns. — Maculae nullae. Perithecia
minima (?/;, mill. in diam.), laxe caespitosa, sub peridermate occultata,
prominentia, denique vertice perforata. Sporulae breve-ellipticae, hya-
linae, eguttulatae, 31/,—5 & 21/;—-3 wu.

Differt a Ph. Lysimachiae sporulis multo minoribus (3'/,—5
2%;—3 w contra 10 X 41/,—5 wu).

33. PHoma TRIACANTHI Oud. n.sp. — On the thorns of Gledit-
schia triacanthos, in company with Ph. Gleditschiae. — Nunspeet,
March 18, 1899; Mr. Berns.

Perithecia nune aequaliter distributa, tune caespitose aggregata,
majoribus et minoribus commixtis, sub peridermate latentia, p. m.
prominentia, denique in fissuris longitudinalibus rectis vel curvatis,
simplicibus vel ramosis, exposita. Sporulae oblongae, ad polos late
rotundatae, hyalinae, nitide biocellatae, 7X2'’3 w.

34. PHOMA TYPHICOLA Oud. n. sp. — On the stems of Typha
latifolia. — Nunspeet, May 21, 1899; Mr. Bens.

Perithecia primo sub epidermide latentia, postremo exposita, mi-
nima, nigra. Sporulae ellipticae vel oblongae, ad polos rotundatae,
continuae, hyalinae, eguttulatae, 31/,—5 X 21/3 «. (Pl. IV, fig. 3).

( 238 }

~

35. PHoma viBuRNIcOLA Oud. n. sp. — On the branches of
Viburnum Oxycoccos, in company with Ascochyta viburnicola. -—
Nunspeet, April 14, 1899; Mr. Berns.

Perithecia numerosa, parva, diu sub peridermate occultata. Spo-
rulae ellipticae, hyalinae, continuae, eguttulatae, 5—6 % 3)/, wu.

MACROPHOMA bBerlese et Voglino.

36. MacropHoMa CaPseLLAE Oud. n. sp. — On the leaves of
Capsella Bursa pastoris. — Apeldoorn, July 26, 1899; O. — Peri-
thecia conferta, primo epidermide velata, denique exposita, nigra.
Sporulae ellipticae vel elliptico-oblongae, hyalinae, continuae, ad
polos rotundatae, biocellatae, 166 «.

The size of the spores does not allow this species to be admitted
into the genus Phyllosticta.

37. Macropnoma Ixicis (Desm.) Oud. — On the leaves of Ilex
Aquifolium. Described by DEsMAzIbres under the name of Phoma
Ilicis in his ,Plantes Cryptogames de France”, 1°5S., 1¢ Ed., N°. 1290,
and taken up by Saccarpo under the same name in Syll. III, p. 106.

Perithecia hypophylla, numerosissima, subconferta, saepe intra limi-
tes macularum pallescentium coacervata, valde prominentia, sub epi-
dermide occultata, vertice perforata, nigra, 1/; ad 1/, mill. in diam.
Sporulae ellipticae vel ovatae, hyalinae, continuae, 12—15 x 6—T w,
initio protoplasmate nebuloso repletae, denique guttula voluminosa
centrali ornatae, ad polos late rotundatae, longe pedicellatae, apice
passim apiculatae.

Now that the genus Macrophoma has been introduced into science
for those species of Phoma, whose spores are 15 or more mikrons
in length, it was necessary to bring Phoma Ilicis Desm. under this
head. With the name in Saccarpo’s Syll. (II, 106) the same ought
to be done.

SCLEROTIOPSIS Spegazzini.

38. ScLEROTIOPSIS POTENTILLAE. Oud. n. sp. — On the leaves
of Potentilla procumbens (Tormentilla reptans). — Nunspeet, August
26, 1898; Mr. Beins.

Perithecia innata, semiglobosa, nigra, submicantia, adulta p. m.
1 mill. in diam., nune ad faciem foliorum superiorem, tune vero ad
inferiorem prominentia, absque ullo ostioli vestigio, membrana fragili,
indistincte parenchymatosa instructa. Basidia filiformia, recta, Spo-

(239 )

rulae acrogenae, solitares, cylindricae, semilunares, indistincte mucro-
natae, hyalinae, continuae, 7—9'/; > 2. — (Pl. IV, fig. 4).

Our description of Sc/. Potentillae corresponds almost entirely with
that of Sci. australasiaca, made known by SPEGAZZINI in SaccaRpDo’s
Syll. III, p. 184. As, however, between the shape and the internal
colour of the perithecia of both fungi, the size of their spores, and
the nature of their host-plant, greater and smaller differences were
to be observed, I thought myself justified in allowing both Scl.:
Sel. Potentillae on Potentilla procumbens and Sel. australasiaca on
Eucalyptus Globulus, to continue as two species and not to join
them to one.

39. SCLEROTIOPsSIS PITYOPHILA (Cda) Oud.; Phoma pithyophila
Sace. Syll. III, 101; Allescher in Wint. Kr. Fl. VI, 199; Sphae-
ronema pithyophila Corda Ic. Fg. 40 et tab. VIII, fig. 116. — On
the leaves of Pinus silvestris. — Nunspeet, 1899; Mr. Berns.

Perithecia amphigena, primo abscondita, in acuum parenchymate
immersa, postremo exposita, corporaque sistentia slerotiformia, nigra,
nune separata et subsphaerica, tune vero coalita et irregularia. Quod-
vis corpusculum e_ stratis quasi duobus compositum: uno scil.
magis superficiali, parenchymatoso, nigrescente, crassiore, densiore ;
altero, magis interiore, parenchymatoso, pallide-flavo, tenuiore, molliore,
dum constat colorem nigrescentem cellularum membranis, colorem
pailide-flavum vero cellularum contentis esse proprium. Sporulae
maturae ex orificio accidentali, irregulari, non autem ex ostiolo natu-
rali protrusae, corpuscula sistunt oblonga, hyalina, ad polos rotundata,
uniguttulata (?)

RABENHORSTIA Fries.

*RABENHORSTIA CLANDESTINA Fr.; Sace. Syll. II. 244. On dead
branches of Sorbus Aucuparia. — Nunspeet, May 9, 1898; Mr.
Berns.

A detailed description of this hardly known fungus, which has
only very superficiously been described by Saccarpo, I gave in
Hedwigia XX XVII (1898) p. 315.

_ *RABENHORSTIA SaLicis Oud. n.sp. — On the branches of Salix
repens. Nunspeet, May 5, 1898; Mr. Berns. — Hedw. XXXVII
(1898) p. 317.

PLACOSPHAERIA Saccardo.

40. PuacospHarRia Prunt Oud. n.sp. — On the young branches
of Prunus domestica. Nunspeet, April 27, 1899; Mr. Bers.

( 240 )

Stromata ad ramulorum superficiem numerosa, oblonga, 1/, ad 1
centim. longa, 2 ad 3 mill. lata, juniora rufescentia, vetustiora fuli-
ginea, intermixtis nonnullis annulo fuliginoso ad ambitum inelusis,
centroque rufescente, subprominente. Includunt cavernulas plures
indivisas, basidiis filiformibus, conidia quoad longitudinem subae-
quantibus, vestitas. Conidia partim cylindrica, ad polos rotundata,
partim fusiformia, subacutata, semper hyalina, 2-vel pluriocellata.

FUSICOCCUM Corda.

41. Fusicoccum Corni Oud. n.sp.— On the branches of Cornus
alba. — Nunspeet, Sept. 15, 1899; Mr. Berns.

Perithecia vulgo maculicola, sparsa, nigra, sub peridermate abscondita,
p.m. prominentia, !/;,—?/, mill. in diam., tandem vertice perforata,
plurilocularia, loculis septisque membranaceis ; sporulae fusiformes, ad
polos anguste-rotundatae, 9—12 X 2—~3'/) , continuae, hyalinae,
eguttulatae; basidia acicularia, sporis duplo longiora.

CYTOSPORELLA Sace.

42. CYTOSPORELLA QuERCUS Oud. n. sp. — On branches of Quercus
Robur. — Valkenburg (L.); April 1900; Mr. J. Rick.

Stromata corticola numerosa, sparsa, polymorpha, saepe sinuoso-
limitata, verruciformi-depressa, 1 ad 3 cent. lata, intus fuscescentia,
incomplete pluricellularia, locellis quoad amplitudinem valde variabili-
bus ; sporulae globulosae, hyalinae, ad basin subcontractae, 9!/;—117/s 4c,
basidiis brevibus suffultae.

Differt a C. Populi Oud. (Ned. Kr. Arch. 2, V, 494; Sace. Syll.
X, 242) stromatibus multo robustioribus et sporulis multo majoribus
(9/3 —11°/3 « contra 7 x).

CYTOSPORA Ehrenberg.

43. CYTOSPORA DASYCARPI Oud. n. sp. — On the branches of
Acer dasycarpum. — Scheyeningen, May 1895; Bussum, April 1900;
Mr. Konina.

Pustulae sparsae, quoad amplitudinem magnopere variabiles, con-
vexae, primo clausae, postea, peridermate varie fisso, perviae. Stromata
nigra, intus lacunosa, lacunis septis spuriis in loculamenta plurima
inaequalia concentrice divisis. Sporulae fere globulosae, cum ellipticis
et brevi-fusiformibus inacqualiter mixtae, continuae, hyalinae, 1—3
< 1—2 wu, basidiis longis, tenerrimis suffultae.

( 241 )

44, CyYTOSPORA FRAXINICOLA Oud. n.sp. — On the young, thin
branches of Fraxinus excelsior. — the Hague, April 1889.

Differt a C. Fraxini Delacroix (Bull. de la Soc. mycol. de France,
1890, p. 184 et tab. XX fig. V; Saccarpo Syl]l. X, 245) basidiis
multo longioribus (25 contra 10) et sporulis angustioribus
(7X 1/, contra 7 X 23 wz).

*CyTOSPORA OPACA Oud. n.sp. — On the branches of Llex opaca,
Cf. N. K. A. 3, I, 492 et Hedw. XXXVII (1898) p. 177.

*CYTOSPORA SELENESPORA Oud. n. sp. — On the branches of
Sorbus Aucuparia. — Nunspeet, March 3, 1898; Mr. Bers. — Cf.
Ned. Kr. Arch. 3, I, 493.

CEUTHOSPORA Greville.

45. CEUTHOSPORA FRAXINICOLA Oud. n. sp. — On branches of
Fraxinus excelsior. — Amsterdam, January 1877; 0.

Stromata numerosa, inordinate distributa, primo occultata, tan-
dem exposita laciniisque peridermatis rupti circumcincta. Perithecia
caespitose aggregata, parte sua dimidia superiore rotundata libere
prominentia, coriacea, nigra, sine ostioli vestigio. Sporulae minimae,
bacillares, hyalinae, simul cum magna mucilaginis copia ex variis
evolutionis centris protrusae, 41/; X 11/, «, singulae basidio filiformi
9 p. m. longo suffultae.

Differt nostra a C. Fraxini Tognini (Seconda Contrib. micol. tose.
p- 10 et Sace. Syll. LX, 510), cujus plena diagnosis adhue desideratur,
sporulis multo minoribus (41/3 X 11/, # contra 6—T7 X 3).

2. Phaeosporae.
CONIOTHYRIUM Corda.

46. CONIOTHYRIUM LABURNIPHILUM Oud. n. sp. — On the leaves
of Cytisus Luburnum. — Nunspeet, Oct. 1898; Mr. Berns.

Maculae amphigenae, orbiculares, oblongae vel irregulares, 2 ad
10 mill. latae, primo saturate-fuscae, postea pallescentes, postremo
albidae, pallide-purpureo-marginatae, fragillimae. Perithecia epiphylla,
epidermide velata, numerosa, minima, diam. !/;) mill. raro superantia,
parte centrali paullo prominente et perforata. Sporulae breve ellip-
ticae, 47/5 31/9 w, pallide-olivaceae, in mucilaginem dilutam immersae,
continuae, eguttulatae.

Differt a C. olivaceo praesentia macularum, peritheciorumque nec
minus sporularum mensuris reductis.

( 242 )

*CONIOTHYRIUM PSAMMAE Oud. n.sp.— On the leaves of Psamma
littoralis (= Ammophila arenaria). Cf. Hedw. XXX VII (1898) p. 177.

47. CoONIOTHYRIUM PYXIDATAE Oud. n. sp. — On Cladonia pyxi-
data. — Valkenburg (L.) 1899; Mr. J. Rick.

Perithecia perfecte sphaerica, minutissima, vix 1/,9 mill. in diam.,
nigerrima; sporulae globosae vel subglobosae, dilute-olivaceae, vix
21/3 «a in diam., laeves, continuae, basi sua applanata vel truncatius-
cula basidio crassiusculo brevissimo imposita.

Differt a C. lichenicola Karst. Symb. XX, 104, sporulis minoribus
(21/3 « contra 3“), neque ovoideo-oblongis vel clavulatis, neque basi
attenuatis, neque fuligineis, basidiis tandem brevioribus (2 w contra
6 «); a C. Cladoniae Ell. Everh. Sace. in Syll. X, 268, peritheciis
fere duplo minoribus (1/),— 1/, contra '/, mill.), non obconico-cylin-
draceis, supra subtruncatis, sporis dilutius tinctis, minoribus (21/3 con-
tra 3 w), basidiis multo brevioribus (2 c. 6 4).

48. ContornyriuM Tamaricis Oud. n. sp. — On the thin branch-
lets of Tamarix gallica. — Nunspeet, Oct. 22, 1898; Mr. Berns.

Perithecia numerosa, sparsa, parva ('/}o — 1/s mill.), globulosa,
epidermide velata, prominentia, nigra. Sporulae ovatae, primo hya-
linae, denique lutescentes, 7 X 31/y #, guttula centrali elliptica insig-
nes (Pl. IV, fig. 5).

Differt a C. tamaricella Brun. (Sace. Syll. XIV, 923) sporulis
pallidis neque ,,intense-olivaceis’’, et longioribus (7 « contra 21/2 — 6 w).

HAPLOSPORELLA Spegazzini.

49, HApPLOSPORELLA JUGLANDIS (Schum.) Oud. n. sp. (Naema-
spora Juglandis Schumacher Flora Saellandiae I, 178; Cytospora
Juglandis Rab. Kr. FI. 148; Sace. Syll. ILI, 267). — On the branches
of Juglans regia. — Naaldwijk, Nov. 1866; the late Dr. J. E. van
DER TRAPPEN.

Perithecia numero 4 ad 7 in stromate verruciformi, fere carboni-
sato, nigro, primo latente, postea in corticis vulnere large hiante,
mill. 1 lato, peridermatis laciniis circumcincto, exposita. Sporulae
globulosae (21/5 4 in diam.) vel breve-ellipticae (4°/; >< 21/3 4e), conti-
nuae, fuliginosae, basidio brevi suffultae.

y. Hyalodidymae.

ASCOCHYTA Libert.

*AscocuyTa AcorI Oud. n. sp. — On the leaves of Acorus Ca-
lamus, — Cf. N. K. A. 3, I, 496 et Hedw. XXXVII (1898) p. 177,

( 243 )

*AScOCHYTA EUPHRASIAE Oud. n. sp. — On the stems of Euphr.
officinalis. — Nunspeet, March 11, 1898; Mr. Brtns. Cf. Ned. Kr.
Arch. 3, I, 496.

*ASCOCHYTA GROSSULARIAE Oud. n. sp. — On the branches of
Ribes Grossularia. — Cf. N. K. A. 3, I, 497 et Hedw. XXXVII
(1898) p. 178.

50. AscocHyTa HypocHorRIDIsS Oud. n. sp. On the flower-stems
of Hypochoeris glabra. Nunspeet, May 5, 1899; Mr. Berns.

Perithecia in maculis pallescentibus inordinate distributa, primo
epidermide velata, prominentia, postea exposita, nigra, vertice perfo-
rata. Sporulae exacte cylindricae vel elongato-clavatae, ad polos
rotundatae, vulgo rectae, rarius curvulae, hyalinae, imo quum in majo
rem copiam condensatae offenduntur, initio biocellatae, postea septo
transversali dimidiatae. In sporulis clavatis pars anterior latior et paullo
longior, pars posterior contra angustior et brevior (Pl. IV, fig. 6).

*AscocnytTa [parr Oud. n. sp. — On the branches of Rudus idaeus.
Cf. N. K. A. 3, I, 497 et Hedw. XXXVII (1898), p. 178.

51. AscOCHYTA IGNOBILIS Oud. n. sp. On the stems of Alisma
Plantago, Nunspeet, March 13, 1898; Mr. Bemys.

Maculae nullae. Perithecia primo epidermide velata, postea expo-
sita, nigra, orbiculari-depressa, vertice perforata, 125—170 4 in diam.
Sporulae cylindraceae, ad polos rotundatae, hyalinae, 9—12 X 3 «&,
indistincte biocellatae, per longius tempus continuae, denique septo
transversali aegre visibili, iodio addito vero mox optime distinguendo,
dimidiatae.

A. ignobilis differt ab 4. Alismatis Ellis et Everhart, Journ. of
Mycol. 1889, p. 148 et Sace. Syll. X, 307, quae in foliis offenditur,
absentia macularum, peritheciis multo majoribus, sporulis paullo
minoribus, praedilectione pro foliis.

52. AscocuyTa Lacrucar Oud. n. sp. — On the flower-stems
and their ramifications of Lactuca sativa. — Naaldwijk, 1874; the late
Dr. J. KE. VAN DER TRAPPEN.

Perithecia in caespites aggregata, globuloso-depressa, epidermide
velata, tandem exposita, nigra, vertice perforata, '/;—1/; mill. in
diam. Sporulae oblongae, hyalinae, ad polos rotundatae, biloculares,
12—15 X 3'/, w, medio superficialiter consitrictae.

( 244 )j

53. ASCOCHYTA LEDICOLA Oud. n. sp. — On the leaves of Le-
dum palustre, together with Thoracella Ledi Oud. — Nunspeet,
Sept. 29, 1898; Mr. Berrys.

Perithecia epiphylla, parum numerosa, inordinate distributa, 1/3
mill. in diam., tandem vertice perforata. Sporulae fusiformes, hya-
linae, ad polos acutae, biloculares, vix medio constrictae, 7—112 u.

Ascochyta Ledi Rostrup (Sace. Syll. X, 295), in caulibus Ledi
palustris degens, sporulas fert oblongas, ad polos rotundatas, volu-
minosiores (12—13 & 3 4).

54. Ascocnyta LyYsIMACHIAE Oud. n. sp. — On the stems of
Lysimachia thyrsiflora, in company with Phoma_ thyrsiflorae. —
Nunspeet, April 15, 1898; Mr. Berns.

Maculae nullae. Perithecia laxe caespitosa, sub epidermidis por-
tiuncula nigricante, in longitudinem protracta, p.m. prominente
occultata, 1/; mill. in diam. Sporulae oblongae, ad polos rotundatae,
hyalinae, bilocellatae, eguttulatae, medio non constrictae, T—9!/3X
21/, we. Basidia ter longiora quam sporulae.

55. AscocuyTa Menyantais Oud. n. sp. (non Lasch, neque
Libert, quae ambae sub genere Septoria militant). — On the leaves of
Menyanthes trifoliata, in company with Septoria Menyanthis.

Perithecia amphigena, vulgo tamen hypogena, una cum peritheciis
Septoriae Menyanthis in maculis fuscis, satis extensis, polymorphis
irregulariter distributa. Sporulae breve-cylindraceae, hyalinae, ad
polos rotundatae, 14—19 21/;—3'/, «, biloculares, loculis nitide
1- vel 2-ocellatis. Septum, vulgo p.m. obscurum, iodio addito statim
conspicuum fit.

*AscochyTaA Marrutorare Oud. n. sp. — On the pods of Mat-
thiola incana. — Cf. N. K. A. 3, I, 497 et Hedw. XXXVII (1898)
p- 178.

*ASCOCHYTA MISERA Oud. n. sp. — On the leaves of Cratae-
gus monogyna. — Cf. N. K. A. 3, I, 497 et Hedw. XXXVII
(1898) p. 178.

*AscocHyTA Myrtitti Oud. n. sp. — On the dried sprigs of
Vaccinium Myrtillus. — Cf. Hedw. XXX VII (1898), p. 317.

(To be continued).

( 245 )

Botanics. — “On the origin of new species of plants.” By Prof.
Huco DE VRIES.

The fact that the species existing at the present moment are, as
far as we observe, invariable, can but be brought into accordance
with the theory of descent when admitting that periods of constancy
alternate with periods of mutability. The former may last hundreds
and thousands of years, the plant, as experience shows, continues
the same, all the time. The latter have, hitherto, escaped all obser-
vation.

Probably, however, because they have not been sought for. And
this again had its cause in our not having a right perception of
what was to be found. For the prevalent opinion that species orig-
inate through very slow changes, is not favorable to such researches.

Side by side to this supposition, the so-called selection-theory, the
possibility of a discontinuous origin of species was already recognised
by Darwin. The differences between closely allied species are in
fact so slight that they may quite well appear at once. This idea
has since continually found a few followers, in particular among
paleontologists, but also among zoologists and botanists. Starting
from this principle there is no longer any ground to suppose the
origin of species as being beyond observation, and consequently,
neither not to look for it.

My conclusion is: plants may, alternately with long periods of
constancy, go through periods in which they produce one or more
new species. On the other hand, each species has originated from
another in such a period. And for this it is by no means neces-
sary that the mother-species dissolves into the new ones, converts
itself into these, it may continue, with all its former properties,
quite unchanged.

Tf this view is right, the one thing necessary is to look for plants
being in such a perio of mutation. The chance of finding them is
of course very slight, but this is no reason not to seek for them.

I have, in these researches, followed two methods. One consisted
in direct observations on the wild growing-places; the other in the
sowing out of seed collected from the natural habitat, or of seed
from plants taken thence and brought into the garden. I sowed the
seed in the garden on as large a scale as possible.

The result of this rather extensive research was the wished for.
One species I found in a mutation-period. It is Oenothera Lamar-
ckiana, introduced here, like O. biennis and O. muricata, from
America.

17
Proceedings Royal Acad. Amsterdam. Vol. ILI.

( 246 )

I sowed its seed for the first time in 1887 and at once obtained
a new form, O. Jafa, and that in three specimens. In 1888 I again
sowed seed and now on a larger scale. I once more obtained OQ,
lata, in five specimens, and beside it a dwarf form, O. nanella,
likewise in five, and a species with narrow, glossy leaves, O. scint-
illans in a single specimen. My culture amounted to about 15.000
seedlings, so that both first mentioned species had appeared at the
rate of 1 specimen on 3900.

I have since repeated these sowings, first on as large, later, with
more experience, on a smaller scale, and now possess the ninth
generation of O. Lamarckiana in a state of mutation.

It produces both the first menticned species nearly every year,
the third from time to time.

Moreover, I have seen arising from it a series of other forms,
formerly unknown, sometimes in a single, sometimes in various,
sometimes, even, in rather numerous specimens. Thus the culture —
of 1895 produced on 14,000 seedlings, 1 O. gigas, 2 O. leptocarpa,
8 O. rubrinervis, 15 O. albida and 176 specimens of O. oblonga,
These forms proved at once constant at the first sowing; they are
still at present, after some generations of culture, just as they were
at their first appearance. Besides, of the three last named, nearly
every year new specimens arise from the primitive stock.

I have now, during my fifteen years’ experiment, observed about
a thousand mutations, in which twelve quite distinct, and mostly
seed-fast species occurred. Moreover, there originated a number of
other, indistinct, sterile, or insufficiently sced-fast types.

The rules followed in these mutations are:

1. The new species originate suddenly, without intermediate forms
or any other preparation.

2. From the beginning they remain unchanged in the course of
the generations.

3. They are mostly, at sowing, perfectly constant, from their very
first appearance. A return to the mother-species, or atavism, I
never observed in those cases. Exception O. scintillans, with strong
atayism.

4. Among them is a dwarf-form, (O. nanella), which may be
taken as a variety; it behaves, however, just as the others. Those
others deviate from one another, and from the mother-species, as
much, and in some respects more, than closely allied, older species
in this and other genera,

( 247)

5. They mostly appear in a great number of individuals, and
repeatedly in a series of years.

6. The new properties are individually variable, according to
QueTELET’s law, like those of O. Lamarckiana. But between this
variability and the mutation by which they took birth, there is no
perceptible relation.

7. The mutations take place in various directions and not by
preference in a determined one. Mostly they weaken the new species
and so are disadvantageous (OQ. albida), sometimes they are indiffe-
rent (0. rubrinervis), sometimes probably favorable (O. gigas). In
many cases the fertility seems lessened, in others not at all.

The appearance of new species may be comprised in the form of
a pedigree. The specimens repeating the type of O. Lamarckiana,
then form the stock, of which each year the mutants are as many
branches. In the pedigree below only these mutants are mentioned ;
the specimens obtained from their seed, which served me in the
investigation after the constancy of the species, are left out.

The pedigree relates only to one of my experiments which was
begun in 1886 with nine rosettes of two years’ plants. These rosettes
themselves were taken from the wild habitat, but had been removed
in the autumn of the said year into the botanical garden, where
in 1887 they flowered and bore seed.

Pedigree of Oenothera Lamarckiana,

Generation. gigas albida oblonga rubrinervis Lam. nanella lata scintillans
$th Generation
1899 5 1 < 1700 21 1
annual. eee
7th Generation
1898 ‘ 9 : 3000 1l é
annual. a
6th Generation
1897 il 29 3 1800 9 y 1
annual. ee __ -
5th Generation
1896 O helio 20 8000 49 142 6
annual, a eee
4th Generation
1895 L 15 176 8 14000 60 73 il
annual. NR ——<$€$—___——— =
3rd Generation
1890/91 il 10000 3 3
biennal. i
2nd Generation
1888/89 15000 o 5
biennal. SS
ist Generation
1886/87 9
biennal,

( 248 )

Physiology. — ‘On muscle-tone’, (abstract). By Dr. J. W.
LANGELAAN (Communicated by Prof. T. PLace).

The researches of late years have revealed a great system of
afferent nerve fibres, partly originating in the muscle itself, partly
in its adjacent tissues. Now it is highly probable, that the afferent
nerve fibres belonging to the muscle, come into relation with the
motor nerve cells in the anterior horn of the same muscle and form
in this manner a muscle-reflex are on which muscle-tone depends.

To ascertain the extent of this tonicity, 1 chose the wellknown
fact, that a normal muscle, the tendon of which is cut, undergoes ab-
ruptly a permanent shortening. This fact shows, that an elastic force
resides in the tonic muscle. Jn order to determine this foree, the
distention of the muscle in rest was registered by means of a weight
increasing with constant velocity. The muscle experimented on was
the gastrocnemius of Rana esculenta, completely left in connection
with its nerves and bloodvessels.

For the purpose of calculating the distensibility of the muscle
from these tracings, the increase of length (A 1) corresponding with
a little augmentation of the charge (A p) was measured. The mean
of two sets of measurements was taken as the amount of the dis-
tensibility at a certain moment, of which the differential coefficient

= is the symbol. This quotient, taken as measure of the musele-

eg
tone, was therefore called the tonicity-quotient, and the tracings

from which it was calculated named tonicity-curves.

From the experiments resulted, that, within the limits of the
proof, succeeding increases of the charge forming terms of a geo-
metrical progression, accorded with tonicity-quotients forming terms
of an arithmetical progression ; or formulated otherwise, that there
existed a logarithmical relation between the value of the succeeding
tonicity-quotients and the correspondent augmentations of the charge.

Tf the supposition made by Fick, Herpennarn and afterwards by
Mommsen, BeNEDICENTI, GOWERS and SHERRINGTON is correct, that
the terminations of the afferent nerve fibres in the muscle are stimul-
ated by tension, it is evident that in my experiments the value of
the distending weight must be a measure of this stimulus. Therefore
if p be the amount of this weight C,;p must be the rate of stimula-
tion, and the result consequent upon this excitement is the according

me ; d é rere
value of the tonicity, symbolized by Cy, = Applying, in this ease,

( 249 )
the law of FrcuNeR we are lead to the following connection:
dl
Cj p=e Op e base of the Nep, log.
By integration this equation leads to the connection:
1=A.p-+B.p. Ign. p.,

lgn. ©; — 1
Cg
1
C,

A=

B=

where 1 denotes the increase of the length of the resting muscle
and p the augmentation of the charge.

The three tables added show how far this formula agrees with
the facts.

A= 0.00724 A = 0.00925 A =0.00777
B= — 0.00080 B=— 0.00144 B=— 0.00103
eee SS
p. |1. meas. | 1. cale. p. |. meas.| 1. cale. p. | 1. meas. | 1. cale.
3.0¢,| 0.013 | 0.017 30¢,| 0.017 | 0.020 | 3.0¢,| 0.016 | 0.019

a

6.2 | 0.030 | (0.030) 6.2 | 0.036 | (0.036) .035 | (0.035)

12.6 | 0.060 | 0.057 12.6 | 0.064 | 0.062 .065 | 0.063

25.4 | 0.102 | (0.102) 25.4 | 0.104 | (0.104) (0.110)

rw
or
AS
So So (>) o
+
~
Oo

33.5 | 0.121 | 0.129 30.9 | 0.116 | 0.119 113) | 0.111

Division of the spinal cord at the level of the second vertebra,
did not change these results in any way.

Severing the tibial nerve above the knee-joint, the muscle is
divided from its reflex-centre, the afferent and efferent paths being
interrupted. The section is succeeded, within thirty seconds, by
an allongation of the muscle, varying in different experiments from
0.3 to 1 pCt.; the distention-curves show quite a different form and
the distensibility is diminished.

The beginning of these distention-curves is a straight line corre-
sponding with an increase of the weight not beyond 5.5—9 gram;

( 250 )
alter a short part of transition, the distention-curve is represented by:
1= Ap + Bp?

The tables added give an idea of the agreement.

A= 0.00441 A = 0.00633 A= 0.00499
B=— 0.00005 B =— 0.000097 B= — 0.00006
| |
p- |1l. meas. | 1. cale. p-. |l. meas. | 1. cale. p. |{1. meas. | 1. cale.
5.45¢,| 0.0226 | 0.0229 6.Ce,| 0.0312 | 0.0313 7.9¢,| 0 0301 | 0.0323
6.45) 0.0269 | (0.0269) 7.0 | 0.0366 | 0.0368 8.9 | 0.0344 | 0.0359
7.45) 0.0318 | 0.0306 11.0 | 0.0527 | 0.0531 9.9 | 0.0376 | 0.0363
12.1 | 0.0484 | 0.0468 12.0 | 0.0570 | (0.0570) 15.0 | 0.0559 | 0.0561
13.1 | 0.0516 | 0.0500 13.0 | 0.0613 | 0.0608 16.0 | g.0591 | (0.0591)
14.1 | 0.0548 | 0.0531 Wy. 0.0763 | 0.0735 17.0 | 0.0623 | 0.0621
0 0
0 0
0
0
0
0.
0.

25.4 | 0.0817 | 0.0807 .0796 | 0.0771 0.0764 | 0.0773

26.4 | 0.0828 | 0.0825 .0827 | 0.0798 0.0785 | 0.0795

27.1 | 0.0839 | (0.0839) .0893 | 0.0894 25.0 | 0.0807 | 0.0816

0914 | (0.0914) 32.1 | 0.0935 | (0.0935)

.0935 | 0.0933

So
ao
i=) o o So i=) (>) (=>)

105 | 0.100

31.8 107 ‘| 0.102

From this it is clear, that the atonic muscle obeys the same
empirical approximative formula of other elastic bodies.

In order to disturd only the afferent path, cocaine was injected
into the spinal canal. The tracings obtained, all showed a rectilineal
commencement, but this part of the curve never reached above a
charge increase of 5.5 gram; for the further part it was found, that
the variation of the distensibility grew slower than the increase of
the charge, but faster than agreeable with a logarithmical relation.

To study the influence of the contraction of antagonistic muscles
upon the tonicity of the agonists, I registered curves of the m.
gastrocnemius, while during a certain interval of time the mm.
tibialis anticus longus and peroneus were stimulated to a continuous
contraction, by the current of a secondary coil. It was found, that

the contraction of these practibial muscles was succeeded by an

( 251 )

increase of tonicity of the m. gastrocnemius of about 25 pCt.
According to the definition of muscle-tone here adopted, the m.
gastrocnemius became more distensible and this fact was already
seen by Bett and afterwards found again by SHERRINGTON.

The variation of the tonicity beeomes discontinuous, when the
muscle contracting under a little charge, retains a residual shortening.
In this case the tonicity-curve is built up of straight lines, at the
end of each of those a part of the shortening is given back, while
at the same moment the tonicity varies. The number of rectilineal
part of which the curve is constituted, is almost constant for the
same muscle, varying for different individuals. The length of each
of these parts is mostly variable, but under favourable circumstances
it is possible to obtain tracings in which they are nearly equal. In
other cases doubtless compensations are found.

Amsterdam, September 1900.

Physiology. — ‘On the determination of sensory spinal skin-
fields in healthy individuals”. By Dr. J. W. LANGELAAN
(Communicated by Prof. C. WINKLER).

What we know about this subject in man, was mainly due to
pathological cases, and the schemas of Heap were the most
complete we had. But the physiological experiments by SHERRINGTON
on Macacus rhesus, carrying on the investigations of Turck and
many others, and tlie minute dissections of Bonk on man, have
given, independently of each other, results so accordant, that we
can believe this problem to be solved in great features. Therefore
not to add new facts, but only to show how it is possible to
determine these fields in normal persons, this paper is communicated.

It was found in a case of locomotor ataxy by my colleague
BeyerMan, that in pricking the skin with a pin, there were
narrow hyperalgetic bands, which closely seemed to follow the
skin-field borders. J saw the same fact in another case of tabes
and we interpreted them as the fields of overlap.

In order to research if these fields could be determined in a healthy
person, I chose intelligent individuals, who could fix their attention
for some time. I began to prick over the skin of the limb first
crossing the mid-ventral line, great care being taken to prick in
equal distances, with the same force and with equal intervals of
time. Approaching the mid-line they all accuse a quickly increasing
seusation of pain. Now I claimed them to note the just perceptible

EEE

( 2524

increase and marked this place with a blue pencil. Pricking from
the opposite side in the same direction a second spot of pain increa-
sing was fixed. In this manner, by all the persons J examined, the
mid-dorsal and mid-ventral lines were easily found as bands extending
along the axis of the limb, from a half to one centimeter breadth.
In no case this crossed overlap on the limbs was found to be larger.

The limits of the fields formed by an anterior and posterior overlap
were much more difficult to find, because the increase of the sen-
sation was slighter and this difficulty grew in the vicinity of the
joints. In harmony with this, it was found by SHERRINGTON, that
the edge of the sensory skin-field is less abrupt at the anterior and
posterior overlap than at the crossed overlap.

When the person under examination got tired, the limits of the
fields of overlap came closer to each other; on the contrary, by
repeating the experiment on the same person after a lapse of time,
the borders became wider, because minuter differences were discri-
minated. The same relations are commonly met in determining the
extent of the tactile spheres by means of the compasses of WEBER.

It is clear, that the fields of overlap fixed in this manner must
be too small, for in the first place we know through the researches
of SHERRINGTON, that the nerve supply from a single posterior root
to its skin-field is less abundant at and near the edge of the field,
and in the second place it is evident, that the increase of the sen-
sation must reach a certain extent, before the difference is perceived.

I am convinced, that the subjectiveness of the method, exposes
to many faults, and therefere I give only the photographical repro-
duction of the areas as found in some cases, without drawing any
conclusions from it.

This method extended to the sensibility of temperature could
perhaps give good results.

Amsterdam, September 1900.

All the persons examined were believed to be healthy individuals.
The roman cyphers denote the number of the posterior root to which
the skin-field probably belongs.

Fig. I. Inner side of the left arm. Person of research J. V.,
aged 27 years */yiit. 2—3.30 P.M.

Fig. Il. Outer side of the left arm; narrow overlap, p. of r.
W. A. V., aged 25 years *8/yn7 2—3.30 P.M.

Fig. 11. Outerside of the left arm; broad overlap. p. of r.
M, H., aged 27 years ‘/rx 2—3.20 P.M.

J. W. LANGELAAN. “On the determination of sensory spinal skinfields in healthy
individuals.”

Fig. J.

Fig. IT.

‘ig. IIT.

Fig. VI.

Proceedings Royal Acad. Amsterdam. Vol. ILI.

:
wei 7) BF

-
.

bigtties, its ule Aad ae
J ‘ » So

( 253 )

Fig. [V. Left half of the chest; the skin round the nipple was
at all hyperaesthetic and the border of this field was not certainly to
determine. p. of r. J. v.D.L., aged 21 years °/yx 10.30—11.30 A.M.

Fig. V. Outer side of the right leg; at the place marked with
a eross skin field XXVII is divided in two parts by a broad over-
lap, p. of r. A. A. J., aged 27 years *%/yy1 1.30—3.20 P.M.

Fig. VI. Left half of the face. The field of overlap round the
eye was not determined. The skin of the ear lays in a broad field of
overlap. p. of r. E. W. DEF., aged 24 years %/1x 2—3 P.M.

Pathology. — “Curious disturbances of the sensation of pain in
a case of tabes dorsalis’. By D. H. Beyerman (Communicated
by Prof. C. WINKLER).

The following case was observed in the service of Prof. WINKLER.

C., 52 years old, married to a husband, who made excesses in
Baecho and in Vencre, had three times abortus, one child born
dead, three others dying a few days after their birth, and only one
child alive. Seven years ago, she complained of diminishing of vision,
afterwards of pains in the limbs and round the chest, the gait
became staggering and difficulties in the deposition of urines with
diarrhoea were obseryed.

On 13 July 1900, the following symptoms are stated.

Internal organs normal. Pupils equal, no reaction upon light and
with convergention. Slight ptosis on both sides. Visus greatly
diminished, large retraction of the field of vision on the right side,
and atrophy of both optic nerves.

No ataxia, no paralysis in the upper limbs, only a slight pa-
raesthesia in the ulnar fingers. Anaesthetic patches on the skin of
the chest.

The ataxia in the lower limbs is very marked, increasing if the
eyes are shut. Muscular force also diminished, the muscles are
weak with marked hypotonicity of the joints. The knee-jerks and
the reflexes of the tendo of Achilles are abolished, the plantar
reflexes are present.

The sensation of pain has diminished in both legs, especially in
the left, except on definite tender spots, where the slight pricking of
a pin, or even a slight touch causes painful expression of the face.

The exact marking of those tender spots gives characteristic figures
(photo’s N°. 1 and N°. 2) in which they appear as joined together

( 254 )

in regular bands, ressembling to the schemata of the root-imnerya-
tion of the skin given by Prof. BoLx (photo’s N°. 3 and N®. 4).

It seems difficult to explain the pathogeny of these hyperalgetic
bands, but the nexus between their anatomical localisation and the
distribution of the root-innervation of the skin seems very probable.

Geology. — “The so called opake minerals in transmitted light”.
By Prof. J. L. C. ScHROEDER VAN DER KOLK.

(Read June 30, 1900.)

Among the outward characteristics of minerals, colour, as we
know, occupies a principal place. With many minerals, more espe-
cially with the sulphides, the colour is so dark, that it often seems
to be black. It is the powder however, which in many cases is the
true indicator of colour. This powder is obtained generally in small
but sufficient quantity by rubbing the mineral on an unpolished
porcelain surface (the streak). Not a few apparent black minerals
produce a coloured streak, but a good many others show one equally
black or at least of as little colour as the mineral itself. Hence it
is that with some dozens of minerals the streak is of little if of
any value. It naturally suggests itself to attribute the absence of
colour in the powder to the too great coarseness of the grains, which
prevents them to become transparent. In fact in a great many cases,
the rubbing down of the powder produces a distinct coleur effect.
It is easily reduced to smaller grains by rubbing out the streak
with a hard object, a piece of quarz or with one of unpolished
porcelain.

The following minerals are striking instances:

Pyrite pale brownish lilac; galena brown, a middle colour between
bister an Indian ink. Clausthalite reddish brown; pentlandite hlac ;
covelline more or less brownish green; stibnite very bright yellowish
brown; chalkopyrite brilliant deep violet; boulangerite reddish brown
and bournonite brown.

It needs hardly be said, that colour cannot be described. Only by
experimenting the thing will become clear. I may recommend here
always to compare the colour with that of a rubbed out graphite-
streak. To facilitate this experiment, I add a list of those minerals,
which are more or less analogical as to the colour. Identity I howe-
ver never met with and even tolerable resemblance of colours in two
different minerals is very rare.

Green are molybdenite and covelline and bornite.

D. H. BEIJERMAN: Curious disturbances of the sensation of pain in a case
of tabes dorsalis.

Proceedings Royal Acad Amsterdam, Vol. III.

( 255 )

Violet are chalkopyrite and pentlandite.

Pale brown, lilac tinged are pyrite, and more or less smaltine,
cobaltine and ilmenite. The colour of the last mentioned mineral ap-
proaches some more reddish brown tetraedrites.

Pale yellowish brown are stibnite and jamesonite, whereas haus-
mannite and manganite in colour approach the following group.

Reddish brown are boulangerite and clausthalite : bournonite is less
red and as to coulour forms a transition from the two last to ste-
phanite, which approaches yellowish black.

Yellowish black are galena (greenish tinge) enargite and chalco-
sine, further berzilianite, argentite and berthierite. Finally anthracite
might be mentioned here.

Pale brownish grey are magnetite and polianite; further stannine
and corynite, although the streak of these last mentioned minerals
is of a rather pure grey colour.

Still purer is the grey of graphite and pyrrhotine.

The above mentioned colours were an immediate result of the
fineness of the particles growing transparent in consequence of that
fineness. Still an other effect is produced by rubbing down the streak
of certain minerals. I will just passingly mention it here, later I
shall treat it more fully.

The effect I mean is most apparent in minerals which contain
copper and best in cuprite. In rubbing out the brownish red streak
the colour grows more and more greenish; at last to dissolve into
a bluish green. However when shutting out the air with a drup of
glycerine, no change of colours takes place. This same final colour
is obtained in azurite and malachite.

I need hardly point out, that all those colours may be a great
help in determining the so called opake minerals.

Mathematics. — On ‘The spacial anharmonic ratio of curves
of order n in the space S, with n dimensions”. By Prof.
P. H. ScHoure.

1. If on the curve vy" in S,, forming the subject of this short
treatise, we take arbitrarily n—i points 4;,(i= 1,2, . . »— 1), we
also determine thereby a space S,—2 containing these points, and we
can assign the points of the curve one by one to the spaces S,—1
through S,2 containing them. This gives rise to a correspond-
ence one by one between the points of the curve and the spaces
S,-1 of the pencil of spaces with the basis S,-2, which proves the

( 256 )

well-known theorem, that the genus of the curve g" is zero, and
that we can just as well speak of the anharmonic ratio of four
points of g” as of that of four points of a right line.

2. This simple consideration proves in general, that an invariable
anharmonic ratio 4 must be found by connecting any space S,—»
through »—1 variable points of the curve by spaces S,—; with each
of four fixed points 4,, 49, 43,44, which of course forms an exten-
sion of the well-known property of the conic g? in the plane, that
the quadruples of lines connecting a variable point P of the curve
with four fixed points of the curve have an anharmonic ratio inde-
pendent of P.

3. With this the generation of og by means of n projectively
related pencils of spaces S,_; is closely connected. Moreover ensues
from it that g” is determined by n+3 points. For, by dividing
n+8 given points into two groups, one of » points and one of three,
we can form by means of the points of the first group nm spaces
S,-2 through »—1 points of the curve and after this determination
of the » bases we can fix with the aid of the three points of the
second group the projective correspondence between the x pencils of
spaces S,_).

4. As is known the conic g? in the plane can be considered
as the locus of the points P which connected with four fixed points
A, Ay, Az, Ay produce quadruples of lines of a definite anharmonic
ratio 4, so that we can speak of the conic through Aj, Ay, As, A,
containing the anharmonic ratio 4; by varying 4 appears the pencil
of conics filling the plane; of this pencil the points A, Ag, 3,44 form
the base. In like manner, if of a curve gy” we give not n+ but
n+2 points Aj, 4o,... Anyo, we find instead of a single og" an n—1
fold infinite system of curves gy”, filling S,. And now arises the
question whether it is not possible to indicate individually the curves
of this n—1 fold infinite system by means of n—z anharmonic ratios.
This question must be answered in the affirmative. For, we have
seen that on a given g” four given points represent a determined
anharmonic ratio, and now out of the +2 given points are to be
formed by completing the triple 4, Ag ds with each of the remaining
A; to a quadruple A, dy Az Aj, (j=4,5,...n+2), exactly n—d
mutually independent anharmonic ratios 4;= (A, 4, A, Aj). From
this follows for the present nothing but this that to a given curve
¢” through the n+ 2 given points belongs a definite set of anharmonic

( 257 )

ratios 2;, whilst on the other hand the possibility is not excluded
that inversely to a given set of anharmonic ratios 4; belongs more
than one curve g” passing through +2 given points. It is however
easily proved that all those curves g” belonging to a given set of
anharmonic ratios — supposing there be more than one — are pro-
Jected from A,,2 by the same conical space of order n—1. For if
we project the figure considered, from the point 4,42 upon the space
S,1 determined by A,,A3,---Anyi, the curves g" through
Aj, Ao,» Ang With the anharmonic ratios 4, A5,..-An+2 In Sn are
transformed into the curves g?—! through A’), Ag,...An41 With the
anharmonic ratios A4,A5,...4an+1 in S,-1. And by repeating this
reduction, passing from the applied space S,-; to the space S,_»
determined by A,, 43,... 4, ete. till we arrive at the plane of pro-
jection A, A; Ay where the original point A, may finally arrive in
A";, two curves y” which pass through the n+2 given points, belong
to the anharmonic ratios A4,2;,...4n+2 and are projected from Ante
by different conical spaces of order x—1, will finally be transformed
into two different conics through A"), A9, As, 4y, to which belongs
the same anharmonic ratio 44. This being impossible the different
curves @" through the x-+ 2 given points which might belong to
the given set of anharmonic ratios 24, 25,...An¢2 , must be projected
from 4,+2 by meaus of the same conical space. And what is true
for the point A,+2 is applicable to all the remaining given points. So
all curves yg which may belong to a given set of anharmonic ratios
Ag, As) ++ Ante , being projected from all points 4;, (= 7, 2,...-+ 2),
by the same conical spaces, must coincide. So in general we find:
“We can determine in S, a curve g” passing through any n+2
points A;, ((=1, 2,...n+2), by indicating the n—7 anharmonic ratios

Aj =(A) Ag A3 Aj), (G=4,5,...2+2). And these anharmonic ratios

assuming all possible values, the determined curve g” generates the

n—1 fold infinite linear system with the base A;, A9,...n+42, filling

the space S,, which system is of course projectively related to the

likewise n—7 fold infinite linear system of the anharmonic ratios

Ay, 45,-.-4An¢2, or in other words to the linear system of points in a

space S,_, of which the coordinates are given by means of these

systems of values.”

The preceding proof wants some completion. We might ask, a. 0.
with a view to the structure of the anharmonic ratios, where on one
side Aj, Ay, A; and on the other side 44, 4;,...4,42 play different
parts, whether we are allowed to extend to all points 4; what has
been found true for A,+2, Yet leaving alone whether it be necessary
to know that all points 4; behave in this respect alike, it is easy to

( 258 )

see at once, that the difference between the points of the two groups
is in this respect but an apparent one. For by giving the n—1
anharmonic ratios (A, A, A; Aj), (j =4,5,...n+2), all anharmonic
ratios of quadruples of points 4; are determined. For, if on aright
line 7, corresponding point by point to g”, we assume arbitrarily the
points belonging to A,, A», As, the given anharmonic ratios determine
the points belonging to Ay, 4;,.-.An+42; so on / the x corresponding
points and thus all the anharmonic ratios are known.

5. Probably it is recommendable to call the complex of the
(n+2) (n+1)n (n—1)
i = Bigren eee

independent ones out of them, simply a spacial anharmonic ratio
and to represent it by the symbol A(,—1). We can then say, that
the n—i fold infinite linear system of curves g" with n+2 points
A; as base is projectively related to that spacial anharmonic ratio,
in so far that a curve of the system corresponds to a definite spacial
anharmonic ratio and reversely. By this the analogy of the obtained
result with the special case n=2 becomes as great as possible.

anharmonic ratios, determined by n—/ mutually

6. The above led us to the following theorem of cyclic inversion,
which we shall first indicate for the special case n=83 of our space.
The net of the skew cubics g? is then given by its five base points.
If we put

(A,A4344) = Aq, (42434445) =, (A434,4541) = Ay
(A,A;A) Ap) — As (A;A) Ao As) — AS

| where (PQRS) always stands for
Ler PS
QR” Qs’

then the question rises by which recurrent relation the five quan-
tities Aj, (i=0, 1, 2,8,4), are connected. By direct reckoning we find

are }

1
ey Am (Am+i—1)

where m,m+1,m+2 are to be replaced by their remainders after
division by five; and really by repeated substitution we arrive at
Am+5==4m. Of course in the general case of an arbitrary x a result
will be obtained of the form ig

( 259 )
7 Oc =i (An, Ames tae Am4n—2) .

However, the definition of the form of the function f we leave to
others.

7. We shall point out a few particularities which already appear
when we restrict ourselves to space with three dimensions.

In the following way the net of the skew cubics g* through five
points is deduced from considerations on conics and cones.

If A, B,C, D, E are five points given arbitrarily in space, the locus
of the vertices ZY of the cones 7(A,B,C,D,E) through these points,
on which the edges 7(A, B,C, D) represent a definite anharmonic
ratio A, is the cone £,(A,B,C,D) through A,B,C,D with vertex £,
on which the edges passing through A, B, C, D determine the anhar-
monic ratio 4. And if A assumes all possible values this cone
generates the pencil with HA, EB, EC, ED as base edges, filling the
space.

For, if P is an arbitrary point of £, (A, B, C, D), then according
to definition

P(AE, BE, CE, DE) =}

and this is identical with
E(AP, BP, CP DP) =A.

If A,B,C, D,E are again five points given arbitrarily in space,
the locus of the vertices T of the cones 7(A,B,C,D,E) through these
points, on which T (A, B, C, DP) and T (A, B, C, £) represent respectively
the anharmonic ratios 4 and w, is the skew cubic Ot. through

A, B,C, D, E, forming with the line DE the complete intersection of
the cones £,(A, B,C, D) and D,(A, B,C, #). And if A and “ assume
all possible values, this curve generates the net with the base
A,B,C,D),E; this net filling the space is projectively related to the
points (A, «) of a point-field.

The anharmonic ratios 7(4,B,C,D) and 7T(4, B,C, £) on the
cone 7(A,B,C,D,E) being identical with the anharmonic ratios
(A, B, C, D) and (4, B,C, Z) on the curve Gas this result is nothing

more but at the same time nothing less than the special case n=8 of
the general result obtained before. Aud from this we could have gone
on to the case n= 4 in order to prove the anticipated general result
by the conclusion from n to »-+ 1. It occurred to us however that
the deduction given above of the general result is shorter and clearer.

( 260 )
8. By assuming between 2 and v the bilinear relation
paw+qih+ru+s=0

we form a projective correspondence between the cones £,(A,B,C,D)
and D,(A, 8, C,£). So we find.

“The locus of the curves g? , for which 4 and y satisfy a given
bilinear relation, is a surface F* of order four, on which the two
triples of lines DA, DB,DC and EA, EB, EC are simple lines, the
points A,B,C are double points and DZ is a double line. All these
different surfaces F#* form a threefold infinite linear system, pro-
jectively related to the Jmear system of the rectangular hyperbolae,
represented by the equation of correspondence, if 4 and ¢ indicate
the rectangular coordinates of a point in the plane.”

“Tf in particular p=0, then Ao and “=o correspond to -
each other and likewise the pairs of planes E (AD, BC) and
D(AE, BC). Then the surface F4, passing through BC, breaks
up into the plane ADE and a surface f°, i.e. the lecus of the
curves ¢? is then an /’* through the edges of the tetrahedron
BCDE. A\l these surfaces pass through A and have B,C, D,£
as double points; so they form a net of course projectively related
to the net of the right lines gA tra +ts=0.”

“Tf at the same time g = 0, we then find A = »nandru+s=0,
so that F* breaks up into the pair of planes Z(AD, BC) and acone
D, (4, B, C, £). By the addition of g=0O a new plane i.e. BCE
has separated from /'*.”

“The linear system of the surface #4 contains a net of surfaces
F? and two pencils of cones.”

Also analytically we can easily find that the surfaces #* having
DE as double line, A,B,C as double points and passing through
the triples of lines D(A, B,C), E(A,B,C) form an at least threefold
infinite series. Firstly we learn out of the equation.

2 po (2, y) + 2 ty (es 9) +070 (ey) +283 (ey) + #5 (2, 9) + Say =O

of a surface /,(e,y,2,t)=0 of order four with the right line
«= 0, y=0 as double line, that of the 35 coefficients of the com-
plete equation only

in

ie ee ee eee eee em NE

or 22 are extant, so that the compound condition of having D# as
a double line is equivalent to 13 simple ones. ‘The condition of ©

( 261 )

having A,B,C as double points and that of passing through six
given lines count respectively for 12 and at most for 6 simple ones,
30 that at least 3 remain at our disposal. Only if each surface F‘
with DE as a double line and A, B,C as double points, which is
brought through five of the six lines, contained by that already also
the sixth — a peculiarity which appears as will be seen in the following
series of surfaces — the number of conditions to be disposed of could
become greater than 3; so this peculiarity does not appear here.

It is also easy to see that the surfaces #% through A with the
double points B,C, D,E£ form a twofold infinite series. For, the
surfaces f;(x,¥,2,1) = 0 with the vertices of the tetrahedron of
coordinates as double points form a linear system

ayzt+bzta+ctry=dryz=0),
etc.

9. If we assume in space six given points A,B, C, ), 2, F, we
arrive in the following way at a generation of skew biquadraties :
“The locus of the common vertices 7 of the cones 7(A, B, C, D, E)
and 7(A, B, C, D, F), on which the four edges 7(A, B, C, D) deter-
mine respectively the anharmonic ratios 4 and w, is the skew bi-
quadratic Gh. through A,B, C, D forming the complete intersection
of the cones £,(A,B,C,D) and F,(A, B,C, D); of this curve EF
and / are two of the four vertices of cones containing it. And
if 4 and « assume all possible values this g* generates the net
with the base A,B, C,D and the vertices £,F; this net filling
the space is a. 0. projectively related to the point-field (A, «).”
“The locus of the curves gf, for which 4 and w satisfy a
given bilinear relation, is a surface #* of order four, having the
points 4, B,C,D,£,F as double points and containing the quadru-
ples of lines £(A,B,C,D) and F(A,B,C,D). All these surfaces

F* form again a threefold infinite linear system, projectively

related to the linear system of the rectangular hyperbolae repre-

sented by the equation of correspondence.”

Some difficulty arises regarding the proof, that the surfaces /
found here really represent a threefold infinite series. For, the con-
dition first of having six double points and secondly of passing
through eight lines connecting four of these points with the remain-
ing two is equivalent to 24 and apparently to 8 simple conditions
more; from which would ensue, that only two simple conditions
remain at our disposal. This difficulty can be removed only by the
supposition, that each surface 7"* with the double points 4, 2,0, D,E, F

ls
Proceedings Royal Acad. Amsterdam, Vol. ILL, :

( 262 )

passing through seven of the eight lines (2, /) (4, B, C, D) also
contains the eighth. In reality the surface of the series degenerated
into four planes show that the series is threefold infinite. For of
the nine degenerated surfaces

I Il III IV Vv VI Vit. Wilt. oa

EAB||EAB||EAB||BAC||EAC|(EAC||EAD||EAD||EAD
| | | Beco

ECD pon||en||a2D\ ame) 3| Rel mel eee

| FAD

|
FAB||FAC||FAD||FAB||FAC||FAD||FAB||FAC
|

|
1"

rac||rop| rep FRE

FCD LpB ID) | BBC aD

|
the individuals of each of the triples (I, II, III), (IV, V, VI),
(VII, VIII, TX), d, TV, VID, Gl, V;. VElD, GI, Vi, EXO itegs
to a same pencil, as is shown by the identity

(e—y) (et) + @@—2) (ty) + et) 2) = 0.

So I, II, IV, V are four degenerations no three out of which belong
to a pencil. Moreover the fourth not belonging to the net deter-
mined by the others — for I, II, IV contain AB and CD and
these lines do not lie on V — they form a linear system of three- .
fold infinity.

10. For seven points A, B, C, D, E, F, @ given arbitrarily in space
we have farthermore:

“Four vertices T are to be found for which the common edges
T(A, B, C, D) determine respectively on the three cones 7(4,B,€,D,E),
T(A, B,C, D, F), T(A, B,C, D, G) the anharmonic ratios J, u,v.
These four points form with A,B,C.D the eight points of inter-
section of the three cones E,(A,B,C,D), F.(A,B,C,D), G,(A,B,C,D).
And if 4,2, assume all possible values, this quadruple of points
generates a biquadratic involution of quadruples of points filling
the space and projectively related to the points (A, 4, v) of space.’
According to the general character of the involution a quadruple

of points P,Q,R,S is determined by one of its points; if P is
given the cones F(A, B,C, D,P), F(A, B, C,D, P), G(A, B, C, D, P)
are determined and likewise the three other new points of inter-
section. In fact, we have not to deal with a// quadruples of points
completing A,B,C, D to eight associated points, in which case we
might arbitrarily assume seven out of the eight points, but only with
those octuples A, B, C, D, P, Q, R,S, for which £, /’,G are three ver-

( 263 )

tices of quadratic cones containing them. Of course a great number
of problems appear immediately. We can ask what Q,h,S ge-
nerate together when P describes a right line or a plane, what the
locus is of the quadruple of points under the condition that one of
six connecting lines passes through a given point or intersects a
given line, ete. In order not to be too prolix we shall discuss but
two other loci.
Of these the first is connected with the trilinear equation

khevtluv+myvyAtndhutpitqutryv+s=0

between A, u,v. We find:
“The locus of the quadruples of points of intersection of the
three cones 2, (A, B, C, D), F,, (A, B, C, D), G, (A, B, C, D), for which
1,4, satisfy a given trilinear equation, is a surface of order
six with A, B,C, D as threefold points, 2, /,@ as double points
and the three quadruples of lines obtained by connecting each of
three points E£,/,G@ with the four points A, B,C, D as simple
lines. All those surfaces /° form a sevenfold infinite linear system,
projectively related to the in like way sevenfold infinite system
of cubic surfaces represented by the equation of correspondence.”
Here is again immediately shown, that the found surfaces /* form
an at least sevenfold infinite series. For of the 83 simple conditions
determining an £® the four threefold points take 40, the three double
points 12 and the 12 right lines at most 24, so that at least 7
remain at our disposal. The system of the surfaces F° being really
sevenfold infinite, from this ensues reversely that the determining
quantities — threefold points, double points and simple lines —
represent mutually independent data.

Secondly we look for the locus of the quadruples of points of
intersection, for which A, “,v are equal to one another. We find:

“The locus of the quadruples of points of intersection of the
three cones E, (A, B, C, D), F, (A, B, C, D), G, (A, B, C, D), for which
4,“#,v are equal to one another, is a skew sextic not passing
through 4A, B, C, D, E, F, G.”

According to the above the locus of the intersection gf, of

E,(A,B,C,D) and F,(A,B,C,D), for which A=vy, is a surface
F* passing through the two quadruples of lines E(4, B, C,D) and
F(A, B,C, D) with the double points A, B, C, D, E, F, which passes —
the values 0, 1, « of A corresponding to equal values of « —
likewise through the edges of the tetrahedron ABCD. .
In like manner the locus of the intersection of E, (A.B, C, D) and
18*

( 264 )

G,(A, B,C,D), for which A=y, is an #’* with the double points
A, B,C, D, E,G@ passing through the quadruples of lines £(A,B,C,D)
and G(A,B,C,D) and the edges of the tetrahedron ABCD. Of the
total intersection ¢!® of these surfaces, having A, B,C, D, Z as four-
fold points, the ten right lines connecting the points A, B,C, D,
two by two, separate; so has been proved what was asserted.

Botanics. — “Preservatives on the stigma against the Germination
of Foreign Pollen.’ By Dr. W. Burck. (Communicated by
Professor Hugo DE VRIES.)

It is well known that the pollen of many plants gets destroyed
as soon as it comes into contact with water. The both coats (exine
and intine) are then seen to burst, while the contents stream out
vigorously !).

Further it is known that frequently pollen is successfully brought
into germination in sugar solutions at different degrees of concentra-
tion, or also in gelatin, agar-agar, gum, dextrine etc., or in mixtures
of these substances with sugar *).

For number of pollen species, however, there has not yet been
found, hitherto, a solution in which germination was observed (many
Compositae, Umbelliferae, Urticaceae, Malvaceae, Ericaceae, and
many others).

The idea that chemical substances occurring in the moisture of
the stigma would here play a part, has been frequently expressed,
among others by Mouiscn®), in 1892, who inferred it from the fact

1) On the relation of pollen to water compare, among others, bener Lrprorss,
Zur Biologie des Pollens. Pringsheim’s Jahrbiicher Bd. XXIX, 1896, pag. 1—39.

HanscirG, Beitriige zur Biologie und Morphologie des Pollens. Sitzungsber. der
kK. Bohm. Gesellsch. 1897, XXIII.

Bruner Liprorss, Weitere Beitriige zur Biologie des Pollens. Pringsheim’s Jahrb.
Bd. XXXIII, 1899.

2) See, among others, van TmGuem, Recherches physiologiques sur la végétation
libre du pollen et de Vovule. Annales des sc. nat. Bot. 5e série, tom, XII, 1872.

L. Kwyy, Sitzungsber. d. botanischen Vereines d. Proving Brandenburg XXIII, 1881.
Ki. Srraspurcer, Neuere Untersuchungen iiber den Befruchtungs-Vorgang bei den
Phanerogamen etc. Jena 1884.

E, Srraspurcer, Ueber fremdartige Bestiiubung. Pringsheim’s Jahrb. fiir w. Botanik
Bd. XVIII, 1886.

Ii. Moriscn, Zur Physiologie des Pollens, mit besonderer Riicksicht auf die chemo-
tropischen Bewegungen der Pollenschliuche. Sitzungsber. der math. naturw. Classe der
K. Akademie der Wissensch. Wien Bd. CII, Abth. [, 1893.

3) Mouiscu, l.c. pag. 429,
) ; pag

( 265 5

that the pollen of Azalea, which could not be brought into germina-
tion in water, formed beautiful pollen-tubes when, together with
the pollen, a stigma of Aza/ea was introduced into the drop of water,

To me, also, it has seemed probable, for years already, that pollen,
which did not germinate in water or sugar solutions, wanted a
special chemical stimulus to call forth the process of germination,
and that in the either or not being present of such a chemical
substance in the liquid of the stigma, in some cases the explanation
might be found of the striking fact, that often the pollen cannot
germinate on the stigma of a plant, which stands in close relation-
ship to the plant producing the pollen, while it germinates very
well on the stigma of a plant belonging to a systematically distant
family ').

Already in 1889 I thought this might be inferred from the facts
following. The pollen of Mussaenda rufinervis, M. frondosa, M.
Teijsmanniana, M. Afzelii, M. Reinwardtiana and M. cylindrocarpa,
belong’ to those species of pollen which resist the action of water and
are not prejudiced by it, but which do not, however, pass into
germination in it.

When now this pollen is introduced into a drop of destilled water,
in which is at the same time put a stigma of the plant, nearly all
the pollen-grains will begin, within the space of two hours, to form
tubes, which rather quickly attain a considerable length.

It is not necessary therefore to use the whole of the stigma; the
germination sets in as well if only a half, a fourth, or an eighth
part is put in the drop of water, and I even saw distinct germina-
tion on addition of !/;, part of the stigma.

The same experiment to make pollen germinate in the thus diluted
stigma-liquid of the same plant, succeeded for many species of
Pavetta and further for Pentas carnea, Eviostemma floribunda, four
species of Begonia, for Uvaria purpurea, U. hirsuta, Torenia Four-
nieri, and for Murraija exotica, plants belonging to the Rubiaceae,
Begoniaceae, Anonaceae, Scrophulariaceae and Rutaceae.

With a great many other plants, however, the experiment did
not succeed.

Furthermore I had found that for Mussaenda it did not matter
whether the stigma of the same species was used, or that of another
species of the genus.

1) Srraspurcer, Ueber fremdartige Bestiubung le.

( 266 )

The pollen of MW. rufinervis germinates as well in the dilute liquid
of M. frondosa and M. cylindrocarpa as in that of its own species,
and pollen of M. frondosa could also be brought into germination
in the stigma-liquid of M. rufinervis and M. cylindrocarpa, whilst
the pollen of M. cylindrocarpa, M. Reinwardtiana and M. Teijs-
manniana, germinated besides in the stigma-liquid of M. rufinervis.

For the different species of Pavetta this was otherwise.

I succeeded indeed in causing the pollen of Pavetta javanica to
germinate in destilled water in the presence of a stigma of P.
javanica and P. fulgens, but not in the dilute stigma-liquid of P.
longipes, P. grandiflora, P. coriacea and P. pauciflora.

The pollen of Pavetta grandiflora germinated only in presence
of a stigma of its own species and of P. fulgens, but not with a
stigma of P. javanica, P. longipes, P. coriacea and P. pauciflora.

That of Pavetta coriacea could not be brought into germination
at all in this way, not even when using the stigma of P. coriacea
itself.

It was also proved that the pollen of Mussaenda cylindrocarpa
did not germinate in the dilute stigma-liquid of Pavetta grandiflora
and the pollen of Mussaenda rufinervis not in that of Gardenia
curvata, etc. All this points to the presence in the fluid of the stigma
of ‘substances which possess the power to bring about the process
of germination, and gives also cause to suppose that for distinet
genera and also for distinct species of the same genus, those sub-
stances may be distinct too. Since I occupied myself with this in-
vestigation, the pollen has repeatedly been the object of interesting
researches, as well with regard to its relation to water (KERNER
Liprorss, Hanscira), and to the negative aerotropism, which may
be observed in pollen-tubes (Moniscu), as to the chemotropical
action exerted by the stigma and by special chemical compounds
on tlie pollen-tubes.

It is not impossible that sometimes the same substances which
exert a chemotropical influence on the once formed pollen-tube, also
possess the faculty to excite the iatent germinal power of the pollen-
grains, but certain it is not; in any case, it has not yet been
proved to be so.

If a stigma of Narcissus Tazetta is passed into a drop of sugar-
gelatin solution, together with some pollen of this plant, then, as
Mouischt has pointed out, the tubes formed are attracted by the
stigma and also by the section-face of the style, but the germination
of the pollen itself is not influenced by the stigma; the process of
germination is accomplished also without a stigma, if only the

(26%)

Narcissus-pollen is introduced into the 7 pCt. sugar solution re-
ferred to }).

The influence of the stigma is first felt when the tubes are
formed, and after all appearance the curving towards the stigma,
in this case at least, reposes on a growth towards the nutrient
source (trophotropism) of a_pollen-tube, formed from the reserve-
substances of the pollen-grain.

The last research of Liprorss®) proved that the stigma can in
this experiment be replaced by organs of foreign plants, for instance
by bits of Al/iwm-root, which made him suppose that a substance,
largely spread in the vegetable kingdom, was here concerned. Frag-
ments of diastase act in the same way and, as was nearer indicated,
it is not the diastase as such, the starch-converting principle, but
the albumen occurring in the preparations, from which goes out the
chemotropical influence.

So, these things should not be confounded; the chemical sub-
stances possessing the faculty to call forth the process of germi-
nation are not, — at least not here — the same that occasion a
chemotropica] curvation of a once formed pollen-tube.

An investigation of chemotropical curvations under the influence
of a stigma was not in my way. Nor was the way in which the
germination experiments were performed, — namely in a medium
in which the soluble constituents easily diffunded from the stigma-
moisture, adapted to observations in this direction.

My object was exclusively to examine in how far pollen, not
passing into germination in water or in sugar solutions, required a
special chemical substance to call forth the germination. For I put
myself the question whether STRASBURGER’s opinion that on the
stigma no preservatives were present to prevent the germination of
foreign pollen, was not taken in too general a sense?

After the said preliminary experiments had pointed out the
presence in the stigma-fluid of special chemical compositions, under
whose influence the germination was brought about, I tried to find
a substance able to exert on the pollen of these different plants,
the same influence as the stigma-fluid.

This research has led to the following results:

It lay at hand first of all to think of some organie acid, not
only because the stigmas react feebly acidly, but in particular on

') Mouiscw 1. c. p. 427.
*) Bot. Centralbl, No. 11, 1900, p. 373.

( 268 j

account of the well-known influence of organic salts and acids on
the spermatozoids of ferns and of Selaginella ‘).

All my efforts, however, to find a solution of tartaric acid, oxalic
acid, or malic acid, able to make the pollen of Mussaenda rufinervis
germinate, remained unsuccessful *).

Since it is become known that Mo.iscu, led by the same course
of thought, tried in 1892, by means of organic acids and salts, to
call forth the development of tubes in pollen of some Compositae,
Umbelliferae, Urticaceae, Malvaceae and Ericaceae, which could no;
be caused to germinate in water, gelatin, sugar, glycerine, or gum,
and that he indeed succeeded in so far as regards that of Azalec
indica, Rhododendron ponticum, and R. arboreum. In solutions o*
1—0,05 calcium malate and of 0.01 pCt. malice acid, germination
was observed °).

The other pollen species were quite insensible to these stimuli.

As little as the pollen of Mussaenda, that of different species of
Pavetta, Begonia and Pentas carnea, was to be brought into germi-
nation in acids or salts.

From the acids I turned to the sugars and allied substances and
then it became evident that it was impossible to cause the Mussaenda-
pollen to germinate in solution of saccharose, whichsoever degree of
concentration this solution might have. I used solutions of 0.05 pCt.
mounting to 40 pCt.

No more were Mannite and Dextrose able to cause germination.
Experiments with Asparagine and Dextrine, too, led to no results.

When, however, the slightest trace of levulose was added to the
water, the process of germination set in within the time of two hours
and soon the tubes proved as long and as beautiful as at the germi-
nation in dilute stigma-liquid.

Here it was perfectly indifferent whether Jevulose was added
to the destilled water, or to the solutions of the said sugars in dif-
ferent degrees of concentration, or to a solution of gelatin. Levulose
proved thus to exert the same influence on the pollen-grains as
the stigma.

That the chemical substance which diffunds from the stigma-liquid
in the drop of water should contain /evulose, is, of course, not ascer-
tained hereby; other substances also occurring in the stigma-liquid

) Prerrer, |.ocomotorische Richtungsbewegungen durch chemische Reize. Unters,
aus ce bot. lustitut zu Tibingen Bd. I, Heft 3.

*) The experiments were performed with solutions of 0.2 pCt. to 0.0025 pCt.
8) Moriscu, |. ¢. p. 429.

(260)

might exert the same influence on the pollen-grains of Mussaenda.
Presently it will become evident, at the mentioning of a related
experiment, that it is necessary to be cautious with such an identification.

The research showed further that the pollen of other species of
Mussaenda behaved towards sugar solutions just in the same way
as that of M. rufinervis; from the facility with which the pollen
of these species germinated in each other’s dilute stigma-liquid, this
might be expected.

The pollen of Begonia corresponds, regarding its relation to sugar
solutions, in many respects with that of Mussaenda, but in this genus
important deviations occur with regard to the behaviour of the pollen
to water.

That of Begonia gorgocensis namely, germinates already in destilled
water, while that of B. Deppii, B. semperflorens and B. imperialis
does not try to form tubes in water. Of all four examined species
the pollen germinates, however, easily in the presence of a stigma
in the drop of water. But here I should observe that it is not
beforehand to be said with certainty whether newly collected pollen
of Begonia gorgocensis will come into germination in destilled water
or not.

Repeatedly in the germination experiments the phenomenon occur-
red that the pollen of this Begonia, having one day formed tubes
in the drop of water, the next day did not manifest a trace of
tube-development, although it was taken from the same plant.

This is a particularity which I later found not to be rare in other
species of pollen neither.

All botanists who have occupied themselves with the germination
of pollen, have likewise experienced that its relation to water is not
always the same by far.

A slight difference in the humidity of the surrounding air can
be the cause, not only that pollen which, under normal circumstances
is resistent to the influence of water, when brought into contact
with it bursts immediately, but also that pollen, which germinates
in destilled water, cannot be brought into germination at a deviating
humidity of the air. Elaborate informations thereabout have of
Jate been given by Benor Liprorss in Prinesnem’s Jahrbiicher,
Bd. XXXIII, Heft 2, 1899, Cap. I en II. This is the reason that
never any experiment can be performed concerning the germination

of this pollen in any liquid without having first examined, — by
control experiments, by preference with the pollen from the same
anther, — whether it passes into germination in destilled water,

either or not. If this precaution is neglected there is great risk to

( 270 )

draw a wrong conclusion from the germination experiments. The
pollen of this Begonia, for instance, I have repeatedly seen germin-
ating in solutions of saccharose, dextrose and mannite of different
degrees of concentration, but as often the same experiment did not
succeed. Now one might be inclined herefrom to conclude, that in
this species of pollen germination can be stirred by the said sugars;
but this is by no means the case: to the solutions mentioned this
pollen is perfectly indifferent. The divergent results are explained
in this way, that the said pollen at one time germinates in water,
at another time not. If it does not germinate in water the process
cannot be called forth by saccharose, dextrose, mannite or asparagine,
if it does, this also takes place in solutions of these substances, and
so, this is to be taken in such a sense that saecharose, dextrose
and mannite have not the power of preventing the germination.

In presence of a stigma of the own plant it invariably germinates
and likewise if the liquid contains a trace of levulose, indifferently
whether the levulose is added to the destilled water, or to a solution
of saccharose, dextrose, mannite or asparagine.

The three other species of Begonia, B. semperflorens, B. Deppii
and B. imperialis, behave towards water, dilute stigma-liquid, and
kinds of sugar, in the same way as the pollen of Mussaenda, i.e.
do not germinate in water, but only in dilute stigma-liquid and
in liquids containing levulose.

Now it is certainly striking that levulose acts quite differently
on the pollen of the Pavettas. Of some of these, namely of P.
macrothyrsa and P. Reginae, the pollen germinates already in
destilled water; that of P. javanica, P. fulgens, P. longipes, P.
pauciflora, P. grandiflora, and others, only in presence of a stigma.

For all these Pavetta-species however, the presence of levulose is
an obstacle to the development of the pollen-tube. Of not a single
specics I have been able to make the pollen germinate in levulose,
and what in particular deserves attention, is that of most Pavettas
the germination is not only prevented, but that the pollen bursts
and allows its contents to stream out when brought into contact
with a liquid containing levulose.

What has just now been communicated about the relation of the
pollen of Begonia gorgocensis to water, holds also good for that of
Pavetta macrothyrsa.

Now it forms beautiful tubes in this liquid, then again no trace
of germination is to be detected. In the latter case the process of
germination is not to be called forth by saccharose or dextrose,
whilst, if it does germinate in water, addition of these sugars docs

(aid \)

impede the process. If now to the liquid a trace of levulose is added,
whether this liquid consists in destilled water or in a solution of
sugar, the coats burst and the contents spread in the liquid.

I have not succeeded in finding a chemical compound able to
call forth germination in Pavetta. What bas been told above about
the different behaviour of this pollen towards the stigma-liquid of
the plant itself and towards that of other species, makes it appear
probable that in distinct species there are also distinct substances
present in the stigma-liquid. Which substances however these are,
I have not as yet been able to detect.

The pollen of Murraya exotica (belonging to the Rutaceae) cor-
responds in its relation to levulose completely with that of many
Pavettas. Put in water, the pollen-grains show a commencement
of germination. As a rule the tubes attain no greater length than
of 1—2 times the diameter of the pollen-grains. In dilute stigma-
liquid or in a solution of saccharose, mannite or dextrose, the
growth of the tubes is not furthered. In this solution the pollen
behaves as in water.

On addition of levulose, however, whether to the water, or to
the sugar solutions, the grains burst and there is no question of
formation of tubes.

What has been said here about the prejudicial action of levulose
on the pollen of Murraya exotica, has induced me to examine
whether this pollen might be caused to germinate in the dilute
stigma-liquid of Mussaenda. If the pollen of Murraya would burst
in a liquid wherein a stigma of Mussaenda is laid, then the suppo-
sition that the chemical compound which in the stigma-liquid of
Mussaenda causes germination, is levulose, would have acquired a
high degree of probability.

It has now become evident to me that this is not the case; the
poilen of Murraya does not die in the dilute stigma-liquid of
Mussaenda rufincrvis; it germinates in it in the same way as in water.

The possibility is not excluded that still we have to do here
with levulose, but that this compound, diffunding from the stigma-
liquid produces a too weak solution to act prejudicially on the pollen
of Murraya; but how this may be, the said experiment shows that
the substance able to cause germination in the stigma-liquid of
Mussaenda, cannot, as yet, be identified with levulose.

The fact that the pollen of some Pavettas is greatly prejudiced
by levulose, while that of other Pavettas and of Murraya exotica
is even destroyed by the presence of that substance in the germin-

( 972 j

ation liquid, has induced me, also for a few other plants, to examine
how their pollen behaves towards levulose, of which research the
results follow here:

The pollen of Zpemoea imperialis, Calonyction speciosum (Ipomoea
bona nox), and of some other cultivated species of Canna, belong
to those species of pollen which are not proof against water.

The grains burst immediately after they have come into contact
with water and the same takes place in dilute solutions of sac-
charose. Only at a concentration of 20 pCt. no rupture of the pollen-
coats occurs; it remains intact, but does not pass into germination.

If now, however, to such a solution a trace of levulose is added,
the grains burst just as in water.

The pollen of a species of Acanthacea: Justicia (Tyloglossa)
cultivated at Batavia and Buitenzorg, is perfectly proof against water
and sugar solutions. It can remain in it for a long time without
any change being observed and without passing into germination.

A slight quantity of levulose, however added to the destilled
water, or to the saccharose solution, causes the pollen to burst.

Of Antirrhinum spec. |Maurandia antirrhinifolia Hort. Bog.|
the pollen germinates in water; a solution of saccharose does not
impede the germination, so long as the degree of concentration does
not exceed 5 pCt. Addition of levulose prevents the germination, the
pollen-grains, however, do not burst.

The pollen of Pentas carnea, of which the germination in water
is doubtful (like that of Begonia yorgocensis and Pavetta macro-
thyvsa) germinates, on the contrary, with very fine tubes in presence
of levulose, whilst, lastly, the pollen of Impatiens Sultani and Im-
patiens tatifolia, which germinate in water, are as little prejudiced
by levulose as by saccharose and dextrose.

It will be remembered that StRAsnurGER?!) has come to another
conclusion.

From his observations, that pollen could often come to germina-
tion on stigmas of plants having no systematic affinity to the spe-
eimen which produced the pollen, and that the pollen-tubes of foreign
pollen, could often penetrate through the canal of the style, a little
way into the ovary, SrRasBuRGER thought himself justified in in-
ferring that no preventives occurred on the stigma against the ger-
mination of foreign pollen.

He was therefore of opinion, that when a foreign pollen species
does not germinate on a stigma this should not be considered as a
favorable adaptation, but much more as an accidental phenomenon

') crmasbencer. Ueber fremdartige Bestiubung, Parscsurim’s Jahrb. Bd. XVIL, 1886.

( 273 )

caused by this pollen being exposed on that stigma to prejudicial
influences, or by its not finding there the conditions of nutrition
required for the development of the pollen-tube.

That foreign pollen-tubes get only rarely into the ovary and still
more rarely between the ovules, would further be related to the
circumstance that the noxious influences to which they are exposed
in the extraordinary surrounding accumulate more and more, and
so the conditions become still more unfavorabie.

Protecting contrivances against foreign pollen would in consequence
not exist, and it was STRASBURGER’s opinion that they were super-
fluous because the investigation had taught him, that the normal
development of the plant’s own pollen was not prevented by the
presence of foreign pollen.

The tubes of the own pollen grew unhindered among the foreign
tubes and arrived to normal function.

It seems to me that SrTRASBURGER’s observations are not sufficient
to prove that no protecting contrivances are found against foreign pollen.

Opposite to the fact that pollen of the most distinct botanic origin
can come into germination on a determined stigma, is the fact that
still a great many other species of pollen cannot be stimulated into
the formation of pollen-tubes on it at all, and this holds good ever
for pollen of plants which stand in close, even in the very closest
affinity to the stigma-bearing specimen.

This latter fact, as it will appear to me, points as clearly to the
existence of protective means, as the reverse points to the opposite.

Besides, when the tube of foreign pollen together with the own
pollen, penetrates a little way into the style-canal, but then ceases
growing, while that of the plant’s own pollen goes on and reaches
the ovule, this is not necessarily the consequence of an accumulation
of unfavorable influences.

It is not impossible, and even not improbable, that the further
growth of the pollen-tube and the penetrating into the micropyle is
bound to special exigencies satisfied only for the plant’s own, or for
allied pollen. Those special exigencies for further growth may be
obtained by adaptation.

I think that from SrRASBURGER’s research no more must be deduced,
than that not always preventive means are found on the stigma against
fertilisation with foreign pollen. Doubtful it is, moreover, whether it is
really relations of nutrition, which govern the germination on the
stigma and the penetrating of the tubes into the style-canal.

The fact that many species of pollen require a determined degree

( 274 )

of concentration in a sugar solution in order to germinate, and cannot
be brought to the formation of the tube above and below that degree,
peints, as it seems to me, to quite other relations than those of
nutrition, while the fact that number of pollen species form beautiful
and long tubes in destilled water, proves that in any case not all
species of pollen must find on the stigma a nutriment specially fit
for their growth.

There are number of facts which decidedly point out, that for some
plants there exist really preventives on the stigma against fecundation
with a particular kind of pollen. SrrasBuRGER calls them exceptions,
but still they ave so striking as to highly draw the attention.

So it is already known since Darwiy, that the long-styled form of
Linum grandiflorum, a heterostyle-dimorph plant, is absolutely sterile
when fertilised with the illegitimate pollen of the same species, and this
is likewise the case with the illegetimate pollen of both forms of L.
perenne. Nobody doubts but the sterility of these both plants when
fertilised with illegitimate pollen should be considered as an adaptation.

With Linum grandiflorum the pollen-grains donot try at all on
the stigma to form tubes.

With Linum perenne they do, but the pollen-tubes do not reach
the ovary, or at least are not able to fecundate the ovules. Would
it not be allowed to conclude therefrom, that both species have the
means to protect them against illegitimate fecundation, that these
means for Linum grandiflorum are already found on the stigma and
for Linum perenne in the style-canal ?

The pollen of Oncidium flexuosum, O. unicorne, O. pubes and of
some other Orchideac!) is not only unable to fertilise its own flower,
but it has even a poisonous effect on the stigma. Here again the
preventive against self-fertilisation is found on the stigma. In
Corydalis cava, on the other hand, whose own pollen germinates
very well on the stigma, but where the tubes do not reach the
ovules, it is evidently found in the ovary, ete.

If now in these cases there is nothing else to be thought of but
a special contrivance, then it might a priori also be expected that
preventives should be found against fecundation with foreign pollen
in general, and that they should be sought in the first place on the
stigma, and if not found there, in the style-canal and the ovary.
To this view I think to have given some support in the above
communication.

Batavia, May 1900.

1) Darwin, Variation ete, Chapter XVII.

(275 )

Physics. — Communication N°. 59¢ from the Physical Laboratory
by Prof. H. Kamertrncu Onnes: “Contributions to the know-
ledge of VAN DER WAALS’ w-surface. 1. Graphical treatment
of the transverse-plait’.

(Read June 30, 1900.)

1. According to VAN DER Waats’ theory it is possible by means
of a sufficient number of well selected observations with mixtures of
two known normal substances, to determine the constants (a. and bj,
of VAN DER Waats), which allow us to construct the general equation
of state for the mixtures of these substances and especially to predict
the phenomena of condensation by y-surfaces derived from that equa-
tion of state.

KUENEN, who among other things aimed at determining VAN DER
Waats’ constants for mixtures of methyl chloride and carbon dioxide,
has mentioned already in his thesis for the doctorate that calcul-
ations had been made in order to construct the w-surfaces from the
observations for mixtures of these substances.

I have carried out and very nearly completed these calculations
for the temperature at which KurneNn has made his most important
observations, i.e. those on the retrograde condensation.

For each of the values.of the molecular proportion of CQ, in his
mixtures +=0, c=1/,, e=1/,, r=3/,, 2=1 KUENEN gives the
values of the constants Rz, be, /?z, Kr = Tax in the equation of state

Ur ff Kr
Pee T (vo + fz)?

(p= the pressure in atmospheres, » =the volume referred to the
normal-volume, T= absolute temperature).

By means of this I calculated the free energy for mixtures of the
composition 2,

Ue =) pd +k T \s log w +- (1 —2) log (12) ;
to which!) a temperature function linear in 2 can be added 2)) for equal
Pp q

v
') In the drawings we have used for fade: fo dv + 9.4883.
% %

*) vaN DER Waats, Théor, Molc¢e. p. Ne

( 276 )

molecular quantities and then represented them graphically (see PI. IT,
fig. 2); the abscissae represent 100,000 parts of the theoretical
normal volume, and the ordinates give — Wer in atmospheres
\< the theoretical normal volume, so that these lines are projections
on the zy-plane of sections of the yw-surface by planes += 0,
a= "4, x= 1/,, e = 4/4, x= 1. The 2-coordinate is chosen perpendic-
ular to the we-plane as in the case of VAN DER Waats. For the
mixtures «= °/, and x= %/; values of az, bz, /?z, Re were chosen as
nearly as possible in agreement with those given by KUENEN and
w-lines were calculated with these also.

We then derived from these lines the projections on the « w-plane
of the sections of the y-surface by planes »=const., which are
represented in Pl. II, fig. 1 and other auxiliary lines were drawn,
which lines together with their projections on the 2 v-plane, shown
in fig. 3 and 4, will be considered in the following §$.

In this way we succeeded in obtaining by means of the constants
az and bz derived from the observations a representation of the
entire first plait in the case of KUENEN’s experiments.

Originally however I expected to attain more in a graphical man-
ner. For the condensation phenomena can be easily followed in all
their details when the binodal curve and the direction of the tangent-
chords are known (comp. following communication § 5), whereas the
determination both of the binodal curve and the tangent-chords them-
selves from the equation of state by analytical processes is certainly
exceedingly complicated even when it is feasible.

I had hoped that this problem of van DER Waats’ theory could
be graphically solved using as a basis the graphical representation
mentioned and that it would have enabled me to determine numerically
all the phenomena of condensation from the knowledge of a small
number of constants (VAN DER WAALS’ dj and by, if necessary
augmented by some empirical constants of correction) in the way
mentioned in the beginning of this paper for any mixture at any
temperature. But this proved to involve great difficulties.

2. The difficulties which hinder us from obtaining an exact numer-
ical solution, proceed from the fact that VAN DER Waats’ theo-
retical equation of state both as originally given and as modified
empirically by KUENEN according to CLausius, do not give with
sufficient accuracy the real behaviour of the pure substances and
the mixtures.

We tried whether from isothermals, experimentally determined by
Kuenen at higher temperatures combined with Ramsay’s simple

( 277 )

relation for the variation of the pressure with the temperature
p= AT-+ B, the isothermals in the unstable part could be extra-
polated. But this did not lead to a satisfactory result.

Therefore it is absolutely necessary to use an equation of state
in sufficient agreement with the observations, however empirical its
form may be, in order to foretell from other observations on mixtures
of two substances the phenomena of condensation of mixtures of
those same substances under definite circumstances.

In the equation of state used by KuENEN we have allowed for
the fact that a; and ag, are temperature functions as has been also
assumed by VAN DER WAALS for other developments. The identity
used by- KUENEN Ta; = Kz where K;z = Ky, 22 + 2Kj9 2 (1—2) +- Kag
(1—z2)? causes the replacement of a2, which probably is also a
temperature function, by the less variable Aj, but this A,, cannot,
any more than a, be determined with sufficient accuracy from the
observations.

As for the empirical correction by means of Craustus’ ?, we
cannot accept that this would lead us to the calculation of the pres-
sure of the mixtures with a definite composition, volume and tempeta-
ture, at any rate not to the calculation of the pressure in conditions
such as that of the co-existing phases, with an accuracy within the
limits of the errors of observation. For it is only within a limited
range that this empirical correction holds in the case of a simple
substance. Much more is to be expected in this direction from the
rational method for the determination of empirical corrections of
VAN DER WAALS’ a and 3b, followed by RetnGAnuM in his thesis
for the doctorate !).

In order to obtain, regardless of any equation of state, empirically
true representations of observed isothermals, I have tried to represent
these accurately by means of a series within the limits of the errors
of observation. The investigation relating to this, has been progress-
ing, so that I hope to be soon able to give a communication
on this subject. The following however has been worked out in-
dependently of the results obtained thereby.

Even if one has at one’s disposal a sufficiently accurate series or
other empirical representation for one simple normal substance, from
which might be calculated that for a second similar substance 2)
(i.e. belonging to the same class of substances) according to VAN DER
~ Waats’ law of corresponding states by means of two constant relations
(for instance that of the critical pressures aud that of the critical

') M. Rerneanum, Theorie u. Aufstell. einer Zustandsgleichung. Diss. G6ttingen 1899.
*) Kamertrncn Onnus, Verh. Kon. A. vy. W. Amsterdam 1881, p. 11.

19
Proceedings Royal Acad. Amsterdam. Vol. III.

( 278 )

temperatures) even then the question remains how far the homogeneous
mixtures of two similar normal substances satisfy the law of
corresponding states. At present it is doubtful whether this is the case
in the same degree as for simple substances of the same group, as
a mixture is generally not mechanically similar to a simple sub-
stance'). According to VAN DER WAALS’ law however the homo-
geneous mixtures satisfy his Jaw of corresponding states. Therefore
we may call this theory, the theory of the ¢deal mixture. According
to that theory we can calculate the isothermal for each mixture
from that of a simple standard substance by means of 2 constant
relations, e.g. those of the critical temperatures 7Z,; and critical pres-
sures pz, of mixtures of the composition z, provided they are homo-
geneous; or expressed differently: the w-curve can be obtained from
that of the simple substance by linear magnification in two diree-
tions”). As a given w-surface corresponds to a given 7, the W.-
lines appearing on it (given by

we = — [ode + RI |e loge + (12) log (12),
; We Wr p dev FF
Re cr, | aloga + (1 —2) log (1— 2),
Cpz Uk IRE Pe Crk ae Tix L LOG 2 ++ ( r) og ( *)\
¥s= p= a mde + Te Fe log x + (1 — x) log (l — al,
RT fz Cc \

where x and @ are the reduced pressure and the reduced volume,
¥,. the reduced wr and C a constant identical for all substances of
the same group ®%)), can be derived from the w-curves for a simple

similar substance, but they relate to the reduced temperatures
ie

tz = ___ ):
xk

In how far mixtures of normal substances deviate from this ideal
case has not yet been investigated, to solve this problem it will!

1) Comp. ibid. p. 24.

2) Comp. ibid. p. 23.

3) Comp. ibid. § 4.

‘) The conditions for thermodynamical similarity have been given by me in Comm.
no, 23. Zittingsverslag 25 Jan. °96. Only when these conditions are satisfied, the
temperature function which is linear in x will vary in a corresponding manner for the
different temperatures.

(279 )

be necessary to make observations, not less extensive than those
by AmaGaT for simple substances.

If we accept that the mixtures obey the law of corresponding
states, we must yet consider how far we may express the critical
temperatures, pressures (and volumes) for such mixtures by means
of two constants a, and 4), by the equations

ay; ®? + 2 ayg ev (1 — 2) + agg (1 — x)?
by) 2 + 2b 2 (1 — 2) + by (1 — a?
a, ® + 2 ayaa (1 — 2) + ag (1 — 2)?
*£by 2 $2 byg @ (1 — 2) + dgg (I — 2)?
Uzk = Cy {by 2? + 2 bya x (1 — 2) + bag (1 — #)}

Ter: — C,

Prk =

in which C,, C, and C3 are the same constants for all substances,
or whether more complex functions of x are required therefor.

For the treatment of these two last problems in the case of
KUENEN’s experiments I refer to a joint communication by Dr. M.
REINGANUM and myself).

With reference to KUENEN’s experiments, it may be mentioned that
a new reduction of the combined observations (by means of graphical
representations and by series) is being worked out, from which we
can deduce more satisfactorily than is now possible what degree of
accuracy is attained in these experiments.

3. Now I return to the treatment of the problem to be solved.

I have made use for this purpose of two methods, and have
sometimes completed the results of the one with those of the other method.

In the first place, from the drawings mentioned in § 1, other
graphical representations are deduced by means of constructions, which
lead to the solution of the problem in hand, (comp. for instance
§ 8); this will be called the graphical method in a plane. In
the second place, a plaster cast of VAN DER WAALS’ surface was
made*) in order to make constructions on it, for instance to
determine the connodal curve by rolling a glass-plate covered with
lamp black over the plait. This will be called the graphical
method by the model. With the first method, when the equation of
state p—f (v, x, T') has once been given, the accuracy can be
raised indefinitely without any material difficulties. The only thing

1) Same Proceedings, following paper.
*) A diagrammatical model of the » surface has been made by VAN DER Waats and
is represented in Théor. Mol. p. 28.

19*

( 280 )

necessary is to make new drawings ona larger scale relating to those
parts of the surface that are to be investigated more in detail (comp. 59°).

With the second method the material difficulties increase, whether
we desire to make casts of greater dimensions, or to add separate
detailed casts on a larger scale as auxiliary figures to the original casts,
as soon as we wish to attain a higher degree of accuracy (comp. 59%),
This becomes obvious when we see how little defined are the plaits by
which the phenomena of condensation are determined, especially in
the neighbourhood of the plait-point which strikes one immediately
when one compares PI. I.

For my first treatment of KUENEN’s experiments I used only the
graphical method in a plane. But as the numerical treatment of
the problem became more difficult, the value of the qualitative
treatment increased.

As soon as I could avail myself of the assistance of a modeller,
Mr. ZAALBERG VAN Zeus, I had a plaster-cast of the y-surface made
from the graphical representation in plane. For this purpose moulds
were used constructed from curves calculated and drawn by me
for Wr =/ (v) and yw = f(x) (comp. § 1).

When the cast — 30 em. long, 20 cm. wide and 40 em. high —
was ready, though able to give a distinct representation of the
plait, it appeared too small for several constructions and so a new
cast was made of twice these dimensions, based on the same draw-
ings. This larger pattern, even when hollowed, is rather heavy
(80 K.G.) but it proved to be highly satisfactory for several construc-
tions. By rolling the glass plate over it, a fairly regular binodal line with
the tangent-chords was obtained, and so the relative positions of
the critical point of contact and of the plaitpoint could be demon-

; x dw
strated. For the construction of the curves ries const., the cur-
VU

ves of pressure, and ~ = const., the curves of substitution potential,
(obtained in the graphical representation in plane by drawing
lines of contact), a hinged pair of bars with
level and scale was used (see fig. 1), which is
placed on the cast by means of two pins separ-
ated by one cm. The curves drawn on the cast
can be easily projected by means of a system
of curves v =const. and «= const. The tan-_
gent-chords to the cast were represented by
stiff wires.
Fig. 1. The cast thus obtained was in the main the

( 281 )

same as that represented photographically on Plate I. Among other
things fig. 5 Plate I in Harrman’s thesis for the doctorate was
derived from it). Photographs of this surface were given by me
to some colleagues at the Naturforscherversammlung at Dusseldorf
(1898), also I presented a few persons interested in it with casts
of the smaller pattern and of that part of the larger pattern which
is near the plaitpoint.

4. If at the time, the construction of a model to accurately represent
the reality involved many difficulties resulting from the complications
mentioned in § 2, it appeared to me, as the number of the applic-
ations of VAN DER WAALS’ theory increased, to become more and more
desirable to know in detail the properties of the plait obtained, especi-
ally in the neighbourhood of the plaitpoint, and to render the gra-
phical construction of the connodal line, the tangent-chords and
the condensation phenomena now more useful rather for explaining
this theory than for calculating the numerical results of the observations
from VAN DER WAALS’ theory. For it is obvious that a true know-
ledge of the behaviour of ideal mixtures is an indispensable guide
in experimental researches of real mixtures. And the difference will
not be so very important if we allow the w-curves in this illustration
to deviate as they approach the side of the small volumes, provided
that this is done in a corresponding manner. I resolved therefore to
modify the cast in order to make it suit the desired purpose.

For this care must be taken, that at any rate the w-curves assumed
for the simple substances strictly satisfy the law of corresponding
states. But on the other hand, the desire to illustrate VAN DER
Waats’ theory for a case, which agrees as well as_ possible
with actual measurements — in this case KUENEN’s — remained
justified. Therefore it seemed to me desirable to apply the empirical
correction, obtained by including Cuausius’ 2, into the equation of
state, which also analytically only slightly changes most of the deve-
lopments of vAN DER Waats. Here the /2, mustsatisfy the condition

3 ; ,
that Pe =n for all mixtures has the same value as for the two mixed
zc

substances.

For a given y-surface, it is of no moment that we put 7a,= K.,
yet this supposition has been inciuded in VAN DER WAALS’ equa-
tion of state in order to link the latter to the observed isothermals

1) Cu. M. A. Harrman, Metingen omtrent de dwarsplooi op het p-vlak van VAN
DER Waats bij mengsels van chloormethyl en koolzuur, Diss. Leiden 1899,

( 282 )

for other temperatures and to better deduce the critical temperatures
and the critical pressures of the homogeneous mixtures Typ, prx-

(The two above mentioned empirical corrections used by CrLau-
situs were chiefly employed to obtain a better agreement with the
density and the tension of the saturated vapour. And so it is
obviously useful to apply them where we have especially in view
the phenomena of condensation.)

For K, and bl, we kept to the (ideal) form of the second degree
in z of VAN DER WAALS.

For these reasons we chose as the equation of state

Vital by Ike

ob La py
K, = Ky 2 + 2 Ky # (1—2) + Kg (1—2)?
= Dy, x + 2 by x (1—az) + bg (1—2)?
B=nb

Be

v expressed in terms of the theoretical normal volume.

The reasons for choosing the new values for a1, 995 @95 51, 5y9s bag

a]

and for x = £, are explained in a combined communication with
Dr. ReInGANUM, who to my great satisfaction I found ready to
undertake together with me the accurate graphical investigation of
that part of the surface near the plait-point which on fig. 3, Pl. II
is shown by the small rectangle. The original cast was modified
in connection with that combined investigation until it agreed with
the new data. I owe thanks for the valuable assistance of Dr.
REINGANUM in this and in the following constructions.

5. Plate I shows a photographical reproduction of the cast ob-
tained in this way, taken from the side corresponding to the methyl-
chloride. The y-curve of pure methylchloride stands out clearly by
the shadow and has moreover been dotted. The depth in the plait
is revealed by the shadow cast by the tangent-chords. The repre-
sentation of the casts did not appear to be so much improved by
stereoscopic photographs, that it outweighed the greater complication
of the process.

Fig. 1, 2 and 3 of Pl. IL are the above mentioned projections on the
we wr, and av planes of curves drawn on the w-surface. *) In fig. 1

1) In order not to render the drawings indistinet we have not drawn a rectangular

system of equidistant lines a thing which can easily be done by every one who wants to
make numerical readings on the drawings.

( 283 )
(projection on the xw-plane) the projections of the substitution potential
d
curves, or more simply the substitution curves, (+ = const. have
p ar

been dotted. In fig. 3 (projection on the xv-plane) the pressure curves

d Sear
(-= ee const. ), are drawn, and the substitution curves are dotted.
v

In fig. 4 the substitution curves are dotted and the curves for which
d d :

y+ F (1—2)— - v = My = const., the potential curves of the second
aL v

component, are lined. According to VAN{DER WAALS’ theory (Théor.
Moléc.) these three curves are sufficient for the determination of the
co-existing phases.

How the substitution- and the pressure-curves have been obtained
is mentioned in § 3. The graphical determination on the cast was
tested with that on the plane.

6. First must be mentioned briefly how the potential curves are
determined, both by construction on the plane and on_ the
cast. In the first case I started from the figures 1 and 2, Pl. II,
which give the sections of the yw-surface by planes containing
the line x=0, z=1,000 (the y-axis on the side of the methylchloride).
If in fig. 2 we rotate?) the azv-plane with the lines x = const. =
A,x«=B etc., (the projections of the wr-curves) drawn on it, round
the v-axis on the wv-plane, the plane of the figure; the sections a, b ete.
of the planes just mentioned, containing the line -=1,000, v=0,
by the zv-plane, rotate into the plane of the figure and appear as
radii (starting) from the point « = !.000, v = 0, whose points of intersec-
tion aA, aB with the rotated lines e = A, r=B ete. vive the value of v for
the point of intersection «4,aB, etc. of the plane a with the curves
wa, we ete. The line drawn in PI. II fig. 2 through the point
of intersection perpendicularly to the v-axis determines through the
intersection aA with the w4-curve the value of the perpendicular height
above the v-axis, for the point ad’ in the rotated figure; while the
value of » for this point in the rotated figure is found by rotating the
radius drawn from z= 1,000 v = 0 to Aa on the v-axis. The points a4’,
aB' etc. combined give the rotated oblique section a’. From one
point g on the w-axis (line «=1,000,v—0 for the y-surface,
v=0 for the plane fig. 2) tangents are drawn to
these rotated oblique sections «',b', whose points of contact

1) The drawing with these constructions can be omitted as it is somewhat complicated,

( 284 )

Maly Mo, Me are points of contact of a plane drawn through the
point ws, with the w-surface, which points of contact fq fy ete.
are rotated on the plane of drawing round the line z= 1,000,
v=0. The co-ordinate wa! of “a in the drawing is also the co-
ordinate yu», of the point of contact in the section with the plane
a, returned into its previous position, while the abscissa v,q, measured
along the radius a gives the place of the projection on the «v-plane
of the point of contact “a. The points ws, 4, . . - are therefore com-
bined by a smooth line into a potential curve for the value «#5. The diffe-
rent curves, obtained by repeating the last constructions with several
values of w, give the system of potential curves in the zv-plane, fig.
4, Pl. Il when the v-axis of fig. 2 is again considered as v-axis
and the w-axis of fig. 2 as «#-axis.

The construction by means of the model is immediately derived from
this. We used a pair of sliding compasses with points, long enough
to continue the construction also within the plait. One of the
points has the ordinary form, and is placed on the top of a rod

ae which is movable in the line
au a=1,000 v=0 and terminating at

=
bo i the height «. The other movable

point is fork-shaped (see fig. 2)

of which the two prongs one cm.

apart are situated in a straight
Fig. 2. line with the fixed point. When,
during the sliding of the fork, we try where the two teeth rest
on the cast, we find the place where a line of contact to the sur-
face, goes through the point w. In order to obtain the projection
of the potential curve found on the cast, we use again the system
formed by the curves v = const. « = const. on the y-surface.

7. The figures drawn seem to me well adapted for giving us a
very clear representation of the thermodynamical properties of the
mixtures according to VAN DER Waat.s’ theory.

Many peculiarities are to be observed in the course of the different
lines. I shall draw attention to only a few. The limiting-forms of
the pressure-curves are for very large volumes straight lines across
the surface, parallel to the «-axis; with small volumes the curve
tends again to become rectilinear, but in that case its general
direction is at some small angle with regard to the z-axis. This
follows immediately from the theory. The point of inflection of the
pressure-curves through the plaitpoint is situated, reckoned from the
liquid-side, farther than the plaitpoint (this property was formerly

( 285 )

communicated orally to me by vay peR Waats). Through both
the ends of a tangent-chord pass the same curves of pressure, of
substitution and of potential (a thing which we can see for our-
selves by laying the tracing of one figure on the other). Through
these points pass also the potential lines for the first component.
These are the chief conditions advanced by VAN DER WAALS.

The curve of pressure touches the tangent-chord in the critical
point of contact. This has been pointed out by HARTMAN (Comm.
N°. 56).

The points of intersection of the theoretical and the experimental
isothermals are situated almost in a straight line going through the
critical point of contact. The point of inflection of the pressure
curves in the unstable part is situated also in a line deviating but
slightly from a straight line towards the side of the small vol-
umes; the critical point of the homogeneous mixture lies also
towards the side of ithe small volumes, with regard to the point of
intersection with the experimental isothermal. (Comp. HarrMan,
footnote Comm. N°. 56).

The substitution curves run parallel to the v-axis for large vol-
umes. For smaller volumes they begin to incline towards the plait,
this inclination increases as they reach farther down into the plait,
it attains a maximum and decreases again in the direction of the
smaller values of #. The lowest point of the bend is outside the
plait.

The substitution-curve of the plaitpoint envelops the connodal line,
according to properties found by Korrewee, and shows a point of
inflection that comes within the plait from the side of the smaller
volumes. The substitution lines intersect the pressure curves within the
connodal line. The divergence of their general direction in the plait
agrees best with that of the tangent-chords.

The general direction of the potential lines for larger volumes lies
obliquely over the yw-surface from the side of the smaller volumes and
smaller composition-ratios towards the side of the larger volumes and
larger ratios. Towards the plait they show a bend, which is more
acute than that of the substitution-line and on entering further into
the plait these increase rapidly in acuteness, so that they, like the
pressure curves project beyond the limits of the surface. The lowest
point of the bend lies within the plait. The greatest convexity
towards the plaitpoint of the substitution lines and of the potential
lines coming from the side of the large volumes within the plait is
‘situated together with the greatest concavity of the pressure-curves
on that side more or less on the axis of the parobola by which

( 286 )

the projection of the connodal-line is approximately represented (in
other respects it is better represented by a hyperbola).

8. The determination of the co-existing phases by graphical
solution in the plane surface. Attention has been drawn to the
difficulties, attending the precise graphical solutions by means of
the plaster-cast. These are very great when we want to determine
the connodal-line by means of rolling a lampblacked glass plate over the
east, which method is in other respects the most direct expression
of VAN DER WAALS’ solution of the problem. Hardly perceptible
deviations of the surface have a great influence on the shape of
this curve. Therefore it is desirable to be able to determine the
connodal-line and also the tangent-chords by a construction for
which we only need to make drawings on a plane!). The
graphical representations discussed in the former sections offer a
means for this. For if we return to the condition advanced by
VAN DER WAALS for the co-existence of two phases, namely

du’ By Se dy : —_ dw is ; mn

= = ae) ’ co — lee 3 Mo — es
where ' refers to one phase and " to the other, then we get to
know the co-existing phases as those, in which (, considered
dw dw

d ;
” and — for the same value of and —
dx dv dv dx

as a function of

twice has the same value.

If now we trace the course of a curve «.—const. in the curvilinear
system of the pressure- and the substitution-lines in the 2» projec-
tion, and if we transform this system of curves into one which is
rectilinear and rectangular and ou which along the axis of ordinates

dw. :
a suitable function of = is measured, and along the axis of

: d ; b :
abscissae a suitable function of =, the «-line by this process will
LUO
become a loop-shaped figure, of which the double-point is at the

1 Ly) , Sie
values of = and = which correspond to the composition and the
av awl

volume of the co-existing phases.

1) RieckE, Ueber die Zustandsgleichung von Cxaustus. Wied. Ann. 54, p. 739,
treats the co-existing phases of a simple substance graphically) Comp. also H. K. O.
Verh. Kon, Akad. v. Wet. XXII, p. 13, 1881), and mentions p. 744 that by means
of the thermo-dynamical potential this could be done in a similar way for mixtures.

<i ke

( 287 )

For the representation of “2 as ordinate we have chosen in fig. 3

32,6 b"

ols3
2069
95.4
y,
tes
JSS
One
049
50.5 |

: d U Blue citar
such a function of Bish.) that the substitution-lines, belong-
b A og

ing to regularly increasing values of this s for large volumes, run
at equal distances in the zv-plane. For simplicity’s sake we have
in order to determine s in this way not taken an infinitely large
volume, for which we should have

ghT de
(1 edy
14 Ae

but the volume at the end of the drawing (0,034) fig. 3, Pl. I;
where the value can be read directly. It does not deviate much

eon ; d
from that for an infinitely large volume. As function of = we
av

: dw\—_ 1
might choose w= (>) =— so that for large volumes the
v P

pressure curves belonging to regularly increasing values of
this w run at equal distances. But in order to be able to read
the value immediately on the drawing fig. 3, Pl. II, we have
chosen that function of p, which for s=0 becomes equal to v.

( 288 )

The shape of the closed loops in the annexed fig. 3, obtained in
this way, still shows small irregularities, which are owing to in-
accuracies in the construction. However I thought the figure of
sufficient importance {o give it here even in its imperfect state.
Part of the loop-shaped figure for small proportions of the most
volatile substance is in this case cut off by the curve s=9, The
line which connects the double points and therefore determines the
pressure for co-existing phases as a function of the substitution

potential a is in this figure a straight line. As the substitution
ar

and the pressure-curves belonging to regular increasing values of
w and s in the av-plane for large volumes, form a nearly regular
rectangular system, the connodal line in the «v-plane will also be
a straight line for large values of the volumes, In connection with
this result I may remark that according to an oral communication to
me VAN DER Waats has derived from his theory, that the
connodal line for the plait into which the one investigated here
passes at 9°,5 the temperature at which Hartman made his experi-
ments, would be almost a straight line on the side of the large
volumes, which is substantially verified by those experiments.

This appears from fig. 4 drawn by Dr. Harrman, in which the
projections of the connodal line with the tangent-chords are repre-
sented for 9°.5. In order to make a comparison the plait on the
model (almost that of Kurnen) has been added on the same scale
as the drawing.

5C00 42009 IFOCS

800)

acco

Q400

Fig. 4.

KAMERLINGH ONNES. ,,Contributions to the knowledge of VAN DER WAALS’

-surface. I. Graphical treatment of the transverse plait.”

PLATE I.

ings Royal Acad. Amsterdam. Vol. IIT.

‘OIAAW HAG WAY to: +

TATA

yahbolwoud odd of anoitudiino00. -2a0M0 HO“L

“ Jislq serovenstt oft To jovitsons (soniqend) I.

( 289 )

Physics. — Communication N°. 59% from the Physical Laboratory
at Leiden, by Prof. H. Kameriinca Onnes and Dr. M.
ReINGANUM: “Contributions to the knowledge of VAN DER
Waats’ w-surface’. Il. “The part of the transverse plait
in the neighbourhood of the plaitpoint in KUENEN’s experi-
ments on retrograde condensation’’.

(Read June 30, 1900.)

1. The most important part of a transverse plait in VAN DER WAALS’
y-surface is no doubt that in the neighbourhood of the plaitpoint.
For investigations of this part however a higher degree of accuracy
is required than was sufficient for the construction of the model
of the whole plait and of the constructions belonging to it, described
in Communication N°. 59¢.

In the following pages we represent the part of the surface shown
by a rectangle in figs. 3 and 4 of Pl. II, which representation is
based on more accurate calculations of p (to 5 decimals) made for
values of z and v in a smaller range by means of the same equa-
tion of state, from which we started for the construction of the
general model. The principles on which the choice of this equation of
state was based for the following illustration of VAN DER WAALS’
theory have been laid down in §4 of Comm. N°. 59¢; in the
present paper we will consider the manner in which the constants
occurring in that equation have been obtained, and in how far by
this choice of constants the accepted equation of state can be made to
harmonize with KuENEN’s observations. As explained in § 2 Com-
munication N°. 59¢ two questions are specially prominent: 1s‘. in
how far do the mixtures investigated by KurENEN agree with the
law of corresponding states and 2°4. in how far can the eritical
constants of the homogeneous mixtures be represented by VAN DER
‘ Waats’ formulae of the second degree.

2. To obtain an opinion on this we cannot directly apply to
KUENEN’s observations the ordinary method of calculating the reduced
values of the pressure, the volume and the temperature by means
of the critical quantities. For the eritical temperature of the homo-
geneous mixture (point A in fig. 3, Pl. IV) is situated according
to vaN DER Waats’ theory in the unstable part and has therefore
not been observed.

Neither are we assisted even to a moderate extent by
Raveau’s method of measuring off the logarithms of the pressure

( 290 )

and the volumes as ordinates and abscissae and by then shifting
the systems of isothermals of the two substances parallel to themselves
until they cover one another. ‘This is chiefly to be ascribed to
the smallness of the range over which each of the isothermals
extends. Those parts of the isothermals that can be drawn, show
no striking curvatures and run almost parallel. Hence there is too
much latitude in the adjustment, so that it is not possible to deter-
mine sharply enough the exact position in which the one system
coincides with the other.

Therefore we can only very roughly consider the ratio of the
absolute temperatures of two isothermals covering each other in the
way mentioned, as being the ratio of the critical temperatures be-
longing to them; the same holds for the pressure and the volume.

It is obvious that we may use instead of the pressure itself,
the product pv, which is moreover of so much importance for
the investigation of the isothermals, draw for one tempera-
ture logpv as a function of logy and determine by shifting the

curve log pv—=f(logv) on the one hand the ratios BEE (or what
Pk2rkg
Lr cal :
comes to the same ——) and on the other hand log As this
k2 Uke

still implies shifting the system in the direction of both the axes
of co-ordinates, it also still offers too great a latitude.
We may do without the displacement in the direction of one of the

BPS
axes, when we measure off not /og pv but a which has the same value

?

or molecular quantities in corresponding states. For large volumes
this quantity has the value 1, for the critical state about 0.29.
In applying this method it appeared that it was not possible to

completely cover the system of a curves of the one substance

by those of the other. Irregular deviations did show themselves,
which may probably to a large extent be ascribed to errors of obser-
vation. The result was that a certain latitude still remained in the
adjustments and the limits were sought within which the coincidence
might be called satisfactory.

The ratio of the critical volumes follows immediately from the
curves of logv covering each other, which ratio could then only be
included within the limits just mentioned.

The ratio of the critical temperatures is given by the temperature

; v \
to which two — curves belong, covering each other, so that this

( 291 )

also can only be included within limits, while the same holds for
the critical pressures, obtained by means of Cpzx, = Ty. For C we
took the value found by AmaGaT for carbon dioxide.

The following table gives the results of these processes starting
from pio = 72.9, v2 = 0,00426, Tyo = 304.85 for carbon dioxide.

|
Proportion of | V kx. Tix.
Viz Tix phe
CH,Cl. | mean. mean.
0.00668 | 413 63.2
p=) EO to / 0,00698 to 416 to
0.00728 | 419 57.8
633 382 mean value
oO: 4/5 to 610 to 386.5
588 | 391 64.7
654 337.5 mean value
O25) to 665 to 339
675 340 52.2
501
2 = 0.25 to 531 indefinite. indefinite.
562

For the critical temperature of pure methylchloride we find the
same value as found experimentally by Kurnen (416.0). The mean
value of the critical pressure (60.5) however deviates much (7,5 pCt.)
from the value found by Kuenen (64.98). The highest value is in
better agreement (3 pCt.)

We will naturally next consider how the critical temperatures of
the homogeneous mixtur2zs Tz, found by us, are situated with respect
to the critical point of contact temperatures Trp found by KUENEN.

This may be seen from the following table:

Mixture. Tr Tr

a 396 386.5

a Te 370.1 339
By 338.4 indefinite

Jn good agreement with the theory, the values of 7), are found to
be lower than those of Zz, and one would be inclined to fill in for
a=}/,, symmetrically with «= */,, 7, = 328. Yet the difference of
31° found for «= 1/, gives rise to some objections against putting
great trust in the determinations. If we also bear in mind the irre-
gular deviations, remaining between the two systems covering each

( 292 )

other, which leaves undecided whether the mixtures deviate from
the law of corresponding states more than the simple substances, and
also the large deviations found in determining the pressure of methyl-
chloride, much uncertainty remains about the critical value itself.

Therefore it is desirable to try to deduce in a different way some-
thing about the critical temperatures and the pressures of the homo-
geneous mixtures from the whole of the observations for each mix-
ture. We find a means for this in the equations given by KUENEN
which express as well as possible the whole of the observations for
each mixture, which equations we at first did not think it advisable
to use in order that we should be as little biassed as possible in form-
ing an opinion from the observations themselves about the problems
in hand. But it is not to be expected that we can satisfactorily
determine the critical quantities, firstly because Kuenen has not
taken for all his mixtures the same temperature function for a, se-
condly as states situated far from the critical point, which have
influenced the determination of the equations, can give rise to errors
by the extrapolation with the defective equations of state.

However it may be considered as a confirmation of our conclusions
from the adjustments when the former can also be derived from
these equations.

With regard in the first place to the fulfillment of the law of
corresponding states, we might conclude from the disagreement of

: Pith, 7
the ratio »z = a given by KUENEN,

zx
B= il nm = 1,40
rh ns, —= 1,26
ee 7 f— 1G
yf m= 1,38
— no = 1,09

that the mixtures investigated do not fulfill the law of corresponding
states). The value of this conclusion becomes smaller, when we
consider that KupNEN has accepted b, somewhat arbitrarily. Both
this and the choice of different temperature functions for @ must
influence the values found for 2, and although we may allow that
the variation of the values of x indicates a peculiarity in the closely
related quantities 6 and /?, they can only support the conclusion
but weakly, that the mixtures would satisfy the law of corresponding
states to a smaller degree than the simpie substances.

') That x must have the same value for all substances that fulfill the law of corre-
sponding states, has been demonstrated by KamMeRLincH Oynes, Verh. Kon. Akad.
v. Wet. XXI, 1881, p. 20; Arch. Néerl. T. XXX, p. 112.

i

Let us consider now what follows from KUENEN’s equations
the critical volumes and temperatures.

for

z | Vek. | Ths. | The.
1 0.00725
fq 606 402 (397.5) 396
Ig 620 350 370.1
VW 489 338 (332.5) 331.4
0 435 304

It is remarkable that (as follows from the values of n and the
linear variation of 6 just mentioned and the relation y%, = 34 + 2/7)
the critical volumes show the same course as that found by means of
the method of coincidence. From KUENEN’s combined experiments
it would hence appear that for mixtures of methylchloride and carbon
dioxide the critical volumes cannot be expressed as a function of the
second degree of the composition, as it is accepted by VAN DER WAALS
in his theory of ideal mixtures, but that at least a function of the

third degree is required for it.

In fig. 5 the curve of x is represented by a dot-dash-line when

0,00700

0,00600

0,00500

0,500

X= 9250

Fig. 5.

0,750 4,000

Proceedings Royal Acad. Amsterdam, Vol. ILI,

resulting from the coincidence
method, and by a dash-line
when resulting from KUENEN’s
equation, and by a complete
line that of the ideal mix-
ture to be considered in the
next section.

Concerning the critical
temperatures, not much can
be derived from KUENEN’s
equations. For the values
between brackets in the table
given above a has been cal-

1 ar
culated by means of aoe

which we have used for K

the numbers given in brackets

by Kuenen. The temperature

values without brackets in

the same table have been
20

(294 )

calculated with values of @ obtained by interpolation between the
values of a given by Kunrnen separately for different temperatures.

Only for the second mixture an acceptable value of 7p — 7; is
found, i.e. 20°, but it is obvious that this difference cannot be
negative as with «= °/, or zero as with «= 1/,. And so the values
from KUENEN’s equations cannot be an argument either for or
against the values found by means of the method of the coincident
systems.

Therefore for the time being no arguments other than those derived
from the deviations of the critical volume mentioned above, can be
adduced to justify the doubt of the possibility of expressing the critical
quantities of the homogeneous mixtures in the case of KUENEN’s
experiments by the formulae given by VAN DER WAALS for the
critical quantities of homogeneous mixtures, together with KUENEN’s,
identity Zar= Kz.

§ 3. In order to obtain for Ay), Kyo, Koo; 611, 19; ba9 in the equation

RL Ke
as v— be T(v + n br)?

Kz = Ky 2% + 2 Ky 2(1—2) + Ky (1-2)

by — by) x? +- 2 big & (1—z) -|- boo (1—z)?

(p= pressure in atmospheres, » =volume expressed in terms of the
theoretical normai volume, R=gasconstant, 7=absolute temperature,
x=molecular composition, while the value of 1.4610 was taken
for 7) values which agree as well as possible with KUENEN’s experi-
ments, a curve of the second degree was drawn almost corresponding
with the critical volumes found from the coincident systems, from
which 6)),0,, and 6:, were found. The convexity was chosen towards
the z-axis, because in that case a value for Ky could be found, for
which A, was obviously of the second degree. This is justified as
the final equations represented KUENEN’s isothermals still within 2 pCt.

Subsequently the observation of the critical temperature of the
point of contact for the mixture «=1/, was taken as a basis for the
calculation of the a’s.

Now that the difference 7,r—Tz, could not be deduced with any
certainty from the observations, we had to confine ourselves to an
estimation of it.

According to the results of the graphical determination of the
connodal curve on a plaster cast constructed previously (see Harr-

(295 )

MAN’s figure derived from it, Communication N°. 59, § 3) the critical
temperature of the homogeneous mixture is situated lower than the
plaitpoint temperature and although the place remains very uncertain,
we thought ourselves justified in searching it at double the distance.

For our purpose it seemed at any rate sufficient to subtract 7°
from the temperature of the critical point of contact for the com-
position %/.. With Zp,—7° = Tyy,*%o Zand Ty, we could now
calculate Ky, Ky.) Koo

When the plaster-cast of the part of the surface near the plait-
point was ready, it appeared that for the ideal mixture supposed
Try—Tx, amounts to about 19° C. which deviates from the value
first accepted in the sense of what had been derived from the obser-
vations of the mixture !/. (i.e. 30° C. from the method of the
coincident systems, 20° C. from KUENEN’s equations.)

The following table gives the constants found and the critical
quantities derived from their combination.

Ky, =6.276 by, = 0.001193
Ky = 3.314 yy = 0.000893

Ky, = 2.176 bg, = 0.000780

Viz | Phx | Uke
Q=Sh 416 64.8 0.007065
iy 391 68.9 6249
r= Vp 363 71.8 5568
e=Yy 336 73.0 5022
a0) 303 72.2 4620

The value of a is thus found to be = The variation
k

aoe
of pe agrees with that of pr (see the usual pT diagram).

§ 4. In the construction of the detailed plaster-cast it was impor-
tant not only to profit by the opportunity of being able to choose
a larger scale for v and « with almost unchanged dimensions of
the whole model, but also to make the curvature of the w-surface

20*

( 296 )

near the plaitpoint as well defined as possible and thus to make
the determination of the connodal curve and the tangent chords as
accurate as possible. As now the surface near the plaitpoint is but
little removed from its plane of contact, an enlargement of y, by
which the differences w" = yw — yw., where yw, is the value of w for
points in the tangent plane lying at the same values of 2 and »,
are enlarged in the same proportion, will cause the surface as a
whole to become much more inclined with regard to the «v-plane,
which again would cause the model to have only limited dimensions
in the z- and v-directions with the same dimension in the w-direct-
ion, in order to make the curvature more prominent. We have avoided
this difficulty by constructing a model in which the properly mag-
nified values yw" of yw — y, for # and of v as independent rectangular
variables are measured perpendicularly to the zv-plane. In this way
the general oblique position of the surface with regard to the ve-
plane is eliminated, and yw— ye can be enlarged as much as is
allowed by the greatest dimension which we wish to give to the
model in the y co-ordinate, through which the curvatures become
prominent as desired. The plane of contact on this model if continued
to v=o would become for «=!/, and for v=o a-plane sloping
to the «v-plane with the angular-tangents a and 6, whereas in the
case of the w-surface it would be parallel to the zv-plane.

yw. in w"=wyw — we is a linear function of 2 and v. VAN DER
Waats has already demonstrated that the addition of a linear function
in x does not influence the properties which are of importance in
the thermo-dynamical consideration of the y-surface. This holds
good also for a linear function of v.

Putting y'= yw + av + br we get

dw

ae de
dys’ d
at
maw Way vt_s aK
py =wmo pg = y— oP pH yt.
For the shape of the projection of the curves s = const.

dy" an
a const. 4); = const. “ =const. on the av-surface it is of no

v

( 297 )

consequence whether each is increased by a constant quantity, for
in the case of «, there is not even difference between the two
values of the quantities #, and gy’.

The values of w" used for the construction of the model and
the drawings are determined in connection with the absolute values
of yw used in the general model of the whole plait (comp. Commu-
nication 59°) by means of the following equations.

yp" = — 81786 yw — 0,25 v +.48000 « — 164780

v

Sy =| pdo— RT (clg2-+ (1—sz) lg 1—2) 4 914383.

ao

§ 5. Plate III is a photographic representation of the detailed
model on which the connodal line and the tangent chords are shown,
the depth of the plait is made clear by the shadow of the tangent
lines. Fig. 1 and 2 Pl. IV shows the sections w"s=/(v) and

py", =f (2). Pl. IV fig. 3 shows the pressure-curves Se ee
v

"

and the substitution-curves aR const., fig. 4 represents the pressure
aC

curves and the potential curves «,'’= uv; = const. (all this on’ the
1

v«-surface). In the two last figures z is ordinate and », in Foo0000m
parts of the theoretical normal volume, is abscissa.

In fig. 3 and 4 the connodal line has been shown as a dot-dash
lire, a shadow approximately indicates how great is the uncertainty
of this line. The exact place of P (the plaitpoint) on the connodal line is
still fairly uncertain. A detailed investigation like the foregoing would
again be required with regard to a limited part round P. A similar
investigation of the two parts round the two points of contact of a
tangent-chord will give us greater certainty as to the exact situa-
tion of that tangent chord. So the point & (the critical point of
contact) can also still be better fixed.

It may be assumed that we have nearly obtained the difference
xp7R—«7K Of the composition ratios of critical point of contact and
of the plaitpoint at the temperature T= 373° C. From this by a
better estimation more suitable values can be derived for the dif-
ference TR),—Tx,, from which we started for the deduction of aj,
etc., through which again values for aj, ete. could be found, from
which a better agreement with KUENEN’s experiments near the
plaitpoint is to be expected.

( 298 )

When we trace by means of the
graphically found connodal line,
the condensation phenomena for
a mixture with composition #
between the plaitpoint composition
xpr and the critical point of
contact composition «zz this will
give us a representation of KUE-
NEN’s observations at 103° C. and
the composition 0.41, which re-
presentation however will only
be an approximation. Fig. 6 is
obtained by reading on Fig. 4
Pl. IV for each a the relation of

Soa
Sia + Soa’
tangent-chord of the piece from
the intersection with the line
which has the composition 2 (for
which we want to investigate the
condensation phenomena) to the contact on the vapour side
— which ratio gives the number of molecules in the liquid state —
and by determining from this the liquid volume at the tangent-
chord a by multiplication with vz. In the figure?) the liquid volume
has been measured as ordinate of the curve and the total volume
as abscissa.

The dotted line is KuENEN’s curve. The composition for which the
construction has been made has been chosen so, that the beginning
and the end of the condensation are in the same ratio as in
KUENEN’s observations.

By reading the values of the pressure at the points of mtersection
of the tangent chords in fig. 4. Pl. 1V, we find that the pressure
during the condensation varies almost linearly with the total volume,
This is also very nearly the case in KUENEN’s experiments. Also
the amount of the pressure is in fairly good agreement. While
KueENEN found an increase of 73,5—83,8, we find from our figure
one of 78,6—93,2.

the ratio to the whole

$00 3000
Fig. 6.

1) Compare also the figure for the retrograde condensation in mixtures of carbon
dioxide and hydrogen. VeRscHAFFELT, Comm. 45, fig. 2 on the plate (Proc. Acad. Amst.
Dec. 798.

Dr. H. KAMERLINGH ONNES and Dr. M. REINGANUM. ,,Contributions to the know-
ledge of VAN DER WAALS’ y-surface.” II. ,,The part of the transverse plait
in the neighbourhood of the plaitpoint in KUENEN’s experiments
on retrograde condensation.”

PLATE III.

Proceedings Royal Acad. Amsterdam. Vol. IIL.

( 299 )

Physics. — Communication N°. 60 from the Physical Laboratory
at Leiden, by Prof. H. Kamer“incH Ones and M. Boupry.
“On the measurement of very low temperatures. III. Coefficient
of pressure variation of pure hydrogen between 0° and 100°”,
(Read June 30, 1900.)

15. Very careful determinations of the coefficient of pressure
variation of pure hydrogen, described by one of us (H. K. O.)
in Communication N°. 27 § 8 (Communication to the meeting
of June 1896 of which this paper is a continuation) have now been
made with the large pattern (comp. N°. 27 §§ 2 and 3) of the
constant volume hydrogen thermometer for low temperatures.

This determination comprises, [the bulb of the thermometer being
placed in ice (lc. § 7) or in steam (l.c. § 8)], measurements of the
temperature in the different parts of the apparatus, and lastly
measurements of the volume occupied by the gas.

16. The measurement of the pressures. The pressure are deter-
mined by the difference in height of the mercury menisci in the
manometer ($2) augmented by the pressure which is exerted on
the outer level of the manometer and which is indicated by a mer-
cury barometer placed beside the apparatus ')*). The level of the
top and the height of the meniscus are read for each of the menisci
by a cathetometer. From the height we derive the correction for
the capillarity according to MENDELEJEFF’s table. The temperature
of each of the mereury-columns is read on thermometers, placed
symmetrically. Moreover we allow for the difference in height between
the top of the manometer column and the lower meniscus of the
barometer.

The manometer-tube has been described in §$ 2 and 3. The
barometer the tube of which has a diameter of 14 m.m., has been
previously boiled very carefully in vacuo and is protected by a
drying tube.

The transportable cathetometer, constructed by the Société Gené-
voise is an exceedingly good instrument, arranged for differences in
height up to 110 cm., and provided with 3 telescopes *) in order

1) By dividing the mercury column which indicates the pressure of the gas in two
parts, we avoid the great difficulty which arises whenever we read great differences
of level owing to the unmanageableness of the cathetometer required for this.

2) For measurements in which quick reading is more important than high precision,
we use an aneroide as Wiese and BortcueEr did. Ztschr. f. Instr. X. p. 26. 1890.

3) Cuappurs on his stationary cathetometer has used 3 telescopes in order to read
3 menisci. Mém. Bureau Intern. T. VI. p. 31.

( 300 )

to read the 4 menisci. For both accurate and quick reading it is
of great advantage, not to be obliged to move the slides over the
vertical column. Therefore the two lower (or upper) menisci are
placed at about the same height and read with the lower (or upper)
telescope; the two upper (or lower) menisci with the two other
telescepes'). A difficulty arises whenever the difference of level
to be measured would lie between about 1 and 10 c.m. Then we
cannot adjust for the two levels either with one or with two tele-
scopes, as the construction of the slides does not allow the telescopes
to be brought to a smaller distance from each other than 10 ¢.m.
The difficulty might be solved by using a fourth telescope or another
cathetometer with two telescopes. But in §18 a method is described
by which the difficulty can be avoided, so that we have always
been able to read the 4 menisci with one cathetometer and only 3
telescopes without readjusting these. Each of the telescopes is provided
with an micrometer-eyepiece (serew-thread 0.25 m.m., and head
divided into 100 parts). The micrometer screws have been tested
on the exceedingly good apparatus for the measurement of photographic
star-plates at the Leiden Observatory, constructed by RepsoLp according
to H. G. van pe SanpeE BAKuUyzeEN’s?) indications, which appa-
ratus had kindly been placed at our disposal. The progressive error
remained except in one or two teeth (revolutions) below 2 micron.
For one of these micrometer screws the formula for the periodic
error was computed *). This was found to be @ (wu) = 0,402° cos. u
— 0.730 sin.uw in divisions of the head, so that for repeated adjust-
ments we may regard this as negligible. The collimation difference
of the telescopes have been measured in pairs at long intervals by
different observers, the telescope-slides having been removed in the
mean time from the cathetometer-tube and again replaced on it,
while the telescopes had been completely taken to pieces. Still it
was found after reading on the verniers of the slides:

I—II Dr. Disken . . . . direct 50.26 m.m.
[is SBownine sees eee ero nent

IiI—II “5 Bate ee :
ie a 53.38 | indirect 50.26
IIJ—II as 3.13

1) In the very diagrammatic figure 1, Pl. I, Comm. 27, only two telescopes have
been drawn.

2) Il. G. v. p. Sanpr Bakuuyzen, Mesure des clichés d’aprés la méthode des
coordonées rectangulaires (Bulletin, Comité de la Carte du ciel, 8e fase. 1889.)

5) EF. Kaiser, Eenige opmerkingen omtrent de periodieke fouten van Micrometer-
schroeven. (Versl. en Med. Kk. Akad. v. W. Amsterdam, 2e Reeks, Deel 1. 1866.)

TIL TOA ‘Wepsojsuiy proy [vsoy sSurpoooosg

}

( 301 )

The correctness of levelling of the cathetemeter was tested by the
menisci in two communicating mercury-tubes, presenting a difference
of azimuth of 90°, and no difference in height amounting to 0.01 m.m.
was found.

The levels have been tested by the level-tester and tables have
been made of the corrections at distances of 10, 20, 30, 50 e.m,
Each time a micrometer head was read, the level on the telescope
was also read. The method we followed was to read the difference
in level observed through the telescopes on a divided bar scale '),
not on the cathetometer-scale itself. For this purpose we used a
standard meter constructed by the Société Genévoise *) of 120 c.m.
length, mounted on a special stand made in the work-shop of the
laboratory which could turn round a vertical axis and was provided
with adjusting screws, rendering it possible to adjust the bar by
means of the cathetometer itself to a vertical position. (See Pl. VI
this paper).

17. The adjustments. The barometer, the manometer, the divided
bar, and the cathetometer are all mounted on stune pillars fixed to
a freestone slab, which in its turn rests on one of the fixed pillars
of the laboratory. The stones are easily mounted and temporarily
consolidated by means of plaster to a rigid block of stone.

In order to be able to adjust accurately, the focussing of the
telescopes not being altered, it is necessary that two of the three
apparatus should be movable. To attain this they are placed
on carefully worked metal stands (see Pl. VI of this paper) which
can be moved in two directions at right angles by micrometer
screws with handles. Tho manometer and the scale are placed on
the stands; the barometer and the cathetometer are firmly mounted
and the telescopes focussed on the barometer menisci. Then the divi-
ded bar is placed vertically and brought at the required distance
by means of the screws. The adjustment of the manometer into
position is more difficult; the best way is to bring one of the sliding
motions of the double sledge on which the apparatus is placed in the
direction of the cathetometer, and then to turn the stand and bring

1) Cuappuis l.c. p. 31. We ascertained by a great number of measurements, that it
was not necessary to read the scale immediately after a meniscus, but that the menisci
could be read successively and the scale at the beginning or at the end of the series
of measurements.

?) IsaacHsEn’s test of H,, has shown the great accuracy of these divided bar scales,
comp. Bureau Internat. 1. ¢. p. 39.

( 302 )

the menisci at the same distance from the cathetometer and to adjust
them with the screw both at the same time.

18. The elimination of variations in the barometer pressure. Ra-
pid variations of the atmospheric pressure are an important cause of
uncertainty in these measurements of pressure '). Though the telesco-
pes need not be moved along the scale, yet some five minutes must
elapse before the reading of the four heights is complete, and during
this time the variations in barometric height are often not negligible.

For example the readings on the 15t® Febr. were

2h 762.50
2h30 761.92
3h 761.51

330 761.30
4h30 760.80

Obviously the resulting uncertainty can be much diminished by a
suitable combination of the observations in special cases of the varia-
tion. Suppose for instance that the changes im atmospheric pressure
p are linear with time ¢ so that we may put p=p, + 7#, further
suppose that the changes in both limbs are equal and opposite in
sense, equally well in the barometer and manometer. When ¢ = 0,
let n, be the lower level, n, the upper level for the manometer, ng
and m, the same for the barometer, further suppose that the levels
are reread at intervals of one minute and that in the formula men-
tioned the time is measured in minutes. The real pressure is then
ny—n, + ny—nz- If we readin the order n,, m4, 3, m2 then the actual
readings are 7, 4 + 2, ny—2 7, ng—d a.

From this we derive

[nz — 30 — ny} + [mg + 2 — ng 4+ 2 a2] = (mg — mj) + (m4 — 0s),

The combination 73, ™j, 2, m4 leads to the same result, while the
insertion of the barometer reading between two manometer readings
AS yy Nyy Nyy N4y M1 MQ Also eliminates a linear rise or fall of the
atmospheric pressure.

We can also find a number of combinations by which a parabolic
variation can be eliminated.

1) Reanaunr, Mém. de I’Inst. XXI p. 69 says: Je ne crains pas (’exagérer en
posant en fait. quon ne peut pas répondre d’une mesure barométrique i plus de 1/19
de millimetre, quelque perfectionnés que soient Wailleurs les appareils de mesure.

( 303 )

Thus let p=p, + at+zt.

A first reading nj, 74 ng gives a second ngn, nj nq gives
ny n, —40 —16z
mat«wt+ 4 Ny —5 0 — 25%
mn; —2u—4%z n + 62+ 36%

Ng —3a—9% agt+ 72+ 49%
npg ping =n, = 4x Ng — Ng + Ng —n, +424

so that the mean of both gives the pressure at time zero independant
of a and z.

But in the first place we have not eliminated by this process the
capricious variations of pressure which often are of considerable
importance, and moreover if the pressure in the manometer had been
correctly determined at a given moment, we are not even then enti-
tled to assume that this is the pressure of the gas in the reservoir.
Especially to be certain of the latter it is desirable to remove as far
as possible the variations in the pressure.

To this end the manometer-tube is connected with the open limb
of the barometer by glass tubes of 3 m.m. diameter well packed in
wool (the wool packing has not been drawn on the plate, in order
not to render the drawing indistinct). In order to diminish the varia-
tions of the pressure which accompany the variations in temperature
of the air contained in these tubes, a bottle of 2 liters capacity is
included in the connections, this bottle being always immersed in ice
shavings prepared with the precautions of § 7’).

The total volume of gas contained in the manometer, barometer
and connecting tubes which is exposed to variations of temperature
is about 60 e.c. and thence the variation of pressure resulting from
a change of temperature of 1 deg. C. will be only 0.07 to 0.08 m. m.
This change can only take place so very slowly and regularly that
it may be eliminated by the choice of the order of observations
according to the above mentioned method. In a complete series
of observations the variations are always less than 0.1 m. m. and are
very regular. Thus on the 10% March we observed

1) The whole apparatus ean now be considered as a differental air thermometer,
We think that PraunDLER first used such an apparatus Sitzb. Wien (2) LXXII, 729.
1876. We found further that CaLLENDaR has proposed to connect the constant pres-
sure air thermometer with a space at standard pressure in order to ayoid the reading
of mereury columns. Phil. Mag. 5. 48. p, 540. 1899.

( 504 )

3h 750.47
3h30 750.50
4h 750.514

4h30 750.52

This arrangement also allows us to avoid the difficulty mentioned
in § 16 as arising from reading the four menisci with only three
telescopes. We have only to alter the pressure by a few centimeters
in the reserve bottle and in the tube connecting the barometer and
manometer with it in order to arrange that two of the menisci are
read either by one or by two telescopes.

19. Determination of the temperatures.

We must know the temperature of the reservoir and of the dif-
ferent parts of the connecting space, which latter consists of the
thermometer capillary outside the constant temperature bath, the
steel capillary and the volume near the point of the manometer-
tube (comp. Comm. N°. 27 § 2 and Pl. II, fig. 4°) where the
adjustments of the meniscus for constant volume are made.

During the determination of the zero the thermometer reservoir
and about 30 em. of the capillary are immersed in shavings of ice
(§ 7). A thermometer gives the temperature of the remainder of
the capillary which has only a very small volume.

Three thermometers are placed against the steel capillary and
divide this into two parts for the temperature of each of which we
assume the mean of those observed at the ends.

For the temperature of the volume near the steel point we read
the last thermometer on the steel capillary and those on each side
of the manometer. These differ only by two or three tenths of a degree.

During the determination of the boiling-point the reservoir and
nearly the whole of the glass capillary is immersed in the boiling
apparatus. The temperature of ebullition is computed from Brocu’s
tables '), in connection with which we used the value g = 9.81318 *)
at Leiden. The difference of pressure observed by the small water
manometer (comp. § 8), was allowed for.

The atmospheric pressure is read by an aneroide, which is
repeatedly controlled by the barometer.

The remaining 10 cm. of the capillary reach above the boiling

') Guintaume, Thermom¢trie de précision, pag. 327.
*) Determination by Dervorces and Bourerors 1892.

( 305 )

apparatus; for this part the mean of the temperature of the boiling
apparatus and of the first thermometer against the steel capillary was
taken; the temperature of the steel capillary itself is accounted for
as in the determination of the zero.

Special precautions have to be taken, that the temperature of the
steel capillary should not be too uncertain owing to the rising hot
vapours and radiation.

At a time when the steel capillary was packed only in wool,
but otherwise the arrangement of the boiling apparatus was that
shown in Communication N°. 27 Pl. III, fig. 1 we read on the
three thermometers :

3h 30 20°.7 14°.3 13°.5
4 30 20°.6 14°.3 13°.4.

And so the means were rather uncertain, due especially to the
conduction of heat which takes place at the beginning of the capillary.

To secure a more satisfactory protection of the capillary an india-
rubber spiral with water-circulation was placed on the thick wool
packing of the boiling apparatus, above this again large sheets of
paper were stretched at a few centimeters distance from each other.
Where the capillary passed through these protecting layers, which
shielded it from radiation care was taken that it fitted well in the
openings so that no hot air could pass.

The ascending hot vapours at the sides of the boiling-apparatus
were conducted at two meters distance from this through a chimney
made also of large sheets of paper, which were slightly inclined and
fitted well against the apparatus. With these simple arrangements
we succeeded in keeping the differences of temperature along the
capillary within the same limits as in the zero-determinations, and
hence they only depend upon the temperature of the room.

Thus on March 10 we observed:

3h 15°,6 15°,2 15°
4h30 15°,4 15°,1 14°,5

No special precautions were taken to keep the temperature of the
room constant. It is not difficult by means of heating and ventilating
to arrange that the variations of temperature do not exceed | deg. C.
in a series of observations.

The influence of the various sources of error resulting from the
uncertainty of the temperature determinations is considered in § 24.

( 306 )

20. The measurement of the volumes. The calibration of the
glass parts of the apparatus has been described in § 2. The steel
capillary has first been separately calibrated (filled by means of the
mercury pump), and again after having been connected to the
volumenometer tube, in which ease they are also filled by means
of the mercury pump. In this way the whole connecting space is
determined at one time. As the upper part of the volumenometer
tube has also been calibrated (Comm. N°. 27, p. 6) the two methods
include a mutual test.

3 measurements by the first | method gave on anaverage 749 mm%.')
3 IDS

5 : » 7» second i nT. OE s

The volume of the meniscus which we want for the determination
of the volume of the gas shut off by it, cannot in a tube of the
dimensions used, be considered as a constant?), derived from the
diameter and a definite assumed angle of contact. For the height
of the meniscus varied between 1.38 m.m. and 1.54 m.m., which
corresponds to a change of volume of about 10 m.m.*, if the top
of the meniscus is stationary, an accidental error that cannot be
admitted as we shall see later. The volumes are computed in each
ease from the height and the diameter like that of a spherical seg-
ment. The systematic error which then remains may be considered
to be small enough to be neglected (comp. § 24). We intend to
determine this volume still more accurately by fixing several points,
say three, to the upper surface of the connecting space, along one
diameter, and to measure the vertical distance of each of these 3
from the mercury, in order to determine the true profile of the
meniscus.

As a meniscus of 1.46 m.m. height occurred repeatedly, we have
considered this as the normal meniscus in a way to be later described
more in detail.

The coefficient of dilatation of the Jena-glass 16™ used indicated
by & was determined by us between 0° C. and 100° C. according
to the method of the weight-thermometer. We found & = 0.0000242.
The small difference from the value generally given for 16! i. e,
0.0000244 *) does not exceed the probable error. The variation of

1) The value 750 mm*. was taken after comparing the accuracy of each method.
2) As done by Cuarpuis |. c. p. dl.
3) Wiese and Borrcner l.c. give 0.0000240.

( 307 )

the volume under the influence of the pressure was determined as
in § 2. With a pressure of 1 atm., the variation of volume of the
reservoir was 4.64 m.m.3 at 15° C. We intend to determine the
amount of this correction for 0° C. and for 100° C. separately. For
the time being we have applied the correction found for 15° invariably
at 0° C. and at 100° C.

21. Modifications in the thermometer. Since the de-
seription given in l.e, §§ 2, 3,4, the following small alter-
ations have been made. In l.c. PI. II fig. 4 we see that
the cap with its capillary is pressed onto the ground glass
capillary of the thermometer-stem. But we cannot then
be quite sure that a perfect contact between the cap and
the upper side of the stem is obtained, and if this is not
the case the connecting space would be augmented by an
unknown amount. Now however to the end of the ther-
mometer capillary another, somewhat wider one (2 m.m.
diameter) is sealed on, into which the steel capillary is
placed (see fig. 5). This passes through the whole length
of the cap and projects beyond it for a few millimeters at
the other end. The connection then is made as in the
ease of the volumenometer (1. c. § 4) the space between the capillary is
entirely filled with sealing wax, the glass capillary is then placed into
it, which is easily done without there being any danger of the
steel capillary becoming blocked, as it projects a few m.m. above
the cap.

To mark off the irregular part of the capillary near the joint, two
marks are made on the glass. The volume of the space between
these marks has been accurately determined, as well as the sections
of the glass and the steel capillary; so that the exact volume is
known.

The connection of the volumenometer with the larger steel cap
on the steel capillary has on the whole remained the same. Instead
of sealing-wax we now use marine glue so as to render the chance
of cracks (causing uncertainty in the connecting space) and leakage
less. But this method requires the cap to be fixed by copper wire
in order to prevent it from being pushed off by the soft marine glue
under the pressure which obtains in the thermometer during the
determination of the boiling point. Lastly the small tube in fig. 1
and fig. 7. Pl. IL lc. is not sealed off any longer, but it is now
provided with a small glass cock. As the apparatus has already
been provided with a cock (& ibid.), this does not involve any new

WAG
WAS

SEIN pn

Fig. 5.

( 308 )

difficulty; the new cock is very useful whenever we want to alter
the pressure of the gas, or to fill the thermometer with another gas.

24. The preparation of the pure hydrogen. The apparatus used
for this purpose (1. ec. §5) has also undergone a few small altera-
tions. In the first place several indiarubber connections have been
removed. ‘The two storage-bottles for hydrochloric acid and potas-
sium hydroxide solution (d and e fig. 3 Pl. I comm. n°. 27) are
now like the WouLr’s wash bottle closed with ground stoppers and
the screw clamp C’ has been replaced by a mercury-closure. The
large drying-towers 7, ¢ are replaced by a U-shaped tube, closed
with ground glass stoppers. Even with careful heating of both the
glass and the india-rubber, it requires much care to make india-
rubber fittings on glass by means of sealing wax perfectly trustwor-
thy; if as often is the case some solution of india-rubber is applied
between the glass and the india-rubber, the solvent evaporates in the
vacuum and the high degree of purity, as we require it for our
hydrogen, is altogether lost.

Lastly for the preliminary filling we no longer use commercial
hydrogen, but hydrogen prepared from pure zine and hydrochloric
acid in a separate glass apparatus.

23. The calculation of results. Our determination comprises the
reading of the menisci and of the various thermometers.

Suppose the reservoir is at fC. Let Hy be the pressure of the
included gas corrected for the temperature of the mercury and the
compression of the latter under its own weight (to be neglected); the
correction applying for the value of gravitation will be discussed later.

Let V, be the volume of the reservoir at 0°C and under the pres-
sure of the gas during that time.

w, the volume of that part of the glass capillary which
is at the temperature ¢ of the reservoir.

Ug the volume of that part of the glass capillary which
is not at the temperature of the reservoir but at the
temperature fg.

wu, and ws the volumes of those parts of the steel capillary

where the temperatures are fs and ft.

U
the variation of the volume V, of the reservoir caused by
the pressure.

=

; the volume near the steel point in the volumenometer.

( 309 )

The volume w; and the temperatures are different for different
determinations, therefore it is desirable to apply corrections which
reduce them to a definite volume w, and definite temperatures.

From the temperatures observed we calculate the pressure, which
would be found under the following circumstances: the whole of the
thermometer capillary is reduced together with the glass reservoir
to the same temperature @°C, differing very little from ¢. Moreover
the entire connecting space must be reduced to 15° Cand this space
must be closed by a meniscus of 1.44 m.m. height touching the
point of adjustment in the volumenometer-iube. Let w be the con-
necting space thus determined. Under these circumstances the fol-
lowing equation will hold- for the pressure, which we call the
reduced pressure H;.

Vij(l+h)+ 2+ Ug Us Us Us
r| l+eat SUR Tap Sa TCR Tee wa tal=
(1) = H; {ze (1-- 4 @)+B+2, +p u
l+ad 1a thi

in which & is the coefficient of expansion of the glass and « the
coefficient of pressure variation of the gas between 0° C. and 6° C.
The differences of the small ws at the temperature of calibration
and at the temperature of observation are too small to he accounted
for’). The corrections from Hr to Hy are made with an approximate
value of a, for which we took 0,003662.
The values of 9, which are now important to us, are 0°C. and
100° C. For all corrections at the same temperature the value of
Hi, is a definite amount, which therefore can be calculated once for
all. The calculation of the value between [|] to the left may be

. u
shortened by computing tables of the values of ——“—, as the
& ty
temperatures #3, t1, ¢; never deviate much from 15° C. 2),
The pressures reduced in this way correspond therefore to the
following circumstances :

At 0° C. a volume Vp -+ u+ uw, at the temperature 0°
ib}
” n

Uu
”
At 100° C. the volume of the reservoir has become Bs

) As for u,, this volume itself is extremely small, and as for uw, v5, us, v; the
difference of ¢,, é,, ¢,, ¢; from the assumed standard temperature 15° C. is very small.
*) Cuappurs 1. c. pg. 53.
21
Proceedings Royal Acad. Amsterdam. Vol. III.

( 310 )
Vy (1+ 100%) +f,
and hence the circumstances are:

V, (1 + 100 4) + 2+ + % at the temperature 100°

& » n Py 15°

@ is then found from !)

u (Vou —-ug)(1-+1004)+/ u
=“ [Votan put mete =Hyo| 11100 a oe
f $f: u 1 aie)
Cag ed Vetus, 1-150 as

Fo 2

same gles Vou Ue e

This equation can be solved by successive approximations, bearing

in mind that Ho, and 4p include corrections depending on @. Hyoo

and H, might then be computed anew with the new value of 2,

and the equation solved anew. The number 0,003662 used by us

in the first approximation is in such good agreement with the correct

solution, that in this case it was not necessary to make a second
series of calculations.

Gli. f
24. Influence of errors*). 100 da = = is easily found when dh
0
is the error in one of the determinations of pressure Hjo, or Hp.

For the accuracy of reading with a cathetometer we may assume
dh =0""01 mm., and to this value corresponds da = 10—‘, an error
which will be perceptible as a unit in the seventh place of decimals
and would change the value 0,0036627 into for example 0,0036628.
The other errors are best considered by reducing them to errors in
the reading of pressure. As for the connecting space which as com-
pared to the reservoir was very large (over 0,01)*) owing to the
special arrangement of the thermometer for very low temperatures,
a reading error in the distance from the meniscus to the point of
0,01 mm., which corresponds to 1,2 mm® error in wu, gives an error

1) Comp. Cuarpurs l.c. p. 52.

*) Comp. Cuappuis, |. c. p. 56.

Wiese en bérrcuer, Zeitschr. f. Instrumentenkunde 10, p. 233. 1890.
*) As in the case WreBE and BorrcnHer Lc.

( 311 )

of 0,01 mm. in the pressure at the zero or 0,02 mm. in the pres-
sure at the boiling point; incorrect determination of volume of
parts of the connecting space causes a similar systematic error.

The capillarity leaves an uncertainty which we estimate at less
than 0.03 m.m., the volume corresponding to the uncertainty of the
form of the meniscus remains below 3 m. m.*, corresponding to 0.03
m.m. and 0.06 m.m. in the pressure; the systematic error, which
thus can arise in @ does not reach 3,10-7.

An error of 0.°01 C in the boiling point gives an error of 0.04
in the pressure; 0.°2 C error in the temperature of the capillary
changes the pressure about 001 m.m. near the zero. In this respect
no other than accidental errors are to be feared. Taking all toge-

ther an accidental error of say 3 units in the last decimal (10-7)
is to be feared. The systematic error may reach the same value.
To illustrate the favourable influence of the precautions mentioned
in §§ 18 and 19, especially of those relating to the removal of the
variation of the atmospheric pressure, we give here a few observations
of the zero, made in February without these precautions but otherwise
under the same circumstances as the series of March in § 26.

In February In March
we found on 4 days: we found on 3 days:
AH, = 1098.24 H, = 1098.35
1098.15 1098.36
1098.08 1098.37
1098.65

In the first series the deviation from the mean rises to 0.4 m.m.,
which corresponds to nearly 0°.1 in temperature, a sufficient accuracy
it is true for most determinations at low temperatures, but much
smaller than we have attained with our apparatus when all
the above mentioned precautions have been taken. The deviation
0.01 m.m. from the mean in the series treated in the latter way
corresponds to 0°.02 or as mentioned above to a unit in the
seventh decimal of the coefficient of pressure variation.

At the boiling point we found on 3 days (comp. § 26).

Hyp) = 1491.04
1491.00
1491.05

The deviation is here twice as large, but yet exceedingly small,
whereas formerly, when the capillary was not so well protected,
deviations of several tenths of m:m. occurred.

It is therefore useless to consider the previous determinations of

the zero and the boiling point with a view to the coefficient of
21*

( 312 )

pressure variation to be derived from each pair of them. These are
only of importance for the measurements at very low temperatures
made at the time.

25. Survey of a determination. In the annexed table all the read-
ings of one determination are given, but in order not to make the
scheme too intricate the means of usually three single readings which
never differ by more than a few hundredths, are given as the normal
readings.

Column A gives the reading on the micrometer heads of the cathe-

March 10 3 10 A. B. C. D. KE. F. G. LE
; 1028 23.42 5.5
Point. 24.19 5b 1029 25.51 5 5
G 1028 23.42 5.5
lower fop...| 24.36.) 5.5) 1999-198 -61-Jea5 25
S \ meniscus. aa 1029 | 25.51 | 5.7 | 15°0 | 16°92
basis 27.44 | 6-0 1030 | a7i61 | 5:7 | 14°8 | 1598 |) adee
oOo
a
S 989 18.86 7-0) 5 96) ase6
= upper TP ERIE | 2 283 | 20.86 | 7.0
meniscus. P 983 20.86 7.0
basis.| 21.97 7.0 984 22°89 70
1027 21.30 bed
lower) Pee alee alee alargag 23.49 | 5.5
a meniscus. . 9¢ 1027 .30 5.5 | 1402
e basic}: 72:20) @-5 | j098)| 98.481 Osea Tacs
a
S 276 6.70 6.0
a upper top. 7.88 6.0 27 8.73 6.0
meniscus. : Q aa 6.0
basis. 8.99 6.0 978 10.75 6.0
; 1028 23.42 5.5
Ibwer fC |) Bel 82 1 Sioag | ace aan
m meniscus. fate 1029 25.51 Bay | LbS2ei 685
< basis, 27.43 | 6-0 | 3930 | 97:61 | 5.7 | 1400 | 16°0 | 14°4
5
a 282 18.86 7.0 | 16°O | 1592
e se top. | 20.40] 6.8 255 | 20.85 | 7.0
meniscus x 3 86 | 7.0
basis.| 21.90 7.0 984. 9989 70
: 1028 | 23.42 | 5.5
Point. 24,99 5.5 1029 95 51 Reb
Aneroide 771.3 Temp. 14°,3

‘Water-manometer + 1 mM.

tometer telescopes, B gives the reading on the levels of those tele-
scopes '), C the nearest division of the graduation on the standard-
meter 2), D and E the readings of the head and the readings of the

1) This reading is not mentioned by Caapputs,
*) Comp. footnote 1, p. 6. *

( 313 )

levels during the adjustments to those divisions. The three last
columns refer to the temperatures. F gives the temperatures readings
of the manometer and the barometer, G those of the capillary, H
of the standard scale.

With these numbers we first compute the readings on the standard-
meter, with allowance for the levels. Then the thermometer readings
are corrected.

In the next table column 4A’ gives the level of the top of each
meniscus and the value of the height of each meniscus.

Column B' gives this level corrected for the capillary depression,
C' the corrected temperature of the mercury columns. D' the cor-
rected temperature of the capillary. E’ the sum of the mercury
columns corrected for the temperature and lastly F’ the distance
from the top of the meniscus to the point.

| A! B! |} © D! E! ¥
_ | lower meniscus. 1025.45 | 1028 29 | 144
: | height. 1.46 13.9
E | upper meniscus. 282.76 | 282.69 | 15.0 15°6
a mm mm
height. 0.76 15°2 | 1492.57 0.09
lower meniscus. 1027.05 | 1027.05 15°0
5| height. . 0.37 14.2
3 upper meniscus. 276.58 | 276.58 | 14.5
% | height. 0.54

Pressure of the water-vapour 771. 6 m.m. Leiden.
771.25 level of the sea 45° L.

by] n ”

From the means in pairs of column D' follows the temperature
of the capillary, from the height of the meniscus and the distance
from the meniscus to the point given in F’ follows the correction
for the space between the horizontal plane through the point and
the meniscus. A correction 0.07 m.m. for the difference in level
of barometer and manometer is then applied to the pressure according
to the law of the communicating tubes !),

*) The difference of pressure between reservoir and manometer — a correction the
necessity of which was remarked by Dr. vy. EverpincEn — could be neglected, the gas
being hydrogen and the difference of level of reservoir and manometer small,

(314 )

So we get the following table:

Volume. Temperature. Pressure Ht
V, (1 kt) + u,| 82.333 | t — 100044
Us 05009) t,—= 602
mm
Us, 0.444 | t,— 15°4 | 1492.50
u, 0.306 | 1,— 15°1
uU; 0.218 | t, == 14°7

The pressure has not been reduced here to the absolute value as
in the case of that for the boiling water, because for the following
calculations relative values are sufficient.

The reduced temperature Hj 9 according to the equation I is now
found from:

82.333 0,009 0.444 0.306 0.218

14100.44@ '1460@ ' 1415.4e@ '1415.la@ ' 1414.7¢
—— 61,177 Ay o0°

1493.50

Ayo) = 1491.03 m.m.

(2 can be left out in this reduction calculation.)

26. Results. Here follow the values found for H, and Hjo9 from
determinations according to the method § 25.

3 March 7 March 13 March
H, = 1098.38 Hy = 1098,38 H, = 1098.34
35 37 30
29 32 38
31 33 mean 1098.34
29 32
mean 1098,32 28
29
mean 1098.33
2 March 8 March 10 March
yo) = 1491.05 Hyo9 = 1491.01 Hyo9 = 1491.03
05 O01 08
07 1490.98 10
06 1491.00 00
1490.96 1490.98 mean 1491.05
96 1491.02

mean 1491.02 mean 1491.00

( 315 )

2p
Vo +u+uy
(1 + 109@) (1 — 0,00395) = —. 1,00245

oO

The equation (2) of § 23 becomes with 100 & + = 0,00245

With the values:

3and 2 March H, = 1098.32 Hj) = 1491.02
Zand 8 March AH, = 1098.33 Foy = 1491.00
18 and 10 March H, = 1098.34 Hyon = 1491.05

We find therefore (Comp. § 24):

3and 2 March a = 0,0036628
Zand 8 March a = 0,0036624
13 and 10 March a = 0,0036628

while the mean of the three determinations is
a = 0,0036627

Mr. CuHappuis was kind enough to send us a survey of the
values obtained by him by means of the apparatus of the Bureau
International !); they are the results of many and very carefully
made determinations. Different apparatus for which the degree of
precision was not the same were used for them.

In the large gas thermometer the relation = (about 0.001) is

o
more favourable than for the small one (0.003); measurements of
the pressures in the former were much more accurate.

With the large gas thermometer for an initial pressure of 1000 m.m.
he found in

1887 platinumiridium reservoir of 1 Liter 0,09366225—0,00366271

in 7 determinations, mean 0,00366254

1889 platinumiridium reservoir 0,00366286—0,00366307
in 4 determinations, mean 0,00366296

1895 reservoir of ,,verre dur” 0,00366201—0,00366224
in 5 determinations, mean 0,00366217

1) M. Pernet, who made the first experiments with the hydrogen thermometer at
the Bureau International found 1884: 0.0036654 at 914™™. initial pressure
0.0036652 at 955mm. ”
Proc, Verb. 1885.

( 316 )

These observations relate to three different fillings. The mutual
deviations in our determinations with a small transportable apparatus
constructed especially with a view to the measurement of yery low
temperatures appear not to be larger than those in CHapputs’ results.
Also the deviation of our mean value from that of CHAPPUIS is
within the limits of deviation of his determinations with the large
thermometer. . We give here in addition the observations with
Cuappuis’ smaller apparatus:

1890 reservoir of ,,verre dur” 0,0036616—0,0036645
1st filing, 7 determination, mean 0,0036629

1890 24 filling, 0,0036630—0,0036642
in 4 deterinination, mean 0,0036638

and the observations with the slightly varied initial pressure of
788 m. m.

1894 reservoir of ,,verre dur” 0,0036624—0,0036638
in 6 determination, mean 0,0036628
1894 reservoir of ,,verre dur’, 0,0936621—0,0036626

mean 0,0036624

As could be expected larger deviations were found with this than
in the determinations with the larger apparatus, in which the utmost
accuracy was the chief object.

Physics. — Dr. E. van Everpineen Jr., “On the Haut-effect
and the resistance of crystals of bismuth within and without
the magnetic field”. (Communication N°. 61 from the Physical

Laboratory at Leiden, by Prof. H. Kamerninen ONNES).

1. In erystals of bismuth it is not possible to give one definite
value to the HHaAtu-coefficient or to the increase of the resistance
in the magnetic field; on the contrary these quantities depend to a
considerable extent on the position of the principal crystallographic
axis with respect to the lines of magnetic force and the direction
of the current. This follows from my measurements, published in
the Proceedings of April 21, 1897, p. 494 and June 26, 1897,

( 317 )

p- 68 +). One of the hypotheses, introduced in order to explain the
observed phenomena, amounted to this, that no increase of resistance
would oceur in the direction of the magnetisation. It would however
have been sufficient to suppose, that the imcrease of resistance is
smaller in the direction of the magnetisation than in the transverse
directions. In order to allow of a decision between these suppositions,
the increase of the resistance of the bars of bismuth N°. 1, 2 and3
from the crystalline piece of bismuth from Merck *) formerly men-
tioned, were measured once more while they were placed in the
magnetic field with their longest dimension in the direction of the
lines of force.

The results obtained with these bars made it appear most de-
sirable to repeat the experiments with other and if possible better
erystalline material. The remarkable results obtained by Mr. F.
Louis Perrot at Genéve for the thermo-electric constants of erys-
tallme bismuth *) induced me to communicate with him. With extra-
ordinary kindness he has put at my disposal one of the prisms of
bismuth *) cut by himself with great care from a block of slowly
cooled bismuth, for which assistance I take this opportunity of
expressing my best thanks.

The complete results of the investigation on resistance, increase
of resistance and Hauu-effect in the bars cut from this prism I hope
soon to publish; at present I wish to communicate separately a new
particularity with respect io the Hatt-effect which occurred during
this work.

2. The observations lead to the following conclusion:

A bar of bismuth cut at right angles to the principal crystallo-
graphic axis, shows, in a magnetic field of about 5000 C. G. S. units
when placed with the principal axis | the lines of force, a Hati-
coefficient of normal magnitude and negative sign (normal); when
placed with the principal axis || the lines of force, a smaller,
positive Ha.t-coefficient.

Hence the same bar of bismuth which in one position shows a
Hatt-effect similar to nickel for instance, after having been turned
through 90° about the direction of its longest dimension, shows a
Haut-effect similar to tellurium and antimonium.

The positions of the various bars before they were cut from the
crystal is shown in fig. L (2 X nat. size).

*) Comm. Phys. Lab. Leiden, N°. 37, p. 7, N% 40, p. 3.

*) Versl. d. Verg. 21 April 1897, p. 500. Comm. N°. 37, p. 16.

*) Arch, d. Se. phys. et nat. (4) 6 p. 105 and 229, 1898, 7 p. 149, 1899,
*) Areh. d. Se,-phys, et nat. (4) 6 p. 121, 1898, Prism A.

( 318 )

ipa

The principal axis, derived
by Perror from the position of
the cleavage planes and charac-
terised by the thermo-electric
properties is indicated by an
arrow. The bars 1, 2 and 3
have been cut along the three
edges; 4, 5 and 6 with their
longest dimension stili parallel
to one of the sides, but at angles
of 30° or 60° to the edges of
that side. If the crystal were
completely homogeneous, No. 2,
3 and 5 fulfill the condition of
being cut perpendicularly to the

principal axis and ought to obey the rule given above.

The table below gives the results for the Hatt-coefficient in two
magnetic fields for each of the bars in 4 positions, always with the
longest dimension perpendicular to the lines of force, but differing
by consecutive rotation through 90° about that longest dimension.
The numbers united by brackets refer to positions differing by 180°;
in accordance with PeRRoT we indicate the positions in which the
principal axis is perpendicular to the lines of force bij J, the other

positions by |].

Hatt—coefticient R.

a: II
MAGNETIC FIELD.
N°
5000 2900 5000 2990
— 99 ei BD — 0.15 — 0.70
Q
(] == Gg ) = TH) (e028 { — 0.51
(val 8.0 ( — 101 + 0.16 — 0.10
3 .
fe——70 sing Se { — 0.56
(oar any, ( £0.58 ( 036
y { — 74 {(— 96 ( + 0.56 { + 0.19

(319 )

A single view of the vertical columns and the corresponding
positions | and || in a horizontal row is sufficient to carry the
conviction, that the above mentioned relation of the Hant-coefficient
to the position of the principal axis with respect to the lines of
magnetic force not only is confirmed, but is even more marked than
was found before. The new rule however, so far as the positive
sign is concerned, is not satisfied in one position of 3 and in both
positions of 2. The following remarks indicate why I nevertheless
regard the results with 5 as normal.

1°. No certainty exists as to whether the original crystal was
perfectly homogeneous, though it is certainly the most regular piece
of bismuth ever tested for Haut-effect. Perrot himself admits the
possibility that small irregularities, ,macles” are present. If this be
the case they are very probably most important at the edges, and
hence particularly in the bars 2 and 3. The rather large discrepancy
in bar 2 between the bracketed values indicates that this especially
cannot have been quite homogeneous. Taking for granted that the
rule given at the head of this § holds, irregularities can only alter
the Haut-coefficient by a negative quantity in the position ||, and
it would not require many to make that coefficient change sign
altogether.

2°. Considering that a rotation of 90° at all events considerably
alters the Hatt-coefficient, the position of the bars would of course
require to be regulated very accurately in order to exclude errors.
With bars of about 3 mm. thickness it will not be astonishing
that this accuracy was not attained. Here as well as with the first
source of errors only diminution of a positive coefficient or even
change into a negative one is to be expected. I suspect that this
cause occurred with 3, the more so because in an experiment made
some months ago in the first position || we also found a positive
value but smaller than 0.16. On the contrary the value + 0.58 for
5 is a mean of values + 0.57 and + 0.59 obtained in rapid suc-
cession.

The observations further agree in this that a decrease in the
magnetic field always causes a variation of the HALt-coefficient in
the position |] with a comparatively very large negative value. This
gave rise to the supposition that the reversal of sign observed with
3 between 5000 and 2900 might occur with the other bars between
other limits. With 2 this remains to be tested, but requires stronger
fields. With 5 however in the first position || in a magnetic field

( 320 )

of about 1300 C.G.S. —0.06, in the other position about 0 was really
found, so that the supposition was here confirmed.

IT am unaware of any disturbances which might cause an apparent
positive Hawt-coefficient in the method used by me. Only if the
galvano-magnetic difference of temperature should rise here to an
appreciable value much faster than usually, for instance in one second,
it might have an influence to that effect. During the experiments
there was no sign of this, and I consider such a disturbance to be
quite improbable.

3. Certainly it will not be easy to give an explanation of these
variations based upon the electron-theory. It seems however to me
as if the reversal of sign need not represent a special difficulty,
particularly because the theory had to reckon already with reversal
by other influences. We take as an example the simplest theory
which assumes the Haut-effect to be proportional to the difference
of the migration-velocities (w—v). Usually in order to explain
the phenomena in bismuth it is assumed that v is especially
important, which constitutes an analogy with cathodic rays and
the ZerMaN effect. Hence in order to get a considerable variation
of the Hawt-coefficient it is certainly necessary to decrease v con-
siderably. If this is carried far enough a reversal of sign of u—v
may be expected. Should the objection be made that wv here appears
to be a non-negligible quantity, I can only remark that the positive
value obtained for D (rotation of equipotential lines) for bismuth is
even smaller than that for antimony and tellurium: and hence this
does not constitute a new difficulty.

Reversal of sign was observed in consequence of:
a. Variation of temperature, with nickel, by CLoucH and Hat),

b. Variation of magnetic field, with alloys of bismuth with
1—6 pCt. of tin, by v. ErrmncsHausen and Nernst *); with
impure bismuth, by BratTis *).

ce. Addition of an other metal in a constant field with bismuth
mixed with increasing quantities of tin, by v. ErtinasHAUSEN
and NERNST?).
To this we can add now as fourth cause:

1) Proc. Amer. Acad. 20 p. 189, 1893.
2) Wied. Ann. 33 p. 474, 1888.
4) Trans, R. Soc. Edinb, 38(1) p. 225, 241, 1896.

( 321 )
d. Variation of position with respect to lines of magnetic force,
in crystals of bismuth.

As mentioned before, in our experiments J also occurred.
In conclusion we note the fact, that increase of magnetic field
always alters the Haut-coefficient by a positive amount, which

seems to indicate that the influence of this increase is felt especially
in v}).

1) See § 6 Communication N°. 58, Versl. Kon. Akad. v. Wetensch. 30 Juni 1900,
p. 195, Comm. N°. 58, p. 23.

(October 24, 1900.)

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday October 27, 1900.

————S eS Oe

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 27 October 1900 Dl. IX).

Contents: “On the pedal circles of the point-field in reference to a given triangle.” By Prof.
JAN DE Vries, p. 323. — “Experimental determination of the Limiting Heat of
Solution.” By Dr. Ernst Conen (Communicated by Prof. H. W. Bakuuis RoozEBoom),
p. 827. — “Contributions to the knowledge of some undescribed or imperfectly known
fungi” (8rd Part. By Prof. C. A. J. A. OuprEmans, p. 332. — “On the MacManon
genelarization of the Newron-Girarp formulae.” By Prof. L. GeagensBaver (Com-
municated by Prof. JAN DE Vries), p. 347. — “On different forms of hereditary
variation of microbes.” By Prof. M. W. Brrseninck, p. 352. — “On the development
of Buds and Bud-variations in Cytisus adami.” By Prof. M. W. Berserinck, p. 365. —
“On the permeability of the red bloodcorpuscles for NO ;- and SQ,-ions’. By Dr.
H. J. Hampurecer, p. 371, — Erratum p. 374.

The following papers were read:

Mathematics. — ‘On the pedal circles of the point-field in reference
to a given triangle.” By Prof. JAN DE VRIEs.

(Read September 29, 1900)

1. If P,, Po, P; are the orthogonal projections of the point P on
the sides of the triangle A; 4,43, the circle a passing through
F’,, Ps, Ps is called the pedal circle of P.

If a intersects the sides of the triangle for the second time in
D', P,', P;', these three points are the projections of the point P’
isogonally conjugated to P, i.e. the angles Az A) P and P' A, 4,, are

22

Proceedings Royal Acad, Amsterdam. Vol. III.

( 324 )

equal. In other words, P and P' are the real foci of a conic
inscribed in the triangle A, A, As.

So each circle 7 belongs to two points P. These points coincide
for each of the four circles touching the sides.

The point P being situated on the circumscribed circle A, Ag As,
the circle a degenerates into the right line p of WaLLace (Srson)
belonging to P and the right line at infinity; P is the focus of a
parabola inscribed in 4\4243. The right lines p envelop the well-
known tricuspidal hypoeycloid, discovered by SrTe1Ner, for which
curve of the third class the right line at infinity is the isolated double
tangent.

2. Through two points P; and P2, lying respectively on aj=A3Ay
and ay = 4, 43, three circles a pass. In the first place of course
the pedal circle of the point P of which P; and P, are two projec-
tions. If a point Q describes the right line 4 cutting a, orthogo-
nally in P;, the locus of the isogonally conjugated point Q' is a
conic 4, through 4), 4), 43. With the right line J, cutting ag ortho-
gonally in P, this parabola has two points Q' and #' in common, of which
the isogonally conjugated points Q and #& lie on 4. Evidently
the common pedal circle of Q and Q' passes through P; and Po;
in like way these two points lie on the circle a belonging to
Rand RF’.

If we take P at infinity, these three circles degenerate into the
three right lines of WALLACE meeting in P;.

3. The locus of the pairs of points P,P’ collinear with a given
point A is a cubic «@, generated by the pencil of rays (4/) and
the projective pencil of the conics isogonally conjugated to those
rays. Evidently this curve passes through the vertices A), A, A,
and through the double points of the correspondence, i.e. the
centres J of the four circles touching the sides. If M is to be
the. mid-point of two conjugated points P,P’, then the point har-
monically separated by P,P’ from 4 must lie at infinity; so it
must be one of the points of intersection of the right line +, with
the polar conic of Mf with respect to ¢@). Now this conic passing
through the four points J is an orthogonal hyperbola; consequently
we can draw through M two lines normal to each other, each of
which contains a pair P, P’.

But one of those pairs is imaginary. For, a conic touching the
three right lines A; A; is entirely determined if its centre 41s known;
so of the two pairs mentioned above one consists of the real, the
other of the imaginary foci of the conic.

( 325 )

For the ellipse a?y?-+ l?2?=a?l*® the pedal curve of the real
foci is the circle 2? + y? =a*; the projections of the imaginary foci
«= 0,y= + ci on the tangents lie in the circle x? + y? = B?,

Evidently this second circle becomes imaginary for the hyperbola;
it becomes a point circle at infinity for the parabola. For the curves
of the second class, of which the tangents form two pencils of rays,
the circle 2?-+ y4?=0? degenerates into a point as well. For, the
tangential equation a*u*+-b?v?=1 of the ellipse is transformed into the
equation of the pair of points «= + a,y= 0, if b is made equal
to zero.

4. By what precedes is proved that each point of the plane ®
in which the triangle 4, 4g 4; lies, is the centre of two circles z.
If, following FrepLer, we represent each circle a by its two poles
on the sphere of which 7 is a main circle, we obtain as represen-
tating surface of the system (a) a surface « of order four placed
symmetrically with respect to ®.

With the aid of w we can easily show that any two points
S; and S, taken arbitrarily lie on three circles a.

For, the circles through S, and S, are represented by an orthogonal
hyperbola y@) of which the plane bisects the right line S, S, ortho-
gonally, the asymptotes intersecting the plane ® at angles of 45°.
Now the points of contact of the asymptotes are to be regarded as
images of the only tangent of the previously named hypocyeloid
having the direction of S, Sj. The remaining six points of inter-
section of y® and wv originate from three circles z.

5. However, three pairs of points can be indicated each of which
lie on an infinite number of circles z. For, if P is a point of A) As,
its pedal circle passes through 4) and the projection By of Ay on Ay As.
From this follows that the plane 7), intersecting ® orthogonally
in the line connecting the mid-points C; and C; of A; Ag and A, As,
contains an orthogonal hyperbola situated entirely on «@).

This plane touches «“ along the right line C, C3. For each
point of this line must be regarded as the centre of a degenerated
eurve of the second class.

So the intersection of «“) and ® consists of four right lines, i. e.
the lines ©; C; and the right line at infinity.

The lines C, C2, C2 C3, C3 C; divide the plane # into seven parts.
If lies inside the triangle C, C, C3; or in one of the angles formed
by producing two sides, then the corresponding conic is an ellipse
and M accordingly the projection of four real points of the represen-

22*

( 326 )

tating surface. If on the contrary ¥ belongs to one of the parts
of @ limited by a side and the productions of the two other sides,
the conic is an hyperbola, so that 1 determines but one real circle
mz and is consequently the projection of two real points of «@).

So in each of the ‘elliptic cases” formed by the planes 7.72.73
lies a sheet of «@, intersecting ® orthogonally in three right
lines and possessing a singular point in the two images of one
of the points J.

The four sheets coincide in the six nodes, which are situated in
Ci, Cy, Cg, and on C;, Cy, Cy C3, Cg C, at infinity.

The “hyperbolic” parts of se pass into the “elliptic” parts along
the hyperbolae situated in the tangent planes yz.

The plane, bisecting orthogonally an angle of the given triangle
or its supplement, containing four nodes, intersects «4 according to
two conics meeting ® on the right lines C, C and at infinity. Con-
sequently one of these conics is a parabola, whilst the other one
must be an orthogonal hyperbola, because its points at infinity are
the images of the right line of WaALLAcE perpendicular to the plane
of division,

6. The circles 2, passing through a point D and touching a
right line J, are represented by two parabolae, of which the planes
form with @® angles of 45°. They have four points at infinity in
common with «@; the remaining points of intersection indicate six
circles.

This result is found back by searching for the coincidences of the
correspondence (3, 3) which is determined on / by the circles 2
containing D.

The circles touching two right lines 7 and m are represented by
four right lines; these determine on «@ the images of eight circles
a having / and m as tangents.

If / and m coincide with two sides of the triangle A; Ag As, the
eight circles coincide two by two in the four inscribed circles.

Prof. ScHouTe draws attention to the fact, that the surface inves-
tigated by the speaker may be called “wave surface of the inscribed
conics”, the cyclographic representation demanding simply that on
the perpendicular to the plane in point ¥@ we take on either side
points, the distances of which to the plane are equal to the two
axes of the inscribed conic having M as centre. The nodes corres-
ponding with the inscribed- and escribed circles are the points of
“conical refraction”’.

( 327 )
The equation of the indicated surface is

(ax + by + ez) (by + cz — ax) (cz + ax — by) (ax + by — ez)
— 16 (22 sin2 A+ y® sin2 B+ 2% sin2 C) I Rw + 16 /?ut= 0,

if z,y,z are the usual trilinear coordinates, u denotes the distance
from the point to the plane of the triangle and a, ,c, A, B,C, 7, R
indicate as usual the sides, the angles, the area and the radius of
the circumscribed circle of triangle ABC.

Chemistry. — ‘Kxperimental Determination of the Limiting Heat
of Solution” (First Part). By Dr. Ernst Conen (Commu-
nicated by Prof. H. W. Bakuuris Roozepoon).

(Read September 29, 1900.)

1. When a substance is dissolved in any medium a quantity of
heat appears which is generally called the “heat of solution’.

It has been shown, particwarly by vAN DEVENTER and VAN DE
Srapt!), that this universal name may easily lead to confusion.
They point out that a precise definition is necessary as the quantity
of heat which is generated (for instance, when dissolving a salt in
water) depends on the amount of substance already present in the
solvent.

If equal quantities of a salt are successively introduced into pure
water each quantity on dissolving will produce a different heat effect
so that there really exists an unlimited number of different heats
of solution which each depend on the concentration of the liquid
into which the new quantity of the salt is introduced.

If a certain quantity of a salt is dissolved in a large amount of
water so that the solution is so dilute, that on further dilution no
heat is evolved, the heat effect accompanying the dissolving is called
(by v. DEVENTER and y. D. Srapr) the “first heat of solution”
(calculated on 1 gram-molecule of salt), This is the quantity which
is generally called the “heat of solution” and which has been deter-
mined for a large number of substances by BerTHEeLoT, THOMSEN
and others.

This heat of solution is also called “heat of solution in much
water’ or “heat of solution to extreme dilution”.

1) Zeitschrift fir phys. Chemie, 9. 34 (1892),

( 328 )

As the quantity of heat evolved during dissolution, depends on
the concentration of the liquid employed, each fresh quantity of salt
will cause a different heat effect until the solution has become
saturated.

Each of these heats of solution excepting the last, is called an
“intermediate” heat of solution. The sum of the intermediate heats
of solution is called the “integral” or “total” heat of solution or
also “heat of solution to saturation’.

2. The last term of the integral heat of solution is particularly
important theoretically. It represents the quantity of heat evolved
when a salt (calculated per gram molecule) dissolves in its own
saturated solution.

This quantity of heat is called “fictitious”, theoretical or ideal
heat of solution also “/ast or limiting heat of solution’. It is this
factor which plays a great part in the thermodynamics of solutions;
we refer to the expressions given by v. D. WAALS!), vAN Tt Horr?),
Le CHATELIER ?) and Bakuuris Roozesoom*) for the relation between
the solubility and temperature.

Le CHATELIER and BAakHuis Roozesoom already pointed out and
ReICHER and VAN DEVENTER demonstrated experimentally that there
can exist a great difference between the first and the limiting heat
of solution and that they may even have a different sign °).

That these quantities coincide in the case of substances which
are but little soluble, will be easily understood.

3. Only the ,first heat of solution” is accessible to determination
by a direct calorimetric method. The other heats of solution may
be calculated from the heats of dilution, by means of Hess’ law,
then from the table of the heats of dilution of solutions of different
concentrations and from the first heat of solution the heat effect
may be calculated with which increasing quantities of salt dissolve
in a definite volume of water, and from this the heat of solution of
the last quantity may be obtained by extrapolation.

1) Zittingsversl. Kon. Akad. van Wetensch., 28 Febr. 1885.

2) van “vw Horr, Lois de lEquilibre chimique ete. Kongl. Svenska Vetenskaps
Akad. Handl. 21. 17 (1886). Osrwanp’s-Klassiker 110. Translation by Brepte, 8. 55.

) Recherches expérimentales et théoriques sur les équilibres chimiques. Extrait des
Annales des Mines, ‘ivraison Mars—Avril 1888, p. 138. (Paris, Dunop).

4) Rec. des Trav. chim. des Pays—Bas 8, 123, (1889).

5) Zeitschrift fiir, phys. Chemie 5, 559 (1890).

( 329 )

Tt will be easily seen that the accuracy of such a calculation will
leave much to be desired and this is why, thus far, the limiting
heat of solution is but approximately known in a few instances.

4. I now wish to describe two methods for the determination
of the limiting heat of solution which do not differ in principle
although at present for certain experimental reasons the second
method is preterable to the first.

In both cases, two electrical measurements and a calorimetric one
(which in many cases has already been executed by BrERTHELOT or
THOMSEN) lead to the knowledge of the desired heat factor which
we will call Ly.

5. In order to be better understood we will choose a definite

example and make it our object to determine the limiting heat of
solution (Ly) of AgNO, say at @.

FIRST METHOD.

We construct a galvanic cell according to the following scheme:

Ne Solution of Ag NOs Very dilute solution ie
o° saturated at eC. | of Ag NOs. me"

| |
| |

In view cf the future determination of the temperature-coefficient
of the cell, the solid phase will not be introduced into the saturated
solution but a clear saturated solution will be employed.

The mechanism of this cell during the passage of the current is
now, according to known principles, as follows:

When one gram-ion of silver dissolves in the weak solution, the
concentration of silver in that solution is increased by 1 gram-ion;
but at the same time, if (1—2,) is the migration constant of the
silver, (l—n,) gram-ions of silver will have passed from the dilute
into the saturated solution.

The increase in the dilute solution therefore amounts to », gram-ions.

The saturated solution has, of course, become correspondingly
poorer in silver.

At the same the NO;-ions have been displaced in the opposite
direction. If », is their migration constant, then n, gram-ions of
NO, have passed from the saturated to the diluted solution, therefore,
during the passage of 96540 Coulombs, ”, gram-ions of Ag and n,

( 330 )
gram-ions of NO; have been transferred from the saturated to the
dilute solution.

6. As the cell described is a reversible one we may apply the
equation of Gipps and von HELMHOLTZ.

Ee

i

E,

As n is here =1 we get:

Eager ( ean
dT
We may imagine the heat effect of the change which takes place
in the cell during the passage of 96540 Coulombs as occurring in
two stages:
1st, Withdrawal of x, AgNOs from the solution saturated at ¢°;
heat effect — n, Ly.
9nd. Solution of », AgNO; in the extremely dilute solution;
heat effect », W, (representing by W, the first heat of
solution).

We thus get:

dE
B. = &) (Be —- T=) =—m Ty tm W,
or
Eo dE
Lp = Wi, —- = (BR -T
fi i = E. ta

If now the E.M.F. of the cell is determined at ¢° and also the
temperature coefficient at that temperature, then all the quantities
on the right hand side of the equation are known and consequently
Ly, which we desired to determine.

7. A single remark remains to be made: the dilute solution
must be so chosen that Wy, is really practically the first heat of
solution. If it is made too dilute, the accuracy with which £ and
di : su Ey
ad can be determined (for instance by PoGGreNDORFF’s compensation
a
method) becomes too small as the resistance would become unduly
great. At the same time any (small) heat of dilution would be

( 331)

neglected. It is therefore, in any case as well to keep within
certain limits !).

It is, of course, obvious that as a rule, electrodes which are
reversible in regard to the anion may also be employed. This
method is not likely to be used at present because the migration
constants in concentrated solutions and their dependance on the
temperature have been studied so little », for saturated solutions of
Ag NOs being quite unknown.

SECOND METHOD.

8. This method which, as already explained, quite corresponds
in principle with the first one, is capable of being realised experi-
mentally.

We take for instance the case that the limiting heat of solution
of thallous sulphate is to be determined and construct a cell according
to the following seheme:

Hg | Solution of Tl SO, | ay

Hg2S0, | saturated at t° C. |
connected in opposition to:
Hg | Very dilute solution TI
Hg2 SO, | of Tl], S50, .

When 296540 Coulombs have passed through this combination,
1 gram-molecule of Tl,SO, has been transferred from the saturated
to the dilute solution.

In the equation

n= 2 therefore

1) When the saturated and the diluted solutions differ very much in degree of
dissociation, there will exist a difference between the ionisation-heats at the electrodes
in those solutions. Provisionally, we only know that difference will be very small.
Still, a numerical determination would be interesting, in which Ostwatp’s equation
(Zeitschr. f. phys. Chemie 11, 501, 1893) might be a guide.

( 332 )

whilst further
E,=—Ly+W,,

in which Zy represents the limiting heat of solution and W, the
first heat of solution of Tl, SO,, therefore :

dE
— Lye + Wi = 26 (Z es t—

dT
or
7 dE
Ly = W,—26 (Z ae, =)
dl

The right hand side of the equation contains again only known
quantities if the E.M.F. of the cell and its temperature coefficient
at 7° have been determined. W, may be borrowed from the table
of BERTHELOT or THOMSEN !).

The advantage of this method over the first lies in the fact that
migration is excluded here and that we therefore, avoid the difficulty
that the migration constants of concentrated solutions are not known.

I hope to describe the measurements in a future communication.

Amsterdam, Chem. University Lab., Aug. 1900.

Botanics. — ‘Contributions to the knowledge of some undescribed
or imperfectly known Fungi” (3'* Part) *), By Prof. C. A. J. A.
OUDEMANS.

56. AscocHyTa Ruet Ellis et Everhart, Proc. Acad. Se. Philad.
1893, p. 160 (= Phyllosticta Rhei Ell. Ev. ante annum 1893);
Sace. Syll. XI, 525, forma caulincola Oud. — On the stem and
branches of Rheum Rhaponticum. — Nunspeet, Oct. 2, 1899; Mr. Berns.

Maculae nune nigrescentes, tune vero pallescentes, irregulariter
limitatae. Perithecia numerosissima, congesta, !/;)>—!/, mill. in diam.,
epidermide velata, depressa, membranacea, vertice perforata. Sporulae
hyalinae, cylindraceae, ad polos rotundatae, biloculares, non aut vix
constrictae, T—14 « 3.5—4 «a.

57. AscocnhyTa PsaAMMAE Oud. n. sp. — On the leaves of
Psamma_ littoralis (= Calamagrostis arenaria = Ammophila arun-
dinacea = Psamma arenaria). — Dunes of Scheveningen, Sept. 1891.

1) See note on pag. 331. The same remarks also apply heres
*) For 24 Part see these Proceedings p. 230.

( 333 )

Perithecia epiphylla, sparsa vel laxe-caespitosa, epidermide velata,
non autem immersa, lenticulari-depressa, membranacea, mollia, nigra,
in luce pervia autem pallide-fusea, !/; mill. in diam., vertice per-
forata. Sporulae oblongae, dilute fuscescentes, biloculares, ad polos
anguste-rotundatae, sine constrictionis vestigio, eguttulatae, 11?/;—
14 X 47/5 wu.

Our fungus must by no means be confounded with Ascochyta
perforans Sace. (Syll. III. 406) or, what according to this author
would be the same, with Sphaeria perforans Roberge (Desm. Ann.
Se. nat. 2, XIX, 357 and Desm. Exs. 1st Series, 1s* Kd., 1843,
N°. 1288), because under this number, in the copy which I possess
of this rare work, there are found Psamma-leaves, but no perithecia
whose spores correspond with those of Ascochyta. They are indeed
bilocular and uncoloured, but each extremity bears a sickle-shaped
appendix, whose convex side is turned upward, and besides shows
two inwardly curved ends and, in the middle, a short, thick stalk,
by which it is joined to the summit of the spore. Perithecia with
such spores can only belong to the genus Darluca, provided its
character be somewhat expanded and, besides the presence of short-
triangular or thread-shaped, there be also allowed comb-shaped, jelly-
like appendices at the extremities of the spores. In this case the
new form found by me might be denominated Darluca cristigera.
These comb-bearing spores are, exclusive of the appendices, 25—26
long, and 14 w wide, a measurement mentioned by DesMazrirys,
not however taken over by SaccaRpo, but which is in any case
much more considerable than was ever found in an Ascochyta, A
slight deviation, in SaccaRpo’s description, when compared to that of
DesMAZIERES, is found in so far as the former calls the spores at
one and the same time “ellipticae’”’ and “acutiusculae”; notwith-
standing these terms seem to exclude each other, and the second of
the two is not found in the latter author.

In his diagnosis of Ascochyta perforans (Syll. III, 406) Saccarpo
also refers the reader to the article on Sphaerella perforans (Desm.)
Sace. in Vol I, p. 538 of the Sylloge, still, it cannot escape the
attention of those who attend to this reference, that by this Sphae-
rella there is meant nothing else but the Sphaeria perforans already
discussed by us, and the same number in Saccarpo’s herbarium
venale. DesMAzibREs’ silence about the existence of asci induced
Saccarpo to doubt of the justness of the name of “Sphaeria”, changed
by himself, in accordance with the more recent ideas, into “Sphae-
rella”. And herein the Italian Professor is right. Follows however
that Sphaerella perforans has no right of existence any more and

( 334 )

can have no meaning but as a synonyme of Darluca cristigera.

Remains the question whether our fungus might perhaps belong
to Ascochyta graminicola Sacc. (Mich. I, 127 and Syll. III, 407).
The answer, however, we think, can be only negative, for though
both species correspond in many respects with each other, still a
nearer investigation proves that Asc. graminicola has ovoid-fusiform,
bicellular spores, whilst in Asc. Psammae are found oblong spores
without drops. — Ascochyta graminicola var. Holci and Asc. grami-
nicola var. ciliolata Sace. (both referred to on pag. 407 Vol. IIL of
the Syll.) may remain out of consideration, the former having large
four-dropped spores, the latter, on account of the gelatinous filaments
at the summits of those organs, being obliged to withdraw to the
genus Darluca-Ascochyta graminicola Sacc. var. Brachypodii Trail.
(Sace. Syll. X, 308) comes not into consideration, its spores being
too large (15 —17 & 5 &) and somewhat crooked; Asc. graminicola
var. Caeruleae not, as here again the spores bear appendices and accord-
ingly belong to Darluca; lastly, neither Asc. graminicola var. lepto-
spora (Sace. Syll. XI, 308), as the spores are too narrow, as may
be inferred from the name of the variety (Aérog = slender).

So, we think ourself authorised to maintain the name of Ascochyta
Psammae, and further, to withdraw the species Ascochyta perforans
with their synonymes: Sphaeria perforans and Sphaerella perforans,
together with Ascochyta graminicola var. ciliolata and Ascochyta
graminicola var. Caeruleue, from the genera to which they hitherto
belonged, bring them over to Darluca.

58. ASCOCHYTA SOLANICOLA Oud. n. sp. — On the leaves of So-
lanum nigrum. — Nunspeet, Oct. 11, 1898; Mr. Brtns

Maculae orbiculares (mill. 5 in diam.) sive ellipticae (1815 mill ),
numerosae, fuscescentes, linea saturatius tincta in pagina superiore
circumscriptae, pallide virescentes in pagina inferiore, vulgo steriles,
denique aridae, fragillimae, foramen circulare vel ellipticum post
destructionem relinquentes. Perithecia epiphylla, sparsa, !/; mill. in
diam., fusca, prominentia, primo epidermide yelata, denique exposita,
vertice perforata. Sporulae bacillares, ad polos rotundatae, hyalinae,
biloculares, sine constrictionis vestigio, LO—12 21/5 uw.

Ascochyta solanicola is distinguished from Asc. Solani Oud. (Ned.
Kruidk. Arch. 2, VI, 44; Sace. Syll. X, 304), on the stems of So-
lanum tuberosum, by the absence of black filaments at the base of the
perithecia, and by the smaller spores (10O—122"%. 4 to 14X74);
from Asc. Lycopersici Brunaud (Sace. Syll. X, 304), on the leaves
of Lycopersicum esculentum, by the brown, not black perithecia, by

( 335 )

the want of the slightest constriction on the height of the partition,
and by longer spores (10—122!/5 « to S—1021/, w); from Asc.
socia Pass. (Sace. Syll. X, 304), on the leaves of Lycopersicum escu-
lentum, by the somewhat longer and somewhat shorter spores (10—12
25 we to S—10X21/.— 3,4); from Ase. Atropae Bresadola (Hedw.
XXXII, 1893, p. 32 and Sace. Syll. XI, 524), on the leaves of
Atropa Belladonna, by the much larger perithecia ((200 « to T77—80 4)
and the narrower spores (LO—12X2!/3 « to 8—124 4); from Ase.
Daturae Sace. (Mich. I, 163 and Syll. III, 402), on the leaves of
Datura Stramonium and arboreum, by the larger perithecia (200 « to
100 ~), otherwise coloured dots, and longer but narrower spores
(10—12X2'/; « to T—8X3«); from Ase. Nicotianae Pass. (Sace.
Syll. III, 401), on the leaves of Nicotiana Tabacum, by the absence
of the slightest constriction on the height of the partition and of
fine granules in the protoplasm; lastly, from Asc. physalina Sace.
(Mich. I, 93 and Syll. II, 401), on the leaves of Physalis Alke-
kengi, by the much smaller spores (10—12X 21/3 « to 25— 28X8 w)
and the absence of vacuoles in the protoplasm.

*AscocHyTA TUSSILAGINIS Oud. n. sp. — On the leaves of Yus-
silago Farfara. Apeldoorn, Oct. 6, 1897. — Cf. Ned. Kr. Arch. 3, I,
498, et Hedw. XXXVII, 178.

59. ASCOCHYTA VIBURNICOLA Oud. n. sp. — On the branches of
Viburnum Opulus, together with Phoma viburnicola. — Nunspeet,
April 14, 1899; Mr. Bers.

Maculae nullae. Perithecia numerosa, parva, depressa, sub perider-
mate occultata, vertice perforata. Sporulae cylindraceae vel cylindraceo-
fusiformes, ad polos rotundatae, rectae, solitariae hyalinae, in massam
condensatae dilute-olivaceae, biloculares, 91/. 21/3 u.

Differt ab A. Viburni, A. Lantanae et A. Tint sporularum dimen-
sionibus, quippe quae exprimuntur numeris

10—123.5—4 « pro A. Viburni.
11X2 4“ pro A. Lantanae.
6—10X35 u pro A. 7int.

CYTODIPLOSPORA Oudemans.
(Ned. Kruidk. Archief 2° Serie, VI, 292).
The genus Cytodiplospora may be considered as to differ from

Cytospora by bicellular spores.
Though Saccarpo p. 523, Vol. XI of his Sylloge, rigutly assigned

( 336 )

a place to this genus among the Hyalodidymae, it was in Vol. XII
of the said work (p. 162), elaborated by Sypow, erroneously men-
tioned as belonging to the Phaeophragmeae, and in the “Index ge-
neralis Generum”, in the back part of volume XIV, much to the
detriment of the reader, an s is added to Cytodiplospora which is
thereby changed into Cystodiplospora.

The first Cytodiplospora found by me, lived on branches of
Castanea vesca, and was described by me under the name of Cytodi-
plospora Castancae in Nederl. Kruidk. Archief, 2, VI, 528. A
second species, found on Birch-branches, I mentioned under the title
of Cytodiplospora Betulae, in Hedwigia XXXVII (1898) p. 317.
A third species, found of late on branches of Acer Pseudoplatanus
and dasycarpum, I here mention by the name of:

60. CyTopipLospoRA ACERUM Oud. n. sp. — On branches of
Acer Pseudoplatanus and Acer dasycarpum. — Bussum, April, 1900.
C. J. Konia.

Pustulae numerosae, irregulariter distributae, peridermate tectae,
parum prominentes, sed praesentiam suam saepe jam ab initio tradentes
macula subeutanea orbiculari vel annulari, nigra, opaca, 1 ad 11/,
mill. in diam. Peridermate rupto, stroma conspicuum fit depressum,
fuliginosum, structura parenchymatica tenerrima insigne, intus lacu-
nosum, i.e. septis pluribus flexuosis imcompletis in loculamenta plu-
rima_ variae dimensionis divisum. Sporulae numerosissimae, biloculares,
fusiformes, rectae, hyalinae, ad polos anguste rotundatae, 12—14X
2!/;—3 w, non constrictae, basidiis brevibus suffultae.

DIPLODINA Westendorp.

61. DieLopina DASYCARPI Oud. n. sp. — On branches of Acer
dasycarpum, — Scheveningen, May 1894.

Perithecia in caespites densos appropinquata, subcutanea, denique
exposita, globuloso-papillata, nigra. Sporulae fusiformes, hyalinae, ad
polos anguste rotundatae, biloculares, non constrictae, eguttulatae,
122", w. — Differt a D. Acerum sporulis minus largis (1221/9
contra 12—164—4.5 w) et sporulis ne minime quidem constrictis.

62. DipLopina Necunpinis Oud. n. sp. — On branches of Ne-
gundo fraxinifolia. — Naarden, Febr. 1900; C. J. Kontne.

Perithecia numerosissima, dense congesta, in parenchymate corticali
leviter immersa, orbiculari-depressa, vertice tandem periderma laxe
adhaerens perforantia, 100 4 in diam. Sporulae bacillares, ad polos

( 337 )

rotundatae, continuae, hyalinae, biloculares, leviter in medio constrictae,
nonnumquam imo panduriformes, 11—143—5 w, eguttulatae, spo-
rulis plurimis continuis, brevibus, phomiformibus (norndum penitus
evolutis?) commixtae (Pl. IV, fig. 7).

THORACELLA n. ¢g. Oudemans.

Stroma piceum, micans, infracuticulare, primo laeve, postea rugosum
et foveolatum, e stratis duobus aequialtis composito: superiore
pseudoparenchymatoso, fuliginoso, inferiove e hyphis intertextis pa-
chydermatosis, hyalinis composito; conceptaculis sporularum in strato
superiore effossis, primo absconditis, postremo ostiolo hiantibus. Spo-
rulae fusiformes, ad polos acutiusculae, hyalinae, in medio 1- septatae,
basidiis filiformibus suffultae.

63. THoraceLLa Lepr Oud. un. sp. On the leaves of Ledum
palustre; Nunspeet, Sept. 9, 1898; Mr. Bers.

Stroma amphigenum, nunc partem tantum fol, tune vere totum
folium occupans, piceum, micans, primo laeve, postea rugosum et
foveolatum, ex ostiolis conceptaculorum perforatis paululum promi-
nentibus p.m. inaequali. Conceptacula p.m. numerosa. Sporulae
fusiformes, hyalinae, 7T—11 2, ad polos acutiusculae, in medio
1-septatae, basidiis filiformibus longiusculis suffultae. — Saepe
Ascochyta Ledi Oud. concomitata.

0. Phragmosporae.
HENDERSONIA Eerkeley.

*HENDERSONIA AGROPYRI REPENTIS Oud. n. sp. On the leaves
of Agropyrum repens. Nunspeet, March 13, 1898; Mr. Berns. Cf.
Ned. Kr. Arch. 3, I, 500.

64. HENDERSONIA GROSSULARIAE Oud. n. sp. On the leaves of the
young branches of Ribes Grossularia. — Apeldoorn, May 19, 1897,
O. — Nunspeet, July 12, 1899; Mr. Bens.

Perithecia. membrana subtilissima praedita, subcutanea, parva,
pallida, denique vertice perforata. Sporulae cylindricae vel fusiformes,
subcurvatae, stramineae, quadriloculares, ad polos rotundatae, egut-
tulatae, 14—23 x 4—4°/s w (Pl. IV, fig, 8).

65. HENDERSONIA TYPHICOLA Oud. n. sp. On the stems of
Typha latifolia. — Nunspeet, May 21, 1899; Mr. Berns.

( 338 )

Perithecia primo epidermide velata, denique exposita, tenera,
membranacea, parva, subfuliginea, denique vertice perforata. Sporulae
oblongae, ad polos rotundatae, rectae vel curvatae, pallide-olivaceae,
quadriloculares, 11°/;—14 x 4°/;s—5 w (Pl. IV, fig. 9).

*HENDERSONIA WEIGELIAE Oud. n. sp. On branches of Weigelia
amabilis. Nunspeet, March 3, 1898. O. Ned. Kr. Arch. 3, I, 500.

STAGANOSPORA Saccardo.

*STAGONOSPORA DASYCARPI Oud. n. sp. (St. Aceris dasycarpi Ned.
Kruidk. Arch. 3, I, 500). — On branches of Acer dasycarpum. —
Scheveningen, May 1895.

«. Dictyosporae.
CAMAROSPORIUM Schultz.

*CAMAROSPORIUM DASYCARPI Oud. n. sp. — This name should replace
that of Camarosporium Aceris dasycarpi, used in the Ned. Kr. Arch.
3, I, 501 and in Hedwigia XXXVII (1898) p. 179. On the
branches of Acer dasycarpum. — Scheveningen, May 1894.

*CaMAROSPORIUM Inicis Oud. n. sp. N. K. A. 3,1, 502 and Hedw.
XXXVIT, 1898, p. 179). — On the branches of Ilex Aquifolium. —
the Hague 1894.

*CAMAROSPORIUM PERICLYMENI. Oud. n. sp. N. K. A. 3, I, 502 and
Hedw. XXXVII, 1898, p. 179. — On branches of Lonicera Peri-
clymenum. — Scheveningen, Aug. 1894.

66. CaMAROSPORIUM TANACETI Oud. n. sp. — On the stems
of Tanacetum vulgare. — Nunspeet, Febr. 15, 1899; Mr. Berns.

Perithecia numerosa, epidermide velata, nunc inordinate sparsa,
tune vero in series lineares digesta, inter peridermatis lacinias ruptas
prominentia, semiorbicularia vel anguste-elliptica, glabra, nigra, 1/5
mill. in diam. Sporulae suborbiculares, ellipticae vel late ovatae,
vulgo 14 x 9 w, quadriloculares, loculo alterutro intermedio septo
longitudinali, perpendiculari vel declivi, diviso.

7. Scolecosporae.
SEPTORIA Fries (emend.)

67. Seproria CapseLLAE Oud. n. sp. — On the dry and
nearly decayed leaves of Capsella Bursa pastoris. — Apeldoorn,

( 339 )

July 26, 1899; Oud. — Perithecia minima, dense congesta, nigra.
Sporulae cylindricae, rectae, curvatae vel flexuosae, hyalinae, ad polos
rotundatae, quadriloculares, maturae 50—60 X 2!/,—31/g w.

68. Seprorra conorum (Sacec.) Oud.; Phoma Conorum Sace.
Mich II, 615; id. Syll. III, 150. — On the cone-scales of Abies
excelsa. — Forest of Bloemendaal, Maart 12, 1900; C. J. J. van
Hau. — Perithecia innato-erumpentia, globoso-depressa, astoma, jure
crassiora, carbonacea, nigra, nucleo griseo. Sporulae fusoideae, rectae,
10—14 X 2—2!/, #, primitus 1-guttulatae, postremo septo transverso
in partes 2 aequales divisae, basidiis sporis duplo longioribus, post
lapsum sporularum uncinatis (Pl. IV, fig. 10).

69. SEPToRIA JAPONICAE Oud. n. sp. — On the leaves of
Evonymus japonica. — Naaldwijk, 1867; the late Dr. J. E. van
DER TRAPPEN.

Maculae pallescentes. Perithecia amphigena, inordinate distributa,
dense congesta, primo epidermide velata, postea prominentia et
epermidis ruptae laciniis dentiformibus erectis circumcincta, nigra,
p.m. micantia. Sporulae breve-fusiformes, 15 X 4—5 w, hyalinae,
continuae, rectae, eguttalatae, anguste ad polos rotundatae. — Differt
a Sept. Evonymi japonicae Pass. (Sace. Syll. III, 482) sporulis
latioribus (15 X 4—5 contra 12—13 X 2.5 w) et linea alba orbiculari
ad verticem peritheciorum absentia (Pl. IV, fig. 11).

70. SEPTORIA OBESISPORA Oud. n. sp. — On the leaves of
Calystegia septum. — Nunspeet, Aug. 15, 1898; Mr. Berns.

Maculae quoad formam et dimensiones admodum variabiles, soli-
tariae vel confluentes, rufescentes. Perithecia epiphylla, minima, inor-
dinate distributa, nigra. Sporulae bacillares, rectae vel curvatae, imo
nonnumquam geniculatae, hyalinae, ad polos rotundatae, plurisep-
tatae, loculamentis omnibus uniguttulatis, 23—28 & 4-5 w. — Differt
a 8. Convolvuli Desm. sporulis multo crassioribus (23—28 4—5 wa
contra 35—50 X 1.5.4); a S. Calystegiae West., sporulis brevioribus
(25—28 X4—5 contra 36—45 X4—5 wu), tandem a S. flagellari
Ellis et Everhart sporulis brevioribus et crassioribus (23—28 X 4—5 uz
contra 35—44 X 1.5 w). (Pl. IV, fig. 12).

RHABDOSPORA Montagne.

71. Reaspospora Eryneicoua Oud. et Sydow n. sp. — Septoria
eryngicola Oud. et Sace. Syll. Addit. ad. vol. I—IV, p. 345, sub.
23
Proceedings Royal Acad. Amsterdam. Vol. III.

( 340 )

no. 298; Sace. (Syll. X, 367, sub 108). — On the stems of
Eryngium maritimum. — Scheveningen, Oct. 1892.

Internodia albido-pallescentia peritheciorum numero notabili obducta,
quorum maxima !/, mill. in diam. habent. Perithecia nigra, primitus
epidermide velata, postea vero exposita, vertice perforata. Sporulae
curvatae, continuae, eguttulatae, 28—30 13/9 w.

Though Septoria Hryngit Pass. (Fghi. Parm. Septoria no. 57 and
Sace. Syll. III, 532), by Professor Saccarpo and myself had formerly
been declared identic with Septoria eryngicola Oud. and Sace., it
will now appear to me that this view was contrary to the nature
of the facts, as Septoria Hryngii not only attacks the leaves of
Eryngium campestre, but.as moreover its spores get no longer than
20—25 we.

Everything well considered, it seems to me that Septoria Eryngii
West. (Not. V, 31) with its straight spores of 50 < 2!/,u belongs
to Eryngium maritimum, and that Septoria eryngicola Oud. (= 5.
Eryngii Pass. l.c. = 8. eryngicola Oud. et Sacc.), with its straight
or curved spores of 25 1—1'/,“, is exclusively found on the
leaves of Er. campestre. — Rhabdospora Eryngicola Oud. et Syd.
then represents a third species proper to Er. maritimum, whose
curved spores of 28-30 X 2!/,4, keep the middle between those
of the two other species mentioned just now.

72. RHABDospoRA MILLEFoLI Oud. n. sp. — On the stems of
Achillea Millefolium. — Nunspeet, May 21, 1899; Mr. BErNs.

Perithecia numerosa, densissime congesta, solitaria vel confluentia,
in series longitudinales, caulium sulcos implentes, voalescentia, semi-
globosa vel a latere compressa et hine cristiformia, glabra, nigra,
primitus epidermide velata, denique exposita et centro perforata,
mill. 1/;—1/) in diam. Sporulae bacillares, reetae vel curvulae, ad
polos rotundatae, primo 3-, postea 2-guttulatae, continuae, hyalinae,
IVs—11*/3 X 24/3, basidiis aequilongis vel longioribus suffultae
(PI. LVsfigo3).

Differt a Kh. Achilleae Bresadola (Roum. Revue Mye. XIU,
1891, p. 30 et tab. CXIV, fig. IX; Sacc. Syll. X, 394) peritheciis
multo majoribus et sporulis bis minoribus.

73. RHABposporA TAanacetr Oud. n. sp. — On the stems of
Tanacetum vulgare. — Nunspeet, April 7, 1899; Mr. Bets.

Perithecia gregaria, punctiformia, epidermide velata, nigra, soli-
diuscula, 90—120 @ in diam. Sporulae filiformes, hyalinae, rectae,

(341 5

curvulae vel p.m. flexuosae, 3-septatae, sub lente multum augente
neque guttiferae, neque protoplasmate granuloso farctae, 50—60 X 2 w.

CYTOSPORINA Saccardo.

*CyTOSPORINA ABIETIS Oud. n. sp. — On the foremost portion
of the under surface of fruit-scales of Abies excelsa. — Nunspeet,
April 8, 1898; Mr. Brins. Cf. Hedw. XXXVII (1898), p. 317.

74, CyrosporIna SyRINGAE Oud. n. sp. — On the branches of
Syringa vulgaris. — Nunspeet 1898; Mr. Berns.

Stromata corticola, immersa, nigra, oblonga, rima_ longitudinali
sinuosa exarata, intus in loculamenta plura p.m. completa sporulas-
que foventia divisa. Sporulae filiformes, uncinato-curvatae, continuae,
hyalinae, eguttulatae, 322 w, basidiis filiformibus aequilongis fultae.

b. Nectroideae.
SPHAERONEMELLA Karsten.

75. SPHAERONEMELLA Wenti Oud. n. sp. (Dedicated to Dr. F.
A. F. C. Went, Professor in Botanics at the University of Utrecht).
— On the putrefying stems of Faba vulgaris. — Utrecht, 1900;
Mr. Pune, candidate of Pharmacy.

Perithecia subglobosa, membranacea, mollia, primo alba, deinde
ochracea, cava, 300 & in diam., sparsa, in telis putrescentibus immersa,
rostro concolore subulato circa 900 longo coronata. Rostrum e
filis tenerrimis, primo per totam Jongitudinem unitis, postremo versus
apicem rostri relaxatis, solutis, retrorsum arcuatis, compositum. Spo-
rulae, basidiis brevissimis e mycelio, conceptaculi fundum obtegente,
sursum tendentibus fultae, maturae decidunt et deinde, in guttulam
mucilaginis ope conglobatae, ad orificlum rostri apparent. Guttula
viscosa, in corpora quibusum in contactum venit statim diffluens,
diam. habet 250 «, et colore albo, nec minus nitore suo oculos allicit.
Sporulae hyalinae, ellipticae, continuae, longae 7 w, latae 4 w.

ec. Leptostromaceae.
LEPTOTHYRIUM Kunze et Schmidt.

76. Leprotuyrium Brtutr Oud. n. sp. — On the leaves of
Carpinus Betulus. — Nunspeet, Nov. 5, 1899; Mr. Berrys.
Maculae nullae. Perithecia scutiformia hypogena, numerosa, aequa-
liter distributa, puncta nigra, convexa, rugulosa, 1/jg,—1/,) mill. in
diam. simulantia. Scutula, ex cuticula mutata et atrata formata, itaque
23*

( 342 )

omnis structurae expertia, cavernulas obtegunt minimas, sporulis minu-
tissimis (7><1/, «), bacillaribus, vulgo curvatis, continuis, eguttulatis,
utrimque rotundatis, basidiis aegre distinguendis fultis, repletas.

77. LeprotHyrium FuncktAg Oud. n. sp. — On the leaves of
Funckia ovata. — Nunspeet, Oct. 11, 1898; Mr. Berns.

Maculae nullae. Perithecia in facie foliorum inferiore p.m. regu-
lariter distributa, !/;,—1/, mill. in diam., nigra, perfecte cireumscisso-
soluta, ad marginem subtilissime fimbriata, orificio nullo. Sporulae
cylindraceae, rectae, ad polos rotundatae, hyalinae, eguttulatae, 21/5 a.

LEPTOSTROMA Fries.

78. LeprosTRoMA ABROTANI Oud. n. sp. — On the stems and
branchlets of Artemisia Abrotanum. — Nunspeet, 1899; Mr. Berns.

Perithecia dimidiata, aequaliter distributa, '/,—1'/. mill. longa,
primo epidermide vel peridermate nigrefacto velata, postea exposita,
Yz—', mill. lata, astoma, saturate-fusca, opaca. Sporulae numerosis-
simae, hyalinae, continuae, vulgo oblongae vel fusiformes, 7—10X
2'/;—3 a, nonnumquam reniformes, 7X3, semper biocellatae, ad
polos rotundatae.

79. LEPTOSTROMA LONICERICOLUM Rabh. Bot. Zeit. 1846, p. 46
(nomen tantum); Rab. H. M. I, N°. 865; Sace. Syll. III, 647
(nomen tantum). On the branches of Lonicera Caprifolium var. cocei-
nea. — Nunspeet 1899; Mr. Berns.

Perithecia inordinate sparsa, cuticula tenuissima velata, planocon-
vexa, atra, nitida, oblonga, centro prominentia, ad polos declivia et
acutata, 1 mill. longa, 4/2 mill. lata, tandem poro pertusa. Sporae
oblongae vel fusiformes, hyalinae, continuae, biocellatae, 7X 21/5 w,
ad polos rotundatae vel acutatae, singulae basidio filiformi tenuissimo,
sporulis bis ad quater longioribus suffultae. — Internodia perithecii-
gera pallescentia, albida vel straminei coloris.

80. LeprostromMA STeLLARIAE Kirchner, Lotos 1856, p. 204;
Sace. Syll. II, 647. — On the leaves of Stellaria Holostea, in
company with Septoria Holosteae Oud. — Nunspeet, April 17, 1899;
Mr. Bens.

Species adhue indescripta.

Perithecia epiphylla, dimidiata, in maculis pallidioribus foliorum
exsiccatorum inordinate-destributa, late-elliptica, convexa, rufo-nigra,
opaca, '/,—%/,<'/s—'/2 &, epidermide velata, tandem fissura longitu-

( 343 )

dinali hiascentia. Sporulae eylindraceo-fusiformes, 91/,—11?/,21/,—
21/. w, ad polos anguste-rotundatae, continuae, hyalinae, biocellatae.

The above description, the first given of this fungus, qualifies us
to remove it from the list of the “Species vix notae” (Sacc. Syll.
III, 647).

SACIDIUM Nees.

81. Sacipium Apieris Oud. n. sp. — In suleo longitudinali
mediano faciei superioris, et juxta nervum medianum prominentem
faciei inferioris acuum Abictis grandis cultae, puncta nigra numerosa
approximata offenduntur, quae, oculo armato

@) examinata, vesiculas simulant minimas, omnis
©) structurae expertes, 60—100 « in diam. ha-
bentes, colore dilute fuligineo affectas, basin

Sacidium Abietis Oud. versus in pedicellum brevissimum, quamvis
amplum, contractas, sporulis singulis basidio filiformi fultis, repletas.
Ipsae sporulae numerosissimae, ellipticae, hyalinae, continuae, guttula
mediana ampla, valde micante, praeditae, J—13 w longae, T—9.5 «a
latae. — Nunspeet, Sept. 1899; Mr. Bers. On the leaves of Abies
grandis.

82. Sacipium Quercus Oud. n. sp. On the leaves of an Ame-
rican species of Quercus. — Nunspeet, April 11, 1898; Mr. Berys.

Perithecia hypogena, caespitosa, orbicularia vel elliptica, 160 ad
180 w lata, inaequaliter inflata, postremo plana et rugosa, dimidiata,
clypeata, atra, astoma, ad faciem internam basidiis numerosissimis,
sporuliferis obsessa. Basidia dense cougesta, filiformia, 14—18*/3 X
1?/, w, recta, hyalina, continua. Sporulae bacillares, hyalinae, continuae,

6 X 1/5.
PIROSTOMA Fries.

83. Prrostoma circinANS Fr. 8. V. Sc. 395; Fuck Symb. 401;
Sace. Syll. HI, 653. On the leaves and leaf-sheaths of Phragmites
communis. — Nunspeet, 1899; Mr. Betns.

Badly known species!

When consulting the different authors who have occupied them-
selves with P7rostoma circinans, it is difficult, if not impossible, to
imagine that their communications regard the same fungus, though
all, for starting point, applied themselves to objects which, although
denominated differently, such as Conéosporium circinans Fr. 8. Me
IT, 257; West. Herb. Cr. n°. 38; Sphaeria circinans Rab. Kr. Fi,

( 344 )

174; Kickx Crypt. des Flandres I, 349; Lambotte, Fl, Mycol. Belge
II, 240; Pirostoma circinans Fr. 8. V. 8. 395; Sace. Syll. III, 653;
Fuck. Symb. 401, — were notwithstanding considered by all of them
as no more but synonymes.

Indeed, while some (Fries 5S. M. III, 257; Rab. Kr, Fl. 174,
Lambotte Fl. Mycol. Belge I], 240) make mention of a Sphaeriacee,
possessing “globular perithecia perforated at their summit”, nay
even “asci and paraphyses” (Fr. 8. V. 8. 395; Kickx J. ¢.; Lamb.
l.c.), others wish the fungus to be allowed but an inferior rank
among the Sphaeropsideae, to which asci and paraphyses are wanting
(Fuck. |. ¢.; Sace. Syll. LI, 653). Wantrorn, who endowed our
fungus with the name of Sphaeria stigmatella (Flora Crypt. II, 786),
ascribes it “very small, slightly-globose perithecia which are closely
pressed against the plant’, while FuckEeL, adopting the nomen-
clature of Frivs, declares notwithstanding: ,Ich kann mir ueber
den Bau dieses Pilzes noch kein klares Bild entwerfen.’’ The char-
acteristics of the genus he passes by, but admits that the species has
globular, brown stylospores of 12 « diameter, concealed under a
lengthwise stretched peltate perithecium.

The supposition that the different authors have possibly devoted
their investigations to two different species, may be represented as
acceptable, still it ought to be rejected, when considering that as
well FRrEs, who introduced the name of Coniosporium, as RABENHORST
Kickx and Lamporre, who served themselves of the expression
Sphaeria to elucidate their divergent opinions, refer all to N°. 330
of the “Plantes Cryptogames du Nord de la France 1¢ Ed. (A°. 1828)”,

which — as is proved by the words added to the name of ,Piro-
stoma circinans”’: ,F RIES, in litteris’’, sent to the renowned mycologue
to be verified — shows neither perithecia, nor asci, nor paraphyses,

and which, moreover, consists of nothing else but very small, flat,

perfectly sterile shields, not unlike those which are characteristic of
the genus Leptothyrium.

The specimens of Pirostoma circinans, published by FucKEL in
his Fungi Rhenani under N°. 791, not without the synonymes
Coniosporium circinans and Sphaeria circinans being added to the
chief name, differ in no single respect from those of DEsMAzIbRES,
while these, in their turn, cannot be distinguished from those of
the “Herbier des Cryptogames Belges” of WrstenporP (N°. 38).

The specimens collected in Holland of Pirostoma circinans, for the
greater part in excellent condition, deviate in no single respect
from those of:

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1. DeEsMAzrIbRe’s Plantes Cryptogames du Nord de la France,
le Ed., No. 330 (Coniosporium) ;

2. RABENHORS?’s Herbarium mycologicum, 2° Ed. No. 59
(Coniosporium) ;

3. RABENHORS1’s Fungi Europaei, Nos. 1031 en 2700 (Piro-
stoma) ;

4. WESTENDORP’s Herbier Cryptogamique Belge, No. 38
(Sphaeria) ;

5. Fucker.’s Fungi Rhenani, No. 791 (Pirostoma);

6. RouMEGUERE#’s Fungi gallici, No. 1082 (Pirostoma) ;

which means, that the microscopic investigation of all these collect-
ions may be considered as to be described in the following lines.

Pirostoma circinans, a fungus, hitherto found nowhere but on the
stems and leaf-sheaths of Phragmites communis, appears at macro-
cospic examination in the shape of stripes, dots, or rings (whence
the name of circinans), of more or less length, circumference, or
diameter, which are first hidden under the cuticula, but later throw
off that membrane and then show a brown tint, which in older
objects inclines to black and, when struck by sunlight, displays
more or less gloss.

When examined with the microscope, the black portions show a
finely granulous surface, which has probably given cause to the
mentioning of an “accumulation of very minute, densely crowded
perithecia”, which expression is still met with in some authors. We
must directly add, however, that this conception reposes on an error,
and that in Pirostoma there are found no perithecia at all, and ac-
cordingly neither asci and paraphyses.

A single granule, subjected to microscopic examination, presents
itself as a low, dome-shaped body, or, in other words, as a plane-
convex (hollow) lens, of which the convex side is turned toward
the spectator, while the flat one reposes on the object which bears
the fungus. The convex side is composed ‘of extremely minute blown-
up cells, which, seen in front, are 2'/, to 4°/3 « wide, and angular,
and have this peculiarity, that the black colour proper to them and
on which depends the dark appearance of the stripes, dots, and
rings, proves to be limited to that outerside, whilst the side-walls
and the inuner-wall are wholly devoid of it. Add to this that the
coloured side in the middle, or close by, shows an extremely small
hole at the bottom of a superficial impression, and that this hole
has the appearance of a brilliant point because it allows the eye

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to penetrate into the colourless back-wall of the cell and into the
colourless tissue behind it, — then it can hardly be denied, that
this concurrence of facts can give rise to the conviction that no better
name than that of Pirostoma (derived from the Greek words zecgo
to pierce, and oroga mouth or opening) could have been chosen
to indicate the properties, which we have above drawn attention to.
Still there is no doubt that Fries, whose diagnoses sprung from
researches with no other instrument but the magnifying-glass, cannot
have been acquainted wiih the finer structure sketched by us just
now, whence it follows that in giving the name of Pirostoma to
objects quite like to those which we examined ourselves, he will
have been led: not by examining the cells of the small granulous
corpuscula, but by the black spots themselves, at which we, however,
never observed anything like an opening. For the rest we repeat that
the presence of “sporae ascis linearibus paraphysophoris receptae”
has neither been found true by ourselves, nor by Fucke, nor by
SACCARDO, so that the fungus, endowed by Fries with the name of
Pirostoma circinans, has remained a riddle to us. The information
of Kickx and Lamsorre, of whom the latter did nothing but simply
copying the formula produced by the former, and that imperfectly,
too, cannot 1elieve our embarrassment, as they refer their readers
to the dried objects of WrsTenporp, at which nothing can be dis-
covered of what they describe; on the contrary, everything cor-
responds with what we have found in our own specimens.

After mature consideration, Pirostoma circinans appears to us a
preliminary, sterile condition of a higher form, and allied to the
genus Leptothyrium. SACCARDO gave the fungus a place among his
,Leptostromaceae phaeosporae’’, no doubt because Fucken had attri-
buted to it “giobular, brownish stylospores”, still we can attach no
value to this view as it is completely contrary to the experience
acquired in the investigation of FUCKEL’s exsiccata.

All those who attribute to Pcrostoma circinans an ostiolum, asci,
spores, and paraphyses, seem to have examined some or other
Pyrenomycete, accidentally got among the shields of Pirostoma or,
without previous research, to have copied the mycologue of Upsala,
or one another,

d. Excipulaceae.
DISCELLA Berkeley et Broome.

84. DiscenLA Berseripis Oud. n. sp. (Discella Grossulariae Oud.
Ned. Kruidk. Arch. 2, V, 506). After it had appeared to me that

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the branchlet on which I had found the above mentioned Discella
had not belonged to Ribes Grossularia, but to Berberis vulgaris, the
first chosen name had of course to be changed. So I here redress
the error committed while calling to mind that the diagnosis of the
fungus ran as follows:

Maculae circulares nigrae numerosae, !/;>—?/; mill. in diam., mi-
eantes, primo neutiquam, postremo parum prominentes, e cellulis
peridermatis, pseudoparenchymate nigrescente repletis, formatae, foveas
minimas, in parenchymate corticali absconditas, operculi ad instar
occludunt. Foveae, sporularum glebula coloris mellei repletae, peri-
theciorum locum tenent operculoqre scutiformi perforato vel delapso
late patentes, contenta amittunt. Sporulae bacillares, rectae vel sub-
curvatae, ad polos rotundatae, biloculares, separatim visae fere hyalinae,
congestae vero manifeste mellae, 7T—10 K 2—3 wu.

(To be continued).

Mathematics. — ‘On the MacManon generalization of the
Newton-GirnarD formulae’. By Prof. L. GeaENBAvER of
Vienna (Communicated by Prof. Jan DE Vrigs).

In his treatise contained in the 15" volume of the “Proceedings
of the London Mathematical Society” “On Symmetric Functions and
in particular on certain Inverse Operators in connection therewith”
MacManon has deduced with the aid of differential operators the
relations

a i ae r+m)!
— A eel: Sa pee eh ir s. =(—1) em) Aj

r!m! Smtr

where Sj denote those symmetric functions of dimension & in the
n quantities 2,2 ,...,% in which every term contains 7 of these
quantities, so that in particular S; is their elementary symmetric
function f; and Sz the sum of their kt powers.

These relations forming an interesting generalisation of the NewrTon-
GIRARD formulae, were proved anew somewhat later by LAacHLAN
in his paper ,On certain Operators in connection with Symmetric
Functions” published in the 18** vol. of the same , Proceedings”. Other
deductions of these formulae have as yet not caught my eye; neither

( 348 )

are any others mentioned in the article referring to it of the
»Hncyklopidie der mathematischen Wissenschaften” (Teil I, Bd. I,
p- 449—479). However, it being not impossible, that one might
wish to read about these relations in the elementary algebraic lessons,
where either no use can or will be made of the differential operators,
I will communicate in the following lines a proof founded upon
another completely elementary basis, which has moreover another
advantage of being entirely analogous to the other one, which is
usually given for the special case m=1 (NeEwron-GIRARD formulae).

1. The Newron-Grrarp formulae are generally deduced by
comparison of the coefficients of the different powers of # in the
two members of the equation

= > ean

ie (x) apex Si (#3 @a)

A=] T—TWAa

where f(x) is a polynomium of degree n and 4, %,...,2%n are its
roots. For the sake of simplicity we shall take the coefficient of
x” equal to 1. This proof is based on the double representation of
the first derivative of a polynomium. In quite an analogous way
the general relations can be found by means of a double represent-
ation of the m derivative of such a polynomium.

By differentiating the equation according to 2, we obtain

A—n

F" (0) = =f (@3 %)
a=1

or with the aid of (1)

(OlF eaicm alee es

By successive differentiation we arrive at last at

(m) x F
f@== i) jCavdaveitn = Lyons Zvi ZB)

A Papin @— 2, \e—a, )ee (e—a,

Now we find that

ee

( 349 )
f (@)

(e—#, (x =m )..(e—a, )

= grim 4 (2, > a + ma 4. r —/)) gn—m—1 --

= [*, =i # bet ze | a ee re af ony fe ae ra ats eee ak ai
A, tat. +5) +f] met
a [es + By bet z+ , ey ae nh, 9,0 be 2, + st

2 2
5 ii jaa ab ieee n—l 7 a A, ¢ Ay % a3 i i A, % Ao tanh in? Tt si pasta ae

2 2 2
—f; (w, + @, tu. + x re a €or we a, eae) a

n—m—3

+h, +e t+) — A] e+

Effecting in this equation the indicated summation according to
the quantities 4},49,--.,4m, we find that of every single term on the
n!}

right side

terms are formed; amongst the group of those,
n—m

which form the coefficient of «*—™~*-*, each term necessary for

the representation of the symmetric function st 42 presents itself

(n—e)! m!

——_—_____ times and so we obtain the relation
(n—m) ! (m—g)!

(m) n! c=n—m

F («) = 2 Cae + SS gam

(n—m) ! =

k=m — (n—k)! m!

een en ee eS)

when we substitute

This leads to the relation

( 350 )

(ine (n—o)! ue i (n—k)!m! (st ae gt

(n—m—o!"" ~ j=o (n—m)!(m—2)!
+ foSi_—-+- + (-l)* fe 8),

which can be written as follows

m™m

SS A Sitar aus s” a rere + (—l) Sr Ss" =

m+r—2

i 0) k=m—1_— (n—k)! nm!

pote Eo (nm)! (m—D!

m! ((n—2 m—r)

k k k ehh E\I
ais fi Swen ie ap) See Pte ay Cle —* dmtr—k S. ) j

by making ¢ = m-r and by separating the term for =m on the
right side from the sum.

2. Now, if the MacManon relation exists for all the values
of the superior index from 1 to m—1 inclusive, this equation trans-
forms itself into

ie ee m m aes Mey geen ee
Ste fi See an Sa Soar, eae ( G i Si =

JE LREn (n—m—7r)! ar st 7 (n—k)!m!(m-+r)!
— (n—m)! (m—2)! (m--r-k)! A! §

m! {(n—2 m—r)1 a Furs

which by introduction of the symbol +)

\s m& — m(m—1)A(A—1) stun m)!A!
Pt bn sig Gel) en

takes the form of

1) In relation to the facts supposed to be known before the demonstration is entered
upon with a view to the previously mentioned aim, we remark that the circumstance
of g (m, a, ”) being finite hypergeometric series with unity as fourth argument at
infinity is not made use of.

( 351 )

m

ta As m+r— ear fy “mer oe ar i = 1)’ tr S 4

(—1)"+r( (n—m—r)! (m-+r)! nt
= waa =

m! ({(n—2m—r!)

g(mym--ryn) Fm+r(2)

(n—m)!

3. We find at once for the function ~ (m,4,x) the equation
, d
\ p(m + 1, A, n) = ~ (m, A, n) — — p(m, A—1, n—1),
n

by which it is entirely determinated for all the values of »>1, if
moreover the equation

Piven G)— il: (@>1,P>1)

is added.
The quantity
(n—m)! (n—A)!
n! (n—m—A)!

satisfying the same functional equation and having likewise for
m= 0 the value 1, we find

(n—m)! (n—A)!

(n—m—A)! n!

p (m, A, n) =

which equation holds good, as is easely shown, as long as > m,
when for n<m--A the right side is replaced by nought. Particular
attention is drawn to the fact, that », m and 4 are supposed to be
integers.

4. The equation (2) therefore transforms itself into the following

SAS, m+r—l + f8, m+-r—2 de ti Wh, =( 3 = aye ee Tess

which teaches us, that the MacManon relations are true for a
definite m for any integer value of 7 and forn >m +r, if they have
already been proved for all the minor values of m. This being the
case according to the Newron-Girarp formulae for m = 1 they exist
in general.

It would be difficult to give a demonstration of these relations
more simple in conception.

( 352 )

Bacteriology. — “On different forms of hereditary variation of
microbes’. By Prof. M. W. BrtsERINcK.

The interesting lecture of Prof. HuGo DE Vries in the last meet-
ing of the Academy on the origin of new forms in higher plants,
induces me to draw attention to some observations regarding the
same subject in microbes.

Though the culture of microbes, compared to that of higher plants
and animals is subject to many difficulties, it cannot be denied
that, these once mastered, microbes are an extremely useful material
for the investigation of the laws of heredity and variability. The
starting from the single individual, which of course is required here,
is commonly almost as simple as for the higher organisms, and it is
want of practice only which makes it appear so troublesome. The
generations succeed each other quickly; hundreds, nay thousands of
individuals can be very easily surveyed in their posterity ; far remote
classes of the natural system are represented by microbes; in many the
variability is great!). Even the difficulty of determining the species and
varieties, which is frequently only possible by means of biochemical
investigation, can become an advantage, for the very reason that
biochemical methods of distinction are very accurate, can be extended
in various directions and compared by measurement. Thus the species
and varieties of lactic-acid ferments are distinguished by titration,
alcohol ferments by means of the saccharometer, while different
carbohydrates can be selected as the base of lactic-acid and alcohol
fermentation. To all this is added the circumstance that it is easy to
perform with microbes experiments of competion, which is difficult or
impossible with higher plants and animals, and itis well-known how
delicate the distinctions are which are thereby revealed.

In comparing the results obtained with microbes to the rules found
in higher organisms, account should be kept, first, with the want
of sexuality, by which the variation of microbes acernee comparable
to the bud-variation of the higher plants, and, second, with the uni-
cellularity of the microbes. As to the first aes the experiences with
the bud-variants of higher plants seem to prove that an essential dif-
ference between bud-variation and seed-variation does not exist. As to
the uni-cellularity of the microbes, itis my opinion that by it the phe-
nomena of variation are rendered clearer but are not changed, when

1) Compare Roper, De la variabilité dans les microbes, Paris 1894. Bibliography
wants in this book und not all data are trustworthy.

( 353 )

compared to the multi-cellular organisms. According to the point of
view, the individual microbe can be compared to the whole indi-
vidual of the higher organism, or to a single tissue-cell of it, —
both comparisons are correct ').

1. Degeneration.

In bacteriological laboratories it is well-know that by prolonged
culture many microbes undergo slow, but great changes, even in
so much, that certain long continued cultures do not agree any more
with the descriptions given of them by the discoverers, short after
their first isolation from nature. In some cases the way in which
the change takes place can be rather minutely traced; three forms
of variability are therem more salient: degeneration, transformation
and common variation.

A species is isolated from nature and it is found that at the
culture during the first series of inoculations, in which hundreds
or thousands of cell-generations succeed each other, it develops well,
so that in the beginning the impression is obtained of a thorough
knowledge of the nutrition and other conditions of life. But by and
by it becomes more difficult to make the new inoculations thrive and
at last the culture-material grows troublesome and uninteresting and
would be quite unrecognisable if not the various phases of the
degeneration-process had been exactly observed. Prolonged cultivation
above the optimum temperature of the growth, and a too strong
concentration of the nutriment are in some cases the cause of degener-
ation. In some microaérophilae, for instance the bactery of the
“lange-wei” (Streptococcus hollandiae)*), the irrational regulation of
the oxygen tension causes a rapid, in few days complete vanishing
of the slimeformation, while after a much longer time, by the
same cause, the vegetative power of the bactery completely disappears.
In other cases, for instance with a phosphorescent bactery, very
common in the sea (Photobacter degenerans Fiscuer), the degener-
ation is accomplished without known cause, and in a very short time,
so that, within a few weeks the cultures may cease to exist. The
degeneration ‘goes not by leaps but continuously and affects all the

') An interesting view herewith connected is found in Wurrman, The inadequacy
of the cell-theory of development. Biological Lectures at the Wood’s Holl Laboratory,
1893, pag. 105, Boston 1894.

*) Used in Holland for cheese-making.

( 354 )

individuals in culture equally, so that it cannot be checked by
colony-selection.

2. Transformation.

At the transformation all the individuals brought im culture lose
a characteristic, while either another comes in its place, or a new
characteristic arises, or, lastly, the characteristic disappears without a
distinct substitute. Thus the cultures of Photobacter luminosum grow
dark in the course of some months by a slow process of transform-
ation,. whereby they change into a more rapidly growing form,
which acts more strongly on the nutriment than the normal form.
Here, thus increase of vegetative power has supplied the decrease
of phosphorescence.

It is remarkable that the transformation in this phosphorescent
bactery sometimes suddenly ceases and is replaced by a process of
variation where, beside a completely dark form (the variant), the
phosphorescent form with the full primitive phosphorescent power
again springs up. This is not the same as common atavism, where
the stock which throws off the atavist does not change further, but
it is probably comparable to the splitting of a bastard into the two
components. Very slow cell-partition, caused for instance by culture
at a low temperature, furthers this phenomenon. On the other hand,
the cause of the transformation may be a too rapid process of cell-
partition in which the photoplasm, which seems to grow more slowly
than the rest of the protoplasm, remains behind in its development.

In another phosphorescent bactery of the sea, common on our
coast, Ph. hollandiae, 1 hitherto only saw transformation, so that
this species quickly disappears from the cultures as a phosphorescent
bactery.

In a pigment bactery (Bacillus viridis) 1 saw, apparently without
any other change, the at first very strong power of liquefying
gelatin, by and by get lost in all the individuals.

On the other hand, I have seen in some vibrions, in a corre-
sponding way, from non-gelatin-liquefying individua's come forth
liquefying ones.

The new forms, thus called into life give, at superficial examin-
ation, quite the impression of new constant species. They cannot,
however, be valued as such as they differ only by one or very few
characteristics from the mother forms. This is the cause why they
must be classified as variants, quite like those of the following case.

ee a

( 355 )
3. Common variation.

The third and most frequent form of variability is common
variation. Here the normal form continues unchanged, but now and
then throws off individuals, the variants, which, from the beginning,
are likewise constant and remain so, but which every now and
then again throw off other variants, among which the normal form
may occur as an atavist. These variants probably correspond with
many well-known so-called varieties or races of culture plants and
domestic animals, and likewise, I should think, with the interesting
new forms obtained by Prof DE Vrigs from Oenothera lamarckiana!).
They remind us in some respects also of the Pleomorphy in the
Fungi, which especially in the Ustilaginae, can easily be observed
in the laboratories and about which, in particular BREFELD, has
made many researches *).

The names variant and sub-variant I have chosen, because in the
here discussed products of hereditary variation, which differ appar-
ently very much, but in fact only little from the normal form, I
think to see the lowest degrees of the natural system following above
the individual, and to them are given those names according to the
rules of botanic nomenclature °).

Regarding the divisions above the species, DE CANDOLLE does not
think it necessary to give definitions, in which I quite agree with him.
But singularly enough he does try to do it for the ranks beneath
the species, where he takes the greater or lesser constancy at
sowing as a criterion for the differences. This is not logical, here
too, definitions are unnecessary.

Probably various causes give rise to the production of variants.
Lengthened growth at insufficient nutrition, and the prolonged action
of the own secretion products of the microbes may, with some
probability, be considered as such causes.

The variant seems seldom, perhaps never, by one single cell-
partition to result from the mother-form, but only after some inter-
mediary partitions, rapidly accomplished. With these latter partitions
correspond the sub-variants, with a disposition for atavism or further
variation, and only keepable by colony-selection.

1) These Proceedings. Meeting of 29 Sept. 1900 pag. 246. Comptes rendus. T, 131
pag. 124 en 561, 1900.

*) Botanische Untersuchungen iiber Hefenpilze. Heft 5, 1883.

§) A. DE Canpox1z, Lois de Ja nomenclature botanique, 2e Ed. pag. 15, 1867, and
Nouvelles remarques, pag. 48 and 63, 1883.
24
Proceedings Royal Acad Amsterdam. Vol. III.

( 356 )

I will now describe some instances of common variation; first a
few cases of the originating of hereditary-constant variants, which
seem unable to return to the stock, then the more complicated case
of constant and variable variants, among which some with a great
disposition for atavism, which case I have nearer investigated in
the West-Indian phosphorescent bactery and its relatives.

I might augment these instances with many more, for most of
the microbes with which I occupied myself for a length of time,
produced in my cultures more or less hereditary-constant variants.
Extremely variable are the mycelia of the Fungi, for which I refer
to the complicated relations of the aethyl-acetate-yeast, which I
described and demonstrated in 18951), and where transformation and
common variation both occur.

4. Variation in Schizosaccharomyces octosporus *).

This curious maltose-yeast I detected in 1893 on dried orient-fruits
as currants, dates, raisins, and figs. I found a good method to
separate this species from the other microbes, by which it is possible
as often as desired to bring it from nature into culture. It proved
to be a generally spread organism, which is found in Greece, Turkey,
Italy, Asia Minor and Java in one and the same variety. After many
isolations I found in 1897%) a new variety on dates from N.-Africa.
The culture is effected in the lke way as of beer-yeast on wort-
gelatin. Maltose, like glucose and levulose, undergoes a vigorous
alcoholic fermentation, cane-sugar not at all.

As well the usual form as the new variety produce 8-spored spo-
angia, the spores of which colour intensely blue with iodium. During
the growing a small quantity of diastase is secreted. The vegetative
condition which precedes the spore-formation, as also the vegetative
variant, which produces no more spores, of which more below,
multiply by partition (not as in other yeasts by budding) and colour
yellow by iodium; glycogene wants completely in it. Accordingly
it is possible, by treating a culture with iodium, from thousands
of colonies, instantly to recognise those containing spores, and from
the intensity of the blue-colouring with some certainty to make out

1) Handelingen van het 5e Natwur- en Geneesk. Congres te Amsterdam pag. 301, 1895.

2) Centralblatt fiir Bacteriologie Bd. 16 pag. 49, 1894 and Ibid. Abth. 2. Bd. 3 pag.
449, 1897. In 1897 I put the variant on a level with a “vegetative race”, but as [
now think, in doing so I rated its systematic value too high.

5) Together with a new quite diferent species of Schizosaccharomyces.

( 357 )

the number of spores present. The variety of dates differs from
the main form by the sporangia of the latter being ellipsoidal and
thickest in the middle, while in the variety, on the other hand, they
are just in the middle constringed, and moreover by several other little
salient characteristics, which only become discernible by practice.

Both, main form as well as variety produce, as the cultures grow
older, a variant so much deviating from the normal forms, that, if
these variants were met with in nature, they would certainly be
proclaimed a new species if no new genus. The cells are globular,
and not as in the normal form elongated, but the multiplication
is here also exclusively effected by partition. Spores are not at all
formed.

This variant springs, so far as I have been able to find out till
now, at once form the normal form, which for the rest propagates
unchanged, and can constantly anew throw off the variant. The
first variants are found in cultures which have continued growing
a few weeks without re-inoculating, and they go on some time
multiplying on the nearly exhausted culture medium, after the
normal form does no more do so. This points to a gain of vegetative
power, at least in the conditions that prevail in the old culture-
medium, but in new nutriment I could observe nothing of this
difference.

The variant after repeated re-inoculation, at present already during
more than three years and consequently after thousands of cell-
generations, has remained perfectly constant; never could even a single
sporangium be found, which, with the help of the iodium reaction,
can be seen at a glance in the microscopic preparation. Whether in
the variant the faculty of forming spores continues latent is possible,
even probable, but not proved.

In the variety, isolated from dates, also occur sub-variants, that
is intermediary forms between normal form and variant, while in
that of currants I have found no sub-variants. The sub-variants still
produce some sporangia, mostly 8-spored. Without much trouble I
could isolate from a thousand colonies three sub-variants, belonging
to two types; both types proved at re-inoculation to be constant,
but growing older they throw off, in the habitual way, the asporgene
variant, so that, in order to be preserved, they must be propagated
from the spores. This can be done by pasteurising the sowing
material at 55° C., by which the vegetative cells die and the
spores alone survive.

In continuing this manipulation I have obtained new sub-variants.
One of these produces 4- or 8-spored globular sporangia and is at
24*

-_

( 358 )

first sight a new species. Cells and sporangia remind of the vegetative
variant which should have regained the power of producing spores.
But all the characteristics are limited between those of the normal
form and the asporogene variant. So that, although this form too is
hereditary-constant, I cannot see a new variety in it, but only a new
variant.

It is noteworthy in this case, that the variants of the same ge-
neration, that is those which result from the same sowing, always
differ by distinct breaks in the tint of the iodium reaction, and form
no flowing series between main form and main variant. But I think
this to be the consequence of the limited number of colonies which can
be overseen at each experiment, and amount to no more than one
or two thousand, and that it will be possible to fill up the gaps
with sub-variants from other cultures, which perhaps grow rarer as
the leaps are smaller. The question why sub-variants are so much
rarer than main variants, I cannot as yet fully answer, but the
existence of sub-variants proves that the great and sudden leaps, observed
in the variability everywhere in the vegetable and animal kingdoms,
are no necessary attribute of variability. Furthermore these sub-
variants prove that even slight deviations may be in high degree
hereditary-constant !).

5. Variation in Bacillus prodigiosus.

This well-known red pigment-bactery is cultured by me in three
distinct natural varieties. One of them does not liquefy the
the culture-gelatin*), of the two others which do, one *) has the
power of causing various carbon-hydrates to ferment under pro-
duction of hydrogen, the other not*). All three produce, in older
cultures, a variant which is completely colourless, but in all other
respects pessesses the properties of the normal form whence it has
taken birth, so that there are non-liquefying and fermenting, and
liquefying non-fermenting colourless variants. All these variants have
remained hereditary-constant in my experiments and produce no

1) For the more complicated phenomena of variation in some species of Saccharo-
myces, I refer to my paper “Sur la régénération des spores chez les levtires etc., Ar-
chives Néerlandaises, Sér 2, T. 2 pag. 269, 1899.

*) Isolated from potatoes grown hollow in the soil and given me by Prof. Rrtzewa Bos.

3) Isolated from tubercles of red clover,

‘) Isolated from bones kept at the open alr on the bone-hill of the gelatin- and
glue-factory at Delft.

( 359 )

atavists like to the mother form, i.e. red-coloured colonies. There
is no doubt but, if these variants were met with in nature, not
accompanied by the normal form from which they arise, they would be
taken for as many new species. Still it would be an error to admit
them as species into the system, as a more minute investigation
shows that, except in the power of forming pigment, they correspond
in all other respects with the normal forms, and one single point
of difference determines only a variant.

I doubt by no means that 2. prodigiosus can also vary in other
directions; this follows already from the fact that I could find three
very different natural varieties, which all produce red pigment ').
But I have not taken pains to trace other variations.

Sub-variants between the normal forms and the said colourless
variants are, or at least seem rarer than the main variants. They
are rose-coloured and at colony-selection almost as constant as the
normal form. They also produce like the latter the constant colourless
main-variant, and moreover show a propensity for atavism. In each
natural variety I have found only one er two rose-coloured sub-
variants.

6. Variation in Photobacter indicum.

This phosphorescent bactery was isolated by Prof, Fiscuer of Kiel,
from seawater in the vicinity of the isle of Santa Cruz, one of the
Antilles, on January 10, 1886. I received material of it in May
1887 and have without interruption cultured it till now. Already
in 1887 I perceived, that with the growing older of the cultures,
two main variants arise and even in so great a number that the
normal form can be supplanted by them for the greater part, though
not quite. One of these is either completely or almost completely
dark, the other grows much more slowly than the normal form
and is almost motionless, while the normal form is extremely
motile. I will call these variants Ph. indicum vnt. obscurum and
Ph. indicum ynt. parvum. Later I found some more variants which
are less common. ‘There are besides sub-variants of which I have
examined those standing between the normal form and obscurum;
they produce now and then atavists, and vary also towards obscurum,
but can be kept constant by colony-selection.

‘) The red pigment of B. prodzgiosus is a product of excretion found between the
living and partly accumulated in dead bacteria. It is in my opinion the product
of specific chromoplasm, which forms a small part of the protoplasm in general,

( 360 )

Notwithstanding this great variability it has been possible, likewise
by means of colony-selection, during the more than 13 years con-
tinued laboratory culture, to keep up the stock unchanged, which
is remarkable, when thinking of the place where it was first found.

The variants and sub-variants always spring from the stock in
the same way. They may be reduced to two types: variable and
unvariable. All phosphorescent variants are more or Jess variable.

The variant parvum shows an extreme disposition for atavism, so
that already after its first re-inoculation on a new culture-medium,
various normal forms spring from it.

The obscurum-variants are more constant. They are either perfectly
constant, so that, as it seems, phosphorescent forms never again
arise from them, er imperfectly, so that after going through a few
cell-partitions, answering to as many sub-varianis, the normal form
returns with the full phosphorescent power. Dark variants, in this
way producing Juminous cultures, prove that progressive variability !)
also occurs in the laboratory cultures

The variant is not the product of a single heterogene cell-partition,
but of the passing through some preparatory cell-partitions, answer-
ing to as many sub-variants. I was able without difficulty to
distinguish two of these leaps or sub-variants, but it is possible that
there are more, too slightly differing for my observation. It is also
probable that by the esnditions of culture, these preparatory cell-
partitions, and with them the sub-variants, existing between the
normal form and the main variant, will grow more or less numerous.

Hele The obscurum-variant is probably produced
Sr in accordance with the scheme of Fig. 1.
— For the sake of simplicity here is only
TORIES A figured one intermediary stadium (sub-variant)

CRED ——_

by the dotted rod; the dark main variant is drawn
Probable course of deyelop- | * : .
ment of the dark variant by black, the normal form white. This scheme
direct heterogene cell-pattition answers to what may be called the development
or eyolution. The first partition ; C za
produces from the singlelumi- Of the cell-vyariant by heterogene cell-partition
nous bacillus one of the same, or evolution

and another of lessened lumin- P A
osity. The second partition | Less probable is the development of the variant

produces from the latter again hy transformation or epigenesis represented in
one of the same luminosity, +y,.

Fig. 2
and another quite-dark. se Sb
1) Distinction can be made between: — retrograding or analytic variability, in which
a characteristic disappears entirely or partly, — replacing variability, in which a

characteristic is wholly or partly supplanted by another, — and progressive or synthetic
variability, in which a new characteristic is added to those already existing.

( 361 )

Fig. 2. The preparatory cell-partitions at the atavism
S> of the luminous normal form from the dark
be fate or fe I inous -variants still liable
or feebly luminous sub variants till hable to
BORMAN EE retrogression, probably answer likewise to the

=m @ schema of Fig. 1.
| a rae aeaelraie If the normal form is indicated by e, the
heterogene cell-partition 0/scusum-variant by —, and the parvwm-variant
eat kar by ++, unreckoned the sub-variants, the pe-
digree of the normal form of Ph. indicum can be represented by
Fig. 3, which means, that at the two first re-
inoculations only the normal form is produced,
and that at the third likewise obscurwm- and
parvum-variants have orginated, but from cells
which were subjected to particular conditions.
mea catia The numbers 2 and 3 for the generations are
normal form. chosen arbitrarily, for the number of gene-
rations, after which the variation occurs, can be regulated at will,
for by early re-inoculating the young cultures on fish-broth-agar (not
on fish-broth-gelatin) the variation can be kept back for a long time !).

For the variant parvum the pedigree becomes somewhat different
from that of the normal form, there being much atavism (Fig. 4).

Fig. 4. The pedigree of obscurum can, as to the
constant form, be represented by a single mark.

The variable, obscurum, again produces ata-
vists, but less than parvum, and besides parvum-
variants (Fig. 5).

In these three last schemes are, as said, the
sub-variants left out.

I have not succeeded from Ph. indicum to
obtain a perfectly constant luminous form, that
is, one which produces no variants, though I have
tried for years to do this by selection. It is
evident that the conditions of culture inavoid-

Pedires’ of variable ably give cause to the rise of variants. That

obscurum. for the rest the faculty of varying in a very
determined way, is deeply rooted in the nature of the cell, is proved
by the following observations.

A few years ago Mr. Fiscuer at Kiel again sent me some material
of Ph. indicum, which had thus during many years been cultiv-

) To these relations I hope to refer at another occasion,

( 362 )

ated in his laboratory. There was a considerable difference, compared
to my stock, but the normal form and the two variants obscurum
and parvum, I could still obtain from it as constant forms by means
of colony-selection.

At the examination of numerous samples of seawater in all the
seasons, taken near Scheveningen, Bergen op Zoom and den Helder,
partly far from the coast '), I have never found Ph. indicum itself,
but, even three times, forms which, with a broad conception of the
species, might be considered as varieties of it, and else as very closely
allied species. I call them Ph. splendidum and Ph. splendor maris.
Short after the isolation already they produced variants, one of which
is quite dark and multiplies in such a number that in cultures which
are negligently re-inoculated the normal form, and with it the pho-
togenic power, wholly disappear.

Thus, a culture at 22° C. of splendor maris, going out from a
single phosphorescent colony, after being in 12 days six times re-
inoculated on fish-broth-gelatin, produced 1800 dark variants on 22
colonies of the normal form. The culture re-inoculated six times in
the same space of time on fish-agar did not yet contain any variants,
whilst at the 12 re-inoculation on agar their number was also very
great. The first not further re-inoculated cultures on gelatin,
which accordingly had only had little opportunity to grow, after 12
days did not contain variants, in accordance with the rule that at
eessation of growth no variability is manifested.

The parvum-variant also is in Ph. splendidum and Ph. splendor
maris as distinctly recognisable as in Ph. indicum itself, and here
too, frequently produces the primitive forms as atavists.

Basing on these experiences I think it probable, that the cause
which calls forth the variants is not exclusively active in our arti-
ficial .cultures, but can also be active in the sea itself, so that in
this case there is a chance that dark forms, isolated from the sea
will at first be taken for particular species, but after more minute
observation, will prove to be variants of known phosphorescent
bacteria.

By observing certain general conditions the production of dark va-
riants can, as said, be greatly slackened, but not wholly prevented.

') Many of these samples 1 owe to the kindness of Dr. Hor. Various species of
Juminous bacteria have been found in them to’ the amount of 0.1 to 5, even 7 pCt.,
of all present bacteria. Especially Ph. Zwminosum, and a species difficult to distinguish
from it, but still quite different, PA. hollandiae, oceur very often, Ph. degenerans also
is frequent. }

( 363 )

Among these are: strong nutrition and vigorous growth a little below
the optimum temperature, free access of oxygen, such as can be at-
tained in cultures on agar-agar, and total exclusion of the influence
exerted by the secretion-products of the bacteria themselves, which
is attainable by re-inoculating the young cultures very often on a
new medium.

7. Conelusion.

I will begin with pointing to the fact that hereditary variability
is a function of growth, in particular of slackened growth, but that
at cessation of growth no change takes place. And furthermore
that variability attacks oniy one independent characteristic at a time.
In the sub-variant one characteristic of the normal form is partly,
in the main-variant it is wholly changed. In new varieties and
species more characteristics are varied.

Furthermore resuming the above given statements I come to the
following conclusions. The here discussed forms of hereditary varia-
bility belong to three types: At degeneration all individuals, by a
slow process of variability, lose their vegetative power, so that the
species may cease to exist. At transformation, which seems to ap-
pear more seldom, all individuals lose a specific characteristic and
acquire either or not another instead. At the common hereditary
variability or variation, the normal form, probably by heterogene
eell-partition, throws off some individuals, the variants, mostly differ-
ing from it by a strongly salient characteristic. The normal form
itself propagates beside it quite unchanged. The variants are constant
in a way corresponding with independent species; sometimes this
constancy is perfect, in other cases atavists are produced, like to the
normal form. Subvariants i.e. intermediate forms between normal
form and variant, are less fownd than the variants themselves, but
they are perhaps never wanting, and are in the same way constant
as the normal forms. Whether the sub-variants are also originally
formed in smaller number than the main variants is uncertain;
what is seen is that they rapidly disappear from the cultures and
are supplanted by the normal form and main variants if they are
not fixed by colony-selection. Besides, each well-defined degree of
yariation, however slight, seems to be fixable.

The rare occurrence of the sub-variants throws some light, First,
(by the comparison of the individual microbes with the individuals
of the higher organisms) on the marked distinctness by which in
higher plants and animals most varieties and species are separated, —

( 364 )

for they originate by repeated variation processes, relative to different
characteristics- aud the chance that the common and distinctly diseern-
able variants will partake therein and not the rare sub-variants, more
difficult to distinguish, is accordingly greatest }).

Second, (by the comparison of the individual microbes with the
tissue-cells of the higher organisms) on the no less marked confines
between the tissues and the organs of one and the same individual,
— for these are constituted of as many cell-variants of the embryonal
cells, cell-varients, which will supplant the cell-sub-variants.

That many so-called new species will prove only variants of other
species and no “good species’, is not improbable. Especially in the
microbes, where the want of crossing must strongly favour the
prolonged continuing of the once formed variants, it is to be foreseen
that im nature will often be found variants, which will long maintain
themselves at their habitat. If they are isolated, the discoverer will
at first be almost sure to see new species in them, and only after
an accurate investigation recognise them as variants of another species.

The sub-variants of the microbes prove, that the characteristics
which in the main variants are quite wanting disappear by little
leaps from the normal forms. In other cases, however, the main
variants seem to appear suddenly, whence it would follow, that a
characteristic can also vanish at a single leap at the cell-partition;
but here the sub-variants may have escaped from observation.

The variants of the microbes, regarded as cell-variants, prove that
out of a cell daughter-cells may spring unlike to the mother-cell.
Though the way in which this is effected is still insufficiently
known, it proves the existence of heterogene cell-formation, whether
by direct heterogene cell-partition (fig. 1), or, by the less probable
transformation (fig. 2).

1) I perfectly agree with Professor pe Vries, that the origin of species should often
be sought in the almost suddenly produced variants, or mutants, as he calls them.
This is also the conclusion to which GaLron has come regarding the races, and to
which he referred repeatedly since 1892, the last time, so far as I know, in Nature
T. 58, pag. 247, 1898 in these words: “I have frequently insisted that these sports
or “aberrances” (if I may coin the word) are notable factors in ihe evolution of races.
Certainly the successive improvements of breeds of domestic animals generally, as in
those of horses in particular, usually make fresh starts from decided sports or
aberrances and are by no means always developed slowly through the accumulation
of minute and favourable variations during a long succession of generations.” Along
quite distinct ways Gauron, pe Vries and myself have thus arrived at the same
conclusion regarding the probable origin of many races and species. But the great
difficulty which lies in the explanation of the adaptions, has not been removed,
neither by Gawron’s vaberrants”, DE Varies’ »mutants”, nor my ,variants”.

( 365 )

In order to show how decidedly heterogene cell-formation is still
considered as impossible, so that it is not superfluous to afford a
new evidence for its existence, I refer to the well-known book of
O. Hertwie “Die Zelle und die Gewebe’’, p. 64 Bd. 2, Ed. 1898,
where we read as follows: ,Die Theorie der heterogenen Zeugung,
wo sie aufgestellt wuide, ist als grober Irthum bald beseitigt worden.
So gilt als ein allgemeines Grundgesetz in der Biologie der Ausspruch
»Gleiches erzeugt nur Gleiches” oder besser ,Art erzeugt stets seine
Art.” Bei allen einzelligen Lebewesen ist erbgleiche Theilung ihres
Zellenorganismus die einzige die vorkommt und vorkommen kann.
Auf ihr beruht die Constanz der Art. Wenn es méglich wiire, dass
bei irgend einem einzelligen Organismus die Erbmasse (Idioplasma)
durch Theilung in zwei ungleiche Componenten zerlegt und auf die
Tochterzellen ungleich iibertragen werden kénnte, dann hiitten wir
den Fall einer heterogenen Zeugung, den Fall der Entstehung zweier
neuer Arten aus einer Art. Wie indessen alle Beobachtungen lehren,
werden auch bei den Finzelligen die Arteigenschaften so streng und
bis ins Kleinste tiberliefert, dass einzellige Pilze, Algen, Infusorién
auch noch im millionsten Gliede, ihren weit entfernten Vorfahren
genau gleichen. Der Theilungsprocess als solcher erscheint daher
auch bei den einzelligen Organismen nie und nirgends als Mittel
um neue Arten ins Leben zu rufen.”

The preceding pages prove that this view is erroneous, so that
the far reaching conclusions, drawn from it in relation to ontogeny
vanish at the same time.

So far there is thus no reason in contradiction with observation,
which forbids admitting, that the ontogeny of the higher organisms
consists in a regular course of variation processes, and that full-
grown plants and animals are built up of as many cell-variants
of the embryonal cells,as they contain different tissues composed of
identie cells.

Botanics. -- ‘On the development of Buds and Bud-variations
in Cytisus adami”. By Prof. M. W. Brerincx.

Cytisus adami is a hybrid between the common laburnum, Cytisus
laburnum, and a little shrub from Styria, Cytisus purpureus, with
purple flowers. Now and then are found on Cytisus adami buds

( 366 )

of both species as bud-variants'). The experience that these buds
appear in particular on oller parts, and have, probably without
exception, passed one or more years in dormant condition before
budding and changing into the primitive forms), induced me to cut
down all the branches and the main stem of four specimens of C.
adami in order in this way to excite the development of the very
old buds which were, since years, in dormant condition on the old
trunk. My expectation, that by these means I should obtain a great
number of bud-variants, proved right: in few years I saw, together
with earlier observations, appear more than a hundred buds of
laburnum and about twenty of purpureus. I was thereby enabled to
establish a few particularities about buds and bud-variations which
follow here:

1. The ordinary axillary buds of Cytisus adami spring not from
single cells but from cell-groups. They grow on by means of a
pluricellular meristem, and not by means of one terminal cell. The
latter fact was long known already and is here anew confirmed.

2. The bud-variants, also, originate from cell-groups and not
from single cells, so that the cause which is active here in producing
variability, must extend over many cells at a time. —

That this cause is in some or other way related to unfavorable
conditions of nutrition cannot be doubted.

Of course the possibility is not excluded that for C. adami buds
and bud-variants can spring from single cells. I think this even pro-
bable as regards some of the many buds which develop from the
“bud-crown” ®). Herewith is meant the sheath of vigorously vegetating
cambium-cells which is found in the callus and the bark, just in
the prolongation of the procambium- or cambium-cells of truncated
or thrown off buds or branches, which sheath is an active centrum
for the originating of new buds. For the rest, it is not the springing
forth of a bud or new individual from a single cell which is remark-
able, but the fact that this can take place from an already consti-
tuted cell-group. That this really occurs, and also, that a meristem

1) The word “variant” is here used in a sense somewhat different from that in the
preceding paper on the variants of microbes, “component” might perhaps be more
precise in this case. But I keep to the usage, as the meaning is clear.

*) This does not hold good for the flowers, which have no dormant period but
constantly develop in the 24 year, and of which the different parts are still more
subject to return to the components than the vegetative buds. But the flower may,
even unreckoned the process of fertilisation, be called the organ of variability.

§) Translated from the German “Knospenkrone”,

( 367 )

constituted of many cells may be subject to the process of variation,
is proved by the following observations.

At about ninety laburnum-buds which
had developed as variants, nothing partic-
ular was to be seen, but at eight or nine
were found at the base a greater or smaller
number of bud-seales which could with
certainty be recognised as bud-seales of
adami (ad Fig. 1 A).

This observation is easy and convincing,
as all parts of laburnum, hence the bud-
scales too, are covered with silverwhite
hairs, especially at the under- or back-side,
while the full-grown portions of adami are
always devoid of hairs. In all the cases,
which I examined more minutely, the line

Hg, 1. of demarcation between the adami- and

Two Jaburnun bud-variants J4hy47num-portion ran in an oblique direction,
on a branch of Cytisus adami; _ oe :
the lower bud beara at its 80 that the whole meristem belonged evi-
base adami bud-scales, but is dently to /aburnum. This was constantly
in the higher portion pure confirmed by the experience at the budding,
laburnum ; the upper bud B is 4, always pure laburnum-shoots grew from
precisely for one half adami,
for the other Zadurnum. these buds.

In 1898 an extraordinarily great number
of /aburnum-variants were formed on my adami-trees. In consequence
of the early pruning all the buds were situated low enough to be
easily examined with the magnifying-glass. Two of them presented
themselves as in Fig. 1 B. The line of demarcation went precisely
over the middle of the bud-scales and not obliquely as in the eight
cases above. The supposition that the said demarcation would also
continue precisely over the middle of the meristem, proved right at
the budding, for both the branches which sprung from these buds
in 1899, were exactly for one half, lengthwise, adami, for the other
half laburnum.

One of these “mixed branches” has attained a length of about
1 Metre, and produced more than 30 leaves with axillary lateral
buds, of which about 15 belonged to laburnum, the other 15 to
adami. At its extremity was in the autumn of 1899 an open
“summer-bud”, still for one half adam/, for the other half labwrnum;
this summer-bud was not closed with bud-scales, and died in the
winter of 1899—1900.

The second branch has become about 3 M. long, and bore more

( 368 )

than 12 leaves with axillary buds, again belonging for one half to
laburnum, for the other to adami. In the autumn of 1899 a closed
,winter-bud” with bud-scales was formed at the extremity. Though
the line of demarcation seemed also to go over the middle of this
terminal bud, a l/aburnum-branch developed from it in the summer
of 1900, which only at the base bore some adami-leaves, so that the
separation within the bud must have run obliquely and divided
the meristem into a larger /aburnum- and a smaller adami-portion.

This description proves that the two halves of the ,mixed branches”
have each grown from an independent half of the meristem, which
half cannot consist of less than one cell, so that the continued growing
of the branches with one terminal cell is out of question, accordingly
it is certain that the branches of Cytisws adami grow with at least
2, and probably many more meristem cells.

The two separating lines between /aburnum and adami which
are seen over the full length of the ,mixed branches’, easily dis-
cernible on the bark as the confines between a portion set with
hairs and another without, ran in 1899 for the greater part of course
between the leaves, but in some places also through the leaves
themselves. Some of these ,mixed leaves” were situated exactly
for one half on the laburnum- for the other on the adami-portion
of the branch. In this case the trifoliate leaf was as exactly for
one half an adami- and for the other a laburnum-leaf, and over
the whole length of the petiole and the midrib of the terminal
leaflet the line of demarcation was distinctly discernible. This
would, if necessary, be sufficient to prove that also each leaf takes
birth from at least two, and probably more meristem cells. But the
pluricellular origin of the leaves of the higher plants has, so far as
I know, never been called in question, though this has been the
case concerning the origin of the lateral buds.

So, it was of importance to establish whether the axillary buds
of these ,mixed leaves”, exactly placed on the confine, would
likewise produce ,mixed branches”, by which the question would
be answered if one bud might spring forth from two or more cells
at a time. The answer was not dubious: all the buds, placed in
the axils of the leaves, which were for one half laburnum, for the
other adami, produced, in the summer of 1900, as well /aburnum-
as adami-leaves, and in this case, too, some leaves again were mixed,
namely partly adami- partly laburnum-leaves.

In most cases the line of demarcation went very obliquely
through the “mixed buds” of this second generation, so that the
whole meristem early in the year consisted of only adami or only

( 369 )

laburnum. In one of these buds however the boundary line went
precisely through the middle, but this bud contained an inflorescence
of which the summit had died off in the winter of 1899—1900.
At the base were however pure laburnum- and pure adami-flowers,
and one flower was precisely for one half /aburnum, for the other
adami, so that also flowers evidently spring not from one cell, but
from a cell-group.

The preceding description proves that in the springing forth of
the /abuwrnum-variant from Cytisus adami, as well a whole meristem
may be concerned as half of it, and that the cause which gives
rise to the appearance of a bud-variant is active when the me-
ristem is completely formed, and not in the far-back moment
when the cell-group, which later manifests itself as a meristem, was
still a single cell. For if this were the case it could not be possible
that a portion of the bud, which produces the variant, continued
to belong to C. adami itself.

Hence it follows that the bud-variant is not produced by variation
of a single cell but by that of a cell-group.

Fic. 2.

One year’s purpureus, ps, sprung as a bud-variant, from a dormant adami-bud,
at the extremity of a “short-shoot” ad. On the left a “long-shoot”
of adami, at the extremity of a “short-shoot”.

( 370 )

To show that also the purpwreus-variant is produced by the vari-
ation of an already constituted adami-meristem, and not of a single
cell, far-back in the evolution of that meristem, I refer to Fig. 2.

Here we see a one year’s purpureus-shrub (ps) placed at the
extremity of a ‘“short-shoot” of Cytisus adami+). Commonly the
purpureus-variants, quite like those of laburnwm, spring from com-
com buds, whence the exact moment of their birth is not clear.
But the peculiarity of the case figured here is that the “short-
shoot”, terminating in purpureus, had already grown for a number
of years as adam, and that consequently it is not possible to doubt,
that purpureus has come forth from the whole adami-meristem. As
this meristem is pluricellular, the cause, which led to produce the
purpureus-variant, must thus also have affected a cell-group and not
have been confined to a single cell.

In a few cases the purpureus-bud was not found alone, but also some
adami-buds of the nearest surrounding were changed into purpureus. So,
this summer, in my garden, of six quite independent, dormant, three
years’ buds at the summit of a “long shoot” of Cytisus adami, separ-
ated from each other by relatively short internodes of the long-
shoot, no less than four are changed into purpureus, and besides,
the two unchanged adami-buds are placed between the higher and
lower situated purpureus branchlets. Accordingly the influence which
caused the variation must have been active simultaneously in four
meristems, the distances between which, at the time of the variation,
must certainly have amounted to some tenth parts of millimeters.

Herewith I think to have made good the two statements expressed
at the beginning of this paper, and I only wish to add that already
before, but at quite another occasion (Cécidiogénése du Cynips cali-
cis. Archives Neérlandaises, Sér 2, T. 2, 1897, pag. 436), I came
to the opinion that variability, though habitually going out from
a single cell, is not necessarily always bound to it, but some-
times has a cell-group as starting point, so that there can be question
of uni- and pluri-cellular variability.

The relatively great number of bud-variants of adami, which I
have examined, consisted, as usually, only of pure /aburnum- and
pure purpureus-branches. Hybrids, in which both factors occur, but
one preponderant as compared to its part in adami, seem never to
be produced. Still I believe that im the cell-layers of the bud-

1) A “short-shoot” consists of a closely crowded succession of nodes, between which
the internodes are not developed; they grow very slowly and point to unfavorable
conditions of nutrition.

( 371 )

meristem, which form the separation between adami and one of the
variants, there must occur transitory cells, which, could they be
independently developed and cultivated into new individuals, would
produce such derivated hybrids. Perhaps the “supplanting” of these
transitory cells by the completely varied cells, may be compared to
the rarity (discussed in the preceding paper on the variants of
microbes) of the sub-variants as compared to the normal form and
the main variants, by which it seems possible to explain, on the
one hand the existence of distinctly marked bounds between the
species, on the other hand, the not less marked bounds between the
different organs and tissues of the higher organisms.

Physiology. — ‘On the permeability of the ved bloodcorpuscles
for NOs- and SO,-ions”. By Dr. H. J. Hampureer.

The question whether cells are permeable for certain substances
and if so, to what extent, is not only important for our knowledge
about metabolic and other vital processes, but is also of great im-
portance from a pharmacological point of view. Here again the red
bloodcorpuscles are found to be the favourable test-objects to study
this question accurately. It is onlv natural that these cells are in
this case equally serviceable as in many other problems of a general
scope. In the first place they are met with in the isolated condition
(in contrast with most other cells) and they can therefore be procured
without being injured; in the second place the influence of different
agencies can in them be better traced than in other cells, thanks to
their change of form and dimension as well as to the extrusion
of red colouring matter, and in the third place the reciprocal influence
between the contents of the cell and its natural surroundings can
be studied in detail by chemical analysis.

It is through the study of the laws of the isotonic coéfficients
(Hugo ve Vries) of the red blood-corpuscles that the problem of
permeability was first brought into the foreground 1).

I will not here enlarge on what has hitherto been investigated
and written on this subject. I only wish to point out that it has
been agreed that there are: 1°. substances which penetrate through
the bloodcorpuscles and destroy them (for instance NH,Cl); 2° sub-

1) Hampuscer, De permeabiliteit der roode bloedlichuampjes in verband met de
isotonische coéfficienten. Versl. en Meded. d. Kon. Akad. v. Wetensch., 1890, bl. 15.

( 372 )

stances which permeate them, but are harmless (for instance urea) ;
whereas there is a great number of substances, amongst others salts
as NaCl, NagSO, ete., which are likewise harmless, but concerning
whose permeating capacities opinions differ.

Some assert that alkali-salts as such can penetrate into the blood-
corpuscles, others say that they are absolutely impenetrable to
these salts.

Formerly I agreed with the former opinion; now I am convinced,
considering the theory of the electrolytic dissociation, that the truth
lies half-ways and that the bloodcorpuscle is not permeable for the
alkali-salt as such, nor for the metal-ion either, but for the acid-ion.

When CO, is mixed with blood the following symptoms will be
observed: the bloodcorpuscle becomes richer in chlorine, richer in
water and poorer in alkali. The serum undergoes just the reverse
change, an exchange of substances has thus taken place.

The kalium- and natrium-contents of blood-corpuscle and serum
have nothing to do with this, these are unchanged (GURBER).

There is now no difficulty in explaining these symptoms.

Through the influence of CO, carbonate appears in the blood-
corpuscles. A part of the bivalent electronegative CO"s-ions leaves
the bloodcorpuscle and is replaced by the double number of electro-
negative Cl’-ions. Therefore increase of the Cl-contents of the blood-
corpuscles and increase of the alkali-contents of the serum.

As two Cl'-ions are needed to replace one CO,"-ion and every ion,
be it mono- or bivalent, represents the same power to attract water
(osmotic pressure), the power of water-attraction in the bloodcor-
puscle-contents must increase more than that of the serum and the
bloodcorpuscle attracts water, it swells.

The following experiment confirms this proposal.

The serum is remoyed as thoroughly as possible from defibrinated
blood and the bloodcorpuscles are then washed with a solution of glucose,
until all the serum has been removed. The intracellular liquid now
reacts neutrally. The passing of CO, through the fluid suspension of
the bloodeorpuscles in glucose does not make the liquid alkaline,
although the bloodecorpuscles have taken in COg, and K, COs has
been formed; but as such it does not extrude. CO; however can
leave the bloodcorpuscle, provided an equivalent quantity of another
ion of the same name takes its place. Thus, when the glucose-solution
is substituted by a Na Cl-solution isotonic with the bloodcorpuscles,
the latter becomes immediately alkaline and the bloodcorpuscles
swell. The reason is this that CO,'-ions have left the bloodcorpuscles
and the double number of Cl’-ions have taken their place. The

( 373 )

kalium and natrium of the bloodcorpuscles and surrounding have
in the meantime remained unchanged.

The question may now be considered what the result will be,
when in a suspension of bloodcorpuscles in glucose not a solution
of NaCl is added, but a solution of Na NOs isotonic with the
bloodcorpuscles. Then the Na NO;-solution also becomes alkaline
through natrium-carbonate, very weak when no CO, was made to
pass through the suspension, but pretty strong when this had been
the case. And in accordance with what is observed in Na Cl,
swelling is also found here after addition of the isotonic salt-
solution to the CQO,-suspension of the bloodcorpuscles in glucose-
solution. This is self-evident, for, when it is admitted that (NOs)’-ions
enter the bloodcorpuscles and CO;"-ions extrude, then every CO;"-ion
which extrudes must be replaced by two (NO3)’-ions, and as one (NO.)-
ion represents the same osmotic pressure as one CO,"-ion, the power
of the bloodcorpuscle to attract water (osmotic pressure) must increase
and the latter will swell.

If the experiment is performed with Na SO,-solution, then this
solution will likewise be seen to become alkaline, weak, when no
CO, was mixed with the suspension of the bloodcorpuscles in
glucose-solution, rather strong when this had been the case. The
volume of the bloodcorpuscles did not increase however. This is
evident; against one SO,'-ion which enters the bloodcorpuscles, one
CO";-ion extrudes; the power of water-attraction of the bloodco r-
puscles-contents remains the same during this exchange.

From these experiments the conclusion may be drawn that the
red bloodcorpuscles are permeable for NOs'- and SO,"-ions; which
was hitherto not accepted even by those who did not doubt a
permeation for chlorine, as based upon direct quantitative analysis.

Meanwhile our conclusions in regard to the permeability of the
red bloodcorpuscles for SO,- and NOs-ions, also find their confirma-
tion in direct quantitative chemical analysis of the added sulphate
and nitrate before and after the mixture with the bloodcorpuscles.

Not for all acid-ions however quantitative chemical analysis can
be performed with sufficient accuracy required for the purpose.

For such cases we now find in the described method a means
which enables us to judge about the permeability of the bloodcorpuscles
for such ions. It only requires to be noted whether alkaline reaction
appears, or if already present, increases, in the bloodcorpuscles washed
with glucose, after addition of the salt-solution containing the ion
which must be examined. A preceding treatment of the suspension

( 374 )

of bloodcorpuscles in glucose-solution with CO, is much to be re-
commended, as the number of CQO;-ions in the bloodcorpuscles
increases thereby and therefore a better opportunity offers itself for
the acid-ions (anions), which are to be examined, to change places
with CO"; and to enter. Consequently the alkaline reaction of the
solution about to be examined will become stronger. That CO, is
able to promote the entrance of ions into cells seems to me of
great importance for the economy of the human body.

(November 21, 1900.)

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parabola
for

and »
(1—2) ly (1—2)
differences
1.46

, 10, 12 and 16 for determination read determinations

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday November 24, 1900.

0 co.

Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundice
fo} 5 S be) i]

Afdeeling van Zaterdag 24 November 1900 Dl. IX).

Contents: “Review of the results of a comparative study of the three dinitrobenzenes.” By
Prof. C. A. Lopry pr Bruyn, p. 375. — “The Weston-cadmium cell.” By Dr. Ernst
Conen (Communicated by Prof. H. W. Baxuvis RoozesBoom)”. p. 380. — “On the
proteids of the glandula thymus”. By Prof. C. A. PEKELHARING. p. 383. — “Contri-
butions to the knowledge of some undescribed or imperfectly known fungi” (4th Part).
By Prof. C. A. J. A. OupEmans. p. 3886. (With one plate). — “A new kind of
formal-(methylene-)compounds of some oxy-acids.” By Prof. C. A. Lopry pr Bruyn
and W. ALBERDA VAN EKENSTEIN. p. 400.

The following papers were read:

Chemistry. — ‘Review of the results of « comparative study of
the three dinitrobenzenes.” By Prof. C. A. Lopry pg Bruyn.

(Read October 27, 1900).

As the comparative investigation of the three dinitrobenzenes,
which was started some considerable time ago and the results of
which have already been partly published !), has now practically
been brought to a close, a short and systematic review of the prin-

1) Rec. 2. 205, 236, 238. 18. 10]. 15. 85. 18. 9. 13. Ber. 24. 3749.

25
Proceedings Royal Acad. Amsterdam. Vol. ILI.

( 376 )

cipal results may be given. The particulars of the part which is
not yet published will appear fully in the “Recueil”.

NO, NO, NO,
NO,
ortho meta para
a NO,

NO,
melting point 116°.5 89°.72 (Mills) 172°.1
specific gravity 1.59 1.575 1.625
boiling point 319° (773.5) 302°.8 (770.5) 299° (777)

The specific gravities increase with the melting points ; o-dinitro-
benzene has the highest, p-dinitrobenzene the lowest boiling point.

The solubilities decrease with the rise of the melting points; this
applies to all of the ten solvents employed. The three dinitro-
benzenes like most isomeric substances, behave therefore conform
to the rule of CarNneLLey and Tuomson which states that of two
or more isomeric bodies those with the highest melting points show
the smallest solubility and vice versa.

The heat of combustion of the three isomers has already been
determined in 1891 by BerrHeLor and MatiGNon with samples taken
from my preparations'). It has been shown that this is largest for
orthodinitrobenzene and smallest fer paradinitrobenzene.

The following tables show the different behaviour of the three
isomers towards reagents.

AQUEOUS ALKALIS.

Ortho. Meta. Para.
Quantitatively in Chief reaction : | Almost quantatively in
0. CsH, NO2.0 Na+-Na NO, | reduction tom.m.dinitro- | p.CsHyNO..0 Na+NaNO3,
LAUBENHEIMER *) azoxy benzene | very little p.p. dinitroazo-

oxydation to oxalic acid. | and azoxybenzene.
Brown amorphous sub- |
stances and HsN as bye-

products.

1) C. R. 118, 246.
*) Ber. 9. 1826.

(377)

ALCOHOLIC AND METHYLALCOHOLIC SODIUM.

Ortho.
Quantitatively in
0. CsH,NO. O CH3(OC2H;)
-+ Na NO,

Meta.
For the greater part in
0,N-CgH,-N-N-C; H, NO,
Nh
O
MiIcHLER'), KLINGER en
| PITSCHKE 2)

Para.
Quantitatively in
p.C,H,.NO.0CH3.(0C2H;)
+ Na NO,

ALCOHOLIC AND AQUEOUS AMMONIA.

Ortho. |

Quantitatively in
0. CH, . NO, . NH, |
LAUBENHEIMER *). |

Ortho.
chlorine. 0. Cg Hy Cl, little,
or no
C, H, Cl. NO,

bromine. o. Cg Hy Br. NO,
and C, H,Bry etc.

todine. 0. Cg Hy I. NO,

Meta.
No action up
to 250°.

HALOGENS.

Meta.

m. C, H,Cl. NO,
and

m. Cs Hy Cl,

Same as ortho.

m. Os Hy I. NO, -
Cs Hy Ty ete.

Para.
p. C,H y.NOz.0CH3.(0C2H;)
-+ p. C,H, NO. . NH,
in varying proportions.

Para.
Exclusively
p. OC; Hy, Cl. NO.

p. Cs H, Br.NO,

p. C; H, I. NO,

HYDROCHLORIC (and Hydrobomic) ACID.

Ortho.
0. C, H, Cl,
0. C, Hy Bry

Ortho.
1 mol. to 1 mol. of Na, 8:
Cy H, NO, .o Na +Na NO,
2mols. to 1 mol. of Na, 8:
O,N CgHy-S-C,;H,NO.+
2 Na NO,

1) Ber. 7. 423.
2) Ber. 18. 2551.
8) Ber. 11. 1155.

Meta. |
m. ©, HyCle+
C, Hs Cl;

SODIUM MONOSULPHIDE.

Meta.
Chief product:
| O, N C, Hy-N-N-C, H, NO,
SSA
O
++ Na,S,0; besides brown,
amorphous substances.

Para
p. Cs Hy Cl,

Para.
Chief product:
O.N-C, Hy-N: NC,H,NO,

( 378 )
AMMONIUM SULPHIDE.

Ortho.
C, Hy. NO, . NH, 1)
O,N Cy Hy S-Cy H, NO,
O,N C, Hy, S-S-C,; H, NO,

Meta.
Chief product:
C, H, NO,.N H,
(Hormann. MUSPRATT.)

SODIUM DISULPHIDE. 2)

Ortho. Meta.
Quantitatively in Quantitatively in
ON Cg Hy-5-5-C, HyNO2 | O, N-C,;H,-N-N-C,H, NO,
+ 2 Na NO, SZ

+ Na, 8, Os

Para.
Chief product:
Cs H, NO2.N Hy")

Para.
Quantitatively in
O,N C,H4-N : N-C,H,NO,
-F Na, 8, 03

POTASSIUM CYANIDE IN AQUEOUS SOLUTION.

Ortho. Meta.
Reduction toamorphous | Dark amorphous reduc-
products. A good deal of | tion products CO,,\H3N
0. CgHy.NO,.OH and HCN | and nitrite.

Para.
Reduction to
O, N-C, Hy N-N-C,H, NO;
ey
O
also KC NO which yields
ammonium carbonate.

SOLUTION OF POTASSIUM CYANIDE IN ALCOHOL OR

METHYL ALCOHOL.

Ortho.
No action up to 170°.
Tarry products at higher
temperatures.

Meta.
Nitrile of nitromethyl-
(ethyl)salicylic acid:
| CgH30 CH; (C2H;). CN.NO,
eres
besides amorphous reduc-
tion products and KNO,.

VELOCITY OF SUBSTITUTION OF THE
OC.H; AND OCH; °).

Para,
On boiling, chiefly
C, Hy NO; . OCHS (C,H;)
+ HCN-+ KN 0,
Trace of azoderivative.

NO2-GROUP BY

Na OC, H; { Na O CH,
Ortho Para Ortho. Para
25° 0,0260 0,211 0,0170 0,0442
35° 0,0786 0,707 0,0484 0,143
45° 0,233 2,21 0,139 0,474

a
1:81 a 9.5

SS
1:2;6 4 3.6

1) Rinne and Zinckn Ber. 7. 869. 1372. — Kérvor Gazz. chim, 1874.
2) Buanksma. Rec. 19, 121. Proc. Royal Acad. of Se. of Amst. Noy, 1899,

’) Anpu. Srecur. Rec. 18, 13.

( 379 )

The close. examination of this review gives rise to the following
remarks.

It is ,only towards hydrochloric acid and the halogens!) that
the three isomers behave in the same way; in all three, chlorine
(bromine) is substituted for the NO.-group. But as regards Cl (Br)
the ortho-derivative differs from the para-compound in so far that
both its NO -greups are replaced by chlorine or bromine whilst in
the latter only one NO.-group is acted on; with the meta-compound
the dichloro- and nitro-chloroderivative have been obtained.

Moreover the meta-isomer always behaves differently from the
ortho- and generally also from the para-isomer. These latter, there-
fore do not always behave identically, or similarly. They do so in
the case of aqueous and alcoholic alkalis which readily cause sub-
stitution for one of the nitro-groups, whilst with meta-dinitrobenzene
a reduction to the azoxy-compound takes place. A difference exists in
the behaviour of ortho- and para-dinitrobenzene towards ammonia;
whilst the ortho-isomer readily yields nitraniline at a low temper-
ature, this is formed with difficulty from the para-compound at a
higher temperature together with the corresponding nitro-oxyalkyl.
The latter is formed in greater quantity when the concentration of
the H3N becomes less. It seems to me that from these observations
the conclusion may be drawn that alcoholic ammonia does not only
contain the HsN mol. but also the H,NOCH, or HyNOC,H;
molecule.

Na,S and Na gS. act on the ortho-dinitrobenzene and form the
substitution products nitrothiophenol or the mono- or disulphide
whilst the two other dinitrobenzenes are reduced. It is a peculiar
fact that meta-dinitrobenzene is reduced to the azoxy- and para-
dinitrobenzene to the azo-compound, whilst in the second place
attention must be called to the circumstance that when applying
Na,S_ the reductions take place quantitatively *). That NagS.O3 is
also formed when Nag is used, points to the intermediate production
of NagSy.

The action of ammonium sulphide on ortho dinitrobenzene has
now become yuite clear; (H,N).8 acts by reduction and substitution;
the liberated sulphur then forms (H,N).S., which gives rise to
the disulphide by direct substitution.

Potassium cyanide in aqueous solution causes reduction and is

') Also partly towards ammonium sulphide.
#) Na; $2 as a deoxidising agent will be further investigated,

( 380 )

itself oxidised to potassium cyanate which of course, yields imme-
diately H;N and CO,. It is by no means such a handy deoxidising
agent as Na)$,. Only in the case of para-dinitrobenzene, was the
azoxy-compound obtained as a properly erystallisable product; in
the case of the two other isomers brown amorphous substances are
formed; the ortho-compound yields a decided quantity of nitrophenol
owing to KOH being set free by hydrolysis.

The action of potassium cyanide in alcoholic solution is of much
more importance. It is first of all remarkable that it does not act
on ortho-dinitrobenzene whilst it behaves towards para-dinitrobenzene
as if its solution were dissociated into KOCH3(C,H;) and HCN.
This difference in behaviour is not easy of explanation. In the
second place, the behaviour of meta-dinitrobenzene is interesting. The
formation of the two substances C;H;.OCH,(C.H;).CN NO, 1.2.3.
may be best explained by assuming that the CN-group first takes
up a position between the two NO,-groups (while H and K reduce
another portion) whilst further on one of the NOg-groups is replaced
by oxyalkyl owing to the formation of potassium alcoholate.

An account of the researches of Dr. A. StEGER on the substitution
velocity of a nitro-group in ortho- and para-diritrobenzene by an
oxyalkyl and the peculiarities observed has already been given 1).

Chemistry. — ‘“7'he Weston-cadmium cell.” By Dr. Ernst ConEn.
(Communicated by Prof. H. W. Bakauts Roozesoom).

(Read October 27, 1990).

1. In a paper on this cell (compare this vol. p. 217—228) it was
stated that cadmium amalgam with 14.3 per cent of cadmium may
occur in two forms which pass into each other at 23° C. The
existence of these forms was assumed on two grounds:

1s. From the fact that the E.M.F. of cells, constructed according
to the scheme Cd-dilute solution of cadmium sulphate-Cd amalgam
with 14.3 per cent of Cd, is not always the same function of the
temperature but that this funetion may. be represented by the curves
shown in the subjoined figure at I, II and at I.

1) Proc, Royal Acad, of Amsterdam, Oct. 29, 1898.

( 381 )

L T
f z
= [y
o
Page on | TE (cc)
o° §° 10° ike? 20° RRS
Fig. 1.

2nd, From the fact that the amalgam of the cells which follow
the curve I, III showed a strong contraction in the dilatometer
at O° C.

The amalgam of the cells I, III was called by me the metastable
(below 23° C.), that of the cell II the stable one.

Dr. W. Borrerr of Leipsic has now been so kind as to call my
attention to the fact that the idea about the supposed metastability
of the amalgam of the cells I, III is incorrect.

That this cannot really be correct may be shown as follows. If
two cells for instance I and II of the previous paper, are linked in
opposition (see fig. 2), and it is assumed that the E.M.F. of the cell
with the metastable amalgam is greater than that with the stable
one (at a certain temperature below 23° C.), then as in both cells
the amalgam-electrode forms the positive pole, metallic cadmium
would be deposited on the passing of the current, at the Cd-pole
in If; stable cadmium amalgam would therefore pass into solution
in II, whilst metallic cadmium would dissolve in I while metastable
amalgam was being formed.

+ | Cd-amalgam -+- | Cd-amalgam
metastable stable
dilute solution of dilute solution of
cadmium sulphate cadmium sulphate
— | Cd — | Cd
I. i

Fig. 2,

( 382 )

The result, therefore, would be that (below 23°) the metastable
system would form at the expense of the stable one by electrical
action and this, according to known principles, is impossible.

Dr. Bérrerr is, therefore, right when he says that the curve
I, III (in fig. 1) relates to the stable and the curve II to the
metastable cadmium-amalgam and that consequently according to
the electrical measurements, the cells of JAGER should have contained
stable amalgam.

2, Against this result obtained by electrical means stands the
result furnished by the dilatometer, which shows that the amalgam
of the cells I and III, (which according to the electrical measure-
ment ought to be stable) is not in equilibrium at 0° C. and undergoes
a change accompanied by contraction.

I cannot at this moment reconcile these two apparently contrary
results, but hope that the researches of Mr. H. C. Brsu on the
behaviour of cadmium-amalgams will throw light on this subject.

3. Meanwhile another new contradictory matter arises, which
has been duly pointed out to me by Dr. BorrcEr.

If the cell II contains the metastable amalgam as positive pole,
then a Weston-cell constructed with this amalgam as negative
electrode (Ila of the previous communication) must possess an
E.M.F. which is smaller than those of the cells (la and I1la), which
contain the stable amalgam as negative electrode.

The measurement however, gave as result that Ia has actually
a greater E.MF. at 0° C. (1.0231 Volt) than Ia and IIa (1.0197
Volt).

Actual repetition and extension of these investigations will only
be possible when we know the circumstances during which the
metastable amalgam is produced, namely when the researches on
the behaviour of the cadmium-amalgams shall have been practically
brought to a close.

On account of these contradictory facts I desire to postpone for
the present any further conclusions as to the suitability of the
Weston-cell.

Amsterdam, October 1900.
Chem. University Laboratory.

( 383 )

Physiology. — Prof. C. A. PexerwarinG “On the proteids of
the glandula thymus’’.

Some time ago I have in this place given an account of certain
researches concerning the fibrin ferment, which led me to the con-
clusion that this enzym should be looked upon as a nucleoproteid,
in this sense, that nucleoproteids of different origin, are capable of
inducing the formation of fibrin out of fibrinogen, nucleoproteids
from the thymusgland and the testis, as well as from the cells that
are suspended in the blood.

These substances however only become an active fibrin ferment,
when they have had the opportunity to form a combination with
lime.

On various grounds I supposed that the fibrin ferment should
yield lime to the fibriogen for the formation of fibrin. I can how-
ever no longer hold this view, since HAMMARSTEN has proved, that
fibrin, when it is prepared in the highest possible degree of purity,
contains so little lime, that this substance cannot be considered to be
a lime-combination. Moreover I have convinced myself of the accuracy
of HAMMARSTEN’s criticism by my own experiments. It cannot be
said that fibrin is a lime combination and originates by the fact of
lime passing from the ferment into the fibrinogen.

Meanwhile this does not alter my opinion about the nature of the
ferment. This opinion is yet further confirmed by a research by
Mr. Hviskamp about the proteids of the glandula thymus, of which
the full description will soon appear.

It is well-known, that out of thymus, by extraction with
water, two nucleoproteids can be obtained of which one has been
specially studied by LitienreLD, who has given to it the name of
nucleohiston.

Mr. Huiskamp now found that the nucleohiston as well as the
other nucleopreteid can form compounds with calcium, of which the
solubility in water depends upon the greater or smaller quantity of
salts of alkali or alkalic-earths, which it contains. Nucleohiston is
quite insoluble, the other nucleoproteid incompletely soluble in water,
which contains 0.1 to 0.5 pCt. chloride of calcium, but by increasing
the amount of lime-salt of the fluid, or by adding other neutral
salts, both proteids dissolve easily.

The substances that are precipitated from an extract of the thymus
by the addition of the necessary quantity of chloride of calcium are
to we considered as salts of calcium, in which the nucleoproteid

( 384 )

plays the part of an acid. They can be decomposed by acetic acid;
then the proteid is left behind as a substance insoluble in water.

By treatment of these compounds of proteid and lime with
oxalate of kalium, oxalate of calcium and the kalium-compound
of the nucleoproteid is formed. The latter is like the natrium-
and ammonium-compound easily soluble in water. The magnesium
and the baryum-compound however are just as the calcium-compound
hardly soluble in pure water, but they do dissolve in water, to
which a very small quantity of ammonia is added. The alkali- as
well as the alcalic earths compounds of the nucleohiston are preci-
pitated from the neutral or extremely weak alkalic solution by the
addition of so much salt, that the fluid e.g. for NaCl contains
0.9 pCt., for KCl 1.13 pCt., for CaCl, and for CaCl, 0.1 pCt., for
MgSO, 0.2 pCt. The other nucleoproteid can be precipitated, always
incompletely however, by the salts of alkalic earths, namely by the
addition of salts so that the concentration is the same as for the
precipitation of the nucleohiston; by alkalisalts it is not precipitated.

Mr. Huiskame succeeded in preparing beth proteids each separately,
with great purity. The results of the elementary analysis of the
different preparations, which very well agreed, proved this.

The composition of the lime-compounds appeared to be thus:

Coie Bega: Dibapaloae
Ca-nucleohiston 45.3 6.5 17.1 3.75 0.51 1.34
Ca-nucleoproteid 49.8 7.3 15.9 0.95 1.19 1.34

Hither lime-compound now can act as a fibrin ferment. The in-
vestigation on this point brought to light that this ferment action
is influenced by the amount of lime salt of the fluid, in which the
fibrinogen and the ferment are dissolved and in such a way, that
the action is most powerful, when the solution contains 0.1 4 0.5 pCt.
CaCl,, namely with such a concentration, by which either nucleo-
proteid is least soluble in fluids, which contain hardly any other
salt. When the precipitate, obtained by adding to a pure solution
of one of the nucleoproteids, which contains little salt, so much
CaCl, that the fluid contains 0.1 pCt. of this salt, is mixed with
a solution of fibrinogen in chloride of natrium, it is dissolved readily.
This solution coagulates in the quickest and most complete way,
whenever so much chloride of calcium is added to it, that the
amount of that substance is again brought to 0.1 pCt.

When the amount of CaCl, reaches 0.5 pCt., the coagulation is

(385 )

already incomplete, when it comes near to 1 pCt., the coagulation
does not take place.

A few years ago Horne!) has found, that the coagulation of
blood can be interfered with or quite prevented, by mixing it with a
solution of calcium-, strontium- or baryumchloride, in such a way,
that the mixture contains 0.5 pCt. of the added salt.

Mr. Hurskamp, before he was acquainted with Horne’s result,
had come to the same conclusion, at least with regard to chloride
of calcium and baryum. He has investigated, whether also the nu-
cleoproteid of the bloodserum, the fibrin ferment sensu strictiori,
just as the nucleoproteids of the thymus, depends in its action on
fibrinogen upon the amount of lime-salt contained in the fluid and
he has received an affirmative answer to that question.

The substance was prepared in the way, before described by me,
by treatment of the diluted bloodserum with acetic acid and, dis-
solved in water, with the aid of very little ammonia. Now it appeared,
that out of this solution this nucleoproteid could also be precipitated
by chloride of calcium and here also in the most satisfactory way,
when the amount was brought to 0.1 pCt.

Now 900 ce. oxblood fresh from the animal were mixed with
100 ec. 10 pCt. CaCl,. The blood, which now contained 1 pCt.
Ca Cl, (apart from the salts already present in it) did not coagulate
and was centrifugated. The plasma showed a slight beginning of
coagulation, when it was diluted with */; of its volume of water, but
coagulated completely in a quarter of an hour’s time, when it was
diluted with 3 parts of water, by which the amount of CaCl, was
reduced to 0.25 pCt., a concentration, which causes the lime-compound
of the nucleoproteid to be insoluble, at least when no other salts
are present in a quantity worth mentioning.

Some time ago I have communicated in this meeting, that mag-
nesium-sulphate can prevent the coagulation of the blood by inter-
fering with the combination of nucleoproteids with lime. Mr. Huts-
KAMP now found that chloride of baryum acts in the same way
but yet more strongly. When blood is added to a solution of BaCl,,
the baryum combines with the nucleoproteid; in consequence of this
the coagulation is prevented and the plasma, separated by means
of the centrifuge, does not coagulate spontaneously, not even after
being diluted with water, but it does so, when not only the amount
of BaCly is reduced by diluting with water but also the amount
of lime is inereased by the addition of CaCl). This plasma again

1) Journal of Physiol., Vol. XIX, p. 356.

( 386 )

coagulates in the quickest and most complete way, when after dilu-
tion with water, the amount of CaCl, is brought from 0.1 to 0.5 pCt.
When yet more lime-salt is added, so that by this alone without
the aid of other salts; the nucleoproteid-lime-combination might be
dissolved, then the coagulation does not take place at all.

The arguments which I have on a former occasion brought for-
ward in order to defend the view, that the nucleoproteids them-
selves and no admixtures, act, with the aid of lime, as a fibrin
ferment, have been confirmed, I think, by the investigation of Mr.
Hurskamp. Chloride of calcium influences the action of ferment, at
those very degrees of concentration, which render it capable of
altering the state of the nucleoproteids.

The supposition, that that influence should be in relation with
perfectly unknown admixtures, which should occur in the now very
purely prepared nucleoproteids of the thymus, is, 1 think, not con-
firmed by a single observation.

The supposition, suggested by ScHArer!), in connexion with
Horne’s results, that the interference with the coagulation by cal-
cium-, strontium- and baryumsalts is fuunded on the capability of
salts of dissolving fibrin, is disproved by the observations of numerous
investigators, also by those of Mr. Huiskamp, from which it is
evident, that a corresponding quantity of chloride of natrium does
not bring about any delay or incompleteness of the coagulation.

Botanics. — “Contributions to the knowledge of some undescribed
or imperfectly known Fungi” (4% Part and end)*). By Prof.
C. A. J. A. OUDEMANS.

77 MELANCONIEAE.,

«. Hyalosporae.
GLOEOSPORIUM Desmaziéres et Montagne.

85. GLorosporium AvucUBAE Oud. n. sp. —
On the leaves of Aucuba japonica. — Bussum,
July 1900. — Mr. C. J. Konine.

Epigenum. In foliis necatis nigrefactis globuli
vel cirrhi subtilissimi, dilute straminei, conspicui
fiunt, qui, orificia epidermidis minima obturantes
Upper face. et e cavernulis infra-epidermoidalibus, 500 ¢ latis,

") Textbook of Physiol., I, p. 170.
*) For 34 Purt see these Proceedings p. 332.

( 387 )

200 « altis, propulsi, statimque
coagulati, ex mere conidiis con-
sistunt. Sunt haee conidia ellip-
tica vel parum oblongata, 4—7
2—3 «4, hyalina, continua, biocel-
lata, basidiisque acicularibus, 35
altis, e strato proligero fuligineo
oriundis, fulciuntur.

aoereracal seokon: *GLOEOSPORIUM ANTHERARUM
Fig. 4. Oud. n. sp. N. K. A. 3, I, 506 and Hedw.
oe (9 XXXVII (1898) p. 179. — On weakened
‘V anthers of Calystegia sepium. — Leimuiden,

July 1894; Mr. L. Vuyex.

id. Basidia with conidia
and conidia separately.

MYXOSPORIUM Link.

*Myxosporiom Coryii Oud. n. sp. N. K. Arch. 3, I, 507 and
tab. VI f. 10. — On branches of Corylus Avellana. — Nunspeet,
March 3, 1898; Mr. Bens.

86. MyXospoRIUM JUGLANDINUM Oud. n. sp. — On the branches
of Juglans regia. — Scheveningen, 1894.

Pustulae prominentes, sub peridermate occultatae, tandem, perider-
mate irregulariter rupto, hiantes glebulamque griseam exponentes.
Continet haec conidia fusiformia, hyalina, continua, ad polos anguste
rotundata, biocellata, 8—102—2!'/; «, primitus basidiis tenerrimis,
20—25X1, suffulta. Differt a Mycosporio Juglandis Allescher (Ber.
Bayer. bot. Ges. V (1897) p. 21 et Sacc. Syll. XIV, 1015) coni-
diis biocellatis, minoribus (S—10x2—2!/3 w contra 10—14%31!/,—
4}/, 4) et basidiorum bene evolutorum praesentia (Pl. IV, fig. 14).

2. Scoleco-Allantosporue.

CRYPTOSPORIUM Kunze.

87. CryprosporiuM Sipnonts Oud. n. sp. — On branches of
Aristolochia Sipho. — Nunspeet, April 12, 1898; Mr. Berns.

Pustulae numerosae, inaequaliter distributae, parum prominentes,
sub peridermatis portiunculo nigrefacto, postremo centro perforato,

( 388 )

occultatae, 1/; mill. in diam. Conidia hyalina, bacillaria, ad polos
rotundata, continua, 10—201/3 «.

LIBERTELLA Desmaziéres.

88. LIBeERTELLA AUCAPARIAE Oud. n. sp. — On branches of
Sorbus Aucuparia. — Naaldwijk, Dec. 1866; the late Dr. J. E. van
DER TRAPPEN.

Pustulae valde numerosae, dense aggregatae, peridermate velatae,
difformes, saepe confluentes, p.m. inflatae, intus nigrae. Conidia valde
subtilia, faleata, 14—16x1!/, w, ad polos acicularia, hyalina, basidiis
aequilongis et aequilatis, hyalinis, rectis suffulta.

Differt a Libertella Ariae Allescher, Ber. Bayer. bot. Ges. IV
(1896) p. 37 et Saccardo Syll. XIV, 1035, pustularum colore neuti-
quam rubente, conidiorumque longitudine paullo majore (18—25 x
1 contra 4—16X11/, «).

89. LipeRTELLA OpuLit Oud. n. sp. — On the young branches
of Viburnum Opulus. — Nunspeet, April 3, 1899.

Acervuli sparsi, peridermate velati, paullo inflati, aurantiaci, elliptici
vel oblongi, !/,—12/.X1/.—*/, mill. Conidia cylindrica, botuliformia,
ad polos rotundata, continua, singula hyalina, aggregata pallide
aurantiaca, basidiis aequilongis suffulta.

90. LIBERTELLA SYRINGAE Oad.
n. sp. — On branches of Syriaga
vulgaris. — Bussum, July 1900;
Mr. C. J. Konive.

Acervuli numerosi, quoad for-
mam et dimensiones maxime va-
riabiles, nigri, saepe confluentes,
nune poro, tune vero rima dehis-
centes, lateque aperti. Conidia
cavernulas septis spuriis radian-
tibus varie divisas, periderma in-

eee Porrgan Duds ter et parenchyma corticale ccllo-
a. corkelayer, é . . .

b. bark. catas, implentia, filiformia, cur-
ieee een Go ae vata vel flexuosa, hyalina, utrim-

que rotundata, eguttulata, 20—24X1.4 «. Basidia acicularia, 10—12
1.5 «, e strato proligero fuligineo oriunda, post conidiorum lapsum
hamato-curvata.

( 389 )

*LIBERTELLA ULMI sUBEROSI Oud. n. sp. N. K. A. 3, I, 507 et
Hedw. XXXVII, 180. — On branches of U/mus suberosa. — Schte-
veningen, Dec. 1894.

y. Phaeosporae.
MELANCONIUM Link.

*MELANCONIUM PersicaAE Oud. n. sp. N. K. A. 3, I, 508 et
Hedw. XXXVII, 180. — On the youngest internodes of Persica
vulgaris. — the Hague, April 1889.

0. Didymosporae.
MARSONIA Fischer.

*Marsonra SEcALES Oud. n. sp. N. K. A. 3, I, 509 et Hedw.
XXXVIT, 181. — On the leaves of Secale cereale. — Winschoten,
June 1897. — Sent by Prof. Rirzema Bos.

SEPTOMYXA Saccardo.

91. Sepromyxa ARIAE Oud. n. sp. On the branches of Sorbus
Aria. — Scheveningen 1894.

Pustulae numerosae, dense aggregatae, peridermate velatae, eoque
rupto hiantes et globulum conidiorum fuliginosum exponentes. Co-
nidia fusiformia, ad polos rotundata, bilocularia, non constricta,
hyalina, 8—11X2—2!/; w, basidiis brevibus suffulta.

92. Sepromyxa Corni Oud. n.sp. — On the branches of Cornus
alba. — Nunspeet, March 5, 1899; Mr. Berns.

Pustulae valde prominentes, orbiculares vel ellipticae, irregulariter
dispersae, longitudinem 2, latitudinem 1 mill. attingentes, primo
peridermate velatae, postremo, peridermate secundum longitudinem
fisso, fissuraque usque ad circuitum dilatata, hiantes, conidiorumque
glebulam griseam, humectatam caseosam, in parenchymate corticali
immersam, exponentes. Conidia sinuose ordinata, fusiformia, hyalina,
bilocularia, ad polos anguste rotundata, 14—19 X 2!/, w.

*SEPTOMYXA NEGUNDINIS Oud. n. sp. — Cf. N. K. A. 3,1, 510;

( 390 )

Hedw. XXXVIT (1898) p. 180. — On the branches and petioles of
Negundo fraxinifolia. — Apeldoorn, Aug. 1896; O.

& Phragmosporae.
CORYNEUM Nees.

Coryneum Poputt Oud. n. sp. — Cf. N. K. A. 3, I, 510;
Hedw. XXXVII (1898) p. 181. — On branches of Poplars. —
Scheveningen, Oct. 1894.

SEPTOGLOEUM Sace.

93. SEPTOGLOEUM CoRNI Oud. n.sp. — On branches of Cornus
sanguinea, — Naaldwijk, April 1867; the late Dr. J. E. vAN DER
TRAPPEN. — On branches of Cornus alba. — Nunspeet, March 8,
1899; Mr. Bets.

Pustulae valde numerosae, dense congestae, !/, mill. in diam., paullo
prominentes, primo peridermate velatae, postremo perforatae, in cor-
tice immersae. Conidia solito robustiora, 40—50 X 21/3 w, cylindrica,
curvula vel flexuosa, pluriseptata, ad polos rotundata, hyalina.

Cirrhi albi.

777 MUCEDINEAE.
a, Amerosporee.
OOSPORA Wallroth.

*OosporA ABileTUM Oud. n. sp. — Zittingsversl. Kon. Akad. v.
Wetensch. Januari 1897; N. K. A. 3, I, 511; Hedw. XXXVII
(1898) p. 181. — On the leaves of Abies excelsa and other species
of this genus. — Apeldoorn and Laren, Oct. 1896. — O. and Prof.
RitzemMa Bos.

SPOROTRICHUM Link.

94. Spororrichum Hetieport Oud. n. sp. — On dying leaves
of Helleborus foetidus. — Hortus bot. at Amsterdam, Febr. 1890.
— Oud.

Maculae amphigenae, valde extensae, fuligineae, fertiles in utraque

( 391 )

pagina. Conidiorum conglomerationes orbiculares, albae, 1/. cent. in
diam. Hyphae substrato applicatae, valde ramosae, laxe intertextae,
septatae, ramulis ultimis subtilissimis. Conidia solitaria, fusiformia,
continua, hyalina, ad polos acuta, 3—3.5 2 4,

MONOSPORIUM Bonorden.

*Monosporium GALANTHI Oud. n. sp. — Zittingsversl. Kon.
Acad. v. Wetensch. 21 April 1897; N. K. A. 3, I, 514; Hedw.
XXXVIT (1898) p. 181. — On rotting bulbs of Galanthus nivalis;
Tessel, Febr. 1897; Prof. Rirzema Bos.

BOTRYTIS Micheli et Link.

*BotrytTis PAEONTAE Oud. n. sp. — Zittingsversl. Kon. Akad. v.
Wetensch. 21 April 1897; N. K. A. 3, I, 516; Hedw. XXXVII
(1898) p. 182. — On young sprouts of a cultivated Paeonia. —
Rijswijk, April 14, 1897.

OVULARIA Saccardo.

*OVULARIA RaNnuNcULI Oud. n. sp. — N. K. A. 3,1, 521; Hedw.
XXXVII (1898) p. 182. — On the leaves of Ranunculus acer. —
Apeldoorn, Sept. 1897; O.

B. Didymosporae.
HORMIACTIS Preuss.

*TIORMIACTIS HEMISPHAERICA Oud. n. sp. — N. K. A. 3, I, 521;
Hedw. XXXVII (1898) p. 182. — On the weakened anthers of
Tris Pseudacorus. — Leiden, June 1894; Mr. L. Vuycr.

y. Phragmospor dae.
FUSOMA Corda.

*Fusoma GALANTHI Oud. n. sp. — Zittingsversl. Kon. Akad. vy.
Weiensch. 21 April 1897; N. K. A. 3, I, 522; Tessel, Febr. 1897;
Prof. Rirzema Bos.

26

Proceedings Royal Acad. Amsterdam. Vol. III.

( 392 )

Fig. 6. 95. Fusoma Heracier Oud. n. sp. — On
the leaves of Heracleum Sphondylium. —
Nunspeet, July 8, 1899; Mr. Berrys.

Epiphylla. Maculae sparsae, parvae, saepe
autem confluentes et majorem superficiei partem
occupantes, niveae vel roseo-variegatae, absque
mycelii vestigio. Basidia nulla, Conidia in ma-

Fusoma Heraclei Oud. culas congesta, varie accumulata, fusiformes,
curvata, basi truncata, vertice acuta, primo continua, protoplasmate
granuloso repleta, deinde serie longitudinali guttularum ornata, postre-
mo septata (?), 45—604 4. Partes dextrorsum et sinistrorsum a
curvatura divergentes quoad longitudinem dissimiles.

SEPTOCYLINDRIUM Bonorden.

*SEPTOCYLINDRIUM MOoRCHELLAE Oud. n. sp. — N. K. A. 3, I,
522; Hedw. XXXVII (1898) p. 183. — On putrified Morchella
esculenta, Leiden, April 24, 1894; Mr. L. Vuycx.

96. SEPTOCYLINDRIUM SecaLis Oud. n. sp. — On the leaves of
germinating rye-plants (Secale cereale). — Diepenheim, March 30,
1899. — Sent by Prof. Rirzema Bos.

Maculae pallescentes in parte dimidia anteriore foliorum viridium
vel rubescentium. Hyphae albae, late extensae, hyalinae, ramosae,
septatae. Conidia cylindrica, ad polos rotundata, 20—50 > 21/2, primo
continua, postremo 3- 7-septata. Haec in exemplis junioribus in
series simplices vel ramosas ordinata offenduntur.

97. PHYMATOTRICHUM BACCA-
RuM Oud. n. sp. — In the nearly
ripe fruits of Ribes Grossularia.
— Wormerveer, July 1900. —
Sent by Prof. Dr. J. Rirzema Bos
and Mr. C. J. J. van Hatt.

This Mucedinea begins and
closes its life in the fruit-flesh of
the just now mentioned shrub,
and thus forms an exception to
the common rule for all Muce-
dineae that the conidia-bearing
Phymatotrichum baccarum Oud. hyphae do not fructify before the

Fruit-pulp with fructifying

mould -filaments. moment they haye come beyond

( 393 )

the surrounding in which their myce-
lium filaments developed.

The greenish but not quite ripe
berries, manifest their less favorable
condition by the forming of light ocre-
yellow spots, mostly close to the
insertion of the fruit-stalk, by which
the supposition gets some probability
that the point of attack of the fungus
is at the base, and not at the summit
of the fruit, notwithstanding the latter,
by the presence of a little hole at
that place, surrounded by the remnants
Idem. Fructifying mould-filaments of ne : als eat Sy one aE

separately. that this would be the very place to
cause the conidia of an earlier generation
, to germinate.

The yellow spots soon become brown
and seem by preference to follow the course
of the nerves or vascular bundles; still it
is not well possible to state whether the
surrounding parenchyma would be spared
by the fungus.

The expectation that the hyphae hidden
in the fruit-flesh, shortly after the affected

Does fruits had been removed under favorable conditions

@ to a glass-bell, would produce fertile little cushions

w% @ at the surface,was by no means realised. There

6° appeared indeed slits which gave the sap within an

Conidia separately Opportunity to come out in drops charged with inde-

pendent conidia, but instead of the expected cushions there appeared

nothing else but very common moulds and these svon took hold of
the greater part of the surface of the berries.

This result induced Mr. vAN Hatt to set in a renewed examin-
ation of the hyphae hidden in the fruit, whence arose the certainty
that the conidia were exclusively produced within the fruits, between
the parenchyma-cells and remained confined in the epidermis of
the berries.

The hyphae which amid the fruit-pulp cross in all directions, have
a sinuous course and are, by rather closely succeeding partitions,
divided into cells of various sizes. Mostly they are in the middle

or thereabout a little swollen. The lower branches, springing from
26*

Fig. 9.

( 394 )

the main hyphae, appear at different heights and resemble the former,
with this difference however, that they degrade in width. Higher
up they become shorter and bifureate so as to form branchlets
which are either both fertile or sterile, or one fertile and the other
sterile. In the latter case the sterile branch is now straight, now
crooked, and besides, mostly surpasses the fertile one in length.
The fertile branches always end in a vesicle-shaped cell charged
with the task of forming the conidia. The latter repose on short
basidia whose number varies from 3—10. They are oblong, colour-
less, T—12 21/,—5 «se, and undivided. When ripe they let go hold
of the basidia, which then remain sticking as little pricks to the
vesicles.

The conidia can be very well cultivated in a moist chamber.
After a short time Mr. van Hatt saw them germinate, i.e. either
without the intervenience of a mycelium form new conidia; or at one
extremity produce secondary conidia and at the other a sterile my-
celium; lastly, also: at one pole form secondary conidia, and at the
other push forward a fertile mycelium, of which the top-cell swells
up into a vesicle, which gives birth to a certain number of tertiary
conidia reposing on short basidia. It may be conceived that in this
way the number of conidia must so prodigiously increase that the
exuding drops can be partly filled with them. The mother-spore
always remains recognisable by its 1 or 2 large vacuoles.

Diagnosis: Caespitibus nullis, sed hyphis in ipsis baccarum
parenchymate succulento fructificantibus, intricatis, hyalinis, valde
flexuosis, septatis, ex articulis utplurimum curtis, saepe p.m. torulosis,
compositis; infra vage ramosis, sursum semel vel pluries bifurcatis ;
ramis ultimis nunc ambobus, tune alterutro sterilibus; ramis fer-
tilibus apice globuloso-inflatis, muriculato-conidiophoris;_ sterilibus
apicem versus angustioribus, obtusis, rectis vel curvatis. Conidiis
oblongis, utrimque obtusis, hyalinis, continuis, 7—12X2'%/;—5 yw,
protoplasmate denso, guttulisque 1 ad 2 voluminosis repletis. Arti-
culis hypharum 7—10 «& crassis.

++7+7 DEMATIEAE.
a. Didymosporae.
FUSICLADIUM Bonorden.

98. FusitcLapiuM CARPoPHILUM Oud.; Cladosporium carpophilum
Thiim. Oest. bot. Zeits. 1877, p. 12; Thiim. Wiener Landwirthsch.

( 395 )

Wochenblatt 1877. p. 480; Thiim. Fgi pomicoli 1855, p. 13; Sace.
Syll. IV, 353. -- On the young fallen fruits of Persica vulgaris,
in company of Monilia fructigena. Raamsdonk, June 25, 1898. —
Sent by Prof. J. Rirrzema Bos.

Maculae orbiculares, !/. cent in diam., primo sub epidermidis
lanugine occultatae et imperceptibiles, postea vero, colore magis satu-
rato fucatae, facilius distinguendae. Obseryantur in iis hyphae erectae,
curtae, rectae vel flexuosae, fuscescentes, 1—3-septatae, ex mycelio
superficiali repente sursum tendentes. Conidia acrogena, ovoidea vel
fusiformia, vulgo continua, rarius bilocularia, conidiophoris pallidiora,
20K5—6 yf.

*FUSICLADIUM Facopyri Oud. n. sp. Zittingsversl. Kon. Akad. vy.
Wet. 26 Juni 1879; Ned. Kr. Arch. 3, I, 524; Hedw. XXXVII
(1898) p. 183. — On leaves of Hagopyrum esculentum. — Goor,
June 26, 1837; sent by Prof. J. Rirzema Bos.

In Hedwigia Pisum sativum was also mentioned as the foster-
plant. This name should however be blotted out.

2. Phragmosporae.

CLASTEROSPORIUM Schweinitz.

*CLASTEROSPORIUM IrtpIs Oud. n. sp. — Hedw. XXX VII(1898)
p. 318. — On the leaves of Iris xyphoides, by gardeners mostly
ealled I. anglica. — Leiden June 17, 1898. — Sent by Prof.
J. Rirzema Bos. (Pl. IV, fig. 16).

99. CLASTEROSPoRIUM Lint Oud. n. sp. — On the roots of
Linum usitatissimum. — Wageningen, Febr. 1900; sent by Prof.
Rirzema Bos.

Fig. 1. Conidia superficialia, solitaria, cylindrica, satis
regulariter distributa, a mycelio in telis internis
abscondito producta, pallide umbrina, recta vel

gy curvata, ad polos rotundata, versus basin in pe-
dicellum breve (7—10 X 2 — 3), hyalinum, con-

= tinuum attenuata, vulgo 4-septata, vix constricta.
Conidia 4-septata mensuris respondent 35—40

10—12 4 compartimentaque ostendunt fere aequa-
Clasterosporium Iridis lia. Membrana conidiorum ad septorum circuitum
Oud. — Conidia. — profundius tincta.

( 396 )
CRYTPOCORYNEUM Fuckel.

100. CryprocoryNruM opovyatuM Oud. n. sp. —On mouldering
wood of Quercus Robwr. Valkenburg (L.), April 1900; Mr. J. Ricx.
— Caespituli suborbiculares, '/;—'/, mill. in diam., numerosi, p. m.
dense congesti, aterrimi. Conidia late-obovata, 4-septata, fuliginea,
fere opaca, ad septa non constricta, 35—46X<161/;—187/, &, cellula
basilari minima prorsus hyalina aucta.

Cellularum omnium tinctarum — numero 4 — duae supremae in
corpus late-ellipticum vel late obovatum conjunctae, maximae, duae
infimae contra, cum cellula basilari hyalina in pedunculum brevem
quasi colalitae. Septum supremum conidium yesiculiforme proprio
dictum in partes 2 valde inaequales: superiorem nempe minorem,
inferiorem contra majorem dividit (Pl. LY, fig. 15).

HELMINTHOSPORIUM Link.

101. HeLMINTHOSPORIUM GRAMINEUM Rabh. et Oud. — Cf. Zit-
tingsv. Kon. Ak. v. Wet. 26 Jumi 1897; Hedw. XXXVII (1898),
p. 183. — Synonymous with ZH. teres Sace. Fgi ital. del. tab. 833
and Syll. IV, 412, and with 4. gramineum Eriksson ,,Ueber eine
Blattfleckenkrankheit der Gerste” a°, 1885, taken over as an extract
Botan. Centralblatt XXIX, 1887, p. 83 and in Frank, , Die Krank-
heiten der Pflanzen” 2° Ed. p. 316 (a°. 1895). — Rabenhorst’s fungus,
published in 1857, in his Herb. mycologicum Ed. 2% n°. 332, does
not differ from the two other mentioned and, accordingly, the name
given by him must be preserved by right of priority.

BRACHYSPORIUM Saccardo.

*BRACHYSPORIUM Pist Oud. n. sp. — Cf. N. K. A. 3, I, 527;
Hedw. XXXVII (1898) p. 183. — On the leaves of Piswm sati-
vum; Warfum, June 17, 1897. Sent by Prof. J. Rirzema Bos.

CERCOSPORA Fresenius.

102. Crrcospora Spinacvan Oud. n. sp. — On the leaves of
Spinacea oleracea. — Nunspect, June 9, 1899. — Mr. Berns.

Maculae amphigenae, utrimque fertiles, pallide viridescentes vel
stramineae, variae extensionis (1—10 mill.), saepe confluentes ; hyphae
simplices, fere bacilliformes, continuae vel versus apicem 1-septatae,

( 397 )

fuligineae, ad polos rotundatae, 40 —70X31/, «. Conidia acrogena,
primo elliptica, denique oblonga vel bacillaria, nodosa ; postremo
eylindraceo-fusiformia, curvata, ad polos rotundata vel acuta, medio
septata, hyalina, 16—20X3 w.

Differt a C. dubia Wint. conidiis multo brevioribus et angustio-
ribus (16—20X3 « contra 60—T08—9 f) et a C. beticola conidiis
multo brevioribus (16—20 contra T0—120) et 1- neque dense
septulatis.

HETEROSPORIUM Klotzsch.

103. Hererosporium ALi Ellis et Martin, Journ. of Mycol I,
100, var Polygonati Oud. n. vy. — On the leaves of Polygona-
tum multiflorum. — Nunspeet, Oct. 2, 1899; Mr. Beuys.

Caespites amphigeni, irregulariter distributi in partibus foliorum
polymorphis, satis extensis, zona purpurascente variae latitudinis cir-
cumscripti; hyphae simplices vel ramosae, septatae, p.m. nodosae,
140—190X 7 «, olivaceo-fuliginosae. Conidia acrogena, primo hyalina,
ovoidea, continua; denique elliptica vel oblonga, pallide-fuliginea ;
postremo oblonga, 2- vel 3-septata, subtilissime muriculata, pallide
olivacea, 28%11—12, ad septorum altitudinem leviter constricta.

104. HererosporiuM AVENAE Oud. Hedw. XX XVII (1898), p.
318. — On the leaves of Avena sativa (Ulrum) and Hordeum vul-
gare (Dordrecht). — Sent by Prof. J. Rrrzema Bos. — Though in
a letter to Prof. Rirzema Bos I changed the above name into H.
Cerealium (see his account concerning the informations given in
1899, issued from the phytopathological Laboratory Witte Com-
MELIN ScCHOLTEN at Amsterdam), because the fungus was found,
besides on Oats, later also on Barley, I have still come back to
my first denomination by reason of rights of priority.

*HETEROSPORIUM SYRINGAE Oud. n. sp. — N. K. A. 3, I, 529;
Hedw. XXXVIT (1898), p. 183. — On branches and fruits of Sy-
ringa vulgaris. Nunspeet, Nov. 1896; Mr. Bets.

y. Dictyosporae.
CONIOTHECIUM Corda.

*Coxroruectum Mucui Oud. n.sp. Hedw. XX XVII (1898) p. 318,

( 398 )

— On the peltate summits of the fruit-scales of Pinus Mughus. —
Nunspeet, April 11, 1898; Mr. Berns.

105. ConrorHecitum PsaMMAE Oud. n. sp. — On the leaf-sheaths
of Psamma littoralis (Ammophila arenaria). — Downs near Brielle.
Sept. 1871; Oud.

Caespites minimi, punctiformes, in sulcis foliorum longitrorsum
seriati, solitarii vel confluentes. Conidia pluricellularia, h.e. in varias
directiones divisa, polymorpha, variae dimensionis; cellulae compo-
nentes glebularum globulosae vel multangulares, ferrugineae, 4°/,—T
im diam.

++ +77 STILBEAE.
HYALOSTILBEAE.
Amerosporde.
STILBUM Tode.

106. Sripum ToMENTOsSUM Schrad. Journ. 1799, II, p. 65 et
tab. III, fig. 2; Grev. Scott. Cr. Fl. tab. 281; Stilbum parasiticum.
Ditmar in Sturm. Cr. Fl. Bd. I, 93 et tab. 46; Sacc. Syll. VII,
566. — Valkenburg (L.) 1899; Mr. J. Rick. — On Hemiarcyria
clavata, sticking to mosses and liverworts.

Myxomycetis sustentaculum praebentis color naturalis non distin-
guendus, quippe qui tota planta fungi parasitantis mycelio involvitur.
Stilbi exempla omnia e pedunculo et capitulo terminali composita,
cum ipso tegumento concolaria. Pedunculus et capitulum a se invicem
distincta persistunt. Superficies pedunculi tomentosa ad nomen speci-
ficum constituendum a Schradero adhibita est, neque vero fila tenuia
quae ex eo assurgunt cum glandulis comparanda, uti passim ab
auctoribus factum est. Sistunt enim hyphas periphericas a corpore
axili extrinsecus divergentes, singulas conidio minimo terminatas.

Pedunculos longos invenimus '/, mill., crassos 35 ; capitula vero
120 « in diam. Conidia perfecte globosa, hyalina, continua, 1!/,
in diam. Hyphae pedunculum constituentes filiformes ad capituli basin
divergunt, corpusculumque formant globosum, cujus superficies farina
quasi obducta, conidia innumera ostentat.

( 399 )
Fig. 12. PHAEOSTILBEAE.

Phragmosporae.

ARTHROBOTRYUM.
c 107. ARTHROBOTRYUM COPROPHILUM Oud.
n. sp. — On horse-turds. Amsterdam, Oct.

1899. — Mr. C. J. J. van Haut.
7 Laxe gregarium. Stipites conidiophori cylin-

dracei, alti 1/, ad °/, mill., lati 60—80 w, stricti
/2 /4 ) (9 ?
laeves, glabri, nigri, ex hyphis filiformibus pallide
fuscis, septatis formati. Capitula globulosa, lactea,
1/,—!/4 mill. in diam. Conidia catenulata, cy-
lindrica, hyalina, ad polos truncata, excepto

Arthrob hil eos
Oud. a Stalk’ wrth eapi- tamen polo anteriore conidii ultimi, omnia 3-

tulum; 6. 3 chained conidia; akc 2, eral)
¢. conidium separately. septata, 16—28 X4—5"/p uw.

+7774 7 TUBERCULARIEAE.
TUBERCULARIEAE MUCEDINEAE.
Amerosporae.
HYMENULA Fries.
*HYMENULA PsaMMAr Oud. n. sp. Cf. N. K. A. 3,1, 532; Hedw.

XXXVI (1898), p. 184. — On the stems of Psamma littoralis
(Ammophila arenaria). — Loosduinen, 1894.

Phragmosporae.
FUSARIUM Link.
*Fusarium Opui Oud. n. sp. Cf. Hedw. XXX VII (1898), p. 318.

— On branches of Viburnum Opulus. — Nunspeet, June 15, 1898;

Mr. Bers.

( 400 )
TUBERCULARIEAE DEMATIEAE.
Amerosporae.
CHAETOSTROMA Corda.

*CHAETOSTROMA CLIvIAE Oud. n. sp. Zittingsversl. Kon. Akad.
v. Wetensch. 28 Nov. 1896, p. 226; Ned. Kr. Arch.:3, I, 533;

Hedw. XXXVII (1898), p. 184. — On the leaves of Clivia
nobilis. — Hees near Nijmegen; October and November- 1896. —

Prof. Rrrzema Bos.

+t eee SPWOERILEA STERELIA,

108. Ecrosrroma TricLocuinis Oud. n.sp. — On the stems of
Triglochin palustre. — Nunspeet, Oct. 8, 1899; Mr. Bemus.

Maculae nigrae, juxta longitudinem ad superficiem caulium exten-
sae, structurae parenchymaticae, e seriebus cellularum partim longio-
rum, partim breviorum, nunc alternatim tunc vero absque ordine
dispositarum, semper vero arctissime inter se cohaerentium, stomatibus
exceptis sine meatuum intercellularium vestigio contextae. Maculae,
vel potius membranae longitudinem attingunt 3 centim. internodiaque
vel caulem perfecte involvunt. Sporulae non visae.

Chemistry. — Prof. C. A. Lopry DE Bruyn presents, also on
behalf of Mr. W. ALBERDA VAN EKENSTEIN a paper entitled:
“A new kind of formal-(methylene-) compounds of some

oxy-acids.”

In the preparation of the formal-compounds of polyhydrie alcohols
and of oxy-acids it has been necessary up to now to call in the
aid of a strong mineral acid to effect the condensation. The change
which then occurs takes place between the formaldehyde-and the
hydroxyl groups which possess an alcohol function; in the case of
the oxy-acids the carboxyl groups take no part in the reaction so
that the formed compounds still remain acids.

In the case of several oxy-acids, namely those which contain in
their molecule only one alcoholic hydroxyl group, the efforts to prepare

a ae

an

is > + a,

awe

EDINGS ROYAL, ACAD. AMSTERDAM. VOL IL.

SBinyi lith PIMidden mm Leiden.
@

( 401 )

formal-compounds have only given a negative result. Even with
tartaric acid which contains two hydroxyl groups, WkBER and
Tottens'!) only succeeded with difficulty in getting a very small
quantity of a compound of which they are still in doubt whether
it may be really derived from the unaltered acid.

We have found some time ago that formaldehyde reacts with
tartaric, citric, malic and lactic acids when operating in purely
aqueous solutions. The compounds found happen to be extra-
ordinarely sensitive towards acids; these at once restore the com-
ponents, The new formal-compounds also differ from those already
known because, at their formation, the carboxyl group takes part
in the reaction. In the case of tartaric acid a compound is formed
which no longer possesses acid properties; the tribasic citric acid
becomes dibasic and the dibasic malic acid becomes monobasic.

The new compounds are formed by repeated evaporation of the
solution of the acids with an excess of formaldehyde. As the acid
itself prevents its reaction with formaldehyde and the compound
already undergoes a slight decomposition in the presence of warm
water, it is not astonishing that each time only a sma!l quantity
(about 5 per cent) is formed which must be extracted by shaking
with ether or better still with chloroform or benzene. Sometimes
the compound crystallises slowly from the concentrated syrup. When
removed by shaking out, the residue may be again treated with
formaldehyde in order to obtain a fresh quantity. We are, therefore,
dealing here with an equilibrium.

From d-tartaric acid was obtained a white substance erystallising
in needles with a melting point of 117° and a rotatory power of
+ 112°. According to the analysis and the determination of the
number of methylene groups by means of phloroglucinol and hydro-
chlorie acid, the compound is OC, Hg Og, or:

OC\ 9 It is neutral, The composition was also deter-
0 mined by warming with a known quantity of

| normal alkali and titrating the excess. On evap-
Hc orating the substance aie pure water, or very soon

l pork 2) by acids or alkalis, the components are reformed.
OC

In quite a similar manner is formed from anti-

1) Ann. d. Chem. 299. 335.

*) Attempts will be made to determine the mol. weights of this and the following
substances,

( 402 )

tartaric acid a compound melting at 106° which, as might be
expected, is inactive.

Tt seems very peculiar that we have not succeeded in preparing
a formal-compound from uvie acid. This again erystallises unaltered
on evaporation even after heating above 100°. It, therefore, seems
that the tendency of d- and /-tartaric acid to unite in concentrated
solutions to molecules of uvic acid is greater than that which causes
the formation of the very unstable formal-compounds. We will
investigate this point more closely as soon as we have the formal-
compound of /-tartaric acid at our disposal.

Citric acid yields a readily crystallisable compound melting at
200°, which contains only one methylene group. From the analysis
and the determination of the formal follows the composition C7H,07;
the most probable formula being :

CHS COOH This substance may be first titrated as a dibasic
i Zz O >CH, but after warming as a tribasic acid, Malic acid

COO ~ also reacts with formaldehyde; this is already ap-
CH,COOH parent from the change in the rotation. By shaking
with benzene an oily liquid may be isolated from the syrupy reaction-
product which still remains liquid when strongly cooled. It is
nearly insoluble in water, has an acid reaction and is laevorotatory.
According to a determination with the aid of phloroglucinol and
hydrochloric acid it contains one methylene group. The formula
is therefore, probably COO H—CH,—CH — C=O

| |
0.CH,.0

With salicylic and oxalic acids no change occurs when they are
treated with formaldehyde in the manner described. Other oxy-
acids, of which it is already known that they yield formal-compounds
by treatment with formaldehyde in the presence of an acid, will
be more closely investigated.

It may be further observed that sugars also react with formal-
dehyde in the absence of an acid. This is shown by the very
important changes which take place in the rotations; that of glucose
is nearly doubled whilst those of galactose, fructose, arabinose and
mannose are considerably lessened; rhamnose which is dextrorotatory
becomes laevorotatory. The new compounds are, however, of a syrupy
nature; attempts to obtain from them crystallisable substances have
therefore not yet been successful. On evaporating them a few times

aan

( 403 )

with pure water, the combined formaldehyde is volatilised and the
unchanged sugars crystallise; the combination is consequently a
very feeble one !).

The investigation is being continued.

1) We observe that benzaldehyde also reacts when heated with aqueous solutions
of tartaric acid, anti-tartaric acid, citric acid and glucose; the products are however,
all liquid, syrupy and very unstable. Tartarie acid becomes left-handed and the rotation
of glucose is much diminished.

(December 19, 1900).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Saturday December 29, 1900.

DOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 29 December 1900 DI. IX).

Contents: Dr. J. F.van Bemueen: “Third note concerning certain details of the Monotreme-
skull” (Communicated by Prof. A. A. W. Husrecar), p. 405. — Dr. E. van Ever-
DINGEN Jk: “On the Hatt-effect and the resistance of crystals of bismuth within
and without the magnetic field” (continued) (Communicated by Prof. H. KaMERLINGH
Onnzs), p. 407 (With one plate) — J. C.ScuaLxwisk : “Precise Isothermals”’. I. (Com-
municated by Prof. H. KamertincH Onyes), p. 421 (With one plate). — Prof. H. A.
Lorentz: “The theory of radiation and the second law of Thermodynamics”,
p- 436. — Dr. P. van Rompurcu: “On the essential oil from the leaves of Alpinia
malaccensis Rose.” p. 451. — Dr. P. van RompurcH: “On the action of nitric acid
on the esters of methyl-phenylaminoformic acid”, p. 451. — Dr. P. van RomBuRGH:
“On the essential oil from Ocimum Basilicum L.”, p. 454.

The following papers were read:

Zoology. — * Third note concerning certain details of the Monotreme-
skull.” By Dr. J. F. van BemMeten The Hague. (Commu-
nicated by Prof. A. A. W. HuBRECHT.)

Ethmoid and Mazillo-turbinale.

In the structure of their ethmoid-bone Ornithorhynchus and
Echidna present great differences: the former having only one single
opening for the olfactory nerve and furthermore differing from all
other mammals by the exceptionally low number of only three
ethmo-turbinals; the latter on the contrary showing a lamina cri-
brosa of uncommon size, while by the very high number of eight
primary and a number of secondary ethmo-turbinals it occupies an
equally exceptional but opposite position.

Comparing the two Monotremes among themselves, the conclusion

27
Proceedings Royal Acad. Amsterdam. Vol, IIL.

( 406 )

seems to be justified that the structure of the ethmoid in Echidna
may have developed from a starting point like that of Ornithoryn-
chus by the conchae increasing in number, and thereby necessitating
the higher differentiation of the lamina cribrosa.

The question then arises: where have these new conchae made
their appearance: before or behind the primary three? The answer
must be in the latter sense, as there is no space left at the anterior
side of the primary conchae for the intercalation of new ones,
because in both animals the naso-turbinal and maxillo-turbinal are
placed immediately in front of the first ethmoidal concha in an
absolutely identical position.

I am strengthened in this view by the observation, that in both

forms the foramen sphenopalatinum is situated just beneath the .

third concha: thus, while in Ornithorhynchus it is found at the
back side of the conchal area, in Echidna it occupies the interspace
under the third and fourth concha.

This opinion harmonizes with the conclusion, which SEyYDEL !)
has arrived at by investigating the development of the nasal area
in Echidna. He found the first rudiment of the ethmo-turbinals as
one single protuberance on the lateral wall of the nasal cavity,
which afterwards became divided into three parts by vertical grooves.
SEYDEL makes reference to the observations of W. N. Parker ®),
on a young of Echidna, which showed six ethmo-turbinals, decreas-
ing in size from before backwards, and thereupon gives as his
opinion: (p. 515): “This gives certain evidence of a successive
formation of new (olfactory) knobs behind the first-formed.”

In most mammals the increase in number of the conchae in a
caudal direction goes hand in band with the excavation of the body
of the sphenoid bone, i.e. the development of the sinus sphenoi-
dalis, by means of which the necessary space is obtained for the
lodging of the new conchae. Echidna is among these mammals,
for at the bottom of the hindmost five conchae a horizontal bony
plate is to be found, taking its origin from the underside of the
floor of the sella turcica, and stretching forward towards the
level of the foramen sphenopalatinum, where it ends in a sharp
concave border.

1) SeypeL. O. Ueber Entwicklungsvorgiinge an der Nasenhohle und am Mundhohlen-
dache yon Echidna nebst Beitrigen zur Morphologie des peripheren Geruchsorgans
und des Gaumens der Wirbelthiere, in R. Semon, Zoologische Forschungsreisen in
Australien und dem Malayischen Archipel. Bd. IIL Lief. 3.

7) Parker. W. N. On some points in the structure of the young of Echidna
aculeata, Proc. Zool. Soc, London 1894.

( 407 )

In other mammals this bottom-plate of the sphenoidal sinus has
been called by SrypEL lamina terminalis or “untere Schlussplatte.”

Though in Kchidna it is well developed and easily visible in a
paraseptal section through the macerated skull, its occurrence in
this animal hitherto seems to have escaped notice, for not only is
it absent in the figure ZUCKERKANDL has given in 1887 in his
»Geruchsorgan der Siiugethiere”, but it is equally omitted in the
more recent illustration of GEGENBAUR’s new Handbook of Vertebrate
comparative anatomy (1898).

The structure of the maxillo-turbinal is the same in both Mono-
tremes; it corresponds to the ,verastigte’”’ (ramified) type of Harwoop-
WIEDEMANN, the only difference between the two forms being that
in Ornithorhynchus it is somewhat larger and more complicated.

ZUCKERKANDL’s statement, that there exists a difference in this
respect between Echidna and Ornithorhynchus, the first having a
doubly-coiled (,doppeltgewundenes”’), the latter a folded (, ¢efaltenes’’)
maxillo-turbinal is erroneous, and it is all the more desirable that
this mistake should be elucidated, as it has found its way unaltered
into GEGENBAUR’s new handbook. Yet, as far as regards Ornitho-
rhynchus, the veracity of the statement had already been challenged
by Symineton!), and for Echidna, by W. N. Parker (l.c.) who,
though agreeing with Symineron, yet came to the conclusion, that
Echidna’s , maxillary turbinal apparently belongs to the folded
,gefaltene”) and not to the doubly-coiled (,,doppeltgewundene’’)
variety.”

Transverse sections through the organ, in the preserved as well
as in the macerated state, leave no doubt that there exists a complete
agreement between Ornithorhynchus and Kchidna, both showiug a
well-marked branching type.

Physics. — Dr. E. van Everpincen Jr., “On the Hawt-effect
and the resistance of crystals of bismuth within and without
the magnetic field” (Communication N°. 61 (continued) from
the Physical Laboratory at Leiden, by Prof. H. KaMERLINGH
ONNES).

4. Complete results for the Hauw-coefficient. It was mentioned
in § 2 of the first part of this Communication *) that the relation

1) Symmneton, J. On the nose, the organ of Jacobson and the dumb-bell-shaped-
bone in the Ornithorhynchus. Proc. Zool. Soc. London 1891, pag. 575.
*) Versl. d. Verg. Kon. Ak. v. Wet. 29 Sept. 1900, p. 277. Comm, Phys. Lab.
Leiden, N°, 61.
27*

( 408 )

found before between the Hatt-coefficient and the position of the
principal axis with respect to the lines of magnetic force was con-
firmed in these recent experiments. The bar N®. 1, with its longest
dimension parallel to the principal axis, and N°. 2, 3 and 5, with
their longest dimension and two sides perpendicular to the principal
axis (for the position of these bars compare fig. 1 in the first part
of this paper) were each tested in four positions. In these the
longest dimension (also direction of current) was always horizontal
and perpendicular to the lines of force of the horizontal electro-
magnet, while each of the four sides consecutively took the upper
horizontal position. Hence with N°. 1 the principal axis was always
perpendicular to the lines of force (position 1), with 2, 3 and 5
alternately perpendicular to and parallel to the lines of force (po-
sition //). For the sake of simplicity the differences between the
results in the four positions of N°. 1 and in the two positions 1
or // of the other bars will not be mentioned, and only mean values
will be given. Very likely these differences are caused by small
irregularities in crystallisation and small deviations from the exact
position in the experiments, and they are not to be compared to
the differences between positions // and 1.

All observations have been reduced to the same magnetic fields ')
and to the same temperature (15° C.).

HALL-coefficient PR.

| Magnetic field.
No. | 4600 2600
| ya
1 ! — 8,0) ==" il Ono
9° ll =10% | ore = 1ave py
8 || 8:8 )| Tose tie eows
|
5 || —8.2| 40.6 | 10.6} —0.1

The small value of the coefficient in the position // and the
reversal of sign with N°’. 5 were first pointed out in § 2 of the
first part of this paper.

1) The numbers given in § 2 for the magnetic field appeared afterwards a little
too high. or this reason and on account of the correction for temperature the num-
bers for 2, 3 and 5 differ slightly from those given before.

( 409 )

From the numbers in the columns headed 1 it appears that the
experiments afford no reason for making a distinction between the
positions in which the cwrent is parallel (as with 1) and those in
which the current is perpendicular to the principal axis (as with
2, 3 and 5). This seems to indicate that, as was admitted before,
only the angle between the principal axis and the lines of force
determines the value of the Ha.t-coefficient.

In order to find the form of this relation the bars N°. 4 and 6,
in which the principal axis makes an angle of 60° with two of the
sides and is parallel to the other sides, were also tested in two
positions.

In isotropic substances the Hatt-effect for currents in an arbitrary
plane V is determined by the product of “the” Ha.t-coefficient into
the component of the magnetic force perpendicular to that plane.
This may however also be regarded as the product of the whole
magnetic force into a specific Hawt-coefficient for the plane V.
This coefficient would be obtained by multiplying the coefficient for
a normal magnetic force by the cosine of the angle between the
actual direction of magnetic force and the normal to the plane V.
We shall apply this principle to the Hawt-effect in a crystal of
bismuth, and for this purpose resolve the magnetic force into the
direction of the principal axis and the transverse direction. Let us
assume that we found for currents in a plane 1 to tke principal
axis and the magnetic force a Hatt-coefficient 2,, for currents in
a plane // to the principal axis and 1 to the magnetic force a co-
efficient #,. The simplest supposition in the case of a magnetic
force M in a direction inclined at an angle @ to the principal axis
is then, that the Haut-effect in the plane 1 to ™@ now consists of
two parts, one caused by the component M cos a, // to the principal
axis, one caused by the component sin a@, 14 to the principal axis.
The Hatt-coefficient FR in this case is then given by

R= R, cos* a@ +. Ry sin® &.

In this deduction for simplicity R, and R, are taken as constants
and not as functions of the magnetic force, as is the case with
bismuth. As we aim only at an approximation this will not be
open to objection; we remark only by the way that with an isotropic
substance where & was a function of M, this method might lead
to wrong results.

As appears from the table the value of , for crystalline bismuth
is very small as compared with &,, so that we may omit the

( 410 )

term with /, (which moreover is rather uncertain) except for very
small values of @. Then & becomes equal to R, sin? a.

We give here the values, observed with the bars N°. 4 and 6 in
a magnetic field 4600 for 2, and A, and the calculated values
Ry sin® a, where & is 30°.

|
|| 10.3 | 2.5 2.6

NO || R, | R | Rg sin?
|

6 | 22.2 | Sele Sil

The agreement between the observed and calculated R is as good
as one could wish, so that the simple supposition leading to the
formula for & is confirmed. The values for Ry do not differ too
much from those found with the bars 1, 2, 3 and 5.

If the equation for #& is written in the following form:

1\2 1 \2
(=) cos? @ (—) sin? a
maa ieee Cl
VR, za)
it appears that & may be obtained by the construction of an ellipsoid

of revolution with |/ A, as axis of revolution parallel to the prin-
cipal axis, and 4/R, as perpendicular axis. The radius vector in the

> : 1
direction of the magnetic force gives the value of —— for the plane

perpendicular to the magnetic force.

Also with a view to the results, mentioned below, obtained for
the resistance in the magnetic field it appeared useless to connect
the Hatwt-coefficient with the magnetisation (MAXWELL’s vector %),
as has been done before !).

5. Resistance of the bismuth crystals.

The first object of these measurements was to test whether in
regularly crystallised bismuth an increase of resistance would occur
when the current flows in the direction of the lines of magnetic
force. For irregular (cast) bismuth-plates this question had been

") Versl. der Verg. 21 April 1897, p. 501; 26 Juni 1897, p. 69. Comm. N°, 37
p- 18; Comm. N*. 40, p. 3.

( 411 )

answered in the affirmative by the experiments of GoLDHAMMER ?)
and others. The result of the investigation with three bars of bismuth
from Merckx and mentioved in Communication N°. 37, likewise
gave an answer in the affirmative. The increase of resistance, though
small, was comparable to that found in positions // when the current
was perpendicular to the lines of force.

It was now considered desirable to carry out a set of measure-
ments so complete that for an arbitrary relative position of principal
axis and magnetic force the resistance in any direction would be
known. The bar of which the greatest dimension was parallel to
the principal axis, Merck N°. 3, was however hardly longer than
the distance between the ‘“resistance-electrodes’, so that for this
research other material was required. I found this in the crystal
of bismuth put at my disposal by Mr. Perror and shall now
publish only the results obtained with that.

In these experiments we must take into account the relative
positions of three directions: principal axis, magnetic force and
current. In the figures 2a, 6 and c (Pl. I) the principal axis is
always represented by a single arrow, the magnetic force by a
doubie arrow, while the direction of the current, always coinciding
with the longest dimension of the bars, is indicated by radii vectores
Oa, Ob, Oc ete.

The experiments in the magnetic field may be divided into three
groups:

I. Magnetic force 1 to principal axis.
I: = hs ,
TE. e » and P » at an angle of 60°.

For group I and JI, and for the resistance without magnetic
field it was very probable that the resistance in any direction with
respect to the principal axis would be found by the aid of an
ellipsoid with its axis coinciding with axes of symmetry of the
crystal. For, these axes will remain axes of symmetry, so that the
relation between electromotive force and current density can be
expressed by equations like:

X=r,u Y=, 0 Z= 15 W.

1) Wied. Ann. 3], p. 360, 1887.

( 412 )

When a current Z flows in a direction determined by the angles
a, /? and y with the axes Oa, Ob and Oc,

u = T1cos a, v= Leos jf, w= Tcosy,

while the potential gradient Z£ in the direction (@, 2, y) which
measures the resistance, is given by

E=Xcosa + Y¥ cos ? + Zeosy
hence

E = I(r cos* @ +- 19 cos* (3 + 13 cos® y) = rl
and

r= 1 cos*a@+-1rycos® 3? +-racos®*y . . . . ~ (*)

This written in the form

eaNe 1 \2 Lx
Gas Get Gee
Gore Mae rn ie ea

indicates that 7 may be found by the construction of an ellipsoid
with the square roots of the conductivities in three principal direct-
ions as axes.

The measurements indicate, that very likely also the resistances
in group IIT can be found by means of such an ellipsoid.

We will treat now successively of:

1st. the resistances without the magnetic field;

2nd, the resistances along the axes in the three groups in the
magnetic field ;

3'4, the resistances in other directions, compared with values
calculated from the results of 2"¢ by means of the above formula (*).

6. The resistances without the magnetic field.

With each of the six bars the resistance was measured at least
four times, i.e. with the resistance electrodes at least once on each
of the four sides (after the method described in Communication
N°. 48) and mean values were calculated from the results.

The results are given here; 7 is expressed in the unit 10%
C.G.8., the conductivity 4 in the unit 10-® C.G.S., YA in the
unit 10 * C.GS.

5
7 - : = VS —————

NO, qa Pa 3 5 4 6
—— al
r 3.48 | 2.99 2.32 | 2.07 2 59 2.85
a QEC7a |S 7 Role CSW TSESBn dS bE
Va 1.70 | 2.09 | 2.08 9.20 | 1.96 | 1.87

i

It appears that the resistance of N°. 1, that is the resistance in
the direction of the principal axis, is considerably larger than that
in the transverse directions with 2, 3 and 5. As irregularities in
erystallisation can only diminish the ratio of these resistances we are
lead to assume that the ratio of the resistances of N°. 1 and 5,
3.48 : 2.07 or 1.68 : 1 approaches nearest to the ratio fora perfect
erystal. (Also according to the results for Haut-effect 5 was the
most regular bar). For the whole prism Perrot found as ratio of

‘ // :
thermo-electric forces a 2.00 as a mean, hence a ratio of the same

order of magnitude.

The mutual differences between 2, 3 and 5 are relatively small.
Hence we may assume that these differences would vanish in a
perfect crystal, so that the ellipsoid of conduction without the
magnetic field would be an ellipsoid of revolution. As axes for this
we take the values of )/4 obtained with 1 and 5, that is 1.70 and
2.20. With these values in the figures 2a, 26 and 2c the lined
eircles and ellipses have been drawn, all dimensions parallel to the
principal axis (<<) being reduced in the ratio 2 : 1.

For the direction of N°. 4 and 6 a value of the resistance may
now be calculated. We have « = 60°, ? = 30° and y = 90° or a = 60°,
(2 = 90° and y= 30°, hence for both rv is found from

r = 3.48 cos® 60° + 2.07 cos? 30° = 2.42

This value is smaller than both the observed values. If conversely
from the numbers 2.59 and 2.85 @ is calculated, then for N°. 4
53° is found, for N°.6 42°, instead of 60°. It is not certain however
that the differences are only caused by deviations from regular
erystallisation. For, Prrror found for the density of his four best
prisms numbers from 9,809 to 9,887, when the bismuth was always
from the same source and had always been subjected to the same
treatment; even in one and the same casting different densities
were found. Hence it is possible that in the prisms too the density,

( 414 )

and with it the resistance, varies in different points, as has been
suggested by Prerror himself !). Accordingly the results with N°. 6
are only partially less satisfactory than those found with 4.

From the remainder of the crystalline piece another or seventh
bar was cut, corresponding in original position as much as possible
with N°.6. The resistance of this appeared to be 2.74, only slightly
differing from N°. 6. Nevertheless in the further experiments this bar
usually gave better results than N°. 6.

7. The resistances along the axes in the magnetic field. Without
the magnetic field in the plane perpendicular to the principal axis
all sets of two lines at right engles may be assumed to be axes.
In the magnetic field a difference is possible between the direction
which lies at the same time in the plane through principal axis and
magnetic force and the perpendicular direction. We choose the original
directions of the bars 2 and 3 as axes. In order that these directions
shall remain axes also in the magnetic field, it is only necessary to
suppose that the crystal revolves about the principal axis untill these
directions coincide with the planes of symmetry determined by the
magnetic force; nothing is thereby altered in the properties of the
crystal as described with respect to the principal axis and the-
magnetic force. In the experiments the bars 2, 3 and 5 can then
be used indiscriminately, for instance for measurements in the posi-
tions Ob and Oc, provided that care is taken to obtain a correct
adjustment of the relative positions of principal axis, magnetic force
and direction of current.

We first give only percentage increases of resistance, always in
a field of 4600 C. G. S., and at 15° C.

Group I. Fig. 2a. Magnetic force 1 principal amis.

| Position

No . =
| Oa Ob Oc
] 13.0
ai 5.1 9.9
3 5.0 84
5 | | 4.5 8.0

') Arch. d. Sc. phys. et nat. (4) 6. p. 255. Septembre 1898.

a reenter mS iy

( 415 )

Each of the numbers under Oa and Ob is a mean of four, each
of those under Oc of two corresponding positions, which usually
showed only small differences.

For the construction of the new ellipsoid (dotted) the values for
1 and 5 were used. These give for the new axis the values:

(Oa) = 1.60 (0b) = 2.16 (Oc) = AY IB

Hence the ellipsoid of conduction has now three unequal axes.
In the plane perpendicular to the magnetic force the resistances are not
proportionally increased. The simple hypothesis, formulated before ')
and reconcilable with the former imperfect material, which assumed
a proportional increase of resistance in this plane, must now be
abandoned. However for the explication of the dissymmetry of the
Hatt-effect in bismuth, which was originally the object of this
research, and for the description of the increase of resistance in
the magnetic field this is a simplification. According to the researches
of Leprer and of myself the unequal increase of resistance in
two perpendicular directions causes the dissymmetry. It has now
become superfluous to take the direction of the magnetisation (3)
into account in order to explain this inequality. As will appear
from what follows, in each case where the principal axis is not
perpendicular to the plate a disproportional increase of resistance,
and with that dissymmetry, will be found.

In the figure the differences between the new axes and the old
ones are drawn on a twice magnified scale in order not to render
the drawing indistinct.

Group II. Fig. 2b. Magnetic force // principal axis.

Position
N°,
Od Oe or Of

|
1 5
2 5.0
3 4.4
5 | 29

|

1) Versi. d. Verg. 21 Apri :897, d. 501. Comm. N°. 37. p. 18.

( 416 )

The number under Od is a mean of four observations, the other
numbers of two observations.

As there is no theoretical difference between N°. 2, 3 and 5 or
the positions Oe and Of the latter are united in one column. So
the ellipsoid remains one of revolution, while the whole variation
is much smaller than in the preceding case. With the values for
1 and 5 the new axes become 1.68 and 2.17. With the value for
1 and the mean for 2 and 3, 1.68 and 2.15. For the figure we
chose as new axes

(Od) n ==| 1.68 (Oe, Of) % = 9% == 216%

In order to keep the drawing distinct it was bere necessary to
draw the variations to the scale of four.

Group III. Fig. 2c. Magnetic force and principal axis
at an angle of 60°.

Position
ING
Oy Oh Ok
1 dae
2 4.1 91
5 4.0 7.6

Here also the three axes of the ellipsoid are unequal. With the
values for 1 and 5 as a basis, the new axes become

(09) 9° —— EG (Oh) 929 = 2.16 (Ok) 98° Ce

hence only slightly differing from those in group I.
In the figure the differences are drawn on a double scale.

8. esistances along other directions in the magnetic field. With
regard to the differences between the results for corresponding bars
even without the magnetic field, mentioned in § 6, it would not be
allowable to directly compare resistances observed in the experiments
of this § with calculated resistances, as in most cases the calculation
will be based upon experiments with other bars. More is to be
expected from a comparison between observed and calculated increases

va

(417 )

of resistance in the magnetic field and we will make the comparison
in this manner. We should not however expect more than an approx-
imate agreement.

For the calculation the following method was used: for each direction
of experiment the resistance was calculated by means of the formula :

r= 71, cos® @ + 19 cos? (2 + 1 cos” y,

in which for 7,, 7. and rs the values applying without and in the
magnetic field were consecutively substituted. From the two results
a percentage increase of resistance for the direction @, 7, y was
deduced, and this was compared with the percentage increase directly
observed.

As an example of calculation:

Magnetic force 1 principal axis. Direction On (fig. 2a).
i 60k ae 90258 7 0
Py 4G Fy — re — 2.07
oy = 3100 ed = 2.16 rt = 2.24
r ==, cos* 60° + rz cos? 30° = 2.42
we ss rio cos? 60° + rn cos? 30° == 2:66

Percentage increase of resistance — ED oo:
2.42

Here follow the results for the three groups; the indices of the
r’s correspond to those of the y’s.

90 90 90
r, = 3.48 Ol r= 3.93 feel r, = 2.24

Pere. increase of resistance.
Direction 2, Br y NDS along the axes
observed | calculated | °f the corresponding ellipse
greatest smallest
EE —————
Ol 60°, 30°, 90° 4 10.2 7.5 13.0 4.5
» 6 9.2 »
» 7 6.6 »
Om 90°, 45°, 459 | 5 5.5 | 6.3 8.0 45
On 60°, 90, °30° 4 8.7 fo 13.0 8.0
= ¢ | 6 10.2 D
» | // 9.4 )

( 418 )

The most important deviations occur with the direction Ol where
the increase of resistance for the axes is most different and accor-
dingly a deviation of the direction of the axis has the largest influ-
ence. In each case the observed increase of resistance lies between
the values of the last two columns.

Group II. Fig. 2b. Magnetic force // principal axis.
As there exists here no theoretical difference between the directions

Oe, Of and Op and also between the bars 2, 3 and 5, for experi-
mental purposes only the aequivalent directions Oo and Og are left.

m= 3.48 | far 2.07. 13.57 r=r=2.15

Perc increase of resistance.

Direction a, B, ¥ NO. along the axes
observed | calculated | Of the corresponding ellipse
greatest smallest
Oo or Og | 60°, 30°, 90° 4 3.5 3.5 3.8 2.5
6 5.1
ff 4.0 ”

Group III. Fig. 2c. Magnetic force at an angle of 60° with
the principal axis.

As mentioned before in § 7 in this case a doubt might arise
whether the resistances will allow of a deduction from an ellipsoid
and whether casu quo the axes will still be in the same directions
as in both the former cases. An experiment which throws some
light directly upon this question is the comparison of the increase
of resistance in the directions Or and Ov. For the ellipsoid these
are aequivalent; but for one of them the current is parallel to the
magnetic force, for the other one the current flows at an angle of
60° to the magnetic force. The result of this experiment was:

Or Ov
with N°, 4 9.3 9.3

» 6 6.8 7.9

> 4 6.8 0)

( 419 )

Hence with N°. 4 the agreement is perfect; with 6 and 7 the
deviations are in opposite directions. Therefore this result may be
considered as confirming the supposition of an ellipsoid.

The results of the further experiments were:

i at 60
7, = 348 PF 20, 7, — 3.87 Ta— 25 f,— 2.29

Pere. increase of resistance

Direction Bry | NO, ri | along the axes
ctocroed® lxealonlated of the corresponding ellipse
greatest smallest
Or or Ov | 60°, 30°, 90° | 4 (rat | 6.6 eZ 4.0
a | aa ar el PR
” 7 6.6 ”
Os 90°; 60°; 30° 5 6.7 jeeGes 7.6 4.0
Of | 60°, 90°, 30° | 4 7.3 9.1 11.2 7.7
Pe 8.5 =

The deviations in this case are certainly not greater than in the
other groups, so that they may be considered as not contradictory
to the supposition that in this case also the resistances in all
directions can be found by means of a conduction-ellipsoid on the
axes of symmetry.

9. This result would at once be explained if we were allowed
to assume that, in the case of a magnetic force inclined with respect
to the principal axis, the increase of resistance for each axis would
be found as the sum of two increases, one caused by the component
of the magnetic force parallel to, the second by the component
perpendicular to the principal axis.

In order to test this hypothesis by means of the experiments it
was necessary to know the function connecting the increase of
resistance with the magnetic force in this bismuth. For this pur-
pose I could use the formula deduced before 2)

LOSS
1+ Cv Je

) Versi. d. Verg. 25 Maart ’99, p. 485, Comm. N° 48, p. 4.

( 420 )

As in most positions the increase was somewhat small for a
reliable determination of the constants in this formula, I assumed
that C, would have sensibly the same value for the various posi-
tions and axes, and only made some experiments for the direction
Oa, in magnetic fields 2300, 3750 and 5800. These furnished for
the constants the valves

C, = 0.19 Cy = 1.29.

In the experiments of group J/7 the component of the magnetic
force // principal axis was 4600 cos 60° = 2300, the component 1
principal axis 4600 sim 60° = 3980. Accordingly the increases of
group J will have to be multiplied by

3.98? 1+ 4.60 x 0.19
4.602°*1 + 3.98 x 0.19

4
= 0.800 —_
12s

and those of group JJ by

2.32 1446 0.19
4.62 “1 +2.8 x 0.19

1
= 0.326 or about a

So we find, using the values for N°. 1 and 5

4 1
Direction Og 5° 13.0 + Pu 2.5 =11.2, observed 11.2
4 1
> Oh —. 45+—.29=> 46 > 4.0
5 3
4 1

The agreement here may be considered very good, it is however
favoured by the fact that in this case the same two bars could be
used for calculation and experiment. Hence the observations do not
afford any reason to doubt the validity of the principle of super-
position in this case.

10. The results of this research may be summed up as follows:

In erystalline bismuth the Hawu-coefficient is large for a magnetic
force 1 principal axis, very small for a magnetic force // principal
axis (same order of magnitude as in other metals), while the coeff-
cient for a magnetic force in any direction can be deduced from
those in both principal cases with the aid of an ellipsoid of
revolution.

.

( 421 )

Without a magnetic field the resistances in crystalline bismuth
can be found for all directions by means of a conduction ellipsoid
of revolution on the principal axis. (Axes in the ratio of 5 : 3),

In a magnetic field // principal axis there is an ellipsoid of
revolution with comparatively slightly varied axes.

In a magnetic field 4 principal axis there is an ellipsoid with
three more varied unequal axes.

In an arbitrary magnetic field there is an ellipsoid with three
unequal axes which can be obtained by superposition of the varia-
tions of the axes in the principal cases.

The resistances in two directions at right angles in a plate of
bismuth will generally increase wnegually in the magnetic field,
which explains the dissymmetry of the Hawt-effect.

Physics. — J. C. ScuatkwuKk: ‘Precise isothermals. I. Meas-
urements and calculations on the corrections of the mercury menis-
cus with standard manometers* (Communication N° 67 from
the Physical Laboratory at Leiden, by Prof. H. Kamerr-
LINGH ONNES).

1. For the accurate investigation of isothermals of gases by means
of piezometer tubes, into which mercury is forced, it is desirable to

‘work with pretty large quantities of gas and to take care that the

surface of the space it occupies is as small as possible with regard to
its volume. For a given range of pressures we therefore desire to read
the mercury meniscus in a tube the section of which is as large as is com-
patible with the accuracy of the adjustment and with the pressures
which the piezometers have to resist. The correction for the capil-
lary pressure to be applied to the pressure observed can only be
applied with sufficient certainty when the piezometer tube is suffi-
ciently large.

For such tubes, the volume of the meniscus may not in general
be supposed to be equal to that of a spherical segment as it
may allowably be considered in verry narrow tubes. This is the less
permissible as the desired accuracy in the determination of the
enclosed volume of gas is greater.

To attain in the measurements with the standard gasmanometers
described in Communication N° 50 of the Physical Laboratory at
Leiden, the high degree of accuracy for which they are designed,
an investigation of the volume of the meniscus which shuts off the
gas is indispensable. For, these piezometers are made to accurately
determine together with the standard open manometers, described in

28
Proceedings Royal Acad, Amsterdam, Vol, III,

( 422 )

N°. 44 of the Communications mentioned above, isothermals to within
1/5999 — the manometer mentioned allowing absolute measurements of
pressure to within 1/jo900.

Only when this accuracy is reached, we can arrive at some cer-
tain knowledge of several interesting questions in the theory of
gases.

As with these piezometers the normal volume can be determined
to within 1/0909, so the volume of the compressed gas must also be
exactly obtainable to within 1/j9999.

We will now demonstrate that in order to attain that accuracy
the volume of the menisci in certain cases must be known to within
3 percent, while it will appear below (§ 9) that the deviation of the
real volume from that of a segment of a sphere may amount to
20 percent.

The pressures of 4—8, 8—16, 16—32, 32—64 atmospheres are
measured (see Communication N°. 50 p. 8) in tubes of 0.4, 0.28,
0.2 and 0.15 ¢.m. radius, each provided at its upper end with a
widened reservoir. The tubes are calibrated by placing them enti-
rely filled with mercury in a space of constant temperature (Com-
munication N°.50 p. 20) and by drawing off repeatedly a small quan-
tity of mercury through a glas-cock, reading every time the level of
the mercury in the tube and weighing the quantity run out.

During the calibration we must reverse the position of the tube,
for in its proper position, owing to the large dimensions of the
reversoir occupied by the gas at a pressure of 1 atm., it would form
a gigantic thermometer, so that a small variation off temperature
would bring about a perceivable displacement of the mercury surface.
The displacement would influence most ef all the calibration of the
upper reservoir and the stem, which thereby as will be shown, would
become less accurate than 1/9999, and this upper reservoir is just
the space in which the quantity of gas is to be compressed.

In the most favourable case — i. e. with the largest tube — the
volume of the gas can become 20 ec. ec. And then only an error of
0.002 ¢. ¢. may remain, and as the volume of the large reservoir
is 160 ¢c. ¢., this error may already be caused by the expansion of
the mercury, when an error of 1/;; deg. C. has been made in the
temperature. As in the calibration of a tube longer than a meter,
these differences of temperature cannot be avoided without very spe-
cial precautions, it is even in this most favourable case advisable
io calibrate the tube in a reverse position, so that each time the
mereury occupies chiefly that volume, which afterwards will be
filled by the gas,

ae

( 423 )

But it is more necessary for the narrow tubes: in the fourth, for
instance, the volume of the gas may fall to 2.5 ¢.c., while a
volume of 175 c.c. is occupied by the mercury in the large reservoir
of the tube. If the volume was measured in the upright position,
the volume afterwards to be occupied by the gas would be measured
as the difference of two mercury-volumes about 70 times as large,
and in order to avoid an error of more than !/j999 in the gas-volume,
we should have to be certain of the temperature to at least 1/,,.
deg. C., a thing very nearly impossible for a tube of this length:
therefore the calibration in the reverse position is absolutely necessary.

But in order to derive the volume of the gas above the mercury
from the calibration of the tubes, we must know the exact volume
of the meniscus; this is a fortiori necessary when the calibration
has been made in the reverse position. For during this the meniscus
points to the large reservoir, but during the observations to the
small one. And so an error in the determination of the volume of
the meniscus is felt doubly in the volume of the quantity of gas.
Take for instance again the first tube, for which the volume of
the meniscus is the most important and use in it the often oc-
curring height 0.14 c.m., then the meniscus at a first rough
approximation taken as a segment of a sphere would have a volume
of 0.0365 cc. While we saw that an error in the gas volume may
not exceed 0.002 cc. in this tube, an error larger than 3 percent
may not be allowed in the volume of the meniscus.

In the following pages are communicated measurements, calcu-
lations, and graphical representations, which render it possible to
determine the volume of the meniscus with the desired accuracy and to
enable us to make the intended step forward in the accurate deter-
mination of isothermals. Successive calibrations of one tube which
without the correction for the meniscus, failed to sufficiently agree,
did so to within 1/j9999 after these corrections had been applied.

The measurements to be communicated concern the direct deter-
mination of the volume of some menisci. The calculations give an
approximate solution of the differential-equation for the capillary
surface in two limiting cases: @ for very narrow tubes, and & for
a very small ratio of the height to the radius of the tube, both
with an approximate value of the surface-tension. By means of the
graphical representation we derive from the menisci measured and
from those calculated for the limiting cases, the value of the volume
for each case. Moreover a test has been obtained § 7 by means of
a graphical solution of the differential-equation '),

') Compare also Sir W. THomson’s Popular Lectures & Addresses [. p. 32.

28*

( 424 )

§ 2. Determination of the volume of some mercury menisci by weighing.
‘ A tube of the bore for which
fi I we desire to know this volume

at different forms of the menis-

cus, is provided at its upper end
with a very narrow capillary
tube and sealed at its lower
end (see fig. 1). On the tube
the divisions P and Q are made
at about equal distances from
the middle of the tube. It is
well cleaned by boiling (comp.

Communication N°. 50 § 5) and

is filled in vacuo with purely

distilled mercury, so that the

\ mercury at 20° ©. stands at H

about 1 c.m. from the end of

the capillary. In order to make
measurements with the tube it

Pa is closed by sealing-wax and

either with the capillary poin-
ting upward (position I) or
downward (position II) it is

a hung in a bath which is kept
e tae C ik at 20° C. in a manner after-

wards. to be described. The

:
:

i’ height of the mercury surface

ls with regard to the divisions

must be read with a catheto~

ey Gj 4. By ! meter. In order to avoid parallax
ia ¢ the tube was hung so that the

marks were on the side and
the adjustment was made at the middle of these, which were seen
as shallow grooves.

The mercury is weighed which must be forced out in order that
after the tube is sealed again and put into the bath with a tem-
perature t it should give the reading / in position I. Let the
weight of this quantity be called Hz. Again the mercury is weighed
which is forced out to bring, after having a second time been sealed
and placed in the bath, the meniscus in the position | at the temper-
ature ¢4 to A, or in the position II at the temperature t, in the
wide tube at B and in capillary at 6, which quantity we call

( 425 }

Hy4, and also when further in the position I at the temperature
tc the meniscus is at C, or in the position II at the temperature
tp at ) in the wide tube and at d in the capillary, i.e. the quan-
tity Hac. Finally we weigh the quantity Hcc, which is forced out
last in order to empty the tube entirely.

In order to pass from the position I into the position II the
capillary is opened, and the mercury transferred by gentle in-
clination to the position /8 or dD without any loss, the capillary
is then again sealed, after which the tube can be wholly placed in
the position II.

The two marks P and Q were made in the immediate neigh-
bourhood of the menisci to be formed, in order to enable us to
determine accurately the distance of those menisci. For this distance
is measured while the tube is immersed in the bath; now suppose
that the tube and the glass wall of the bath are not perfectly pa-
rallel, or that in that glass wall ihe inner and outer sides are not
perfectly parallel, then owing to the refraction of the light, the
distance read on the cathetometer will not be equal to the distance
of the menisci. Now by making the two marks P and Q we have
only to measure in the water the very small distances from P to
the meniscus very near to it and from Q to the meniscus quite
near to it, so that only very small errors can occur, while the
distance PQ outside the water can be determined with the greatest
accuracy. By means of the temperatures tr, tz, ta etc. and the
weights Her, Hra, Hac, Hcg it is possible to determine at 20° C.
the volumes of the glass reservoir corresponding to them ; as these tem-
peratures deviated at the highest 0.05 deg. from 20° C. a rough value
for the apparent coefficient of expansion of the mercury is sufficient.
Let Vac be the volume between the planes going through the
levels of the menisci A and C, and VY(4c) the volume between the
curved surfaces of the menisci A and C, and V4 the volume of the
meniscus A ete.; o the cross-section of the capillary; o4c the bore
of the tube derived from Vac and agp the same bore derived from
the volume Vep.

So we get:

Va+ Vo= V(@4) + Vierp) — Vrg— Van.
Ve + Ve = Vem + Vive) — Vrg— Vac.

Let pa be the height of the meniscus A, then we can
always put:

( 426 )
V4=m-+npa +2;
Va =m+npet+ys
Vo=m+npo—%Ms
Vp=m+npp— 2.

We then get the following values:

A. For the tube of 0.28 cm. radius:

Hrr = 0,1046 gr. Viner = 0,00772 com’, BF = 3,415 em.

Hira) = 14,8137 » Vira) = 1,09352 » bF= 0,934 »

Hac) = 20,0136 » Viec) = 1,47735 » dF = 0,385 »

Heng = 35,2969 » Ving) = 2,60553 » AC=1.527 »
BD = Wb 2

From this we derive 6 = 0,00266 c.m?
the volumes of the menisci:

.. and if first we equalize

OAG= 0,2513 c.m?,
OBpD=— 0,2505 »
and so on an average 0.2509 »
from which we get with sufficient accuracy Vec = 0,1305 ¢.m?.;

Vap = 0,1305 ¢.m?.
And further

paA=0,098, m= — 0,00212, V4 =0,01307 + 2, cm?
pp = 9,100, n = 0,155, Veg=—0,01388 +4, »
po = 9,103, Vo = 0,01384—y, »
pp = 9,113, Vp=0,01539 — x, ».

If the values of 2, and y, are small, as really will appear further
on, then the volumes now found can serve to again determine
the bore of the tube more accurately; we get: 4c = 0,2519;
opp = 90,2518 c.m?, and from this follows again the more accurate
yalues :

( 427 )

VA = 0,01305 a 7) €.C.
Vp = 0,01336 + y, »
Vc = 0,01381 — y, »
Vp = 0,01536 — a, »

B. Tube of 0.38 em. radius. In quite a similar way we have
found here:

pA = 0,104 cm., V4 = 0,02775 + ay ce.

OAc = 0,4584, pB=0,067 » Vp = 0,01665 + yo »
no = 0,110 > Veo = 0,038015 — yp »
DDi= 0, bisn ss Vp = 0,0310° — ay ».

C. Tube of 0.41 e.m. radius. In this only two menisci have
been determined, which chanced to have the same height, the meas-
urement itself was less accurate:

o = 0,525 p = 0,126 V = 0,0406.

§ 3. I intended to represent the volume of the meniscus as funct-
ion of the principal dimensions by a surface. But as the surtace
which is obtained by drawing in three mutually perpendicular direct-
ions: 1. the radius of the tube, 2. the height of the meniscus,
3. the volume of the meniscus, would rise rapidly for increasing
values of the radius of the tube, I have plotted not that volume
itself, but its ratio to the bore of the tube; that ratio is called
the mean height and is represented by the letter f. Moreover I
have taken as ordinates: 1. the radius R of the tube, and 2. the
ratio 0 between the height » and the radius R.

We then obtain the following values from the menisci measured :

R 3 f

0,2832 0,346 0,0518 .2,'
> 0,353 0,0530 +y,'
> 0,364 0,0550 —y,'
> 0,399 0,06115—2,'

0,382 0,175 0,0363 +-y,'
> 0,272 0,0605 +2!
> 0,288 0,0658 —y,'
> 0,296 0,0677 —25'

0,409 0,308 0,0733,

( 428 )

§ 4. With these few data it would be impossible to obtain suffi-
ciently accurately the surface which gives the mean height as a
function of R and 0, if the theory did not allow us to determine
that surface approximately near the limits R=0 and 0=0. For
the purpose I had in view a greater accuracy than 3 percents in
g the determination of the volume of the
meniscus was not required, so I neglected
s in the calculation those terms whose in-
fluence remained below this value, as soon
as it helped to simplify the calculation;
for the sake of simplicity we have left
uninvestigated other terms of perhaps still
smaller influence but which did not give
any difficulty in the calculation. We first
will consider here the vase that R is very
small.

Let PP’ be the axis of the tube, QQ' the
wall; the surface N the level on which
the mercury stands outside the tube; OS the
horizontal tangent plane to the top of the
meniscus; let further + be the horizontal
coordinate and / the distance below the sur-
face OS; d the depression, H the surface tension, and s the specific
gravity of mercury, then we have the well-known differential equation:

ial

1 dh ( 1 (S)} Ph
(ny eae r dr t dr » } dy?

i oe

With very small values of & the depression d will always be
great and the height /% very small: and so the first member will
differ little from d. Therefore I will in the first member replace
h by some function of 7, f(r), which in a more or less approxi-
mate degree corresponds with the exact value /, and trace what
influence that accepted function has on the solution following from
the modified differential equation, assuming that f(r) is in all cases
small with respect to d.

For f(r) = 0, the differential equation has the known solution

— O—V g—r,
2H

a circle with a radius g=
sc

( 429 )
If further we assume f(r) fd, in which & is a very small
constant we again get a cirele with radius ae = e(1 —2).

The increase of height becomes therefore :

The greatest value has the relative increase of height at the wall,

i

If we call 0, the angle of contact in the air

then the last value becomes ark Now as the minimum value of d=
sin

5c : k
about 51° that relative increase of height becomes Te

’

= 1,29 &. As long

as k<0,00777, the relative increase of height at the wail is
smaller than 1 percent, and then the relative error in the volume
will be much smaller than 1 percent. As moreover the relative
increase in height is proportional to /, a certain error in & passes
proportionally over into the increase of height. Preceding considera-
tions show that if we substitute for f(r) in the differential equation
an arbitrary function but so that its greatest value is always
smaller than 0.777 percent of d while at the same time that
function increases from 0 slowly and always in the same sense to
that greatest value, the deviations in height and therefore certainly
im the volume also remain smaller than 1 percent. We will avail
ourselves of this result to judge of the limit to which we can
continue this approximation.

It is obvious after we have obtained the first approximate
solution 4) = (7), the circle, when we suppose /(7) = 0, we look
for the solution /;=/,(7), as a second approximation, which is
obtained by putting in the first member of the differential equation
h==hj=f,(r), and when this solution is obtained we look again
for a new one, in which in the differential equation 4= h, =f, (7)
is put ete.

Difficulties however appear in the integration. In order to avoid
these we may try for instance development in series, in which
the first term in the development of 2, = f(r) in terms of r is
first considered. It comes to this, that we do not assume hy = /, (r)
as approximate solution but another 4,; =f) (7), which contains

( 430 )

only the 2"¢ power of 7, i.e. which gives the meniscus as a first
approximation the form of a parabola. If now however we assume
a parabola, a better correspondence must be obtained by means of
the parabola which passes through the top and the level of the
meniscus, and therefore

hoy = ar,

in which p represents the height of the meniscus. The in this way
simplified differential equation gives as first integral:

dh
1 1 H di
Sipe 2 :
2 4 h? 8 FIA
Ee)
dr

This equation cannot as yet be integrated in a simple way, but
can be easily made integrable by neglecting terms of the same
order as we have done already. Therefore I take:

in which then only & always remains very small. We then get:

72-An38
h= | Reosa— 6 8 | ote ale teed cost ce
cos" Conte
a g RS 1
+( 9 —1) Py =~ 1].
; COS~ & cos*a ly 1 — 2? cos* a

By substituting in this 2 = 1, we have h=p, from which

~1l—si
eS ond —Csna +l —ncra—0.
cos
From the first condition it appears that @ is the angle of contact
which we should have, if the meniscus was a segment of a sphere.
And from the second condition follows then: 9 = 4¢(1 + 0%),

Therefore :

By pa
p= (1 —V T= 2 cos? a) —
cos &
RE oS eee 1
—_ —. Se6) 2 amallon) ee 1
aes [1 V 1 — 2° cos? a — sina ie Pia

90-4 ¢

£50

SE ——

( 431)

In order to find out whether it is necessary to continue the work
to obtain a third approximation I have calculated for a tube of
0,1 cm. radius (the widest to be considered here) the vaiues of
f(r), the circle, f:(7), the parabola and j,(r), our second approxi-
mation, and have drawn them in fig. VII of the plate, for a value
of 0 = 0.35, which often occurs with narrow tubes. I found :

| Height for the circle Height for the Second approximation

x represented by the | parabola represented | represented by the
line B. by the line C. line A.

0.1 0.000312 0.000350 0.000305

0.2 0.001203 0.001400 0.001006

0.3 0.002808 0.003150 0.002218

0.4 0.005054. 0.005600 0.004333

0.5 0.008022 0.008750 0.006974.

0.6 0.011711 0.012600 0.010270

0.7 0.016043 0.017150 0.014340

0.8 0.021337 0.022400 0.019634

0.9 0.027594. 0.028350 0.026415

1 0.035000 0.035000 0.035000

The relative diminution of height according to the solution, ob-
tained by introducing the parabola fo (7), amounts at a maximum
to 1/, of the height which is obtained by putting = 0, According
to what we have found with the substitution 2= kd, the relative
decrease of height which would be found in the second approximation
with jf) (7), therefore will deviate from f, (7) at a maximum !/, x
the relative deviation which remains between fo, (7) and f, (r). As
the latter amounts at a maximum to '/; we should not expect a greater
relative deviation than 1/5 <1/;=1/so. If further we take into
consideration that the exact value of the meniscus and f(r) are
the same at the top and at the level of the meniscus, then it is
obvious that the deviation in the volume will be much less than
M/s) and thus is below the limit fixed above.

We now will determine the volume; this is:

1
1 re f 2hede= 1B | : fn EE | tain el].

cos a( 3 cos? @ } 3 cos® al

0

( 432 )

If we substitute the values found for « and % then we find for
the volume of the meniscus itself:

V= 1,0 R? p+ Vea p® + Hog - ap R*(1 + 0%),
Here I have calculated for several values of O the volumes

of the meniscus for tubes of 0,04 and 0,1 em. radius; for

H
=== 050354 em?:

8
3 2
| 3
| | | ac |
ed [ie ae Ae 0,15 | 02 | 0,25 cee 0,35 hea |e
| |
] |
0,04 | 0,000005 | 0,000010 | 0,000015 | nnn | 0,000026 | 0,000031 | 0,000037 oer | oon 0,000042
0,1 | 0,000079 | 0,000158 | 0,000238 | anes 0,000404 | 0,000489 | 0,000577 | 0,000668
| |

§ 5. We will now consider the case that 6 is very small. For
this I will develop % in a series. If we substitute in the differential
equation for the series er? + /#r* +-.... then we find by equalization:

iS

(a) eae

ee an} 2880( a) a7 +2520 (— 7) na 328 (5) @+(;5)4 :

We see that the x» term itself of this development in series
consists again of n terms, and these terms should first be summed
before we can conclude to the convergency of the series. For this
the general term should be found, which is very difficult. But |
still we see that this development in series will become valid
when d is very small, so that terms of higher powers than the
second can be neglected. This now is the case when 0 is very
small. But we cannot neglect d in the first member of our original

( 433 )
differential equation, because 4, and so the whole first member

3 ‘ ; : Th
itself is small. But if 0 is small - must be small and so we can
ar

i dhy® :
first begin to neglect the second member as compared with 1.
ar

Then we find by substitution:

= 1 & ya i
Y= Bn ig ia

These are exactly the coefficients which we get when we make
the approximations mentioned in the solution of the complete dif-
ferential equation. This series converges rapidly, as the ratio of

is
=i th th ay ] — = 2,
the (m-1)th and xth term is aan?

If we now suppose that in the differential equation we do not

: dh? : : 3
entirely neglect () as compared with 1, but that we give to it

ar.
the small constant value c¢

, then we get:

We see thus that by the introduction of the small constant ¢ all
coefficients have become greater by an amount proportional to c,
and that the series remains convergent, because the coefficient of c
in the terms written as above, ean beecme at the highest °/; and
so the limit ratio of two successive terms is the same as in the
preceding case,

( 434 )

For the same reason as in § 4 we shall approach more nearly to
the exact solution if we substitute in the second member of the

dh dh : :
differential equation in the factor 1+(5 =) fo or a function which
Tr

dh
has about the same course as the true value of a and which
ar
yet gives easily summed series. For this also the parabola
h= an is useful.

With slight approximation we then can put for the equation:

dh p? a dh 6 2 )
pata Tl1ak 2h dE Se pi aa
If we substitute h=a@,r? + a,r*+..... .
we find:
a) a d
an (3 )
On+1 = rij ie 2n(3 n—1) 5 +A

Pp
The limit ratio becomes therefore here 6 ae and this ratio is

according to our supposition very small. All coefficients are propor-
tional to @, and of this the value is determined from

p= = a, R.

In order to test the validity of this formula, we will apply it
to our narrowest tube, for which R= 0,2832 c.M., for the value of

a= = 0,35 hence p = 0, 02807 cm. We then find:

Gy = 1,888 a),
ts = 1,998 con,
eg —— Oe reals
a, = 90,3008 ;

d = 0,0424 em.

h = 0,3003 r? + 0,567 r# + 0,599 r6 + 0,48 r8 4-2...

ae

( 435 )
and near the wall

dh ah
= ? ees
p=0,02807; —=0, =
If we substitute these values in the original differential equation
the first member becomes:

d+ h=0,0705

and the second member
1 dh dh\*)
= oN) yi
H ral a (
8 ( =i We
1+(—
( a dr j
Hence the difference is about 1 percent, so that for this case the
formula can be applied, and the more so because we especially want
the volume, in which the deviation will be still smaller because
we can again secure coincidence at the top and at the level of the
meniscus, by means of the formula p= = a, R2. For wider tubes
the formula will certainly hold also, if the height is not greater than
the one used here i.e. 0,028 ¢eM., while for narrower tubes it will
hold for the same value of 0, about 0.1. In order to test it still better

I have calculated the first coefficients of the complete solution (§ 6,
beginning) for the same tube. We find:

dr?

= 0,0697.

u=0,3003 =0,5567 y=0,632 d=1,027
p = 0,02408 + 0,00358 + 0,00033 + 0,00004 +... = 0,02803...

differing very little from the accepted value 0,02807.
From = = a, 7r2" we find for the volume of the meniscus:
Vw Vy eee
‘ Vv? n+ 1 j
In this case, for R = 0,2832 cM. and d = 0,0991 V = 0,00373 ce.
If however we had used the coefficients of the solution obtained
from the complete equation then

V = 0,2519 { 0,02803 — (0,01203 + 0,00119 + 0,00008 +
+ 0,00001 +...}= 0,00371 ce.

thus differing by less than 1 percent from the approximate value,

( 436 )

We calculate :

for R=0,2832cM.; 7 =0,25hence p=0,0201 and 0=0,0708; V=0,00265ce.

J) 2 >; »=0,15 » »=0,0120 » »>=0,0425; »>=0,00158 »
>» 20,382 »; »=0,2 » »=0,0292 » »—0,0765; »—0,00725 »
>» »= » >»; »>=—0,1 » »=0,0146 » »>=0,0383; »>=0,00362 »

For still smaller values of 0 we may use the development in series,

HANS : é
in which (>) is wholly neglected as compared with unity. We get

vd yi
a mislan [

and for the volume of the meniscus

enya

i s R n—l
(n!)? = )

(To be continued.)

V=apF* 31 —

Physics. — H. A. Lorentz. —“ The Theory of Radiation and the
Second Law of Thermodynamics’.

§ 1. In his celebrated theoretical researches on the emission
and absorption of rays of heat and light, KrrcuHorr was led to
introduce a certain function of wave-length and temperature which
is independent of the particular properties of the body considered.
This function, whose mathematical form later investigators have
tried to determine, represents the ratio, at a definite temperature
and for a definite wave-length, between the emission E and the
absorptive power A of a body, both taken in the sense assigned
to them by Kircnnorr; indeed, by his law, this ratio is the same
for all bodies, being always equal to the emission of what Kircn-
HOFF calls a perfectly black body.

§ 2. The function in question has yet another physical meaning.
If a space which contains nothing but aether is enclosed by per-
fectly black walls of the temperature 7, it will be traversed in all

directions by rays, and the aether will thus be the seat of a cer-
tain amount of energy. We may consider this energy as made up
of a large number of parts, each of them belonging to the rays of
a particular wave-length, and, for a given state, this repartition of
the energy over the radiations of different periods can only be
effected in a single way. Hence, if for unit space, we write

f(D aa

for the energy, as far as it corresponds to the rays of wave-lengths
between 4 and 2+ dA, and

ul =| F(T, Ada
0

for the whole energy, the function /(7, 4) will be wholly determinate.

Now, this function is intimately connected with the emission of
the black walls, and from Kircunorr’s law it follows that the
state of the aether which it defines may also be the result of the
radiation of a body that is not black.

To begin with, the walls of the enclosure may be made on the
inside perfectly reflecting, instead of perfectly black. If, then, a
certain part A, of the enclosed space be occupied by a black body
M of the temperature 7’, and the remaining part R, by aether, it
is easily seen that the state characterized by /(Z, A), if once existing
in R,, will not be disturbed by the presence of 1, but will be in
equilibrium with the internal motions of the ponderable matter. It
will even be the only state having this property, and must there-
fore of necessity be produced by the body, provided the geometrical
conditions are such that, after a certain number of reflections by
the walls, every ray in the space 2, must ultimately strike the body I.

Krrcuuorr’s law further proves that the equilibrium will conti-
nue to exist, if the black body is replaced by any other body M of
the temperature 7, whatsoever be its physical and chemical state
and its properties. What is more, such a body will also give rise
to the same state of radiation as the black body did before, at least
if the above geometrical condition is again fulfilled, and if, besides,
the body has some absorptive power, be it ever so feeble, and con-
sequently some emissivity, for every wave-length that is represented
in the radiation of the black body. This may safely be assumed.

The function /(7,A) is thus seen to have a second universal phy-

Proceedings Royal Acad, Amsterdam, Vol, IIL,

( 438 )

sical meaning. The state of the aether to which it relates may for
the sake of brevity be called the state corresponding to the
temperature T,

§ 3. Since Krrcunorr’s time great advances have been made
in the investigation of the form of the function. By a most ingenious
reasoning, founded partly on thermodynamic principles and partly
on the electromagnetic theory of light, Bottzmann ') has shown that
the total energy per unit of volume must be proportional to the
fourth power of the absolute temperature, so that, if this is hence-
forth designed by 7,

fr@anarsor, oo... 5
0

where C is a universal constant, whose numerical value will of
course depend on the choice of the units.

A result that has been obtained by W. Wien”) is likewise very
remarkable. He found that f(7,4) is of the form

1

Tae i) = 12% (TA) = 7

wi(DDide saree

p(T) or w(LA) being a function of the product 74. Evidently
BoLTzMANN’s result is contained in the latter law.

Wren *) and Pranck*) have also endeavoured to discover the form
of the function gy, but we need not here speak of these researches.

§ 4. The experiments of Pascuen, and those of LumMEr and
PrincsHEIM have furnished a very satisfactory verification of the
laws, expressed by (1) and (2), and have thus confirmed the fun-
damental supposition that the second law of thermodynamics holds
in this domain of physics, as well as the validity of the reasoning
by which the two formulae have been established. In fact, I don’t
see that any but perhaps some far fetched objection could be raised
against the theories of BotrzMANN and Wien. In my opinion, we
cannot but recognize all that has been said as legitimate deductions

1) BourzMann, Wied. Ann, Bd. 22, p. 291; 1884.

2) Wren, Wied. Ann., Bd. 52, p. 182; 1894.

3) Wren, Wied. Ann. Bd. 58, p. 662; 1896.

4) Pranck, Drude’s Ann. Bd. 1, p. 116; 1900, Verhandl. der deutschen Physik.
Ges. Jahrg. 2, p. p. 202, 287; 1900.

=——.~

( 439 )

from Carnot’s principle, but in so doing we are forced to aremar-
kable and, at first sight, somewhat startling conclusion.

The state of the aether which corresponds to a given temperature
is characterized not only by the amount of energy per unit of volume,
but also by at least one definite linear dimension. We may for
instance fix our attention on the wave-length for which (7,4) has
its maximum-value, and which I shall call 2,, or we may calculate
a certain mean wave-length by means of the formula

Now, the form of the function may very well be such that the ratio
between 2,,, 4 and what other lengths!) it might be deemed con-
venient to introduce, is expressed by definite numbers, but we have
to explain for what reason one of these, for instance 4m, has pre-
cisely the length that has been found for it by observation. In
considering this question we shall have to take into account that,
by Wien’s law, Am is inversely proportional to the absolute temperature.

We have good reasons for believing that, in so far as the aether
is concerned, the phenomena may be exhaustively described by means
of the well known equations of the electromagnetic field. If this be
true, it cannot be the properties of the aether which determine the
amount of energy and the preponderating wave-length, the velocity
V of light being the only constant quantity which these equations
contain. Hence, within the enclosure considered in § 2, the value
of the energy per unit volume and that of 4m must be forced upon
the aether by the ponderable body J. But then there must exist
between different bodies a certain likeness, expressible by the equality

') We might for instance, without decomposing the vibrations in the aether by
means of FouriEr’s theorem, define a length 7 by the formula

[@*]
oa? da? da) ’
se) +Gy) +5) ]
oz oy dz
in which « is one of the components of the dielectric displacement or the magnetic

force, whereas the brackets serve to indicate the mean values, taken for a space
whose dimensions are large in comparison with the wave-length, or with Z itself,

29*

a

( 440 )

of numerical quantities; else it would be inconceivable that two
bodies call forth exactly the same values of «and 2,,. Without some
conformity, of one kind or another, in the structure of all substances,
the consequences of the second law and this law itself cannot be
understood. If it did not exist, we could not even expect that a piece
of copper and a mass of water for instance, after having been
brought by contact into states in which they are in thermal equili-
brium, would, under all circumstances, remain in these states, when
exposed to their mutual radiation.

§ 5. It is by no means surprising that the validity of the rules of
thermodynamics should require a certain similarity in the structure
of different bodies, for in reality these rules do not teach us some-
thing about a single body, but always about two or more bodies
and about the way in which these act on one another. The pro-
position that two bodies which, when brought into contact with a
third one, do not interchange any heat with it, will also be in thermal
equilibrium with each other, is clearly of this nature, and it is
easily seen that our remark applies likewise to the law, that the
absolute temperature is an integrating divisor of the differential
expression for the quantity of heat, required for an infinitesimal
change of state.

Let us suppose that an experimental investigation of the states of
equilibrium of which a body (or a system of bodies) 44, when con-
sidered by itself, is capable, has led to distinguish these states by
the values of certain parameters @, 1), 71--- Then, an infinitely
small change of state may be defined by the simultaneous incre-
ments d@,, df,, dy,,-.. If, in every case, we measure the amount
of heat dQ, that has to be supplied to the body, say by determining
the equivalent mechanical energy, we may establish an equation of
the form

dQ, == A, d a) a By d /?, + Ci dy, -b ease . . . . (8)

in which the coefficients A,, 2), C),... are known functions of @), Pry Yigees
The integrating divisors

Ay, Ay ey eee oe

of which the expression (3) admits, and which we may imagine to
be determined by an ideal mathematician, will also be functions of
the parameters.

Next, let 4M) be a second body or system of bodies. Operating

( 441 j

with this, as we have done with the first one, we shall be led to the
introduction of certain parameters cg, /?2, 7)--.-) t0 an expression, cor-
responding to (3), say

AQs = Ay dey a By dj? — Cy dy + eee
and to its integrating divisors
LE RA eM Rat oy yk. (BY

These will be functions of @g, /2g, 72,..... Now, the proposition that
the temperature is an integrating divisor, ascribes a particular signi-
fication to one of the functions (4) and one of the functions (5),
the inequality or equality of these functions, calculated each for a
determined state of the body, having to decide as to whether the
bodies, taken in these states, and placed near each other will exchange
heat or not. However, in calculating the functions (4), we have not
even thought of ihe body M/,, and in forming the functions (5), we
hare not had in view the system IM). Therefore, the two functions
could not be invelved in what happens in the mutual action of the
two bodies, if these had nothing at all in common.

§ 6. In our ordinary molecular theories, which leave out of
account the phenomena in the aether, the question is very simple.
So far as we know, the total want of order in the molecular motions,
precisely the state of things which justifies the introduction of the
calculus of probabilities, is, in these theories, a sufficient ground for
the general validity of Carnov’s principle. This irregularity in the
motion of the ultimate particles seems to be the only common feature
of different bodies that is required. It has been found sufficient to
prove the proposition that the mean kinetic energy of a molecule
is the same for all gases of the same temperature, a result,
which is of the highest importance in the theory of molecular
motion, and is likely to be so too in that of radiation. Indeed, it
is to be expected that in studying the state of the acther, corresponding
to the temperature 7’, we shall meet again with the same definite
amount of energy, with which a molecule of a gas, of that tempe-
rature, is, in the mean, endowed, and which must also play a part
in the internal motions of a liquid or solid body.

I shall denote by this mean kinetic energy of a gaseous mole-
cule at the temperature 7’,

§ 7. We shall now return to the question what similarity in
the structure of all ponderable matter must lie at the bottom of the

( 449 )

thermodynamic theory of radiation. Evidently, a perfectly satisfying
answer could only be furnished by an elaborate theory of the meca-
nism of emission and absorption, such as has not yet been worked
out, though Puanck !) and vAN DER WAALS JR.”) have published
interesting researches in this direction. We may however attack the
problem in a way that does not require a knowledge of peculiarities.
By comparing two systems, both composed of ponderable matter and
aether, and which are, in a wide sense of the word, ,similar’’, i.e.
such, that, for every kind of geometrical or physical quantity involved,
there is a fixed ratio between its corresponding values in the two
systems, I shall try to show that, in all probability, the likeness
in question consists in the equality of the small charged particles
or electrons, in whose motions modern theories seck the origin of the
vibrations in the aether. We shall begin by supposing that, in pass-
ing from one system to the other, the dimensions, masses and
molecular forces may be arbitrarily modified; then we shall find
that the charges of the electrons must remain unaltered, if the second
system, as compared with the original one, is to satisfy BoLTzMANN’s
and WIen’s laws.

The consideration of similar systems has already proved of great
value in molecular theory. It has enabled KamertincH Onwes to
give a theoretical demonstration of VAN DER Waats’s law of cor-
responding states; moreover, the experimental confirmation of this
law has taught us that a large number of really existing bodies
may, to a certain approximation, be regarded as similar.

Of course, if the theory is also to embrace the phenomena going
on in the aether, we have less liberty in choosing the systems to be
compared. Since the properties of the aether cannot be changed,
the velocity of light is not in our power, and the similarity im-
plies that all other velocities must likewise be left unaltered.

§ 8. Let the first of the two systems be the one that has been
considered in § 2: a ponderable body M, and, next to it, a certain
space, filled with aether, both enclosed by walls that are perfectly
reflecting on the inside.

Let the ponderable body be built up of a large number of small
particles, each of which has a certain volume, so that the density

1) Puanck, Drude’s Ann, Bd. 1, p- 69, 1900.

*) Van per WAALS Jr., Statistische behandeling der stralinysverschijnselen. Disser-
tation, Amsterdam, 1900.

( 443 )

of ponderable matter is finite everywhere. To these particles we
shall ascribe an irregular “molecular” motion and the power of
acting on one another with certain “molecular’’ forces.

We shall further suppose them — or some of them — to be
electrically charged, and, for convenience’ sake, we shall consider
each charge to be distributed over a small space, with finite volume-
density y. This density may be treated as a continuous function,
which sinks gradually into 0 at the surface of the electrons.
Of course, if some of the particles have no charge, we have only
to put for these g= 0.

Finally, we shall take for granted that the aether pervades the
space occupied by the particles, and that a dielectric displacement
d and a magnetic force may exist as well inside as outside a
particle.

Then, if dz, %y, 2, Hx, Dy, H are the components of > and $, and
2, 0y, vz those of the velocity, we have the following equations '):

as Se 4 7 Vy: —
dy dz 3 (em + =
0Dx 0 ih) dy\

vad 0d,

oe = ope ——A7G (¢ =)

ddzx ddy dd-
Fe a ager ee Bie he sail fey (it)

4a Viet ee) oe

dz dy/ at
(dz ddx\ _ ODy
4 ee oa Main) * 5-8 (8)
aol angink ai!
a ea) = at?

0H: , ODy , 0.02
0 nS oy a3 0<

rere ss 5. ss (9)

1) See f.i. Lorentz, Versuch einer Theorie der electrischen und optischen Erschei-
nungen in bewezten horpern. 1895,

( 444 j

These, with g@=0 everywhere outside the electrons, and if we
add proper conditions at the reflecting walls, serve to determine the
state of the aether, as soon as we know the motions of the electrons.

The energy of the aether per unit volume is given by

1
2a v2 d? + ey S$, or Vs On wart co.) we . (10)

and the components of the force, exerted by the aether on the elec-
trons, will be for unit charge

4m V? dx + by D2 — %2 Dy,
Aap V2 by J 8: ie, Gol ds on
4a V* bd. + 7 Dy — vy Do-

Besides these forces, there may be (molecular) forces of another
kind, acting on the electrons.

§ 9. We have next to compare this really existing system S
with a second system S', which perhaps will be only an imaginary
one. Its enclosure is to be geometrically similar to that of S, the
linear dimensions being @ times what they are in the first system.
By corresponding points in the spaces within the two enclosures,
we shall mean points that are similarly situated, and to every
instant in the interval of time, during which we consider the phe-
nomena in §S, we shall coordinate an instant for the second case,
in such a way that the interval between any two moments in S'
is a times the interval between the corresponding moments in S.

Let it further be assumed that, if at a particular instant ponder-
able matter or an electric charge is found at some point of one of
the two systems, this will likewise be the case at the corresponding
time and the corresponding point of the other system. As a con-
sequence, the distribution of matter and of electric charge will
be, at corresponding times, geometrically similar in the two cases,
the dimensions of the particles in S' and their mutual distances
bearing the ratio a to the corresponding quantities in S.

What has been said suffices to determine the internal motions in
S', as soon as one knows those in S; the velocities will be the
same in the two systems, because we have supposed the ratio of
corresponding times to be equal to that of corresponding lengths.
Of course, the motions in S and S' will present just the same degree
of irregularity.

( 445 }

Now, our description of the state of the second system will
become complete, if we indicate, for each of the physical quantities
involved, the number by which we must multiply its value in S,
in order to obtain its value in S’ at corresponding points and times.

Let this factor be 4 for the density of ponderable matter, ¢ for
the density of electric charge, and ac for the dielectric displacement
and the magnetic force. Then, since the phenomena in the system
S, which exists in reality, agree with the equations (6)—(9), those
in S' will likewise satisfy these relations. Nor will the conditions
imposed by the nature of the walls be violated. We may also remark that
the formulae which are obtained for the two systems, if the motions
are analyzed by means of Fourter’s theorem, will differ from each
other only by the constant factors a and c. The ratio between
corresponding wave-lengths, e.g. between the values of Am, will of
course be a.

As to the motions we have attributed to the electrons in S’,
these will only be possible, if a, 4 and ¢ satisfy a certain condition.

: : : 1
The ratio of the accelerations being —, and that of the masses of
a

corresponding elements of volume (or of corresponding particles)
a*b, the forces acting on such elements must be in S' a?d times
what they are in S. Now, whereas the ,molecular” forces may be
supposed to be regulated according to this rule, the action of the aether
on the electrons in S' has already been fixed by what has been
said. The cemponents (11) of the force on unit charge are, in
S', ae times what they are in S, and for the charges of correspond-
ing elements of volume the ratio is a’c. The factor for the forces
exerted by the aether on such elements will therefore be a*c?, and
we must have the relation

or
Baa Ne ee (12)

This being the only condition, we may imagine a large variety
of systems S’, similar to S, and which must be deemed possible
as far as our equations of motion are concerned. The coefficients
a and ¢ having been chosen, and 0 calculated by (12), we should
find, by (10),

a® ¢

(13)
for the ratio of the kinetic energies per unit volume, and

a® b,

( 446 )

or, m virtue of (12),
Pee. 15,04) yd deo Reepthrgalen| har he

for the ratio of the kinetic energies of a molecule or an electron.

The latter number will at the same time be the factor by which
we have to multiply the temperature 7 of S in order to obtain
that of S’. Indeed, in the formulae (1) and (2), we may suppose 7
to be measured by observations in which radiation does not come
into play, say by means of a thermometer; we may therefore apply
the result of molecular theory that 7’ is proportional to the mean
kinetic energy of a particle.

§ 10. If we had only to satisfy the equations of motion, a and
e might be arbitrarily chosen. We could tien take

and b=a~*. By this the value of (14) would become 1 and
that of (13)

a3 ,
which might have any magnitude we like. In this way we should
have got two systems S and S' of equal temperatures, but with diffe-
rent amounts of energy in the same space. This being in contra-
diction with the results, deduced from Carnot’s principle, the choice
of a and ¢ must be appropriately limited.

If the two systems we have compared with each other are to
agree with BourzMaNN’s law, (15) must be equal to the fourth power
of (14). From this we conclude

a eT. so es. ee

that is to say, the charges of corresponding elements of volume,

1) A moving charged particle produces in the surrounding aether an electromag-
netic energy, which, for small velocities 1, may be reckoned proportional to v*. It
may therefore be represented by 1/, /v®. The factor & plays the part of a mass, and
may be called the electromagnetic or apparent mass, in order to distinguish it from
the (true) mass in the ordinary sense of the word. Now, / is found to be proportional
to the square of the charge, and inversely proportional to the dimensions of the
particle. ‘The condition (12) therefore means that the ratio between the true and the
electromagnetic masses is the same in S and S'. There would be no necessity to
introduce a condition of this kind, if there were no true mass at all; neither, if
some of the particles had no charge, and the remaining ones no true mass.

We may also express the relation (12) by saying, that the ratio between the elec-
tromagnetic and the ordinary kinetie energy has to be the same in the two systems,

( 447 )

and also those of corresponding electrons must be the same in S and S'.

If (15) is satisfied, the two systems will accord with Wren’s law,
as well as with that of Botrzmann. In the first place, the ratio of
the temperatures, for which we found the number (14), now reduces to

1

a

As the values of 2, are to each other as 1 toa, they are inversely
proportional to the temperatures of the two systems.

We may remark in the second place that the repartition of the
energy over the rays of different wave-lengths will be similar in the
two systems. Consider for instance the rays in S whose wave-lengths
lie between 4 and 4+ dA; by Wren’s law, the energy in unity
of volume, depending on them, is

RE BD dss © Bete \ AER Reeds RON

The corresponding rays in the second system have their wave-
lengths between 4’ and 2'+ d4’, if

i Da—vard a.
and, in order to caleulate the energy in unit space which is due to
these rays, we have only to multiply (16) by the factor (13), which

ie. : :
becomes —, in virtue of (15). Now, one gets the same expression
a

ie
—- Tg (Tijd,

if, in (16), one replaces 4 by 4’, dA by di’, and the temperature 7’
i be :

of S by the temperature 7'= -— of S'. It appears from this that the
a

distribution of energy over the different rays in S’ is exactly what
it ought to be by Wren’s law at the temperature of the system.

§ 11. What precedes calls forth some further remarks. It might
be argued that two bodies existing in nature will hardly ever be
similar in the sense we have given to the word, and that therefore,
if S corresponds to a real system, this will not be the case with
S'. But this seems to be no objection. Suppose, we have formed an
image of a class of phenomena, with a view to certain laws that

( 448 )

have been derived from observation or from general principles. If
then, we wish to know, which of the features in our picture are
essential and which not, i.e., which of them are necessary for the
agreement with the laws in question, we have only to seek in how
far these latter will stil hold after different modifications of the
image; it will not at all be necessary that every image which agrees
in its essential characteristics with the one we have first formed
corresponds to a natural object.

We have many grounds for expecting that a theory of radiation
ean be developed on the lines drawn in § 8. In such a theory
we shall have to distinguish between the hypotheses concerning the
uncharged particles, the ordinary molecular motions and forces, and
those which relate to the electrons, their dimensions, masses and
charges and the non-electrical forces which, conjointly with the
electromagnetic ones, determine their motion. Now, it seems natural
to admit that in a theory of radiation the hypotheses which relate
to the electrons form the essential part of the explanation, and that
all the rest may be freely modified within the limits indicated by
the ordinary molecular theories.

If we had a right, likewise to change at will the dimensions of
the electrons, their true masses and the forces to which they are
subject, the considerations of § 10 would only leave room for the
conclusion, that a definite magnitude of the electric charges must
be reckoned among the essential features of our picture. One might
however be of opinion that these dimensions, masses or forces con-
tain already elements that are necessary parts of the theory. For
instance, the electrons could have a fixed, constant diameter, the
same in all ponderable matter. [f this were the case, our factor a
could not be different from unity, and the formulae (12) and (15)
would give 6 = 1, ¢=1. The system S’ would be identical with S,
and it would be impossible to learn anything from it. Again, the
ratio between the densities of ponderable matter and of electric
charge might be a universal constant. This would require b=c, and
by (12) and (15) a = 6 =c¢ = 1. The way in which we have
treated the molecular forces acting on the electrons is also liable to
objection. If a definite intensity of these forces were a requirement
in the theory, it would be impossible so to regulate them, that they
are in S' a*c® times as great as in S.

These remarks do not, however, invalidate the general con-
clusion, that the electrons in two ponderable bodies cannot be wholly
different. We may even remark that, if it were found necessary to
ascribe equal dimensions to the electrons of different bodies, it would

( 449 )

be not unnatural to suppose them equal in all other respects. This
latter hypothesis would likewise recommend itself as the simplest
possible, in case we ought to assume a constant ratio between the
masses and the charges, and a fixed relation between the above
mentioned forces in different bodies would in its turn point with
some probability to an equality of the electrons.

Of course I do not mean to say that all electrons in nature must
be of one and the same kind. Anyways, there must be both po-
sitive and negative particles, and we may imagine any number of
kinds of electrons we please. The conformity between different sub-
stances should in this case be attributed to the existence of each
of those kinds, with their definite charge, in every body.

We must leave these questions for future research. The theory
will also have to explain why the phenomena always depend on
the temperature in the way expressed by the equations (1) and (2).
It is true, we have compared cases in which the temperatures were
not the same, but in those cases we had to do with different bodies,
whose molecular weights were such, that the velocities of the particles
were equal at the two temperatures compared. It will be necessary
also to compare the same body at different temperatures, and this
cannot be done by barely comparing similar systems.

§ 12. The question remains, on what quantities that are involved
in the constitution of ponderable bodies the values of 4m and the
energy 4 per unit space may be taken to depend. We have spoken
of the dimensions, the masses and the electric charges of the electrons,
or of a particular kind of electrons. These might be the same
through all nature, and besides these there is the mean kinetic
energy @ of a molecule at the temperature 7. Now we may con-
ceive different ways, in which 4m and yw could be derived from
these quantities. For instance, a given electric charge e, taken
together with a given amount of energy @, may determine a definite
length. This follows at once from the dimensions” of ¢ and a,
but we may explain it as well by remarking that, if a charge e is
uniformly distributed over a sphere of radius 2, there will be an
electrostatic energy

e2V2

Rk

1
2

(e being expressed in electromagnetic units). Henee, if we desire
this energy to haye the value @, the radius must be

1 e V2

ie 2itte

R

PP ia pene (1)

This is a length, entirely determined by e and @, and it may be
that Am bears always a fixed ratio to R. As to the energy per unit
volume, it will probably be determined by some such condition as
this, that the energy, contained in a cube whose side is /,,, is in all
cases the same multiple of 1).

We may add that @ varies as 7, and that therefore the line R,

: pes
calculated by (17), will vary as ae Hence, the length of 4,,, if deter-

mined in the way we have indicated, will be found inversely pro-
portional to the temperature, as we know it to be. Moreover, in
accordance with BotrzmMann’s law, the energy in unity of volume
would become proportional to 74, if a cube, whose side varies as

1 : Fem A
—, contained an amount of energy, which is itself proportional to the

temperature.
I shall conclude by mentioning that Prof. PLancK, after having,
found for the function f(7, 4) the form

has calculated from experimental data the coefficients @ and b econ-
tained in it, and has used these coefficients, together with the velocity
of light and the constant of gravitation, for the purpose of establishing
units of length, mass, time and temperature that are given by nature,
without it being necessary to choose some standard body.

If the above considerations are to be trusted, this universal sys-
tem of units would be based on the velocity of light, the constant
of gravitation, the mean kinetic energy of a molecule and the pro-
perties of the electrons, present in all ponderable matter.

1) What multiple this is, may be deduced from the observations on radiation, com-
bined with what we know about the mass and the kinetic energy of a molecule, It
is also implicitly contained in the considerations by which PxuaNnck terminates his
last paper. By his formula, which, as he shows, agrees with the results of the kinetic
theory of matter, I find that the energy of radiation in a cube whose side is A (§ 4)
amounts to a little more than 5,5 @.

( 451 )

Chemistry. — “On the essential oil from the leaves of Alpinia
malaccensis Rosc”. By Dr. P. vAN RomBurGH.

In a communication!) on the occurrence of methyl cinnamate in
the rhizomes of Alpinia malaccensis, I incidentally mentioned that
the leaves of this plant yield an essential oil, which is likewise
rich in this substance. Since then, I have prepared this oil in
larger quantity and investigated the same jointly with Dr. Tromp
DE Haas, Assistant to the Agric. Chem. Laboratory of the Govern-
ment Botanical Gardens at Buitenzorg.

From 700 Kilos. of fresh leaves, with the stalks attached, 1100 c. m.
of oil were obtained. The yield is, therefore, 0.16 percent. The
sp. gr. at 26° was 1.02. Rotation + 6.5°. When treated with aqueous
soda 25 percent of the oil are not attacked, forming a liquid com-
pound, the bulk of which boils from 160°—170°. This liquid may
be isolated in a still more simple manner by treating the essential
oil with steam; it then readily distils over whilst the methyl cinna-
mate, of which the oil consists to the extent of 75 percent, remains
behind in a practically pure condition, and forms beautiful crystals
on cooling.

By fractional distillation, the liquid portion yields a liquid, boiling
from 158°—160°, having a sp. gr. of 0.857 at 26.5°. Ina 200 m.m.
tube it showed a rotation of 43° 20’ to the right. The analysis and
the vapour density agreed with that of a substance of the com-
position Cyo Hy¢.

This hydrocarbon clearly belongs to the pinene group; with
nitrosyl chloride it yields a compound which ®*), by the action of
piperidine, gives pinene nitrolpiperidine melting at 118° — 119°.

Chemistry. — ‘On the action of nitric acid on the esters of
methyl-phenylaminoformic acid.* By Dr. P. vax Rompurcu,

Some years ago, I have shown that by the action of nitric acid
on the esters of phenyl-aminoformic acid, under definite circumstan-
ces, two or three NOg-groups simply enter the benzene nucleus
without any substitution of NO, for the amino-hydrogen, or libera-
tion of the formic acid-residue taking place.

1) Report of ordinary meeting Kon. Akad. v. Wetensch. 23 April 1898.

2) This nitrosylchloride compound does not, however, melt at 103° but at 108°.
I also found that melting point for an analogous compound from the terpene from
the leaves of Myristica fragrans.

( 452 )

In continuation of that research, I have now studied the action
of nitric acid on the methyl derivatives of the esters :

CH,
C, H; NC
COO R

The possibility should exist here that, besides nitration of the
nucleus, the formic acid-residue might be replaced by NO» with
the formation of trinitrophenylmethylnitramine which is very stable
towards nitric acid, or the methyl group might be replaced by
hydrogen or, what is least likely, by NOg.

The result of the research was, howevér, quite different from what
was expected. The methy] group as well as the formic acid-residue
remain intact and the reaction is limited to the introduction of NO,-
groups into the benzene nucleus. Whilst, however, when dealing
with phenylaminoformic esters, it is an easy matter to introduce
three nitrogroups into the nucleus, this is not successful with the
methyl compound and only di-nitroderivatives are obtained of
the formula I:

“Cll. CH,
NCooR NCOOR

Trinitroderivatives of the formula IL may however, be prepared
by an indirect way, so that one is led to suppose that there exists
a so called sterical obstacle to the introduction of the third NOs-
group in the place 6.

The methyl ester of methylphenylearbamic acid was prepared by
the action of methylaniline on the methyl ester of chloro-formic acid
in the presence of water and obtained in the form of a nicely crys-
tallising compound melting at 44°. The boiling point is situated at
243°. When its solution in sulpharic acid is added to very con-
centrated nitric acid a substance is obtained, which crystallises in
beautiful glossy transparent crystals melting at 98°. This is the
dinitroderivative,

( 453 )

The ethyl ester of methylphenylcarbamic acid has already been
prepared by GEBHARDT!) by the action of methylaniline on the
ethyl ester of chloro-formic acid in ethereal solution. I also
succeeded very well with the preparation in the presence of water. I
found the boiling point 5° higher than that of the methyl ester.

By the action of nitric acid a product is obtained melting at
112° which is the dinitro-compound ®),

Heating in sealed tubes with fuming hydrochloric acid at 150°
breaks up both dinitrocompounds with formation of carbon dioxide,

4 2 1
alkyl chloride and dinitromethylaniline C; H; NO, NO, NH CHs,
melting at 178°, which for the purpose of identification was treated
with fuming nitric acid, which formed trinitrophenylmethylnitramine
melting at 127°.

When both dinitroderivatives are boiled with fuming nitric acid
they do not appear to become altered. Up to the present I have
not succeeded in introducing a third nitrogroup.

As it did not seem without importance to ascertain whether the
desired trinitrocompounds might not be prepared by another method.
I have made the following experiments.

An aquevus solution of the potassium compound of the methyl
ester of trinitrophenylcarbamic acid was treated with silver nitrate,
which forms the sparingly soluble silver salt. This is then treated
with methyl iodide in the presence of methyl alcohol. Silver iodide
is formed, and from the methyl alcohol may be isolated a yellow
compound, which after being recrystallised a few times, melts at
112—113° and is the desired trinitrocompound.

In an analogous manner, I prepared the ethyl ester, which melts
at 65°.

That indeed the methyl group in these compounds is linked to
the nitrogen of the aminogroup could be demonstrated by boiling them
with a solution of potash which caused a liberation of methylam’ne
which could be proved beyond doubt by the reaction with bromo-
dinitrobenzene, which formed dinitromethylaniline melting at 178°
and yielding, by treatment with nitric acid, trinitrophenylmethyl-
nitramine melting at 127°.

The reaction with methyl iodide has, therefore, proceeded normally

2.4.6 1 (oe) O R ‘e 2.46 1 /CO O R
Op Hy. (NON yy + CHI = Cy He (NO2)s NC Gy + Ag S

1) B, B. 17, S. 3042.
2) It is peculiar that this nitrated ethyl ester has a higher melting point than the
corresponding methyl ester.
30
Proceedings Royal Acad Amsterdam, Vol. LI

( 454 )

Chemistry. — “On the essential oil from Ocimum Basilicum L.”
By Dr. P. van Rompureu.

In the Botanical Garders at Buitenzorg are cultivated three
varieties (?) of Ocimum Basilicum L. which, although containing
essential oils of very different composition, seem not sufficiently
to differ from a botanical point of view to make different species
of them. The natives call them by the jnames of Selasih hitam,
Selasih hidjau and Selasih Mekah (or S. besar).

The oil from the first one, which has dark-green leaves, has been
prepared by me many years ago, the yield is, however, very small
so that the material for a more extended investigation is still
wanting.

As regards the oils of the two others, some preliminary commu-
nications will be made here.

From the variety Selasih hidjau, which is distinguished from the
previous one by a light-green leaf, 0.2 percent (of the fresh herb)
of an oil with a fennel-like odour is obtained by distillation with’
steam; this was investigated jointly with Dr. Tromp pe Haas.

The specific gravity of this oil was 0.948 at 25°. On distillation
the greater portion passes over between 214°—218°. Analysis and
vapour density point to a substance of the composition Cy Hy, O.

On treatment with alcoholic potash, anethol is produced whilst
on oxidation with chromic acid, anisie acid is formed. The said
properties lead to the conclusion that the chief constituent of this
oil is methylehavicol, which has been found by Dupont and
GUERLAIN?!) in French-, and by Berrram and Wa.BaumM ”) in
German-, and Réunion-Basilicum-oil.

In the lower fractions of the essential oil the probable presence
of pinene could be ascertained.

From the fresh leaves of Selasih besar, I obtained 0.18—0.32
percent of an oil which possessed a strong odour of eugenol; the-
varying quantity probably depends on the age of the herb and to
some extent on the duration of the distillation. Both the specific

") Bull. Soc. Chem. III, 19, p. 151.
2) Archiv d. Pharm. 235, S. 176.

( 455 )

gravity and rotatory power varied with different samples (sp. gr.
0,890—0,940; rotation in a 200 m.m. tube —22°.5 to — 36°).

The amount of eugenol varied from 30—46 percent.

The liquid remaining after removing the eugenol by dilute aqueous
soda boils at 170°—250°, but its lower fraction cannot be separated
at the ordinary pressure by fractional distillation as this alters its
properties, which further investigation has shown. It may be readily
isolated by treating the original oil with steam. One third part then
readily passes over. A little eugenol which has been carried over
is removed and the liquid distilled in vacuo. As chief product is
then obtained a very agreeably smelling, optically inactive liquid
which boils at 21 m.m. pressure at 73°—74°. The specific gravity
is low, namely 0,794 at 22° and 0,801 at 15°, whilst the index of
refraction was found vp = 1,4861. Analysis and vapour density
(according to HorMANN) agrees with a substance of the composition
Co His. This substance to which I will give the name of Ocimene
eagerly absorbs oxygen and then resinifies. If, for instance a little
is introduced into a tube filled with oxygen and inverted over mer-
cury, this is soon observed to rise and gradually fill the tube. On
heating at the ordinary pressure, the boiling point, which is at first
situated at 176°—178°, is gradually raised and after a few hours
boiling under a reflux condenser in an atrosphere of carbon dioxide
a liquid is obtained which boils at 195° at the ordinary pressure
(at 93° at 25 m.m.), has a somewhat higher specific gravity and
shows a stronger refraction !). A portion of the original liquid has,
moreover, been converted into a product boiling at about 250°.

In its properties, this low-boiling liquid reminds of myrcene, iso-
lated by Power and Kueper from Bay-oil, a so-called olefinic terpene
(boiling point 67° — 68° at 20 m.m.; sp. gr. at 15° 0,8023, np =
1.4673) which, however, as I convinced myself is distinguished from
the same by its behaviour towards oxygen *).

I am still engaged with the study of these substances, also of a
product with a higher boiling point from Selasih besar, which is
probably a sesquiterpene.

1) A preliminary determination gave np = 1.5361.

®) Keser and Power, (E. GinpeMeIsTER und Fr, Horrmann , Die aetherische Oele”
S. 668), state that myrcene gets polymerised after a week. I did not find this obser-
vation confirmed, fcr I could keep unaltered for months a specimen prepared by me
from Bay-oil, kindly presented to me by the well-known firm of Scarmmen & Co. of
Leipsic.

(January 23, 1901.)

__a———
aa eee i el ee he ae

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TH AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday January 26, 1901.

DG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 26 Januari 1901 Dl. IX).

Contents: Dr. J. J. Branksma: “Organic polysulfides and the polysulfides of sodium”. (Com-
municated by Prof. C. A. Lopry pe Bruyn). p. 457. — N. Scnoorzn: “On urea
derivatives of sugars”. (Communicated by Prof. C. A. Lopry DE Bruyn), p. 459.—
Prof. A. F. Worreman: “On the nitration of orthochloro- and orthobromobenzoic
acid”. (Communicated by Prof. C. A. Lopry pte Bruyn), p. 462. — Dr. J. H.
Apriani: “Eutectic curves in systems of three substances of which two are optical
antipodes”. (Communicated by Prof. H. W. Baxuatis RoozesBoom), p. 463. —
Dr. H. B. Horssorr: “On heats of solution in general, that of Cd SO,, 8/, H,0 in
particular”, (Communicated by Prof. H. W. Baxknuis RoozeBoom), p. 467. —
Dr. Erxsr Conen: “The Enantiotropy of Tin” VI. (Communicated by Prof. H. W.
Baxuvis RoozEBoom), p. 469. — Dr. G. Bakker: “Contribution to the theory of
elastic substances”. p. 478. — J.C.ScuaLkwigsk; “Precise Isothermals” I. (Continued).
p- 481. (With one plate).

The following papers were read:

Chemistry. — Dr. J. J. Bruanksma: “Organic polysulfides: and
the polysulfides of sodium.” (Communicated by Prof. CL A.
Losry DE Bruyy).

In a former communication!) attention has been called to the
fact that sodium disulphide lends itself to double decomposition both
with o. and p. chloronitrobenzene and o. dinitrobenzene; the disul-
phides so formed may then (as was already known of tetranitro-

‘) Proc. Royal Acad. of Amsterdam Nov. 25, 1899.
Bal
Proceedings Royal Acad, Amsterdam, Vol. LIT

diphenyldisulphide) be converted by nitrie acid into the correspond-
ing sulphonic acids.

On continuing this research it has been shown that NaS, is in
general very adapted to double decomposition; a large number of
aromatic and some more aliphatic disulphides have been prepared.

As these disulphides are nearly all readily converted into sulphonic
acids by IINO;, we possess in Na,S, a general reagent for the
preparation of sulphonic acids. This is of all the more importance
because in this manner many sulphonic acids may be prepared which
do not form by direct sulphonation.

In the previous communication it was suggested that substances with
more than two sulphur atoms might be formed by direct substitution.
This has now been proved to be true; with the aid of an alcoholic
solution which contains 2 atoms of S for 1 mol. Naj2S, trisulphides
are obtained, for instance from o. dinitrobenzene o. o. dinitrodiphenyl
trisulphide : NO . Cy Hy. $3. CgHy. NO. which on oxydation with mitric
acid yields 1 mol. of sulphuric acid for 2 mols. of 0. nitrobenzene-
sulphonic acid.

Tetrasulphides were further obtained both by direct substitution
with the aid of Na,S,, and by removing, by means of iodine, two
atoms of sodium from two mols. of sodium, dithiophenolate :

2 NO,. C,H4. SSNa = I, = IN. C,H, S4 C,H,. NO, a 2Na I.

This is, therefore, the application to a dithiophenolate of a method
which is aiready known for monothiophenolates and was just the
way according to which the aromatic disulphides could be prepared,
for instance:

2 Cs H; S Na + IJ, = Cy H; S. C, H; + 2 Nal.

The above reaction is also comparable to the iodometric process
where sodium tetrathionate is formed from thiosulfate.

Some general conclusions, which do not appear to be devoid of
interest, may now be drawn from the above observations.

First of all this, that the di-, tri- and tetrasulphides of sodium
really exist in an alcoholic solution. This appears from the di-, tri-
and tetrasulphides obtained by double decomposition, (Special expe-
riments abundantly proved that the aromatic di-, tri- and tetrasul-
phides could not be obtained by boiling the alcoholic solution of the
mono- or disulphides with sulphur).

( 459 )

A second conclusion of general interest is the one which relates
to the constitution of anorganic polysulphides.

From the fact that sodium disulfide causes the formation of or-
ganic disulfides one mol. of which on oxidation with nitric acid splits
up into two mol. of a sulphonic acid, it follows that in sodium
disulfide one sodium atom is linked to each of the sulphur atoms;
its constitution is, therefore, NaS—S Na and those of the organic
disulfides RS—SR'. As, moreover, tetrasulfides are quantitatively
formed from RS—SNa and iodine they may be assumed to have
the constitution RS—S—S—SR' which supposes the existence in
the molecule of a series of four atoms of sulphur linked to each
other, comparable to those of carbon atoms. For the trisulfides the
formula R-S—S-S—R' is then arrived at.

Finally, attention may be called to the fact that sodium disul-
phide acts as a deoxidiser on those nitro-compounds on which it
does not act with double decomposition. The reaction takes place
without formation of bye-products; so for instance m.m. dinitroazoxy-
benzene is formed from m. dinitrcbenzene and p. p. dinitro-azobenzene
from p. dinitrobenzene. The Nag S. itself becomes Nag Sg Og ’).

For further particulars the dissertation should be consulted; its
contents with a few additional observations will appear later on in
the “Recueil”.

Amsterdam, Dec. 1900.

Chemistry. — Mr. N. Scuoorn: ‘On urea derivatives of sugars’.
(Communicated by Prof. C. A. Lopry pe Bruyy).

The investigation as to the existence of these compounds originated
in the vain efforts to readily detect lactose in urine in a short time
and to distinguish it from glucose. Lopry DE Bruyn and ALBERDA
van EKENSTEIN have attempted this by inverting the sugars and
then reducing the same with sodium amalgam, the dulcito] for-
med from the galactose may be identified by its benzal-compound
which is very adapted for this purpose. The negative result given
by these experiments made it seem possible to me that on treating
urine with a dilute acid the sugar combines with the urea and got
removed as such.

*) See Proc. Royal Acad, of Amsterdam Oct. 27, 1900.
31*

( 460 )

From the following experiments it appears that under the influence
of dilute acids glucose reacts with urea even at the ordinary tem-
perature and more rapidly at an elevated one.

At 25°: 10 grams glucose, 2!/, gram of urea, dissolved in
5 pCt. sulphuric acid up to 50 c.e.

rotation at the commencement: 20° 20'

> after 7 hours PAV? AM!
> >» 24 » TES oy
> rs Wills oss 17° 40’
> » 101 » 15° 15'
> ny eK) 53 TP

At 50°: 5 grams of glucose, 1,6 gram of urea, dissolved in
5 pCt. sulphuric acid up to 50 c.e.

rotation at the commencement: 10° 10’
» after 42 hours 6° 10'

> >» 96 > Be IMO

I did not succeed in isolating from the so obtained reaction products
a compound of glucose with urea, chiefly because the change seemed
to be a limited reaction and because the excess of sugar formed
a syrup and prevented a separation by solvents.

Therefore, another way was tried which led toa favourable result.
Glucose (1 mo].) and urea (2 mols.) were warmed with 5 percent
sulphuric acid for 20 days at 50°; the liquid was then freed from
sulphuric acid by neutralisation with barium carbonate and filtered.
By fermenting during 5 days the excess of glucose was removed
and the now laevo-rotatory liquid evaporated to a syrup. After
some days, a crystallisation took place, the crystals containing besides

the excess of urea also a laevo-rotatory substance which was ob-’

tained pure by recrystaJlisation from alcohol and possessed the fol-
lowing properties.
Melting point: 206°. Rotation: [a]; = — 23° (1 percent solution).
Easily soluble in water, difficult in absolute alcohol, not or very
little in ether, petroleumether, benzene, chloroform and acetone.

( 461 )
Analysis:
Substance: 0,1705 gram, CO ,: 0,237 gram, H.O: 0,0976 gram.
Nitrogen estimation (according to KJELDAHL):
Substance: 0,121 gram = 10.65 ee. N/y. acid.
Found: C: 37,9 percent, H: 6,4 percent, N: 12,2 percent.
Calculated for Cy Hj. O;. N. CO. NH, :
C: 37,8 percent, H: 6,3 percent, N: 12,6 percent.

On boiling the aqueous solution the rotation remained about con-
stant; on warming with dilute acid it rapidly became positive.

FeHLING’s liquid was reduced although less rapidly than by
glucose. 0,040 gram of glucose-ureid reduced a quantity corresponding
with the following amounts of N/; thiosulfate :

after 1 minute boiling: 8,7 cc.

> 2s eae. Eas §
> Bye Se Osis
>» 10 > ae LOS) as.

while the quantity of glucose (0,0324 gram) corresponding with
0,040 gram of glucose-ureid reduced copper to the extent of 10 ce.
after boiling for two minutes.

Neutral copperacetate is not reduced by glucose-ureid. With a
solution of phenylhydrazine in acetic acid it yields no osazone at
first, but only on prolonged boiling.

An analogous compound of glucose with phenyl-urea [melting point
223°, [@]p = — 55° in 1 percent solution] was prepared in prac-
tically the same manner. The analysis gave:

Substance: 0,1596 gram, CO ,: 0,3014 gram, H,O: 0,0875 gram.
Nitrogen estimation (KJELDAHL). Substance: 0,151 gram=9,9 N/;,) acid.
Found: C: 51,7 percent, H: 6.1 percent, N. 9,2 percent.

Calculated for: C, Hj, 0;. N.CO. NH. C,H;:
C: 52,4 percent, H: 6,0 percent, N: 9,4 percent.

( 462 )

The chemical properties proved to be analogous to those of the
urea derivative.

Besides by heating in acid solution, it was found that the reaction
of glucose with urea and phenyl-urea also takes place by melting
these together at 100°— 150° and also by heating under pressure
in methyl- or ethylalcoholic solution.

It was further noticed that lactose, galactose, mannose, arabi-
nose and xylose also react with urea. On the other side
the following derivatives of urea were tested as to their behaviour
towards glucose: methyl-, phenyl-, benzyl-, symm. dimethyl, symm.
diethyl- and symm. diphenyl-urea and it was noticed that the first
three did react with sugar but the last three did not. On account
of this and of the properties of the obtained glucose-ureids cited
above, it may be assumed that at the condensation the carbonyl
group of the sugar combines with one of the amido groups of urea
with liberation of water:

= [0H,| N—CO—NH,

—-oQ-

and that these derivatives are, therefore, comparable with oximes
and hydrazones.

It was also ascertained that thiourea and phenyl-thiourea react
with glucose, although slower.

The study of these substances, which may also be important to
physiology both by their possible occurrence in diabetic urine and
with a view of a future synthesis of albuminous substances, will
be continued.

Amsterdam, December 1900.

Chemistry. — Dr. A. F. Houtteman: “On the nitration of ortho-
chloro- and orthobromobenzoic acid” (Communicated by Prof.
C. A. Lopry DE Brvutsy).

Montagne has shown in his dissertation’) that in the nitration
of orthochlorobenzoie acid with nitrie acid, there is formed besides
the already known chloronitroacid (COgH : Cl : NO;.=1:2:5)a
second mononitroacid which, however, he could not isolate in a

pure condition. In this, I have sueceeded by fractional crystallisation

Compare also Rec, 19, 54.

( 463

of the potassium salts. he K-salt of the main product crystallises
first in thin long needles; in the very last motherliquors the bye-
product has accumulated. This is liberated by hydrochloric acid and
further purified by repeated crystallisation from dilute alcohol. It
then has a melting point of 185°; in dilute alcohol it is a little less
soluble than the main product.

In the nitration of orthobromobenzoic acid only a single mono-
nitroacid has, as yet, been noticed, namely the acid (CO.H: Br.: NO.=
1:2:5). Here, however, is also formed a second mononitroacid
which may be also obtained by fractional crystallisation of the
K-salts. After repeated crystallisation from dilute alcohol, it melts
at 191°. Its solubility in this liquid is about equally great as that
of the main product of the nitration.

The nitrogroup enters the place 3 both in the o-Cl- and the
o-Br-acid, so that the structure of two bve-products is CO, H :
Cl (Br): NO. =1:2:3. This was proved by heating the acids
with ammonia to 150° when from both the same nitroamidoacid is
obtained (CO, H:NH,: NOg =1:2:3) which was identified by
its melting point (204°), its solubility in water, benzene and chloro-
form and by the melting point of its ethyl ether (104°).

The quantity which is formed of both bye-products will be
determined accurately.

Chemistry. — Dr. J. H. Aprtani: * Eutectic curves in systems of
three substances of which twe are optical antipodes”. (Com-
municated by Prof. H. W. Bakuurs Roozenoom),.

In my dissertation “Systems consisting of optical antipodes”’
(Amsterdam, 1900) I mentioned briefly (p. 53) a paper by Brunt
(Rendic. Acead. dei Lincei, 9 April 1899, pg. 332) in which he
describes a method of deciding whether an externally-compensated
inactive substance is a conglomerate, a racemic substance or a
pseudo-racemic mixed crystal. Bruni-proposes to determine the
eutectic pomt of a solution of one of the antipodes, to afterwards
dissolve mixtures of the antipodes in known proportion in the
same solvent and again find the eutectic points. If all mixtures
from 100 percent d- to 100 percent /- are tested in this way
such a point will be found for each mixture. ‘These temperatures
may be considered, for the solvent under consideration, as functions
of the composition of the mixture of antipodes and a figure may

( 464 )

be thus obtained from which the nature of the inactive substance
can be deduced. If three curves (a, b, ¢ or a’, b', c', fig. D
are obtained one has to deal with a racemic substance; two curves
(e, f, fig. II) are obtained when the inactive substance is a conglo-
merate of the antipodes; and one curve (g, / or @, fig. III) when
one has got mixed crystals.

Fig. 1. Fig. I. Fig. III.

BruNI appears to have had in mind only aqueous solutions, but
I fancy that the advantages of this method will be more particularly
apparent when substances with a higher melting point are used as
solvents. If a number of different compounds with different melting
points are employed as third substance, a series of eutectic curves
is obtained for the same system of antipodes, and the nature of the
inactive substance at different temperatures may thus be elucidated.
Because if with the same system two solvents are taken, of which
one has a higher melting point than the other it will be found in
general that the first line of eutectic points is situated at higher
temperatures than the second. It may, therefore, happen that the
first line has a character different from that of the second because
the inactive substance at the first set of temperatures is racemic
and at the second set a conglomerate or a mixed crystal. By now
varying the third substance until the eutectic line at a given set
of temperatures has been found, it will be possible to answer the
question as to the nature of the inactive substance at a definite
temperature or at least in a definite temperature zone. The method
of Brunt has not yet been applied; I, therefore, resolved to try
it on camphoroxime, which I had already previously examined.
[ had found that above 103° i-camphoroxime must be looked

~

Ee ee ee eee

tal i,

( 465 )

upon as a mixed crystal, below 103° as a racemic substance. As
third substance it is necessary to take one which has no chemical
action on the oxime, may be obtained perfectly pure, crystallises
on cooling in a form clearly distinguishable from the oxime and
does not form mixed crystals with it: napthaline, phenantrene,
benzoin and anthracene were used. None of these substances acts
chemically on camphoroxime; it is only when this condition is ful-
filled that the point of change of the oxime is not altered by the
admixture. Moreover, none of these substances forms mixed crystals
with the oxime; this is also a condition for the unchangeability of
the point of change.

The temperature at which the crystals of the oxime and the
third substance melted simultaneously was taken as the eutectic
temperature. This temperature was sometimes difficult to determine ;
easiest with napthalene. The determination was done in the appa-
ratus first described by vAN Eyk (Dissertation pg. 26). First, by
determining the whole melting line, the eutectic point of the d-oxime
with the third substance was found; in the determination of the
other eutectic points the investigation of the whole of the melting
line was superfluous, for the relation oxime: third substance at the
eutectic point remained nearly constant with the different mixtures
of d- and /-oxime, so that only a small part of the melting line
needed to be examined in the neighbourhood of the eutectic point.

The results are as follows:

Eutectic Temperatures.

%/) d- Jy 1- —-‘Napthalene = Phenanthrene —Benzoiin Anthracene
m. p. 81°,4 m.p.99°,4 m.p.1379,0 mp. 213°.
100 0 61°.0 716°.2 100°.2 109°.2
$5 5 60 .0 — = =
90 10 59 .6 75 .6 99 .1 107 .6
80 20 59 .2 74 9 98 .2 106 .8
75 25 59 .4 — 97 .8 —
70 30 60 .1 74 «2 97 .4 106 .2
65 35 60 .8 74 .8 — —
60 40 61 .3 75 .6 97 .0 105.1

50 50 61.9 76 .2 97 .2 105 .6

( 466 )

Of the eutectic lines, only the one half of 100 percent d. to
50 percent d.—50 percent /. has been investigated ; the other half
which is perfectly symmetrical with this has been dotted in the
figures to give a better view.

100 ¢ 160 d 100 /
Fig. IV. Fig. V.

Naphtalene. Phenanthrene.

106

160 Z 100 d 100 / 100 d@
Fig. VL Fig. VIL

Benzoin. Anthracene.

These results confirm on the one hand the theoretical views of
Brunt and on the other hand the results which I had previously
obtained with camphoroxime. The limes show that near to 60°,
the eutectic point of the 7¢oxime is situated higher than that of
the antipodes; at that temperature the solubility of the 7-substance
will be as a rule smaller than that of the antipodes as is also the
‘ase at the ordinary temperature with different solvents. At a higher
temperature this difference becomes smaller; when nearing 76°
(phenantrene)the eutectic points of the antipodes and the /-substance
coincide; at higher temperatures this point has become lower in

( 467 )

the 7-form than in the antipodes. It may, therefore, be suspected
that at that higher temperature the solubility of the ¢form in
different solvents will be greater than that of the aetive forms.

The line obtained with benzoin as third substance shows that the
racemic compound still exists at 97°.2; the zone is, however, very
restricted. Finally, at a still higher temperature the racemic com-
pound has disappeared; the investigation with anthracene as third
substance gave a continuous curve with a minimum at 50 percent
d.—50 percent /. At 105°.6 the 7-oxime must, therefore, be regarded
as a mixed crystal of equal quantities of the active oximes.

This is quite in concordance with my previous investigations on
camphoroxime, the results of which have been communicated in
the report of the meeting of June 24, 1899.

Chemistry. — Professor Baxuuis Roozepoom presents the disser-
tation of Dr. H. B. Honspoer: “On heats of solution in
general, that of Cd SO,,*'3 1,0 in particular” making the
following communication regarding it.

Since 1884 it has been recognised that the calculation of the
course of the solubility curves of solid substances in liquids as
functions of temperature requires a knowledge of the so-called
theoretical heat of solution, that is the heat of solution of the solid
substance in its saturated solution. In 1885 I discovered a graphic
construction by means of which this quantity, which cannot be deter-
mined experimentally, may be obtained from the curve of the heats
of solution in different quantities of solvent. Later on VAN DevENTER
and STACKELBERG devised methods of calculating the same quantity
from such determinations.

For salts whose saturated solutions are very dilute, the theoretical
heat of solution differs but little from that in pure water; for salts
with large solubility the sign may even differ. With some salts a
minimum of solubility is shown at a definite temperature, the solu-
bility, therefore, first decreases with an increase of temperature and
then increases when past the minimum. On the first part of the
curve the theoretical heat of solution must, therefore, be positive,
on the second part negative and n7/ at the temperature of the minimum.

Up to the present, this change of sign of the evolution of heat
has not been accurately proved to occur in any such case. Dr.
Hoxsporr has investigated cadmium sulphate with °/; mol. of H.O

( 468 )

which shows a minimum of solubility at 15°. He determined accu-
rately the heat of solution of this hydrate in much water at 15° and
also the heats of dilution of all kinds of solutions beginning with
the greatest possible concentration. He further determined the specific
heats of a series of solutions and of the solid salt, so that the heats
of solution of solid salt in varying quantities of water at different
temperatures could be calculated from the values at 15°. He obtained
the following results.

Heat of solution of Cd SO, 8/, H,O in (2—5/,) H,O.

x 5° 10° 15° 20° 25°
400 2075 2303 2530 2758 2985
200 2194 2306 2418 2530 2642
100 2118 2203 2288 2373 2458

50.6 2013 2065 2118 2170 2223
30.6 1835 1876 1918 1959 2001
20.6 1657 1645 1633 1621 1609
15.6 1405 1332 1258 1185 1111

13.5 1061 966 870 775 679

The saturated solutions contain, at the temperatures given:
15.03, 15.10, 15.17, 15.10, 15.03 H,0.

The determinations of the heats of solution go beyond these con-
centrations. It was, therefore, easy to deduce the theoretical heat
of solution from the course of the curves for the ordinary solutions
in the immediate neighbourhood of the point corresponding to the
saturated solution.

The following results were obtained :

Theoretical heat of solution.
Di + 219 cal.

10° yy-Re65o is

( 469 )

The agreement between the signs of the heats of solution and
the course of the curve of solubility and the position of the minimum
is very good.

The influence of temperature on the heat of solution is also very
considerable.

It appears also from the table of the ordinary heats of solution
that with dilute solutions the heat evelved increases with the tem-
perature, owing to the fact that the specific heat of the solution is
smaller than the sum of the values for solid salt and water. With
concentrated solutions the reverse is the case. From this it follows
that there must be a concentration where the heat of solution is
independent of the temperature because the specific heat of this
solution is equal to those of solid salt + water.

This appears to be the case with a solution with 22.5 H.O.

In the graphic representation al! the heat of solution curves
intersect each other at the point corresponding to this con¢entration.
For want of investigation of concentrated solutions, this peculiarity,
which no doubt occurs with many substances, has up to the present
escaped notice.

Chemistry. — Dr. Ernst Conny: “The Enantiotropy of Tin” (VI)
(Communicated by Prof. H. W. Baksurs Roozesoon).

Contributions to the history of grey Tin.

1. In the journal Prometheus!) E. Krause referring to my
previous investigations on the Enantiotropy of Tin*) makes the
following communication: “Schon die Alten wussten, dass dieses
weiche Metall, welches ,schreit’’, wenn man es biegt, seine Mucken
habe und der Verfasser eines mit Recht oder Unrecht dem Aristo-
TELES zugeschriebenen Buches (de Mirabilibus Auscultationibus Cap.
51 Edit. Beckmann) sagt: das keltische Zinn habe unter anderen
merkwiirdigen Higenschaften auch die, nicht bloss (wie die anderen
Metalle) in der Wiirme zu schmelzen, sondern auch eintretender
Frost bewirke dasselbe.

Auch Prurarcn in den Tischreden (VI, 8) berichtet von in strengen

') Jahrgang XI, 44, S. 701 (1900).
2) These Proceedings 1899 and 1900 also Zeitschrift fir phys. Chemie 30, 601
(1899) 33, 57 (1900) 35, 588 (1900).

( 470 }

Wintern herabgestiirzten Bildsiitulen, weil das Metall, mit dem es in
den Postamenten vergossen, durch den starken Frost geschmolzen sei:

Diese Thatsachen waren so bekannt, dass ARISTOTELES sich um
eine physikalische Deutung bemiihte. Das Metall, sagte er, ziehe sich
im Froste so stark zusammen, dass die in seinen Poren enthaltene
Wiirme es durch die Zusammenpressung zum schmelzen bringe. Wie
alles, was ARISTOTELES sagte, wurde dieser Angabe bis zur neueren
Zeit Glauben geschenkt, und noch Monrarene fiihrt die Frost- und
Hitzeschmelzung des Zinns zum Beweise dafiir an, ,dass sich die
Extreme beriibren’”’.

As the question whether the Ancients were acquainted with the
peculiar phenomenon shown by tin at low temperatures, interested
me very much, I have endeavoured to find further particulars in
connection with KRause’s communication.

It is only through the kind assistance of Prof. Speyer of Gro-
ningen, to whom I here wish to express my hearty thanks, that
it has been possible to control this matter; to him I am prin-
cipally indebted for the following particulars.

2. In ArtstorTte (or Pseudo-ARIsTOTLE), Heoi Oavpacton
axovonetwr 50, the following passage is found!) To» zxacotregor tor
xedtixon rijxedIai pao rod te&yLoy wod dou" Gyusion dé TIg EvTYS(as,
Ot rijxecJae doxsi xai év TH date yowkse yotr, we ome, raye.
tyxetar dE zai ep TOs WYEON, Oran yévytae mayy, éyxaradscouévov
Evtdg, WS Padt, xai GvVYM@OMovuevov TO GeQuot tot Evvadoyortos atta
ha tip aodévear.

It is said that Celtic tin melts much more quickly than lead.
A proof of the fusibility is the statement that it also melts in
water; apparently it seizes *) quickly. It also melts in the cold when
frost has set in, because, as is said, the heat contained in it is
inwardly confined and compressed on account of its weakness.

3. The passage from Monratcne cited by Krause is found
in his Essais des vaines subtilités®): L’extreme froideur, et l’extreme

1) Bibliotheca scriptorum graecorum et romanorum Teubneriana, Lipsiae 1888.
Editio Orro APELT.

2) Prof. SpeYER in commenting on the translation of ypw&es by seizes says: this
translation does not satisfy me. The word means to touch, to catch, to stain, but
xpéles is active and I cannot see how it could mean here “it discolours”. I am
more inclined to believe that the idea is “it is sensitive to outside influences’’.

3) I am quoting a Parisian edition (Dxsorr, librairie, rue Christine 1818), Nou-
velle Kdition, livre premier, LIV, pag. 104,

( 471 )

chaleur cuisent et rotissent: Aristote dict que les cueux de plomb
se fondent et coulent de froid et de la rigueur de Vhyver, comme
dune chaleur vehemente.

At this passage the editor adds in a note: “Ici Monraicne
ne rapporte pas exactement la pensée @ARISTOTE, qui, apres avoir
dit que l’étain des Celtes se fond plutot que le plomb, puisqu’il se
fond méme dans l'eau, ajoute: L’étain se fond aussi par le froid
quand il géle ete. de mirabilibus auscultationibus p. 1154 Edit.
Paris, Tome |.

That MonraicNe made a mistake when he cited ARISTOTLE in
this place appears from the fact that what he attributes to Arts-
TOTLE') may be read in PLuTARCH (Symposiaca VI, 8).

Referring to the fact that ravenous hunger occurs after great
fatigue, for instance after having walked through snow, and then
disappesrs after partaking of only very small amounts of food,
particularly a morsel of bread, one speaker contends that the heat
being withdrawn from the interior and heaped up on the outside
of the body, as for example the perspiration and the warm and tired
hands and feet of the fatigued person, show, leaves inwardly a state
of cold which causes a craving for food. Another says, no, the
eraving 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
severe winter. There it is seen that cooling does not only cause
congealing but also melting for in severe winters caxpérar worisdov
occasionally melt away, consequently something similar may be
supposed to take place in the intestinal process, ete.

Probably, leaden grindstones are meant. (Plumbese cotes in
WIITTENBACH’s translation, cueux de plomb in MonvatGne’s).

4. According to a private communication from Dr. Krause he
has borrowed PLUTARCH’s citation (see pag. 469) from a translation
by Katrwasser (Bd. 5, 8. 594, Frankfurt a. M. 1793) where may
be read:

Uebrigens ist es ausgemacht, dass die Kalte die Kérper nicht nur
verdichten, sondern sie auch zerschmelzen kann. In strengen Wintern
geschieht es zuweilen, dass grosse Stiicke Blei, womit die Bild-
siulen an den Postamenten befestigt sind, zerschmolzen werden und
herabfallen.

') Plutarchi chaeronensis varia scripta quae moralia vulgo vocantur. Lipsiae, ex
officina Car, Tauchnitii 1820, Tomus LV, 339,

( 472 )

Of this, however, nothing is to be found in PLurarcu himself
at the place mentioned.

5. Whilst ArisroTLe makes a very clear distinction between
xacotregos (tin) and podAvpdog (lead) the question might be put whether
PLurarcH when using this last word really means what we under-
stand by 'ead or whether we have also to think there of tin.

BeRTHELOT says in his Introduction a UEtude de la Chimie
des Anciens et du Moyen Age’): “tout métal et alliage blanc,
fusible et altérable au feu, s’ appelait‘d Vorigine plomb. Plus tard on
distingua deux variétés: le plomb noir, qui comprenait notre plomb
et plus rarement, notre antimoine, ete.; et le plomb blanc, qui
comprenait notre étain et certain alliages de plomb et d’argent.”

Of importance is also what BerTHeLot*) afterwards wrote in his
“La Chimie au Moyen Age (1893) where he devotes a chapter to
the names of t/n.

“Le nom que zxecotregos, employé dans Homire, (+ 800 a. Chr.)
parait signifier un alliage de l’argent avec le plomb, peut étre associé
a I’étain: il n’a pris son sens actuel, dans toute sa précision, que
vers le temps d’Alexandre (356—323 a. Chr.) et des Ptolémées...
mais on sexposerait & toutes sortes d’erreurs, en l’appliquant aux
auteurs qui ont employé le méme mot 4 des dates plus reculées.”

We may, therefore, assume also in connection with the distine-
tion made between zaooitegog and podvBdog (see above), that in
the time of ARISTOTLE (384—322 B.C.) the meaning of xaootregos
corresponded with our idea of tin *).

It certainly seems worth while to study the behaviour of lead
also at low temperatures.

Summarising, it appears from the above that there is reason to
suppose that the changes which tin may undergo at low temperatures
had already been observed at the time of ARIsToTLE, whilst nothing
definite can, as yet, been said about an analogous conduct of lead.

Amsierdam, Chem. Lab. University, December 1900.

1) Paris, 1889, p. 230—231.
2) Paris, Imprimerie nationale. Tome I, 367.
5) The statement that it also melts in water might make us again entertain a doubt,

( 473 )

Physics. — Dr. G. Baxxer: “Contribution to the theory of elastic
substances.”

If we leave electrical and magnetical forces out of consideration,
the forces acting on a body are gravitation, external pressure or
tension and the internal molecular pressure and thermic pressure.
Though in the theory of elasticity the substance is substituted by a
continuous agent and we have therefore strictly speaking not to deal
with mutual action of molecules, I shall yet keep to the usual
term, though the term cohesion seems more suitable to me than
the term molecular pressure.

In the theory of elasticity, just as in the theory of capillarity,
forces are assumed, which are only perceptible at exceedingly small
distances. If these forces are supposed to have a potential, the
potential function

—gqr

_@
— f=
rT

which is a special case of the general function of Dr. C. NEuMANN,

Alena Be-* Ce-"
se

Ts 7. t

might be of great use here, for if we take g very large, the forces
between two volume-elements will rapidly decrease with the distance.

In his thermo-dynamical theory of capillarity VAN DER Waats
has found this potential function to be a probable function for the
eapillary forces. Afterwards I have further discussed this function
in two papers, presented to the Academy the 28 of October and
the 25% of November 1899, and I further applied it in my treatise
“Zur Theorie der Kapillaritét” (Zeitsch. fiir phys. Chemie XX XIII,
4. 1900).

Let us imagine an “infinitely small” volume-element in the body
in consideration, and let us take that space as unity of volume.
If U, B and &# are respectively the virial of the external forces,
that of the molecular attraction and that of the thermic pressure,
then the total virial per unity of volume is e.g.:

Ra Ue eee os sy Cl)

1) The influence of gravitation is left out of consideration,

Proceedings Royal Acad, Amsterdam, Vol. ILI,

( 474 )

I imagine the element to have the shape of a cube, the sides of
which are parallel to the principal pressure-axes of the point in
consideration, which I take as coordinate axes. Then the general
expression for the virial:

F=— 24 (Xv + Vy + Zz)
gives immediately :
U=43(py+ Pot ps) - oe 3 sy

Pi P2 and ps representing the principal pressures.
If S,,S, and 8S; represent the molecular tensions in the same

o

directions and @ the thermic pressure in the point in question, then:

Y= O0—S), P2 = O—Sy, and E= O—Ss
or
Pi + P2 + ps = 3 O — (S, + Sy + Ss).
So:

3 il
rg arming Sic gs . . . . . (8)

As the thermic pressure depends only on the condition of the
substance in the immediate neighbourhood of the point), where
the value of the virial of the thermic pressure is @?), we may
take for @ also the value which this quantity would have if at the
same temperature the substance round the point in consideration
had the same density as in the point itself. If we take for the
agent, which in these considerations is used as a substitute for the
body which is thought to be isotropical, the potential function:

Gantt,

=
the following differential equation holds good for that agent:

V2 V=_qV-+ 4nfv 9).

) In contrast to the molecular forces of attraction.
*) Zeitschrift fiir phys. Chemie XXXIIT, 4 1900 p. 478.
5) Konink, Akad, y, Wetenschappen: Proce Noy. 25th 1899 p. 2.

( 475 )

For a region which is large enough and for which we think the
density ¢ to be the same everywhere, V2 V = 0 and so:

V= — 4nfi?e
Sone - 1
or substituting a for 2a fA*: (a = =)
V = — 2a@

the tension S now becoming:

V2
Sa) le eee aera te:
ie? ) (4)

If in this case we call the pressure p, then:

p=O—ag? %). (5)

p is the pressure of the homogeneous phase with the density @ of

the point in question and at the temperature of that point.
From (5) follows :

3 ee: iat “fo vol
er mace Ca 8 (v = specific volume) .

(6)

If F, is the virial of the homogeneous mass per unity of mass,
then :

3 3
Fit ei rai? Orta Apis teepe (sl)

Vn ;
for, as may be easily shown, the virial is = X the potential energy

with reversed sign. (See Zeitschrift fiir phys. Chemie XXI. 3. 1896,

1) Konink. Akad. v. Wetenschappen: Proc. Noy. 25th 1899 p. 219 and 320.
*) If the expression § = =i held for the thermic pressure for an isotropical sub-
—h

stance with a certain density, we should get the same equation of state as that of
VAN DER Waats’ for gases and liquids,

32*

( 476 )

3 F ae
pag. 503). Further ed Os the virial of the external forces and
9, that of the thermic pressure (per unity of mass).

3)
If we substitute in (7) the value for Bye derived from (6) we get:

3
N=; Ov+ A.

If we suppose that the total virial of the mass-unity is a pure
function of the temperature, just as for liquids and gases, and further
that % depends only on the density (and temperature) then :

PO = and a9 ol,
and so according to (1):

3
By substitution in (3):

1
B=—> (+545)... +... &

or in words:

the virial of the molecular forces per unity of volume is half
the sum of the three principal tensions.

If we put A=—/f and B=0 in the expressions which in the
paper already mentioned I found for the tensions pro, Py, and pz:
(pag. 318), through which the potential function

Ae—a +. Be 9 ev
_— — becomes —f

AV \2 dV\2 dV \2
Li
ate: dx dy dz q Ke

By addition :

The sum of the tensions prx + pyy + pz: 1s therefore independent
of the direction of the sides of the cube-shaped element in conside-
ration. We may therefore represent the sum by S; + Sg + S; and
find then:

R? 3V2 1
aie ey eet eee ee ye Meg ON = =)
16s fF 16s f2* q

The tensions S, and S; normal to the lines of force appeared to
be the same. We found for them:

S, S. se eos
ie Seas | Sn ph
and
R2 v2
Ss) ——— i aa
8nxf 8afi?

while we found for the potential energy per unity of volume:

R2 V2

fie 28 eed Dae aay.
Snf Saf

Now we can easily derive the relation:

SS i eee x (10)

or in words:

The difference of the tensions normal to and in the direction of
the lines of force (per unity of surface) is three times the work
required to rarefy the substance infinitely, diminished with twice the
virial of the molecular forces of attraction (per unity of volume).

( 478 )
Dilatation.

If 4 and wu are two constants, we have according to KIRCHHOFF
for the projections of the displacements of a point, whose coordinates
are xv, y and z:

Ou dv dw (— X, is there-
(A + 2) an +4 ay +4 A =— Xz ‘forea tension)

2 $US fe aan,

du dv ow

= — 2 ———
A a +4 ay + (A + 2 fe) a 2

By composition :
Ou

B+ 2m) (+= oS) = et Vy + 2).

The second factor in the left-side member represents the dilatation,
and is generally indicated by the symbol 7. Therefore:

Keay

Cy Raa a)

v=-

The quantities X,Y, and Zz correspond to the quantity which
we should call the hydrostatic pressure in case of aliquid. If there-
fore the molecular tensions are represented by S,, ete., we have:

= 0 — Sra
Yy=0—Sy
bg, = (j) = See

By substitution of @ from (3)

Xz + Y, + Zz = 3 Z ay (Srx -{- Syy -- S.,) = 30 —(S, +- Sg -+ Sai 2 U
or according to (11)

(12)

( 479 )
Applications.

1. Elongation of a prism. We imagine at the two ends a force S
per unity of surface in the direction of the longitudinal axis. If we
apply formula (12) to every volume-element of the prism, the total
increase of volume becomes:

2 f var
[vas

Tyee

For space-elements which are quite inclosed by others, the increase
of volume for the external virial (external with regard to such an
element) is neutralized by that of the surrounding ones and finally
the total external virial is that of the external forces acting on

the prism. That virial is in this case: — 4 Sld.
Therefore :
ie 2 ae se a [PA
fy 7 Sy ee (d = section).

The dilatation is therefore:
S
BA+ 24

2. Dilatation of a hollow cylinder. Vet S be the corresponding
force just mentioned, P and p the forees per unity of surface, normal
to the outer and inner surface, taken positively in the direction
of the radius, then, :f / represents the length, r and R the radii
internal and external, the virial of S is:

— iSl(a R? — x7),
the virial of P:
—i=>PR=—}RX2I2nKRIP
and that of p:
—47rX 2arlp.

Therefore:
—20=Sin(R?—r) 4 Anl (PR + pr).

The total increase of volume divided by the yolume a (2? — r2)/
yields for the dilatation:

3. Dilatation of a spherical shell.

Let p be the internal, P the external pressure, both calculated |
positively in the direction of the radi r and hk, then is, according |

sha 3 oe
to the general expression of the external virial — 3 BY the virial
of p:

3 4 3
5 re and eee
Le a and of p 5 Xzak

After having divided by 34+ 2 and by the original volume

4
ee —r°), we get for the dilatation:

2U 4 38 = PR3 + pr
7 == a (BSS) SS eee ane LE
San 8 BA+2n Be

4. OrrstED’s Prézometer.

If V is the external and x the internal volume, then the virial

es ‘
of the external pressure is p : = pV and that of the internal press-

3 vas :
ure: — > pv. As the original volume of the substance forming

the shell is V—v, the dilatation becomes:

3
2x —(V—v
z 1 Agere 3p
V > 39 oom V—v = Paes 2

So we see that the value of the ratio V7 does not depend on the
external or internal volume nor on the form. The external volume
is therefore compressed in a proportion as if the vessel were massive,
which corresponds with the views of CoLLapon and Sturm and
is opposed to those of OgrsTep.

( 481)

Physics. — J. ©. ScuankwuK: “Precise isothermals. I. Meas-
urements and calculations on the corrections of the mercury
meniscus with standard gas-manometers* (Continued.) (Com-
munication N°. 67 from the Physical Laboratory at Leiden,
by Prof. H. KamMEeRLINGH ONNES).

§ 6. We now can change the formulae found so, that they repre-
sent the surface of interpolation meant in § 3 for the mean height
up to the limits R = 0 and 0O=0.

For the narrow tubes we find then:

1 1 es
Semen y « BN 2, oe 3 Sie Lo og
Pag, Ohi ae? Haag Ore) (1)

and for small values of 0:

1 s n—l
a
(n!)? (n+1)\44

f=OR\1— —( °° °° a
2

s

(n!)? 4H

It should be noted that in both the expressions the factor of OR
is greater than 4.
In order to be able to calculate f in the limiting cases by means

5 : 8 ake
of these formulae, we must introduce the value of rE This is not

: te :
exactly known to us. Fortunately an uncertainty in moe of little
interest for the correspondence meant in § 4, since for small values

oO

of R, 3 in the formula (1) occurs only in that term in which also

. é . .
R® appears, so that a change in a has only little influence on f.
In the same way in small values of 0 the influence of a change in
ve ;
the value of aoe unimportant for values of & smaller than

0,045 em.
In order to demonstrate this I have calculated for 0 = 0,05 two

el ; H ;
menisci, for which I have not accepted — = 00354 em*, which
s

number may be derived from the data of Quincke for mercury,

( 482 )

three hours after the formation of a drop‘), but 0,04533 em*. for
mercury, immediately after the formation of the drop. Then we
have for:

R=0,588 em. f= 0,0168,

i 105455 ee —OnO oe
; H
while for — = 0,0354 cm?. we get for:
s

R= 0,588) em: a= O07 25

fi (OAb oy es ef 00M

And so we may easily complete the direct measurements by the
che H

limiting cases calculated on the supposition — = 0,0354 cm?. up to
8

the surface of interpolation. From § 7 it will appear that th’s value
may certainly be put in stead of that which existed with the menisci
observed by us.

I will now first draw the curve which represents / as a function
of 0 with the tube of 0,283 em. radius (curve I in fig. VI of the
plate) 2).

For this I have drawn 0 from the point A in a horizontal direct-
ion for which 0,0025 = 1 mm. is taken and / in a vertical direct-
ion for which 0,0005 = 1 mm.

In this manner from the menisci measured the points B, C, D
and / have been obtained; but here it must be borne in mind that
the curve is not determined by these points themselves, but by the
condition that B and / and in the same way C and ) must always
be situated at equal distances on either side (comp. §§ 2 and 3).

Further are computed by means of the yet unsimplified formula:

1) But even this number is far from being certain, for from two kinds of series of

il
experiments at 20° C., Quincke found also values corresponding to —=0,0391 and
8
I
— = 0,0396 cm?.
8

2) Given in the Proceedings Dec. 1900,

( 483 )
the following values:
= 0,0991 ; f=0,0148 represented by the point 7’;
5 = 0,0708 ; f= 0,0105 : Seas Iecoh Kes

O = 0,0425 ; f= 0,00627 > > > yp wah

And then the line I is drawn.

In the same way line II in fig. VI is obtained for the tube of
0,382 em. radius. From the point 4, 0 and / have been drawn in
a similar manner and so we get the points Z, M, N and O, for
which the paired points are again Z and N, together with Mand 0.
The points P and Q have again been calculated.

Line III in the same fig. VI applies to the tube of 0,5814 cm.
radius, and has been drawn from the point 4. Here the paired
points are S and Z, and also U and V; W and X have been cal-
culated. The points S’ and 7’ as well as U' and V' belong to
measurements in a tube of about the same width. It is difficult to
draw the line through W and X and also between the paired points.
But as I do not use tubes of more than 0,4 cm. radius, I have
not considered this much further, because in such wide tubes the
rim is no longer perfectly circular and parallax can not easily be
avoided in the measurements.

Then fig. IV is drawn in which f as a function of 2 has always
been drawn for the same value of 0. The scale vaiues are again
for f: 0,0005 =1 mm. and for R: 0,0025—=1 mm.

First we have drawn the points with & = 0,2832 cm. in the line
I for the values of 0: 0,05; 0,1; 0,15; 0,2; 0,25; 0,3; 0,35; 0,4;
the straight line on which these points are situated is in fig. IV
also numbered by 7.

Secondly the points with R= 0,382 cm. in the line II for the
same values of 0; the straight line is also marked 2,

Then the points for R—0,04 cm. and R=0O,1 em. have been
calculated and lastly a number of points are calculated according
to the formula (II), all for d = 0,05.

: . el
The points Y and Zare those calculated with the value —=0,0433 cm?.
8

Now the line for 0 = 0,05 could be drawn, by which the type for
the lines d)=constant is known. Moreover we could draw each
time the beginnings of those lines at small value of 2, and so they

( 484 )

could be continued through the points given by the lines 7 and 2.

The rest of fig. VI has been derived from fig. IV by seeking
each time for the same value of # in fig. [IV the corresponding
values of 0 and /, and by drawing them anew as in the case of
the curves I, II and II! in fig. VI.

Curve V in fig. VI belongs to the tube of 0,409 cm. radius, of
which only one meniscus was measured. The remaining lines in
fic. VI belong to 0,05; 0,1; 0,15; 0,2; 0,25; 0,3; 0,35; and
0,4 em. radius. :

§ 7. The form of the meridian section of the meniscus can, if

H : ,
— were exactly known, also be found graphically in the way shown
s

by Lord Ketvin !). For if g is the radius of curvature at the top
of the meniscus, 7 the radius of curvature at the point P of the
normal section perpendicular to the meridian plane and ry the radius
of curvature in the meridian plane, then we can write the equation:

eps 1
Say ihe eon’

so that, if we start from the top with a given radius of curvature
we can always calculate 7. if we have accepted some value for

s 5 :
for = For this I have again taken the value 28,25, hence

Al
— = 0,0354 em*. and then all the values must be expressed in
s

em. And so fig. VIII has been drawn on a 10 times magnified
seale, in which g=0,8 cm. has been taken”). For 7 and 4 we
have each time taken the values which they have at the starting
point of each element of the meridian curve so that the curvature
is sure to be too small. In the same way fig. IX has been drawn
in which A has been taken, as it is at the end of each element,
so that the curvature is too large.

1) To a request to Prof. Perry about the drawings of the menisci made after this
method, Prof. Perry answered that they were not published in the paper in the
Transactions of the Royal Society of Edinburgh and were afterwards lost.

2) This drawing, as well as fig. 1X was originally constructed on a 30 times mag-
nified scale and the curve was not divided into four as in the figure, but in twenty-
four elements; in the reproduction on a 1/, seale only four lines of construction
have been drawn.

2

en zips ‘

an mort
® we
ry
i
il
oe ]
“, il 7)
fos rm. ue sr

HOE deebsa zis!

aly "ke

ey aes ’
A
— : ym
NS ‘
a."
Jf >a : Bf
j Be |
rye
j PS

A. Swol) Taxol egaeiiaaae

1

" a
s
ye
7
-e
-
~
il
-
“.

Ai Us
~

_
ee Wha igi ls

nr, VE

iW a

aul iT hi) ae
e

¥ Ag iia

( 485 )

The two curves are combined in fig. X on the original 30 times
magnified scale and there the mean curve has been drawn as a
probable meridian section. Fig. XI represents the meniscus when
the radius of curvature is 1,1 cm. at the top; it was drawn on a
25 times magnified scale, but is here again reproduced with some
construction lines on a *°/, scale; while for 4 we have here always
taken the height of the middle of each curve element and in the
same way for 7, the value, which that radius of curvature would
have in the middle.

From the original drawings of the figures X and XI I have
again calculated for several values of 2 (the radius of the tube),
the height and the volume of the meniscus and from them again
O and f and I have also indicated these values in fig. VI by little
squares; the deviation from the curves drawn already remains below
the limit we require. The following values are found:

in fig. VI
es p. }. De V5 indicated by:
0,2 0,038 0,15 «2x 0,000619 0,0155 p
0,25 0,0487 0,195 wx 0,001582 0,0253
0,2832 (I) 0,0653 0,230 2x 0,00278 0,0346
> 0,0424 0,150 ax 0,00180 0,0225 n
0,3 0,0758 0,253 a x 0,00367 0,0408 E
> 0,0493 0,164 aX 0,00288 0,0264 0
0,35 0,115 0,329 wx 0,00786 0,0642 C
: 0,0727 0,208 2X 0,00484 00,0395 ,
0,382 (II) 0,092 0,241 2x 0,00748 0,013 x
0,4 0,105 0,262 2X 0,00976 0,0610 r

§ 8. It follows from the given dimensions for menisci derived

H ot ise
from the value —=0,0354 cm®*. that the difference in value which
$

— has had in the menisci which I measured directly cannot have
s

had much influence on the determination of the volume,

( 486 )

The mercury in the tubes used for that determination of the
volume of the menisci was treated in exactly the same way as for
the calibration of my piezometer tubes. And so we have as much
certainty as can be obtained, that the values derived from the direct
measurements of the menisci are applicable to the menisci which
occur in the calibration.

fal
Also for values of — not deviating much from 0,0354 cm?., as
§

they may occur perhaps, when the piezometertubes are used with
compressed gas, it will be allowable to use the values for the
menisci which we have now found.

In general it is obvious that from the differential equation for
h and r the same relation will be found when the unit of length

: dale H y
is changed in the ratio of the square root of —. Thereby 0 remains
&

HT
unchanged. If therefore — changes from 0,0354 to 0,0433 em?., in
&

order to be able to use the same values the unit of length must
be taken 1/1,225 or 1,107 times larger. If for instance we desire

HT
to know f for 0=0,35 and R=0,3 cm., —=0,0433 em?. then
s

we must look for it at 0 = 0,35 and R= 0,271 em.; we then find
f=0,0506 and the value desired is 0,0560, while we find from
the values measured: 0,0566; which would give a deviation of about
1 percent, and so within the limits we have indicated. For wider
tubes the deviation increases; if for instance we want to know / for

H
o=0,35 and R= 04 em., — — 0,0433 em*., then we fiudiiim
s

Fig. IV at 0 =0,35 and R=0,361 cm., by continuing the curve
a little 70,0735 and so the value sought is 0,0814; while from
Fig. VI 0,0904 follows for the value measured, a large difference,
for which it should be borne in mind that these numbers have not
the accuracy of the values at a smaller 0, because they are obtained
by continuing the curves for R=const. and d= const. a little
beyond the range of observation. From the two instances given
it appears that when J increases, for wide tubes (R=0,4 em.),
the mean height decreases perceptibly. From the situation of the
points ¢, x and 4 it would then follow that in the experiments

1 : : 5
bc would have been just a little smaller than 0,0354 em*. While

é
as we see our results can be applied with a great certainty for the

( 487 )

calibration, when we use compressed gas, this is dependent on the

. H E Hy
question how —— or as we must write that factor then:
2 81 — 8

varies with the pressure of the gas. Corresponding to the important changes

of

arising from contact of the mercury surface with the air, the
s

contact with a highly compressed gas can also influence it. As I
could not obtain any indications on this point, I have assumed in
Ey»

Pr

my calculations that the influence of the pressure on may be

§]|— 8g
neglected; it may be that later on we will be able to apply these
corrections again.

That however these corrections will not probably become important
for my determinations of isothermals, follows from the fact that the
wide tube has only been used to 8 atm. for which the change of
— by the pressure will certainly be only very small; while at
8
high pressures the volume is measured in narrower tubes, and we

HH
have proved that the influence of —— decreases as the tube becomes
s§

narrower.

§ 9. Although my research on the volume of the mercury
meniscus has been made in order to evaluate the correction in the
calibrations of our piezometertubes and in the measurements made
by means of them, I have with a view to possible researches, for
which the meniscus must be known still more accurately, read the
values of f as accurately as possible in the figures IV and VI on
the original drawing of which the scale was twice and a half as
large again as that for the plate. We can now combine the values
obtained in the following table; those which deviate imperceptibly
from the mean height of the segment of a sphere have been priated
in a small type.

To make it prominent for which menisci the deviation from a
segment of a sphere begins to become important in our accurate
determination of isothermals I have underlined them in the table').
The values obtained by extrapolation are in italics.

1) In the calibration of the piézometertube of 0.4 cm. 15 menisci occurred, the
heights of which varied from 0.087 ($= 0.22) em. to 0.143 (3 = 0.36) cm., mean height
0.114 (3 = 0.28%) em.; in the measurements 80 menisci occurred from 0.092 (3 =0,23) em.
to O44 ($ = 0.36) cm. height; most of them between 0.108 (3 = 0.27) and 0.127

ee re ae
3
R in cm 0.05 Onn | 0.15 0.2 | 0.25 0.3 | 0.35 0.4
|
0.05 || o.o012° 0.00257 0.0088 | 0,0050° 0.006371 0.00773) 0.0091 | 0.0107
0.1 | 0.0025? | 0.0050 | 0.0076 | 0.0102 | 0.0128 | 0.0155 | 0.0183 | 0.0213
0.15 | 0.0037° 0.0075° | 0.0114°| 0.0153 | 0.01925} 0.02325) 0.0274 | 0.0318
0.2 | 0.0050? | 0.0103 0.0155 0.0206 | 0.0257 | 0.0310 | 0.0366 | 0.0426
0.25 | 0.00655 0.0181 | 0.0196°| 0.02615) 0.0327 0.0393 0.0462 0.0536
0.3 I 0.0080 | 0.0159 | 0.0239 | 0.0320 | 0.0401 | 0.0483 | 0.0566 | 0.0657
0.35 | 0.0093°| 0.0188 | 0.0283 | 0.0384 | U.0489 | 0.0592 | 0.0700 | 0.0815
0.4 0.0108°| 0.0218 | 0.0331 0.0453 | 0.0583 | 0.0737 | 0.0904
aes | See | SE SE | SE

I thought it better to let the table stand in this form, because
on account of the slight curvature of the lines in fig. IV and VI
a better interpolation is possible than if I had expressed the volume,
in terms of the height and the radius.

But if many menisci at one width of the tube must be calculated,
then tables must be derived for them from the preceding table.

If finally we reconsider the numerical example of § 1 we cal-
culate from this table a section of 0,5 em.? and a height of 0,14
em., a volume of 0,045 cc., while the segment of a sphere gives
0,0365 ce., and so we find a difference of about 0,0085 ce. or
23 percent, or more than 7 times the error allowed in our measure-
ments, so that the correction calculated in these communications is
indispensable for the accurate measurements aimed at.

(3 =0.32) em., on an average 0.115 (3 = 0.29) em. For the tube of 0.283 cm. radius
I obtained in the calibration 16 menisci from p= 0.042 ($= 0.15) to p= 0.095
(3 = 0.335) cm., on ap average p== 0.073 (3 = 0.258)cm.; in the measurements 33 me-
nisci from p=0.031 ($= 0.11) to p= 0.121 (3 = 0.43) cm., on an average p = 0.075
(3 = 0.265) em. The third and the fourth tube are sufficiently narrow, so that we can
omit the correction on the segment of sphere.

(February 20, 1901.)

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday February 238, 1901.

DOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 23 Februari 1901 Dl. IX).

Contents: Prof. F. A. F. C. Went: “On the Influence of Nutrition on the Secretion of Enzymes
by Monilia sitophila (Mont.) Sace.” p. 489. — Dr. A. Smits: “Determination of the
decrease ‘of vapour-tension of a solution of NaCl at higher temperatures”, (Com-
municated by Prof. H. W. Baxuuis RoozeBoom), p. 503, — Dr. A. Smits: “Some
observations on the results obtained in the determination of the decrease in vapour-
tension and of the lowering of the freezing point of solutions, which are not very
dilute”, (Communicated by Prof. H. W. Baxuurs RoozERoom), p. 507. — Prof.
J. D. van peR Waats: “The equation of state and the theory of cyclic motion”,
p- 515. — Prof. H. G. van pe Sanpr Baxkuvuyzen: “Report of the Committee for
the organization of the observations of the solar eclipse on May 18th 1901”, p. 529.

The following papers were read:
sp

Botanics. — Prof. F. A. F. C. Went: ‘On the Influence of
Nutrition on the Secretion of Enzymes by Monilia sitophila
(Mont.) Sace.”. ‘

(Read January 26, 1901).

The mould Monilia sitophila is used in the West of Java to cause
decomposition in cakes of Arachis seeds; these are then eaten by
the Sundanese under the name of onchom.

Spontaneously this mould occurs on putrefying bread and wheat-
flour and has also been found in France; in Java I met with
this Monilia growing spontaneously on dead leaf-sheaths of the
sugar-cane in the residency of Pekalongan (where onchom cakes are

33

Proceedings Royal Acad. Amsterdam. Vol. IIL.

( 490 )

unknown). Material for investigation I received by the interference
of Dr. A®G. VorpermAN, whilst the determination was done with
the kind help of Prof. C. A. J. A. OUDEMANS.

Like other Monilia species this mould possesses a branched my-
celium from which arise the conidia-bearing hyphae up in the air;
these are strongly ramified and are often for the greater portion of
their length built up of chains of conidia, which are elliptically
shaped, much varying in size (from 5 to 14 « diam.); they separate
very easily, after having for a time been united by a connecting
part. In rich cultures the hyphae are often united into tree-shaped
masses, whilst the walls of the culture vessels are mostly coated with
fringelike, downward pending, loose conidia-bearing filaments. I
found that the presence of a moist atmosphere is a condition for
the appearance of conidia; hence, their formation can be almost
totally suppressed by keeping the air above the cultures as dry as
possible, especially when the nutrient liquid is much concentrated.

Probably the fungus has yet another form of reproduction; at
least I repeatedly found characteristically wound hyphae, which
gave the impression of young perithecia. I did not however succeed
in bringing them to further development, however much I
varied the culture conditions (neither, for instance, when suddenly
introducing a strongly fed mycelium into water, which has in some
cases been successfully applied by Kuss’).

Pigment.

Monilia sitophila is a most striking mould by its bright orange-
red colour. The pigment can be solved in absolute alcohol, ether,
benzol, chloroform, etc. by which a solution is obtained of gold-
yellow to brown-red with a faintly green fluorescence; after eva-
poration of the solvent, brown, fatty drops remain; insoluble is the
pigment, inter alia in water, acetic acid and hydrochloric acid.
The absorption spectrum of the pigment-solution shows a dark zone,
embracing the whole of the blue and violet portion of the spectrum,
from about LP’.

Under the microscope the protoplasts often give the impression
of being coloured uniformly orange, but the pigment is also seen
lying in drops in the protoplasm. I suppose that this is always
the case, but that these drops are often so small that they cannot
be distinguished separately.

‘) Jahrb. fiir wiss, Botanik 33. 1899, p. 518.

( 491 )

The mould has the remarkable property of exclusively forming
this pigment when exposed to the light. If Monilia sitophila is
grown in the dark, the mycelium and the conidia remain colourless ;
if however such a culture is placed in diffuse day-light, a light rosy
tint sets in after 2 to 3 hours, which slowly passes into orange.
Exposure to the light during only 15 minutes is sufficient to bring
about a faintly rosy tint after a few hours, which however does not
pass into orange in this case. A still shorter exposure to light seemed
to cause a slight change of colour, if the action however was shorter
than 5 minutes, the mycelium remained white.

It was furthermore proved that the blue and violet rays (the
same which are absorbed by the pigment) are those which exert
the above influence. If the mould is grown in the light, which
has passed either through a kalium-bichromate solution or through
a solution of the pigment itself, the mycelium continues colourless,
whilst a bright orange-yellow tint appears when the culture is
lighted by rays that have passed through a solution of cuprammo-
niumoxide.

The signification of this pigment production for the life of the
plant is not yet clear to me; perhaps it protects the enzymes,
produced by the mould, against the infiuence of the light; it is my
intention to make a further investigation of this point.

Very frequently the medium on which the mould is grown, takes
a brown colour, especially in old cultures. This stands in no relation
whatever to the influence of the light, but, on the contrary, depends
on the chemical composition of the nutrient medium. This brown
colour, namely, appears only then, when the medium contains
alouminous matter, peptones, or tyrosin, so that this is probably
due to a secretion of tyrosinase.

Conditions of Nutrition.

Monilia sitophila thrives very well on number of natural media,
such as Arachis seeds, bread, carrots, milk, broth, infusions of plums
or raisins, somewhat less on the white of eggs, potatoes or sliced
apples.

The use of media of exactly known composition proves that albu-
minous substances and peptone can serve as sources, both of carbon
and nitrogen for our mould, whence the value of suchlike sub-
stances, as nitrogen food alone, is difficult to determine. Excluding
these, one of the best sources of nitrogen (glucose being given as
carbon nutrient), proves to be tyrosin, further asparagin, asparagin

33*

( 492 )

acid, leucin, anorganic nitrates, ammonium salts and_ nitrites,
lastly, alanin and glycocol. Bad sources of nitrogen are urea and
hippuric acid, whilst kreatin and coffein can still Jess serve as
such. Many of the here mentioned organic compounds can serve as
carbon food too, though mostly no vigorous mycelium is formed
in this case.

As sources of carbon stand foremost, besides the already mentioned
albuminous matters and peptones, the carbohydrates.

Of the substances examined, we must first of all mention raffinose,
whilst also the following ones can be quite well utilised as sources
of carbon: starch, dextrin, maltose and cellulose, in less degree glucose,
fructose, mannose and glycogen, lastly cane-sugar, galactose, lactose,
arabinose, arabin and inulin. Aromatic compounds seem unfit to
serve as sources of nitrogen; on the other hand several non-carbo-
hydrates of the fat-series may serve as such: among the alcohols in
the first place glycerin, further mannite, erythrite, dulcite and in
very small degree ethylaleohol; of the acids (in the form of salts)
may be mentioned acetic acid, tartaric acid, lactic acid, malic acid,
finally also acid-amids and amidoacids, such as asparagin, asparagin
acid and glycocol. Fats are bad sources of carbon, yet the mould
succeeds in getting some nourishment out of them.

Although in this short paper I will not enter into ampler details
concerning the conditions of nutrition, a few points are worth special
mention. The optimum temperature for the development of Monilia
sitophila lies at about 30° C.; at this temperature several substances
can still be used as nutrients, which at + 15° C. are valueless as
such. Hence, if the object is to grow the mould at the ordinary
room temperature, this will only succeed when the conditions of
nutrition are well chosen, but even then, the development goes
on rather slowly.

Furthermore it should be observed that the value of a nitrogen
food depends on the carbon food present, and the reverse. If for
instance, maltose, glucose, lactose, cane-sugar and glycerin are
offered as sources of carbon, then maltose proves to afford the most
vigorous development when tyrosin, glycoco], hippuric acid, kreatin,
or leucin serve as source of nitrogen, whilst cane-sugar is the
best source of carbon with asparagin as source of nitrogen, and
finally, when alanin is used, the development at the nutrition with
glycerin is three times more vigorous than with any of the other
examined substances. It appears to me that the explanation of this
phenomenon should perhaps be sought in the greater or smaller
facility with which the plant can form proteids from the carbon and

( 495 )

nitrogen food which it receives. For we know from experiments
with higher plants by Hansteen!), that Lemna can form proteids
from asparagin and glucose, but not from asparagin and cane-sugar ;
on the other hand, it can form them from cane-sugar and glycocol,
but not from glucose and glycocol.

Lastly, in such experiments distinction should be made between
the value of a carbon food as plastic material for the production
of the constituents of the plant-body and as respiration material.
It seems to me that this is most evident when comparing the result
of nutrition with glycerin alone, raffinose alone, and with both
combined. If as food is used 100 em. of a liquid which contains,
besides 0.5 pCt. NH, NO;, and the other required anorganic salts
3.27 pCt. glycerin, then after about two weeks, a crop is obtained
of +25 mers. (expressed in dry matter of the mould). If instead
of glycerin 0.16 pCt. raffinose is taken, the crop is under the same
circumstances about 19 mers.; if however these two are combined,
so that the nutrient liquid contains 0,16 pCt. raffinose and 3.24 pCt.
glycerin then the crop is 150 mgrs. In order to get an equal crop
with raffinose as the only carbon food, 2,5 pCt. of this substance
must be added to the nutrient liquid, whilst with glycerin such
a crop is not to be obtained. This can be explained when we
admit that glycerin is not a fit material for the production of pro-
toplasm or cell-wall (at least with NH, NO; as source of nitrogen),
but is, on the other hand a good respiration material.

As well on an acid as on an alkaline medium the mould can
grow; to 100 cm. of nutrient liquid can be added 10 em. of 1/,,
norm. sulphuric acid, even 25 ccm. of +/;9 norm. caustic potash,
and yet development will take place.

The mould can live anaerobiontically; as well in BucHNER’s tubes,
where the oxygen is absorbed by pyrogallol and caustic soda, as in
a current of hydrogen, a rather vigorous development is obtained,
though less than in the air. It seems to me that the development
decreases, when the last traces of free oxygen are better removed,
so that in complete absence of this element the development is
probably quite stopped. In an atmosphere of hydrogen, CO, is
developed and alcohol is formed.

Decompositions caused by Monilia sitophila.

Fats as well as proteids and carbohydrates are liable to certain

1) Jahrb. fiir wiss. Botanik. 33, 1899, p. 117.

( 494 )

decompositions when introduced into a culture fluid in which Mo-
nilia sitophila is present.

Fats are, although very slowly, splitted up into glycerin and free
fatty acids. Probably the mould uses the glycerin as food. This can
be easily demonstrated by growing Monilia sitophila in a fluid which
contains as carbon food butter-fat or Arachis-oil or another fat and
to which is added a little litmus. The development of the mould
takes place very slowly and at the same time the solution is seen
to grow more and more red; in the absence of fats the mould forms
no acid. This decomposition is probably caused by a secreted enzyme,
a lipase. If the mould grows on milk, this becomes acid, and at the
same time the casein precipitates, which in my opinion, should be
attributed to the decomposition of the fats of the milk. Hence, when
milk, rendered free from fat by filtration, is used as medium for our
Monilia, no precipitate appears but on the contrary, the slight
deposit which forms at sterilisation, is gradually solved. This is a
consequence of the secretion of a proteolytic enzyme, to which I
shall presently return. The dark brown colour which these liquids
thereby assume, is, as mentioned above, a consequence of the presence
of proteids.

Nutrient gelatin is liquefied by the mould, as well in reutral,
as in alkaline or feebly acid condition, in absence and in presence of
free oxygen. So it was obvious that a proteolytic, more particularly,
a tryptic enzyme, is secreted. If a culture is made in a peptone
solution, filtered after some time, and introduced into tubes of co-
agulated gelatin (with addition of an antisepticum, such as toluene
or thymol), then the gelatin at the surface is slowly liquefied,
this does not occur when the said liquid has first been boiled;
hence it is evident that a gelatin-liquefying enzyme was secreted
by the mould. The quantity of this enzyme is however very small
which renders its examination troublesome. Moreover the secretion
proves to depend on the nutrition of the mould; it is, e.g., found
when peptone is given as fvod, not when glycogen and NH, NOs
are the nutrients. I did not, however, pay much attention to this
fact as something similar is much more distinctly observed with the
carbohydrates and can there be better measured.

The splitting of the proteids goes certainly further than the ap-
pearance of peptones, so it is easy to state the formation of NHs.
It is also evident from the following experiment, that peptone is
decomposed by the enzyme (or enzymes) in question here: When
from a peptone liquid the mould is filtered and the liquid is allowed
to stand with a sitll toluene, the rotation to the left which is a

( 495 )

consequence of the presence of peptone slowly decreases. This change
of rotation does not occur when the liquid has first for a short
time been heated to 100° C. The decomposition products of proteids
are however also found in cultures to which no trace of any
proteid has been added, eg. in glycerin and K NOs solution. These
can here have only taken origin from the protoplasin of already
dead cells of the mould.

I have given much attention to the action exerted by Monilia
sitophila on carbohydrates. Starch, dextrin, cane-sugar and maltose
are hydrolised by the mould, lactose is not changed, although, as
said above, it can serve as food. Cellulose is attacked and converted
into a reducing sugar, which is howeyer evidently soon consumed
as food, so that only a feeble reduction of FeHLinG is observed in
culture liquids where cellulose is present as carbon food. That
the cellulose is attacked is easily seen under the microscope,
when the mould is grown on Arachis seeds, the cell-walls are
in all directions infested by the hyphae and so the cells are
disjoined. I think that in this action on cellulose and in the
saccharification of the starch (wherewith compared the converting
of proteids and fats is very subordinate) the chief signification of
Monilia sitophila as technical mould should be sought.

Cane-sugar is hydrolised into invert-sugar, maltose into glucose ;
in both cases there is question of enzymes, as will be nearer explained
below. The saccharification of the starch also, should be ascribed
to the secretion of an enzyme (or perhaps two enzymes). This
saccharification can best be observed when the mould is grown on
boiled rice. The tough viscous matter is slowly liquefied; whilst at
first the iodine reaction is distinctly blue, it gradually grows more
reddish and finally all the starch proves to have vanished. ‘The
sugar formed is d-glucose, this follows from the extent of the rotation
of the polarisation plane, compared with the reduction of FrHnine
and from the formaticn of glucosazone with phenylhydrazine acetate.
During the beginning of the hydrolysis however, the rotation proves
to be much greater than corresponds with the cupric-oxide reduction,
when this is rated as glucose; this is a consequence of the formation
of dextrin as mid-product. If the dextrin is precipitated with alcohol
then the rotation and the cupric-oxide-reducing power quite correspond
with those of glucose. If the conversion products are daily determined,
there is found in the beginning much dextrin and little glucose;
by and by the latter increases whilst the former diminishes and
at length disappears, when the glucose has reached a maximum
(about 43 pCt. of the weight in rice); afterwards the glucose also

( 496 )

decreases, evidently it is consumed by the mould. The auxanographic
method of BrtyerRINcK-WissMAN is difficult to apply whilst moulds
as these soon completely overgrow an agar-agar- or gelatin-plate.
Still the conversion of starch can be observed therewith, when
an agar-plate is made and Monilia allowed to develop on it. When
after a few days a dilute iodine solution is poured over the plate,
it remains colourless at the place where the development of the
mould has begun; round about a red zone is seen which gradually
passes into the blue of the further portion of the plate.

From starch of different plants, under for the rest like circum-
stances, do not result equal quantities of sugar. [ did not minutely
investigate this fact; I only refer to it as it corresponds with what
has before been described by me conjointly with Mr. PRINSEN
GEERLIGS about Chlamydomucor Oryzae ).

The carbohydrates undergo still further conversions, as Monilia
sitophila produces also alcohol and besides various esters; the latter
cause the cultures to spread a pleasant odour, reminding of apple-
essence. If these ethereal substances are distilled off they give a
distinct jodoform reaction, whilst at a fractionated distillation of
this product, the chief portion of the distillate, when shaken with
benzoylchloride and caustic soda, produces a substance which by its
smell is known as ethyl-benzoate.

Influence of the Nutrition on the Secretion of Enzymes.

The conversions of cane-sugar, maltose, and starch are caused
by enzymes, which are secreted by the cells and so are to be
found in the nutrient liquid. This can easily be shown by freeing
the liquid with the help of filter-paper from the mycelium and the
conidia of the mould and then mixing the filtrate with a solution
of cane-sugar, maltose, or soluble starch, with addition of a little
toluene or thymol, to prevent the growth of micro-organisms. After
some time a conversion appears to have occurred, which can be
measured by the change in the rotation of the polarisation plane or
by the cupric-oxide reduction test, and can be qualitatively estimated
by making the osazones. For control an experiment was made at
the same time with the other half of the liquid, after it had
been boiled a moment; with it the conversions did not take
place. The enzyme (or better the mixture of enzymes) could be

‘) Verhandelingen hon, Akad. y. Wet. 2e Sectie, Dl. IV, No. 2, 1895.

( 497 )

precipitated with alcohol; after washing with alcohol a yellow-white
powder was obtained, partly soluble in water. The solution proved
to possess the properties of the original liquid, though in an atten-
uated degree; as is known for other cases, here also alcohol seems
prejudicial to the activity of the enzymes. In pure state (albeit a
mixture) they are surely not obtained in this way, because, as I
hinted above, decomposition products of proteids occur in every cul-
ture liquid, and these are also partly precipitated by alcohol.

Are these enzymes secreted under all circumstances? It is known
that for the glands of the intestinal canal of the higher animals,
the experiments of Paviorr and his disciples have demonstrated, that
the secretion of enzymes is indirectly influenced by the nutrition,
but here the presence of the nervous system makes the phenomena
extremely complex, so that the idea lay at hand to seek, whether
not in plants something similar might be found in simpler form.
For bacteria, Fermi!) had observed that a gelatin-liquefying enzyme
is only produced in the presence of food containing proteids, whilst
WortMann?) had thought to find a similar fact for diastase; but
it should be called to mind, that the latter investigation was not
done with pure cultures. Brown and Morris *) have shown that
embryos of grasses secrete no diastase when growing in strong
sugar solutions. Karz*) thinks that Penicillium glaucum would
secrete no diastase when a sufficient quantity of cane-sugar or glucose
is present in the nutrient liquid; to my opinion, however the method
of investigation used does not allow to draw this conclusion. Finally
DucLavx®) gives some brief remarks concerning Penicillium glaucum
and a not nearer determined Aspergillus, which secrete certain
enzymes only when they are fed in a special way.

Monilia sitophila enabled me more amply to study similar pheno-
mena. As I said above, the proteolytic enzyme is secreted only
with a particular nutrition, but I have not nearer investigated this
point, because I wished to measure the quantity of enzyme and
this can only be done exactly, when the conversion products can
also be well determined. With the amylolytic enzyme we meet with
the difficulty, that we do not know whether this is really a simple
conversion or a co-operation of more enzymes. Hence, I wish only

1) Centralblatt fiir Bakter. u. Parasitenk, Bd. X. 1891. p. 401.
*) Zeitschr. f. physiol. Chemie. Bd. VI. 1882. p. 287.

*) Journal of the Chem. Soc. LVI[. 1890. p. 458.

*) Jahrb. f. wiss. Bot. 31. 1898. p. 599.

*) Traité de Microbiologie I1, 1899, pg. 84—88.

( 498 )

to observe, that a starch-saccharifying enzyme is secreted when
starch and dextrin are given as carbon food, but furthermore also
with maltose, glucose, glycerin, lactic acid, malic acid, and acetic
acid, only the amount of enzyme is by no means always equally
great. The sugar thereby resulting, was identified by the osazone
in the case where the enzyme was produced in a glycerin-liquid ;
here, too, it was d-glucose. Presently it will be shown why this is
of importance.

On the other hand, the inversion of cane-sugar or the hydrolysis
of maltose can be very exactly determined. I therefore fixed my
attention on these two conversions and in particular on the latter,
because it was soon evident that invertase is secreted in all the
examined cases, albeit not always in equally large quantities (i. e.
when as carbon food were used cane-sugar, maltose, glucose, gly-
cerin, lactic acid, malic acid, and acetic acid). Quite different is the
case with the maltose-enzyme, which I will give the name of
maltoglucase.

As is known, an enzyme forming glucose, has been named glukase
by Brtertyck and the German investigators. If the view of
Crorr Hiti!) that this conversion is a reverse action proves to be
right, this name already gives rise to confusion, still more, how-
ever, if one and the same plant, as Monilia sitophila, secretes two
enzymes, both forming glucose, one from dextrin (starch), the other
from maltose. The nomenclature of Ducntaux and his school would
be “maltase’, but here we find the same difficulty, for starch is
not always converted in the same way by different enzymes; would
it then be correct to speak of amylase in every case? The confusion
becomes still greater by the fact that maltase is quite another thing
for Ductaux than for Betyerinck and Wissman. In my opinion
the problem is best solved by using a double name and thus to
speak of maltoglucase. The same nomenclature can be used in all
cases where the product of the conversion is well known and simple.

Maltoglucase now (with a single exception of which presently
more), is exclusively secreted at the nutrition of Monilia sitophila
with certain carbohydrates, and that in a very unequal degree.
The following non-carbohydrates, when serving as carbon food,
give no rise to the secretion of the here meant enzyme: glycerin,
erythrite, mannite, dulcite, isodulcite, sorbite, ethyl-acetate, acetic
acid, lactic acid, malic acid, succinic acid, citric acid, glycocol,

') Journal of the Chem. Soc, 1898, p. 684.

( 499 )

asparagin and tyrosin. In this list we find, among others,
glycerin; in this liquid, in which no maltoglucase is produced, the
amylolytic enzyme is found, and it is worth mentioning that it
causes the production of glucose from the starch. This proves that
here Ductaux’s!) view is untenable, according to which in all
cases, where, by the action of enzymes glucose takes rise from starch,
there would first be formed maltose, which then, by another enzyme
would be converted into glucose. Nor is the opinion of BEIJERINCK*)
tenable in this case; his glucase would convert as well maltose,
as erythro- and malto-dextrin into glucose. Hence we must admit
that here the conversion into glucose is effected, either by a
single enzyme, or by two enzymes, one of which converts starch
into dextrin and perhaps corresponds with one of the constituents
of diastase (i.e. the dextrinase of Wissman *), the other hydrolysing
dextrin into glucose.

Neither does Monilia sitophila secrete malto-glucase at nutrition
with the following carbohydrates: arabin, l-arabinose, lactose and
inulin (when Ammonium salts or nitrates serve as source of nitrogen).
Here it should be borne in mind that my meaning is of course:
no measurable quantities of maltoglucase. As the most accurate
measurements may be done by means of the polarimeter I have
used this instrument and have then considered changes of rotation
below 0.10° as to lie within the limit of errors. Only arabinose
lay about near this limit, but if this might point to the secretion
of traces of enzyme, it could still be attributed to impurities. That
these can indeed be of influence, was for instance shown with
lactose. Pure commercial milk-sugar gave rise to the secretion of
small quantities of enzyme (when a 5 pCt. solution was used the
decrease in rotation was 0.36° in 3 days), but after I had purified
it and then repeated the experiment no enzyme was secreted anymore.

Large quantities of maltoglucase are secreted, when the mould
can use, as source of carbon, first of all raffinose or maltose, further,
commercial dextrin or starch. In less degree cellulose gives rise
to the secretion of the enzyme; still less galactose, xylose, gly-
cogen, whilst last of all, come cane-sugar and d-fructose. With the
last mentioned carbohydrates, peptone stands about ona level, whilst
also in milk a slight quantity of enzyme is secreted; in this latter

1) Traité de Microbiologie. II. 1899, p. 471 vig.
*) Centrafbl. f. Bakter. u. Parasitenk. 2e Abth. I. 1895, p. 221.

8) De diastase beschouwd als mengsel yan maltase en dextrinase. Amsterdam 1889.

( 500 )

case the cause cannot be sought in the lactose or the fat, so that
here, too, the proteids of the milk must cause the secretion of the
maltoglucase. Would not the carbohydrate-rest, which probably
occurs in the proteid molecule, explain this fact?

It is in general the best-feeding carbohydrates, which cause the
secretion of the greatest quantity of enzyme, but this does not
include that there should be a direct relation, as proved by the
following data:

Carbon food. Relative quantity of Quantity of mould
secreted enzyme. obtained (dry matter).

10 pCt. raffinose 10.17 257 mGrs.

5 > dextrin Teel 61 »

2,5 » maltose 5.14 41 >»

5 » galactose 0.68 12 »

5 » glycogen 0.55 36 >

5 > cane-sugar 0.26 21 »

5 > lactose 0 30 >

5 > peptone 0.50 124 »

Another question to be answered was, whether, at the nutrition
with the same substance but in varying quantities, there exists a
direct relation between the quantity of the food and that of the
secreted maltoglucase.

For the measurement of the relative quantity of enzyme, there
are two ways: one is to observe how much time is required to
convert equal quantities of the substance; the quantities of enzyme
are then inversely proportionate to those times. Or, the quantities
of substance, converted in equal times, are determined; in the
beginning of the reaction these quantities are proportionate to the
quantities of the enzyme. I have used the latter method after first
having convinced myself of its usefulness by some preliminary
experiments.

( 501 )

The result of a series of experiments, taken in particular with
raffinose, but also with maltose, was that the quantity of secreted
enzyme rises with the amount of sugar given as food; so long as
the latter is still present in a slight quantity, both increase almost
proportionately. But as the concentration of the solution becomes
greater, the increase of the secreted enzyme is seen to diminish,
until it reaches a maximum, then to decrease at still higher
concentration of food. This maximum lies for raffinose and maltose
at a concentration of about 10 pCt.

Very possibly the idea might arise that in these strong raffinose
and maltose solutions, the quantity of secreted enzyme becomes
smaller by the great osmotic pression of the solution; this is not
however the cause. In order thereabout to get certainty, I have
mixed the raffinose and maltose solutions with dilute glycerin of
such a strength that all solutions of varying sugar amount were
isotonic. Glycerin was taken, because, as said above, it has
no influence on the secretion of maltoglucase, neither does it act acceler-
ating or retarding on the reaction of the enzyme, at least not in
the used concentrations (as shown by other particular experiments).
It was thus proved that under these conditions the quantity of secreted
enzyme mounted likewise with increasing concentration, about to
the same maximum; only the proportionality at feeble concentrations
was sometimes less striking than in absence of glycerin. This is
probably a consequence of the more vigorous development of the
mycelium of Monilia when, together with the slight amount of
raffinose or maltose, glycerin was also present, which fact was already
briefly discussed above.

The question arises whether the different amounts of secreted
enzyme, cannot be a consequence of the degree of development of the
mould. For it might be thought that each cell of the mycelium, so
long as it lives, secretes a certain constant quantity of enzyme, hence,
that the more vigorously the mycelium has developed, the more
enzyme will be secreted. I have tried to answer this question by
also weighing in every case the crop of mould obtained (after drying).
I will give one of the series of figures thus obtained.

In column I is found the constitution of the nutrient liquid, in
column II the crop of mycelium in mgrs., in column III the quantity
of secreted enzyme, whilst column IV indicates the quantity of
enzyme secreted on 100 mgrs. of dry matter of the mycelium.

a IE Ill. TY.

1. 0 pt. raffinose 3.27 pCt. glycerin 25 0 0

ee wll) > > o.20 2 > 21 0 0
3. 0.16 >» > 3.24 » » 141 0.32 0.23
4, 0.31 » > 3.22 » > 116 0.24 0.21
5. 0.62 » > 3.16 » > 208 0.57 0.27
Gs lead! > > 3.06 » > 211 1.03 ).49
Tis a | 2.86 >» » 230 Masters 0.77
Cro, ae > 2.46 >» > 257 3.16 1.23
Oo 0s > 163 » » 342 3.87 11133
WO) PAU 5 > 0 > > 528 3.74 0.71

When considering only the figures of rows 3, 4 and 5 in column
IV, they are rather alike, but further there hardly appears any
relation between the development of the mycelium and the quantity
of secreted enzyme. Though it will not be possible to make a pure
comparison, as then for the total weight of mould obtained allowance
should be made for the portion present in the air, the dead cells,
etc., still rows 9 and 10 show that the mass of mycelium can
increase considerably (and here in both cases all was nearly comple-
tely immersed) whilst the quantities of secreted enzyme have remained
rather unchanged.

Whilst we saw already that the nature of the food is of great
influence on the secreting or not secreting of maltoglucase, it is now
evident that the quantity of the food offered, likewise exerts influence
on the quantity of secreted enzyme, in such a sense, that both
increase conjointly, but that very great quantities of food act preju-
dicially on the secretion of the enzyme.

There is a certain disposition to admit that the secretion of
enzymes in general would be the consequence of the want of
certain nutrients, and would indicate, as it were, a hungry condition
of the cell. The investigations here communicated do not agree
with this view; they contain a warning against too rashly drawing
conclusions on this head.

( 503 )

Chemistrie. — Professor H. W. Baxuuis Roozesoom presents a
communication from Dr. A. Smits entitled: “Determination
of the decrease of vapour-tension of a solution of NaCl at
higher temperatures.”

(Read January 26, 1901).
Introduction.

Continuing some earlier researches,!) J have performed some
measurements between 5(° and 80° with regard to the decrease of
vapour tension of NaCl solutions. The apparatus, which I used for
that purpose was a small Bremer oil-tensimeter*). The source of
heat was an oil-bath, the temperature of which could be kept con-
stant within 0.15° by means of a stirring apparatus and an elec-
trical regulator. The accuracy of the method applied did not appear
to be greater than 1 m.m. of oil. This is the reason, why I could
not continue the measurements below the concentration 0,1 gram
molecule per 1000 grams of H,O. The results were as follows:

Concentration | Observed difference | Difference
in gram mols. of Na Cl, Temperature in m.m. of oil at tue ob in m.m. of
per 1000 grams of H,O servation temperature | H, O at 4°.

, i
52°.15 36.5 32.5
54°.0 40.0 35.6
0.7414 60°.38 55.0 48.7
68°.75 80.0 70.5
(hoa) $8.0 77.4
56°.4 30.0 26.6
| 64°.6 43.5 38.4
0.4958 |
| 74°.0 65.0 57.0
| 77°.0 75.0 65.6
54°. 4 5.5 4.9
| 63°.0 7.0 6.2
0.0996 { RAO 10.0 §.8
| 73°.0 11.0 9.7
\ | 84°.§ 21.0 18.2

) Report Kon. Akad. v. Wet. 30 Sept. (1899) p. 160; 27 Jan. (1900) p. 471;
21 April (1900) p. 714.
*) Rec. des Tray. Chim. des Pays-Bas 6, 126.

( 504 )

To express the observed difference of level of the oil at different
temperatures in m.m. of H,O at 4°, the specific gravity of tke olive
oil was determined at various temperatures.

By means of the figures occurring in the fourth column, the
decrease in the vapour tension of the three different solutions is shown
at different temperatures in the following graphical representation.

100

90

80

ah a ee

1
1 ie
1 '
! fl
| | !
60 | ; =
!
I
!
1
i
!
1
!
i
1
1
!
i
1
1
t
!
i]
1
1
|
1
H
1
ye
!
i]
1

=
=

Decrease in vapour-tension in mm. H, 0.

52 4:6 8 60° 2) 4 (6 48970 92 7476 1S 80" 2G oe

Temperature.

The molecular decreases of the vapour tensions of the three
solutions have been calculated for three temperatures: 56,4°, 64,6°
and 74,0°.

The pressures of IL were known for these temperatures; for I
and IIL they have been obtained by graphical interpolations. The
value of I at 74° has been got by a small extrapolation which, on
account of the regular course of the line, is sufficiently accurate.

Decrease in vapour | Molecular decrease
Concentration | Temperature tension in m.m. | in vapour tension | t
H, O at 4°. Hg. at 0°.
0.7414 74° 89.0 8.83 G7)
0.4958 » 57.0 8.49 1.7
0.0996 » 10.5 7.8 1.6
0.7414 64.6° 59.0 5.85 1.77
0.4958 » 38.4 5.66 Wot/
0.0996 » 6.5 4.8 1.5
0.7414 56. 4° 39.8 3.95 1,75
0.4958 » 26.6 3.92 Gy
0.0996 » 5 3.4 1.5

The value of 7 has been obtained by dividing the experimentally
found decrease in vapour tension by the calculated decrease, when
no electrolytic dissociation had taken place. This theoretical value
was obtained by means of vAN ’T Horr’s equation

n

oe a

If we now take a solution, which contains 1 gram mol. per 1000
grams of water and then ask what will be the decrease of the
vapour tension of this solution at 74°, then the data are n=1,
N = 55,6 and p = 276,6 (REGNAULT) and consequently

1

A Pago = 55,0 x 276,6 = 4,98.

For 64,6° we find

A pete = 1 x 183,7 Ue

55,6 ’
and for 56,4°

1

A P564— 55,6 x 125,65 _ 2,26.

34
Proceedings Royal Acad, Amsterdam, Vol. ILL.

( 506 j
Review of the Results.

Although better results are obtainable by using my micromano-
meter and boiling apparatus, the above method is still accurate
enough to demonstrate the course of the molecular decrease of vapour
tension as a function of the concentration. It appears from the
experiments, that the molecular decrease of vapour tension does not
show a minimum between 56° and 74°, but continually increases
with the concentration.

To pronounce on the strength of these results, that the minimum,
which has been found at 100° by means of the boiling point method
between the concentrations 0,5 and 0,1 gram mol. per 1000 grams
of H,0, has already disappeared at 74° appears to me to be too
sweeping. A repetition of these measurements by means of a more
accurate method might enable us to answer this interesting question,
but provisionally there is not much chance for this. The great
difficulty is caused by the temperature. In order to proceed further,
it would be required to keep the bath constant at each temperature
within 0,05°; this has been unattainable as yet. It is perhaps
possible to obtain a bath of a very constant temperature by allowing
some liquid or other to boil under a pressure, which is kept constant
to 1 m.m. of H,O by the manostat') but in how far this method
will be a practical one for my purpose remains to be seen.

The state of affairs at the moment is as follows:

1. It has been found by means of the micromanometer that at
0°, between the concentrations 0.05 and 2 gram mol. per 1000
grams of H,O, the molecular decrease of vapour tension increases
with the concentration in the case of either electrolytes or non-
electrolytes except with K N Os. '

2. An increase of the molecular decrease of vapour tension, when
the concentration is increased has also been observed with the oil-
tensimeter from 56°—74° between the concentration 0.1 and 1 gram
per 1000 grams of H,O in the case of NaCl solutions.

3. The same progressive change of the molecular increase of
the boiling point has been observed with my boiling apparatus at
100° for solutions of NaCl and KCl between the concentrations
+ 0.3 and 1.0 gram mol. that is to say an increase of the molecular
increase of the boiling point with a rise of the concentration.

Between the concentrations 0.1 and 0.5 gram mol. at about 0.3

1) Report Noy. 27 1897.

( 507 )

mol., a minimum of the molecular increase of the boiling point
was, however, observed with this method and with this a minimum
of 7, which did not appear in the sets of measurements | and 2.
It is very remarkable, that it was also found by the boiling point
method, that solutions cf KN Os, of the concentration 0.05 to 1
gram mol. make an exception to the general rule.

It is strange, that this phenomenon has not yet been brought to
light by tke freezing point method.

Amsterdam, Chem. Lab. Univers. January 1901.

Chemistry. — Professor H. W. Baxnurs Roozesoom presents a
communication from Dr. A. Suits entitled: “Some observations
on the results obtained in the determination of the decrease
in vapour tension and of the lowering of the freezing point
of solutions, which are not very dilute.”

(Read January 26, 1901).

With the aid of the theory of the thermodynamic potential, VAN
Laar!) has calculated accurate formulae for the decrease of the
vapour tension, elevation of the boiling point and lowering of the
freezing point. These formulae have the advantage, that they may
be applied to dilute as well as to more concenirated solutions, which
renders it possible to compare quantitatively the results of investi-
gations of solutions, which are not very dilute.

The formula for the decrease of the vapour tension is as follows:

P

yee ane Re (1)
Pp

Po = Vapour tension of the solvent

i. s > » solution
: n
e¢ =concentration = ———
N+n

f is a quantity which = 0 for dilute solutions.
For the elevation of the boiling point we have the equation:

Rrt,

Atv=r—) => m7 Oh lage ee. 45) ny “=. (2)

1) Zeitschr. Physik. Chemie 15, S. 457 (1894).
34*

(508 )

rt and r, are the absolute boiling points of solvent and solution.
W = molecular heat of evaporation of the solvent.

R= gas-constant.

For the lowering of the freezing point we have the analogous
formula

RTT

3 (Fs=tegic) ey ve) ee)

UNG Sy SS

in which S means the molecular heat of fusion of the solvent.

As the values of f in the different formulae are only comparable
at the same temperature, we can for instance calculate for the tem-
perature 0° the relation, which must exist between the lowering of
the freezing point and the lowering of the vapour tension.

From (1) and (3) follows:

or

S
a a i Pere eens 6s ((/2)

In the case that water is chosen as a solvent we have:

So eel 18.016
Rr, 1.863 1000

The equation (4) therefore becomes:

Po Az 18.016 rv )
log? = ae a Ga) A
9, = 1.863 * 1000 ares: ©)

If, however, we neglect the powers higher than 2 then

Po Po
log — = log = log =
i re peee
Po
——— log (1 2 Tl = a =F 2 (=?)
Po Po Po
Consequently
A Ap,? At At 18.016
—? + 3(-2) =e! +=) X aaa Beaters (6)
Pr p,/ 1.863 T) 1000

If we now calculate Be from Raov.t’s!) determinations of the
P

freezing point by means of equation (6), we obtain the following
figures for cane-sugar.

Cane-sugar.

RA B ER Sf.
Concentration
Ar Ar Ar\| Ap 1 /Apy? Ap
ees P| Ar | sees. | tie08 ( + =| aga 4 pie
1000 gr. HO
1.0107 2.0897 1.122 1.1380 0.02036 0.02015
0.5056 0.9892 0.5310 0.5329 0.009600 0.009554
0.2500 0.4806 | 0.2580 0.2585 0.004657 | 0.004646
0.1250 0.2372 | 0.1973 0.1274. 0.002295 0.002292
0.0652 0.1230 | 0.06602 0.06605 0.001190 0.001189
0.0285 0.0532 0.02856 0.02857 0.0005147 0.005147

By multiplying the figures in the last column by p, = 4,62, we
obtain the decrease of the vapour tension corresponding to the
lowering of the freezing point observed by Raoutr.

In order to be able to compare these figures with my latest results,

1) Zeitschr. f. Physik. Chemie 27, S. 638 (1898).

(510 )

obtained with solutions of cane-sugar!), I have calculated by inter-
polation the decreases of the vapour tensions for the same concen-
trations as used by Raovuur in his determinations. The result is
as follows:

TAB Ee
Concentration | in net Hg | in mim of Hg Difference %
RAOULT. Smits.
1.0107 0.09289 0.09090 — 0.00199 — 2.1
0.5056 0.04414. 0.04446 + 9.00032 + 0.7
0.2500 0.02146 0.02167 + 0.00021 + 0.9
0.1250 0.01059 0.01072 + 0.00013 +1.0
0.0652 0.00549 0.0055 + 0.00008 ae eiea
0.0285 0.00238 0.00240 | + 0.00002 | + 0.8

The agreement is, therefore, a very satisfactory one, the differences
being within the range of the experimental errors.

If we now calculate in a similar manner the decrease of the
vapour tension from the lowering of the freezing point of Na Cl-
solutions observed by Raovutt and then compare these figures with
those obtained by direct measurement, we find the following:

Sodium chloride.

T ASB ey ae

| 2
Concentration Ar si | oa ¢ +5) | EY ip Se) AY
Ar 1.8638 7? PY 2\ | Po
1.0000 3.4237 1.838 1.8610 0.03353 0.03297
0.4887 1.6754 0.9048 0.01630 0.01617
0.2393 0.8211 0.4420 0.007962 0.007930
0.1179 0.4077 0.2191 0.003947 0.003939
0.05829 0.2073 0.1114 0.002007 0.002005

1) Report Kon. Akad. y. Wet. 30 Sept. 1899, p. 162. It is stated there that the
greatest concentration is 1.0811; this should be 1.0089.

(511)
T ACBsiy, WIV.

__ ee a ee Se eee eee
Ap Ap
Concentration | in mm. of Hg | in mm. of Hg | Difference | O%
RAOvwtt. SMITs.
ssl
1.0000 0.1523 0.1437 0.00860 — 5.6
0.4887 0.07470 0.06937 0.00533 —7
0.2393 0.03664 0.03367 0.00297 ; —8
0.1179 0.01820 0.01646 0.00174 — 9.5
0.0582 0.00926 0.00800 0.00126 —13.6

Here there is absolutely no question of agreement and at the
same time we observe, that the difference continually increases with
the dilution.

Before proceeding further I will just show, that if I had compared
Raovutt’s results with mine by calculating the factor 7, I really
would have committed an error, although as we will see presently,
this error is so small that it is only revealed at the greatest con-
centration.

According to vAN ‘Tt Horr, the factor ¢ may be calculated from
the decrease of the vapour tension and the lowering of the freezing
point by means of the formulae:

4 A N

pee Le a
Po a

and

A = Md 8

VSS AG _—

: RE, n (8)

From this follows:

Ap S

—=At 2 (9

Po Rr,” (®)

This equation is perfectly true for exceedingly diluted solutions,
but it no longer applies to solutions, which are not very much
diluted. For these, van Laar has found indeed the relation (4)
instead of the equation (9):

S
log Po. — To
P Rr? T
or
Ap = Ap ‘i _ s To
Po 2 ( Po Rr? t

(512 )

From this we see that for solutions, which are not very much
diluted both sides of the equation (9) are too small. If the error
were the same in both sides it would naturally be eliminated from
the difference of the equations (7) and (8), so that a comparison of
the results of solutions, which are not very much diluted, might be
arrived at by applying the equations (7) and (8).

If the equations (7) and (8) were of universal application, then
we ought to find for all concentrations

and because

we should find

2N
1 (=") = =% (2-1) 2
Tt

This equation is no longer true for solutions which are not very
much diluted, for in that case we find

1 (22) “>. (2 ye oe

For most of the solutions which have been examined this difference
is, however, so small, that it may be neglected, but when the greatest
concentration 1 gram mol. per 1000 grams of water is reached it
becomes distinctly perceptible. This is easily shown by the following
table in which i has been calculated from the molecular lowering
of the freezing point, and from the molecular decrease of the vapour
tension by dividing these by 1.863, and 0.08316 respectively.

Cane-sugar.
TASB aah R Ve

Costin. cg ft| Mtge tan | Race) Se Disa
1.0107 2.0676 0.08994 1.110 1.082 —2.5
0.5056 1.9565 0.08761 1.050 1.057 +0.7
0.2500 1.9224 0.08668 1.0383 1.042 +0.9
0.1250 1.8976 0.08576 1.020 1.031 +1
0.0652 1.8860 0.08543 1.013 1.027 +1.4
0.0284 1.8667 0.08421 1.004 1.013 0.9

G htge)
Sodium chloride.

TASB i NI:

mol. lowering of| mol. decrease of the ; | Difference

Concentration. |,1. freezing | vapour tension. espe SmItTs | in %
1.0009 3.4237 | 0.1437 1.838 | 1.728 — 6.)
0.4887 3.4283 0.1419 1.840 | 1.707 —7
0.2393 3.4313 0.1407 1.842 | 1.692 — 8
0.1179 3.4581 0.1396 1.856 | 1.679 — 9.5
0.05829 3.5564 0.1372 1.909 | 1.650 —13.6

If we now compare the differences in the last column of these
tables with those of the fifth column of tables II and IV, we see
that on the whole they agree with each other; only at the greatest
concentration the differences are 0.4 and 0.5 percent greater. For
this concentration the disparity, as represented by equation (11), is
very perceptible.

If, for instance, we calculate for the concentration 1.0107 gram
mols. (Table V)

we find for the first quantity the value 0,013 and for the second
0,008. If we now add to Raouxt’s 7 0,008 and to my own 0,012,
we naturally obtain again, just as in table II, a difference of 2,1
percent for this concentration. In the same manner the difference
of 0,5 percent disappears at the greatest concentration of Na Cl.

The foregoing teaches us up to what concentration we can in
this case make a comparison by means of 7. We are therefore,
obliged to stop at the concentration 1 gram molecule. Up to
the concentration 1 gram mol. the values of 7 must agree within
0,1—0,2 percent by whatever method they have been obtained. In
this we must, however, not forget that the factor 7 is not to be
considered as a dissociation factor, but as a quantity of which we
do not as yet know the true significance.

I consider it an indisputable fact that ¢ generally increases
with the concentration in solutions which are not very dilute.

(514 )

The determinations of the vapour tensions at 0° and between
50° and 70°!) and also the determinations of the boiling point
(from the concentration + 0,3 gram mol. up to higher concentrations)
lead to this conclusion.

The fact that Raoutt, who continued his experiments up to the
concentration 1 gram. mol., observed a fall of 7 with an increase
of the concentration points to an error. RAOULT ought also to have
observed a rise of 7 with the concentration of his stronger solutions.

The possibility of an error in Raout’s determinations is also
corroberated by the latest communication from CHROUSTCHOFF *)
entitled Recherches Cryoscopiques’’ where the thermometer has
been replaced by a thermo-element accurate to 0.0005°. In the case
of NaCl, he found between the concentrations 1/, and ¥/44 gram
mol. a constant molecular lowering of the freezing point. In the
case of K Br, he found between the concentrations }/, and 4/193 gram
mol. an increase of the molecular lowering of the freezing point
with increasing concentration. In the case of Ky 50, however, he
noticed the reverse change between the concentrations 1/, and eq
gram molecule. The fact that a small alteration in the method
influences the results and even alters the course proves that the
freezing point method is attended by unknown sources of error, in
the case of electrolytes at any rate. I consider that CHROUSTCHOFF
has made a great improvement by determining the concentration of
the solution after the separation of ice.

Finally there are also determinations of the freezing point where
a minimum of 7 has been found; I obtained this also by means of
the method of boiling in the case of solutions of Na Cl or KCl.
Jonrs, CHAMBERS and FRAzER®) found minima for the solutions of
the chlorides and bromides of Mg, Ca, Ba and further for Cu SO,,
H; PO,, HCl, CHs COONa, Cdl,, Sri, and Zn Cl,; as a rule
these minima lie below the concentration 0.5 mol.

Finally I wish to express my hearty thanks to Mr. van LAAR
for the assistance he has rendered.

Amsterdam, Chem. Lab. Univers. Jan. 1901.

1) See preceding article.
2) Comptes Rendus CXXXI p. 883 (1909).
3) Amer. Chem. Journal Vol. 28, p. 89 and 512 (1900,,

(515)

Physics. — ,The equation of state and the theory of cyclic motion.”
By Prof. J. D. vAN DER WAALS.

It may be taken for granted that in the deduction of the equa-
tion of state the molecules at all temperatures under all pressures
are assumed to be invariable systems. As soon, therefore, as associa-
tion to more complex systems takes place, at which even the number
of atom systems (molecules) changes, this equation of state does not
hold good. But even when the systems are subjected to a less
radical change and e.g. the dimensions of the molecules in different
circumstances change, a and b can no longer be thought constant.
It is noteworthy that for the very first substance at which I tested
my equation of state (CO, according to the experiments of ANDREWS)
a value of 4 was found increasing with the temperature, and that
the only reason why I have not taken into account the variability,
was that the dependence of } on the temperature is unknown.

The very fact that the value of the specific heat at constant
volume for complex molecules does not at all square with that
found for monatomic molecules, shows that besides molecular motion
we shall also have to accept internal motion (atomic motion). The
fact that this atomic motion is more violent at higher values of 7
justifies the thought, that the molecules are really larger at higher
temperatures than at lower ones. The equation of state with constant
value of @ and 6 can therefore not hold good for substances with
any but monatomic molecules. That it has been applied to substances
with very complex molecules can be justified as an approximation
only when we assume that the internal forces which bind the atoms
together, are so considerable that by approximation the expansion of
the molecules may be neglected. Just as a liquid at a low temper-
ature, so if it is subjected to a great internal pressure, expands but
little, we may expect the expansion of a molecule to be slight, as
the molecule may be considered as an atomic system with a perhaps
much higher internal pressure.

That we shall have to consider the molecules themselves as
variable with p and 7’ and that there is therefore question of an
equation of state of the molecule itself, I have already indicated in
a communication, inserted in the Proceedings of the meeting of
Oct. 29% 1898, p. 138, in the following words: “The equation (f)
may be considered to contain the conditions for the stationary state
of the molecules.’ And in the way indicated there, so by means
of the virial-equation, I had since deduced an equation of state
for the molecule; but as many questions which arise in the

( 516 )

course of the deduction, could not be decided with perfect certainty,
and as it was impossible to fix on any grounds except those of
probability the relation which exists between the vis viva of the
atomic motion and that of the molecular motion at different temper-
atures, and in how far that relation can be variable at different
degrees of density of the substance, I have cast about for other
means to see in how far the form I am going to give would hold
good at least as an approximation. First of all by a way which
may be called chiefly thermodynamic, secondly by availing ourselves
of the theory of the cyclic motion.

From the equation of the virial we find |. c. also for substances
with complex molecules, the equation of state:

1
(pt N)@ 0) = 2m Ve,

whereas according to the method of deduction followed there, it is

not necessary to assume the molecules to be spherical. It only

appears that the value of J, being a multiple of the volume of the

molecules which themselves are in motion, must be thought variable.
dé -

For the value of —, which may be determined by means of

v7
dp aie
1S aD we find from:

== ae (sn) + (5):

Even if we assume N as function of v to be known, this equation
is not to be integrated, if we do not know in what way 0 is
dependent on v. But probably ¢ will have the following shape:

c= F(T) + P,—7( a) +P—7(S).

( 5ET)

If we namely imagine a substance with invariable molecules and
a molecular pressure not dependent on 7’, we find:

e= F(T) - #B,

: ; : dP,
in which P, is such a function of v, that N= ai
v

If the molecular pressure should be a function of the temperature,
we find, as according to thermodynamic rules is always the case

dP,
when the force depends on T, also the term — 7’ (=), and there-

fore :

e= F(T) +P,— r(=).

If the molecules should also be variable, and the atoms which
attract each other at varying distances from each other, the whole
energy will also vary with that which the atoms in the molecular-
aggregate have with regard to each other. Take P, as such a

x dP. : Hs Bi
function of b and 7, that =) , as will presently appear, is in
T

close relation with the forces which keep the molecule together, then
two new terms will be added to the value of «, at least if we
think also these forces as variable with 7’, and we shall find the
form of ¢ given above.

d
If we deduce from this (=) , we find:
Ti

dN Taye S dP, @P, dP, d?P, \ (db

=o ae 7 a Ee dT do e= mean) Gs)

. : : d
Having chosen the quantity P. in such a way, that N=(=-)
es

dN a st : aye
) =I , the above equation is sim-
v

and theref Tt Ga
erefore also 7 aT aa

plified to:

( 518 )

] 2

This equation gives the relation between the partial differential
quotients of 4 with respect to v and 7, and it can be satisfied if
il

we put ib =f |— ++

C |
Rae
P
Gale

1
From b—b) =f — ie

if namely the quantity C represents

C |

BTS we deduce:

LN eo ia a aay | }

(ale d li pet RT h=7 Rr RI?
and

Anes

(=) fier pe Saal eeeal ad

or
eS
Qe Shima

or

mman) = (aaa
dP,
d

tC — Ge equation (1) is satisfied.

So the following formula may be a solution of (1):

ARIE
b—by = L ’
IRR C
gs
or
VRT ee
by se ae
ptN+C 4+ (5) 4 (52)
P ‘dv 7 \db/r

(519)

Equation (2) is drawn up from the virial-equation by supposing
that at a given temperature the relation between the vis viva of
the atomic motion and that of the molecular motion is independent
of the degree of density of the substance and may be represented
for all temperatures by the constant value y. The quantity 4) in
equation (2) represents the value of 6, if 7 =O or at infinite
pressure, and may be called the limiting volume of the molecule.
It will therefore be in close relation with the voiume of the atoms,
of which the molecule is composed.

I did not, however, consider the way in which I had deduced
(2) from the virial-equation, to be perfectly reliable, and specially
the constancy of y seemed open to doubt. It is true that the result
of the thermodynamic deduction shows, that the given form (2)
is a probable one, but it remains an open question whether other
forms than the one given can also satisfy the partial differential
equation (1) — leaving the question whether the chosen form of «
is the most general, out of account.

These considerations made me attempt to investigate what might
be derived from the theory of cyclic motion for settling these questions.

Let us consider a gas at a given temperature and in a given
volume as a system which is in cyclic motion ').

If we take as first case the gas consisting of material points but
always, also in the following cases, as a statistic gas, so that all
velocities oceur equally at any time in any point in all directions.

Let the slowly variable coordinate be the volume; for the fluction
of the rapidly variable coordinate we choose the number of shocks,
to which an arbitrarily placed surface-unity, which we think impe-
netrable to substance, is subjected in one sec. If we call that number
s, the velocity of the material points may be proportionate to
and to a linear dimension of the volume, and the total vis viva
may therefore be represented by: “ea

LT = Av'ls §°.

We conclude also to this form, if we think, as Cuausius already
did, that the particles describe closed orbits, the linear dimensions
of which, with change of volume, are proportionate to Pv, and if

1) For the theory of the cyclic motion see: H. voN HrLMHoLTz, KRONECKER’s
Journal, Vol. 97, Pages 111 and 317. —L. Bourzmann, Vol. 98, pag. 68.

( 520 )

we think for the fluction of the rapidly variable coordinate a quan-
tity inversely proportionate to the time of revolution. The conception
that s represents the number of shocks against a certain surface,
has a closer analogy to the way in which MAXWELL applies the
cyclic motion to the behaviour of two currents. In this case s would
represent the number of particles which has touched the surface
counted from an initial moment or if we prefer, which has passed
the surface.

If from the given form of LZ, we derive the force which keeps
the stationary system in the given volume, we find:

dL 2
= — = — Ay" 52
P dv 3 wat
or
pv = ?/, L,

the wellknown relation, which is generally given in the form:
1
p= 3mm Ve

If we take secondly the case that the particles have a dimension
which may not be neglected and at the same time that besides the
pressure there are internal forces, the dimensions of the similar
orbits have the ratio (v—b)'/s and we have therefore the relation:

L= A(v—b)ls 52
and we find:

dP. dL :
p+ ( *) = — = 7/3 A (v—b)~"s 8°
dv

or

p+ CE fe-na te

The case, that P, is also a function of the temperature, can pro-
perly speaking not be treated according to the theory of cyclic motion,
at least not in so far as it has been developed as yet, but it could
not lead to a different result.

dL dP. ‘
For = Wwe find — (» + —), which means that the molecules
av

have to exercise as great a force in the opposite direction as is
exercised on them by the stationary system.

If we now put the case that the molecules themselves form com-
plex systems, the first question which arises is, whether the motion
of the atoms satisfies the condition which must be put to a cyclic
system. If we think that each of the atoms describes a closed orbit
round the centre of gravity, then we may consider the number of
times that the atom passes a certain point of its orbit again as
fluction of a cyclie coordinate, and the distance from the point chosen
to the centre of gravity as the slowly variable coordinate. Then
the velocity might be put proportionate to the product of 7 and 5;
but the question remains unsettled whether the forces which keep
the atoms together work in such a way, that the orbits with another
value of » and another of s may be considered as being similar.
This difficulty has no weight for circular orbits. Nevertheless, it
seems advisable to me not to consider in the first place circular
orbits, but rather radial ones. In order to be able to apply the
theory of the cyclic motion, we shall have to assume that the atoms
move along their way with a constant velocity, and that at the
end of their amplitude their motion is reversed by the collisions
with other systems and by the force which compels them to form
a system. If we take the distance counted from the centre of
gravity and if 7) is the shortest distance to which they can approach
the centre of gravity, the velocity may be represented as propor-
tionate to (r—r,)s, if s e.g. represents the number of times that
the atom reaches the end of its course in 1 sec.

The vis viva of this motion is then B (r—r,)? s?.

For the ease of diatomic molecules, we may therefore put:

L = A (vo—b)'/s 5? + By (117)? 8;° + Bg (ro—1 9)” 89”.

Just as for simple molecules we find:

iL IP. 2 Ae
Stes g claw "= — A (v—b) 3°
v 3

or

re 2 cae 2
(p+ <*) @-Y= ATF Hs Ty.

dv

35
Proceedings Royal Acad. Amsterdam. Vol. III.

(522 )

Before deriving the equation for the stationary state of the mole-
cule, we must first settle the question, what the quantity 4 is accord-
ing to this conception, and in what relation it is with (7;—79;)
and (72—ry9). A spherical form for the complex molecule is now
quite out of the question, even though the atoms should be spherical.
The form is more like a cylinder, which has the direction of motion
as axis, and one half of which has a section equal to the middle
section of the first atom and the other half a section equal to that
of the second atom. The molecule gets its smallest length when the
atoms touch, and the distance of their centres is equal to 9) + 79;
its greatest length when the atoms are forced to reverse their motions.
The molecule has therefore a variable length and so also a variable
volume. But there is question of a mean value of the volume
and in the same way we may choose mean values for r and 7, so
that, if the sections are S; and Sy, the equation is:

and

5 HL :
If we now determine a? and call the force which keeps the
av

dP,
atoms together rie find:
¢

dL dPy __ 2) \ poe LOB 9 Ay
i an AF oe aa (v—b) sg” -- 2 By (r;—701) 51 db a5
- dry
218) Chip) G2
BS 2 (72—T 2) 82 db

or

4+ Se

As we take the motions with a fixed centre of gravity as atomic
motion, the following equations are of force:

( 523 )

Mm, To} = My To
my) 1} == M1
m (71—7)) = My (72—7 09)
dr, dry
ry ~— -T3—To9
S, dry Sy dre S, dr, + Sp dry _ 4b

S) (73—791) = S2 (r2—7 02) ae S} ("3-1") + S) (r2—T 9) ¥ b—by j

So equation (3) furnishes

CHE CHE
(p++) 6 Bese Ge Es), aoe o ee)

which equation assumes the form of (2), if we may put y RT’ for
2 (Ly + Lo).

So we have still to deal with the same question, which we put
above. But it was to be expected that the theory of cyclic motions
would enable us to decide this question, as in many cases in these
cyclic motions the vis viva had proved to be an integrating divisor
of what we have to consider as heat which is to be supplied.

As the required heat will have to serve 1‘t to increase the vis viva
of the molecular motion, and 2¢ to perform the work of the different
forces both internal and external we may put:

dL \aL dL dry dL dry)
dv

1 — 1 ae
en! ay | ae? aah a ah

or

2 aN 2 ae.
gal A (v—b) 3 2 do ree A 0b) 3g? db +

+ 2 By (7) — 791) 81° ary + 2 By (7g — 1799) 89° Arg.

35*

(524 )

Let us write:

1 2
2 See —-
dLy = A(v—b) 5 Fd (v—b) + A (vB) Fa"

dL, = 2 By (ry — 701) 8? ary + By (1 — 701)? ds,"
dLg = 2 Bg (rg — 19) 82” rg + Bg (rg — 109)? d 89”.

Now we may bring dQ under the following form:

dIQ=L, d log [(v—b) “Is Lg] 4-Ly dlog [7 1791)? Ly) + Lo d log [(r2—1 92)? La-

This form may be simplified if we take into consideration that
my (7% —71) = my (rg—79g) and mL) = my Lg, and that we may sub-

; dl dr dr
stitute —— for and >. We get then:
—by Pula "2 T02

dQ = Ih log [(v—by'ls Ly] + (Ly + La) d log [(b—by)? (Ly + Le)].

If we call LZ, the vis viva of the molecular motion Z,,, then
[,+ LI, is the vis viva of the atomic motion Lg; and we may
also write:

dQ = Lm d log |(v—b) 73 Im] + Ly d log [(b—b,)? La].

It is assumed as being beyond doubt that L, is proportionate

OKO
to the absolute temperature, and that therefore che is a total differ-

m

ential.
Now

dQ

L .
= d log ((x—b) ‘Is Lm] +5 * d log ((b -by)? Lal.
sm

“m

( 525-)
The condition that the second member is a total differential is
Pt a La
satisfied if we put — = constant = /?).

“m

3

ee = RT, the entropy becomes:

\ a),
= R \ log (v—b) T's + log (b—2,)8 ° T? *

For the specific heat at constant volume we find from:

(e) = (Oe
LT OT

db 1)
cm er]? 4 SP sap ly
and for
)
eu. => Ra + A43—PR =

It is noteworthy, that we found for the molecular motion:
dP.
(p +S) (0-8) = "Js Dm

whereas we find for the atomic motion:

( Hes. sale; )

PG + aj Ota) = 2 Le

1) The condition that the second member is to be a total differential, would also

La E
be satisfied, if we could put = = ¢ [La (¢—-4)"). In so far, however, as I have been

able to examine, no acceptable results are to be deduced from such a supposition.

L
The supposition that = is constant at all temperatures and under any pressure, is
. m

however still open to doubt, as long as the impossibility of such a supposition has
not been proved.

(526 )

That the factor of the vis viva in the case of the atomie motion
is three times as great as in the case of the molecular motion, is
a consequence of the fact, that the molecular motion takes place in
all directions, whereas the atomic motion is thought as in only one
direction, and at any rate shows but one direction for the motion
of the two atoms at the same moment. Also if we had thought
the motion of the atoms in circular orbits round the centre of gravity,
we should have found the value 2 L, for the product of the forces
directed towards the centre and the space between the atoms.

1 { ‘
It is now but natural to assume, that Lag = mi Lyn, and in this

way to equate the product of the pressure and the space, which is
assigned to the motion, for the two cases. Then y=1. And we
come the more certainly to this conclusion if we pay attention to
what follows.

Let us imagine in the midst of particles moving in all directions,
a group which is forced in some way or other to move only in one
direction, e.g. in the vertical direction. Let this group be inclosed
in a vertical cylinder with mathematic walls. This group could not
resist the pressure which is exercised in a horizontal direction, so
against the vertical walls — unless we think this group so thin,
that the cylinder is but one molecule thick, in which ease the
matter of the molecules resists those horizontal pressures. Then the
motion has only to resist the pressure on the upper and lower
surface, and the product of pressure and volume must be 2 La.
If now this pressure is equal to the external pressure, brought
about by particles moving in all directions, then only the vis viva
in vertical direction contributes to that external pressure, which is
Mg of the total vis viva.

: 1 s Aen c
By putting Lig = | bamy we bring continuity between the vis

viva according to the vertical direction and so the theorem that at
given temperature the vis viva of the particles is equally great, is
extended also to those components of the vis viva, according to
which motion is possible. And just as in co-existing gas- or liquid
masses the great internal pressure to which the liquid is subjected,
does not disturb the equality of the vis viva, and only influences
the degree of density of the substance, in the same way it is not
to be expected that the perhaps much greater internal forces which
keep the atoms together, influence the equality of the components
of the vis viva of the still possible motions, and we have to regard
as the only influence of these forces the determination of the dis-

_— ee

a

( 527 )

tance of the atoms. We shall, however, have to apply this with
caution. We could easily think, that as two atoms move in the
molecule, the vis viva of each molecule would be equal to '/5 Ln.
This conclusion would be inaccurate were it only for the fact that the
vis viva of these two atoms is not equal, but that we have the
relation :

m, L, = my Lg.

We have to regard these two atoms, for which the motion of
the one is completely determined by the motion of the other, as
one, just as we do not take every half of a particle as a separate
whole.

3 T db

If we put this value of ? in Qa. = —R(14+/)+3 2R—___

P 8 e ol / v 3 (l+/)+3; (=) aT

we find:

f fH ‘db
ieee ay [2 autestw —) |.
+ aaa Rane

The unknown part which is to be added to 2 R, represents the
increase of the potential energy of the atoms. At infinite rarefaction
the equation of the equilibrium is simplified to:

LP
=? ()—b,) = RP.
db

But as by the deduction from the theory of the cyclic motion the
ease that P, should be a function of the temperature, is excluded,
we find by differentiating logaritmically :

d? Py
db? 1 Jan 1
yp souls “a
dP, b—b, (dT 1h
db
or

' PA:
db? fhe db
dP C= Cae

db

( 528 )

or
d?P,,
TP db Tdb db®

b=), dT a ee
“db

The supposition that the forces which attract the atoms towards
the centre of gravity, are proportionate to the deviation from the
shortest distance, would make P, of the second degree in b—,, and

dP, F
so —— of the first degree, and it leads therefore to:
€

pilings? 50
C= cee ce

With this value we find for a diatomic molecule:

(65 — 25 Tee

4975 : 4,94
(m the molecular weight), C,= :

a m
For CG, we find 3'/, R, and we get therefore:

As 2 may be equated to

. 4,94
For air CG, = 1,4 Sees 0,24. The value found by ReGNAULT

is 0,2377. But it is of course very doubtful whether the suppo-
sition Py = @ (b—bo)? is quite correct for all diatomic molecules.

In a following paper we shall have to apply the theory of the
cyclic motion also to polyatomie molecules and we shall have
to examine what influence this value of 6 whieh is variable with
the temperature and the pressure has on the equation of state.

( 529 )

Astronomy. — Report of the Committee for the organisation of
the observations of the solar eclipse on May 18 1901

a

drawn up by Dr. H. G. VAN DE SanDe BAKHUYZEN.

At the meeting of May 27 1899 the Academy appointed a com-
mittee to organise a Dutch expedition for the observation of the total
solar eclipse on May 18" 1901, which will be visible almost exclu-
sively in the Dutch-Indies.

This eclipse is of extraordinary importance because of its long
duration, (in the central line on the west coast of Sumatra it will
last 6!/, min. and on the east coast of Borneo 5'/, min.), so that
a great number of accurate observations can be made. The photo-
graphic plates will probably show indications of details, of which
nothing or only very little has been seen at former eclipses owing
to the short time of exposure together with the faintness of the light.

The organisation-committees in LHolland and in the Dutch-Indies.

The above mentioned committee appointed by the Academy, from
some of its members and other scientific men not belonging to the
Academy, consisted of by Messrs. J. A. C. Oupemans, J. C.
Kartryn, W. H. Junius, KE. F. van pe Sanne Baxkuvyzen, J. P.
VAN DER Stok, A. A. Nynanp, J. H. Witrerpink and H. G. van
DE SANDE Baknuyzen. It was very desirable however to assure
the co-operation of a committee in the Dutch Indies and in consequence
of a correspondence with the Colonial Minister, the Indian Govern-
ment asked the board of the “Natuurkundige Vereeniging in Neder-
landsch-Indié” to take upon them the preparations for the observa-
tions. For this purpose the board appointed a committee formed by
its President, our corresponding member Major J. J. A. Mucuer,
Rk. E. of the Staff, chief of the triangulation in Sumatra, Dr. S.
Fieve, acting-director of the Royal magnetical and meteorological
Observatory at Batavia and A. C. Zeeman, Inspector of the Govern-
mental navy, and of the beacons, lighthouses and _pilotage.

The two committees, always working in collaboration, had a twofold
purpose, first to prepare a Dutch expedition for the observation of
the important phenomenon, secondly to gather data in order to be
able to give information to foreign astronomers who intended to
observe the eclipse in India.

Financial support.

A large sum of money was required for the preparation and sen-

(530 )

ding out of an eclipse party, not only for the instruments and for
the voyage and the maintenance of the observers, but also to enable
some members of the expedition to take part in the observations
of the total eclipse of May 28 1900, and to visit some foreign
observatories in order to prepare themselves for the task in India.

Already before the committee had been appointed Mr. NyLanp by
means of private contributions had collected a considerable sum for
this purpose. This sum, though large, was not sufficient and has
afterwards been greatly augmented, in the first place by the resolution
of the East-Indian Government, which, at the request of the
“Koninklijke Natuurkundige Vereeniging in Nederl.-Indié’’, has allowed
the yearly sum on the budget for scientific expeditions, to be used
for the Dutch eclipse-party and moreover by the sum which his
Excellency the Home-minister had placed at the disposal of the
committee in 1900, and which, we expect, will be granted us again
this year.

The “Hollandsche Maatschappij der Wetenschappen te Haarlem’,
the “Proyinciaal Utrechtsch Genootschap” and the “Koninklijke
Natuurkundige Vereeniging te Batavia’, have also sent us consider-
able contributions, but we are especially glad to record the fact that
several private persons, besides those who at the beginning had pre-
sented us with large gifts, were ready to give us financial support
in the most liberal way.

Another important contribution was received by the committee
from the Indian Government, which put at the disposal of the “Ko-
ninklijke Natuurkundige Vereeniging” at Batavia 30 copies of 27 maps
of differents parts of Sumatra and Borneo. Lastly I have to express
my indebtedness to the directors of the steam-navigation company
“Nederland”, who allowed a reduction in the fares for the members
of the expedition and their luggage, and has done much to render
the transport of the instruments safer and more convenient.

When it appeared that the financial conditions would allow the
sending out of an expedition, one of the chief requirements was to
find competent persons to make the observations. The committee
was fortunate enough to find two of its members Mr. J. H.
Witterpink, lecturer of astronomy and observer at Leyden and
Professor A. A. Nytanp of Utrecht willing to take this task upon
themselves, while Mr, J. J. A. MULLER in India was ready to officiate
as chief of the expedition. His scientific abilities and his thorough
acquaintance especially of the west part of Sumatra, of which the
triangulation was made for the greater part under his direction, ren-

a

(531)

ders Mr. Mutver’s collaboration of great importance for the success
of our expedition.

When afterwards it appeared desirable for the spectroscopic and polar-
imetric work, that a physicist should go with the expedition, we were
happy to find the member of our committee Prof. W. H Juttus
ready to join the party. Mr. MULLER informed us that Captain
Wacker at Batavia who has taken part in the triangulation of
Sumatra and Dr. Fragen, acting director and Dr. vAN BEMMELEN
acting vice-director of the meteorological observatory will join the
Dutch expedition whereby a valuable addition to the observing staff
is secured.

In India moreover we hope to avail ourselves of the assistance
and collaboration of some officers of the general staff and of the
officers and the men of a man of war, which probably, thanks to
the kindness of the commander of the navy, will lie during the
eclipse in the neighbourhood of the observing station chosen by the
committee.

Observations and instruments.

The observations which the members of the expedition expect to
make are:

1. Photographs of the corona.
2. Spectroscopic observations of the corona.

3. Spectroscopic observations of the flash in the immediate neigh-
bourhood of the sun.

4, Determinations of the polarisation of several parts of the corona.

5. Determination of the heat radiation from the corona.

6. Determination of the brightness of the corona.

7. Observation of the shadow-bands.

8. Determination of the electrical condition of the air during the
eclipse.

9. Determination of the terrestrial magnetism.

10. Observations of temperature, atmospheric pressure and force of
the wind.

For these observations the following instruments will be used.
1. Photographs of the corona.

As the brightness of the corona at different distances from the

( 532 )

sun’s limb is very different, it is impossible to obtain in the ordinary
way a photograph, on which all parts are equally visible. If the
image of the corona near the sun’s limb shows distinct peculiarities,
there will be no visible impression at a greater distance from the
sun, and if those more distant portions are visible on the plate, the
image of the inner part of the corona will show no detail at all.
For this reason it has been resolved to use a number of different
photographic cameras: a. of great focal length and accordingly with
a small value of f/a (f=focal length a=aperture) giving large images
of small intensity, and therefore suitable for the reproduction of the
inner parts of the corona; b. of small focal length and with a great
value of f/a giving small but very bright images, and showing
the most remote parts of the corona; and finally c, a photographic
telescope with an arrangement according to BURCKHALTER, where a
specially shaped screen rotates with great rapidity directly in front of
the sensitive plate and so diminishes artificially the intensity of the
light of the coronal portions near the sun’s limb. In this way a
distinct image of a very great part of the corona may be obtained.
The photographic apparatus are then:

1. A photographic object glass lent by the Observatory at Was-
hington of about 12 m. in focal length and about 11 c.m. in aper-
ture. The proportion f/a is 1: 92, and the diameter of the image
of the sun is about 0.5 ¢.m.

By means of a light-tight tube of wood and cloth the object glass,
firmly mounted on a pillar, is connected with the plate-holder also
in a fixed position. A mirror sends the sunlight through the object
glass into this telescope.

2. A photographie object glass of SrEmNHEIL, belonging to the
Utrecht observatory, 3,45 m. in focal length and 27 ¢.m. in aperture;
fia = 1: 12,8, giving an image of the sun of 3.2 ¢.m.

For this object glass an iron tube is constructed, which is fastened
to a parallactic mounting from the Leyden Observatory, which by
means of a clock follows the diurnal motion of the sun. Three of the
above mentioned revolving discs of BURCKHALTER have been constructed
after the indications of Mr. Nytanp to be used in conjunction with
this object glass (one for each plate), the axes passing through holes
in the sensitive plates are rapidly revolving by means of a clock.
Mr. Nytanp had also a simiJar revolving screen of BURCKHALTER
made for the long telescope of 12 m. focal length.

3. A photegraphic object glass of DALLMEYER lent us by “TEYLER’s

Dos )

Genootschap” 1.52 m. in focal length and 10.8 c.m. in aperture ;
f/a =", with an image of the sun of 1.4 c.m.

4. A photographie double-lens of VorGTLANDER und Sonn 0.87
m. in focal length and 10.8 c.m. in aperture; f/a = '/, giving an
image of the sun of 8 m.m in diameter.

5. <A photographic double-lens of VorarnanbeR 0.38 m. focal

length and 10.8 c.m. aperture; f/a = '/35, diameter of sun’s image

to) ) / ’ to)

3.5 mm. For each of the three last object glasses a teak-wooden

tube has been constructed, carrying at its other end the wooden
) ‘ te)

plate-holder.

6. An amateur-camera with the back-lens of a collinear object
glass of VorgTLanper, 0.35 m. focal length and 35 m.m. aperture,
which probably will be reduced by a stop. The image of the sun
is 3.3 m.m. in diameter.

During the observations the four last photographic apparatus will
be fastened to a square wooden case, provided at both ends with steel
axes running on ball bearings, by which a very smooth motion is
obtained. At one end of the case a wooden secior of about 2.7 m. radius
has been fixed perpendicularly, and by means of a chord attached
to the sector and clockwork, the case with the cameras rotates at
the rate of the diurnal motion. If the axis of the case is adjusted
in the direction of the polar axis and the cameras have once been
pointed to the sun, they will remain in that position.

2 and 3. Spectroscopic observations.

For this purpose 4 spectrographs and one visual spectroscope
will be used.

One of these spectrographs is a prismatic-camera of COOKE, con-
sisting of an ordinary camera with an object-glass, Cooke’s triplet,
achromatized both for actinic and visual rays, of 16,2 c.m. aperture
and 2.60 m. focal length; in front of the object-glass are placed
two prisms with an angle of 45°, covering the whole aperture of
the object-glass.

When this apparatus is directed towards the totally eclipsed sun,
we obtain on the sensitive plate a series of images of the corona
and of the ring immediately surrounding the sun’s disc, of the different
colours which compose the light of the corona and of the ring.

The dimensions and shapes of these different images, which pro-
bably will be very numerous, will show distinctly where the sub-

( 534 )

stances are situated, whose light forms the pictures on the sensitive
plate. Moreover it will be possible to determine the refrangibility
of those different kinds of light from the positions of the images
although the accuracy of this determination will probably be less
than that of the refraction-indices from the measurement of the
spectra obtained by means of the slit-spectrographs.

Another spectroscopicinstrument is a slit-spectrograph, constructed
by Mr. Torprer at Potsdam after the indications of Mr. WILTER-
DINK in consultation with professor SCHNEIDER of Potsdam.

The lens projecting the image of the sun on the slit is a photo-
graphic double-lens of VorarTLinper of over 10 c.m. aperture and
38 cm. focal length; two photographic double-lenses of 36 m.m.
aperture and 13 c.m. focal length of Zetss serve as collimator- and
cameralenses. The dispersion is obtained with two large Rutherfurd
prisms 60 X 35 m.m. from C, A. STEINHEIL of Munich.

We intend to use this spectrograph for the general corona spec-
trum and for the spectrum of the upper parts of the photosphere
the so-called flash.

By accurate measurements of this corona-spectrum the uncertainty
still existing about the refrangibility of the corona hght will prob-
ably be removed. Moreover we hope to learn from its spectrum
something more about the origin of the light of the flash.

The hypothesis, developed by Prof. W. H. Junius in his in-
teresting paper read at the meeting of our Academy of February
24th 1900, that this light (flash) may be caused by an abnormal
dispersion of the ordinary sunlight, has received new support by
the investigations of Prof. Woop of Wisconsin University. The
determination of the refractive-indices of the different lines in the
spectrum of this light will probably prove to be an important con-
tribution towards a judgment about this question.

The flash appears immediately after the second contact and as
the layer which sends the light to us is thin, it disappears on the
central line within one or two seconds. In order to obtain a photo-
graphic image of this spectrum, while the calculated moments of its
appearance can be several seconds in error, the sensitive plate will
be exposed some time before totality begins, and will be slowly
moved by a clock, belonging to the Utrecht Observatory, until a
few seconds after the second contact. The plate will then show
next to each other the ordinary spectrum of the sun and the
spectrum of the flash with its bright lines. ‘This juxtaposition of
the two spectra has the advantage that the situation of the dark
and the bright lines in the two can be easily compared.

i i i i i

Rw ne

( 535 )

Another slit-spectrograph, also made after Mr. WILTERDINK’s
design by Torprer, has a greater dispersion than the foregoing.

The image of the sun is formed on the slit by a photographic
doublet of 8 c.m. aperture and 61 c.m. focal length, while two
photographic double-lenses of 5.5 c.m. aperture and 42 c.m. focal
length, like the first of VorarLANDER, served as collimator- and camera-
lenses. The dispersion is obtained by three large Rutherfurd prisms
made by SternHein 6055 m.m. We hope that it will be possible
to determine with this spectrograph the motion of the particles
which make up the corona, by a comparison of the spectra
of the corona on both sides of the sun at the place where the
greatest velocity of the particles in the direction towards and from
the earth is to be expected.

The spectrograph will be pointed so that the centre of the
image of the sun falls on the middle of the slit, and as the
length of the slit is much greater than the diameter of the sun’s
image, the spectra of the two parts of the corona situated on both’
sides of the sun will be obtained on the sensitive plate.

In order to determine the mutual position of the corresponding
lines in those two spectra, which on the plate are at a rather large
distance from each other, a comparison spectrum of iron will be
formed in the intermediate space by electric sparks between a pair
of iron electrodes before the slit.

A fourth spectrograph on purpose to still better examine the
bright line spectrum of the sun’s limb, consists ofa plane diffraction
erating of RowLaNnD, 3755 m.m., of 14438 lines to the inch;
the object glass has an aperture of 62m. m. anda focal length of 1 m.

This instrument is to be mounted near the limit of the zone of
totality, because there the moon’s limb at the end of the sun’s
diameter, perpendicular to the direction of the lunar motion, moves
along the sun’s limb so that the duration of the flash will be very
much prolonged.

Lastly visual observations will be made with a fifth apparatus,
namely a slit-spectroscope with great dispersion belonging to the
Utrecht Observatory; the condenser is an object-glass of STEINHEIL
of 10.8 e.m. aperture, and 0.864 m. focal length.

All this spectroscopic apparatus will be mounted in an approximately
horizontal stationary position and the solar light will be reflected into
the instruments by means of silvered glass mirrors. As the sun
moves on during the observation, the mirrors should move so that
during the totality the reflected rays keep a constant direction.

With Row Lanp’s diffraction grating this will be obtained by means

( 536 )

of a coelostat with a mirror of Sremnem of 108 em. in diameter,
belonging to the Utrecht Observatory; while the prismatic camera, the
two slit-spectrographs and the visual spectroscope will be used with
siderostats made by Gautier of Paris.

These consist each of an axis, mounted in the direction of the
polar axis rotating by means of a clock in exactly 24 hours; to
each of the ends of this axis a mirror is attached, and this being
once adjusted so that it sends the light of a given point of the sun’s
limb in the direction of the polar axis towards one of the spectro-
scopic apparatus, the direction of that reflected pencil will remain
unchanged.

But it is the direction of this pencil only which is stationary,
and which forms a single image, the reflected images of all the other
points will rotate very slowly round the image of that fixed point.
This slight movement does not influence the spectroscopic observa-
tions, but if the reflected image were required for obtaining a
picture of the corona, its distinctness would be lessened by the
motion.

If a stationary reflected image is desired, as for instance for
photographing the corona with the above mentioned horizontally
mounted long telescope of 12 m. focal length, the reflection must be
brought about in an other way. For this purpose the coelostat of
LIPPMANN is very suitable; in this apparatus the mirror, parallel to
the polar axis is attached to a metal axis also adjusted in the same
direction and rotating once in 48 hours. According to Mr. WIL-
TERDINK’s indications GauTIER has in a simple manner attached
such a coelostat to one of his siderostats, and its mirror reflects the
sun’s rays into the long telescope of 12 meter.

4. Determination of the polarisation of the corona.

Prof. Junrus intends to make a number of polarimetric meas-
urements in order to get to know, for as large a number as possible
of well determined places on the corona, the percentage of the
polarised light.

For reasons easily to be understood the use of a mirror had to be
avoided; therefore a telescope of STEINHEIL-SCHRODER (belonging to
the Leyden Observatory) equatorially mounted was arranged for these
measurements. The object-glass has an aperture of 10.8 ¢.m, anda
focal length of 275 c. m.; the diameter of the moon’s image is therefore
about 2.5 e.m. During the observation an assistant will keep the
central point of the moon’s image in the optical axis of the telescope,

(537 )

by means of a finder and of a system of rods. Instead of the eye piece
a modified polarimeter of Cornu, is attached to the end of the tube
so that the diaphragm with a square hole, 1 m.m.?, (of which the
polarimeter forms a double image) is situated in the focal plane.
The whole polarimeter has two motions, one radially on a slide, so
that the diaphragm may come at any desired distance from the axis
of the telescope and secondly a rotatory motion round the optical
axis of the telescope. The distances radial and angular of each
chosen point of the corona can thus be read.

In order to be able to choose those places of the corona most fit
for measurements of polarisation, the following arrangement is made:
by a quick movement the small diaphragm will be easily removed,
and a glassplate put in its place on which an etched square of
1 m.m*. indicates exactly the spot, which afterwards will be taken
up again by the hole in the diaphragm. If the place is chosen, an
assistant reads the distance and position angle and the analyser is
moved so that both images will have equal brightness. From the
position of the analyser the quantity of polarised light may be derived.

The polarimeter with its accessories has been made in the physical
laboratory at Utrecht.

Preliminary experiments, made by means of an artificial corona,
showed that it will be possible under favourable circumstances to
obtain in 6 minutes for at least 12 places of the corona trustworthy
values for the ratio of polarised light.

5. Determination of the radiation from heat of the corona.

The investigation of the heat radiation from the corona, is also very
important for the explanation of this phenomenon, the more so as
a great uncertainty still exists, not only about the distribution of
this radiation over the spectrum, but also about the question as to the
order of magnitude of the total radiation, as appears from the con-
tradictory results obtained on one hand by Axsort, on the other
by Destanpres during the eclipse of May 28, 1900 and later.
Prof. Junius thought it therefore best to try in the first place to
express the amount of radiation of heat from the whole corona in
absolute measure, by comparing it directly with the amount of the
radiation from the uneclipsed sun, the sun’s constant.

For the determination at the eclipse station of the latter radiation
a pyrheliometer of Knur Anasrrém of Upsala will be used. Prof.
Ayastrim has been so kind to test himself the instrument destined
for the expedition and to indicate some of its constants.

36

Proceedings Royal Acad. Amsterdam, Vol. LIT

(538 )

The pyrheliometer however is not constructed for very weak
radiation, and cannot be used for it. Therefore Mr. Junius has
made a very sensitive thermopile, which in connection with a resist-
ance-box purposely made for it and a galvanometer of Du Bois
and Rupens, will enable him to compare amounts of heat-radiation
in all ratio’s from 1 to 100000.

The thermopile is exposed directly to the radiation without mirrors
or lenses, and each time the resistance is so adjusted that the
galvanometer gives trustworthy indications. When disturbing influences
are eliminated, we may accept without restriction that, when the
amount of the radiation is very small, the current is proportional to
the absorbed heat.

For strong radiations we can examine by means of the pyrhelio-
meter, in how far the proportion still remains. As the difference in
temperature between the junctures of the thermopile, when it is
exposed to the sun’s radiation in the tropics, will probably not exceed
30° C. it is to be expected that the deviation from the law of propor-
tionality will not be very large; at any rate it can be accounted
for. The plan of observation is to repeatedly measure the heat
radiation during the whole time of the eclipse, from before the first
till after the fourth contact, at well determined moments which comes
to us from the sun and its immediate surroundings. The apparatus in
which the thermopile is mounted, has been so arranged that the radia-
tion is received only from a circular portion of the sky 3° in diameter.

As long as the radiation of the disappearing or the reappearing
disc of the sun is strong enough, observations will also be simulta-
neously made with the pyrheliometer for testing purposes ; it is expected
that the thermopile will be able to give indications of the radiation
during the whole eclipse. During the totality the apparatus is
alternately pointed to the corona and to neighbouring places of the
sky outside the corona; from the variations of the galvanometer
readings, the amount of the corona radiation will be derived, as a
suitable zero cannot be obtained by covering the opening with a
screen.

A description of the arrangement of the thermopile and of the
elaborate precautions taken to eliminate all disturbing influences,
which cause difference of temperature between the junctures, will
be given later. Here I record only that in October 1900 on
the same day the radiation of the sun and that of the full moon
was measured with a provisionarily constructed thermopile and
galvanometer, both of which were much less sensitive than the
instruments to be used for the eclipse. ‘The radiation of the moon

( 539 )

falling through a diaphragm (opening 5.5 m.m. in diameter) gave
then a deviation of 4.5 divisions, with an error of about 0,5, the
proportion of that radiation to the radiation of the sun at noon
was found to be 1 : 80000. With the new instruments at least
1/5, of the amount of the moon’s radiation will be sufficient to make
the galvanometer show measurable deviations.

6. Determination of the light-intensity of the corona.

It will be possible to derive the relative photographic brightness
of the different parts of the corona from the photographs made.
But there will be made also observations of the total visual intensity
of its light, by means of a photometer of WEBER (comparison with
a benzine flame at a variable distance) belonging to the meteorolo-
gical Observatory at Batavia.

7. Observation of the shadow-bands.

The direction and the velocity of these shadow-bands during the
eclipse will be determined by observing their motion across horizontal
and vertical screens suitably placed.

8. Determination of the atmospheric electricity.

An electrometer of the meteorological Observatory at Batavia wiil
register the atmospheric electricity, first on the ordinary rotating
cylinder, and then during a period of 6 hours (from 3 hours before
till 3 hours after totality) on a cylinder of which the period of
rotation is only 1/, of the former, so that it will be possible to
determine the variations during the eclipse with greater accuracy,
and to investigate whether the electric potential decreases during
the totality.

9. Terrestrial magnetism.

The observations of the three elements of terrestrial magnetism will
be made at Buitenzorg or Batavia. At Padang the declination and
horizontal intensity will be measured by a self-registering EscHEn-
HAGEN’s intensity-variometer and other variation-instruments, to be
provided by the observatory at Batavia.

( 540 )
10. Determinations of temperature, atmospheric pressure

and force of the wind.

The temperature will be determined by AwtsMANN’s aspiration
thermometers of the Observatory at Batavia, and further by means
of a thermograph (large pattern) of RicHARD.

The atmospheric pressure will be determined by ordinary baro-
meters and further, by a barograph (large pattern) of RicHarD.
The pressure of one millimeter mercury is represented on the scale
by 3 millimeters.

The direction and force of the wind will also be determined in order
to know whether at this eclipse, as in former cases, a sudden eclipse-
wind will be observed.

Selection of the observing station.

For almost all the observations it is necessary that the observing
station should be in the neighbourhood of the central line, because
there the totality lasts longest and the sun is covered by the moon
symmetrically to the direction of its axis. This central line runs
from about west to east a few degrees south of the equator. In our
East-Indian colonies it passes over Sumatra, a little south of
Padang, over Borneo south of Pontianak, and then over Celebes south
of the gulf of Tomini, over Boeroe and Ceram and over New Guinea.
On the central line the duration of the totality decreases from West
to East, at the west coast of Sumatra it lasts 6 min. 30 sec., in
New Guinea about 3 min. 30 sec.

Besides the duration of the phenomenon ihe selection of the
astronomical site depends for a great part on the convenience for
the transport of the many heavy boxes with instruments, the state
of the ground with a view to the mounting of the instruments and
on the possibility of getting assistance in the transport and the
preparatory work. The examination of these circumstances and the
advice to be given accordingly, had to be left to the care of the
Indian committee.

For the determination of the weather to be expected, the meteoro-
logical Observatory at Batavia could dispose of rain-observations over
a long period in a great number of places in our East-Indian
colonies and further of general records on the cloudiness in differents
parts of the Indian Archipelago.

(541 )

But as it was important to know the cloudiness and the duration
of the sunshine especially at different points on the line of totality,
the meteorological Observatory at Batavia has in twelve places orga-
nised observations on the cloudiness and the sunshine during the
months April, May and June 1900.

The results of all the meteorological observations, which are im-
portant for the selection of the observing station, have been recorded
by Mr. J. J. A. Munuer and Dr. 8. Ficke in a paper “Informa-
tion for observing parties and climatological conditions along the
track of the moon’s shadow’, in which also information is given
about the character of the different regions, the means of transport,
residence etc., which will have special interest for foreign astrono-
mers, who will go out to observe the eclipse.

The meteorological condition near the equator is on the whole not
very favourable ; at the several meteorological observing stations hardly
any day in May 1900 was perfectly cloudless. But then the clouds
do not cover the whole sky, and in the cloudless parts the air is
clear and very transparent.

The number of days on which at noon (the moment of the eclipse),
the sun was visible near the central line in Sumatra and Borneo, in
May 1900 varies from 10 to 30; in most places the number is more
than twenty; but it is not allowed to derive general conclusions from
these numbers as they represent the results of one month only.

The difference between the meteorological conditions in May 1900
at the different stations was not large, except in a single case.

Perhaps in the interior of Borneo the probability of bright
weather is a little greater than in Sumatra, but in Borneo the trans-
port and the mounting of the instruments would give more difficulties.

Jn order to obtain as much certainty as possible for their report
about the most suitable observing station, Messrs. J. J. A. MULLER
and §. FicEE visited many places in Sumatra from 16 September
to 1st October 1900. As the result of their considerations they
have recommended to us for our observing station a place in the
neighbourhood of Painan, on the West-coast of Sumatra, south of
Padang; and for the present this point has been chosen as the
station of the expedition.

It offers the advantage of being in the neighbourhood of Padang,
the seat of the government of the West-coast of Sumatra and the
residence of the director of the railway in Sumatra and of the work-
shops belonging to it, of which much use can be derived for the
arrangements of the observing camp.

( 542 )
Information for the observers of the eclipse.

As I have mentioned already, one of the purposes of our com-
mittee was to give information to persons who wanted to observe
the eclipse in India, in the first place to foreign astronomers. And
it is especially for them that Messrs. MULLER and FiceEr have published
the above mentioned “Informations ete.”, which have been sent by them
and by the Dutch committee to those societies and astronomers
who were thought to have an interest in them.

As I have mentioned we have received from the “Koninklijke
Natuurkundige Vereeniging” at Batavia 30 copies of 27 maps chiefly
of different parts of Sumatra and Borneo, put at their disposal by
the Indian government.

We have distributed a great number of those maps among the
astronomers who intend to observe the eclipse, so that they will be
able to find their way in the stations they have selected. When
these astronomers apply to the local authorities on their arrival in
India, they will there obtain any assistance and information they
require.

The following foreign expeditions, as far as we know, will go to
the Dutch Indies :

1. Mr. Newaur from Cambridge and Mr. Dyson from Greenwich.
2. Mr. Lockyer from London.

3. Count DE LA Baume PLuvINEL from Paris.

4. A Russian expedition.

5. Prof. Barnarp from Yerkes Observatory near Chicago.

6. Prof SkinNER from the U.S. Naval Observatory in Washington.
7. Prof. JeweLL from the John Hopkins University.

8. Prof. BurcKHALTER from California.

9. Prof. Perrine with some assistants from Lick-Observatory.
10. An expedition from the technological Institute of Boston.

11. Mr. Topp from Amherst Observatory.

Probably still other English observers will join these.

Besides the information mentioned, especially for the use of astro-
nomers, some members of the committee have given a list of
instructions for eclipse work for amateurs not provided with great
astronomical instruments. These instructions were sent to India
some time ago.

( 543 )

At the end of this report the committee would like to express
their indebtedness to all who have helped them in their task and
have enabled them to send out the expedition.

To His Excellency the Home minister, the “Hollandsche Maat-
schappij der Wetenschappen”, the “Provinciaal Utrechtsch Genoot-
schap”, the “Koninklijke Natuurkundige Vereeniging” at Batavia, and
especially to the various persons who have given financial support.

To His Excellency the Colonial Minister, who has supported our
requests to the Indian government; to the Indian government itself
who not only gave us a considerable contribution, but who also
enabled Messrs. MuLier and Fick to make the above-mentioned
expedition in September 1900, and allowed them and other Officers
of the General Staff and of the Observatory at Batavia to join the
expedition, and who in May will send a man of war to Padang,
of which the officers and men will assist in the observation of the
eclipse. Our last but not our least thanks is due to the Hast-Indian
eclipse committee, who have taken every pain and trouble to prepare
things in such an excellent way in India.

After this report was written tidings are received that according
to a royal decree of February 16% 1901 N°. 33 Dr. W. H. Junius
and Dr. A. A. NynaNnb, professors at the University of Utrecht
and Mr. J. H. WivrerpryKx lecturer and observer at the Uni-
versity of Leyden are charged to go to India with a view to the
university interest, in order to observe the total eclipse on 18%
May 1901.

This new proof of the interest shown by our government in
this expedition is received with much thanks.

(March 22, 1901).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday March 30, 1901.

OG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 30 Maart-1901, Di. IX).

Contents; J. H. Bonnema: “On the occurrence of remains of Leperditia grandis ScHrENCK
>

sp. in the erratic blocks of the Groningen diluyium” (Communicated by Prof. J. W.
Morr), p. 545. — Prof. J. A. C. Oupemans: “On the contents of the sixth and
last part of the Report “Die Triangulation von Java’, p. 549 (with one plate). —
Dr. Ernst Conen and E. H. Bucuner: “Erarp’s law of solubility (Communicated
by Prof. H. W. Bakuuis RoozEBoom) p. 561. — Prof. J. C. Kiruyver: “On the
expansion of a function in a series of polynomials”, p. 565. — Prof. J. D. van
DER Waats: “The equation of state and the theory of cyclic motion” II, p. 57i. —
J. Branp: “Researches on the secretion and composition of bile in living men”,
(Communicated by Prof. B. J. Sroxvis) p. 584. — Prof. M. W. Bewerinck: “On
oligonitrophilous Bacteria” p 586. — Dr. C. H. Wiyp: “On the irregularities of the
cadmium standard cell”, (Communicated by Prof. H. W. Bakuvis RoozEBoom) p. 595. —
S. L. Scuouren: “A pure culture of Saprolegniaceae”, (Communicated by Prof.
F. A. F. C. Went) p. 601.

The following papers were read:

Geology. — J. H. Bonnema, at Leeuwarden: “On the cccurrence

of remains of Leperditia grandis SCHRENCK sp. in the erratic
blocks of the Groningen diluvium.” (Communicated by Prof.
J. W. Mott).

(Read November 24, 1900).

1852. Cypridina grandis A. Scurenck. Survey of the upper silurian

shaft-system in Livonia, Esth- and Kurland. Dorp. Archi-
wes; series I, Vol. I) p58:
37

Proceedings Royal Acad. Amsterdam. Vol. ITI.

1858.

1858.

1859.

1882.

1883.

1884.
1891.

( 546 )

Leperditia Baltica FR. von Soumipt. Researches into the
silurian formation of Esthland, North Livonia and Oéesel.
Dorp. Archives, Series I, Vol. 274, p. 171 and 192 (ex
parte).

Leperditia gigantea F. Roemer. On a gigantic species of the
genus Leperditia. Journal of the German Geological society
Vol. 10%, p. 356.

Leperditia grandis FR. VON ScHMIDT. Some communications
on the geognostic condition of the Isle of Gothland. Dorp.
Arch. Series I, Vol. 2"4, p. 455.

Leperditia grandis Ercuwawp. Leth. ross, anc. per. page 1332,
plate 51, fig. 9, a, b,c.

Leperditia gigantea J. BARRANDE. Supplement to Vol. I, on
the silurian system of central Bohemia, page 535, plate
a4, figs 4. 5.0;

Leperditia grandis FR. von Scumipt. Miscellanea Silurica I.
On the Russian silurian Leperditiae, Academ. Memoirs
St. Petersburg, Vol. XXI, No. 2, page 10, fig. 3,4, 5, 6.

Leperditia (Isochilina) gigantea F. Roemer. Leth. pal. Atlas,
plate 19, fig. 8.

Leperditia grandis Koumopin. Ostracoda silurica Gotlandiae.
Scientific Acad. treatise. N°. 9, page 135.

Isochilina grandis Jones. Some Cambrian and silurian Leper-
ditiae and Primitiae. Ann. and Mag. Nat. Hist. series 5,
Vol. 8, page 347.

Leperditia grandis FR. v. Scumipt and Jones. On some
silurian Leperditiae, Ann. and Mag. Nat. Hist. series 5%,
Vol. 9%, page 169.

Leperditia grandis NévLinc. The Cambric and silurian erratic
blocks of East- and West-Prussia. Annais of the Prussian,
geol. government Institution, p. 295. (Preuss. geol. Lan-
desanstalt.)

Leperditia grandis Fr. von Scumipr. Miscellanea Silurica
III. Sequel to the Russian Silur. Leperditiae, Academ.
Memoirs. St. Petersburg, series VII, Vol. XX XI, N°. 5,
page &.

Leperditia gigantea F. Roemer. Leth. errat. page 84.

Leperditia gigantea Krause. The Ostracoda of the sil. dilu-
vian erratic blocks. Seientifie supplement Program of the
Luisenstidtischen Oberrealschule at Berlin (a first-class
High-school, a town institution).

(547 )

One of the most remarkable phenomena, I observed, when study-
ing the sedimentary boulders of the Groningen Hondsrug, I consider
to be, the repeated occurrence of limestone, with remains of Leper-
ditia grandis Scurenck sp. For of this interesting Lep. species
twenty-two, more or less intact valves, of different sizes, are kept
in the Geol. Museum of the Groningen University, among the col-
lection: “Groningen Erratic Blocks”; the specimens found still out-
numbering those of the collection.

That large number is rather remarkable, considering that in the
whole of Germany, only three specimens have been found, i. e. in
East Prussia, one at Lyck, and two in the neighbourhood of Konings-
bergen.

Up to now no statement has been made of a single specimen having
been found in the whole stretch of land, between East Prussia and
Groningen.

Leperditia grandis SCHRENCK sp., can be easily recognised, both
for its dimension and for its morphological characteristics. As the
name indicates, it may attain to an extraordinary size, for Leper-
ditia. So e.g. the largest valve (a right one) that has been found at
Groningen, has a hinge-line, 20 m.m. long, whereas the largest valve
of the other Leperditia species, found there, has a hinge-line of 15 m.m.
Jt is a vight valve of Leperditia Baltica His sp. The eye-tubercles
are very strongly developed. The ventral border is nearly straight,
and gradually slopes up from the back to the front. The greatest
thickness (distance from one valve to the other) is found close to
the ventral border and diminishes paraHel with it.

Both valves have behind the eye-tuberele a groove (sulcus), which
from the central spot runs vertically up to the dorsal margin.

At the anterior and posterior borders both valves present a wide,
depressed margin.

The right valve has a round opening im the places where those
marginal rims end.

The left valve behind the suleus. which from the central spot
runs up to the dorsal margin, has bulged out in growing, a thing
which is most distinctly to be seen in the oldest specimens.

Only in the middle of the ventral border, this valve has a little
developed inverted ventral plate.

The species of stone, in which by far most remains of these
Leperditae have been found, may be easily recognised.

It is a sort of close grained slivery limestone, of a light grey,
some times greenish colour.

Through corroding, it turns more yellowish grey.

Os
-!
*

( 548 )

Through it run, in crystalline calc. spars, petrified coral trees of
the species called Laceripora Cribosa Ercnw.

In this stone-formation, besides Leperditia grandis SCHRENCK sp.
and Laceripora cribrosa Ercuw. sp.: Iliona prisca His, and Meres-
tina didyma Dalm sp., have been found.

The very nature of this species of stone, renders it, as a rule,
difficult, to get the specimens out undamaged.

There is greater, possibility of success, when they are embedded
in layers of a softer substance, which one now and then comes across.
Much rarer than in the above mentioned slivery light grey limestone,
remains of Leperditia grandis occur in fine-grained, more brownish
limestone, which also contains coral trees of Lacipora cribosa.

Remains of Leperditia phaseolus His. sp. and of Proetus conspersus
Ang. are also found in it.

As to their age, both sorts of limestone, must be ranked with
the Upper-Oesel layer and more especially, with the yellow zone of it.

This sufficiently appears from the fossils, they contain.

To conclude, there remains to be traced whether such like stone-
formations are still known to exist as compact rocky masses.

Limestone, with remains of Leperditia grandis, is found in a compact
rockey mass, in Gothland and in Oesel. In the first mentioned island,
near Ratthammersvik. According to von ScumiptT (Researches etc.
page 171) it occurs in Oesel, in a quarry, not far from the “Ticko-
Krug’’, near Hoheneichen and in another one near Liimmada, in
a wood on the road to Arensburg.

When travelling through those parts, which I had the honour of
doing under the mentorship of von Scumuipr, I collected two pieces
of limestone, which contain remains of Leperditia grandis accord-
ing to the labels, named to me by von ScumiptT, the one comes
from the quarry at Liimmada, the other from the one at Puzza.
The latter find-place being no doubt the same, von ScumipT l.c.
states to be the one near the Ticko-Krug. The Groningen erratica
differs from the piece found at Liimmada.

Some light-grey, slivery pieces however, petrographically, perfectly
resemble the stone-formation of Puzza. Still, they are not altogether
alike, the valves of Leperditia grandis, which occur in the Groningen
erratica, in size, remaining considerably below those found in the
stone-formation of Puzza. According to von Scumipt, (Miscellanea
Silurica IlI, page 9), the valves of Leperditia grandis in Gothland
are, as a rule, smaller than those in Oesel; so in this respect the
Groningen erratica which are the subject of this paper show resem-
blance with the Katthammersvik stone-formation.

(549 )

Whether they do so also petrographically, I cannot decide, having
no specimens of the last mentioned place to compare them with. So I
cannot ascertain whether, and if so, where, limestone, with remains
of Leperditia grandis, found in the Groningen diluvium, still exists
in a compact rocky mass. —

Geodesy. — On the contents of the sixth and last part of the
Report “die Triangulation von Java’, lately presented to the
Academy, in the name of the Netherlands Government, by
Prof. J. A. C. OUDEMANS.

(Read February 23, 1900),

As I had the honour to state at the meeting of January 2, 1897,
the fifth part of this Report contains the complete results of the
triangulation of Java, primary and secondary !). It contains the
length in metres and the azimuths at both ends of every side of the
triangles. Finally a table exhibits the geodetic longitudes and
latitudes of all the stations, as they were calculated, starting from
the station Genoek in the Residency of Djepara, where the late
Geographical Engineer Sorters made an accurate astronomical
determination of latitude and azimuth; the same table contains also
the heights above the mean level of the sea, (see IV Abth., p. 206,
line 4 from the bottom.)

How these heights were obtained had hitherto not been explained;
it is done in the now completed 6% part.

I beg to communicate in a few words some particulars about
these calculations. At any station near the seaboard the height
above the mean sea level can be measured directly, taking as far
as possible the tides into account. This was done for 19 stations,
8 primary and 11 secondary ones, and these were the starting points
for obtaining the heights of the stations situated further inland, but
for the last a knowledge of the refraction is required.

Owing to the diminution, of the density of the atmosphere with
increasing elevation, a ray of light traversing it in a nearly
horizontal direction is bent downwards.

Now if at one station be measured the zenith distance of

') The primary triangulation was already treated of in the 4th part, but the results
were reprinted in the 5th,

( 550 )

another, whose distance is known, the difference of height may be
calculated, provided the mean radius of curvature of the ray of
light between the two stations be known. If that radius be » times

: ; ; Le
that of the earth’s surface between the two stations, — is generally
n

called the coefficient of terrestrial refraction, and its half, which is
used in the calculation of the difference of height, if the path of
the ray is supposed to be circular, will here be called the factor
of refraction 2).

This factor may be found, either, as BAUERNFEIND did in Bavaria,
by measuring the zenith distance of a distant station, whose height
above the observing station has been accurately determined by spirit
levelling — or by measuring, at each station, the zenith distance
of the other. Both these methods, especially the latter, have been
repeatedly applied, but the results were very discordant. Theoretically
the factor is known to depend on the indications of barometer and
thermometer, but still more, nay principally, on the law of diminu-
tion of the density of the air with increasing height.

As this law was unknown for Java, and as the factor was sus-
pected to be very variable, being dependent on the time of the day
and on atmospheric conditions, the design was long ago formed in
the Geographical Service to make a special determination of this
factor, by reciprocal and simultaneous observations of zenith distances
at different hours of the day. This design has been carried out
since I left Java, under the direction of the late engineers WOL-
DRINGH and SOETERS.

In 1876 Engineer WoLDRINGH made two determinations, assisted
by Assistant Jacques OuDEMANS. On one day the reciprocal zenith
distances were simultaneously measured five times between the
south end of the Simplak base and the summit of the Salak, and
shortly afterwards three times between the same base end and the
station Tjitjadas; the difference of height being 2015 metres in the
first, and only 44 metres in the last case. (The heights above sea
level were: base end 195, Salak 2210, Tjitjadas 235 metres). The
results were different, and in the last named determination there
existed from half past seven till half past ten a.m. a considerable
diminution of the value of the factor of refraction. This led to the
arrangement of systematic series of observations. A first series

1
1) In Clark’s Geodesy, the half of —, which we call the factor, is called the coef-
n

ficient of refraction

ne =

(551)

was observed between the stations Banjoepahit, Penoenggalan and
Basé in Middle Java, by Messrs Sorrers, JAcQquES OUDEMANS and
De Vuetrer. Unhappily the observations of the last named observer
are lost; perhaps this is the reason, why the same observers per-
formed new series between three other summits in Kast Java, viz.
in March and April 1878 between the stations Djoerangsapi, Poetri
and Tanahwoelan, and in November of the same year between
Petjaloengan, Poetri and Tanahwoelan. (The heights were: Djoe-
rangsapi 230, Poetri 976, Tanahwoelan 761, Petjaloengan 534 metres).

Between each pair of stations the zenith distances were repeatedly
measured strictly simultaneously, e.g. at 8 h. between the first and
second, at 8 h. 20 m. between the first and third, at 8 h. 40 m.
between the second and third station, and so on. The observations
were commenced early in the morning and continued as long as
rising clouds did not interfere.

The general conclusion from these researches was, that the factor
of refraction diminished from early in the morning till noon, at
first rapidly, and afterwards more slowly; of course this is easily
explained by the rising of the heated inferior layers of air.

But a remarkable result was, that each pair of stations gave a
different value for the factor of refraction; thus, while in March 1877
Penoenggalan and Banjoepahit gave for the mean 0,0547, (minimum
at noon 0,0510,) the mean result from Petjaloengan and Poetri

was 0,0882, (maximum at 8 h. 0,0973).

It was thought that these differences could be accounted for by
deviations of the plumbline, caused by local attractions; for such
attractions displace the zeniths and so alter the zenith distances ;
but the attempt to explain the observed differences in this way,
proved unsuccessful ; at least it would have been necessary to assume
very large deviations of the plumbline, different in sign, besides as
has been already stated, in March and April of 1878 the observa-
tions were made at T’anahwoelan, Poetri and Djoerangsapi, and in
November of the same year at Tanahwoelat, Poetri and Petja-
loengan; now the deviations of the plumblines at Tanahwoelan
and Poetri, needed to render concordant the observations of March
and April, did not agree, either in direction or magnitude, with
those which would have harmonized the observations of November.
Attempts to explain the variations of the factor of refraction by
the indications of barometer and thermometer, were equally un-
successful and it seemed necessary to conclude that the layers of
air of equal density are by no means parallel to the spherical or
ellipsoidal surface of the earth, but that they follow the sinuosities

( 552 )

of the ground, so that every pair of mountaintops or rather of
stations has its own factor of refraction.

As it was nevertheless desired to obtain a mean factor of refrac-
tion, my zealous coadjutor, Coronel M. L. J. vAN ASPEREN, late
of the R. D. N., who had executed most of these calculations,
proposed to me to select ali the pairs of stations between which
reciprocal zenith distances had been observed, whether simultaneously
or not. In this research Kast and West Java were kept separated,
but they gave very nearly the same result, namely 0,068. In all
there were 114 results, ranging from 0,0392 to 0,0879.

These 114 values were then divided and ranged in 11 groups,
in three different ways; 1%. according to distances, varying from
23,9 to 69,5 kilometres; 24. according to mean heights, ranging from
123 to 2673 metres, and 3". according to zenith distances, taking for
each pair of stations the arithmetical mean between the smaller
zenith distance and the supplement of the other.

My reason for arranging the results according to distances, was
that in the triangulation of Hanover, Gauss found the factor of refraction
to be dependent on the distance between the stations, the greater
distances giving a larger factor, but this was easily explained by
the flatness of the country.

Between two stations that were not far apart, the ray of light almost
grazed the surface of the ground, and it is a known fact, that in
this case, by the heating of the soil and the so caused diminution
of density of the undermost layers of the air, the factor of refraction
often diminishes, and not seldom becomes negative, in which case
the convex instead of the concave side of the ray of light is turned
to the earth. Of course in Hanover great distances were only to
be found between relatively high summits, and so the ray of light
between such stations was often free from this influence.

In Java no influence either of distance or of zenith distance on
the refraction was remarked. As regards mean height, its increase
was accompanied by a feeble diminution of the factor of refraction,
but not until the mean height amounted to 2000 metres. For this
reason the theoretical diminution of the factor with increasing height
has been ignored.

As we now came to deduce the differences of heights from the
zenith distances, and to calculate from these, in connection with the
heights measured directly at the seaboards, the heights of the inland
stations above sea level, it seemed proper to use the 114 cases,
in which, as above stated, reciprocal zenith distances were observed,
but not simultaneously; in such cases the difference of height may

( 553 )

be calculated by a known formula), not involving the factor of
refraction.

For calculating the remaining differences of height the value of
the factor of refraction had to be taken into account. Fortunately
its influence on the shorter sides of the secondary triangulation was
always small; very often a method was used which had the advantage
of diminishing considerably the influence of abnormal refraction, viz:
measuring the zenith distances of both the stations from a third
station simultaneously, or at least the one immediately after the other.

As the general rule was, to measure from every station zenith
distances of all the surrounding stations, there were many more
given quantities than were necessary to determine the heights of all the
stations, primary as well as secondary; so the differences of height
had to be deduced by the method of least squares; but as the
stations were too numerous to be all included in one solution, it
was necessary to combine them in groups. The manner in which
the division of the work took place is clearly indicated by a map
printed in colours, of which I give a pair of reprints to circulate *).
As already mentioned, the heights of all stations near the seaboard
were measured directly, the heights of the other stations being derived
from these. The heights given in the Report are those of the tops
of the triangulation pillars, generally built up 1,1 metre above the
ground, upon a foundation of one meter depth.

In the deduction of the most probable values the weights of the
measured differences of height were taken into account; it was
therefore necessary to distinguish between the three ways in which
these differences had been found, viz. by measuring from one of the
two stations concerned or from both reciprocally, or from a third
station. The report gives these particulars. In the primary work
reciprocal zenith distances were almost exclusively used.

After the heights of the primary stations had been fixed, the heights
of the secondary stations were deduced, taking into account the
weights of the several determinations.

The result of an elaborate examination was, that the average
mean error of a deduced difference of height was about half a metre.

I also computed the mean error (in seconds) of a single zenith

Wh

2h

2) Plate III of the Report. As the stones, that have served for this plate, as also
for the plates I and II, have been ground out, it has been impossible to join them
to the printed abstract.

1) Viz. the formula: 4’ —2=S ( 1+ ty 3 (2! —2).

( 554 )

distance, such as had been used in determining the differences in
height. The result found was + 9"\6, whereas the mean error of
the reciprocal simultaneous observations was only + 2",2. The inference
is, that, if we wish to find the accurate difference in height between
two stations, between which the ground is too hilly for spirit levelling,
simultaneous reciprocal zenith distances ought exclusively to be taken.

In Java the determination of the heights was of quite secondary
interest, and the results (which were confirmed by further researches)
were sufficient for the purposes of the Survey; but at other times
and in other regions there have been cases, where the difference of
height was the chief aim, and this rule was not observed.

In the operations executed in 1825, under the direction of colonel
CoRABOEUF, for the geodetic determination of the difference of
height between the Atlantic and the Mediterranean, every care was
bestowed on the triangulation of the summits of the Pyrenees;
the zenith distances too were often repeated, three or five series,
each consisting of ten observations, being taken on each occasion ;
but the reciprocal zenith distances were not observed simultaneously,
though the double staff rendered it practicable. The result might
have been more satisfactory, if this precaution had been taken, but
it must be allowed that at that time attention had not yet been
drawn to the point.

A separate chapter of the Report is consecrated to the dip of
the horizon, observed at 53 stations. It soon appeared that these
observations could not compete with those already mentioned for
determining the heights above mean sea level; they have accordingly
not been used for this purpose.

But it was quite another thing, being given the already fixed
heights of those 53 stations and the observed dips, to deduce a
posterior’ a formula by which the height above the sea might be
calculated frum the dip.

This problem also initiated several inquiries. The height is best
calculated by a series containing the even powers of tgd. Now,
in trying to determine, by the observed dips, the coefficient of tg? d,
(on which the 5} times smaller one of fg*d depends), the computed
heights of the low stations were generally too great, a result easily
explained by the already mentioned inversion of the curvature of the
ray of light near the level of the sea. Indeed, following a ray of
light from the sea to a distant mountaintop and supposing a point
of inflexion to occur near the sea level, then it is easy to see, that
in determining the height of any point on the ray by the dip, the

( 555 )

error made will be the same for all points on the ray. Indeed, as
a diagram immediately shows, this error is equal to the linear quantity
by which that part of the ray of light, which is concave on the side
turned to the earth, dips under the level of the sea, if prolonged
at the sea-end.

By the method of least squares, it was easy to find this so called
coustant, as well as the coefficient of fg? d, and thence the factor
of refraction.

The first step was to take the arithmetical mean of all the dips
observed at the same station; the second term, containing tg*d, proved
small enough to be neglected if the height did not exceed 2000
metres; and so the problem was reduced to the solving of 53 equa-
tions with 2 unknown quantities. The coefficient of fg?d being thus
determined, the factor of refraction was calculated!), and agreed
almost perfectly with the value found before; finally the coefficient
of tg'd was deduced. The result was

h = (6,56546) tg2d — (5,82716) tg'd — 2,475,

h being in metres, and the numbers in the brackets being logarithms
of the actual coefficients. The value of the factor of refraction,
deduced from the first coefficient, is 0,0692, whereas the reciprocal
zenith distances gave 0,068. Considering the diverging values that
are found for this number, the agreement is more than sufficient.

The same material, however, seemed to invite a more detailed
inquiry. Often, at the same station, the dip has been observed at
different hours of the day, and it seemed to be worth while to
examine the changes of the factor of refraction during the hours
of observation. The result is shown graphically on plate II. At 11
a.m. both methods give nearly the same value, viz. 0,0680; before
and after, the dips give a smaller value than the reciprocal zenith
distances.

The same plate shows in a little map at the bottom, all the
stations where the dip has been observed. They appear to be very
regularly distributed along the south coast of Java and in the
eastern part of the north coast; we also see that the dips were
observed in different azimuths. Now, as the radius of curvature
of the earth, (or of the ocean), differs with the azimuth, it is

1) Calling the coefficient of fy2d a, the factor of refraction *# and the radius of the

th 2 i = is k—4) z
i : oe Oe
ear ,» Wwe have a aay: or ye

( 556 )

necessary, if we wish to calculate with precision, to take this into
account and to reduce the observed dips (for instance) to dips
belonging to a mean radius of curvature.

I was sorry not to be able to take the tides into consideration,
though they have been thoroughly investigated’), for a great number
of stations, by our honoured Correspondent Dr. J. P. VAN DER STOK,
who embodied his results in tide tables. But these tables commence
with the year 1891, and it would have been a laborious operation
to extend them to the period containing the observations (1865—
1880) and to deduce, by the cotidal lines, (also drawn by the same
author), the height of the sea at the moments of the observations.

In most cases neither the azimuth was noted, nor the hour of
the observation; and it was necessary to make assumptions with
regard to both; as to the azimuth, the dip observation was supposed
to be made in a direction perpendicular to the coast line; as to
the hour of observation, it was supposed that the horizontal obser-
vations commenced at half past six, and that every observation,
horizontal or vertical, occupied five minutes. This gave the time
of the dip observation.

This investigation led me to frame the following rules for future
observations of dip.

1. At every observation the apparent time is to be noted, as also
the indications of barometer, thermometer and psychrometer,

2. Repeating the observations on several days is recommended,
in order to neutralize accidental deviations and to discover extra-
ordinary perturbations.

3. It is useful to take the measures in different azimuths, espe-
cially, if possible, in the meridian and in a direction perpendicular
to the meridian, in order to examine whether the theoretically
existing difference of the dips in these two directions, which may
amount to one part in 150, or to 24” in a dip of one degree, is
confirmed by experience.

1) These researches have been published in fifteen papers; 13 of these in the /Tijd-
schrift van het Koninklijk Instituut van Ingenieurs, Afdeeling Ned. Indié, 1890—1896”.
The title of the first paper, translated, is “The Harmonic Analysis of Tides, applied
to Observations made at Tjilatjap”; that of all the following: “Studies of the Tides
in the Indian Archipelago”; IL and IIL contain theoretical matter, IV—XIL the
results of the harmonic analysis, applied to the indications of the tide gauges
established in different parts of the East-Indian Archipelago. X1V (Statistics) and
XV (Predictions) have been published in the Journal of the Royal Physical Society
of Batavia, Vol. LVI, 1896.

( 557 )

4. The stations are to be so chosen, that the height of the tide
may be calculated by the tide-tables.

I have thought that a review of previous investigations of terrest-
rial refraction, would not be unwelcome to those interested in the
subject. It includes an account of the work of JzAN DominiIQue CassINI
in 1661, Cesar FRangors Cassini in 1742, Topras MAyer in 1751,
Lampert in 1759, Boucuer in 1749, Roy and MupceE from 1787
to 1799, MéicHAIN and DeLampre from 1792 to 1797, Von Zacu
in 1795, Warren in 1804, von Linpenav in 1805, TRALLES in
1806, Gauss in 1823, Winnetm Srruve in 1826—27, CoRABOEUF
in 1827, CaccIaTorE in 1831, Bessex in 1834, Baryer in 1835,
SaBLER and Srruve in 1838, ATKinson in 1825, DENZLER in
1842, Paar in 1846. Then follows a description of the theories
of LAPLACE, BAEYER, BABINET, SAWITSCH, BAUERNFEIND, LINDHAGEN,
HeELMERT, JORDAN and Water. The chapter closes by mentioning
the value of the factor of refraction which on my suggestion Coronel
M. L. J. van AsperReN has deduced from the observations of the
Peruvian Committee for measuring a degree in Peru in 1735, and
finally by summing up a number of papers on terrestrial refraction,
published since 1850 in different periodicals.

The second section of this sixth part contains the determinations
of latitudes and differences of longitude, made for comparison with
the results of the triangulation, with a view to detecting deviations
of the plumbline by local attraction.

Determinations of latitude by circummeridian zenith distances were
made at 63 stations. For reducing these observations the knowledge
of the declinations of the stars employed was requisite; and though
most of the stars were taken from the Nautical Almanac, whose
places for the northern stars rest almost exclusively on observations
made at Greenwich, it was thought desirable to take into account
some other determinations, especially as the declinations of those
southern stars which could not be observed at Greenwich were very
uncertain.

For the determinations of azimuths made, (in absence of our Pole
star), by Karser’s method, by measuring the difference in azimuth
between stars in the east or west and some visible station, the
precise knowledge of the declinations of the observed stars was
also of much interest; sometimes stars were employed for the
azimuths which had also served for latitude, yet the choice of stars
was guided by different considerations in the two cases and stars

( 558 )

fit for the determination of latitude, were not always appropriate for
that of the azimuth *),

The late Dr. N. M. Kam, whose catalogue of ‘stars is well
known, undertook, at my request, to furnish a list of the
declinations of the stars employed; the numerous star catalogues
which he had to consult being forwarded to him from the library
of the Utrecht Observatory. He carried out this task very thoroughly,
including corrections for the systematic differences of the catalogues.
I must add, that when Kam undertook this work, it was not known
that Auwers, of Berlin, was about to undertake a similar one.

Neither for the determination of the latitudes, nor of the azimuths,
was it deemed necessary to submit the right ascensions to an
equally severe examination. In the determination of latitude a
small error in the R. A. was entirely eliminated by the circum-
meridian observations; in the determinations of the azimuths, which
were made for 20 stations, the influence of such an error was always
either 0, or so small that the Right Ascensions could be taken
directly from the Nautical Almanac.

That a careful determination of the declinations was not without
utility, may be shown by the following instances: the correction of
the declination of @ Andromedae in the Nautical Almanac for 1854
was — 0",86, in that of 1871 + 0",03; that of the declination of
y Pegasi was + 0",7 in 1876, 78 and 79; that of ¢ Leporis, from
1871 to 1880, was nearly a second; that of the declination of
Sirius varied from + 1",30 to — 1"\89, that of the declination of
Procyon from —0",55 to + 1",58, and so on.

Dr. Kam also charged himself with the deduction of the definitive

1) For the determination of a latitude generally stars were employed (commonly
four on the north and four on the south,) that culminated at 20° or more from the
zenith; the rule was to choose them so that the sums of the zenith distances on the
two sides of the zenith were nearly equal; whereas for the determination of an
azimuth, the stars ought to be so chosen that at a low altitude their azimuths changed
as little as possible. Therefore Katspr, in his “Treatise on the astronomical deter-
mination of geographical positions in the East Indian Archipelago” proposed to
choose, for this purpose, stars, which, having an altitude of from 10° to 30°, were
either in the east or in the west.

Those stars were of course preferable, that moved vertically ; (astronomically : whose
parallactic angle was 90°;) which was only possible if the stars southern deeli-
nation exceeded the latitude of the station; but even if the star be not in this most
favorable situation, still, provided it stands not higher than 30°, a possible uncer-
tainty of the time, as well as of the latitude, has only a very smell influence on
the azimuth.

( 559 )

latitudes and azimuths, taking into account the flexure of the telescope’).

All these determinations of latitude were made for the purpose
of finding the differences between the astronomical and geodetic
latitudes, due to deviations of the direction of gravity from the
normal to the adopted ellipsoidal surface, on which the whole
network of triangles is supposed to be projected. In German these
differences are called “Lothabweichungen”; I think an unequivocal
Dutch expression would be: “afwijking van het paslood” or “pas-
loodafwijking”. It may arise either from the stronger attraction of
mountains or heavy underground masses, or from the feebler attract-
ion of less heavy masses on the opposite side. Which cause is the
true one in any particular instance, may be decided with more or
less probability by measuring the force of attraction by pendulum
experiments.

The deviations are represented on plate 1V °) by arrows, directed
to the north or to the south, according to the direction of the
attraction. It must be kept in mind, that if the arrow points to
the north, the astronomical observations indicate a greater (meridional)
latitude then the geodetical ones.

Though attraction by the mountainous country is undeniably
indicated, the arrows on the south coast being all directed to the
north, and those on the north coast almost all to the south, yet
some decided irregularities may be noticed. Though, for instance,
seven stations, situated within or near to the Residency of Semarang,
indicate an attraction to the south, we find at Genoek, near the
north point of Djepara, very little or no attraction, notwithstanding
the vicinity of the mountain Moeria. Again, while several stations
situaied on the north coast, Anjer, Gedé, Batavia, Pakis, Indramajoe,
Boetak (in the Residency of Rembang), show an absence of attract-
ion, which might have beea expected from their great distance
from high mountains, the enormous deviations, 37” in Poelo Tindjil
and 26",5 in Pogor II, both near the south coast, are very remarkable.
An explanation, however, of this phenomenon may be found, not in
the attraction of a high mountain on the north, but in the lack of

1) Dr. Kam examined also, at my request, the changes that would result in these
latitudes, (4,) if the flexure of the telescope was not calculated for each night sepa-
rately, but its mean value fer the whole period was employed; (B,) if the flexure
was simply put —0, so that the arithmetical mean of all the determinations was
adopted as the definitive value of the latitude.

The result was, that, owing to the suitable choice of the stars on both sides of
the zenith, the differences were extremely small, and in the great majority of cases
did not reach a tenth of a second. ;

*) As the stone, on which this plate was engraved, was not yet ground out, it has
been appended to this abstract. bate

( 560 )

attraction to the south by the deep Indian Ocean. The southward
attraction at Patjarloewong is strange, there being no remarkable
mountain to the south of this station, and the near lying Pliken
showing already clearly the attraction of the Slamat on the north
east. We are also struck by the southward arrow at Magetan, which
has the mighty Lawoe rising near it on the northwest.

Other remarks could be made with regard to the directions and
lengths of the arrows on this map, but I think these are sufficient
At all events I think the conclusion is evident, that the deviations of
the plumbline, detected by the determinations of latitude, show the
desirability of a much larger number of such determinations. If
we wish to combine the study of plumbline deviations with triangu-
lation, it is desirable to make a determination of latitude at every
station; it is then not necessary to attain a high degree of precision;
a single series of say, eight circummeridian zenith distances of a
star south of the zenith, combined with an equal number of a
star at nearly the same distance to the north of the zenith, would
be sufficient. If I were to have again under my direction a triang-
ulation of Java or a similar mountainous country, I certainly should
prefer this method to that which has been followed. Moreover
every mountain offers a wide field of research; and very interesting
results might be attained by executing a large number of measures
of plumbline deviation and gravity in the whole region affected by
a vulcano.

As Yvon Vit~arceau has shown, the deviations of the astro-
nomical azimuths from the geodetical ones may be expressed in
deviations of longitude: unfortunately they must then be multiplied
by the cosecant of the latitude, a factor, having for the 20 stations,
where azimuths were determined, a mean value of more than 8.
Moreover the said differences were too much affected by the accu-
mulation of errors in the horizontal measures; so the results of this
reduction were untrustworthy. They gave, (and this is not to be
wondered at) improbably large deviations in longitude.

Much smaller discrepancies were obtained by comparing with the
triangulation the differences of longitude which I determined, in con-
junction with the Assistants JAEGER and VoswINKEL DORSELEN, by
the telegraph, in the years 1859—1863, before the resumption of
the suspended triangulation. Our stations were not identical with
those of the triangulation, but the relative positions have since been
determined and allowed for. Though the comparisons are only eight
in number, they show clearly the attraction by land.

Utrecht, February 19, 1901.

(561 )

Chemistry. — Dr. Ernsr Conen and E. H. Bicuner: ,On
Erarb’s Law of Solubility.’ (Communicated by Prof. H. W.
Bakuurs Roozesoom).

1. In 1894 Erarp!) formulated the following rule: When the
solubility of different salts at different temperatures is expressed in
grams of the salt per 100 grams of the saturated solution, the
curves representing the solubility as a function of the temperature
are straight lines and may be represented by an equation of the
form y = a-+ ét. Erarp has determined the solubility of a number
of salts in water (and other solvents); in some cases the temperature
was so high that it came near to the melting point of the dissolved
salts.

2. Erarp’s views have passed into the literature (books of
reference) and thus we find in the second edition of the Physikalisch-
chemische Tabellen of LaNvoLT and BéRNSTEIN the accompanying
solubility equation (y=a- bt) for each of the salts investigated
by Erarp.

3. Knowing the difficulty of preparing a really saturated solution
of any salt, that it has been proved necessary to shake or stir the
particular solvent for a long time (1—3 hours) with an excess of
the finely powdered salt at a constant temperature, it is surprising
to find Erarp making the following statement: ,pour obtenir une
solution saturée de sel dans l’eau, il suffit de mettre dans un verre
de Bohéme un mélange de sel concassé et d’eau & volumes sensible-
ment égaux.... le thermométre destiné 4 prendre les températures
sert en méme temps d’agitateur... La rapidité de la saturation est
telle dans les conditions que je viens d’indiquer, qu’on peut, pendant
Vascension continue mais trés lente du thermométre agitateur, prendre
autant d’échantillons qu’on le désire de la solution parfaitement
saturée aux températures f°, f°, 4°, &°..... La régularité et
la concordance des résultats suffiraient 4 démontrer la vérité de
affirmation précédente. Cependant des expériences comparatives
ont eneore été faites pour la mettre hors doute, et elles ont montré
quen effectuant la saturation dans un ballon agité pendant des heures,
ainsi qu’on le recommande souvent, on n’arrive pas & une précision
plus grande. Cela sont des précautions illusoires”’.

4. Investigations conducted by one of us with Mr. KounstammM
some years ago”) on the solubility of cadmium sulphate had shown

1) WiepemManns Annalen, N. F. 65 (1898) 344.

*) Annales de chimie et de physique, 7e série t. IL, aoit 1894; t ILI, Octobre 1894,
38

Proceedings Royal Acad, Amsterdam, Vol, ILL,

( 562 )

that the solutions used by Erarp in this case were quite unsatur-
ated and that his figures for some temperatures were about 35 pCt.
below the truth. The new figures were confirmed by the simult-
aneously conducted experiments of the Physikalisch-Technische
Reichsanstalt at Charlottenburg (Mynius and Funk)!) as shown by
the subjoined table:

100 grams of water dissolve grams of Cd SO,.

Temperature. | Earp. CouEN & KOHNSTAMM. | Myuius & Funk.
0° 55.52 75.52 75.47
10° | 60.92 | 73.90 | 76.00
15° | 63.7 76.11 76.05.

Later investigations on the solubility of zine sulphate by CALLENDAR
and BarNneEs*) and CoHEN®) as well as the elaborate determinations
published by the Reichsanstalt as regards a number of other salts
created a suspicion that also in those cases Erarp’s determinations
had not been made with saturated solutions. The above mentioned
law of solubility stands or falls, of course, with the correctness of
ETARD’s measurements. We have, therefore, carefully tested that
law in a number of cases where very trustworthy determinations of
the solubility have been executed (this number is comparatively
small) and the result is given in the following lines.

5. ANDREAE’s determinations *) have been conducted with great
care. He took great pains to keep temperatures constant and was
only satisfied when he had obtained the same result by three different
methods. His determinations are certainly the most reliable ones
which have ever been made in this direction.

In the following table we give the results of ANDREAE for NaCl,
K Cl, Ky SO,, K NOs, recalculated by Erarp’s method. Under
EraAkD are given the solubilities derived from his own determina-
tions (or from his equations) whilst along with ANDREAE’s figures
the temperature coefficient of the solubility is given which according
to ETARD, must be constant for each salt.

1) B. B. 80 (1897) S24.

*) Proc. Royal Society, 62 (1898) 147.

5) Proceedings Kon. Akad. v. Wetenschappen 80 Dee. 1899. 334. Zeitschrift fiir
physikalische Chemie 34. (1900) 179.

*) Journal fiir praktische Chemie, N. I’, 29 (1884) 456.

"806 (8881) 901 Ua G

are te =—— —— —— _— 8116 F916 | 008
; ; E > é 9%0°0 |
=e aa iin aa aes —S- £916 8626 | od
FE0'0 |
E69 sl08 9618 86°26 FOLE |
969'0 6cl 0 960 180'0
T0'9F 60°66 00°08 #0 18 £3°96
01.0 Oslo ZEt0 6100
66°88 60°86 £9°88 61°96 #9'9%
FoLO 8810 SFL'0 Stoo
oF 18 10°46 SUZ $5'96 6F'9%
tHLO 8710 T9l0 TLO'0
60°FS 9°96 PS'SG 6698 88°96
$19'0 9sv'0 FLT0 £00'0
8e'LT 69°86 08°86 09% 20°96
O90 98T'0 900°0 y
a LVR 89 86 06°S¢ 18'98
gse'0 09T0 6060 0000
im BL TL g's 28°9 OL'TB L816 8°96 ot a
98 +
ssoro+soo= 4 |
') Nh 5 96; bs |
~= i ¢
Tee Gy 4 LOV0+3'1=4 PoteroTs6I= 4 4 840'0-+8'sg=4
. Vv . Vv be . .
‘auvig 2 gy ‘“avauany (, ‘Cuvag or “‘AVAMANY “UV IT ae ‘AVANANY “UV ae ‘AVANAGNY
“ONM “os ° ‘ON ‘TORN

(564 )

It will be seen that in ANDREAw’s determinations there is no
question of a rectilinear course of the solubility line. The temperature
coefficient constantly changes.

6. If to this we add the table of solubility for zine sulphate as
obtained from the coneordant determinations of CALLENDAR and
BARNES and COHEN

TEMPERATURE. SOLUBILITY. . =
| |

ag) | 98.21
0.260

0°] | 29.54
} 0.274

9°.1 | 32.01
0.290

15°.0 33.72
| 0.288

25°.0 36.60
| 0,328

30°.0 38.24
| 0.846

35°.0 39.97
0305

39°.0 43.19

it may also be observed that contrary to Erarp’s data, the tempe-
rature coefficient is not constant. Erarb seems to have worked
here again with unsaturated solutions.

He found the solubility 29.1 at + 1°
and 40.9 at + 49°

Erarpb’s curve shows nothing of the existence of a transition
at 38°.5 which has been proved to exist by a number of methods,

7. The following table relates to cadmium sulphate:

| SOLUBILITY.

TEMPERATURE, | Erarp. | Mytius en Funk.
CoHEN en KOHNSTAMM.
g° | 357 | 43.01
10° | 37.5 | 43.18
380° | 42.0 43.75
86° | 43.5 | 85° 89.6

94° 41.6 95° 38.1

( 565 )

As will be seen, Erarp has experimented here below 86° with
unsaturated and above 86° with supersaturated solutions.

8. Finally, it is shown from the latest determinations which
have been executed with great care and accuracy in the Physikalisch-
Technische Reichsanstalt by Dierz, Funx, v. Wrocuem and Mynivs}),
that Erarp when he determined the solubility of the salts inves-
tigated by these authors has always worked with unsaturated solu-
tions. In some cases the existing differences are not large. It is not
worth while to insert here all the tables as the general result seems
to be thoroughly established.

9. LENOBLE?) pointed out in 1896 that the data formerly com-
municated by Erarp did not lead to straight lines but to curves
of the fourth degree or higher with slight curvature. As it now
appears that Erarp’s original material does not represent the true
state of affairs, a closer investigation in this direction has become
superfluous.

Result of the Investigation.

Erarp’s law of solubility is not in agreement with the facts; a
simple relation like this between the solubility of salts and the
temperature does not seem to exist. Repetition of ETarp’s experi-
ments at high temperatures is desirable.

Amsterdam, Chem. Lab. University, February 1900.

Mathematics. — Prof. J. ©. Knuyver: “On the expansion of a
function in a series of polynomials.”

According to BoreEt’s remark ®) the fundamental problem consists
in expanding 1:1—z. For, having once obtained an expansion of
the form

1 2 a) i
oe = tt zPa()=1+ = («mn top eS ogg ES ered )
—e 1 1

1) Wissenschaftliche Abhandlungen der Physikalisch-Technischen Reichsanstalt.
Ba. Il, 427.

*) Bulletin de la Société Chimique de Paris, XV (1896) 54.

8) Annales de l’école normale, t. 16, p. 132.

( 566 )

that can be rendered converging in every finite region of the x-plane,
not enclosing any part of the straight line (+ 1,-+ ~), from

f (2) = & en(e—ayn

we may deduce
Ae) = es U,, («-a)= ees [ean ¢1 (wa) + Gon Cy (a—a)? +... Cnn Cn (2-u)| ;
1 1

and the series of polynomials U,,(w—a) can be made to represent
f(z) in every finite region of MirraG-LEFFLER’s “star’’.

Solutions of the fundamental problem are given by Murrac-
LEFFLER !), PAINLEVE?) and others; still as yet new solutions are
not devoid of interest. Perhaps the solution described here is not behind
in point of simplicity at least from a theoretical point of view.

As was shewn by Parntevs the problem of expanding 1: 1—a#
is connected with a problem of conformal representation implying
a certain want of determinateness. This problem requires the mapping
of the interior of a u-circle, centre the origin and radius unity, on
the interior of a nodeless closed z-curve, going round the origin and
passing through z=+1. The homologues of w=0, w=-+1 are to be
the points z= 0, 2=-+ 1; moreover the shape of the z-curve must
be made to depend on a single or on several arbitrary parameters
in such a manner, that by their assuming appropriate values the
z-curve takes more or less elongated forms, varying from a 2-circle,
centre the origin, to an area of infinitesimal breadth covering the
stroke (0, + 1).

In no other way is the choice of the z-curve limited. We take it
here to be an ellipse having one focus in z= 0 and the farther
extremity of the axis major in z= -+ l.

ScuHwakz’s functional relation

uw)

a ares

z==csin sn

makes a u-circle and a ¢-ellipse conformal areas; since however by
this formula the centres of both curves are corresponding points,
and in our case the centre of the circle should be the homologue
of one of the foci of the ellipse, a slight alteration is necessary.

1) Acta Mathematica, t. 23, p. 43 and t. 24, p. 183 and 205,
*) Comptes rendus, 23 May and 3 July 1899.

( 567 )

It will be seen that the correspondence defined by the equation

4q\/2 sagt (28 ge)
CSS SS Pita OT Lie —
; = sin 12K n P \?

meets all requirements.

As to k, K and q, they are the usual JACOBIAN constants in the
theory of elliptic functions; we will consider & and K as functions
of g, thus making the latter quantity serve as an arbitrary real
parameter able to assume all values between 0 and 1. Putting

the functional relation between w and z maps the w-cirele on a
z-ellipse represented in polar coordinates by the equation

te
R= Bi secant
1—é cos pp

When q tends to zero, the excentricity ¢ vanishes, the 2-ellipse
becomes a 2-circle and ultimately we have =: on the contrary
when qg approaches its upper limit unity, the z-ellipse transforms
itself into a narrow loop stretched round the stroke (0, + 1).

Obviously we may deduce from the functional relation an expan-
sion of 2 in ascending powers of uv. Writing

Qq'z 2
q > Chul

TRO
Cana) a
the coefficients C;, are obtainable by means of the differential equation

<

doz ol : Elodie
u (k—u) (L—hu) a ol. a [k—2 u(1-+- hk?) +8h u?] reer T Te:

ee) a
a

We shall find for the first and second terms ')

1) The notation of the $-constants is that of Tannery and Mouk, Eléments de la
théorie des fonctions elliptiques.

( 568 )

2 o, = 2st +981)
Sd Po” ; ¥ 3 dy" Fo*

(hes

and we may then use the relation

412 (Sst + 9s) — 1), @— YEA}
Q@r+D@t+Aj020" ° G2 Dene

Cia = A=

to obtain the higher coefficients.

Similarly it is possible to expand 2. For 2 as well as @ itself
is simply an aggregate of cosines of constant multiples of the quantity

3 u
Pp = on Ve ’

and the expansion of cos2m(/? gives no more trouble than that of
cos 2 ?. In particular it should be noticed that the series for 2” begins
with the term wu’.

The foregoing considerations enable us to express the function
1:1—zz as an integral series of w. For, in fact, we have only to
expand the different powers of 2 in the series

ltazgta®2tezAt..

and to arrange the result according to ascending powers of w.
In this way we obtain an expansion of the form

1
1 — 2z

ao
=1+4+ 27, (a, q) uv,
1

where the coefficient 7, (7, y) is a polynomial in x of order n, the
coefficients of the polynomial involving the parameter q.

Putting now « = ge we will ask under what conditions as to
and to g this w-series has its radius of convergence at least equal
to unity. This point is examined in the following way. Suppose w
to move at random through the interior of the w-cirele, centre the
origin and radius unity, then 2 simultaneously moves within the
corresponding 2-ellipse and the motion of the point wz is restricted
to take place in the interior of a second ellipse of the 2-plane. Evi-
dently this #2-ellipse is obtained by turning the 2-ellipse round z=0
through an angle @, stretching at the same time its radii vectores
in the ratio g:1. Hence if only the point = 1 hes outside this
xe-ellipse, given by the equation

( 569 )

(1 —a)e

R= —-—_—__——__,,
1 — € cos (? — 0)

the function 1:1—z remains uniform and finite, whatever may
be the position of w within the w-circle or even on its boundary.
Therefore as soon as # and g be such that

1 (1—e) @
1—ecos 6’
or what is the same that
1 E
Se ey)
es 1—e 1—e a

the w-series will converge unconditionally for | w| <1.
We assume a and g to satisfy the condition imposed upon them
and put «= +1; thus we obtain

1 2)
a 1+ = T, (#, 9),
L

——

a development of 1: 1—a holding good for all points # inside the
limagon

1 &
= —— — 0.
e l—e_ I1—é8 te

This limagon has its acnodal point in a = 0 and the nearer vertex
in x=1. Its shape depends on the value of g; by variating this
parameter we may regulate to a certain extent the region of con-
vergence of the series of polynomials. Take g = 0 and the limagon
degenerates into a circle, centre 2 = 0, radius unity. Suppose g tending
to its upper limit’and the limagon covers larger and larger parts of
the x-plane. Ultimately for g = 1 the limacgon would enclose all points
w of the plane except those lying on the straight line (+ 1, + o).

Thus we infer that the expansion of 1: 1—a can be made to con-
verge in every finite region of the plane not including a part of the
line (+1, + 0) and we may use it in the manner indicated at the
beginning to form an expansion representing a given function f (2).

So, for instance, taking g=¢~7, we have for all points x inside
the limagon

(570 )

0 = 1.663 — 0.663 cos 0,

1
p> = EF [0.5785 2] + [0.2138 » + 0.8847 29]
——
4+ [0.0968 x + 0.2468 22 + 0.1936 23] +
1 [0.0488 x + 0.1575 22 + 0.2142 23 + 0.1120 24] +

+ [0.0262 x +: 0.0978 2 + 0.1762 «3 + 0.1652 # + 0.0648 25] +

If we now multiply the coefficients of #°,a!,...2°,... respectively

1

1 : : 2
by 0, 1, 0, — 0, Bet that is by the corresponding coefficients

3?
of the power series

ee Se rae eee
Y hae rere es SPOOR OT

we obtain the expansion
bg tg « = [0.5785 2] + [0.2133 2] + [0.0968 « — 0.0645 23] +
+[0.0488 e—0.0714 2°] + [0.0262 x—0.0587 28 + 0.013025]+...,

and the equivalence of the function and the series is valid for all
points common to the interiors of the limagons

g = 1.663 + 0.663 sin 0.

And again in the same way we deduce from

1 ea em ernas ey
os —a+—r7?+ —; ge
Jina bah gt ig? Hye diets aur 2
1
Amy = 1+ (0.2892 2] + [0.1066 « + 0.1255 28] +
—wr

+ [0.0484 « + 0.0925 22 + 0.0605 2°] +
+ [0.0244 x +. 0.0592 22 + 0.0669 «3 + 0.0306 «*] +

+ [0.0131 240.0367 224 .0.0551 22+40.0452.244+0.0159 29] 4 ...,

(571)

the region of convergence being the same as for the expansion of
1:1—z.
For a test we may make the substition «©=—1; we shall find

_

s= 0.5000 = 1-0.5785-+.0.1214-0.0436 +-0.0065-0,0042+....

—0.5016+...,

bg tg(—1) = — 0.7854 = — 0.5785 — 0.2133 —0.0323 +
+ 0.0266 -+ 0.0195 +... = — 0.7820 +...,
1
an, = 0.7070 =1— 0.2892 + 0.0159 — 0.0164 — 0.0015 —
00022 S28 0: 7096-6 «x
Phycics. — Prof. J. D. van per Waats on: “The equation of

?

state and the theory of cyclic motion.” II. (Continued from

page 528).

Before we are able to calculate the equation for the equilibrium
and the entropy and the specific heat of a substance with triatomic
molecules, we must first know the mode of motion. If the motion
should be such, that the first atom is placed exactly in the centre
of gravity, and consequently only the two other atoms move, such
a molecule must be regarded as a diatomic one, and the equation
of the equilibrium will be again equal to:

d

JE. CHER
Ral
dv

db

(v 4 ) (=) = RF.

But the value represented by }, will include besides the space of
the moving atoms, also the space occupied by the stationary atom.

If the motion of the three atoms relative to their centre of gravity
should be such that the distance of one of them quite determines
the place of the two others, as would be the case when they move
along three lines, which enclose constant angles, and if the case is
therefore to be considered as a vibrating system with one degree of
freedom, then such a molecule must be treated in our considerations
as a diatomic one.

(572)

Only if the motion of two of the
three atoms relative to each other is
such, that it is independent of the
motion of the third atom relative to
the centre of gravity of the two first-
mentioned, the molecule may be called
a triatomic molecule also from our
point of view, and we shall find a
greater specific heat and a modified
equation of state.

Let Z in the figure be the centre
of gravity of the molecule, and A, B and C indicate the instanta-
neous position of the three atoms. If D is the centre of gravity of
A and #B, then the points C, Z and D must of course lie on the
same straight line. Let us take the distances DA—7r), DB =r,
CZ=r; and DZ=r, Let us now imagine the motion of the atoms
to be such that A and B move along their connecting line, and that
at the same time, but imdependent of this, C and D approach each
other. Then the vis viva of the first motion may be represented by :

By (73—1'01)? 81° + Be (r2—"09)? 82°
and that of the second motion by:
C3 (rs—""¢3)* 83° + Cy (r74—7 04)? 84°
Then A (v—b)"'s s° added to the sum of these quantities represents

the whole vis viva.
From this we deduce for the equation of the equilibrium:

vo

+ p+—2=2}

Ty dr, Lig dry Jip drs, D4, a
db dv (r;—19, db | rg—rog db © r3—13 db ~ r,—14 db

Let us call the increase of volume in consequence of the existence
of the first motion :

bbq) = Sq (1 — 17:01) + Se (7%2—7o9)
and in consequence of the existence of the second motion:
by—bog = Ss (rg—103) + Sy (74-704)

The way in which in these expressions 7 and ry depend on each

—————— a

intents

(573 )

other, is known, just as that of 73; and ry; 7 and 7, however must
be considered to be independent of each other at any moment. The
sum of b,—09, and b,—o, is the quantity which we may consider
as the increase of volume of the molecule, and so:

b—bo, = (6; 01) + (02—L9)-

On account of the independence of the two atomic motions, we
get therefore two equations of the equilibrium:

dl dP, - 2 (1) +- Dy 2)
Tema =-
db, dv b, bo,
and
db dP, 2(Lg + Dy)
dby ees avi on by—bog

the former applying to the direction in the molecule which connects
A and #8, the latter for the direction which connects C and D. In
other words, the molecule has two directions, according to which
it can possess a different degree of compressibility. A form for the
petential energy, which does not take these different properties in
different directions into account, is therefore insufficient. The ther-
modynamic deduction of the equation of the equilibrium is therefore
wrongly simplified by assuming the quantity P;, and we should act
more in accordance with the difference in properties in the two
directions by introducing two quantities P;; and P),. By means of
them we may write then:

dP», F ya
(e oe =158 = <=) bon) = 2 (Ey + La) = RI
and
Ge, ‘ dP 4 . a
(p+ S24) Cabos) = 2 Le + L,) = Re.

If we calculate in the same way as is done for diatomic mole-
cules on page 523, the value of dQ, we find for triatomic molecules,
the atoms of which move in the way described:

dQ = Ly d log [(v—b)'/s Lo] + (Ly + La) d log [(b,—bo)? (Ly + La) +

+ (Ls ++ Li) d log [(bg—bo9)” Ls + L4)).

( 574 )

L 1a 1 Loe 1f
If we put Bratetsttie At | SS Hs Th ea

we get:
? to)
Lo 33 Lo

y= R flog (v—b) L'a + log (b; by) T "/s + log (bo—bog) L'l3}
and therefore for the value of the specific heat at v=o:

Td (bj—b5}) _ Td (by—bgs))

Cepia) egy. sways : :
pect fac 18 o> (pas ayaa Digan

If we take for P;; the form : P;; = 4 @ (b;—b))? and in the same way

for Py the form: Piz = 4 2 (b2—bog)”, we find, supposing

@, and @, independent of the temperature, from the equations of
the equilibrium for which »=o, so from

Q@) (b;—b,;)* = RT
and

Gy (bo —bya)? = RT
Td(b\—B) _ , Td (bo—by3)
—_——_———_ and

both 7 Cc Tae ae
(6; —b9,) dT (bg—bo) dT

equal to 4, and we get:

7 9
Cy = Rand G= = RB,

and consequently

For carbonic acid values for this relation are given varying from
1,274 to 1,3221). For N,O the values vary from 1,267 to 1,327.
For SO, we find the values from 1,238 to 1,262.

In this calculation of the specific heat both of diatomic and of
triatomic molecules, we have taken FP, as dependent of the tem-
perature, and on the supposition that P,—= 4a@(b— d)?, we have
found a contribution to C, of the same amount, as if there were in
each case one degree of freedom more for the atomic motion than
we assumed. If we had taken @ as depending on the temperature,
we should have found another amount for this contribution to C,
which we may regard as a kind of potential energy. Specially if we

1) See O. E. Meyer: Die kinetische Theorie der Gase. 1877 pag. 91.

(575 )

put « as proportional to the temperature, this contribution to C, is
equal to zero, as is evident without further calculation, if we put
for the equation of the equilibrium at v=o:

a'T (b— b,)? = RT.

If we want to make the calculated value of C, agree with the
above mentioned, we have to assume every time one degree of
freedom more for the atomic motion, than we put above. For the
diatomic molecules we have then to assume besides the radial motion
a motion normal to the radius vector. For the triatomic molecules we
have then to assume besides the motions already assumed, still other
motions, e.g. such a one that the line which connects 4 and B,
leaves the plane of the figure, and that the line which connects
C and D rotates in the plane of the figure.

Accordingly on the supposition that « is proportional to 7, we
find the potential energy of the molecule (i.e. the amount with
which the total energy exceeds the vis viva) equal to zero, as
appears from:

oa ry (AP o mn (dPs
SOE ae a alee
v b

For then 7 oe

But it was not chiefly the calculation of the specific heat of the
complex molecules, which induced me to this investigation. And
though I am of opinion that its true knowledge is urgently required
for getting an insight into the way in which atoms are grouped in
the molecule and move relatively to each other, and though I think
that through its value we shall often be able to take a decision,
when other methods for the determination of the formula for the
structure of the molecule fail, there is as yet still too little
experimental material at hand to test different ideas which might

7

) is always equal to P;.
b

“1: aes p
suggest themselves. The prevailing opinion, that — must de-
F €

v

erease with the number of atoms, may be true in general, still there

C,
are remarkable exceptions. So the value of fur NH, found ex-

v
perimentally is not in accordance with what we should expect for
a tetratomic molecule. It points more to a molecule in which not
four, but only three atoms move with respect to the centre of

(576 )

gravity. This leads to the idea that the atom N is placed in the
centre of gravity of the three atoms M and docs not take part in
the atomic motion.

But let us now return to what I consider as the principal part
of this investigation, viz. the two equations of equilibrium;

aP; dP,
eres he Sen SS IIE
(pes zm os R
and
dP 2

dP, 5 bo) = RT
(p+ = + 7) o> og) = KT.

There are two cases in which we might substitute one single
equation of state for these two equations.
1st if eet could be taken as very great with respect to ie
db, dbs
or rather if we assume Ps; = } @ (6;—b 9)? and Py2 = $ ag (ba—boe)?
a, as being very great with respect to @. In this case b;—b9) is
small with respect to b:—bog and b,—by, may be equated to b—Dp.
The equation of state becomes then:

dP,
d

v

p+ 2 + ea) — by) | (bby) = BT,
just as for a diatomic molecule.
Qnd if a@; = ay. Then is 6;—bp, = b2—bog = } (b—b,), and we get:

dP,
pa

dv

as ) a. m
“itp Op) (b—b,) = 2RT.

For the suppositions as to the value of @, and @ which lie
between these two limiting cases, there remain two separate equa-
tions, but as an approximation it may be admissible to put in all
cases :

( CHE. Bae
iP -|- ae + @(b—b,)} (b—bo) =f LT,

if 7 has a value between 1 and 2.

For carbonic acid I had expected 7 to be little different from 2—
and with this value for f 1 have tested this equation of state of 6
to the series of values for this quantity which occur in the Chapter

( STi)
“Experiments of ANDREWS” in the first part of Continuity ete., in
order to see whether the observed variability of b might be explained
in this way. For the calculation of this series of values for 4 I

dP: (Ge

had assumed, that as equal to @ for a I had put the value of
0.00874. It has afterwards been doubted whether the molecular
pressure is expressed perfectly accurately by this simple value.
Nevertheless this form has always seemed the only rational one to
me, and the accuracy, with which by means of this form the coeffi-
cient of compressibility can be calculated, as I have shown in the
paper, which has been inserted in the volume of the Archives
Néerlandaises dedicated to Prof. Lorenrz'), has confirmed this
opinion.

It is not to be expected that I should have hit upon the exact
value of a, and in fact there is reason to assume, that a must be
about 3 percent lower, as will be shown presently. From this
follows that the series of values for 0 is not perfectly accurate either.

Aa (v—b)? c >
But as A, = RT a the error in 6, which at v= @ equal to
4a will continually b smaller with decreasing volume, and
pp Will continually become smaller with decreasing volume, an

become zero for the limiting volume; and as the value of 0, as will
appear presently, also decreases from a certain limiting value at
v=o to zero, it will have decreased approximately in the same pro-
portion. Consequently the series of the given value may serve as a test
for the given equation. The constants occurring in the equation will,
however, get a value somewhat different from what they would have
if they were derived from a perfectly correct series of values for b.

It is obvious that whatever formula we may take for the mole-
cular pressure, we shall find a certain course in the value 0, of such
a nature that if we on the other hand presume this series of values
of b, we can trace back every particular of the course of the pres-
sure curve. It is only the question whether the course of the values
found for & is such as we have a priori cause to expect. Now the
series of values of J first fulfils the condition that for large volumes
b does not sensibly differ and seems constant. Not before we get
volumes of the order of } (formerly I had thought volumes of 2),

1) Dr. G. Bakker informs me, that he made such a calculation of the coéfliciént
of compressibility already 14 years ago. It appeared from some pages of a M.S.
sent to me that he had calculated 6 for ether at 25° as equal to 0,000179.

39

Proceedings Royal Acad. Amsterdam, Vol, IL.

( 578 )

does this value decrease sensibly, And it seemed then to me a strong
proof of the accuracy of the values chosen for the molecular pres-
sure, that this condition was fulfilled in the values found for b. The
proof becomes much stronger if we can show that the values found
for b quite answer to a before calculated formula for this value.
The endeavours for finding such a formula for >, made by BoLrzMAnNnN,
Jicer, VAN Laar, myself and several other investigators, have
as yet always been based on the supposition, that the molecules
are rigid bodies of a spherical shape. The endeavours have
failed. Not only do they require hopelessly elaborate calculations,
but I have had to convince myself that the calculated values of the
coefficients found for such an equation cannot be in accordance with
the observations. Now that I have found that for complex molecules
of whatever shape, we find the same form for the equation of state
of the substance as for a substance composed of simple molecules, I
have thought that I might give up the rigidity and the spherical form
of the molecules, and I have wished to try whether the compress-
ibility of the molecules might be able to explain the decrease of b
with the decrease of the volume. In the followmg pages I shall
communicate the result, obtained in that investigation. Whether we
have quite to reject the correctness of the considerations, on which
the earlier attemps at the calculation of the variability of b are
based, I shall not make bold to decide. I have only tried whether
the equation :

Ip +i+e (b—b,) (\—b,) = f RT

represents the value of b found at every value of v.

This formula gives a value of 6 which changes exceedingly little,
if the value of v is great, and which decreases strongly for small
values of v.

Let us begin with modifying the equation somewhat. Let us viz.
introduce the limiting value of b for v=o. Let us represent it
by ly. It is ealeulated from:

Soe a,
If we write for p + — its value viz. ———, we get:
we

b—by pes fs ie ( a
en ad bob, 7)

(579 )

Let us take the series of values of v and b for ¢=35°.5 and for
t = 32°.5, which temperatures differ so little that the same values
may be assigned to the constants, and let us put 6,=0.0026. Then
two more constants occur in the equation, viz. f and b,. For both
we have some indication as to their value. For f we might take 2,
and for 0, (the smallest pessible value which 4 can assume) I had

1 :
thought that I might conclude to a value of wie according to the

earlier view of the cause of the variability. As f is much easier to
ealeulate than 6,, which can only be found by solving an equation
of the third degree, I took for 6, the value 0.00065. For the value
of f we find then, beginning with the smallest volume :

f=21l4, f= 2.08, f= 2.175, fo 2.14 ete.

Then I increased 0, a little, viz. so much that it became

0.0007 = ea g, and then we find with f= 2:

3,7
calculated found
b = 0,001798 v = 0,002622 0,002629
b = 0,00184 v = 0,002731 0,00275
b = 0,00195 v = 0,003050 0,003026
b = 0,0020 v = 0,0038213 0,00321

For the great values of v,6 draws so near to the limiting values,
that here the list of values of 5, which increase and decrease
regularly, are of no importance.

Only the value of v which is given for 6=0,00234 does not
agree, but it would perfectly agree if we might put 6=0,002295.

As I observed above, if the course of the value of d is represented
perfectly correctly by the equation, the isothermal caleulated by the
aid of it will have to possess all the peculiarities of the isothermal
| See pe > ped: Op
determined experimentally. So the value of v, for which — and —

dv dv*
are equal to zero, will have to coincide with the critical volume
and in the same way the value of a will have to possess for

AT
that volume the value which the experiment has determined for it.

39*

PE %
y

(580 )

Now if & is kept constant, the equation of state has shown such
large differences between the calculated and the experimental values
> PRE on a 5 4 °
of v, and RE,” that it is advisable to examine whether the varia-
bility of b according to the given formula can annihilate these

differences.
For the determination of the critical point we have now the
following equations :

awe al (1)
P ves v=—D :
2a JE (1 db (2)
ee (v—by’ i)
db dab
Bel = =) —_
3 . dv dv
2S aed ee)
v v—b 1 db
dv

The last of these equations, in which neither p nor 7 occurs,
will have to serve asa determination of »;, and that in connection with:

Loh b—b, \2)
Sela | ee

Let us write (3) in the form:

Pb

3(e—)) _, es “dv?
ae Se ee

For the determination of the critical volume we have therefore to

; db d*bh :
choose such a value for v, that the values for 6, — and —, which
dv dv?
according to (4) belong to it, satisfy (5).
From (4) we find:
db 1
dv 9 v—b 2 ; ( )

( 581 )

and
db
Ps 9 (=A) ( v—b )- — : ‘dv
Oe —by byg—b,y b—by ita db
v—b de> db dv
wo 142 a v aa ( v—b y aaa aaah)
do b—b, bp bs)

Such a value for v satisfying (5) can only be found by repeated
Suegahe ee anes _, ab
approximation. For this it is useful to get to know the course of 4, =
db
v—b dv?
2 1—db’
dv
With regard to } we point out that at v=o the value of b
approaches 4, asymptotically, that ) decreases continually with v and
that v and } assume at the same time the value J.
So if we take two axes, a v axis and a 0 axis, and if we draw
the point Pj, for which » =, and b=), then the line representing
b, will ascend trom the point P. The initial direction in Py is

and

aa. db 3 1b 2 :

indicated by —= J or in our case by ——-—. The value of
“dv 1+7 + hy ~ 83

db

7 is at v=o equal to zero, but may become considerable if v is
= \

9

: , : d-b ,
very small, and increase to */;. This value of ot Gas always nega-
av~
tive, but in the equation (5) this quantity does not occur separately ; it
d*b
=—b dv?

: ea.)
occurs however, in the combination —— a

It appears from (7)

uD
that this expression is negative, and of the order of ~ The factor,
av

‘ me sD mas : . .

with which a to be multiplied in order to get this complex, is
au

equal to 1, if v=, and descends to zero with diminishing volume.

db. Paldoe
It was necessary that J 8 never greater than 1. For if 7 sla
adv v

dp . , :
ger than 1, — is necessarily negative, and then we should get unstable
dv x

( 589 )

phases for very small values of », which is quite opposed to the expe-
riment. With the coefficients found in the earlier attempts at explaining
the variability of 6, I repeatedly met such unstable phases.

It is obvious that a value for v, satisfying (5) can be found, and
probably but a single value, if we pay attention to the fact that the

: 3
first member varies regularly between the values > and 0, and the

a

second member between 1 and 1/5.
But when determining the value of + which satisfies (5), we meet
with the difficulty, that we must be able to calculate not only 4,

1b ab : :
but also = and aa perfectly from the equations given for them,
v v0

while a slight change in the value of f and b, might cause a very
great change in the value of these quantities which is to be calculated.
So the equation (5) is not perfectly satisfied, if we take vr equal to
the observed critical volume. With J=216,7 we calculate »x=0,004082,

Th : ;
and we find the value of - equal to 0,16 40,17 and for the relation
v

db
v—b dv?
2 db

C=
dv

db ;
and 5 the value 0.71. Now (5) may also be written:
v

(8)

and calculated with this we do not get back » = 0,004082, but
v—0,00411. With 6 = 0,00223, we find v—0,004406, so the

db
gs it = Le
assumed critical volume, then — 0,132 and — (a) has a
dv 2 db
1 eee
dv

value very near 0,1. Then we find from (8) » = 0,000457, so a
greater difference between the two values calculated in different
ways. But the cause of this may be that the given equation for
the determination of & is drawn up to represent the series of
values which I have caleulated for them by aid of a not quite
accurate value of a, And moreover it appears sufficiently from the

( 583 j
deduction of the formula for 6 that it can only be meant as ari
approximation.

pi by ode ale - ;
If we put in future for — as it is in the critical point @, and 7

av
db
i) RS
for — are : , then
2 db
dv
Bhp
ee
1+ 2(a@+/9)
8 a l—ea—fyP(l+ 2(e+4 f)]
pe eS ea
oe aor bE ie
ea 27 l1—e—f
hie Geer |s$—=*—s
Pk = 97 = + («+ A)| l1—«a 5]

If @ and ? are equal to 0, then we find the known values which
have been calculated on the supposition of constant value of 0.

Let us take @—0,138 and #—0,1, which in the proximity of
the critical point of carbonic acid is not exaggerated. From the

: : ewe : ene
series of values of b a value for — =— is even calculated, if v is

adv o
between 0,00496 and 0,00321.

Then we find a very great difference in the critical volume, and
the factor 4; descends even to 2,03— to which must be added that
be is smaller than 4, and may be put at about 0,86 by.

But RT), and pz are comparatively little mfluenced by this value

seca sae fern
of @ and 7. The factor with which — — is to be multiplied, descends
= Ne
2 : 1 Z : f Ie
by it only from 1 to 1 — iG And the factor, with which Fae
= ‘ ( 20 O72

-

: Lae : : ; Lika ee 7
is to be multiplied in order to find pz, rises from 1 to < Therefore

Pktk —. Shy ok

the value of ane will be smaller than is found on the supposition of
tL

constant ) and that approximately in the same proportion, as is the

ease with vx, which is in perfect accordance with the experiment.

v °
For the value of (*) we find the expression :
RT/;

pr 3 i 9 1—@
( Jf 21—a—f 8(l—a—/p)’

Rr) ee Taye ae.

which leads to the wellknown value °/,, if @ and /? are O and

oi asa
descends to EMA with the given value of @ and ?. From the deter-

?

minations of VERSGHAFFELT we derive for this value
2)

(To be continued.)

Physiology. — Dr. J. Branp: “Researches on the secretion and
composition of bile in living men”. (Communicated by Prof.
B. J. STOKvISs.)

Nine cases of cholecystotomy, performed in the surgical wards of
the Binnen-Gasthuis at Amsterdam in the years 1896—1899, afforded
the occasion, to examine in the first place the rapidity of the flow
of human bile. The secretion is a continuous one, sinking during
the night, and showing its minimum in the early hours of the morn-
ing. After awakening the flow is rising generally fastly and attains
a maximum a few hours after midday. In the evening the flow of
bile presents a second maximum, which is much smaller than the
first. These maxima probably depend on the taking of meals. The
quantity of bile produced in 24 hours may be as great as 1100 ce
(so that it comes near the quantity of urine produced in the same time),
the smallest quantity found was 500 ce. There was no difference
in the concentration of the bile at different times of the day. The
quantity of the produced bile is very little influenced by the body-
weight ; it is chiefly depending on metabolism, which is exactly mea-
sured by the quantity of the essential substances of the bile. The
amount of solid matters in freely along the bile-ducts flowing human
bile (bile of the liver) attains 1.41 pCt. ; in bile, stored up in the gall-
bladder, it can be as high as 20 pCt. The colour of human bile isa
bright golden yellow one, and the amount of the colouring matter :
the bilirubin is rather low: 0.06 pCt. Human bile contains besides
bilirubine urobilinogen or properly speaking reduced urobiline in rather
large quantities as a constant compound, and probably also very
small quantities of haemato-porphyrine, which is almost never absent

eee

( 585 )

in bile of the gallbladder. As to the bile acids, the proportion between
taurocholate and glycocholate in human bile was varying between
1.45 and 1.54. Conjugated or ether-sulphurie acids were also found in
human bile, at the rate of 6.4 pCt.—11.7 pCt. of the sulphur they
contained, to the sulphur of taurochojate.

The physico-chemical properties of human bile were examined with
great care, as there are till now but very few investigations in that
direction. The molecular concentration of human bile, with its neu-
tral or alkaline reaction to litmuspaper, with a rather low viscosity
(the amount of mucine in bile of the liver is varying between 0.2
and 0.9 percent), examined by the method of determining the lowering
of the freezing point, proved to be almost perfectly equal to the
molecular concentration of the blood. This fact, which was also
stated for the bile of the gall-bladder, is a very remarkable one, in
as much as the amount of water and solid matters in bile of the liver
and in bile of the bladder can be most widely different; yet the mole-
cular concentration remains invariably constant. It may therefore
be concluded, that in the more concentrated bile, containing a large
quantity of great molecules as bilious acids, bilirubine etc. the rate of
inorganic salts and especially of Cl Na must be a low one. In fact
in bile containing 3.7 percent of taurocholate the rate of imorganic
salts proved to be 0.955 percent, in bile with 20.9 of taurocholate
this rate being only 0.265 percent. During secretion of bile resorpt-
ion of a salt-solution, which is isotonic with blood, must therefore
undoubtedly take place in the bilious ducts and the gallbladder.
Moreover the secretion of the mucous membrane of the bilious ducts
and bladder being also isotonic with blood, there can be an exchange
of molecules of salt for molecules of mucine, the molecular con-
centration i.e. the osmotic pression remaining unchanged. The influ-
ence of mucine in the process of resorption is not yet clearly deter-
mined. As a high amount of mucine accompanies as a rule a high
amount of inorganic salts, it may be assumed, that mucine is influen-
ving dissociation, or is linked to mineral compounds.

Finally, the electrolytic conducting power of bile was determined
by Konirauscn’s method. It proved to surpass the conducting
power of blood, (A 37° C = 18.21—18.30 + 10~* in unities of mer-
eury), as could easily be presumed by the great amount of salts it
contained. Yet the rate of inorganic salts is no measure for electro-
lytie conductibility.

( 586 )

Bacteriology. — Prof. M. W. Betnrinck presents a paper: “On
Oligonitrophilous Bacteria’.

By “Oligonitrophili” I understand those microbes, which develop
in media to which are not purposely added nitrogen compounds, but
without precautions having been taken to exclude the least traces
of these compounds.

They give rise to two different series of ,accumulation experi-
ments’’, the development being caused: /%rsf, in the light, without
any other source of carbon in the food but the carbonic acid of
the atmosphere, when chromophyll-containing oligonitrophili are
to be looked for. Second, in presence of a source of organic carbon
in the medium, when colourless oligonitrophili may be expected.
In both directions [ have made many experiments, of which those
in the light have a very slow course and are still in process; here
follow some results concerning “accumulation experiments’ with
colourless oligonitrophili.

1. Aérobiosis and Anaérobiosis in Oligonitrophili.

The “elective culture” of oligonitrophili in nutrient liquids with
organic carbon compounds, has first been practised by WINOGRADSKY,
under circumstances which secured anaérobiosis '). He used 2 to
4 pCt. glucose solutions with the required mineral nutrients and
4 pCt. CaCO%, but without purposely added nitrogen compounds.
For the infection was used garden-soil, and he constantly obtained
a culture of a microbe belonging to the butyric-acid ferments.
The experiments were performed in ordinary glass jars under
cotton-wool plugging, when first a rich culture of aérobics deve-
lops, which renders possible the life of the anaérobie oligonitrophi-
lous butyric-acid ferment, called by WunoGrapsky Clostridium
pasteurianum. He also worked with pure cultures of this species at
exelusion of air. When repeating his experiments I found that traces
of nitrogen compounds are indispensable for success, and the same
is the case for the aérobic oligonitrophili found by myself, so that in
culture liquids, prepared with all the precautions that exclude the
presence of compounds of nitrogen, as well with aérobiosis as with
anaérobiosis in a nitrogen atmosphere, the growth of otigonitrophili
is extremely feeble and soon ceases.

1) Recherches sur l’Assimilation de VAzote libre de Atmosphere par les Microbes.
Archives des sciences biologiques, St. Pétersbourg. T. 3 N. 4.1895. ,[lective culture”
js the name given by W. to the accumulation experiments,

( 587 j

My own experiments differ from those of Wrvoarapsky by my
having rendered possible either aérobiosis only, or by sufficiently
promoting the access of oxygen at least partly to counteract the
butyric-acid fermentation. So doing I came to the discovery of a not
yet described genus of oligonitrophilous bacteria, belonging to the
aérobies !), This genus, which is easily recognisable by the large dimens-
ions of the bacteria, I will call Azotobacter. Hitherto I found two
well distinguished species, one, A. chroococcum, is extremely common
in garden-soil, the other, 4. agi/is, is as common in the canal-water
of Delft.

Sufficient access of oxygen is easily to be obtained in my experi-
ments by cultivating in thin liquid layers on the bottom of spacious
ERLEMEIER-jars. As the butyric-acid ferment, however, can by no
means do quite without oxygen, but, being ,microaérophilous’’, does
want oxygen, albeit of low tension for vigorous development (which
has been overlooked by W1NoGRADSKY), the regulation of the access
of oxygen is not sufficient completely to keep this ferment out of
the aérobic cultures. I have therefore tried to prevent its growth by
selecting carbon sources which are well assimilated by Azotobacter,
but cannot, or can only with difficulty give rise to butyric-acid fer-
mentation. As particularly fit for this end I found to be: mannite
in 2 to 10 pCt. solutions, and calcium propionate in !/y pCt. solutions,
of which the former is hardly, the latter not at all attacked by the
butyric-acid ferment). Less adapted for the experiments are cane-
sugar and glucose, these sugars, especially the latter, easily getting
into butyric-acid fermentation. But I must remark that a feeble
butyric fermentation, at least when calcium carbonate is present,
is by no means prejudicial to my experiment, as calcium butyrate,
too, is a source of carbon easily assimilated by Azotobacter.

2. Accumulation of Azotobacter chroococcum from Garden-soil.

This species is obtained as follows.
In an ERLEMEIER-jar is introduced a thin layer of a not sterilised
culture liquid of the following composition :

1) More exactly of which one species is “macroaérophilous”, the other “mesoaérophilous”’,

?) It is also possible to prevent butyric-acid fermentation by introducing a piece
of pure red copper into the cultures, by which Azotodacter is not prejudiced. This
artifice occurred to me by observing the flame reaction of copper, when burning ina
Bunsen-flame, common 4zofodacter-tilms, grown without addition of copper, from a
erude culture, in tap-water with 2 pCt. mannite and 0,02 pCt. K®H PO*, and infected
with garden-soil.

( 588 )

100 Gr. Tap-water '),
2 , Mannite,
O02. ke HPOs

and for the infection is used a not too slight quantity, say 0.1 Gr.
or more, of fresh garden-soil *).

Accordingly, other nitrogen compounds but the small quantities which
occur in the tap-water and the infection material, are wanting. But
by numerous experiments, made under very different circumstances,
many of which with nutrient liquids prepared from pure destilled
water, whose composition was thus perfectly known, I have, as said,
come to the conclusion, that this slight quantity of compounds of
nitrogen is absolutely necessary for the success of the experiments
with Azotobacter, and that the same is true for WINoGRADSKY’s Clos-
tridium pasteurianum.,

In presence of nitrogen compounds in a rather considerable quan-
tity, e.g. 10 milligrams or more of potassium nitrate or ammonium
phosphate per liter of culture fluid, Azotobacter is no more proof against
the competition with the common nitrophilous microbes and does not
develop. But this is by no means the case with Clostridium pasteu-
rianum, which excellently develops even at much higher rates of
nitrogen compounds, though only then when the nitrophilous micro-
bes have nearly quite consumed those compounds, so that diphenyl-
amin shows no more nitrates, NEsSLER’s reactive no more ammonia.

If the culture jars, prepared in the said way, are kept at 28° to
30° C. then, after 2 or3 days, a floating film develops at the surface
of the fluid, externally resembling Mycoderma, but consisting of
Azotobacter chroococcum, and wherein, it is true, some other species of
small bacteria are present but not in sufficient quantity to determine
the character of the culture. These small bacteria have greater
want of nitrogen than Azofobacter, but less than the common
saprophytic “polynitrophilous’” species; they may accordingly be called
“mesonitrophilous’. The best known instance of mesonitrophiil is
Bacillus radicicola of the tubercles on the roots of the Papilionaceae,
but I have not succeeded to find this species in the crude Azotobacter
accumulations. The mesonitrophili relate to Azotobacter as the vinegar
bacteria to J/ycoderma in the films which are found on flat
beer, and their volume, when compared with that of Azotobacter

') The tap-water of Delft comes from the downs at Loosduinen,

*) From pasteurised soil aérobie oligonitrophili do not develop.

ee

( 589 )

itself, is so insignificant that at a chemical analysis of the culture,
they would hardly be perceived. By carrying on the experiment
with 1/, pCt. calciumpropionate as carbon source, instead of 2 pCt.
mannite, and with garden-soil as infection material, after 3 or 4 days
Azotobacter-films are obtained, in which microscopically no other
bacteria at all are to be found but A. chroococcum only, and of
which culture on solid media is necessary, in order to detect the
not absolutely failing strange species.

Besides these small bacteria are sooner or later found in the Azo-
tobacter-films a great number of Amoebae and Monads, sometimes
also Infusoria. !)

The common soprophytic bacteria, such as the fluorescents, the
various species of Aérobacter, Proteobacter, Saccharobacter, and the
hay bacteria, are quite wanting in the Azotobacter-films, although
their germs abound in the infection material.

Moulds and yeast species, too, are in the beginning totally absent, |
so that the rough culture of A. chroococcum can be regarded as one
instance more of a “perfect accumulation experiment”, of which I
recently described another case. *)

The number of carbon compounds which can be assimilated by
A. chroococcum is considerable. Thus mannite can be replaced by
2 to 10 pCt. cane-sugar, whereby, however, a more slimy film is formed,
which sooner or later sinks down. For glucose, in quantities of 2 to
6 pCt., the same may be observed. But these two sugars, especially
the latter, give most easily rise to butyric-acid fermentation, which,
by the free acid, acts injuriously on the growth of Azotobacter.
At simultaneous addition of calcicum carbonate a butyric-acid ferment-
ation may first occur, which is succeeded, in the same culture, by
the growth of an Azofobacter-film at the expense of the butyrate,
and producing crystals of calcium carbonate. With galactose,
levulose and maltose, I Jikewise obtained magnificent Azotobacter
cultures; galactose gives with difficulty, levulose, on the other hand,
gives easily rise to butyric-acid fermentation.

1) Amoebae feed with great avidity on dzotodacter itself, and, multiplying very
rapidly, can bring about much destruction in the cultures. They belong to different
species, which also easily propagate on the solid medium, fit for the pure culture
of Azotobacter. ‘hereon they produce the pure ‘‘veils of amoebae”, free from
bacteria, described by me at another occasion (Centralblatt fiir Bacteriologie Bd. 19,
pag. 257, 1896 and Bd. 21, pag. 101, 1897) and hence, may be obtained in pure
culture by the here described experiment, together with Azotobacter, and be cultivated
with other microbes at will for nutriment. Brief, also for the study of Amoebae the
Azotobacter-experiment forms the best starting point.

*) Centralblatt f. Bactericlogie, 2e Abt. Bd. 7, pag 35, 1901.

(590 )

With glycerin the experiments have a slower course; moreover only
with solutions of 2 to 5 pCt. I could obtain closed Azotobacter-films,
whilst 10 pCt. proved to be too concentrated. Milk-sugar is not assi-
milated by Azotobacter, but quite well by the butyric-acid ferment.
Furthermore, the following substances are assimilated with variable
intensity, the first best, the latter with more difficulty: propionates,
butyrates, lactates, malates, succinates, acetates and citrates. Form-
iates and tartrates are not attacked at all.

As from this list we may safely conclude, that Azotobacter is
able to assimilate still various other sources of carbon beside the
here mentioned, the oxidising faculty of this bactery is evidently
developed in a great many directions, and may perhaps be best
compared to that of the fluorescents, which, however differ from
Azotobacter by their much greater want of nitrogen, by which they
belong to the polynitrophili.

The crude Azotobacter-film obtained in the way described, consists
at first of extremely Jarge short-rods of ca. 4 « thick ard 5 «@ to
7 # long, with rounded ends, and which often have the shape of diplo-
cocci. !) Mostly all are in rest but some specimens swim stately
round. Remarkable is the presence of a lateral vacuole in some
individuals.

The cell-wall is slimy and easily visible, or rendered visible by
introducing some small bactery into the microscopic preparation,
whereby the slimy coat, which in water alone is not to be seen,
becomes distinct, as the small bacteria do not penetrate into it. At
nutrition with mannite most individuals are filled with exceedingly
small regularly placed drops of fat.

When the cultures grow older the floating film changes color
and first becomes brown, later on sometimes even black. But this does
not always occur and depends on known and unknown circumstances,
Thus the color changes slowly or not at all at the direct nutrition
with sugars, but the change can with certainty be expected when
butyrates or propionates are used as carbon food, or, with sugars,
in presence of calcium carbonate, and after previous butyric-acid
fermentation.

The coloring matter is not soluble in the usual solvents as water,
alcohol, chloroform, ether and CS, and is quite different from chromo-

1) On propionates and acetates as sources of carbon, and with garden-soil for infection
material, [ have in these accumulation experiments sometimes obtained a much
smaller form, which [ consider as a variety of 4. chroococcum and not as a separate
species. A second variety of A. chroococcum I obtained from canal-water,

as

(591 )

phyll. It induced me to choose the word chroococcum for the name
of the species.

With the change of color the microscopical appearance of the
bacteria themselves changes also considerably. The dimensions grow
smaller and the shape becomes more globulous, so that we should
think to have common, even small micrococci before us, but at the
partition these older cells remain united in sarcine lumps. The
shapes of the involution forms of Azotobacter are very singular. They
can attain gigantic dimensions, e. g. 1LO—15 w, and remind of
amoebes and yeast cells. They are especially met with in the Azoto-
bacter-films of the crude cultures.

3. Pure culture of Azotobacter chroococcum.

The pure culture of this species from the crude floating film is
easily effected by streaking it off on a culture plate of the following
composition :

100 ir. Destilled water.
2 "Agar:
2 » Mannite.
O02 a ok? EL POs,

The 2 pCt. agar contain the other necessary mineral nutrients in
sufficient quantity. Grown at 30° C. Azotobacter becomes after one
day already visible as white, starch-like colonies, among the, for the
greater part watery, transparent nitrophili. Though in the crude
cultures the latter had slackened their growth, on the plates they again
acquire a considerable development, evidently in consequence of the
presence of nitrogen compounds in the agar. The number of the

zotobacter-colonies is always much smaller than might be expected
from the number of germs brought on the plate, so that some attent-
ion is necessary to find them out when still young; but later they
become quite distinct. On the said medium, if containing sufficient
mannite, e.g. 5 to 10 pCt., the Azetobacter-colonies can grow a
very long time, and thereby attain much greater dimensions than
those of the nitrophili.

Contrary to what we have seen in the crude cultures, Azotobacter
ean develop in pure condition on the most different media. On broth
gelatin it grows however slowly and little characteristically ; it
hardly or not liquefies the gelatin.

Grown in liquids the presence of small quantities of nitrogen com-
pounds furthers considerably the growth of the pure cultures. Espe-

(592 )

cially nitrates are easily assimilated and may even be added to an
amount of 0,1 pCt. Thus I sometimes, but not always, saw an enor-
mous growth in

100 Gr. ‘Tap-water
2 to 10 , Mannite
0.02, 5. KH. PO?
Oa SA KaNO?

With ammonia salts the growth of the pure cultures is slower
than with nitrates, and the amounts which act not deleteriously,

are slight. Still I saw a considerable devolopment in

100 Gr. Tap-water.

2 to 4 , Glucose.
0:02 2 sKeHEOs
0.02... (NHS) EEO:

Asparagin acts about as ammonia salts. Peptone is assimilated
with great difficulty.

After being kept for some weeks the pure cultures, in particular
with glucose as carbon food, grow dark brown, quite like the crude
films mentioned above, and in other respects too, they seem somewhat
to alter their character. I could at least in no way produce on nutrient
liquids, with the pure cultures, the magnificent films which are
obtained by the crude infections; the newly formed cells remaining
constantly immersed. But I should call to mind that this is partly
explained by the use of non-sterilised materials in the crude cultures,
which of course cannot be used in the experiments with pure
cultures.

The motility of this species is always restricted to a very small
number of individuals. By this reason, as also in consequence of the
slimy constitution of the cell-wall, the experiments to color the cilia
had given no result in my laboratory. But Professor Zerryow at
Berlin, whose advice I have asked, procured me very beautiful
preparations, from which it is certain, that at least the great
majority of the moving individuals, possess one polar cilium of
nearly the same length as the body of the microbe itself.

4. Azotobacter agilis.

This species is obtained by the “accumulation experiment” de-
seribed for A.chroococcum, with this difference, that the tap-water is

( 593 )

replaced by canal-water'), and that the infection with soil is omitted,
as the very question is to develop the oligonitrophili present in
the canal-water itself. Good agilis-films are produced, when

100 Gr. Canal-water.
2 » Mannite
0.02. ,. K*H PO?

in a thin layer is allowed to stand for some days at 30° C.

It is true that glucose is much better assimilated by A. agilis
than mannite, but it causes more easily butyric-acid fermentation,
which should here be avoided. Nevertheless I have in some cases
obtained good results with glucose, and with cane-sugar also. Likewise
when using '/) pCt. calcium lactate, or 1/, pCt. calcium acetate. Even
2 pCt. alcohol is a very good source of carbon, but, like the last
mentioned organic salts, produces an agilvs-film much later than the
different sugars. With propionates I obtained less good results, as
therewith very numerous monads and amoebae originate, which feed
on agilis.

The canal-water of Delft being rich in organic matter, the addition
of a little K* HPO* only is mostly also sufficient to form a beautiful
film of Azotobacter agilis, which however, as a matter of course,
remains poor in bacteria material.

The pure cultures are obtained in the same way as described for
A. chroococcum. The best medium is

100 Gr. Destilled or tap-water
2 » Agar
2 » Glucose
0:02, KH PO!

In the streaks, inoculated on this medium the colonies of agilis,
always intermixed with those of many other kinds of bacteria, among
which Azotobacter chroococcum commonly occurs, are easily recognised
after 24 hours already.

Tf in this latter solid medium the glucose is replaced by !/, pCt.
calcium propionate and if streaks are made of the crude culture, then
also a considerable growth follows, and around the colonies of A.
agilis a greenish diffusion zone arises, reminding of the coloring
matter of the fluorescents.

1) From the water of the North sea I could not obtain oligonitrophili.
40
Proceedings Royal Acad. Amsterdam. Vol. IIL.

( 594 )

In the pure cultures of A. agilis on broth agar, on broth gelatin,
or in broth without gelatin, the growth is not very vigorous, but
the motility is great.

The microscopic appearance of this bactery, in particular of the
pure cultures on glucose-agar, is extraordinary. The large, transpar-
ent, extremely motile cells, show a wall, a small cell-nucleus, a pro-
toplast with some granules hardly discernible from the nucleus, and
often a very distinct vacuole. They measure ca. 5 we or less, some-
times however more, and are very like small monads, or, when they
dou’t move, like small yeast-cells. At the cell-partition in the living
preparation a distinct nucleus-spindle is visible in many cells.

Spores are wanting.

The cilia-coloration is difficult and did not give satisfactory results
in my laboratory, I therefore addressed myself, as in the case of
A. chroococcum, to Professor ZetTrNnow in Berlin, to whom I
sent A. agilis, with a request for his opinion. He had the
kindness to supply me with magnificent preparations, which prove
most convincingly that the cilia are placed in bundles at the poles.
He thereabout writes as follows: ,..... In Spirillen-Bouillon !)
war kein Individuum, das sich nicht auf das lebhafteste bewegt
hatte... Nach der Art der ruhigen, wogenden, wenn auch kriftigen
Bewegung, welche mich sehr an derjenigen kleiner Monaden
erinnerte, hatte ich 1, resp. mehrere Polgeisseln vermuthet, und
diese Ansicht haben auch die Preparate aus Spirillen-Bouillon,
in welcher die Kultur in vollstem Leben durch Formalin abgetitet
wurde bestitigt. Hs hat mir jedoch Schwierigkeit gemacht zu
diesem Resultat zu kommen. Die 6 bis 10 am Pol, resp. beiden
Polen befindlichen Geisseln, legen sich nimlich meistens an der mit
vielem stark klebendem Kctoplasma versehenen Oberfliiche so an,
dass sie scheinbar von der Seite zu entspringen scheinen.” I also
was at first in doubt and believed to see lateral cilia, but after a
minute examination of the preparations I consider Prof. Zerrnow’s
description as quite correct.

The relation to nitrogen of <A. agilis is about the same as
in Azotobacter chroococcum; to oxygen, on the other hand, it is
different, as is proved by the following experiment.

If “respiration figures’’ *) of agilis are formed in ordinary micros-
copie preparations, between object-slide and cover-glass, the most

') Broth with the addition of 0.1 pCt. KNO* and 0.1 pCt. (NH*)? SO*.
*) For this term to compare; Centralblatt fiir Bacteriologie Bd. 14, pag. 827, 1898,

(595 )

strongly motile cells prove, like spirils, to be “mesoaérophilous”’,
but they accumulate somewhat nearer to the meniskus than spirils
would do, so that they approach the ,macroaérophilous type’. When
continuing to grow in the glass-room, many cells stick to the glass
and then display their mesoaérophilism with great distinctness.
A. chroococcum, on the other hand, is macroaérophilous.

If the canal-water cultures, with mannite or other sugars as
carbon food, are allowed to stand for some weeks at about 18° C.,
many, but not all, are crowded with an exceedingly rich flora and
fauna, so that sugar solutions of 2 pCt. may literally become thick
with microbic life, of which, besides A. agilis itself, spirils and
other bacteria form the main portion, but where amoebae and other
protozoa too, are present in great number.

It is a remarkable fact that oligonitrophilism can be the foundation
of such a profuseness of life, if only care be taken for sufficient
access of air.

Chemistry. — Professor Baknurs Roozesoom presents a paper
of Dr. C. H. Winn: ‘On the irregularities of the cadmium
standard cell.”

1. Some cadmium standard cells constructed in accordance with
the directions of the Physikalisch-Technische Reichsanstalt exhibit
abnormal phenomena as shown by the observations made in that
institution '), and also by the researches of CoHEN 2) and others.

COHEN investigated a cell made up as follows:

Cd | dilute solution of CdSO, | Cd-amalgam of 14.3 %,,

and found in the case of two cells I and II which had been con-
structed in accordance with this type a difference in EMF. In the cell
I it amounted to 56 mV at 0° and to 50 mV at 25°, with an almost
linear slope; in cell II it amounted to 51 mV at 0° and to 50 mV at
25°, with a maximum of 52 mV at an intermediate temperature.
COHEN assumes provisionally*) that we are dealing here with diffe-
rent modifications or states of equilibrium of the 14.3 per cent amalgam.

1) W. JAcER u. R. WacHsmuta — Wied. Ann. 59, p. 575, 1896; W. JAczeR —
Wied. Ann. 65, p. 106, 1898; Dr. Ann. 4, p. 123, 1901.

*) E. Conzn — Vers]. K. A. v. W. Amst. 9, p. 125, 1900.
Sid) — 1. c. p. 137.
40*

( 596 )

In fact he found that the cell II after being cooled for the first time
from 25° to 0° showed at first a higher EMF (55 mV) which era-
dually passed into the lower value (51 mV) and that the amalgam
I showed a contraction in the dilatometer at 0° while the volume
of the amalgam II seemed to remain constant.

From these facts CoHEN at first concluded that between 0° and 25°
(more correctly 23°) the amalgam I is metastable and the amalgam
II stable. Afterwards!) he has seen reason to modify this opinion
and to look upon I as the stable and on II as the metastable form,
although this would render the experience with the dilatometer rather
obscure.

In his arguments, CoHEN starts from the supposition that the
amalgam in both cells had the same quantitative composition and
in my opinion it is questionable whether this supposition agrees
with the facts. I conceived a doubt about this when reading JAGER’s *)
note on the dependence of the EMF of the cell

Cd-amalgam 14.3 /) | solution of Cd SO, | Cd-amalgam x

on the molecular relation « of the mercury to the cadmium in the
amalgam which forms the second pole. This research gave me an
idea which may perhaps lead to an explanation of the irregularities

observed.
=

ee 2. The curve (fig. 1) repres-
Voll enting the EMF of JAGErR’s
cell in its dependence on the
Initial concentration of the variable
“ve analgam pole, shows a_ part
which is parallel to the axis
of concentrations: the EMF
has proved to be nl in the
case of all cells with amal-
gams of 6 to 14,3 °, of Cd as

second pole.

ea 20!

001 op ee From the phase rule it may
/o be concluded that the variable
cS fe & 4% “amalgam pole will not have been
Big. 1. homogeneous in the case of the
1) id. — Versl, K. A. v. W. Amst. 9, p. 368, 1900.

) W. JAcrrR — Wied. Aun. 65, p. 106, 1898.

( 597 )

compositions to which this horizontal part of the EMF line relates,
but will have consisted of two phases in equilibrium. For it is
evident from the course of the above EMF line that in the system
Cd-amalgam | solution of CdSQ,, if the cadmium content of the
amalgam be > 14,3 or < 6 per cent and the temperature, exter-
nal pressure and strength of solution are kept constant, one of the
variables which, along with those above mentioned, determine
the condition of the system must still be arbitrary; because a
change in the cadmium content of the amalgam produces a (perfectly
definite) change in the potential difference. Under these circumstan-
ces there is therefore a complete equilibrium in the system with one
arbitrary variable. As there are four independent components (Cd,
Hg, Cd S04, H,O) whilst three of the quantities governing the con-
dition of the system possess a previously given value, there must be
4+ 1—3=2 phases in the system. One of those phases is the
solution, the other is the amalgam. Between the above mentioned
limits of concentration the potential difference is, according to J AGER’s
measurements, a perfectly fixed value. We are consequently dealing
here with an equilibrium in which none of the quantities determining
the condition of the system is arbitrarily variable; the number of
phases must have increased by one and the amalgam therefore have
split up into two phases. The concentrations of these phases will
be the limits of concentration of the region of constant EMF, viz.
about 6 and 14.3 percent.

As far as it appears from JAGER’s communications he has not
himself drawn these conclusions; nor is it at all sure from what he
states that he has noticed any heterogeneities in his amalgams.
LinDEcK, however, states in an article also cited by JicEr!):
» Withrend bei Amalganen mit hohem Gehalte an Metall Schichten
mit verschiedenem spezifischem Gewicht sich manchmal abzusetzen
scheinen,....”. Dr. E. Conen, who does not mention anything in
his paper about a possible splitting up into two phases, orally
communicated to me that he considers this by no means impossible.

Prof. H. W. Bakuuis Roozesoom informed me that the two-
phased equilibrium of cadmium amalgam, the existence of which he
had long ago suspected, has been proved in his laboratory in the
course of a not yet finished research by Dr. Bisu. Moreover this
research has already shown that the limits of concentration for the
amalgams, in which that kind of equilibrium is found, are pretty
accurately 6 and 14.3 percent of cadmium,

1) 8. Linpeck — Wied. Ann. 35, p. 328, 1888,

( 598 )

3. If we admit the existence of two-phased equilibria in the
cadmium amalgams, it is not difficult to suggest causes which may
explain the singular phenomena occurring when experimenting
with them.

Let us first consider the phenomenon!) observed by JAcer that
the EMF of his cell when the second amalgam pole contained 15
percent or more of cadmium, was ni/ immediately after the construct-
ion of the cell and arrived at its final value only after the lapse
of several hours or even days. The explanation of this phenomenon
offers little difficulty, especially when it is taken into consideration that
these strong amalgams, as JAGER observes, are already rather solid
so that changes in the distribution of the cadmium can take place
but very slowly.

It may be very well imagined that immediately after the con-
struction of the cell, the amalgam poles are not quite homogeneous
even when their percentage of cadmium is such that the true equili-
brium would consist of one phase only; further that where the
amalgam is in contact with the solution of CdSO, some parts of
it are particularly poor in cadmium and may even contain less than
6 percent. If this is really the case, these parts of the surface will
possess a greater potential value in reference to the solution than
the parts of the surface which are richest in cadmium. This will
then cause electric currents in the solution from the richer parts
of the surface to the poorer; and these currents will withdraw cad-
mium from the richer and deposit it on the poorer parts and by
this way soon create a condition in which, at the surface layers of the
amalgam which are in contact with the solution, no other concen-
trations occur than such as fall within the region of two-phased
equilibria. By all this there will be, however, no equilibrium as yet
between those surface layers and the interior of the amalgam with
its high percentage of cadmium, and consequently diffusion will occur
and in the long run lead to a homogeneous distribution of the cad-
mium in the amalgam and to a potential difference between amalgam
and solution as corresponding to the final equilibrium.

4. The difference observed by CoHEN between the two similarly
constructed cells I and II (v. § 1) may be readily explained by
supposing that CoHmN in making the cells unconsciously used portions
of a two-phased amalgam, It is then only necessary to assume that

1) L. c. p. 108,

(599 )

he happened to use for the cell I a mixture of the two phases in
which each of them was present in somewhat considerable quantity
and for the cell IJ a mixture in which the phase containing least
cadmium was represented only to a small degree. Indeed if this
supposition be true both cells ought at the commencement to show the
same EMF, but on cooling to 0° they might behave differently.
There are again grounds in this case to expect two distinct states of
equilibrium, a provisional one, which is established quickly after the
lowering of temperature, and a final equilibrium, into which the
provisional one gradually passes and which will continue to exist
as long as the temperature is not again changed. For if the pole
of the cell in question is a two-phased amalgam at the higher
temperature it will after the fall in temperature still remain hete-
rogeneous at first, while under the influence of local electric currents,
as in the case of Jiaur, the potential difference which is established
between the amalgam pole and the solution will be the one cor-
responding to the two-phased equilibrium of the lower temperature.
In other words shortly after the fall of temperature we may equally
expect in cells I and II the voltage belonging to a two-phased
amalgam pole of the new temperature.

What will happen next, depends on the amount of cadmium in
the amalgam pole, that is to say on the relative quantities of the
two phases in it,and also on the shape of the curve limiting in the
diagram of the EMF-isotherms the region of two phases (fig. 2).

Pot.ca-amalg. — Pot.ca.

( 600 )

In the case of the amalgam pole I we have assumed that each of
the two phases are present in not too small quantities so that the point
which indicates its composition on the isotherm of 25° is situated
somewhere in P; not too near one of the limiting points. The point
Q, on the isotherm of 0° that lies in the same vertical with P, may
then easily fall within the region of two phases ; it will, however, gene-
rally speaking, indicate a considerable change in the ratio of the
two phases for the final equilibrium. From this it follows first of all
that the potential difference corresponding to the final equilibrium
at the lower temperature will not differ from that corresponding to
the provisional equilibrium, so that the final voltage of the cell will
be the same as that shown shortly after the cooling. On the other
hand, however, the final equilibrium will not be reached until the
corresponding ratio of the phases has been fully established in the
mixture, a process which will probably be a very slow one. If we
now assume that this process is accompanied by contraction, the
dilatometric experiment of CoHEN with the amalgam I will be fully
explained too.

In the case of the amalgam pole II we have assumed that the
phase poor in cadmium was present only in a small quantity so that
the point Py which represents the initial composition of this amalgam
lies in the horizontal part of the isotherm of 25° but rather close
to one of the limiting points. If we now suppose that here the curve
limiting the region of two phases approaches the EMF-axis as the
temperature falls, as indicated in fig. 2, then the vertical line drawn
through Py may cut the isotherm of 0° somewhere in a point Qe on
the descending branch. This point Q. gives the EMF belonging to
the final equilibrium of the amalgam at 0° and also the nature of
this equilibrium. If, therefore, our suppositions are correct, this
equilibrium must be one-phased and the final EMF be lower than
the one corresponding to the provisional equilibrium.

So it is quite clear why cell II, after cooling to 0° could at first
show an EMF of 55 mV and afterwards only one of 51 mV. Whether
the limiting curve really takes the above supposed course, may be
decided by the experimental investigation of the two-phased region +).

Another peculiar fact in CoHEN’s investigation is this. The cell
Il, after having been again heated to 25° and having shown there
the same EMF as the cell I, when once more cooled to 0° did not

') From a little sketch forwarded to me a few days ago by Prof. Baknurs RoozEBooM
I think I may coneclnde that my idea about the course of the limiting curve is correct,

( 601 ) |

at first possess the EMF 55 mV, as formerly, but immediately
showed the EMF 51 mV!). This may be explained by assuming
‘that the amalgam pole after having become homogeneous by the
first cooling has remained so when the temperature increased (its
state of equilibrium having perhaps been “metastable” towards the
end), so that during the subsequent cooling there was not occasion
for a distinct provisional equilibrium, as formerly.

5. It appears to me that many of the phenomena observed in
the investigation of the Wesron-cell in the Physikaliseh-Technische
Reichsanstalt which have as yet remained obscure may be explained
in an analogous manner by the existence of two-phased equilibria
in the cadmium amalgam and by retardations in the attainment of
the equilibria.

A result of some practical importance of the above considerations
would be, that the Physikalisch-Technische Reichsanstalt by altering
their prescription for the construction of cadmium standard cells so
as to recommend now a percentage lower than 14.3 of cadmium
— whether this was done on sufficient theoretical grounds or not
— have found the right way of insuring a cell with a perfectly
definite EMF, and so of making the cadmium element more capable
of serving as a standard.

Botany. — 8. L.Scnouren: “A pure culture of Saprolegniaceae’.
(Communicated by Prof. F. A. F. C. Went).

A new method which J devised for making pure cultures as well
of bacteria as of other micro-organisms and of which a preliminary
account appeared in the ‘‘Handelingen van het 7de Nederl. Nat. en
Geneesk. Congres’ amounts essentially to what follows.

On a cover glass, greased with a little vaseline and then passed
through a flame 3 or 4 times, a drop is placed in which among
others, the micro-organism occurs, which we wish to breed. At a
distance of about 2 millimetres another drop is placed of the nutritive
fluid in which we will produce the pure culture. Then the cover
glass is laid on a moist chamber under the microscope. The right
and left sides of this moist chamber have a horizontal slit, closed
with olive-oil a little thickened with sulphuret of lead paste. Through

1) E. Conen — Versl. K. A. v. W. Amst. 9, p. 129, 1900.
.*) L. ce. p. 110.

( 602 )

the slits 2 glass needles protrude, the ends of which are differently
shaped according to the larger or smaller size of the micro-organism
to be isolated. By means of a simple mechanism the needles can
pivot about a point of support so that their ends can touch the
lower surface of the cover glass. Moreover it has been made possible
to do this in any place of the field.

On the bottom of the moist chamber a drop of water has been
placed beforehand; hence its space is saturated with water vapour.
This water vapour is condensed on the lower surface of the cover
glass and this having previously been treated with vaseline, the
vapour is condensed as small, globular, non-coalescent droplets.

Before being used the needles are sterilised in a way on which
we will not dwell here.

Now suppose that we want to isolate a small micro-organism ¢.g.
a bacterium. With the strongest magnification (oil-immersion) the
edge of the drop, containing the bacteria, is examined. When the
bacterium has been found, the needle on the right is moved up-
wards, so that it reaches the drop close to the bacterium. Now the
whole of the moist chamber is moved to the left; to this end it is
held in a movable object-stage. By this movement the bacterium
together with a very small drop, will be extracted from the large
drop. The moist chamber is steadily moved to the left until the
small drop with the bacterium in it has come quite near the big
drop of nutritive fluid in which the pure culture is to be bred.
Now the needle on the right is moved downwards; one makes sure
for the last time that no more than that one bacterium has been
isolated and then the bacterium and the little drop are carried with
the needle on the left into the edge of the big drop in which it is
to multiply. The cover glass is then placed on an ordinary moist
chamber and allowed to remain for 24 hours at the required tem-
perature. It will appear that in that time a colony has formed at
the edge of the drop which may again be examined with the
strongest magnification. Bacteria are isolated with a straight, fine-
pointed needle.

Larger bacteria e.g. threadshaped ones and other micro-organisms
of average size are isolated with a fine inoculating eye; for the
largest micro-organisms (such as spores, conidia, zoospores of
moulds and algae, myxomycetes, infusoria, yeast-cells, etc.) a coarse
open inoculating eye is used. In the latter case we isolate with
a feebler magnification and only control what has been isolated
with the strongest magnification. Also in this case the isolated cell
is on its way passed through a drop in order to remove any

( 603 )

bacteria that may accompany it. This drop should be placed
between the two others.

I will not dwell on the technical detaiis of the preparation of
the needles, on the question why two needles are used, etc. Here I
will only give some information about an application of this method,
viz. about pure cultures of Saprolegniaceae. These living for the
greater part saprophytically, occur mostly in water, teeming with
bacteria. Here we have a case in which it is a great advantage
to possess a method through which we can isolate under the
microscope a single cell (in our case a zoospore) which is not cont-
aminated with bacteria.

A zoospore of Achlya spec. was isolated in an infusion of weevils;
after 24 hours it proved to have germinated into a mycelium,
occupying nearly the whole drop. This drop with the mycelium
was transferred into a tube containing weevil-broth and from this
culture inoculations were made on various nutrient materials as
weevil-broth with gelatine or agar, pease-water, glucose-peptone
(glucose 5 percent, peptone !/, percent. potassium phosphate !/;9 per-
cent, magnesium sulphate 1/,) percent), the same with gelatine or
agar, rice, albumen. Less suitable were Lérrner’s gelatine-broth
and agar-broth.

Very little being known about the physiology of nutrition of
moulds, living on animal substrata, some points relating to this
subject were investigated with Achlya, the more so since the method
applied with the same purpose by Kuxps !) on Saprolegniaceae, is
open to objections.

In order to find out which nitrogenous food is most advantageous
for the mould, a number of flasks were provided with a fluid, con-
sisting of 5 percent commercial glucose 1/;) percent pot. phosphate
and 4/s.) percent magn. sulphate and so containing all elements
excepting N. Then the N-containing food was added to these flasks,
a different one to each. To one flask nothing was added. From an
experiment of this kind it appeared that sodium nitrite, potassium
nitrate and urea were not used as food; the first even acted as a
poison. Asparagine was a bad food, amm. sulphate was better, lastly
peptone was by far the best.

In a similar way the nutritive value of various C-containing
substances was investigated. Here all the flasks were provided with
a fluid, consisting of 1/2 percent amm. sulphate (peptone could not

1) Jahrb. fiir Wiss. Bot. XXXIII pag. 517.

( 604 )

be used as an N-source, as it also contains ©.) 1/;) percent pot.
phosphate and !/,, percent magn. sulphate. The result was that
potato-starch was the best C-food; much less good was maltose and
then came in descending order milk-sugar, commercial glucose, syrup
of laevulose, cane sugar. Pot. citrate, pot. tartrate, sod. benzoate,
sod. butyrate, pot. acetate were not used as food. The last three
substances even acted more or less as poisons. Peptone appeared to
be both a C- and an N-food. From the group of fats Arachis-oil
was chosen for determining its nutritive value. It was not used as
food however.

In glucose-peptone the mould causes acid reaction. Bred in anaérobie
conditions in the same fluid (by BucHNeER’s method) it forms alcohol.
From amylum (e.g. in cultures on rice) it forms sugar, dextrine
appearing as an intermediate product. This is clearly shown when
one follows the auxanographie method of Bretserinck-WsMAN. An
agar-plate, containing 1/, percent of soluble amylum, is inoculated
in the middle with a bit of mycelium. After about 2 days the plate
is almost entirely overgrown. A diluted solution of iodine is then
poured out over it; that part where the mould has not yet entered
or where it is just entering, turns blue; inside the blue one sees
a violet-red zone and the large middle part remains colourless.

'The fact that the mould liquefies gelatine, made it probable that
a proteolytic enzyme would be secreted. The rate at which this enzyme
acts and the circumstances under which it is produced, were inves-
tigated a little more closely.

At first the method, given by Fermr!), was followed. In this
method a mixture of 100 ¢.c. water, 7 grammes of gelatine and 1
er. of phenol is poured into ordinary test-tubes. After cooling, 2
percent of phenol is added to the liquid the proteolytic enzyme of
which one wants to study. Instead of phenol thymol is also pre-
scribed as an antiseptic, otherwise toluene, sodium arsenite ete. One
now sees whether the gelatine is liquefied and how soon this takes
place. With not very quickly acting enzymes one may have to wait
for many days and sometimes weeks before any effect is seen.

Therefore Frrmi’s method was modified in such a way that the
results become visible as soon as possible. To this end one takes
water saturated with thymol and adds to it 71/, percent of gelatine
and so much pounded cinnabar that the liquid looks thoroughly red.

rv

This mixture is poured into test-tubes, 5 c.c. into each. When the

1) Arch, f, Hyg. XII, 240.

( 605 )

gelatine has solidified the tubes are put in a beaker of water, kept
at 40° C. The gelatine having melted, the tubes are held for ten
seconds in a slanting position under a fan-shaped jet from the
water-conduit, which surrounds all the gelatine at once. By this
bath of 10 seconds’ duration the gelatine does not become solid but
viscous. If the tube is thereupon placed vertically, a thin film, of
very nearly semi-elliptic form, will remain behind on the wall above
the surface of the gelatine. After having cooled, these test-tubes
ean be filled in the ordinary manner with the fluids we wish to
study, with the addition of a little bit of thymol.

The aim of this method is, to bring the enzyme into contact with
as large a gelatine-surface as possible. Besides, the gelatine being
spread in a very thin layer, it can rapidly be dissolved. By the red
colour the liquefaction is sooner observed. The way in which these
tubes are prepared, warrants us that the thin layer has the same
thickness in all the tubes, which renders a comparative study possible.
When the thin film has liquefied, we can by means of the rest of
the gelatine at the bottom of the tube, control the action of the
enzyme during longer periods, as well as in the old method.

With this modified method and at the same time with the old
one, the question was studied whether the mould secretes proteolytic
enzymes in a nutrient medium of 5 percent albumen in water
and in one of glucose-peptone. In both cases the liquid from the
culture-flask was used after simple filtration and also a filtered watery
infusion of the mycelium crushed with glass-powder.

At 9 o'clock in the evening the experiment was started. The
result was already clearly visible the next morning, that is after
12 hours: the thin red layer had almost entirely disappeared in the
liquid, obtained from the squeezed mycelium of the albumen-culture
and also in the culture-fluid itself; in two similar liquids, obtained
from the glucose-peptone culture, the red layer had not yet been
noticeably attacked, but only disappeared after 2'/, days. With the
old method no effect was visible after 3 days.

Also during a longer period the action of the enzyme was
observed. After 20 days the amount of liquefied gelatine was:

in the albumen-culture liquid TD, RCC:
> é x (squeezed mould) IED
>. glucose-peptone-culture liquid HLOM ae

» » ” : » (squeezed mould) 1.00 ,

( 606 )

So we see from this, in accordance with what already appeared
from the vanishing of the thin layer, that the enzyme of the albumen-
culture acts more energetically than that of the glucose-peptone cul-
ture and in both cases we see that the liquid obtained from the
squeezed mould-threads contains a less active enzyme than the liquid
in which the culture has developed. The enzyme further proved to
act in the presence of acid as well as of alkali.

Observations were also made as to whether the mould can, by
secreting an enzyme, split up fats into glycerine and free fatty acids.
In the culture-flasks a little litmus solution was put, which showed
a neutral tint and which accordingly would turn red if sucha split-
ting up took place. The fat chosen was Arachis-oil, which however
appeared not to be split up.

It is generally assumed that Saprolegniaceae live saprophytically
on animal and vegetable substances, but that they prefer the former.
Surely the widely known method for obtaining material of Saproleg-
niaceae (viz. by throwing weevils or flies into a trough of ditch-
water) is one of the causes of this opinion. From the preceding
investigations it appears however that we may safely assume vegetable
substrata to be at least as advantageous as animal ones. The use
of animal substrata for obtaining material finds a probable explana-
tion in the fact that there are relatively few moulds, which live
saprophytically on animals, so that other undesirable fungi will not
easily develop on those animals.

(April 23, 1901).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TH AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Saturday April 20, 1901.

—ICe—

Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
fo) re} t=) 5 (=)

Afdeeling van Zaterdag 20 April 1901, Dl. 1X).

Contents: Prof. H. A. Lorentz: “Borrzmann’s and Wien’s Laws of radiation”, p. 607. —
Prof. H. Kamerzincu Onnes and H. H. Francis HynpMan: “Isothermals of diatomic
gases and their binary mixtures. I. Piezometers of variable yolume for low tempera-
tures”, p. 621, (with 2 plates). — Prof. H. Kameriincu Onnes: “On pe Heren’s
experiments about the critical state”, p. 628. — Prof. J. D. van per Waats: “The
equation of state and the theory of cyclic motion” III, p. 643. — Prof. J. L. C. ScurogpEer
VAN DER Kok: “On hardness in minerals in connection with cleavage” p. 655. —
Prof. J. C. Kapreyn: “On the luminosity of the fixed stars”, p. 658. — H. D.
Beyrerman: “On the influence upon respiration of the faradic stimulation of nerve
tracts passing through the internal capsula”, (Communicated by Prof. C. WiNKLER),
(with 1 plate) p. 689. — Prof. H. Kamerzineu Onnes: “On differences of density in
the neighbourhood of the critical state arising from differences of temperature’’s
p- 691. — Prof. Jan pe Vries: “Involutions on a curve of order four with triple
point’. p. 696. — Dr. F. A. H. Scnurememaxens: “Notes on equilibria in ternary
systems”, (Communicated by Prof. J. M. van BeMMELEN), p. 701. — Dr. P, K. Lunors:
“Substitution velocity in the case of aromatic halogen-nitroderivatives”, (Communi-
cated by Prof. C. A. Lopry pe Bruyn), p. 715. — Dr. A. Smirs: “On the progressive
change of the factor z as function of the concentration”. (Communicated by Prof.
Hi. W. Baxatis Roozresoom), p. 717.

The following papers were read:

Physics. — Prof. H. A. Lorentz: “Boutzmann’s and WIEN’s
Laws of Radiation.”

(Read February 28, 1901)

The theoretical proof of the laws, to which BonrzMann?) and
Wren”) have been led by the application of thermodynamics to the
phenomena of radiation may be made to depend directly on the
equations of the electromagnetic field, a method which has the

1) Bonrzmann, Wied, Ann. Bd. 22, p. 291; 1884.

®) Wien, Berliner Sitz, Berichte, 1893, p. 55.

4]
Proceedings Royal Acad, Amsterdam, Vol, IL.

( 608 J

advantage that the notion of “rays” of light and heat is almost

wholly avoided.

§ 1. Let us consider a space, enclosed by walls that are per-
fectly reflecting on the inside, and containing a ponderable body M,
the remaining part being occupied by aether. In this medium we
shall then have a state of radiation, the nature of which is determined
by the temperature 7’ of the body M; in virtue of this state the
aether will exert on the reflecting walls a certain pressure, the
amount of which for unit area we shall denote by p. Let v be
the volume within the enclosure. It may be enlarged or diminished
by a displacement of the walls. We shall also suppose that by
some means or other heat may be imparted to the body M.

Now, choosing v and 7 as independent variables, and denoting
by é€ the energy of the whole system, we shall have

de

= a7 w+(E+p) dv

for the heat that is required for the infinitesimal change, determined

iQ. ,
by dT and dv, and, by the rule that ae is an exact differential,

a

op

ty pata

Here the first term represents the energy of the aether per unit
volume, which we shall call U. Indeed, if we increase the volume
v, Tessin the temperature constant, the ponderable body will remain
in the same state (the pressure p exerted on this body by the sur-
rounding aether will not be altered, being a function of 7’ alone);
the increment of ¢ will therefore be the energy contained in the
new part that is added to ». Hence

U pe 1
92S ign: joctels ot) eames

the last term containing an ordinary differential coefficient, because
p is independent of v.

( 609 )

§ 2. We shall combine this result with the simple relation
Dia ee gehen’ st sae 21 (2)

which we now proceed to prove. To this effect we remember in
the first place that the energy per unit volume is given by !)

1
2a Vio + — $2
4

We shall therefore write
= ‘ieee
i Seon e eye = Sper h BMORY we (a
82

the horizontal bars indicating mean values with respect to place
and time, which we might calculate by computing in the first place
the mean values for all points of a certain space, and by taking
then, for a certain lapse of time, the mean of these space-means.
In this it is to be understood that the dimensions of the space in
question and the length of the lapse of time have to be large, as
compared with the wave-length and the time of vibration.

If we confine ourselves to such mean values, the forces acting on
the walls may be regarded as due to a state of stress in the aether.
If @, # and y are the direction-cosines of the normal » of an
element of surface, the first component of the stress on this element
will be

1 ase

Sar (2 Dz Dn — @ DH);

—— 2a Vv 2 Dd, Dd, = a d®) +

ie., this will be the force in the direction of OX, exerted by the
part of the medium which lies on the side of the element, indicated
by the normal x.

Now, the state of radiation we are considering has the same
properties in all directions. From this it follows that there are no
tangential stresses and that the normal stress is the same for all
directions of the element of surface. It is given by

1) The notation is the same as in my » Versuch einer Theorie der electrischen und
optischen Erscheinungen in bewegten Kéorpern”, from which memoir I have also
borrowed several formulae.

41*

( 610 )

eet lee
Nz = 2a V2(202—¥) + —— (2 §P—-H%),
t

But, in an isotropic state, F

Therefore:
ies 1
ie ame
and
r ) 1
XS an Vi Be
24 Tt

In comparing this formula, in which the negative sign indicates
a pressure, with (3), we arrive at the relation (2).
In virtue of this the equation (1) now takes the form:

dU
4U= T—,
dT

and so we find the law, enunciated by BoLtzMann, that the energy
U per unit volume is proportional to the fourth power of the
absolute temperature.

§ 3. If the volume ~@ is increased, the system will do an external
work and a larger volume of aether will be filled with the
energy of radiation; for both reasons the temperature of the
body M will sink, if the operation is conducted adiabatically. We
may also, before increasing the volume, remove the body M; in
this case we start from a volume v of aether in the particular state
of radiation that corresponds to the temperature 7’, and we get new
states by letting the walls recede with a velocity which we shall
suppose to be extremely small in comparison with the velocity of
light. Now Wien has shown in the first place, by a train of
thermodynamical reasoning, that these new states, of smaller energy-
density than the original one, are precisely such as can be in
equilibrium with ponderable bodies of temperatures lower than T.
Using BotrzmMann’s law, we may express this as follows: After’
having diminished, by means of an adiabatic expansion, the energy
per unit volume from U to U', we shall have arrived at a state —

( 611)

of radiation which may be in equilibrium with a ponderable body

of the temperature
4 T
ne rv o
U

This theorem, which I shall here admit without further discussion,
enables us to determine the relation between the states of radiation
corresponding to the temperatures 7’ and J”. For this purpose it
will only be necessary to compare the states of the aether before
and after the expansion. This is the second part of the proof given
by Wien, and it is this part we shall present in a modified form
by applying the well known equations of the electromagnetic field
to the phenomena in the aether within the receding walls. If we
suppose the expanding enclosure to remain geometrically similar to
itself, the problem may be treated by the introduction of a suitable
set of new variables. In seeking for these, I have kept in mind the
substitutions that had proved of use in the theory of aberration, a
theory in which we have likewise to do with moving ponderable
bodies. Of course there is a difference between the two cases; in
the problem of aberration the velocity is the same for all bodies
concerned, whereas, in the question now under consideration, it is
unequal for different points of the enclosures.

§ 4. I shall suppose the dilatation of the walls to be equal in
all directions, and to have the same amount in equal infinitely small
times. This may be expressed by assuming

mi eShyya——e tame 6h ek es oy (A)

with a constant value of a, as the relation between the coordinates
x, y, @ of a point of the walls at time f, and the coordinates
a’, y', 2’ of the same point at the instant f= 0, at which we
begin to consider the phenomena. Indeed, the velocities are by (4)

Gi lie CEB oo er og a aha

during the time dt the linear dimensions will therefore be changed
in the ratio of 1 to 1 + ade.

As to the constant a, we shall take it so small that the velocities
(5) are extremely small in comparison with the velocity of light.
Notwithstanding this we may, by sufficiently increasing f, assign to
the factor e* any value we like.

( 612 )
After having assumed for the walls the formulae (4), it is natural

to replace the coordinates x, y, 2 of any point of the enclosed space
by the new variables

2 == wie Ot, gy! e—wyle— Ole 2 eat, ae OD

The fourth independent variable, the time f, will likewise be
replaced by a new one. For this we take!)

a

1
t' = mr (1—e— at) — 2 V2 (a? ++ y? -f- 2”) e—a, ° . . (7)

The dependent variables which occur in the equations of the
electromagnetic field are now to be considered as functions of
x', y', 2', t. In doing so, we have to use the relations

é ax
0 0 Ok ;
Ow 0 v2 Ot!
LE — fol, Ale mi nA r (8)
oy Oy pee dt
oO —— eee pas —at cs 9
0s Z Vy? Ot
f) a 0
— = e—at | | ue 2 oN
a epee Ne
f) 3
— au eat — aye—u yy —aze—u aa Sali ok (9)

r ° . .

Ihe variables which serve to determine the state of the aether
are bi, dy, d-, Dn Hy, Oz We shall replace these by the quantities
' ’ ' - ra a . ny . .
Day Dy, Dz, Dr, 9), H.', which are defined by the following equations *)

) As regards the last term, this value of ¢ is an imitation of the expression for
the “lceal time”, which I have introduced into the theory of aberration (l.e. p. 49).

) The latter terms in these equations correspond to similar terms in the equations
of the theory of aberration.

( 613 )

d= e—2at i 4 iE == (y D2 —e<z Dy),

dy = e— 2at b!, —

2 Dal ; 5 a CI
¥— poe fe — 2G) (10)

= e=2at 9), —

re @ fy D0)

Dx = e—2t H', + 42 a(yd, — =z d,),
Dy = e—2at H', + 4aa(zd,—-27d,),). . . ~ (11)
Hz = e— 2at J', + 4a (x dy — y dz). }

It must be kept in mind that the coefficient a is very small.

Let 7 be the largest value of any dimension of the system during
the interval of time we wish to consider. Then, by our assumption,

al
Vv
ar ea az ‘
has a very small value x; evidently, — =) = = will be of the same

order of magnitude. Hence, if we es quantities which, compared
with other terms in the same equation, are of the order z*, we
may omit in (9) the term containing a*. By this, the relation
becomes

0 f)
—— = e—4t —— ax e—tt — __ qy e—tt@—___qze-at—_, . , (9')

dt ot’ Ou"

We may add that for vibratory disturbances of the natural state
of the aether, the operations s ay" s are comparable to —-
as regards the order of magnitude of the result, and that is of
the same order as V». From this it follows that, in the equations
(8), (9'), (10) and (11), all terms containing the factor @ are of the
order %, relatively to the terms in which a does not occur. Similarly,
attentive consideration of the formulae that will be deduced in the
next article shows that, in comparison with the terms without
a, all those which contain the factor a? are of the order #2. We
shall therefore neglect all terms in which a? appears.

( 614 )

§ 5. The first equation of motion is:

80: 200) Se (12)

ag) 02 a UE

Putting for §, and 6. the values (11), we find for its left-hand

side:

e—2at (Ge) +4ma

Since

we may also write for it
00': dH'y 0dz Odz de
et heey ee a {8} o— ee aes == |,
é ( a ae ) mad Ana(s a +y aE +z =)

and, if we neglect terms with a?,

! '
e202 _ 209) — 8 wae—24 »', —

oy dz
Obie phoihle . vee
—4inae axi(e ae ES aay eS) “

Again, using the same simplification,

Oni hatngis Cod uae

oy dy’ Vote’

r) ‘ 0 az 0

— — e— ut __

dz de’ V20e°
Ogee Oy 1 1 06': 0, af 0s’: 0H",
ae oe if aa ome Biuiba teoue

( 615 )
In the last term of this equation, = and —— may be replaced

by e2t bby and 2.at = as appears from (11). The expression
Mf dt c at 7 & appears . xp 55

(13) therefore becomes

en, VEN! 3

eset (

d'. d', d'..
—S8nac—24 >'.— 4nae— sot (22s shee pee), (14)
Ow oy dz

The right-hand side of (12) is, by (10),

0d’ a ‘ “0 N- fr)
y < :

—8nae—2t py’, + 40 e—2at ——|y—~—--<
oT ot V2." Ot ot

or, if (9') is taken into account,

bd’
—S8aae—-2tt Nef An est Se _

eye ge)
da" oy’ dz

= 4nacnsat(

Finally we shall find, instead of (12), after division by e—%4?,

dN2 | ODy dd’,

SS
dy! de" dt

The other equations may be treated in the same way and all
relations between the new variables will be found to be of the same

form as those between the original ones.

§ 6. We have also to attend to the surface conditions at the
walls. These latter will be perfectly reflecting, if made of a substance
-of infinite specific inductive capacity, and then, if the wall is at rest,
the tangential components of the dielectric displacement in the
adjacent aether will be zero. ‘Therefore, if

( 616 )

WUD hi to) wie SG 5 6 cg) (GIG)
is the equation of the wall, we shall have

wad eile Qin gRee Om
peda Ba Nees PR Sig . . . . . (17)

In examining the phenomena of aberration, I have had occasion
to consider the conditions that have to be fulfilled at the surface
of separation of two bodies. These Jatter were supposed to move
with a common velocity p, and it was found that all equations,
the surface conditions as well as those for the interior of the bodies,
might, by an appropriate choice of new variables, be reduced to the
form that holds in the case of bodies at rest. Instead of the
dielectric displacement with the components

be, tyctk G4 ee

a new vector with the components

d; +

nV? (py Dz — Pz Dy),

1
d, Sf: 22 9, &), oe eee
y + Zap Ps Oz — Pe $2)

1

4n V2

be (Pz By — Py Dx)

was introduced. Hence, it will be this new vector, whose tangential
components must vanish at a moving perfectly reflecting surface.

Let us apply this rule to an element of the walls of the expand-
ing enclosure. The velocity-components »,, py, Pz must now be
replaced by a2, ay, az. Using at the same time the formulae (10),
we find for the expressions (19)

e—2aty!,, e—2at d'y; e—2aty!,,
It thus appears that the vector
e—2aty’

must be perpendicular to the wall. The vector >’ must be so

( 617 )

likewise, so that, if at any moment

E' (a 4,\2) = 0

is the equation of the walls, we shall have
oF of oF

te Shh, She == 5 S65 =
if ox dy dz

(20)

Now, if at the instant ¢=0, the walls coincide with the surface

determined by (16), the equation at any later time will be
BG 7,2);

=
Zo eae oe

where
ma Pe oy ye— Fh z

agreeing with (4). Thus:

F' (a, y/2) = F(2',y's @')s

and, if we differentiate for a constant ¢,

OF OF OF oF OF OF
Qe dy dz 82" dy! ae"

so that the surface conditions become
aF aF ar
Sa sek Yl

(21)

vis: dy 1 a,

On the right-hand side of this formula, 2’, y', 2’ occur in exactly
the same manner as «, 7, 2 in the formula (17).

§ 7. If the enclosure were permanently in the position it occu-
pies at the time t = 0, 0,, dy, dz, Dx, Hy, H2 would be certain

functions of x,y, 2,¢, say
ds = g, (7, y, % t); Dr = Zi(% y 2, #), ete;

these will satisfy both the equations of the field and the surface

vonditions (17).

( 618 )

Now, from all that has been said, it appears that the values
Die (2's 25 Os De eet eee = (eo)

will be a solution of the equations of the field, taken conjointly
with the conditions (21), we have found for the receding walls.
We have thus got expressions representing the state of the aether
during the expansion.

Now, we shall especially consider the state of things, existing at
the moment when the dimensions have become

eat — ok

times what they were originally. A definite value of this coefficient
i may be reached in a shorter or a longer time, this depending on
the value of a. We shall however consider the limit to which the
state of the aether tends, if, while we keep & fixed, ¢ is continually
increased and a continually diminished. By (10) and (11) we shall
have ultimately

>’ 5!

==, and H= [5

tu he

therefore, at the limit,

1 etn es ‘ 1 FS - ae ee
m= BAG gr grt) oe = ga Guero (24)

As to the variable ?', it is related to ¢ in a somewhat complicated
manner; the relation between the differentials takes however the
simple form

1
a' = ; dt.

It is easily seen that the function (24) will satisfy the surface
conditions such as they are for walls that are kept at rest. This
is what we might have expected. By sufficiently diminishing the
velocity of the walls, we make the system pass through a series
of successive states that may, each of them, be regarded as a state
of equilibrium. By Wren’s principle (§ 3) we know already that
each of these states might continue to exist if the enclosure contained
a ponderable body of a definite temperature.

( 619 )

The series starts with the state (22), with which (24) coincides
if / =1; it then passes to increasing values of &.

We shall denote by 7’ the temperature of a ponderable body that
may be in equilibrium with (22), and by 7" the corresponding
temperature for (24).

§ 8. Let us now compare the states (22) and (24). At first sight
there is a difficulty in as much as the variables ¢ and ¢ have
widely different values. It is to be borne in mind, however, that the
state (22) is a stationary one; i. e. all particulars that may be
deduced from observation are independent of the time ¢.

We may therefore begin by choosing the instant for which we
wish to consider the state (24); a definite value having in this way
been assigned to ¢, we may give an equal value to the time ¢ in
(22). In other words, we shall compare the quantities (24) with
the values

Orgy (eyes) da = 44s Ys cre yy Clays oe) (ae)

the latter state existing in a certain space S, and the former in a
space S', whose dimensions are /& times as great.
The values of > and $ in corresponding points of S and S' are

to each other as 1 to and the energy per unit volume will be

2?
in (24) k* times smaller than in (25). Hence, remembering Bourz-
MANN’s law,

In examining the phenomena, represented by (25), it may be
convenient to decompose, by means of Fourier’s theorem, or other-
wise, the values (25) into functions of «,y,z2 of a less complicated
form. After having accomplished such a decomposition for (25), a
similar development of (24) may at once be written down. For
instance, if
= W1 (@ ys 2 #)

is one of the parts of >, in (25), the corresponding part in (24)

will be
1 x Ona
pe 0 (= zk. ae ).

( 620 )

There is also a simple relation between the space-variations in
the two cases. Let PQ and P' Q' be corresponding lines in S and
S'. Then, if we denote by 7 one of the components of > or $, and
by apy %Q) Vp; Ng its values in the points considered, we shall
have

a= ip a Gia— Pan
np np’ :

i.e. the relative variations along corresponding lines will be equal.
From this it is immediately seen that, if one of the parts into

which we have decomposed (25) is characterized by a definite wave-

length /, the corresponding part of (24) will have a wave-length

Therefore

i.e. corresponding wave-lengths in the two states are to each other
in the inverse ratio of the temperatures.

We have already spoken of the ratio between the values of the
energy per unit volume. We may add that this ratio, equal to that
of the fourth powers of the temperatures, does not only hold for the
really existing states of motion, but also for the parts into which
these may be decomposed in the way that has been indicated. If,
in the state corresponding to the temperature 7’, there is a certain
amount of energy w per unit volume, depending on the vibrations
whose wave-lengths lie between certain limits, and if, in the
state for which the temperature is 7", w’ is the energy per unit
volume due to the vibrations of corresponding wave-lengths, we
shall have ;

uiwu—T!;: T"4,

This equation, taken together with (27), is the expression of the
law of Wien.

( 621 )

Physics. — Dr. Kamerzineu Onnzes and H. H. Francis HyNDMAN:
ptsothermals of diatomic gases and their binary mixtures.
I. Piezometers of variable volume for low temperatures.”
(Communications from the Physical Laboratory at the Uni-
versity of Leiden. No. 69.)

(Read March 30, 1901).

§ 1. On theoretical grounds, for accurate measurements on the
isothermals of pure gases and their binary mixtures, we should have
preferred to use monatomic gases alone since results obtained from
them would certainly be the most important.

Unfortunately of the three monatomic gases available for this
kind of work i.e. He, A, Hg, the two first are costly and the latter
has a critical temperature so high that the research would offer
great experimental difficulties.

From these we naturally turn to the next group, that of the
diatomic gases. Very complete researches on these gases have been
made at temperatures above 0° C. and with pressures up to 3000 At.
especially by Amacar. At low temperatures however no data exist
with the exception of two pioneer researches by v. WROBLEWSKI !)
on Hydrogen down to — 180° C. and by WirKkowskr®) on air
down to — 145° C.

The series of experiments which we now consider has been before
alluded to in Comm. No. 14 p. 4, 1894 and Comm. No. 50 p. 4,
1899 and has been kept in view in the arrangement of the cryogenic
laboratory with its auxiliary apparatus as weli as for the standard
manometers. (Comms. 44 and 50.)

In order to obtain the required data two methods present them-
selves. In the first a constant volume is filled at a constant
measurable temperature and pressure by compressed gas which is
afterwards expanded so that its volume can be obtained under
normal conditions. This method has been used by ReGNnautr,
v. WRoBLEWSKI and WiTkowskI and where the purity of the gas
is not of the greatest importance and especially at high tempera-
tures it is excellent, but to arrive at high precision piezometers of
a relatively considerable volume are necessary. Since the piezometer
must be refilled for every measurement, somewhat considerable quan-
tities of compressed gas are required for a series of measurements.
For determinations in the neighbourhood of the critical point however

1) Wien Sitz. Ber. 1888.
*) Bull, Int, Acad, Cracovie Mai 1891,

( 622 )

it is absolutely necessary to employ only gas of the greatest purity
to obtain any definite results. A method which requires large
volumes of such gas is necessarily both troublesome and costly, so
that we have been obliged to introduce some modifications and
additions. Of these the most important is a compression cylinder in
which the gas after expansion to normal volume can be collected
and compressed again into the piezometer, without any loss of purity.
However even with this modification a considerable volume of
compressed gas is required to fill the piezometer and the necessary
connecting tubes. In subsequent communications we will consider
the application of this modified method for measurements in the
critical region and of a higher accuracy than we are concerned
with below.

In the second method, which we are employing for the present
investigation because of its relative simplicity, we use a piezometer
of variable volume in which a quantity of gas that has once been
measured under normal conditions is employed for a series of deter-
minations. In principle this method is an adaptation of the one
described in Comm. N° 50 with which ScuaLKwisK has determined
the isothermal of Hydrogen at 20° C.

The results of these measurements which will soon be published
show that the method is capable of great accuracy under these
advantageous circumstances, but we have been unable to maintain
this high standard in modifying it for low temperatures. A con-
sideration of the various difficulties to be surmounted in the ap-
paratus we shall describe and the unavoidable errors belonging
000
and that very special apparatus, again of large volume, would be
required to reach a higher degree.

This accuracy is not sufficient to determine the deviations of the
hydrogen isotherms from the law of corresponding states relatively
to other gases, for it follows from the available data that unless
constant temperatures of below 200° C or very high pressures are
employed determinations to this accuracy will not teach us much
on the most important questions.

However with the other gases of this group and especially for a
review of the relations between Oxygen and Nitrogen and their mix-
tures this accuracy may be considered to be sufficient.

Te oe ; :
thereto, show that an accuracy of 7000 2° not of easy attainment

§ 2. General arrangement. The apparatus which is in use for
these measurements has been designed to allow of the determination
to}

( 623 )

of volume in a room where the liquid gases to produce the low tem-
perature baths can be most readily obtained, and of the pressure
in the room containing the precision piezometers and standard ma-
nometer. The pressure has thus to be transferred for a distance of
some 25 meters by a tube filled with compressed air. The general
arrangement of the apparatus is shown diagrammatically in Plate I
where the manometer (cf. § 5), is not drawn. The steel cylinder A
is connected to the reservoir C and the level tube C3 (cf. §3) by
steel tubes of 2 mm. bore provided for manipulation with steel
eocks C; and C, of the type given in Comm. N° 46 fig. 10. Dry air
under pressure is admitted at the brass cock C; its approximate
pressure being read by the operating metal manometer M while its
actual pressure is determined by the gas manometer (cf. § 5) con-
nected at Cs. The cock C, is for emergency and for reducing the
pressure and Cj), Cj; for manipulation.

The washers at the numerous joints are all of prepared leather and
require much trouble and attention before they are quite tight, though
this is now satisfactorily attained.

§ 3. The Prezometer. Although the principle of the method
employed is the same as that described in Comm. N°. 50 many
modifications are necessary to adapt it for measurements at tempera-
tures below the freezing point of mercury. The simplest would be
to separate the bath and graduated tube by a long fine glass capil-
lary bent twice at right angles so that the bulb could be immersed
in the jow temperature bath while the graduated tube remained at
an ordinary constant temperature. Such a rigid connection would
give much difficulty in manipulation and would be liable to fracture
with apparatus of the weight and dimensions here used, so that a
more flexible arrangement is necessary.

The one first tried, which combines the accuracy of the above with
the required flexibility, is shown diagrammatically in fig. 1, plate II
where d, is the graduated tube at the end of the large reservoir
(Cf. b. fig. 2), d, a steel capillary, d; another graduated tube, d, the
glass capillary and d; the bulb. After many trials however and even
after measurements had been made, we had to abandon this arran-
gement owing to the impossibilily of cleaning the steel capillary
so thoroughly that it should not spoil the mercury meniscus after
this had passed through it.

The arrangement finally adopted is that shown in Plate II, fig. 2.
The dimensions of the present apparatus were controlled by the size
of the steel apparatus available (designed for 500 At). The steel

42

Procecdings Royal Acad. Amsterdam, Vol. LI

( 624 )

cylinder A Plate I has a length of about one meter and a capacity
of about one liter. The glass tube bs was chosen as large as possible
and has a capacity of about 600 ce. This with its graduations d, is
connected to the various piezometer bulbs and is of the same type
as the piezometer for the highest pressure described in Comm. N°. 50,
the internal diameter of 6, being about 3 mm. The graduations
were only made on 20 cm. in order to keep the apparatus within
manageable dimensions. The tube ), terminates in a capillary tube
6; of sufficient internal diameter to admit a steel capillary.

The various piezometers, which are all of the same type as that
shown in fig.2 f and fig. 3, are of dimensions corresponding to the
various temperatures to be employed so that the pressure which will
cause the mercury to appear at the middle of the graduations of the
tube 4, shall be within the prescribed region. The stems /2 are fine glass
capillaries some 70 em. long to enable them to project above the cryostate
Comm. N°. 51, and with internal volumes of about 50 mm.’ in order
that the temperature correction may be redaced to a small order
without at the same time offering too great a retardation to complete
equalisation of pressure. At the end of the capillary stem fg of the
piezometer fig. 4 a small cavity fs is made to receive the end of
the steel capillary. This cavity must be large enough to avoid any
chance contact between the glass and steel and yet not large enough
to introduce uncertainties in the volume. It was found most satis-
factory to open out the capillary tube in the blow pipe to a diameter
and depth of some 1.5 mm. and then to bore the first mm. cylin-
drical at the lathe. The upper surfaces of both 4 and f are ground
off at right angles to produce a more constant and perfect joint.

The connecting steel capillary g fig. 2 must be long enough to
allow of the manipulation of the piezometer without incurring the
danger of bending the capillary sharply at any point, a proceeding
which usually results in a leak. Under some circumstances a eapil-
lary of 40 cm, Jength could be used, but for the majority of the
measurements jt was found most convenient to employ one of 130 em.
The capillary is furnished at its ends with screw-connections 9), J
(see fig. 2) to enable it to be fastened securely to 4 and f.

The various parts can now be readily removed for cleaning, filling
ete. while the arrangement is such that it allows the parts to be
replaced without producing any appreciable change in the volume
up to the graduations on the tube.

The steel tube /, with hexagonal portion /; and thread /; is made about
1

io mm. larger than fg and is fastened to it by red sealing wax.

Between the steel flanged tube gy, and the glass fy fig. 4 a washer
7; of prepared leather is introduced; as however leather gives
somewhat under compression it has been found necessary to employ
washers which have been subjected for some time to considerable
pressure. When the requisite precautions are taken, a joint is obtained
which is perfectly tight at 60 A% and which only requires screwing
up one half turn (about 7 mm.) during a long period under this
pressure, thus insuring a practically constant volume.

Connections of the type described in Comm. N°. 60, fig. 5, appeared
not to allow of sufficient accuracy in the determination of the volume,
when the joints were made to stand the pressure in our experiments,
Moreover in that case the connection of different piezometer-bulbs
to the same graduated tube presents much greater difficulties.

At the lower end of the U tube 0, fig. 2 of which the leg con-
nected to d; is calibrated, the short capillary tube ), carrying a
ground joint has been made parallel to the whole length and not
bent at an angle as in fig. 4 Comm. No, 50.

The connection with the gas apparatus is made by the short tube
h carrying two ground joints h; /, and a cock h3. By means of
this the tube / containing the requisite mercury can be easily and
quickly brought into a nearly horizontal position, when it is neces-
sary to fill it with gas, and the joints closed by rotating tube 4.
When the tube is filled 4, is shut 4 and / removed together,
brought into a vertical position and the cock again opened; the
mercury then runs quietly into place and tube can be removed.
By this contrivance the troublesome process of turning about the
tap h, described in Comm. No. 50 § 1, is no longer necessary.

§ 4. The compression cylinders, reservoirs and connections. Like the
apparatus described in Comm. N°. 50, the compression cylinder is
filled with pure mercury only to which the pressure is transferred also
by mercury from the reservoir where it is produced by means of com-
pressed air. Owing to the large volume of mercury required for the tube
b the reservoir C must have a capacity of nearly a liter, the level of
the mercury in it being indicated by the level tube Cs. A scale Cy
is attached to this tube and the position of the mercury is read by
the eye. The distance between the zeros of this scale and that on
b, is determined by the cathetometer.

The steel head 4, must be put onto the glass tube /, with the
precautions mentioned in Comm, N°. 50 especially as the clearance
is only some 2 mm. at the bottom of the tube J. On to this head

42*

( 626 )

b, is screwed a water bath b, bs through which flows a constant
upward stream of water of constant temperature. ')

The steel nut a; Plate I and fig. 6, Plate II is divided into two
portions connected by screws to enable it to be applied more con-
veniently. At every joint of this apparatus there is a prepared
leather washer between two flat steel surfaces provided with concen-
tric depressions and a central tube. In consequence of the two large
washers at dg and cs being in contact with mercury it has been
possible to entirely eliminate leakage at the pressures employed.

§ 5. The manometer. The glass portion of this apparatus, made
especially for this research, differs little from those employed by
VERSCHAFFELT and JH[ARTMAN and could be replaced if necessary
by one reading to higher pressures used by the former. The eylin-
ders, reservoir and level tube are identical in construction with those
described above for the piezometer only of smaller dimensions. These
were so chosen that pressures from 20 to 70 A‘ could be read with
an accuracy of = Such an accuracy is however only actually
obtained by careful preliminary calibrations to determine the volu-
mes of the bulb etc. and the inequalities of the stem, combined
with comparisons with the standard manometer at many points over
the entire scale.

No attempt was made to determine the normal volume (cf. Comm.
N°. 44 note 1) as several measurements of the pressure at the zero
of the scale by the standard manometer give an accuracy to this
point of some = Ji. The capillary depression in the manometer
capillary is 7 mm. when the height of the meniscus is 0.1 mm. and
in the level tube about 1.5 mm. with a meniscus of 1 mm. The
difference must be considered, but is small enough to allow us to
assume a constant value the small differences from this being
considered as accidental errors.

If we assume that 0.2 mm. can be read with certainty by the
eye, and this is probably an underestimate if a mirror is employed,

the reading error in the middle of the scale is some a though

it is not probable that the comparisons and calibrations can be quite
trusted to this high degree.

1) The constancy of the temperatures will be discussed in a later communication,

( 627 )

The manometer is filled with pure dry hydrogen and is read at
temperatures between 15° and 20° C,

In a further communication more details will be given
with the measurements, it is sufficient to mention here that
the higher pressures deduced from the lowest pressure and determined
directly agree very satisfactorily, which we believe is an advance
on former apparatus.

§ 6. Errors belonging to the construction. In conclusion we
may consider the accuracy which we may reasonably expect from
such apparatus as that described in § 3.

The volumes of the various portions have been determined to
less than

2 mm.® in the piezometer bulbs, 1 mm.® in the piezometer stem,
1 mm.® on the total volume of v4 (6.0 ec) and certainly less than
3 mm. from point to point.

The principal cause of error will undoubtedly be the steel capillary
with its connections for among many measurements a difference of
1 mm.° was found in the longest capillary with a volume of about
lee., we will however assume the error 3 mm.® as reckoned in
Comm. 60 § 20.

The cathetometer used to observe the meniscus reads with care

1 1 ; :
to — mm. so that an error of 55 mm. may occur in reading the

position of the meniscus in v, corresponding to a volume of
1.2 mm?.

The volume of a meniscus of the average height of 1 mm. in a
tube of 30 mm.” cross section © 10 mm.° with an error at a

maximum of 5°/,!) = 0.5 mm®,
Hence the total error in the position of the meniscus may be
evaluated at 1.2 + 0.5 = 1.7 mm.? The most unfavorable case

gives for the total error 2+14+3+3+2=11 mm. and if we

put the probable error 5 mm.°, it appears that the arrangement of
soe

the apparatus allows us to reach an accuracy of i000 with piezometer

bulbs larger than 5 ce.

1) Scuatkwisk, Comm. No. 67.

——

( 628 )

Physics. — Prof. H. Kamerninau Onnes: “On pr Hurn’s ex-
periments about the critical state.” (Communication N°. 68
from the physical laboratory at Leiden).

§ 1. Purpose of this communication. Wxperiments have been
repeatedly described which were alleged to disprove the notion
of the continuity of the liquid and gaseous states according to
VAN DER Waats’ theory. They especially were said to deny
that a simple substance should have only one critical temperature,
one critical pressure and one critical volume, that it should possess
at a given pressure and temperature above the critical temperature
one density only; and that below the critical temperature it can
present stable co-existing phases in equilibrium for each temperature
only at two definite densities.

Each time however it was possible to point out circumstances
which had been overlooked in the experiments. If the experiments
mentioned were repeated with due regard to the necessary precau-
tions, they proved to confirm VAN DER WAALS’ views.

It required much care to find out the circumstances to which we
must attribute the deviations observed in GALITZINE’s experiments.
At the Leiden laboratory where VAN DER WAALS’ theory was made
the starting point of several investigations, KUENEN has undertaken
this difficult and lengthy work. He succeeded (Comm. N°, 11
May and June °4) in explaining experimentally the phenomena
observed by Gatirzine by the influence of admixtures, impurities
which amounted to only a few tenthousandths of the substance,
considered pure. By this elaborate research we not only considered
GALITZINE’s views to be refuted but also ideas so nearly related
to them as those of pe Herren. At least it seemed decided, that
heneeforth no value might be attached to researches on the critical
state with simple substances, unless it was proved that even such
small impurities as occurred in GALITZINE’s experiments were avoided.

KUBNEN’s experiments failed however to convince DE Hen that
his objections against VAN DER WAALS’ theory were not justifiable ;
nor did it make him aware of the necessity to bestow as much care
on the purifying of the experimental substance as we are wont to
do. On the contrary, in 18961) pe HrEn has published new experi-
ments, made with carbon dioxide, again without stating anything
concerning precautions taken for its purification.

According to him these experiments would show:

') Bulletin de l'Institut de physique de Université de Litge, deuxitine fascicule
(Bull. de I’Ac. Roy. de Belgique 8e Sér. t. XXXT, °96).

( 629 }

that a definite critical density, of which the existence has hitherto
been accepted, is an entirely ficticious quantity, that in reality
there are two critical densities, Ist. the critical density of the liquid,
0.640 for carbon dioxide; 2"¢. the critical density of the gas, 0.298
for carbon dioxide, and that the quantity hitherto measured as critical
density is the mean of these two limiting densities.

Shortly afterwards a visit of pe Hen to Leiden offered an
opportunity for a discussion in which I pointed out, that very small
deviations in temperature, pressure and composition near the critical
state can lead to great variations in density. My remark that in
prE HeEeEN’s experiment the carbon dioxide had not been perfectly pure
was not contradicted. Whereas to me this circumstance seemed very
important, D&B Heen did not set much value upon it.

It seemed that the controversy could be solved by repeating at the
Leiden laboratory DE H&En’s measurements in his own apparatus
with carbon dioxide of the same purity as it is used with us for
similar experiments. During the repetition of these measurements
other precautions which seemed desirable to me might also be taken.
I found Dr. J. E. Verrscuarrett, then assistant at the Leiden
Laboratory, willing to undertake the work and Prof. pE HEEN
was kind enough to send to Leiden the “analysateur de l'état
critique”. But when we began working the apparatus, it proved
unfit for experiments with very pure carbon dioxide, For the
liquefied gas came into contact with the packing. This was made
of leather soaked with wax or grease, which substances dissolve
in the liquid carbon dioxide so much that they can even be
distinctly smelt when the liquid is drawn off. The packing boxes did
not allow us to substitute for the leather packing, cork or lead.
Even if the carbon dioxide before being admitted into the apparatus
had been as pure as we desired it, the results obtained would not
have related to pure carbon dioxide. Besides the introduction of
new packing boxes, the apparatus called for radical modifications
in order to allow us to inquire whether, even though it remained
impossible to verify the homogeneity of the phases, the two quan-
tities of the substance, of which pr I[gen in each case compares
the densities, have indeed the same temperature and_ pressure.
De Hern supposes that this is true, but the construction of the
apparatus used by him does not permit of a proof.

Hence we could only profit from the presence of the apparatus at
Leiden by studying some of its peculiarities, and the matter was not
further entered into.

In 97 pre Heen thought that he found a proof of the exactness

( 630 )

of his observations in those of AmaGat. He derived from AMAGAT’s
experiments that there are two densities near the critical point,
which are in the ratio of 1:2 and he wrote: J’ai du reste la con-
viction que la théorie que je vieus de soutenir ne commencera a se
généraliser que lorsque les expériences — namely those with the ana-
lysateur de I’état critique — auront été répétés un grand nombre
de fois par plusieurs physiciens. Ce n’est que dans ces conditions
qu’on peut porter atteinte & des convictions — the existence of one
critical state — ayant poussé de si profondes racines.

The result of a careful repetition of those experiments could however
not be doubtful in our opinion. For who ever wishes to repeat
DE HEEN’s measurements of density, will want to arrange the work
so that it will be possible to verify the homogeneity of each of the
phases, and to measure accurately small differences in temperature,
pressure and composition of the phases to be compared, in order to
calculate by them corresponding corrections. It would also be desi-
rable to apply even now similar corrections to the numbers given by
DE HEEN, in order to arrive thereby at the true results of his
researches. But as DE Hern has paid no attention to the data
for the determination of these corrections, this is not possible. We
nevertheless can form an idea of their general character. And so
Dr. VERSCHAFFELT and I in going over DE HeEn’s experiments were
soon convinced that these, however improbable this may seem
to him, would agree with van per Wadats’ theory within the
limits of the errors of observation after the necessary corrections
had been applied.

In order to show moreover experimentally that such corrections

must be actually applied an apparatus —— chiefly consisting of two
reservoirs connected by a cock, from each of which the contents
could be collected by a small cock — was constructed of several

pieces available in the laboratory, with which we intended to repeat
some of DE HEEN’s measurements with the necessary precautions.

When Dr. VerscHarrett left Leiden, I have myself devoted some
time to preliminary observations with an improved apparatus better
answering the purpose. Among other things I had introduced a thermo-
element in each of the reservoirs mentioned.

During these preliminary measurements nothing was observed (see
following sections) that could point to the important deviations
which were derived by DE Hern from the experiments chosen for
repetition, and it was confirmed that it was necessary to apply
corrections to the densities given by him.

Hlence a continuation of this repetition of ps HEEN’s experiments

( 631 )

appeared to be only useful in that it exhibited by means of his
results the amount of deviation which can be found, whenever
we are not guided by the theory of the mixtures and of the adiabatic
variations of state in measurements with compressed gases in the
neighbourhood of the critical state. The most important point in
this question, namely the influence of small admixtures on the phe-
nomena in the neighbourhood of the critical state, will be illustrated
by other investigations which are being made here and as I hope
even better than could be done by the measurements mentioned.

More urgent work obliged us to leave undone the measurements
in which the conditions for the deviations given by DE HEN were
intentionally realized, and the apparatus was taken to pieces. Nor
did my time allow me to make further investigations in connec-
tion with DE HEEN’s experiments. In the “Mathemathische Encyclo-
pedie”’ I hope to return to some questions relative to the theory of
the critical state. And what could be remarked on DE HEEN’s expe-
riments, seemed to me after I had tried to write down something
on them not sufficiently interesting for a paper.

But a few days before the last meeting I received DE HrEN’s
paper ,les légendes du point critique’, in which he expresses in a
friendly tone his earnest wish that I should now communicate
publicly my opinion on his work.

I avail myself of this opportunity to express to Prof. pp HEEN in
return my feelings of friendship and respect. I have tried to satisfy
his request by what I have said above and by explaining it more
in detail in the following sections.

2. Investigation of one of the systematic deviations. KUENEN has
already pointed out how unsatisfactory is a refutation of theories so
little defined as those of Dr Hern. The refutation of the results
derived by DE HeEEN from his measurements by repeating ;them is as
little inviting. Since it is a repetition we are bound to a method
of working deviating much from that, which we should think it neces-
sary to follow in similar investigations. Moreover what we call
taking precautions may be considered by Dr HEEeN as sacrificing an
artifice, lastly to attain a moderate accuracy in measurements with com-
pressed gases, operations are necessary which require much time
and care. If therefore in the repetition of DE HEEN’s experiments
a high degree of accuracy was required I would not have under-
taken it. But a determination of density to within 3 percent is suf-
ficient, as the deviations between De H&EN’s results and those which

( 632 )

can be derived from the laws generally accepted, even at several
degrees’ distance from the critical temperature, amounted in some cases
to 30 and 40 percent !). Also for the experiments to be considered
below, the deviation is large enough to be refuted by measurements
of the accuracy mentioned. Besides it is a favourable circumstance
that all the deviations are connected systematically. It is easy to
see this from DE Hnen’s table. (I. ¢. p. 386). If therefore one of the
important deviations mentioned by De Heen can, by the repetition of
the experiment from which it was derived, be reduced to zero within
the limits of the errors of observations, this involves the refuta-
tion of all the others.

Although I will not dwell on the theoretical considerations re-
futed by Kuenen I must shortly explain which is the chief point
in the experiment to be repeated.

pE Hern assumes the existence of so-called liquidogen and gas-
ogen molecules. The former would only be decomposed far above
the critical temperature. If we succeed in filling a space near or just
above the critical temperature entirely with liquidogen molecules then
the substance enclosed therin will have one of the limiting densi-
ties given by pE Huen for the critical state; if we succeed in doing
the same for the gasogen molecules, the second limiting density will
be observed. Above the critical temperature, mixtures of those kinds
of molecules can be made in all proportions. If a space filled with
liquidogen molecules is in contact with an other containing gasogen
molecules, so that mutual diffusion can take place, the liquidogen
and the gasogen molecules will be mixed. Only when they have
been completely mixed — and so after some time — the difference
between the densities in these two spaces disappears.

Dre Heen’s analysateur de l'état critique renders it possible by
means of a cock to divide the volume occupied by a substance into
two parts at a moment of pressure equilibrium and in this way
if one space contains chiefly liquidogen, and the other chiefly gasogen
molecules, to prevent the mixing of these two. The substances in
each of the two reservoirs mentioned in § 1, which are placed
above each other and are separated by a cock, can moreover be
separately collected by means of cocks made for this purpose.
According to Dr Hen it would be possible by taking care that
at first the lower reservoir should be filled chiefly with liquid,
and the upper reservoir chiefly with vapour, to fill above the eriti-

') Wor instance, influences like those of gravitation (Comp, Comm, N®, 17 Kurnen,
May °95,) can be left out of account.

( 635

cal temperature one space chiefly with liquidogen, to other chiefly
with gasogen molecules under the same pressure. At the same pres-
sure and the same temperature different densities would then be
found in the two spaces.

De Heen has not made clear, what could be learned better from
the experiments with the ‘analysateur” than from the experiments
with the tubes of GALITZINE.

For in the latter case the two phases, the one consisting chiefly
of supposed liquidogen molecules, the other chiefly of supposed gasogen
molecules, are heated separately, while the movable mercury thread
which separates them is constantly yielding to the difference of pres-
sure between the two phases, and indicates if the equilibrium is
not attained, for which difference of pressure a correction is to be
applied in the comparison of the densities.

As compared with this contrivance the making of a partition
between the space where more liquidogen, and that where more
gasogen molecules are supposed to be, by means of a cock which
is only opened now and then, may be considered as a step back-
wards. In this way mixture by means of diffusion cannot be avoided
so well, nor can the equilibrium of temperature and pressure be so
well attained or accounted for, If De Herren had succeeded in
separating perceptibly the liquidogen and the gasogen molecules,
then they ought to have been observable certainly in GALIrziNn’s
tubes, as indeed this physicist thought. Kurnen by his experiments
has proved that this was not the case.

If discussion of DE Heren’s theses was primarily required then
we might argue that everything derived by Dr H&reEn from the expe-
riments with the ‘analysateur’” has been a fortiori refuted by
KUENEN’s criticism of GALITZINE’s arguments.

But our aim was to demonstrate by the repetition of DE ITREN’s
experiments with the necessary precautions, that they lead to other
results than those given by DE Hern. Like De H&EN we used for
this purpose two metal reservoirs separated by a cock.

I must still mention one point of difference between the ,analy-
sateur” and our aparatus meant in § 1. The reservoirs of our appa-
ratus have an invariable volume. This is not the case with the
punalysateur’’. In each of the cylindrical reservoirs of the “analy-
sateur’”’ a piston can be moved and these two pistons are so con-
nected, that when they are moved the volume occupied by the sub-
stance in the two reservoirs together remains unaltered. By
adjusting the pistons properly and by filling only one of the
reservoirs, any suitable quantity of liquid can be admitted into the

( 634 )

apparatus, which may be distributed by means of the connecting
cock over the total space of the two reservoirs, after which by re-ad-
justing the pistons the total space can be again divided into two
parts of a desired ratio by means of the cock. And so it is easy to
make a series of different measurements for different ratios with the
same apparatus. It is also possible to alter the proportion of the
two volumes during an experiment. It is obvious that the first
mentioned speciality is useless in the repetition of a given experiment,
it being moreover df little importance, as the desired filling can also
be made in an other way, for instance by distillation, and as Dp Hren
uses for the first series of experiments only one proportion and for
the other only two extreme proportions. As wil] be seen, what might
be attained by moving the piston during the experiment, is from
DE HEEN’s reasoning of no importance for the results to be obtained
by repeating his experiment, or may be arrived at in another way.

After this digression we come to consider the experiment of DE HEEN
which I had chosen for repetition. In this (Bulletin de 1’ Institut de
Litge Deuxiéme fascicule p. 150) the pistons of the analysateur are
placed so that the volumes of the two reservoirs are equal. Then
the two reservoirs are filled at 10°C. with liquid carbon dioxide
and the connecting cock is closed. The carbon dioxide from the upper
reservoir is blown off, the connecting cock is opened, the carbon
dioxide is allowed to fill the two reservoirs and to reach equilibrium,
and then the apparatus is heated to 35°C. After the connecting cock
is closed the contents of the two reservoirs are separately coliected.
For the density at 35°C. in the upper cylinder DE HEEN gives
0.456, for that in the lower cylinder 0.544, whereas according to
VAN DER WAALS the densities of two quantities of pure carbon-
dioxide, no matter how they are obtained, must be the same under
the same pressure at 35°C.

The reason why this special experiment has been chosen for
repetition is that it lies not too near the critical temperature and
yet shows important deviations; also because according to AMAGAT’s
data the surface of the liquid in the apparatus at 28°C. stands
very near the cock; and lastly and chiefly because in this case
pe Herren does not move the pistons of the “analysateur”. For
this reason it could be repeated with the apparatus described above,
as the latter has two metal reservoirs of unvariable and almost
equal volume with a connecting cock. And so the apparatus is for
this experiment equivalent to that of DE HEEN.

Carbon dioxide was admitted into it which had been distilled at
ordinary temperature over phosphorus pentoxide and boiled at a
low temperature, and which in the liquid state had been into contact

( 635 )

with clean metal only. Before the carbon dioxide was admitted, the
apparatus had been evacuated by a BesseL HacGen’s airpump.
Auxiliary apparatus of which the volume had been measured, ren-
dered it possible to admit by distillation the exact weight of carbon
dioxide into the two reservoirs with open connecting cock. Care was
taken that the liquid carbon dioxide was exclusively contained in the
lower reservoir. During the heating namely, the temperature of the
upper reservoir was kept a little above that of the lower reservoir,
so that below the critical temperature no liquid could distil over
from the lower reservoir into the upper reservoir. It seems to me
that in this way better than by the method of the moving pistons,
as followed by DE HEEN in his later experiments, certainty may be
obtained that at the beginning as little liquid as possible is found
in the upper reservoir.

The connecting cock was closed at 28°C., then the temperature
was raised to 35° C. by streaming water of this temperature.
During the heating the cock was opened six times for 4 secunds,
and after the heating another 6 times for 4 secunds at constant
temperature. Several experiments had proved, that 4 secunds was
a time long enough to secure equilibrium of pressure. In this
time equilibrium of temperature was not yet attained, but it
was not necessary with my apparatus to wait for it, as the
temperature could be determined by the thermo-element in the
two reservoirs separately, and so a correction could be applied. In
DE HEEN’s reasoning the liquidogen and the gasogen molecules in
my experiment must have had less opportunity of escaping observa-
tion by their diffusion, than with his own experiment, where the
cock was left open while heating from 28°C. to 35°C. When

the cock was closed at 34.°8C. the ratio of the densities was
0.448 : . :
0496 — 1,052. By applying the correction for the difference of tem-

perature 0.8 deg. as given by the thermo-elements (the real difference

_ = 0.96. For per-
manent gas no correction was required as it amounted in the
analysis of the original gas-phase to 0.00018 only and in that of
the original liquid-phase to 0.00016 only.

And so only a small deviation was found becoming opposite in sign to *
that of pe Hren by a correction of uncertain amount, which result,
taking into account the errors of observation, would be expressed in
DE HeeEn’s language by the statement that the liquidogen and the
gasogen molecules are the same.

A second experiment must be mentioned in which the connecting

was probably smaller) this ratio would become

( 636 )

cock was left open during the heating from 28°C. to 35°C., heat
being applied from above, and where I ailowed 10 minutes for the
attainment of equilibrium in the temperature and pressure. This period
is probably too long to allow us to consider this experiment as a
repetition of DE HeEEN’s, but certainly not sufficient for the two
kinds of molecules to get mixed in a considerable degree through
the narrow cock by diffusion according to our ordinary views. When
the cock was closed at 35°.4C. the ratio of the densities was
0.448
0 432
of 1°.15C. as given by the thermo-elements, this proportion would become
0.448 : P

~~ and by correction for the permanent gas, found at the analysis

0.492
0.449
to be 0.002, ie — 0.91.

=1.037. By applying the correction for the difference of temperature

Although as said in § 1 T[ attach no other importance to
these numbers than that of preliminary observations, yet they
are sufficient to regard DE Heen’s measurement, which gave the
ratio eee as disproved (especially by the first experiment).

0.456

Even if I suppose the error of observation in my densities to
exceed 3 pCt., then DE Hren’s much larger deviation still remains
disproved.

Nor can my proof be weakened by the fact that the differences
of temperature were certainly over-estimated, and that with other
less complete measurements of the same series which, as I have
said already, were treated entirely as preliminary observations, devia-
tions of the uncorrected densities were found which amounted even
to more percents and which were in the sense of De Henn; on the
contrary they showed, I think, that the errors which are likely
to be made, tend towards the direction of the deviations found
by DE HEEN.

And so DE HErEN’s statement
cette proposition tant contestée que nous avons émise depuis long-
temps: La température et la pression ne suffissent pas toujours pour
définir la densité d’un fluide’” — is not in the least supported by his

“ainsi se trouve mis hors de doute

experiments.

§ 3. Bxplanation of the deviations found above the eritical tem-
perature. It is certainly remarkable that the differences given by
pe Hern which we have shown to be due to the neglection of cor-
rections, are so considerable.

( 637 )

There is no objection for supposing that differences in temperature
have remained e.g. in consequence of compression in the one reservoir
and expansion in the other, which necessarily attend the transport
of substance from the lower into the upper reservoir, which moreover
was very likely also warmer for other reasons.

I would be inclined however to ascribe the deviations for a
part to the presence of impurities. The carbon dioxide obtained
from commercial cylinders, contains sometimes a few percents of
its volume of admixed air, besides traces of water vapour. De Hern
has compressed it by means of a compression-pump, and it is known
how difficult it is to keep a gas pure during this operation.
Moreover it appeared necessary in DE HEerEN’s experiments in order
to condense the carbon dioxide at 10° C in the apparatus to raise
the pressure to 75 atmospheres, whereas the saturation pressure of
carbon dioxide at that temperature amounts to only 45 atmospheres.

We have seen that the liquid carbon dioxide dissolves the wax
and grease of the packing. In the gaseous phase the molecular
pressure will decrease by the admixture of more volatile substances, and
in the liquid phase it will be increased by the less volatile admixtures.
Owing to the large compressibility in the neighbourhood of the critical
state, the densities belonging to a same external pressure may show
considerable differences.

If the two phases of different composition are raised to a higher
temperature the influence of the deviation in the molecular pressure
will be diminished. And so the differences of density will be smal-
ler. ‘This is also the result obtained by DE HEEn.

In order to avoid as much as possible the diffusion of the liquid-
ogen and gasogen molecules during the long time which is required
to attain the equilibrium at a higher temperature, by HeeN makes
these experiments in the following way:

,il suffit de porter Pappareil & une température peu supérieure a
la température critique, par exemple 35°, puis de termer la clef D
(the connecting cock) tout en continuant & chauffer jusqu’au point
voulu. Lorsque celui-ci est réalisé on ouvre D, on laisse |’équilibre
sétablir. Puis on recueille séparément l’acide renfermé dans les deux
eylindres.”’

From this it may be seen that the artifice of which we availed
ourselves in heating to 35° C. has been borrowed from DE HEEN.

From the system of isothermals (pressure, volume) may be seen
at a glance that the pressure for the two phases with densities on
either side of the critical density will increase very differently by
heating at constant Volume, so that when the desired temperature

( 638 )

is attained, a considerable difference of pressure will exist between
the two phases before the cock is opened. This causes on opening
the cock a difference of temperature, which would prevent the
equalization of densities from being completed when the process
was purely adiabatic. With the slow transport of heat, which in
reality takes place, equalization will be still retarded.

Before DE Hren could therefore set any value upon the densities
found after the closure of the cock, as belonging to a same temper-
ature and pressure, he ought to have shown that the equilibrium
of temperature had been obtained. With my apparatus treated in
§ 2 the process might be interrupted at any time, as soon as the
equilibrium of pressure had once been attained, because the remaining
difference of temperature could be determined and accounted for.
But this was not so in the case of De HEEN.

It is obvious that as the cock is left open during a shorter time,
a greater difference of temperature will remain. The corrections to
be applied will accordingly be the greater. In a series of observa-
tions, if the cock is opened in the same way every time, they
will follow a systematic course, like the corrections for the small
admixtures, if the carbon dioxide used was always of the same
composition, and like any other correction, which belongs to an
operation always performed in the same way e.g. the manner of heating.

Obviously larger corrections must be applied to DE HEEN’s second
series of experiments, which he performed in order to avoid diffusion,
in the following way:

“T] faut done amener les pistons dans la position (fig. 6) ou (fig. 7)
— giving a definite ratio between the volumes of the reservoirs —
& une température un peu inférieure au point critique, puis on ferme
D et on continue & chauffer jusqu’ & une température voulue.
Pendant que la température s’éléve on ouvre de temps en temps
et rapidement?) le rebinet D, de maniére 4 permettre & la pression
de s’équilibrer dans les deux cylindres, tout en empéchant les molécules
liquidogéniques du cylindre inférieur de se diffuser dans le cylindre
supérieur.”

Whereas in the experiment discussed in § 2 DE H&en arrived
at the two densities 0.456 and 0.544 or the ratio 1.19, he gives
as results in the second series under almost the same circumstances
the densities 0.360 and 0.550 and so a ratio of 1.44, where I
found the theoretical ratio 1.00 sufficiently verified. And so in my

1) About 5 times, lasting 4 seconds each, as pE Heen was kind enough to
inform me.

ee ~~»

——

( 639 )

opinion an extraordinary large correction must be applied for
systematic errors.

Part of the systematic errors must be due to the shortness of
the time during which the cock is opened. Near the critical state
it is indeed an inefficient means for obtaining the desired equilibrium
of pressure and temperature.

De Heen has been aware that when the cock was opened once
only, a difference in temperature could arise by the expansion of
the substance in the lower reservoir. But it seems to have escaped
his notice, that in the very neighbovrhood of the critical state the
adiabatic process is not at all favourable to equalization of pressure.

The process can be traced graphically by means of a diagram of
the isothermals and adiabatics near the critical point.

It will be sufficient to show its character. Hence it will be
allowable to simplify it and to trace the variations of two equal
masses of the two phases, which are heated both at a constant
volume, then are adiabatically brought to equilibrium of pressure,
then again heated isometrically to a higher temperature, once more
brought to equilibrium of pressure adiabatically etc. We then
neglect the modification undergone by each of the phases owing
to the exchange of substance which takes place from the one
reservoir into the other.

In order to arrive at a definite diagram of the adiabatics and the
isothermals, we may for simplicity imagine it as derived from VAN
DER WAALS’ equation of state. Near the critical point the adiabatics
coincide almost with the lines of constant volume, and so adiabatic
equalization of the difference of pressure will hardly give a variation
of the specific volume. The phases which first at equal temperatures
ditfered in pressure, after equalization of pressure differ so much in
temperature, that the density is only slightly changed. The difference
of pressure has been transformed into a difference of temperature
almost equivalent with regard to the difference of density, and this
difference of temperature with a slow transport of heat will in reality
not vanish when the cock is closed after a few seconds.

When the cock is opened for a short time this should be repeated
very often in order to ensure the equilibrium of temperature.

This reasoning was confirmed by my observations with the thermo-
elements. After having heated the apparatus from 28°C. with
closed cock to 35° C. and opening the cock according to DE HEEN’s
method only 5 times for 4 seconds, I repeatedly found after
successive further openings of the cock a renewed difference of
temperature.

43
Proceedings Royal Acad. Amsterdam, Vol, Il,

( 640 )

The observations have not been made accurately enough to set
much value upon the numbers obtained, but they always tended
to show a heating of the upper reservoir by the opening of the
cock. (On an average 0°.27 C. in the experiment of § 2).

Besides the difference in the treatment of the cock, pe HEn’s
second series of experiments is distinguished from the first by a
second modification, which favours greater differences. Let us here
consider only pk HrEn’s two experiments mentioned above. In both
cases the apparatus is heated from 10° C. to 35° C. and it contains
a quantity of substance, which when distributed over the whole
space, would show almost the critical density (according to current
views). In both cases the apparatus is filled by first adjusting the
pistons so that the total volume is exactly divided into two parts,
and by then filling the one reservoir completely with liquid at 10° C.
and distributing this quantity of substance over the two reservoirs.

But in the first series the apparatus is then heated without further op-
erations. In the second series by readjusting the pistons all the substance
is first brought below the cock, the apparatus is heated to a little
below the critical temperature and then the piston is adjusted until
a definite ratio between the space of the lower reservoir and of the

vik salen Oukdo ‘
upper reservoir is obtained. That ratio is 0.845 when a determi-

od

0.229
of the density of vapour is wanted. And so the surface of the liquid
is shifted in the apparatus while the ratio of the phases remains constant.

I may here mention that for this operation I constructed the com-
pound hydraulic pump, which vAN Expr has used for his measurements
on the capillarity of mixtures (Fig. II. Communication N° 39 May
97). This apparatus seems to me preferable to the “analysateur”’
because the phases can be observed in a glass tube and need not
come into eontact with the packings but only with mereury and

nation of the density of liquid is wanted when a determination

lass.

The influence of the packing on the observations with the “ana-
lysateur” has been mentioned previously. We have now to consider
the influence of the operation mentioned on the result of the ex-
periments.

The experiments, in so far as they deal with a temperature below
the critical, will be considered sub. 5, it will here be sufficient to
say that the experiments above the critical temperature have to decide
whether the substance, originally in the liquid state (at an almost
constant volume) will have a higher density when raised above the

or
5

SE lr

( 641 )

eritical temperature than the substance which originally was in the
‘aseous state and assumes the same temperature and pressure. The
movability of the pistons is of no consideration for the experiments
above the critical temperature, the only important thing is that be-
low the critical temperature the same distribution is obtained which
DE HEEN had realized at the moment when the pistons are brought
into their last position. One of the ways in which I obtained that
distribution in an apparatus with two reservoirs of the ratio given
by DE HEEN in his second series was distillation.

Probably in choosing the ratio mentioned, DE HEEN expects to be able
to separate from the gas above and from the liquid below a phase more
exclusively consisting of liquidogen or gasogen molecules than when the
reservoirs have the same volume. The substance chiefly consisting
of gasogen molecules is related according to him to that chiefly
consisting of liquidogen molecules as a dilute solution of salt is to
one more concentrated on which it floats. If the two have during
some time been in contact the nearest approach to the original con-
eentration of the two solutions of salt will be obtained by drawing
off at one end the upper layers, at the other end the lower layers.
In this reasoning we may put in the place of DE HeEEn’s hypo-
thetical liquidogen molecules the really existing very small admix-
tures to the carbon dioxide. In the initially wholly or chiefly li-
quid portion of the carbon dioxide they amount to another num-
ber than in the initially wholly or chiefly gaseous portion and only
gradually they will be distributed equally by diffusion. According
to §2 it is obvious that greater corrections must be applied to the
observed densities when the substance of which the density is mea-
sured is taken from the extreme layers than when they are taken
from the intermediate layers. And so a more unequal distribution
of the admixtures over the two reservoirs may also have attributed
to the larger differences given by DE HEEN in his second series.

At any rate, now that pe HeeEn’s first series of which the devi-
ations are systematically related to those of the second, has been
refuted, his measurements of the second series do not in the least
prove his theses:

“Tl est aisé de conclure de ce résultat que la densité critique qui
a été admise jusqu’d présent est une densité purement fictive (and
further what has been cited in § 1). 3° la loi du diamétre est
parfaitement observée, ainsi que la planchel’indique. Si l’on pro-
longe celui-ci jusqu’’ la température critique, on obtient la densité
critique fictive qui avait ¢té admise jusqu’d présent, 0.470.
4° Les courbes exprimant les variations de densité du liquide et

43*

( 642 )

de la vapeur se prolongent au dessus de la température critique, et
ce n’est que vers 60°, en général que la masse devient homogéne
dans toutes les parties du tube (en employant toutefois les précau-
tions indiquées).”

4. Explanation of the deviations below the critical temperature.
De Heen’s statement that for carbon dioxide in the case of the
co-existence of liquid and vapour as far as about 20 deg. below
the critical temperature no definite densities would exist for the va-
pour and the liquid, but that for instance at 28° C. this density
would be situated for vapour between the limiting values 0.288
and 0.533, for liquid 0.408 and 0.650, disagrees in my opinion
with the experience of all who have made accurate measurements
with liquefied gases.

And though in repeating pre Heen’s determinations with the
above-mentioned apparatus I have found small deviations from the
liquid and vapour densities found by AmaGat, they could always
be attributed to errors of observation.

This statement of DE HkrEeN may be explained by the fact that
the meniscus cannot be seen in the ‘analysateur.”” And so DE HEEN
may have given as density of the vapour phase the mean density
of matter in a reservoir in which the meniscus had risen already,
and as density of the liquid phase the mean density of matter ina
reservoir in which the liquid surface had fallen already.

Dr. VerscHarreLtT has combined in a very clear diagram DE HEEN’s
data by plotting the densities given by the latter for the vapour
phase and those given for the liquid as ordinates, and the mean
density of matter in the two reservoirs of DE HrEN as abscissa.
For simplicity I borrow from that diagram only a small number of
limes (see fig. 1 p. 643) and give by its side in fig. 2 those which
indicate the mean densities mentioned, in each of the reservoirs
according to AMAGAT’s vapour and liquid densities (the line applying at
the critical temperature and higher, has been drawn at an angle of 45°),

It is obvious from these figures that be HeeEn in the calculation
of his densities has neglected the correction from non-homogeneous
to homogeneous substance. By applying this correction his observa-
tions would give a vapour and liquid density almost independent
from the mean density of matter, which by means of corrections
systematically related to those considered in §§ 2 and 3, would very
likely be made to agree with those of AMAGAT within the limits
of the errors of observation.

Everything being considered it appears desirable that Dp Hren should

repeat his experiments with due regard to the circumstances and the
corrections indicated in this paper.

I think I have sufficiently justified the opinion that these expe-
riments bring no arguments against the truth and the completeness
of the theses from van pDeR WaAAts’ theory on the critical state
mentioned at the beginning of § 1.

Physics. — Prof. van per Waats on: “The equation of state and
the theory of cyclic motion”. IL], (Continued from p. 584).

There is another quantity relating to the critical point, which
ealeulated from the equation:

a r
(> +) e—y= Rr, Lede iiun. ua)

if b is kept constant, yields a value strongly deviating from what

. 1 : 7 = i It dp

is found for it by means of the experiment. The quantity es ~),
pa

caleulated for the tension of saturated vapour, coincides in the critical

( 644 j

T dp
dT ;
its value ies not differ much from 7, whereas from the equation
of state, if 6 remains constant, we find no more than 4.
If we write:

point with & i) The experiment shows that for many substances

(2) ee

it appears that this value is quite determined by the properties of
the substance at the critical temperature; but that it is not deter-
mined by the course of the critical isothermal alone. Not from every
equation, which perfectly represents the course of this isothermal, a

en)
which is quite determined by the isothermal, and for which therefore
the true value may be found from every equation which represents
the isothermal. Only for such an equation which besides representing
correctly the isothermal, also assumes the accurate value for € and

v
correct value will be found for it. In so far it differs from (4

; dé - Td
so also for (=) , the true value for (= 2 can be found.
dv AE P aT’ k

It is known that if in the equation (1) 6 is kept constant, and if
we take a as depending on the temperature, the factor 4 rises to
7, if we assume such a dependance on the temperature, that:

T da 4
andl i
>
at T= Ty. Tt will appear from what follows, that the compressi-
bility of the molecule, or to use a safer term the variability of 8,
L’ dp = : :
-,) to nearly 7, even without @ being
Pp a7 ie .
a function of the temperature.
Let us write again:

c= /(1) +P, —7() = hee (>),

will raise the value of (—

then we find:

(—) ee i \adP, iy a°P, db Ee r os
I (dup ~ dvaT * dup db db dT

( 645 )
' dP, He
If we restrict ourselves to the term e,? 80 if we do not assume
Ur
1

the quantity « in the expression — to be a function of the tem-
we

perature, then:

(Bear (4),
p at. pvr] i.

ie ; nt
On the supposition that & is constant, py has the value of
T' dp
and wv, the value 34 and we calculate (—=) eo
id le)z.

If however, is variable and if this quantity follows a course as
dj 4 rat 7 a f
iscussed in the preceding pages, then pr = 6 Bae and v.=2,08 b;,
and we find:

in perfect accordance with what I had previously caleulated for it,
2,9 eats af : :
04343" (Continuiteit I p. 159). Also to this quantity applies

WY

: pe ; is ig
what has been observed for (= , viz. that if a reason is found
4 /k

>

which reduces the critical volume from 3 to about 2, the other

quantities characterizing the critical point, which differ much from

the previously calculated values, are at the same time corrected.
3ut then it appears at the same time that:

(1 db ja ip BP, 1)
dbp db || Vi

(pr: dup
must be equal to 0, or at any rate so small that it may be neglected.

OREN .
Now () is equal to:
lb 77

€

( 646 )

Grey e+e)
or

dP, wa? Be { v—b be: i!
(= (eee gs, i
If we therefore put:
e=f(Q)—-—+F;

then:
Gia0+ Ss) aa,

, db v—b 3 on
According to the values which aR and ane have in the critical

0
point :

db ( v—b

7

21
— 1) would be 0,138 (2 es 1)

dor

or about 0,248.

Ey
From this follows that if 7 Z

72
db dT

a

was equal to zero, we should

a Al

Td
have to add nearly 1/, of 6,7 to the value of (—4)- and conse-
Pp a k

quently this value would not be found too small, but much too
large. This error is avoided, if we put:

dP, __ aby
db dT db

a al

which is the case, as we observed when calculating the specific
heat, if we assume the atomic forces as proportional to the temperature.

The consequences of such an assumption are somewhat strange.
In this case 6,—b) would be the same for all temperatures, and b
does not depend on the temperature. Then the molecules are com-
pressible, but do not expand by heat, which is in opposition
to what I expected at the beginning of this investigation. And I
must confess that in spite of the many remarkable results which
we have obtained, and which are aeceptable, this result has made
me doubt whether the caleulated formula for 4, though it indicates

( 647 )

the course of % fairly accurately, has really the theoretical signifi-
cation, which we should assign to it, if we use it to explain such
large changes in the value of 4, as is given for it by the equation
of state. But we met already with the same difficulty in the deter-
mination of the specific heat, for the rotations, which we have to
assume, if there is no potential energy for the molecule, are in
themselves very probable. That the result is very near the truth
seems to appear from what follows. A gas follows the law of BoyLe
at very large volumes, as:

If we introduce the critical temperature, which according to what
precedes is but little below:

8 a
1), = = —
E 27 by
we find:
ee ttine OT.

So, if we keep 4 always constant in the equation of state, the
result is that the temperature, at which a gas in the utmost rarefied

; Sanna ie
state follows the law of Boyut, is = times higher than the
eritical temperature. If on the other hand, we assume / to be
variable with the degree of density, and if we bear in mind that
6, amounts to about 0,86 of b,, as it is at the critical temperature,
the preceding equation becomes :

T 27 X 0,86 (On), (bo) r:

Peo D08 (69) 7 (b9) 7°

rraveees

According to a remark of Danten BerrarLor (Quelques remar-
ques ete. Arch. Néerl. Tome V pag. 439) the experiment furnishes the
value 2,93 to 2,98 for the proportion of these temperatures. From this
value we may most likely conclude that the value of by is the same at
these two temperatures which differ so widely. If therefore I continue
speaking of the compressibility of the molecules, I do so with
reserve, but yet in the expectation that this question may be decided

( 648 )

by further investigation, when some more trustworthy series 6
values of & at widely differing temperatures will have supplied
values for the evefficients of the equation.
If we accept the result, that the temperature has no influence on
: Tdp
the value of 6, as perfectly correct, then ce may be brought

under the following form:

wv \ ‘T’ dp : ;
Between i and (— = we find the following relation:
RT. 11

bo| o9

pr T dp
a (aa
lie p dv /;. l1—a—-/?

: v 3 T dp
If d is kept constant, then (7) = 2 and E yah and the

product furnishes */2, the value of the second member if @ and 2p

~ { pe 1 ‘T dp Bie
are zero. If =) = == pill {= =) — 6.7, as we have calculated
\RT/, 3,4 p al

for COs, we find 1 — « — ? = 0,762, quite in accordance with the
formerly accepted values of «@ and /.

So the equation of state of a substance continues to contain two
parameters @ and . For a we have assumed that this quantity is
constant, but for 6 that it depends on 3 constants, viz. by, 6, and f.

By means of the given relation between and the three constants,
on which it depends, the three quantities b,., @ and /? are deter-
mined (we shall presently return to this determination). The experi-
ment furnishes four data, from which inversely the four unknown
quantities a, lz, @ and # might be calculated. The four data of

gal

t T dp 7
the experiment are, vz pr RT_ and (— =) — for which we ean
p dij,

pe (I dp
also take pz, RTs r) and {— ) j
uso take pz, RT x, = i ( fr iD).

The two last mentioned are numeric values, and therefore indepen-

v T d
dent of a and bx. If we put ae X and 2 ma ae Y, we

ee

( 649 )

calculate @ and 7? from the two equations:

e 1
i
3 1—e
oe
41—e—(7
x—2 1 9 l1—e
Se tae ek eSyne
The result is:
l
ee
a XY
1 2
1 ak
3 = j
[ MOK

If the above considerations are perfectly accurate, then /? must
be of the order of @, and smaller than a.

In order to calculate 6; we can make use of the equation:

Bean ate tf)
~~ 8 pe (l—ae— py

by (l—e@—4f).

If @ and 2 =0, we get the well-known equation:

RT},

Es :
5 pk

By means of the above values of « and /? for CO,, we find:

TRAN
p= SSS 0
6,807 px

From this we calculate 6, = 0,00225, from which would follow
the value of 0,002615 for b,.

Also by the introduction of the quantities X and F we should
be able to calculate % from :

1
With SS and Y =6.7 we ealeulate:

oOo.

liste, Al
fe = 77

pe 6.9 :

from which follows that 6, = 0,00222 and b, = 0,00258.
The quantity @ may be caleulated from the equation:

(At) (l1—eae— (3)
fe 22 ae) ee a

from which we find for a the value of 0,00855. If we introduce
the quantities X and F instead of @ and /?, we have for the caleu-
lation of a the equation;

RT)
a- ant a X?(¥ — 1).
Pk

1
If X and Y are = and 6,7 we find from this for @ the value

3
0,008484, so about 3 percent lower than was assumed for the cal-
culation of the series of values of 0.

When determining the critical volume of carbonic acid, we observed
(p. 582) that the equations (5) and (4) of p. 580 are not perfectly
satisfied, if for # the value 2 and for b, the value 0,0007 was assumed.

This might in the first place be owing to the fact that we have
to consider equation (4) only as an approximation. But even if we
erant this, it remains desirable to investigate in how far such an
equation can make the observation and the calculation agree. There-
fore I have investigated what values / and 6) ought to have in
equation (4), in order to make the agreement perfect.

This remains a work that requires longer caleulations. For this
purpose I brought equation (5) of p. 580 under another form. If

( 61 )

: b— by\?.
the quantity ( ; ) is represented by a, we find from (4):

bg — by
v—b rs VY «
by — by fl —2)
and
v ( 1 } by
RY SEE te de fie ce Me es OL
as acy T FG Sees

, then:

If we put « for
by — bg

v—b 1

‘ Thee fe

lh ; :
Now = for which we found the value:
v

db
tt Garg iat er.)

0

~ can also be given under the following form :

db 1
aes ay
fea

and so:

For

See oo ___ db f (=) +G) (Sr
Tair TANS ate Q
oe er)

( 652 )

we find:

d? 1 1l+¢e 1 1

ele healt dv? f (l—2) i (1 — 2)(1 + 2)
2 db \ 1 Jee }2
Seat § euler =

If we introduce this value in (5), we get the following equation:

3 ic ae
2 _ Pd=9 "F490
rau yt ee
: IAC Cee) iH a if (i—z)2)
or
3 _sl—ay3
9 o I ey Gee )
1—z)?
yeaah) pater

Here we haye a relation between the 3 quantities f, 2 and «. By
; ; db ;
making use of the value which «¢ = TE must have in order to pro-
v

perly represent the critical quantities, we have a relation between

f and «. Be:

The

oe = 0,152 and | 52 ° = 1,327.
l+2a

We write therefore:
1,9905

1 es)

+S 1+
If we assume f= 2, we find 1 — «= 0,358, and we ean calcu-
late w. With these data we find « = 0,284, whereas the equation

=1+4/(1—2) (1 ++).

ae 7 ;
for b, which we had drawn up, contains for « the value 5 = 0,368.

( 653 )

If we had kept this value for «, we could have calculated /, and
we should not have found 2 but about 1,8.

So there is no perfect concordance. Whether this involves that
the given equation is only an approximation, or whether the imperfect
agreement is the consequence of the certainly not absolute accuracy
of the observations, cannot be decided for the present.

So I have to leave unexplained the result furnished by the series
of values for &, which are given for t= 13°,1. This series agrees
aecurately with a formula of the given form, which appears from
the following values. Take again f= 2, but 4, = 0,0008, and put
b, —by as unknown; then we find, beginning again with the smallest

volume:

; » = 0,0020527 b, — by = 0,00165

20937 164
CR 21822 1635

volumes.

22234 161
226147 1622
12933 1654

Gasvolumes. 13036 160

| 13764 168

Though this proves convincingly, that the liquid portion of the
isothermal and the gas portion follow exactly the same equation, it
remains unexplained that J, is found to be here greater than
in the series of values at higher temperature. In reality 6, is
0,00165 + 0,0008 = 0,00245 for this series; but the difference
between this value and 0,0026, as it is at a little more than 30°,
eannot be explained either.

Finally I will point out a result of the given equation for 6. If
we write:

a RT
[ed if aed bs .

ay

a
p+ ab)

( 654 )

or
(0 +5) 6) +e? 2) __ at per,
rear aA Lh)

it appears that at a very high degree of density, when «@ (b—,)
° a 0
will have become but a very small part of p + 3 the equation of

state tends to: °
a ‘ i 14 A
(» a =) (—b) =) RE

The condition comes nearer and nearer to such a one for which
the complex molecules may be considered as broken up into single
atoms. With the disappearance of the atomic forces the mode of
motion will naturally tend more and more to a free motion of the
atoms in all directions, and so to an amount for the specific heat,
as if there were as many molecules, as we else should say atoms.
For the liquid state we have no experimental data in this respect.
But for the solid state the law of DuLone and Perrr points in that
direction. Moreover we have to assume with BonrzMann for the
solid state, that the specific heat will be found twice as great, on
account of the property of a solid body to keep every material point
fixed at a certain place. This double amount will, however, not be
found for the liquid state.

a(b—b,) . :
The amount of oO oe) is calculated from the equation:
a
p+ ry
_ RT
b—b, Laer = ii
ae a 7 a (b—by)
p+ ta(—b) 147
pie eo)
or
a (b—b,) v—b 1
a b—b
p +. =. 0
v

For v= 0,0020527, b,—=0,0008 and f=2, we find for it a
value of nearly 0,275.

( 655 )

Mineralogy. — Prof. J. L. C. SchRoEDER VAN DER Kok: “On
hardness in minerals in connection with cleavage.”

In 1852 Kenneorrt tried to find out the connection between the
hardness of minerals on the one hand and their specifie gravity and
molecular weight on the other. For the purpose he choose corundum
and hematite and taking in consideration the molecular weight of the
two minerals found the specific gravity of corundum to be very
high, comparatively speaking, although practically it was lower than
‘that of hematite. Comparing a great number of other minerals in
the same way (taking them in twos) he found the rule, that a
mineral which has, as KeENnNGorr calls it, the greatest relative
specific gravity also has the greatest hardness.

A standard for the relative amount of specific gravity may be
found, when dividing this by the figure representing the molecular
weight. We shall then find for corundum (the harder mineral of
the two) the quotient 0,039, for hematite, it will be no more than
0,033.

In his investigation Krnncorr has limited himself to minerals,
which erystallographically bear great resemblance, of which the com-
position chemically is analogous and which possess an equal degree
of cleavage. This, as we shall see, is of great importance to obtain
satisfactory results.

However I thought desirable to try and compare those minerals,
which are less analogous. Even though the results should be con-
tradictory, that very fact might open new vista’s.

A first trial with the elements, in which the specific gravity had
to be divided by the atomie weight was not unsatisfactory.

Diamond, by far the hardest substance proved also to yield the
largest quotient (compactness) i.e. 0.293; the only substance, which
somehow comes near to it is crystalline borium, the quotient being
().245. Good results I also obtained among others, with the following
metals: nickel (0,147), manganese (0,145), iron (0,141), chromium
(0,133), iridium (0,119), platinum (0,109), gold (0,098), lead
(0,055), sodium (0,042), potassium (0,022) ete. TI shall later speak
of some few exceptions which, as we shall then see, are however
only apparent ones: instances of these apparent exceptions are be-
ryllium (0,233) and copper (0,141).

When however we compare the quotients with those we obtain
with corundum and hematite, they seem contradictory; for corundum
a very hard substance, we found 0,039, for lead (a soft substance)
a higher figure 0,055. A moment’s consideration however, will lead

44

Proceedings Royal Acad. Amsterdam, Vol. IIL.

( 656 )

us to conclude, that it won’t do, in the one case, to divide by the
figures representing the atomic weight, in the other by those repre-
senting the molecular weight; instead of dividing by the latter, we

Mm. g. ;
J 1) or, which comes

must do so by the average atomic weight

to the same, multiply the quotient we obtained, (with the molecular
weight as divider) with the number of atoms of the molecule. Then
we can better compare the results; for corundum multiplied with
5 yields the very high quotient 0,195; hematite that of 0,165.

On further trial, I found, that hydroxyl, in the topaz for instance,
isomorphously, as it is called, replaced by fluor, must in our caleula-
tion be treated as one single atom; the same holds for NH, in
salmiak.

300 minerals I have submitted to this caleulation, as will be more
fully expounded on in a treatise, for the moment I left unconsidered
the zeolithes and such like minerals.

Truly, by multiplying with the atom-number, we have in a great
measure, added to the possibility of comparing minerals, but still
the first list of results looks far from promising; for a mineral,
which is generally known for its soft substance, such as graphite,
yields the high quotient 0,188, whereas tale, which is known for
the same quality has for quotient 0,141, just as iron. On the other
hand quarz, known for its hardness, yields the comparatively low
quotient 0,132. Still, too many good results were obtained, to give
up further trial.

In order better to overlook the matter, I have arranged the minerals
according to their quotient making use of the scale of Mous to state
the respective hardness, however not in figures but by a sort of ordi-
nates. The tops of these ordinates may be joined and by doing so, we get
a peculiar zig-zag line, which gets lower as the quotients diminish :
consequently the hardness on the whole, diminishes with the quotient.
The irregular zig-zag line however shows, that there are still disturb-
ances, which we have not taken in account, but then these disturb-
ances are explained, when we consider cleavage a factor, for in
the minima we find the minerals known for their perfect cleavage,
in the maxima those known for imperfect cleavage. *).

1) n=number of atoms in the molecule.

*) Besides the faculty of more or less perfect cleavage the number of directions is
of significance. Vor when a cleavage-plane is rich in molecules, the richness will
decrease with the number of the cleavage-planes. With an indefinite number of
cleavage-directions practically not a single cleavage plane would stand out for richness

Gina)

This rule holds till the maxima on the zig-zag line fall below
the hardness 5 (Mons). From that moment all regularity stops.

The cause of this new disturbance is soon found, when we look
for the minerals on the scale of Mons. It then appears that the
mutual position of the highest 5 degrees of Mons remains on the
whole the same on the list, that on the other hand the lowest five
minerals on the scale of Mons (those of the hardness 5 and lower)
are scattered all over our list in irregular order. The condition of
hardness of the lowest degrees of Mous is only apparent, the results
of more or less perfect cleavage, so for instance number 1 of Mons
admits of cleavage only in one direction, number 2 in two, number
3 in three and number 4 in four!). So we should distinguish
between two sorts of hardness, a theoretical one, which will princi-
pally depend upon the quotients and an experiment, one which ina
high degree depends on cleavage.

It is true not one single metal can practically reach its theoretical
hardness, so we must consider it to be the limit which — the quotient
given — experimental hardness can approach; still theoretical hardness
is a quantity, which is important.

For since on the one hand we have found, that cleavage may in
a high degree lower experimental hardness, there are on the other
hand phenomena showing, that an inpediment of cleavage may con-
siderably increase the quality hardness. The cases are perhaps not
numerous, but they are not lacking.

For instance biotite, a mineral known for its perfect cleavage,
almost entirely loses that faculty and changes into so-called rubellane,
but then the hardness increases. Something of the same kind we
see happening in tale, which by heating loses its cleavage and gets
considerably harder. Also inclusures of foreign minerals, though ever
so few may impede cleavage. The microscope shows many instances.
I.e. amphibole, which is of perfect cleavage, is often interspersed
with apatite-needles, which here more or less act the part of nails
and prevent cleavage. What makes the phenomenon peculiar is, that

of molecules and we should have to deal with a substance that admits of no cleavage-
directions. A substance with 4 or 6 cleavage-directions, in hardness experiments,
comes to the same with a material of imperfect cleavage; in a smaller degree this is
the case in cubic cleavage, in a still smaller degree in rhombohedral cleavage and in
the smallest degree in cleavage, in one single direction.

1) This faculty of cleavage acts a great part in all researches, undertaken to find
out the experimental hardness. Consequently the succession of the scale of Mous
has remained unaltered both when experimenting with the sklerometer as with the
boring-methods of Prarr or with the pressure of a lens against a plane (AUERBACH),

44*

( 658 )

the addition need be but very small and the degree of hardness not
very great: the question here is only to impede cleavage or gliding.

But then similar phenomena we know excellently well in alloys, in
which very small additions may considerably increase the hardness
of the main substance, and these additions in themselves need not
be very hard. This is a known fact of iron, but the quotient of
copper (its theoretical hardness) is equally great as that of iron; so
copper by the addition of small quantities of other elements must
be able to acquire not only the hardness of iron, but also that of
steel. So by these additions we must impede cleavage or gliding in
copper. For this purpose it is preferable to choose elements, which
are not too near akin to copper, because they may possess the same
cleavage or form an isomorphous mixture.

What has been said of copper as a matter of course, holds for
all metals, not one, as we may say, entirely lacking cleavage or
translation. So not a single metal will reach its theoretical hardness.
In the first place however this may be said of the metal berylhum,
which yields the very high quotient 0,233. According to its quotient
(theoretical hardness) it should be able to attain an experimental
hardness, which greatly exceeds that of steel.

Astronomy. — On the luminosity of the fixed stars. By Prof.
J. C. Kapreyn.

1. Wean parallax of stars of determined magnitude and proper
motion.

In a paper published elsewhere ') I found for the mean parallax
Tty..m Of stars of a determined proper motion « and a determined
magnitude m (Potsdam system) the formula

= yi ——
Tu. m sy 4 | a aie C(O (1)

The values of the constants were derived as well for the whole
of the stars as for the stars of the first and second spectral type
(Secchi’s notation) separately.

) Publ. of the Astr. Labor. at Groningen No, 8, On the mean parallax of stars
of determined proper motion and magnitude.

( 659 )

I found
Type I. Type Il. All the stars.
A 0.116 0.0262 0.0387
> 141 1.54 1.405 ie (2)
é 0.905 0.905 0.905

The spectra were there, as they are in this paper, taken from
Pickering’s ,Draper Catalogue’. Exceptions to this rule will be
expressly stated. This catalogue will be denoted by the letters D.C.
The relation (1) was derived:

1st From directly measured parallaxes, almost exclusively using
the longest and most reliable series of such measures.

2nd From the mean parallax of stars of different magnitudes,
according to the determination which was communicated to the
Academy in the meeting of October 1897 }).

A further confirmation of the values of the parallax given by
formula (1) for the stars with extremely small proper motions was
found in the strong condensation towards the milky way of the bright
stars with very small proper motions (see Proceedings Jan. 1893),
as compared with the condensation for the whole of the fainter stars.

The values for type I are, comparatively speaking, very uncer-
tain. This is explained by the fact that for this type large proper
motions are exceedingly scarce, in consequence of which the paral-
laxes of very few stars of this type, and these exclusively very bright
ones, have been directly determined.

For type II the circumstances are much more favourable. Still
the values given for this type and for the whole of the stars must
only be considered as preliminary results, which may be altered some-
what by the here following considerations.

2. Probability that a star’s parallax exceeds its mean value in

a given proportion.

In the paper quoted I also tried to derive the probability that
the parallax of any arbitrarily chosen star shall exceed its mean

1) The only alteration made in the figures there given is a small correction, which
has been applied to the mean magnitude of the stars 0—3.5, in order to bring them
in better accordance with the best photometric determinations,

( 660 )

value, computed by formula (1), in a given proportion. This deter-
mination, which necessarily must be very rough, was based on the
hypothesis that the quantities

ae bape toempacnint arituleh eMpaeas
1 9
where a is the true, and a, the probable parallax, are distributed
according to the law of errors.

By this hypothesis the determination of the required probability
was reduced to the derivation of a single quantity, for which the pro-
bable amount (y) of 2 was chosen.

The relations between the probable parallax +, and the mean par-
allax 7 is given by the formula

p?

1) = = ; 4 mod? (0.47694...) = = e—5.827p2

The value of g was derived from the observed parallaxes in dif-
ferent ways. The value which was finally adopted is

e= 0190.02. Ye el eee
Introducing this value, (4) becomes
Hy = 0.810 570- asians ode ote nem

The true uncertainty of this value of g is somewhat larger pro-
bably than is indicated by the p. e.; it can not be doubted however
that the true value of 9 must be very small. It thus appears that
the proper motion, combined with the magnitude of a star, affords
a very good criterion of its distance. It is not difficult by means
of the value (5) of g to compute a table giving the probability that
the parallax of an arbitrarily chosen star exceeds a times its mean
value +. Such a table is given in the paper quoted above. It appears
that the probability is 0.5 that the parallax of a star taken at random
shall be included between

0.523 > and 1.255 | or between =: and 1.55 a,
v0

where z, is the probable parallax computed by the formulae (1) and (6).
The accuracy of all these determinations (with the exception per-
haps of those for type 1) is already so considerable as to justify

( 661 )

an attempt to determine from these data, combined with the known
number of stars of determined magnitude and proper motion, the
number of stars of determined apparent magnitude within a given dis-
tance from the solar system, and from these numbers again to con-
elude the relative frequency of stars of determined absolute luminosity.

3. Data for proper motion, magnitude, and number of
stars of a given magnitude.

For the northern hemisphere the necessary data about the proper
motions of stars brighter than 6.5 can be derived from AUWERS
BRADLEY.

To the proper motions derived from this source I have applied
the following corrections :

a. A correction originating in a correction to the constant
of precession of — 0.000446 of its amount.

b. A correction to the motions in declination of —0”.008
for declinations south of + 51° 30' and of — 0".001 for more
northern declinations.

These values of the corrections are uot yet the best which can be
derived, but they differ very little from them. For the fainter stars
the data about proper motions are much more uncertain.

Still I think I have succeeded in collecting even for these stars
such data as will suffice to furnish a good check on the results
derived from the brighter ones.

To derive data for the number of stars of a given magnitude the
following sources were used:

a. Gore. The hundred brightest stars. Knowledge Sept. 1900 p. 202.

b. Kobold. (Vierteljahrsschr. der A. G. Vol. 34 p. 213).

From these two sources I could derive directly the numbers of
stars of different magnitudes up to 5.5, according to photometric
determinations. A correction of +- 0™17 (see Potsdam Obs. Vol. 13,
p. 459) has been applied to reduce the Harvard results to the
Potsdam scale.

c. For fainter stars the data of the B.D. were used. The correc-
tions which are necessary to reduce the magnitudes of this work
to the Potsdam scale are now known with tolerable accuracy. For
the magnitudes 3.0—7.0 these corrections are given in the Potsdam
D. M. (Potsd. Obs. Vol. 13, p. 454); for the magnitudes 6.5—9.0
by the investigations of SexLiaER (Betracht. iib. die raiimliche Ver-
theilung der Fixsterne. Abh. der K. bayer. Ak. der Wiss. 2° Cl.
19% Bd. 3¢ Abth. 5. 21). The mean was taken of SrrLIGER’s values
for the declinations 0°—49°. SreLiaEr’s data, when reduced to the

( 662 )

Potsdam scale, agree very well with the values which have been
found in Potsdam for the magnitudes 6.5 and 70.

From all these data I find the following comparison of the mag-
nitudes of the B.D. with the Potsdam photometric magnitudes. For
the latter we have as is well known

o intensity of star of mag m

to}

BD.
3.0

4.0
5.0
6.0
6.5
7.0
7.5

8.0

8.5

9.0

intensity of star of mag m 4-1 m

0.4.

Potsdam.
3.38

4.25 |
5.08
6.01
6.59
7.18
7.68
8.18
Saif

9.37 /

(7)

(8).

It was assumed that the magnitudes of AUWERS BRADLEY are
homogeneous with those of the B.D.
For the numbers of stars I find from the just mentioned sources,
after a careful reduction to rounded off values of the magnitude
according to the Potsdam scale:

Potsd. mag.

brighter than 1.50

1.50—2.50
2.50—3.50
3.50—4.50
4.50—5.50
5.50—6.50
6.50—7.50
7.00 - 8.59
8.50—9.50

total
18

51
145
466
508
944
370
530

830

Typ. Z + J only.

17

47
133

\
\
\

>» (9)

( 663 )

The numbers of stars belonging exclusively to the first and second
spectral types, which are given in the last column were derived:
for the magnitudes 0—3.5 from Me. CLEAN’s determinations; for
the other magnitudes by multiplying the numbers of the foregoing

46
column by 7

This ratio was found by actual countings in the D.C.

4. Numbers of stars whose proper motion is included between
given limits.

In the following table are given the numbers of stars which I
found between different limits of proper motion and magnitude.
The reason why not the total numbers, but only those for types
I and II are given, is simply that the latter could be more easily
derived from other countings which had previously been made. The
difference is practically of no importance for the present investigation.

The stars brighter than 1.5 are entirely omitted ; of all these
stars the parallaxes have been measured. For the formation of the
following tables they can be taken directly from the observations.

Magnitudes 1.5—3.5. The proper motions were taken from NEw-
coms’s Fundamental Catalogue. The spectra of those stars, which
are too far south for the DC. were taken from Mec. CLEAN’s Spectra
of Southern Stars (London 1898).

Magnitudes 3.5—6.5. The corrected proper motions of AUWERS
BRADLEY!) were counted, the magnitudes having been previously
corrected by (8). In all there appeared to be of the magnitudes
3.6—4.5, 4.6—5.5 and 5,6—6.5 respectively 297, 652 and 1017
stars. Thus, in order to get the numbers (9) for the whole of the
sky, the numbers of stars in BrapLey had to be multiplied by the
the respective factors 1.535, 2.264 and 4.756. (Consequently to get
the numbers of stars which are actually in BRapLEy, the numbers
of Table 1 must be divided by these same factors).

Magnitudes 6.5—9.5. Different sources (AUWERS BRADLEY,
Auwers AGC, Boss AG C, Porter’s catalogue of proper motions,
combined with countings in the catalogues of LALANDE and BEssEL)
were consulted to determine what fraction the numbers of the stars
with proper motions 0"00—0"10, O"10—O"L5, O"15—O0"20.....

1) Rejected were all the stars which have been incompletely observed by BRADLEY,
and a few others, There remained 2640 stars in all.

( 664 )

TABLE 1. Number of stars Type I + Type IL in the whole sky.

Mag. | 15-25! 2.5-3.5 3.54.5 | 4-55 | 55-65 | 64-7.5 | 75-85 | 85-95
i | | iz be |

ire AfeanN hE aut | a | 7 =
Ls desc Noobs Betts etebuel ebay alba Belated Bots). God
| \ | | |
0.000 —0".C09 | 0".005 | 6 5 | 92 90 | 343 11504 | 9010 | 38257

Ol0O— 019, .015|| 4 | 15 | 52 | 194| 638 j1s96 | 7313 | 28184
.c20— .029| 025 | 1 | 10 | 41 | 177 | 595 |1910 | 5852 | 21285

030— .039, .035| 3 | 16 97 | 188/542 |1910 | 4768 | 15809

.010— .649| .045 |) 3 | 12 | 97 | 93 | 461 11499 | 3877_—(| 19048
050— .059) 085 | 13 | 92 | 86 | 357 “ia 3342 | 9184
o60— .069| .06| 1 | 4 | 95 | 77 | 952 | 963 | 2540 | 6775
o70— .079| .075 || 9 | 2 | 18 | m1 | o47 | 752 jaser | 4908
.080— 089 | .085 | | 5 | 95 | 45 | 209 | 692 | 1337 | 3614
.090— .099; .095]/ 1 | 9 | 17 | 54| 200 | 646 | soz | 2409
100— 149} 195 || 5 | 10 | 57 | 188] 494 | 963 | 1649 | 4873
aso— 19] .175|| 5 | 9 | 3 79/181 | 420 | 1070 | 20883
200— 299) 25 |. cA Bee | 73 | 200 315 | 670 | 919
300— .309/ .35 |] 1 | 3 | a7 | 48) 105 | 75) Ms | 492
400 — 499 | 45. || 5 12 18 | 34 | 121 | 133 | 196
.500— .599 55 1 3 8 7 \Ji84 0) 238ie 253h) saa
.600— .699| 65 | 2 2 1105 | 24 | 32 | 36
700— .799| . .75 ee Ow einer animar =
soo— soo} .ss | 1 | | 3 ¢| | ae | aaa
0.900— 0.999 | 0.95 | ieee 8) | 6 9 1) ee
1.000— 1.199 | 1.1 | | 1 | 3 | 5] | 7.6| 29. || ake
1.200— 1.399 1.3. | | 3 2). 5 | 12.0] 9 7.6
}.400— 1.599 i | } 2 el 4.4 6.0
1.6C0— 1.799 | 1.7 | | |. 1.5). 4.4), as
1.800— 1.999} 1.9 || | | 9 ee S| | 2.5). 0-0) mae
| | |
2.000— 2.999 | 2.5 Porat | | 6.0) 8.9 6.0
s.000— 3.909] 3.5 || | | | tom |) \sx0}e* ease ames
4.000— 4.999 | 4.5 || |. #2] 1.5 3.0
5.000— 5.999 | 5.5 | | 5 | |
| | | 4.5 |

6,000— 6.999 | 6.5 | | \t 1.5 | 4.5
7.000— 7.999 | 7.5 || | | | | |

Total | | 46 | asa | 466 | 1476 | 4549 | 15049 | 44.576 | 150.607

ss

i} | } 1 » | i

( 665 )

ate of the whole number of all the stars. The subdivision of the
proper motions 0”"000—O0"100 was then made by the aid of certain
plausible conditions, which are certainly or probably fulfilled by the
numbers of small proper motions. Further explanation about this
point will be given in a subsequent more detailed publication. The
numbers given in the table were derived by multiplying the total
numbers (9) by the fractions which have been found in this way.

In order to simplify the computations without sensibly impairing the
accuracy, all the stars of which the maguitude is between 3.5 and 4.5
between 4.5 and 5.5 ete., were reckoned to be of magnitude 4.1 2)
respectively 5.1 etc. Similarly for all the proper motions between
0.000 and 0."009; 0."010 and 0."019 ete. the mean proper motions
0."005, 0."015 etc. were substituted.

For each magnitude and each proper motion occurring amongst
the arguments of table 1, the mean parallax was now computed by
the formula (1). I thus found e. gy. for

p.m. 0"045, mag 6.1, 2 =0"0102,

)

which value thus represents the mean parallax of the 461 stars
of which according to table 1 the p.m. and magnitudes are included
between the limits 0"040 and 0050, respectively 5™,5 and 5™,6.
By the aid of the table which was quoted above it is now easy
to compute the number of stars amongst these 461, of which the
true parallaxes are included between given limits. We thus find:

2) If the number of stars of magnitude m or brighter is Am = k. a™, then the mean
magnitude m of the stars, whose apparent magnitudes are included between the limits
: = a = é a .
m and m+1, will be mn=m— —+- T For photometric magnitudes [ find in
a as

the mean a=3,266. This gives m=m-+ 0™596, for which I have taken m--0.6,

( 666 )

Limits of x

000000 and 0"00100 0.001
00100 » 00158 004
00158 » 00251 028

00251 » 00398 .097
00398 » 00631 .209
00631 » 0100 1275
0100 » 0158 .226
0158 » 0251 116
0251 » 0398 0358
0398 » 0631 .0068

> 00631 .0009
1.000

fraction of
the whole

Number.
0
2
13
45
96

127

3.1
0.4

461

Repeating the same computations for all the numbers of table 1,

the following summary is obtained }),

In the second column are given the mean puarallaxes 5, which

were computed by the formula

1 1
5 1 ae a?
eee Cray
ao ms

(10)

The mean parallax > given by this formula sat:sfies the condition
that the absolute magnitude (see next §) computed from it corre-
sponds to the mean of the absolute magnitudes of all the stars whose

parallaxes have values between 2, and ag.

In the last column are given the volumes of the spherical layers.

1) A similar table was published by me last year. (Publ. of the Astr. Lab. at Gro-
ningen, No. 1, p, 93). Since that time I found occasion to repeat the whole inves-
tigation with greater care, so that the present results must be considered as more

trustworthy.

( 667 )

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( 668 )

included between two spheres of which the radii correspond to the
parallaxes of the first column. As unit of volume I took the volume
of a cube, of which the side is the distance corresponding to a
parallax of O"1. The numbers entered in the columns of the
apparent magnitudes —0.9, 0.1 and 1.1 show simply the number of
stars whose measured parallax lies between the corresponding limits
in the first column.

6. Absolute luminosity and absolute magnitude.

As unit of luminosity I will adopt the total luminosity of the
sun. It is true that our knowledge of the relation between the
quantities of light which we receive from the sun and from certain
fixed stars is still very imperfect. This is however of little impor-
tance, because, when this relation will be better known, it will only
be necessary to multiply all our results by a certain constant, in
order to bring them into accordance with the new determination.

I will here adopt: light of the sun = 40.000.000.000 light
of Vega '). According to the Potsdam measures the apparent
magnitude of Vega is 0.41. From these data it can be easily
derived that the sun, when transferred to a distance corresponding
to the parallax « = 0"10, would have the apparent magnitude 5.48.
I will adopt 5™,5, which accidentally agrees exactly with the mean
magnitude of the Bradley stars. If we put further:

L = luminosity, or total illuminating power of a star of appa-
rent magnitude m and parallax = 7,

we find easily by the relation (7):

log L = 0.2000 — 0.4 m — 2 log a. A ye ey

We further define the absolute magnitude (M) of a star, of which
the parallax is « and the distance 7, as the apparent magnitude which
that star would have if it was transferred to a distance from the
sun corresponding to a parallax of O"L. It is easily seen that

M=m—5logr =m-+5-+4 5loga = 5.5 — 2.5 log L . (12)

For the sun 4 = 1; the formula thus gives for the absolute magni-
tude of the sun 4/ = 5.5, in accordance with what has been said above.

') Young, General Astronomy p. 213.

( 669 )

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( 670 )
7. Derivation of the star-density and the lwminosity-curve.

By the aid of (11) and (12) table 2 can be so altered that the argu-
ment: apparent magnitude is replaced by the argument log L or M.

If this is done, and if further the numbers of the table are divided
by the volumes given in the last column and logarithms are taken,
we get the following table: (p. 669)

The numbers of the last row of this table require some explana-
tion. If this tow had been derived in the same way as the others
the resulting numbers would have been those corresponding to the
values 1.94, 1.54, 1.14... ete. of log Z. For the sake of unifor-
mity I derived from these, by interpolation between the logarithms, the
values corresponding to the values 2.02, 1.62, 1.22... ete. of log L.

It is still possible to enter this table with the argument: apparent
magnitude; for the logarithms belonging to the same apparent magnitude
are now placed in an oblique line descending towards the right. In
order to facilitate such an entering of the table, the logarithms
belonging to the apparent magnitudes 3.1—7.1 have been included
between heavy lines. This enables us to judge more readily of the
weight of the several numbers tabulated. Thus it is seen at once that
the numbers which are in the table to the left of the heavy lines must
have a very small weight because they are relative to the stars of
the magnitudes 2.1, 1.1... which are exceedingly few in number.
Similarly, though for a different reason, the numbers which are
outside the heavy lines on the right hand side, and which belong
to the magnitudes 8.1 and 9.1, have a small weight, at least for
the smaller values of the parallax.

The table virtually is nothing else than a table for the loga-
rithms of the relative densities of stars of different absolute magni-
tudes (or absolute luminosity). The absolute density, ¢.e. the total
number of stars per unit of volume, can not be determined of course,
because we know nothing about the very faintest stars. We can
however determine that density expressed in its value at a ceriain
distance from the sun as unit.

For this distance I will provisionally adopt the distance corres-
ponding to a parallax of 0".0296. I will adopt the hypothesis that
the luminosity-curve is the same for different distances from the sun.
Luminosity-curve I call the curve which for every absolute magnitude
gives the number of stars per unit of volume, or in other words,
which gives the proportion in which the stars of different apparent
magnitudes would be distributed over the sky, if they were all placed
on the surface of the sphere whose radius corresponds to the paral-

( 671 )

lax 0’1. In the following tables I will give not the numbers of
stars of each absolute magnitude, but the logarithms of these num-
bers. As a consequence of the hypothesis which has been mentioned
the ratio of the absolute densities is necessarily the same as that of
the densities for the separate absolute magnitudes.

If the density was constant, the numbers in each vertical column
of table 3 should be identical. For the middle of the table this
condition is roughly satisfied; for the large and for the small distan-
ces however it is not.

The manner in which the densities given in the last column are
determined, is perhaps best explained by an example.

The number of stars (not the logarithm) per unit of volume for
the stars of the four absolute magnitudes — 6.55, —5.55, —4.55,
—3.55 together is:

for « = 0"00118, (app. mag. 2.5—6.5) 0.000 0623
» » = 0"00187, (app. mag. 1.5—5.5) .000 1215

We thus get for the ratio of the densities A, and A,

Bt 953
As
As a second determination we have for the stars of the absolute
magnitudes —6.55 to —2.55:

for ~ = 0"00118 (app. mag. 2.5—7.5) 0.000 2743
» » = 000187 (app. mag. 1.5—6.5) 0.000 5095

from which we get
aS (GEE
Ag

The mean was taken of the two values 0.518 and 0.538, giving
to the first value (which depends chiefly on the stars of the apparent
magnitudes 6.1 and 5.1) twice the weight of the second value (which
depends chiefly on the stars of the apparent magnitudes 7.1 and 6.1).

In the same way the ratio was found of the densities at conse-
cutive distances from the sun (w = 0"00118, 0"00187, 0"00296 ete.)
These ratios, together with the adopted density 1.0 for the distance
corresponding to a parallax of 00296, gave the values of the last
column of table 3.

If now from the logarithms of each row of the table we subtract
the corresponding logarithm of the density, or in other words, if the
whole is reduced to the density for 7 = 0"0296, the following table
is derived:

45

Proceedings Royal Acad. Amsterdam. Vol. III,

( 672 )

TABLE 4.

Log. number of stars per unit of volume, reduced to 7 = 00296.

—6.55|—5 .55|—4..55|—8.55/—2.55|—1.55/—0.55| 0.45 | 1.45 | 2.45 | 3.45 | 4.45 | 5.45 | 6.45 | 7.45 | 8.45 | 9.45 [10.45
|
| 5. 4,82 | 4.42 | 4.02 | 3.62 | 3.22 | 2.82 | 2.42 | 2.02 | 1.62 | 1.22 | 0.82 | 0.42 | 0.02 | 9.62 | 9.22 | 8.82 | 8.42 | 8.02
| |
0”.00118 4.42 14 72 15.381 | 5.947 | 6.599 | 7.240] 7.982 | 8.627
.00187 4.74 | 5.01 5.16 5.917 | 6.615 | 7.220 | 7.819] 8.469 | 9.077
.00296 5.56 5.98 6.546 | 7.231 | 7.807 | 8.371 } 8.922 | 9.490
00469 6.06 6.660 7.174) 7.811 | 8.373 | 8.909 9.384 9.902
00743 5.96 |5.96 {5.96 | 6.674 7.270 7.775 | 8.371 | 8.919 | 9.427 9.850 0.286
0118 | 7.29 7.885 | § 384) §.906 | 9.430 | 9.891 0.232 | 0.658
0187 7.96 ee 8.962 | 9.410} 9.879 | 0.282 | 0.567 | 0.922
0296 8.00 | 8.52 8.949 9.476 | 9.857 | 0.269 | 0.596} 0.830} 1.113
0469 8.36 |8.64 |9.059}9.402 | 9.945 | 0.238} 0.590 | 0.850} 1.037 | 1.240
0743 8.98 |8.98 | 9.503]9.790! 0.351 | 0.560} 0.823 | 1.043 1.181 1.301
118 9.64 |9.64 |9.84 |0.110/0.690| 0.818 | 0.993 | 1.227] 1.294 | 1.331
. 204 0.17 10.17 |0.41 |0.19 |0.361) 0.851 | 1.052 | 1.229 | 1.398} 1.454] 1.445
a es - S
Mear. (4.42) | 4.72 | 5.27 | 5.948) 6.601 | 7.222 7.809! 8.376 8.920) 9.431 | 9.879 | 0.264) 0.583 | 0.8380 | 1.024) 1.229 | 1.398 |(1.45)| 1.44)
(4.38)| 4.68 | 5.27 | 5.0381]6.589 | 7.215 | 7.806 | 8.372 | 8.909|9.410| 9.863 | 0.261 | 0.601 | 0.857 | 1.048 | 1.239 1.408 | (1.46) |(1. 45°)

( 673 )

The numbers given in this table evidently define what we have
called the luminosity-curve.
In taking means the following weights were given:

A. In the columns of abs. mag. —6.55, —5.55..... to + 0.45
/ a oe dr - 1.455 DAD oc. sneeis 8.45
apparent magnitude A B.
brighter than 2.5 0 0

3.1 2 2
4.1 5 5
5.1 14 7
6.1 21 7
wal 3 1
fainter than 7.5 0 0

These weights are roughly proportional to the numbers of stars
in BrapLey which have contributed to the formation of the num-
bers of table 4.

It is evident that the final means depend only in a very small
measure on the values which were found for the densities. They can
be derived quite independently of these densities. So we find e. g.
directly from table 3 for

Ou

number of stars of absol. mag. —1

Dt
” ” » ” ” ” 9)

ol

the following values (the assigned weights are added in brackets)

0.599 (3)
0.576 (5)
0.637 (3)
0.505 (1)
Mean. 0.591.

If in the same way the ratios are derived of the numbers of stars
belonging to any two consecutive magnitudes, it is only necessary,
for a complete knowledge of the luminosity-curve, to derive the num-
ber of stars per unit of volume for one absolute magnitude. This
number was obtained by effecting the best possible agreement with

45*

( 674 )

the curve which has already been found. The resulting values are
given in the last row of table 4. It will be seen that the discre-
pancies of the values derived by the two methods are very small,

8. Influence of the uncertainty of the constants of formula (1).

In order to investigate in how far the values here derived are
affected by uncertainties in the fundamental quantities @, & 755, I
have altered these quantities by amounts which are almost certainly
outside (in some cases far outside) the limits of the teue uncer-
tainties.

As far as the values of 7;; (i. e. the mean parallax of stars of
mag 5.5 and p. m. “) are concerned, the principal causes of uncer-
tainty are: 1s¢. the remaining uncertainties in the measured paral-
laxes and 2"¢, the remaining uncertainty in the linear velocity of
the sun, by the aid of which the mean secular parallaxes derived
from the parallactic motion were reduced to parallaxes in the usual
acceptation of the word.

Now it is evident that, if every parallax is multiplied by the
same factor not much different from unity, then also all densities
will be multiplied by a certain constant factor not much different
from unity. Thus, if provisionally we do not aim at the most refined
precision in the absolute values of the densities, it is clear that we
can make these two uncertainties to bear either wholly on the large
and directly determined parallaxes, or wholly on the small paral-
laxes derived from the parallactic motion.

I chose the latter course, and consequently I took care that the
directly measured parallaxes were as well represented by the new
formula as by the old one.

In deriving the formula (1) the value!) h = 16.7 + 1.15 kilo-
meter per second was used for the velocity of the solar system.
A few months?) ago CAMPBELL, derived from the material given
by his own observations, which is much more extensive than that
from which the above value was derived, the valued = 19.9 + 1.52
kilometer. For the mean linear velocity of the stars he finds 34.1
kilometer. From this latter value we get, by the method explained
in Proceedings October 1897, another value, which cannot differ
much from # = 18.3. As the final value from CAMPBELL’s obser-
vations we must thus adopt about = 19.0. Everything considered
the value:

') Proceedings October 1897.

*) Astrophys. Journ, Jan. 1901, p. 81 599,

( 675 )
P= ASAGS oes SMe Oe S.-Y

appears to me to be the most probable value which can at present
be adopted.

I now derived anew the values of 7, in formula (1) in the follow-
ing suppositions, to which I add the constants which were for-
merly found (sol. I):

Sol h A D | € p

I 16.7 | 0.0387 1405 | 0.905 | 0.19

Il 16.7 | 0.0387 | 1405 | 0.905 | 0.00 . (14)
Il 16.7 =| 0.0387 1.405 | 1.000 0.00
Iv 20.2 | 0.0454 | 130 0.905 0.19

Vv is45 | 0.049 | 1.355 0.87 | 019

In these solutions the stars fainter than 2.5 and in some of them
also those brighter than 7.5, which have no influence on the
result, were, for brevity’s sake, omitted.

These different solutions give for the densities (A):

TABLE 5. Density A.

ze |
weet) oy Ul UI 1V v
Limits. Mean. |
i ee Eee Ee Eee

0".00100 —0".00158 | 0”.00118 | 0.122 | 0.187 0.162
.00158— .00251 .00187 | 0.234 | 0.345 0.292
.00251— .00398 -00296 | 0.418 0.223 0.184 0.568 0.465
-00398— .00631 .00469 0.656 0.592 0.571 0.789 0.684
.00631— _ .0100 .00743 || 0.869 1.072 1.294 0.968 0.852
-0100 —_ .0158 .0118 0.985 P19 1.507 1.040 0.945
.0158 — .0251 .0187 1.031 1.122 1,403 1.050 0.984
-0251 — .0398 .0296 1.000 1.000 1.000 1.000 1.000
-0398 — .0631 0469 0.917 1.045 0.889 1.007 0.980
.0631 — .100 0743 0.829 0.771 0.497 0.875 0.957
-100 — 158 118 0.742 0.728 0.406 0.813 0.933
> 0.158 | . 204. 0.648 0.627 0.220 0.780 0.929

( 676 )

For the luminosity-curve we find (after adding to the values I, IT
and III the constants —0.081, + 0.056 and — 0.104)

TABLE 6. Luminosity-curve.
(Log. number of stars per unit of volume for 7=0!'0296).

aan WJ ul 1V Vv
Mu.
+ 0.056

5.22 | — 7.55 (4.34)

4.82 | — 6.55 4.64. 4.65 4.60
4.42 | — 5.55 5.19 (5.71) (5.82) 5.29 5.17
4.02 | — 4.55 5. 862 5.71 5.94 5.960 5.928
3.62 | — 3.55 6.520 6.46 6.58 6.601 6.586
3.92 | — 2.55 7.141 7.165 7.142 7.189 7.210
9.83 | =-155 7.728 7.838 7.682 7.764 7.815
2.42 | — 0.55 8.295 8.431 8.297 8.323 8.380
2.02 0.45 8.839 8.993 8.735 8.852 8.992
1.62 1.45 9.350 564 9.311 9.340 9.413
1.22 2.45 9.798 9.995 9.763 9.769 9.839
0.82 3.45 0.183 0.285 0.174 0.117 0.190
0.42 4.45 0.502 0.480 0.591 0.452 0.478
0.02 5.45 0.749 0.533 0.622 0.660 0.680
9.62 6.45 0.943 0.601 0.687 0.850 0.836
9.22 7.45 1.148 1.132 1.389 1.084 1.026
8.82 8.45 1.317 1.20 1.607 1.248 1.102
8.42 9.45 (1.37) (1.3) a.7) (1.10)
8.02 10.45 (1.36) (1.4) (1.8) a.)

The discussion of the densities must be deferred to a subsequent
communication, because it will be necessary in that discussion to
keep the stars of different galactic latitudes separated ab initio.
There seems to be reason to believe that this discussion, if therein
we include some additional data furnished by observation, will lead
to a better understanding of the real structure of the galactic system.

The table 5 might therefore have been omitted here but for the
fact that it brings out clearly a defect of our solution I and indicates
at the same time the means to correct it. This defect lies in the
rapid decrease of the density A for the larger parallaxes. A graphical

a

a e

i aceite i

( 677 )

representation in which the densities are taken for ordinates, while
the abscissae are not the parallaxes, but the distances from the sun,
shews the enormous rapidity of this decrease. Such a rapid decrease
appears entirely incredible, as compared with the slow and gradual
change for larger distances. If we could actually use stars which
are evenly distributed cver the whole sky, instead of almost exclu-
sively over the northern hemisphere, and if the density varies con-
tinuously with the position in space, then the mean density in the
immediate neighbourhood of the sun must even be found constant.

The values of A, show the same decrease. A variation of @ has
thus no influence. The As’s on the other hand show a still more
rapid decrease. It follows immediately that by a diminution of e the
defect in question can be corrected. It anpears from the Ay’s that
a change of the distances in the direction which is made necessary
by CaMPBELL’s results, has also an effect in the desired direction.

It is easily inferred from the table that the defect must nearly
disappear by a new computation, if therein we determine the paral-
laxes in accordance with the value (13) of the sun’s velocity, and
adopt

Se BOON es es cs oe wy ee eR
This alteration of ¢ is just inside the estimated limits of uncertainty
of this quantity ').

The last column of table 5, which was computed with these data,
shows that the density becomes indeed tolerably constant for all
parallaxes larges than 0".01.

For this reason the solution V is the solution which in my
opinion is to be preferred, though it remains possible that the sub-
sequent discussion of the densities will necessitate further small
changes in the values of the constants.

9. Reliability of the results derived for the luminosity-curve.

The values which were given to g in solution II, and to g and « in
solution III are outer limits, which were taken for the sake of the
simplicity of the computations. With regard to g the alteration is
9 to 10 times the p.e., for ¢ it exceeds nearly three times the esti-
mated limit of uncertainty. Also the solution IV was made with
values of the constants, the deviations of which from those of solution
I probably exceed the real uncertainties of the latter.

Nevertheless the discrepancies between the different curves in
table 6 are inconsiderable. It thus appears that the form of the curve
is very little affected by errors in the constants of formula (1).

1) See Public. of the Astr, Lab. at Groningen No. 8, p. 10,

( 678 )

Excepting the extreme ends of curve, which for evident reasons are
rather uncertain, errors of 0.1 in the values resulting from solution
V must already be considered as unprobable. In the middle of the
curve this corresponds to only about 0.2 of a magnitude.

Besides on the uncertainties of the constants, the correctness of
the curve also depends on the greater or smaller degree of comple-
teness and certainty of the data about the magnitudes and the proper
motions which form the basis of the whole investigation. We can
however easily estimate the effect of these causes, as it is possible
to derive the curve:

1st. exclusively from stars of app. mag. 3.1, 5.1, 7.1;
one 5 : Cving Gao Pages ele Lasse

These two determinations are absolutely independent of each other.
The computation was carried out with the data of solution 1}),
in precisely the same way as that for the last row of table 4, 7. e.
entirely independently of the densities. The results are given in the
following table

M. on ae 71 ine yea I-it
—6.55 4.730
—5.55 5.183 5.272 | —0.039 :
—4.55 5.957 5.930 + 027
—3.55 6.638 6.561 +. 077
—2.55 7.229 7.238 — .004
—1.55 7.815 7.883 — .068
—0.55 8.349 8.454 — .105
0.45 8.875 9,013 = 188
1.45 9.368 9,482 =) aa
2.45 9.821 9,927 =HO6
3.45 0.222 0.280 — .058
4.45 0.576 0.593 == 2017
5.45 0.882 0.797 + .085
6.45 1.163 0.968 + 195
7.45 1,291 1.165 + 126
8.45 1.509 1.269 + .240
9.45 1.390

1) Afterwards this computation was also made for solution V. The results are all
but identical to those of sol. I.

( 679 )

Keeping in mind that we may legitimately expect that the errors
in the adopted curve, so far as they depend on the uncertainties
here considered, will range between limits only about half as wide
as those of the differences I—II, we come to the conclusion that
these differences are already very satisfactory. All things considered
I think we may safely expect that (excepting the extreme ends of the
curve) the values resulting from solution V will never be in error
much more than 0.2, which corresponds to about 0.4 of a magnitude
in the middle of the curve !).

Moreover our knowledge of the proper motions is increasing
rapidly, so that we may reasonably hope that within a comparatively
short time, we may be able to reduce still more the uncertainties
of the curve.

Especially for the fainter end of the curve, which depends exclu-
sively on the large proper motions of faint stars we will certainly
soon have better data by which it can be corrected and
continued.

From the above numbers the curve appears to reach a maximum
about the absolute magnitude 10.5. Whether for fainter stars it
will descend as rapidly or more rapidly, and whether it will soon
reach a limit, below which no luminous stars exist, are questions
to answer which a knowledge of the number of large proper motions
of stars fainter than the ninth magnitude is required. It seems not
at all impossible by the aid of photography to derive, even within
a few years, an approximate knowledge of these proper motions for
stars down to the 13" or even somewhat higher magnitudes.

At the brighter end the continuation will cause more difficulties,
as it must depend on an accurate knowledge of the extremely
small proper motions, which can only be slowly attained in the
course of years.

A number of conclusions can at once be drawn from our results,
which however I will defer till after the discussion of the densities.
I will here only illustrate the meaning of the curve by afew num-
bers. According to the curve V, there will be in a space which
contains

1) The uncertainty resulting from errors in the adopted position of the Apex and
in the corrections to Bradley’s declinations, was left out of consideration here. I hope
shortly to be able to give the alterations which result from these causes,

( 680 )

2.000.000 stars of the same luminosity as that of the sun
1 star with 100.000 times greater » than » » » »
38 stars » 10.000 » > > > > > > »
1800 > » 1.000 » > > > ~>, >)
36000 > 100 » > > 32 9 2) cs See
440000 > 08> 10> > > > > 2 >: %
over 5000000 > » 10 » smaller » > > a. 28 Gs
7500000 > > 100 » » > PRE ee eke

Below this degree of luminosity it seems that the number of stars ceases
to increase. The first and last numbers are of course very uncertain.
It may also be remarked that we find a total density which is
much larger than is commonly assumed.
The mean parallax of the stars of magnitude 5.3 becomes 0”.0158
by the solution V. Inside a sphere with a radius corresponding to
this parallax I find (by sol. V) already 43000 to 44000 stars whose

SEF 2 Tos
luminosity is not smaller than 7 of that of the sun. The number

of the still fainter stars can not be determined. If on the other hand
we adopt the usual approximation which assumes the same luminosity
for all the stars, the number of stars inside the same sphere will of
course be the number of stars of the apparent magnitude 5.3 and
brighter. This number is (Potsdam system) only about 1730, that

is only = part of the number which was found above.

10. Stars of the first and the second spectral type.

Although the data relating to the separate spectral types are by
far less certain than for all stars together, I will nevertheless mention
the results which I derived from them, as they bear on the conclu-
sions arrived at in a former paper.

The uncertainties are of two kinds:

1st, For Type I the constants (2) are very uncertainly determined.

2-4, Our knowledge of the spectra is far from so complete and
accurate as could be wished.

For these reasons the following results, at least those for type I,
do not deserve the same confidence as the preceding ones for all the
stars together. With regard to the first point, it has already been
mentioned that the total weight of the direct determinations of paral-

( 681 )

lax, which were available for type I, is very small. It is not one
sixth part of that for type II.

Moreover these parallaxes belong exclusively to bright stars of
comparatively small proper motion. It would be of the highest impor-
tance for an investigation like the preseut, if observers, who devote
themselves to the determination of parallaxes, would pay especial
attention to the comparatively few stars of the first type with large
proper motions.

As to the second point:

Having regard to the fact that the D.C. is only complete down
to the stars of about the 6t* magnitude, it is to be feared that of
the fainter stars which it contains a larger number proportionally
will belong to the photographically brighter stars of the 1s¢ type
than to the stars of the same (visual) magnitude of the second type.
If this is so, our results will be systematically affected.

In order to get more certainty about this point I derived the ratio

number of stars of Type II

a . (16)

” » ” n n 1
for different magnitudes, not only from PickerINa’s data!) but also
from the spectroscopic Dm (Decl. — 1° tot + 20°) of Potsdam *),
which is complete down to the visual magnitude 7.5 and is thus of
special value for our purpose.

PICKERING’s results are given with the argument: photographic
magnitude, while we require here visual magnitudes. The necessary
data to effect this reduction are given in PickERING’s work; never-
theless the accuracy of the results is considerably impaired by this
circumstance,

The result of my computations was:

Vis. mag. Number stars in DC, Pe
Typ L Typ I.
3.50—4.00 74 52 0.70 \
4.00—4.50 157 109 0.70
4.50—5.00 301 234 0.78
56 (LIA)

5.00—5.50 633 494 0.78
5.50—6 00 1348 1045 0.78
(6.00—6.50 2717 2220 0.82) /

1) Annals of the Astrophys. Obs. of Harvard Coll. vol. 26, Part 1, p. 147.
*) Publ. des Astrophys. Obs. zu Potsdam Ser Bd. 3es Stiick.

( 682 )

The data for stars fainter than the 6 magnitude are included in
brackets, because we cannot be sure that the two types are observed
equally completely; there is even a strong probability to the contrary.

The Potsdam Dm gives a classification which differs from that of
the D.C.

According to Harvard. Obs. 26, part I, p. 177 we have approx-
imately :

Class I of Vogel = A+ F'+G Draper Cat.

Bie eee K ‘ : oe -) (UBT

Now I find by countings in the Potsdam Dm.:

mag. BD, Cl. I. Cl. IL.
0—3.5 40 | 10 0.25

3.1—4.5 27

|
3.6—4.0 19 | 86 = 16 $ 4000.84 $0.47 |
14 0,52)

4.6—5.0 44 39 | 0.89

5.1—5.5 68.) 276 “39 } 151, 105s [
5.6—6.0 164 73 0.445

6.1—6.5 300 185 0.62 (19)
6.6—7.0 552 0 308 ) 953 056 ss
7.1—7.5 856 460 0.54 |

7.64 66 | 35 0.53

S==e05 38 | 113 16 \0 57 0.43 es
8.6—9.0 9 6 0.67

It follows from these numbers that, at least down to the visual

i does not sensibly vary with the

itude 7.5 th gent oe
magnitude 7.5 the quotient G7

magnitude.
Accordingly we have by (17) in the notation of the D.C.

—— vs -»

( 683 )

K

fee eeg — a!
from which
ie a ee typell FG
meetin oT a » (20)

From the data of the D.C. reduced to visual magnitudes I find

: Number Number FAG
vis. mag. FLE : A
3.5—4.0 21 63 0.34
4.0—4.5 44 134 0.33
4.5—5.0 94 255 0.37
5.0—5.5 200 560 0.36%
5.5—6.0 425 1269 0.33°
6.0—65 908 2629 0.345

Thus also the last term of (20) appears to be eminently constant.

From the Potsdam Dm we thus derive the conclusion, which is
in good agreement with the directly derived table (17), that the
value of P does not sensibly vary with the magnitude (at least not
down to mag. 7.5).

The numbers of stars of the two types were now derived as
follows, the very few stars brighter than 2.5 being omitted:

1st. Magnitudes 2.5—3.5. All stars of these magnitudes in the
whole of the sky were brought together, as explained above.

2rd, Magnitudes 3.5—6.5. The spectra of the Bradley stars !)
were taken from the D.C. and the whole of the stars which are in
this catalogue were counted between the same limits of proper motion
and photometric magnitude as in table 1. From these countings the
total number of these stars for the whole of the sky was then
derived in the manner which has been explained above. Finally
the numbers of stars of the different magnitudes (2.5—6.5) were
multiplied by such factors (differing little from unity) that the con-

1) The stars which have been excluded have already been mentioned above,

( 684 )

dition P=const. is fulfilled, while the total numbers (TypeI +
Type IL) are left unchanged.

3:4, Magnitudes 6.5—7.5. To begin with the same method was
used for these stars as for those of the magnitudes 3.5—6.5. The
number of stars in Bradley belonging to these magnitudes is so small
however, that the numbers for the individual proper motions neces-
sarily run somewhat irregularly. Therefore I first divided the whole
of the stars in two parts, viz. those with proper motions < 0"10
and those with proper motions > O"L0.

: number of stars of 1 Type ;
= t
The ratio a id. 1* Type 2° Type was then determined

separately for each of these parts and compared with the analogous
ratio for the magnitude 6.1. It appeared that the factors, by which
these ratios for the magnitude 6.1 must be multiplied to give those
for the magnitude 7.1, were very near unity. These factors were
then used to derive the ratios a for the separate proper motions
0".00—0".01,, 0”.01—0".02...ete. for the magnitude 7.1. Once
these ratios a found, the table 1 furnishes the necessary numerical
values.

In this way I found finally the numbers which are given in
the following table: (p. 685)

It appears from this table that the numbers for type I show still
considerable irregularities, which are still more apparent, if the table
is condensed by taking wider limits of proper motion, and if then
all the numbers are expressed as fractions of the analogous numbers
of table 1. It appears in this way that e.g. the number of stars of
large proper motion of the magnitude 5.1 is considerably smaller
than might be expected from the same numbers for the magnitudes
4.1 and 6.1. At first sight such an irregularity is rather surprising,
as it is not at once apparent how the spectrographic observations
can be subject to systematic errors depending on the proper motion.

A closer scrutiny shows however that such a thing is not at all
impossible in the present case.

In Astronomy and Astrophysics Vol. XII, p. 811 are given a
number of corrections to the data of the D.C., which corrections
I have duly applied.

The corrections bear exclusively on stars of large proper motion,
whose spectrum has been reinvestigated on the indication of Mr. W. H.5S.
Monck. In how far these corrections influence the number of stars of
the first type with large proper motions is apparent from the preceding

( 685 )

TABLE 7. Number of stars in the whole sky.

a

&
0".000— 0".009
.010— .019
-020— .029
.030— .039
-040— .049
.050— .059
-060— .069
.070— .079
.080— .089
.090— .099
-100-- .149
-150— .199
.200— .299
.800— 399
400— .499
-500— .599
-600— .699
.700— .799
.800— .899
0.900— 0.999
1.000— 1.199
1.200— 1.399
1.400— 1.599
1.600— 1.799
1.800— 1.999
2.000— 2.999
3.000— 3 999
4.000— 4.999
5.000— 5.999
6.000— 6.999
7.000— 7.999

hs) 234 753 2485 | 7

731 | 64 (223 722

[<> ©» i D> °° °° <>)

ore won F-& @ wo

TYPE I.

4.1

10(3)

2

21 (2)
5(12)
2(4)
2

17

TYPE II.
3.1/4.1] 5.1 | 6.1 | v (ea!
7 |

3| 8] 17] 121 | 590
7|16} 68} 199 | 669
1] 14] 54] 262 | 9038
7| 7| 73) 194 | 756
5| 8| 45) 174] 618
5| 5 | 384] 155 | 584
2) 7| 98} 121 |} 493
2/ 6) 46] 186 | 482
3]}13] 24 97 | 343
2) 7| 34} 186 | 447
G6 | 32] 88] 253 | 572
2} 24) 56} 182] 808
9 | 22 | 65} 185 | 286
2} 14} 39} 107) 75
Sai elela aS 30 | 104
3} 8 7 24} 38
2 7 5 | 24
8 5 10] 17
3 2 12
2g 6

ies 5 7.5

3 2 5} 12.0

2 4.5

1.5

2 2 1.5

1 6.0

5 3.0

2 1.5

5
1.5
| 2356 | 7311

( 686 )

table. If the corrections had been neglected, the numbers of stars of
the magnitudes 4.1, 5.1, and 6.1 would have been increased by the
quantities which are added in brackets.

For the magnitude 7.1 the analogous increase could not easily
be derived, owing to the particular manner in which the numbers
for that magnitude were obtained. It will be seen that by these cor-
rections the proportions are entirely changed in the case of the very
large proper motions of type I).

If the corrections which are still necessary are so considerable,
we cannot expect very reliable results.

The manner in which I tried as completely as possible to remove
the irregularities, will best be shown by an example: The total num-
bers of stars ofttype I for the magnitudes 4.1, 5.1 and 6,1 are 234,
753 and 2485. If now every number of the third column is multi-

7
plied by = and every number of the fifth column by = these

three columns are reduced to the same total number.

After this was done the numbers of the 34, 4% and 5% columns
were added; the sums were divided by 3 and the resulting values
were adopted as corrected values for the magnitude 5.1. In the
same way the corrected numbers for the magnitudes 4.1 and 6.1
were derived. In order to be able to do the same for mag. 3.1 the
numbers for mag. 2.1 were also derived. The numbers for mag. 7.1
were not altered.

In the case of type Il the number of large proper motions is so
considerable, and the influence of the corrections which have just
been discussed is so small, that the numbers of table 7 were adopted
as they stand.

In order to derive from table 7 (altered for type I as just now
explained) the densities and the luminosity-curve in the same way
as explained above, a first computation was made with the values
(2). Afterwards a second computation was carried through in which
the corrected value (15) of ¢ was used and the parallaxes were made
to agree with the corrected velocity (13) of the solar system.

In the case of type I the alteration of ¢ had a large influence
on the value of 75,5 derived from the directly measured parallaxes,
owing to the fact that these direct determinations belong exclusively
to very bright stars.

1) According to Mr Moncx 60 percent of the stars of type I, to which he called
attention on account of their large proper motions, were actually altered to type II.

( 687 )

The following are the values of the constants for the two solutions

(A and B):
Type | Sol. h b A | Pp P
| |
I A 16.7 0.116 111 0 905 0.19
v B 18,45 0.0753 1.20 0.87 0.19 |
I A 16.7 0.0262 1.54 0.905 0.19 oe
” B 18.45 0.0316 1.47 0.87 0.19

With these data the following densities were found:

TABLE 8. Densities a.

= Type I. Type IL.
Limits. Mean. Sol. A Sol. B Sol. A Sol. B
| |
000100 — 000158 | 000118 0.280 lo.978 (0.070 0.102
.00158 — 00251 .00187 .470 0.478 0.156 0.190
.G0251 — .00398 00296 .738 0.726 (0.254 0.314
00398 — .00631 .00469 —|/1.006 0.986 0.440 0.474
.00631 — .0100 00743 1.202 1,172 0.622 0.655
0100 — .0158 .0118 1.215 1.171 0.802 0.790
0158 — .0251 0187 1.189 1.283 0.960 0.933
0251 — .0398 0296 1.000 1.000 1.000 1.000
0398 — .0631 .0469 0.822 0.826 0.993 1.186
0631 —- .100 .0743 0.669 0.669 0.940 1.083
MOO) .— 2158 118 0.338 } 0.583/0.505 } 0.619 lee 1.059$1.072
> 0.158 204 0.290 0.368 0.598 0.981
46

Proceedings Royal Acad. Amsterdam, Vol. ILI.

( 688 )
For the luminosity-curve we find:

TABLE 9. Luminosity-Curye.

(Log. number per unit of volume for 7 = 0'0296)

Type L | Type II a
et] [ete | sae | Sie | me
4.82 |, —6.55 4.433 4,382 4.182 4.192
Aree ecules 4 951 5.900 4.702 4.678
4.02 | —4.55 5.640 5.636 5.375 5.371
Bh6ae | sh ba 6.223 6.262 6.104 6.131
3.22 | —9.55 6.804 6.854 6.767 6.849
Oe nd eee D3 7.358 7.422 7.443 7.491
2.49 | —0.55 7.902 7.972 8.046 8.116
2.02 0.45 8.413 8.477 8.634 8.703
1.62 LAB 8.902 8.907 9.170 9,982
1.22 2.45 9.308 9.362 9.635 9.691
0.82 3.45 9. 644 9.632 0.062 0.054
0.42 4, 45 9.927 9.843 0.401 0.422
0.02 5.45 0.093 0.002 0.670 0.640
9.62 6.45 0.297 0.139 0.937 0.818
9.22 7.45 | (0.50) | (0.08) | 1.080 1.004
8.82 8.45 | 1.306 1.115

In table 8, Sol. A. we again find, for both types, a strong
decrease of the density with diminishing distance. By the alteration
of « to 0.87 and the slight alteration to the distances in Sol. B.
this decrease disappears practically entirely for type II. For type I
the decrease has become somewhat less rapid, but it has not
disappeared. The weight of this result is but very small however.
The number of stars of type I whose parallax is > 0".063, is so
small that any conclusion based thereon is of necessity little reliable,
especially in a case like the present where, as has been shown
above, the adopted number of stars with large proper motions may
be very materially in error. For reasons which have already been
mentioned, it must be considered as probable that, as soon as more
reliable data will be available, we will, for this type also, find the
density not far from constant for parallaxes larger than 0".02.

( 689 )

As a consequence of this result some of the conclusions, at which
I had previously arrived (Proceedings Jan. 1893), must be withdrawn,
or at least considerably altered.

These conclusions were based on the result, derived by Srumps,
RISTENPART, and others, viz. that, if the stars are arranged in
groups according to their proper motions, the mean parallaxes of
these groups are approximately proportional to the mean proper
motions. It is only subsequently that I found that this result was
arrived at by an illegitimate reasoning and is certainly not in
accordance with the facts.

For the stars with large proper motions (say larger than 0".10)
it follows from the above that the variation of the quantity Q in
the paper quoted, is, either entirely or at least to a large extent,
a consequence, not of a condensation of the stars of type II in
the neighbourhood of the sun, but of the fact that the number of
faint stars of the first spectral type, as compared to the number
of bright stars of the same type, is not so large as in the case of
the second type.

Physiology. — H. D. Bryerman: ‘On the influence upon respira-
tion of the faradic stimulation of nerve tracts passing through
the internal capsula.” (Communicated by Prof. C. WINKLER).

In a recent publication WinkLeR and Wiarpi BeckMan!), in
stimulating with the faradic current the lateral part of the praecrucial
circumyolution in a dog’s brain, have proved the influence of this field
of the cortex upon the respiratory movements. Acceleration of
rhythm and an inspiratory position of the thorax were the effects
generally obtained during the faradisation of this spot (fig. 1,
compare the fields 11, 12, 15 and 16).

Repeating their experiments 1 found, that faradisation of the
most proximal parts of the above mentioned spot (the fields 15 and
16) causes only acceleration of rhythm (or if respiration is very
frequent, increase of the amplitude of each respiration), whereas
faradisation of its caudal part (the fields 11 and 12) is followed
by a forced inspiratory position of the thorax,

Hence there are to be adopted, two cortical spots regulating the
respiration, one, proximal, accelerating rhythm, the other caudal,
forcing the inspiration. Both are situated on the lateral end of the
praecrucial circumyolution.

1 Winker und Wrarpt Brockmann. Proceedings Vol, 1, 25 March 1899.

4()*

( 690 )

In repeating the experiments of Spencer!) I succeeded to define
the traject of the efferent fibres from the two above mentioned
centra through the corona radiata and the capsula interna.

Forced inspiratory position of the thorax is always obtained,
during the faradisation of a distinct spot situated, in horizontal
sections through the brain (fig. 4 and fig.6 in ++), about the middle
of the corona radiata and of the capsula interna. In frontal sections
it was found (fig. 9 in +) in the pes pedunculi (curves fig. 5, 8
and 10).

The central traject of the pyramidal tract is stimulated in these
experiments, and even if the hemispheres are totally removed, forced
inspiration (accompanied by stretching of the neck, by lifting up the
tail, and by ejecting urine in a jet) still follows during the stimula-
tion of this tract.

Acceleration of rhythm is always caused by faradisation of a
distinct spot, situated in horizontal sections through the corona
radiata and through the higher level of the capsula interna (fig. 4
and fig. 6 in 0) proximal to the former, close to the foremost
part of the caput nuclei caudati.

In frontal sections this spot is found (fig. 9 in 0) on the latero
ventral face of the nucleus caudatus, and dorsal in respect to the
former spot (to compare curves in fig. 5, 7, 8 and 10).

Therefore this nerve tract, by which the acceleration of rhythm
is conducted, runs through the proximal part of the corona radiata,
in the foremost part of the internal capsule, proximal to its knee,
close to the antero- and ventral face of the nucleus caudatus.

Perhaps this nerve tract may find a preliminary end in the
basal ganglia, but my efforts in following its traject through them
are not crowned by a positive result. SpENcER followed it until a
region in the vicinity of the grey surroundings of the third ven-
tricle, where it perhaps could be identified with the centrum of
acceleration of rhythm, mentioned by CHRISTIANI.

Jn horizontal sections, cutting through the capsula interna, two
more spots, (fig. 6 on A and ©) are found, the influence of which
upon respiration may be demonstrated by faradisation. The more
proximal one answers to faradisation with a slight retardation of
rhythm, whereas the faradisation of the caudal part, reaching as
far as the white layer round the cornu Ammoni, sets a very intense
inhibition. The respiration is retarded, or may be even stopped
in an expiratory position of the thorax.

1) Spencur. Phil. Transactions, Vol. 185, p. 609

( 691 )

Physics. — Dr. H. Kamertincu Onnes: “On differences of
density in the neighbourhood of the critical state arising from
differences of temperature.” (Appendix to Communication N°.
68 from the Physical Laboratory at Leiden).

§ 1. At the former meeting I have demonstrated (Communication
N°. 68) that the deviations from VAN DER WAALS’ theory mentioned
by DE HEeEN, are not to be found when his experiments are repeated
with pure carbon dioxide. From which I derived that systematical
corrections must be applied to his results. Moreover I have proved
experimentally that pe Hen has wrongly left out of consideration
differences of temperature resulting from adiabatic processes.

Other and perhaps very important differences of temperature may
have arisen from pE Heen’s method of heating, as I briefly mentioned
in § 3. As long as there are no proofs to the contrary we must
consider that they have really existed. If other sources of
errors could not be undoubtedly demonstrated, as has been done
in Communication N°. 68, and if not small differences of pres-
sure, which may have remained, might have had a similar influence
as the differences of temperature meant here, we would be fully
justified in ascribing entirely to them the deviations found by Dr HEEN.
For in the different experiments these deviations are related in a
manner such as we should expect if the temperature in the upper
part of the apparatus was higher than in the lower part, in
agreement with the supposition laid down in § 2 l.c. It seemed to
me desirable to explain here more in detail that this was the case,
especially because with other experiments on the critical state,
attention must be paid to deviations of the same kind, even when
figs they are reduced to much smalier

Ice ii dimensions by the precautions of
the observer.

From Amacat’s observations
in the neighbourhood of the eri-
tical state plotted in a diagram
with regard to density and pres-
sure the densities at intermediate
temperatures are easily found by
interpolation with the coefficients
of pressure. In fig. 3 at a: (the
density at the temperature ¢) as
abscissa I have plotted as ordinates
0 itself and also 0:41 and 0;—1,

apa ~| an) |

the values which under the same pressure are related to temperatures
which are situated either 1 deg. C. higher or 1 deg. C. lower than ¢.
The isothermal of density d: gives in this figure the same line for all
values of # (it is drawn as a dotted line at an angle of 45°). Two curves
d:+1 and d:—; belong to each temperature ¢ and indicate by the
difference of their ordinates from that of the line drawn at an angle
of 45° the variation of density for 1 deg. C. difference of temperature
from the density d: at ¢°. In this way the deviations for 1 deg. C.
at 35° C., 40° C. and 45° C. are each represented by two of these
curves of deviation.

This figure shows very clearly that at some densities even small
differences in temperature at 35° ©. may lead to important
variations in density. For the correction to the experiments treated
in Communication N°. 68 § 2 it gives much larger values, than
those derived there by means of a mean coefficient of expansion.
The latter had wrongly been calculated from the difference in density
between two limits of temperatures within which the coefficient of density
variation has a maximum. The use of a mean coefficient of expansion
is only allowed within narrow limits of temperature in that case.
However in judging DE Heen’s experiments, I have attached small
value to this correction. The measurement of the difference of tem-
perature, from which it must be calculated, left much to be desired
in my preliminary determinations; (the reason why further determi-
nations were not made has been explained in § 1 of Communication
68). During the experiments one of the wires of the thermo-element
was broken, so that a correction must be applied to the differences
of temperature measured. This is not of any account for the measu-
rement of the variation of the difference in temperature (Comp. § 3)
of the two reservoirs caused by the opening of the cock, but yet
leaves uncertain this difference in temperature itself. And the chief
arguments for the refutation of pe Hnen’s hypothesis was that I
found the densities in the upper reservoir only slightly smaller than
those in the lower, although it was certain that the former had a
somewhat higher temperature than the latter.

§ 2. With very small differences of temperature the difference
of the mean densities in two parts of a cylinder in which the tem-
perature varies with the height according to a given law (e.g. linearly)
can easily be calculated. In a case such as the experiments of DE
HEN it seems to me probable that we may put:

t=ty+ 20h,

( 693 )

in which ¢ stands for the temperature at a given height, for
instance that of the cock of his apparatus, and ’ for the height of
the layer with temperature t, above that given height.

If 3,, represents the density at a given pressure and temperature
then we may put, at very small differences of temperature

Opt => 0 pto “SAGs to)s

: ; do ;
in which A => can be deduced from fig. 3. If the upper end of
Cc

the upper reservoir stands at 4s and the lower end of the lower
reservoir at Aj, then the mean density ds in the upper reservoir
and d; in the lower reservoir is:

Os = Opi + AANs
dr = Opt + AAR y

dew, Syed ental CD

In the case of DE HEEN, putting h,—/i=1, 4 gives the difference
between the temperature at the middle of the upper and of the
lower reseryoirs.

For the mean density én in the whole reservoir from

0s hs I 0: h; — On
we find
SP Ao et a ROARS 1h EF C2 IBY

In pe Heen’s first series of experiments, neglecting the dimens-
ions of the cock we find

hs = 0,5 i 0,5 Om => 0 pto

and so what DE HEEN gives in this series as the densities of vapour daz
and of liquid @.7 we find to be

ddl = Om + 0,5 AA |

Greate meare Ai) Bj
oS Om = 0,5 AA

and the difference of the so-called vapour and liquid density at
the same dn

Or— dara — AA ov we ve oe (89)

( 694 )

In pe HeeEn’s second series of experiments a difference must be
made between a determination of what he calls a vapour density and
what he calls a liquid density. (Comp. Communication N°. 68).

In the first case we must put h, = 0,229, 4; = —0,771 and
according to (2)

a _ a + 4 1(0,229—0,771)

m
in the second case

a” =a + A1(0,845—0,158).

So that by means of (1) we find for the vapour density daz and
the liquid density 0.77 given by De Heen in the series

da = 8 40,771 41

(4)

do = — 0,845 Ad |

or also for the same value of a and a”
Ovll — dart = — 1,62 Ade . 2 2) eee

In the two series the same value will have to be put for A, and
A will also be the same at the same Q; hence it follows from
(37) and (4%) that the deviations, which originate in 4, will be much
greater in the second series than in the first.

De Heen found for the experiment treated in Communication
N°. 68, § 2 and § 3 in the first series

Ov = dal = 0,088

in the second series, where another source of error occurred (comp.
Communication N°. 68).

Ovi — da = 0,190.

From the combined deviations at 35°, 40° and 45° C. in DE HEEn’s
second series according to the table considered in Communication
N°. 68, if we desired to attribute the deviations found exclusively
to the differences in temperature considered now and if we equalise
4 for all temperatures, I find 24=1°,35. Here I have put the
deviation for 1 deg. increase for A in the dg equation, that for 1 deg.
decrease in the d» equation, both derived from fig. 3.

( 695 )
Then approximately we have

(d)
8a = 9, +A

(v,
877 a an —4

The so-called liquid densities and vapour densities of this series
of pE Herren (as in § 4 of Communication N°. 68) if drawn as
ordinates against the mean-density as abscissa, must then give the
same figure as fig. 3. From fig. 4 may be seen that this is actually the
rds case. This figure gives the curves for
Hal 35° C., 40° C. and 45° C. for DE
irl oa (ie Maia ea [4 HeeEn’s experiments borrowed froma
k \ | drawing by VERSCHAFFELT (comp.
Communication N?. 68). Except for
accidental errors the figure is in
sufficient agreement with fig. 3.
The whole system of deviations
from DE HEEN’s experiments agrees
therefore with that which would
result from the supposed distribu-
tion of temperature.

§ 3. Also the increase of the
vapour density with regard to the
p- mean density in DE HEEN’s experi-
°& ments below the critical temperature
(see fig. 1 of Communication N°. 68) is in correspondence with the
supposition that the temperature increases in the direction from the
lower reservoir to the upper. In fig. 2 of the same, calculated from
AMAGAT’s observations supposing that in the two reservoirs of DE
Heen the temperature was everywhere the same, this rise of
the curve on the vapour side, as long as the liquid surface does
not enter into the upper reservoir, does not of course occur. If
however the temperature in the two reservoirs increases in the said
direction the temperature at the height of the liquid surface in the
lower reservoir will be higher at a greater than at a smaller mean
density. The maximum vapour tension increases therefore and also
the density in the upper reservoir. This will be even more the case
with temperatures coming nearer to the critical than with lower
temperatures. This peculiarity is also found in the deviations of
DE HeEen’s results.

( 696 )

Mathematics. — Prof. J. pz Vries: “Jnvolutions on a curve of
order four with triple point.”

1. If the points of a plane curve of order four, Cy, having in
O a triple point, are arranged into the pairs Pj, P» of a quadratic
involution, Iy, the right lines P, Py euyelop a curve, 13, of the
third class (envelope of involution).

For, through O no other tangents of the envelope of involution
can pass than the right lines connecting the points of contact
O', O", O” of the three tangents of C, in O with the points
conjugate to them in I).

The tangents from any point J/ to Fr evidently contain the three
pairs of points which I, has in common with the biquadratie invyo-
lution, the groups of which are determined by the rays through M.

Let us now consider two pairs P), Py and Q), Qo of I, and a
point S' of Cy. The pencils of conics having as basepoints O, 8’,
Pi, Po, and O, S', Q:, Qs intersect C, in the pairs of two new
quadratic involutions having one pair 8", S' in common. The
involution Iz, completely determined by the pairs P), P, and Qi, Qs,
can be generated by means of the pencil of conics with the basepoints
OFS SUE Ses Sox

Hach quadratic involution can be generated by means of an infinity
of pencils of conics whose variable basepoints form a cubic involution.

The degenerated conics of the pencil (OS'S"S"") furnish three
pairs of I,, lymg on the sides of the triangle S'S" S'. Each pair
Aj, Ao of I, lies in a right line with a pair 7", T” of the “con-
jugate” I;; for, if the conic connecting any pair of I, with O, T', 7",
intersects C, still in 7", then O, 7’, T'", T'" are the basepoints
of a pencil generating Iy. So:

The two conjugate involutions I, and 13 have the same envelope
of involution I,

2. Of the tangents from 8, passing through the point P; = 8S’ of
Cy, one bears the point P, conjugate to Py, in I,; the other two
tangents connect S’ with the points S" and S", forming with S' a
group of Is.

If V' is a branchpoint of Is, the corresponding points V" and
V"" coincide; their connecting line is a common tangent of C, and
I’, V' lying on 2°, because the right lines V'V" and V'V"" are
coincident,

If the right line S'S" coincides with the right line containing P; 8!
and Po, then P; and Py take the place of the pair Q), Qs of Ip lying

( 697 )

ai)

on S'S". So this case can present itself only when (, coincides
with S’, so that the curves Cy and J? touch each other in S’. The
number of those points of contact corresponds to the number of
coincidences of the correspondence which arises when two points
Q, and S’ lying on the same tangent of J°* are made to correspond
to each other. Each point S' indicating two pairs Q), Q_ whilst
each pair Q:, Qs. furnishes a pair S', S’, the correspondence has
the symbol (2, 4). So Cy and I touch each other in six points R.

So the 18 common tangents of Cy, and F* are represented by the
6 tangents in the points & counted double and by the right lines
forming the 6 coincidences of I, and Is.

Each point R takes the place of two points of intersection of
Cy, and I; these curves having moreover still the branchpoints of
J, in common; the envelope of involution 7 is a curve of order
four, thus of deficiency zero. The double tangent of J”* contains the
two pairs common to I; and I; or, what comes to the same, two
pairs of Ig.

3. If the points O' and O" form a pair of Iy, the envelope 1”*
breaks up into a conic of involution I and the point O.

Now the pairs of the points S’, S", in which Cy is intersected
by the right lines P, P., form a second quadratic involution Jo.
For, one of the tangents out of P; = U' contains the point P,, whilst
the other bears a pair Qi, Q2 of I, and the point U" conjugate to U'.

Evidently the “conjugate” involutions I, and J, have the pair
0’, O’ in common. The tangents from O to ZF? connect O” with
the points conjugate to O"' in I, and Jo.

The right line bearing the pair A,, A of I, and the pair 2), By of
J, can become a tangent of C, in two different ways. First, when
A, coincides with A, or B' which B’; the coincidences of the two
involutions furnish four common tangents of £7? and Cy. Secondly
when «A, coincides with B'; then this gives rise to a point of con-
tact of IF? and ©, As Cy is of the sixth class, there will be four
suchlike points of contact; indeed, this also ensues from the fact,
that between the points 4; and Ji’ exists a correspondence (2,2). So:

The conics of involution V* touch Cy, four times.

The conic /’* is determined by one of its points of contact P;
for of I, and Jy we then know two pairs, namely O’, and O” and
the pair consisting of # and one of its tangential points.

The points of contact of the envelopes Z’? form a biquadratic
involution given at the same time with Cy, which can therefore be
called a fundamental involution,

( 698 )

The points 0’, 0", 0" forming three pairs there are three funda-
mental involutions and three systems of conics touching four times.

The conjugate I; being broken up into Jy and the point O, the
pairs of I, le in conics through two points B', B’ of J», touching
in O a fixed right line, which forms with B: B’ a conic of the
indicated pencil; so it has in O four points in common with C, and
is therefore the tangent ?¢” in O".

Each pair of I, can be connected with each pair of J, by a
conic touched by #” in O.

4. If B' and B" coimeide in a point D,, the corresponding pencil
contains two envelopes touching C, still in a second point D,,.

The quadratic involution J, determined by the pairs O', O" and
D,, Dy, evidently coincides with its conjugate Jy; for, Je contains
the same two pairs. The tangents drawn from any point of C, to

2 connecting this point with the two points with which it forms
pairs of I, and Jy, the envelope £? will in this case degenerate
into a point A to be counted double.

Each ray through A bears two pairs of I, conjugate to itself.
Two tangents from A to Cy contain each a coincidence of the invo-
lution; the remaining four are represented by two double tangents,
taking together the place of the conic belonging to I, and touching
C, four times.

The second point 2, belonging to D, determines in the same
way a similar particular Ip, of which the point of contact, counted
double, of the remaining two double tangents is to be regarded as
Tae 0's

Each of the six points of intersection of the double tangents is the
centre of a pencil of rays, each ray of which bears two pairs of a
fundamental involution ').

We may suppose that the notation for the double tangents dj, do,
ds, dy has been chosen in such a way that the points Ay, = d, d, and
As, = d;d, belong to the fundamental involutions having the pair
O', O" in common, Ajs, Agy being in likeway conjugate to O', O”
and! Ajay Age to Ol 0":

The right lines connecting a point Dy; of C, with Aj, and Agy

1) These fundamental involutions present themselves also on a C, with three nodes
(comp. J. pe Vries, La quartigue trinodale, Archives Teyler, t VII, § 16). Also
a C, with two nodes contains similar involutions (comp. J. DE Vries, Over vlakke
kromme lijnen van de vierde orde met twee dubbelpunten, Nieuw Archief voor Wiskunde,
vol. XIV, 1888, p. 197.)

( 699 )

contain respectively the points Dy and D", conjugate to Dy in the
corresponding fundamental involution. Now it is easy to see that
the right lines Aj, D" and As, Dy intersect each other in a point
of C;.

For, if we determine an involution I, by the pair O', 0" and the
double point Dy, then Diy and D’ are the double points of the con-
jugate Jo. In the second double point D’ of I, the curve C4 touches
a conic, touching it moreover in D’ (Dy) and in O'; consequently
D', D’ and D', Diy are pairs of the indicated fundamental involu-
tions. So:

Any two opposite vertices of the quadrilateral formed by the double
tangents are therefore two adjoined vertices of an infinite number of
quadrangles described in Cy").

An involution Ip being projected from O by an involution of rays,
the theorem holds good: “The pairs of rays projecting from O the
points of contact of two double tangents, lie in involution with a
pair of tangents in O and with a pair formed by the third tangent
in O and the ray through the point of intersection of the double
tangents.’

5. The cubic involution conjugate to a quadratic (§ 1) is not
the most general one. One of its groups contains the points O', 0",
0", so that its envelope of involution consists of J* and the point
O to be counted three times.

The general I; has an envelope of involution of the sixth class:
the six tangents through O connect respectively O', O", O" with the
two points conjugate to them.

We shall consider the two groups A,, As, A; and B,, Bg, Bs.
The pencils of conics having as basepoints (0 A, Ay A3)and (O By By Bs)
intersect Cy in two quadratic involutions. Let P’, P" be the common
pair of points and Q the fourth point of intersection, not situated
on C4, of the conics (O P' P" A, Ay Az) and (O P' P” B, By Bs),
then I, can be generated by means of the conics of the pencil
(QBrP*Q). So:

Each cubic involution can be determined by a pencil of conics.

Each of the degenerated conics (O P', QP") and (O P", Q P') fur-
nishes a linear group, that is, a group the three points of which
lie in a right line.

So the envelope I’® has two triple tangents.

1) Comp. § 15 of the previously mentioned paper: ”La quartique trinodale”.

( 700 )

It also possesses double tangents. The points S and S' lying ina
right line with a pair of I; are conjugate to each other in a cor-
respondence (4, 4). For, two of the tangents out of S= P, to I’,
connect P, with Py, and P,; each of the remaining four contains
a pair of I; as well as a point S’. The system (S, S/) has eight
pairs in common with I;; so there are 4 right lines, each bearing
two pairs of I;; that is, 2° possesses four double tangents; so it is
of deficiency zero and of order ten.

To every point S eight points P, to every point P 4 points S
correspond. In each of the 12 coincidences f of the system (S, P)
the curves C%, and 7%, touch each other. The remaining 12 com-
mon tangents originate from the 4 coincidences of I; and the 8
coincidences of the system (S, 5’).

Besides the 12 points of contact A, the curves C%,and 1%; have
still 16 points in common, four of which belong to the double points
of I; as branchpoints; the remaining twelve are points of S for which
two points S' coincide.

6. When O', O" form a pair of I; the envelope of involution
breaks up into a point O and an envelope 7°.

An involution IT; is fully determined by a triplet 4), dy, 4; and
two pairs B,, By and O'7,0". The conie through Aj, 49, 42 touching
C, in O” intersects it still in a point P. Through 4), #2, and P
we draw a second conic touching Cy in O"; it has with the first
another point, not situated on Cy, in common. The pencil (O" 0" P Q)
contains the conic (O" P,O"Q) determining on Cy a triplet of
points, two of which coincide with O' and O”. So the involution
I; in which Cy is intersected by this pencil contains the triplet
A,, Ao, Az and the pairs By), B, and O', 0"; so it is identical with
the given inyolution.

The right line PQ bears a linear group and is therefore a triple
tangent of 7°. The system (5, S') being now qualified by the symbol
(3, 3) it has 6 pairs in common with I3, so that 7”% possesses three
double tangents; so 77° is of deficiency zero and of order eight.

The system (S, P) has now the symbol (4, 6); consequently
C6 and /,° touch each other in 10 points Rk. Their remaining
common tangents are determined by 4 double points of I; and the
6 coincidences of (S, iS’).

( 701 )

Chemistry. — In the absence of Dr. J. M. van BemMeten,
Prof. H. Kaweriiyen OnNes presents a paper from Dr.
F. A. H. Scurervemakers entitled: “Notes on equilibria in
ternary Systems.”

(Read March 30, 101).

The experimental difficulties encountered in the determination of
the composition of conjugate liquid phases are sometimes so great
that, however desirable a knowledge of these compositions may be,
the investigation of them has to be abandoned. Such cases occur
for instance :

1. When the two liquids, which are in equilibrium, form an
emulsion which does not separate into two phases, or does so only
after an extremely long time.

2. When analytical chemistry does not provide us with the means
of quantitatively determining the components.

Nothwithstanding this we may in such cases gain our object, if
only approximately, and by indirect means, as I will demonstrate
in what follows.

Let us take as an example the system: Water, Pheno! and Acetone.
A short communication on this system is to be found in the pro-
ceedings of the Academy 1899—1900 and a more full account in
Zeitschr. f. Phys. Chem. 33.78. The results communicated in those
papers concern the forms and positions of the connodal curves at
different temperatures. To obtain these, the following course was
adopted. Varying quantities of phenol were introduced into a mixture
of water and acetone of known composition, obtained by direct
weighing of the components, and the temperature was determined
at which the two liquid phases formed passed into a single one.
In this manner mixtures of water and acetone containing
1,83, 4,24, 7,94, 12,2, 15,6, 24,6, 31,8 40,3, 50,2, 59,9 and 64,9
percent of acetone were tested.

From these determinations we may easily obtain the connodal
curves for different temperatures by interpolation and this method
should always be applied when it is only possible to weigh the
components. The difficulties mentioned in 1 and 2 are thus without
influence. Table I contains the compositions of the solutions of the
_connodal curve at 56°.5 obtained in this way.

( 702 )

TABLE I.
Compositions of the solutions of the connodal line at 56°5.
pCt W. 85,5 89.0 89.1 86.5 82.5 79.1 67.9 59.3 48.1 36.9 26 22.7
pct Ace 0 1.7 3.9 7.5 11.5 14.6 22.2 27.7 32.5 37.1 34 22.8

pCt Ph. 14.5 °9.3 7.0 6.0 6.0 6.3 9.9 18.0 19.4 26.0 40 54:5

pct W. 23.9 25.9 27.9 308 32.0 34.5 36.9 38.8 40
pct Ac. 16.1 12.1 9.1 5.7 4.5 3.0 1.6 Ube v

pCt Ph. 60.0 62.0 63.0 63,5 63.5 62.5 61.5 60.5 60

By means of table I the connodal curve for 56°5 may now be
drawn; in Fig. 1 it is indicated by the curve a @ 4p. {t is, of
course, known that the liquid phase a may be in equilibrium with
dz because both are only binary liquids, but how matters are situa-

( 703 )

ted as regards the ternary phases is quite unknown, as is also the
position of the foldpoint @. It is known, for instance, that at the
given temperature a liquid phase 6, may be in equilibrium with
another, but with which other is not known; it is also known for
instance that a liquid exists which may be in equilibrium with
another one; with which other, however, is as yet unknown.

If we now wish to analyse the conjugated liquid phases which
occur in this system we meet with the difficulties stated in I; with
certain concentrations of phenol and acetone the two layers only
formed emulsions which did not separate even after waiting for
hours; as we shall see, however, the top layer was present chiefly
on the surface and the other at the bottom of the emulsion. In order
to learn the composition of the two layers which were in equilibrium
with each other, I proceeded in the following manner.

Into a small bottle, I weighed known quantities of water, acetone
and phenol so that the composition of the total liquid was accurately
known. Let / in fig. 1 be the point showing the composition of this
mixture and ¢; and cy the two liquid phases into which the mixture
separates at 56°5. In order to obtain equilibrium, the two layers
were thoroughly shaken which caused an emulsion to form. After
this had been at rest for some time a portion was removed by means
of a pipette from both the top and the bottom and submitted to
analysis.

The composition of the one part is indicated in the figure by /;, that
of the other by /, and it is natural that the three points /, /; and
/, must be situated on a straight line which is to be used as a
check on the analysis. If the straight line 7,17, is now drawn and
its points of intersection with the connodal curve c, and co deter-
mined, these will then indicate the composition of the two liquid
phases which are in equilibrium with each other and which constitute
the emulsion. In this manner, I have determined the position of
different chords of the connodal curve and therefore, also the com-
positions of the liquid phases which are in equilibrium at 56°5.
From the determinations communicated in table 2, to which have
also been added the determinations of some clear solutions, it appears
that the chords have the positions approximately indicated in fig. 1.
For instance bg lies further from the side W.— PA than /,, c, further
than ¢, or in other words, if we call the solution of branch « « the
aqueous and that of a,@ the phenolic layer, acetone dissolves more
readily in the phenolic than in the aqueous layer.

47

Proceedings Royal Acad. Amsterdam. Vol, IL,

( 704 )

TABLE II.

Composition of the conjugated solutions at 56°5.

Brauch a, @. Branch ag @.
pCt. W. pC, Ac. —pCt. Ph. pCt. W. pCt. Ac. Ct. Pk
88.5 0 14.5 40 0 60
88,8 1.2 10.0 29.3 7.3 63.4
89.1 3.9 7.0 230 17.1 59.4
88.62 5.28 6.1 22.5 22.8 54.7
86.7 7.3 6.0 22.5 28.0 49.5
85.5 8.5 6.0 22.9 28.8 48.3
76.0 169 7.1 28.6 36,1 35.3
75.1 17.5 7.4 28.8 36.3 34.9
69.5 21.5 9.0 34.0 37.5 28.5

From the foregoing it is plain how the difficulties mentioned in 1
may be got over if we can only determine quantitatively the three
components or two of them. If this is also impossible, there is still
at our disposal another method for determining the situation of the
chords, namely determinations of vapour tensions.

Let us take, for instance, a mixture represented in figure 1 by q;
at 56°5 this mixture will separate into the two liquid phases }, and
by possessing a certain vapour pressure. If we take a mixture gg
this will also separate into two layers 4, and, although the relative -
quantities of these phases will, of course, be different. The vapour
tension however, will be the same. This is, of course, also the case
if we take mixtures like g, and gy and generally for all mixtures
represented by points on the chord 0, dg.

All mixtures represented by points on the chord / by have there-
fore, the same vapour tension. Inversely the position of the chord
may be determined when the compositions of different mixtures having
the same vapour tensions at the same temperature are known.

In the system: water-acetone-phenol I have made many determi-
nations of vapour tension which [ hope to communicate more fully,
later on; 1 will now mention only a few of the determinations and

( 705 )

show how the position of the chords may be determined from them.
The vapour tension of each of the mixtures investigated has been
determined at 10 to 15 different temperatures; in what follows I
only mention the vapour tensions at 56°5 which have been obtained
from these determinations by interpolation.

Let us first consider the side W-Ph of fig. 1, that is mixtures
which contain only water and phenol.

TABLE 3.

Vapour tensions at 56°.

09/o Ae.
fo Ph. 0 2.0 5.58 7.42 10.88 14.5 60.0 69.2 76.7 80.34 88.06
P in mM. 125 125 197 197 - 197 126 !96 124 122 118 102

7.949/, Ac.
0 Ph. O 1.22 2.41 5.93 10.02 15.19 19.81 29.93 40.48 49.28 62.67 70.15 74.25 80.76
Pinm.M.278 271 262 236 216 1938 180 158 147 140 185 180 126 119

15.69/) Ac.

0f) Ph. 0 1.89 3.03 6.14 9.63 14.30 19.81 29.74 38.81
Pin m.M. 387 369 350 318 292 9262 232 193 171
of) Ph. 49.60 60.13 66.98 74.88 $3.00

P in mM. 155° 144 8618700 «180115

22.520/, Ac.
fy Ph. 0 3.08 8.58 13.95 20.01 24.38 929.72 35.95
PinmM. 446 408 359 318 277 253 226 205
0/) Ph. 41.69 49.51 59.49 69.29 79.68.

Pememem. 186 167 Tob * 140 192:

31.829/, Ac.

9/) Ph. 0 410 7.68 13.86 2013 24.77 29.99 34.13 39.29
Pin mM. 524 468 428 379 335 302 274 251,5 224
7) Ph. 40.93 45.57 51.48 57.64 62.96 71.06 79.77

PinmM. 218 202 186 170, 160,,.141 .128.

J

The vapour tensions are given in table 3 under 0 pCt. of acetone.
It will be seen that as the quantity of phenol increases, the pressure
first rises from 125—127 m.m., falling again to 126 m.m. when
the liquid contains 14.5 per cent of phenol. If more phenol is added,
two liquid phases appear and the pressure remains 126 m.m. until
the mixture contains 60 per cent of phenol; if still more phenol is
added, there only remains one liquid phase and the vapour tension

47*

( 706 )

decreases continuously. This
is represented in the usual
way in fig. 2. The amount
of phenol is given on the
horizontal and the pressure
on the vertical axis. A line
is thus obtained which is
indicated diagrammatically by
the one marked 0 pCt. of
acetone. At the left hand side
A consist of a part with a
maximum, in the centre,
where both liquid phases oceur,
of a horizontal part and for
the remainder of a slanting
line. Passing now, in fig. 1,
along the side W—Ph from
Fig? W to Ph, the pressure at first
increases, reaches a maximum
and then decreases until a in reached; from a, to a, the pressure
remains constant and from ag to Ph it again decreases; the pressure
therefore remains constant in the region in which two liquid phases
are present.

It is different, however, if we move along a line through the
triangle, for instance from rz to Ph, along the line rz Ph; from rs
to d, we then move in the homogenous field; from d, to e, we
traverse the heterogenous and from e, to Ph we find ourselves again
in the homogenous field. It is, of course, plain that if we move
over the parts 73 d; and e, Ph the pressure will be continually
altering, as was the case with the parts Wa, and a, Ph; on the
part d, &, the behaviour is, however, different from that on ay ag.
On the part a, a, the vapour tension remains unchanged; on dj e
it changes continuously. This will be easily unterstood if we reflect
that the pressure at d, is the same as the pressure of the two
conjugated phases d,-+ d); at 1 the vapour pressure is that of the
system ¢, + ¢); in gg the vapour pressure corresponds to that of the
system b, + 69; in ¢ the vapour pressure is the same as that
of the system ¢, + e,. We therefore see that if we move from d, to
ey the vapour pressure must be changing continually just as it alters
along the connodal line from d, to e, or from d to e. From the
determinations it follows that the vapour pressure increases along
the counodal line from «a, and ag in the direction of the foldpoint «.

O% Ph. 100% Fh.

(707 )

If, therefore, we move from d; to eg we must notice a continual
decrease of the vapour pressure.

All the solutions situated on the line 73 Ph have the peculiarity
that the relation between water and acetone is the same in all of
them. The vapour tensions of the solutions on this line may there-
fore be represented as though we had a binary mixture of the
components of which one is phenol and the other a mixture of water
and acetone in constant proportion. We, therefore, put down in
figure 2 the amount of phenol on the horizontal and the pressure
on the vertical axis. Let us take as example the solutions in which
the relation between water and acetone is 84.4 : 15.6 or in other
words those which contain 15.6 percent of acetone if we disregard
the presence of the phenol. These determinations are given in
table 3 marked 15.6 percent acetone. Under P the vapour pressure
in m.m. is given and under pCt. Ph the total amount of phenol in
the liquids. The first determination, therefore, gives the vapour
tension of a mixture which contains no phenol, that is of a mixture
of water and acetone containing 15.6 percent of acetone. As may
be plainly seen from this series, the vapour pressure decreases
continually with increasing quantities of phenol.

In fig. 2 this series is indicated by the curve marked 15,6; the
curve is not continued to its endpoint, 100 percent of phenol, but
only to 63 percent. It must, of course, end at the same point as
the line indicating the vapour. tension of water and phenol only.

In table 3 some other determinations are given under 7.94, 22.52
and 31.82 percent acetone, the significance of which will be suffi-
ciently apparent after the foregoing explanation. The corresponding
vapour pressure curves in fig, 2 are marked by the same figures.
Each of these curves consists of three parts, namely the two portions
at the sides which relate to the homogenous liquids and the portion
in the middle (between the two crosses) which relates to the mixtures
which separate into two liquid phases on the connodal curve. In
the two points where these three meet, they exhibit a discontinuity.

From fig. 2 the situation of the chords of the connodal curve at
56°.5 may be obtained.

Let us draw an horizontal line ss; which intersects some of the
vapour tension curves; each point of intersection indicates a solution
or a complex; all the solutions and complexes situated on this line
have the same vapour tension. Let us confine ourselves to the
complexes only or to those parts of the vapour tension curves, which
are indicated in figure 1 by points within the connodal curve and
therefore belong to the heterogenous field, Let us draw the line

( 708 j

ss, In such a way that it indicates for instance a vapour ‘tension
of 180 mm. We then have 4 complexes, indicated on the curves
by 7.94, 15.6, 22.52 and 31.82 percent acetone, which at 56°.5
have a vapour pressure of 180 m.m. and must therefore in fig. 1
be situated on the same chord as for instance the points 4), do, 93
and q4.

The composition of these complexes may be ascertained from fig. 2;
from the. figure we may obtain the amount of phenol in the complex,
whilst the relation between the other two components, that is
between water and acetone, is known. Thus it is found, for instance,
that the point of intersection of the line ss, with the vapour tension
curve of 15.6 percent acetone indicates an amount of phenol of
34.6 percent. The complex, therefore, contains 100 — 34.6 = 65.4

ve del DOheere ;
percent of water and acetone of which too * 65.4 percent is acetone

and nay X 65.4 pereent is water. We, therefore, find that this

complex consists of 55.2 percent of water, 10.2 percent of acetone
and 34.6 percent of phenol. In the same manner, the composition
of the complexes, indicated by the other parts of intersection may
be calculated.

In the foregoing, we have drawn the line ss; in such a manner
that it indicated a vapour tension of 180 m.m.; this vapour tension
may, of course, be taken differently; we then obtain other points
of intersection and consequently other complexes and also other
chords. In table 4 a few results of these calculations are given
for 180, 220, 260 and 300 m.m.

TABLE 4.
Temperature 56°5.

Composition of the complexes with a vapour pressure of 180 m.m.

pCt. W. pCt. Ae. pCt. Ph.
73.8 6.4 19.8
55.2 10.2 34.6
43.4 12.6 44.0

31.6 14.8 53.6

( 709 )

Composition of the complexes with a vapour pressure of 220 m.mi.

pet. W. pCt. Ac. pCt. Ph.
83.7 7.3 9.0
65.3 12.1 22.6
53.0 15.4 31.6
40.7 18.9 40.4

Composition of the complexes with a vapour pressure of 260 m.m.

pct. W. pCt. Ac. pCt. Ph.
72.2 13.3 14.5
59.7 17.3 23.0
46,1 21.5 32.4

Composition of the complexes with a vapour pressure of 300 m.M.

pCt. W. pCt. Ac. pCt. Ph.
Ged 14.3 8.4
64.7 18.8 16.5
51.2 23.8 25.0

Let us first take the 4 complexes which at 56°.5 have a vapour
tension of 180 m.m.; if these are placed in the triangle it will be
seen, that they are situated on a straight line; the same is the case
with the 4 complexes with a vapour pressure of 260 m.m. and also
with the three complexes whose vapour pressure amounts to 300 m.m.

We have, therefore, again found four chords; for the determina-
tion of each of these, of course, only two points were needed ; the
others only serve as a check to control the accuracy obtained.

It is worthy of attention that the chords derived from table 4
are, theoretically, not altogether comparable with those from table 2;
the latter belong to a connodal line at 56°.5 at a constant pressure,
the former, to a connodal line at 56°.5 at 7fs own vapour pressure.
As however, a small change in the pressure has generally a very
small influence on the composition of the two liquid phases in
equilibrium, the chords determined in the two ways are practically

(710)

comparable. That this is the case is seen when the chords obtained
from the figures given in the two tables are set out in the tri-
angular diagram.

An examination of figure 2 reveals some further peculiarities
which may be explained. From the vapour tension curve, marked
0 percent acetone, it is seen that the vapour tension of water is
increased by the addition of small quantities of phenol. I have
already shown in a former article that this is in accordance with
the formula of vAN DER WaALs which applies in this case. But it
we add phenol to a water-acetone mixture it is different, for, if we
take mixtures of water and acetone containing 7.93, 15.6, 22.52 or
31.82 percent of acetone, we notice from the corresponding vapour
tension curves in fig 2 that the vapour pressure falls. The question
is now whether the addition of a new substance to a binary mixture
has the same influence as the addition of the same toa simple liquid.
As I will show this is by no means the case.

We take for example a liquid of the composition

1MolA 2, MolB y, Mol C.
which is in equilibrium with a vapour of the composition

1Mol A «Mol By MolC.

Let us call the thermodynamic potential, the entropy and the
volume of this liquid ¢), 7, and V, and that of the vapour phase
c, 7 and V.

In equilibrium we have:

: a Wr O_O
$1 rian sae aE Y9y
; . (1)
a _ a ah _
Oa, v ay ¥y

Assuming that the relative quantities of the components 4 and
B is kept constant in the liquid, 7, is also constant. If we also
keep the temperature constant the only variable quantities remaining
are y, « y and P. From the equations ([) we obtain:

— (8) x} +tandan+("% Sa ome: Sage fencers
av] oy

f)
oV aV
= —(re+ ap) de — (ox + ty) dy + (V2 —y —) dp
dw oy
aV, OV (I)
8, dy, + — dp = rdu + sdy + — dp
02’) 0a
V, V
t) dy, + ah dp = sdx +- tdy + we dp
oy dy
in which
a5 eG ee Se Oe ae) ac
— go a 1 i T _ FATERS s —_ t =
day Oy, dy” wv dw dy oy?

If we multiply the second equation by «# and the third by y
and add the results to the first we find:

[sy (@—2) + 4 (y—an)] dy. + "1 ote eae 4G nd dp = Vdp

a = ay Ss LD
VY, + (#1 — 2) de, + A—-Y oy,

This equation shows the change in pressure which occurs when
we add new substance to a liquid made up of the components A
and &. Let us assume that the quantity y, of the new substance is
exceedingly small so that y is also very small. We then find for the
limit value !):

RT
i

41

Formula III now becomes:

Y
an 8; (e—27,) + R ee =)

a eer ue
. Vy be iY wv) a

Shae (20)

1) Zeitschr. fiir Phys, Chem, 25, 327,

(ert29)

which may, therefore, be applied when only small quantities of the
new substance are added. As will be readily understood, the sign
of the denominator is always positive; as to the sign of the nume-
rator, this cannot be judged without further information. The quantity

— is the partition coefficient of the new substance between vapour
Yi
and liquid. This coefficient decides whether, on adding a new sub-
stance to a simple liquid, an increase or decrease of P will take
place; this, however, is by no means the case here, as there is, in
addition, another term s,(#—#,) which may be either positive or
negative.
dp , ;

The value of 7 from IV may also be considered as a function
of 2, that is of the composition of the binary mixture to which
the new substance is added. It may, therefore, happen that if a, is

hie wants a d é
allowed to vary within wide limits, 7 may change sign.
Yi.
We, therefore, come to the following conclusion:

yif we add a new substance to a binary mixture, either an
increase or a decrease of the vapour tension may take place accor-
»ding to the composition of the binary mixture.”

This is in accordance with observations made on the system
water, acetone and phenol. If we take water and add phenol to it
the vapour pressure increases (sce fig. 2). This is also the case
when, instead of pure water, we use water containing but little
acetone. If, however, we use mixtures containing 7.94 or more of
acetone a decrease of vapour tension will be noticed as shown in fig. 2.

The difference between the behaviour of a single substance and
of a binary mixture is even more evident when the addition af a
new substance, which does not appear in the vapour phase, is
considered.

In formule IV we must then put y—=0 and we obtain:

4 (e—2,) — KT

dp 6 ae ratervet 5 V
a ana av, (V)
diy V—V, + (—2) ——

dey

The numerator of this fraction may now be either positive or
negative so that we come to the following conclusion: ’
yif we add to a binary mixture new substance not passing

(STDS?)

,into the vapour, the vapour tension may be either increased or
» decreased.”

We, therefore find an important deviation from the law of decrease
of vapour tension in the case of simple substances. Let us assume
that the binary mixture has a maximum or minimum vapour pressure.
We then must put «= 2, causing the term s; (r—z), to disappear
from the formula ; 2 will consequentiy be negative so that we
find that:

yif we add to a binary mixture with a maximum or minimum
,Vapour pressure a new substance, which does not pass into the
»Vapour, pressure is decreased.”

We, therefore, come to the conclusion that the law of the decrease
of vapour pressure for a simple liquid is still applicable to a binary
mixture with a maximum or minimum vapour pressure, but that
in general either an increase or a decrease of vapour pressure may
oceur with binary mixtures.

When calculating the formula II from I we have taken the pres-
sure as variable and the temperature as constant. If we now take
the pressure as constant and the temperature as variable we find
in a similar manner that:

pif we add to a binary mixture a new substance which does not
pass into the vapour, the boiling point may be either increased or
decreased. Only binary mixtures with a maximum or minimum
boiling point obey the ordinary law of increase of boiling point for
simple substances.”

In the equilibria of the system water, ethylalcohol and sodium
carbonate investigated in our laboratory by Mr. KretTNer, we also
meet with an example of the deviations which binary mixtures show
on adding a third substance, in contrast to simple substances.

The boiling point of water rises when sodium carbonate is added
to it; if however, we take mixtures of water and alkohol, the boiling
point is depressed by the addition of this salt, provided that the
amount of alcohol in the mixture exceeds a certain limit. The deter-
minations are given in table VY. As will be seen these determinations
have been made for alcoholic mixtures containing:

0, 1.2, 2.2, 5.0, 9.8, 21.38, 35.6, 45.4 and 55.0 percent of alkohol.

Under percentage of salt are given the quantity of added Na, CO, to
100 parts of the water-aleohol mixture; under AT the change in

(714)

the boiling point, the sign + indicating the increase and — the decrease
of the boiling point.

TABLE V.
Change in the boiling point of water-alcoholmixtures on addition of Nay COs.
0 °/, Aleohol. 1.2 °/, Alcohol. 2.2 9/, Alcohol.
osalt, 2A, \ Ytpalis es oA O79 Balt: «SAT
0.65" = 0°.10" ~ 0.80" °° -+'0.05° “0:44 =F 0.01
162 + 0°21 1.79 +013 0.91 + 0.01
2.57 +0.16 175 + 0.03

3.38 +0.20 2.52 0.00

5.0 °/) Alcohol 9.8 °/) Alcohol 21.3 °/, Alcohol.

o/, salt AT % salt AT of) salt A T
0.48 —0.04 oy m2 0.61 —0.14
1.31 —0.07 1.38;4 ong 1.04 —0.27
De 0d 2.02 —0.29 1.72 —0.46
2.67 —0.80 2.37 —0.66

3.23 0.91

35.6 °/) Alcohol 45.4 °/, Alcohol 55.0 °/, Alcohol

oF, salt "AT C7, salt AT WY FE Up aN
0.52 —0.14 0.43 —0.08 0.16 —0.03
1.06 —0.29 0.84 —0.16 0.60 —0.15
1.62 —0.45 145 —0.31 1.19 —0.25

2.09 —0,42 1.80 —0.35

2.63 —0.52

( TS J

Chemistry. — Dr. P. K. Lutors: “Substitution velocity in the
case of aromatic halogen-nitroderivatives.” (Communicated by
Prof. Lopry DE Bruyn).
(Read March 30, 1901).

Some two years ago Dr. ALPH. STEGER made an investigation of
the velocity of the substitution of oxymethyl and oxyethyl for the
nitro-group in ortho- and paradinitrobenzene !). This research included
the influence exercised by a change of temperature, decrease of
concentration, addition of a substance with a common ion and the
regulated addition of water to the alcohol.

It now became important to extend this investigation to other
substances. After preliminary experiments with various compounds,
Dr. Luors has in the first place confined himself to chloro-, bromo-
and iododinitrobenzene 1.2.4. Of these compounds it had been long
since established that the halogen atom is liable to all kinds of
substitution for instance by alkalis, ammonia, amines, alcoholates
ete. It now appeared that the reaction with the last named substances
lends itself very well to a quantitative research and for this reason
sodium methoxide and sodium ethoxide were again chosen here.

As a first result it was established that the chlorine atom is
much more easily replaced by oxymethyl or oxyethyl than the
nitro-group in ortho- and paradinitrobenzene. It was further confirmed
that of the three halogens the chlorine is the most and the iodine
the least readily replaced by oxyalky]; this had already been observed
by K6rNER by comparing the periods in which the reaction is ended.
The constants for the reaction of the three halogen compounds with
sodium ethoxide in absolute alcoliol at the same concentrations are
in the proportion of 3.26 : 2.03 : 0.455 (temp. 15°). It is remark-
able that in the case of the aliphatic halogen compounds the beha-
viour of the halogens is just the reverse; in these compounds the
iodine is in the weakest and the chlorine in the strongest combination
with the carbon atom.

In the second place Dr. LuLors studied the influence of the decrease
of concentration on the constant. It had been proved by Dr. Srecer
that the reaction between orthodinitrobenzene is not influenced by
dilution. On the other hand Conrap and Brickner *) had found
that during the formation of an ether from an alkyl iodide and an
alcoholate, this influence most decidedly exists in this sense that
the reaction-constant increases with dilution.

1) Rep. Meeting 28 Oct. 1898; Dissertation 1898 and Recueil 18, 13.
2) Z. phys. Chem, 5,289. This result was contirmed by Srecer (1. c.),

(716 )

This last result, as we know, agrees with the electrolytic disso-
ciation theory and may, therefore, be used in support of the view
that the formation of ether is due to an ion-reaction. We are
therefore confronted by the remarkable fact that the first reaction is
not influenced by dilution whilst the second is affected by it, so that
the second only should be considered as a reaction between ions.

In the reactions investigated by Dr. Lutors, the reaction-constant
is found to increase (as in the case of ether formation) with dilution
and particularly when ethyl alcohol is used. In the case of chloro-
dinitrobenzene, the constant rises from 2.94 (gasconcentration) to
3.56 (one-fifth of that concentration); under the same circumstances
the constant of the bromo-compound rises from 1.88 to 2.33.

It is a peculiar fact that the rise is much less marked when
using sodium methoxide in methyl alkohol, being from 1.10 to 1.18
in the case of the chloro-compound.

In the third place, some experiments were made by Dr. LuLors
on the influence of the addition of a common (Na) ion. Dr. STEGER
(Il. c.) had found that this influence does not exist in the case of the
reaction with orthodinitrobenzene, but that in the formation of ethers
it is well marked, producing, in accordance with the electrolytic
dissociation theory, a diminution of the reaction-constant. In the
present case agreement with the last reaction was observed; for
instance an addition of sodium bromide to the mixture of bromo-
dinitrobenzene and sodium ethoxide caused a decided lowering of
the constant.

We therefore see that in this case as well as in the case of
dilution, the aromatic nitrohalogen compounds behave like the aliphatic
halogen derivatives. The totally different behaviour of orthodinitro-
benzene in an otherwise quite analogous reaction remains unex-
plained.

In the fourth place it was ascertained in what manner the reaction
coefficients depended on the addition of water to the two alcohols.
The reaction with orthodinitrobenzene and those in which ethers are
formed had previously yielded very interesting results in this respect. 1)
Dr. LuLoFs was in a position to show that chloro- and bromodini-
trobenzene behaved in the same way. The coefficients remained
constant even for an alcohol mixture containing 40 percent of water.
In dilute ethylaleohol they decrease with the increase of the amount
of water; on the other hand when dilute methyl alcohol is used they

') Lopry pp Bruyn and A. Srecer. Proc, 30 Sept, 1899. Recueil 18, 41, 311.

THE)

first increase, then remain constant and finally decrease when the
amount of water reaches about 40 percent. When using alcohol-
water mixtures as solvent, it appeared that the decrease in concen-
tration causes a rise and the addition of a substance with a common
ion a lowering of the constant.

Dr. LuLors research'); which may be usefully extended in various
directions, points, like the results quoted, to the desirability of a
study of the conductivity of the alcoholates when dissolved in the
pure alcohols (partly carried out by CARRARA) or in mixtures ot
alcohol and water. It will then be possible to ascertain whether there
exists a parallellism between the change of the reaction-constants
and that of the conductivity.

Chemistry. — Professor BAkiuuis Roozesoom presents a commu-
nication from Dr. A. Sirs: ,On the progressive change of
the factor « as function of the concentration.”

(Read Mareh 30, 1901),

Of the salts, which I have already investigated, K N Og, *%) is
the only one for which the factor ¢ decreases with increasing con-
centration. It, therefore, seemed to me very interesting to ascertain
whether other nitrates behave similarly.

K NO, being an anhydrous salt, I purposely chose nitrates of
which no hydrates are known.

In this investigation I have availed myself of my improved
Landsberger apparatus °), which is sufficiently accurate for my purpose.

Before proceeding to mention the results, I will first draw attention
to some points to which attention should be paid in the determi-
nation of boiling points by this method.

In determining the boiling point of pure water, it is noticed
that the boiling point continuously rises during the progress of the
experiment. In my apparatus this rise amounted 0.01° in 25 minutes.
The explanation of this phenomenon is found in the continual
increase in height of the column of water in consequence of the
condensation of the aqueous vapour, which takes place. When the
column of water increases in height, the pressure and consequently

1) Further particulars in his dissertation, Amsterdam, L901.
2) Proc. 21 April L900 714.
8) Proc. 26 May 1900 31,

( 718 )

the boiling point is raised. As I wished to make up solutions of
different concentrations by adding to the water (of which I had
determined the boiling point) some salt thereby causing an increase
in the height ef the column, it was necessary to know the increase
of temperature, which corresponded to a certain increase in the height
of the column of liquid.

I, therefore, conducted a series of boiling point determinations of
pure water in which the height of the liquid was varied. In this
way I found, that an increase of 10 m.m. in the height of the column
corresponded with a rise of 0.01° in the temperature.

Theory requires for 10 mm. water at 100° an increase of the
boiling point about thrice as large. The explanation of this difference
must be looked for in the vigorous mixing, which occurs in the
boiling liquid owing to which, as will be readily understood, the
theoretical increase cannot be obtained. As the degree of mixing is
moreover dependent on the relation between the amount of steam
transmitted in umit time and the volume of the boiling liquid, the
observed rise in temperature will depend on the dimensions of the
apparatus and the method of working. That a fairly complete mixing
took place in my apparatus was proved by an investigation of the
temperature of the different liquid layers. This investigation originated
in the following phenomenon. I happened to find that, when the
thermometer inside the liquid was raised or lowered to the extent
of 1 c.m., a change of 0.005° was noticed in the temperature. Was
this to be considered as a proof that the temperature of the different
liquid layers was unequal, or must the explanation be found in the
change of the height of the column of liquid caused by the altered
position of the thermometer?

This question was decided by first ascertaining the influence of
a certain increase in the height of the column of water while leaving
the position of the thermometer unchanged and then repeating the
experiment taking care, that the thermometer before and after the addi-
tion of water reached to the same depth. Both determinations gave
exactly the same result from which follows, that the temperature
of the different layers of water of the strongly moving boiling column
of liquid is the same and that, therefore, the small increase of tem-
perature of 0.005° was caused by the change in the height of the
column of liquid already mentioned. From the foregoing it appears
that an increase in the height of the column of boiling liquid
exercises an influence which cannot be neglected, so that it is
necessary to find out by measurement of the inerease of height,
whether or not on addition of salt a correction ought to be applied.

Concentration in gr. mol.

per 1000 gr, H,O.

0.0462
0.0852
0.44148
0.8630

0.0461
0.0868
0.4233
0.8890

0.0429
0.0848
0.4142
0.9005

0.0473
0.0908
0.4409
0.9146

0.0474
0.0869
0.4174
0.8793

( 719 )

RESULTS.

Na NOs.

Increase of the boiling

point of the solution.

0.044°
0.080°
0.398°
(ariAle

Ba (NOs)2.

0.070°
0.104°
0.466°
0.911°

Sr (NOs)».
0.050°
0.098°

Pb (NOs)o
0.0709
0.090°
0.418°
0.8249

Mol. increase of the

boiling point.

9.516
9.389
8.948
8.876

15.190
12.103
11.009
10.248

11.664
11.561
11.903
12.148

9.294
9.246
8.665
8.102

14.760
10.351
10.014

9.371

we

wo wo wo wv

HK S&S

81]
72

( 720 )

These tables show that while the factor 7 for NaNO3, Ba(NO,)o,
Ag NO; and Pb (NOs), diminishes perceptibly with the imerease of
the concentration, it takes in the case of Sr(NOs;). a course, which
quite agrees with that observed with K Cl and Na Cl.

Although five out of the six anhydrous nitrates investigated gave
the same result, the exception, noticed in the case of Sr (NOs),
shows that the fact, that a salt is anhydrous or not anhydrous, has
no definite influence on the progressive change of 7.

Let us now consider what is to be learned from the determina-
tions of the electrolytic conductivity of solutions of the salts K Cl,
K NO3, NaCl and Na NOs.

KRANNHALS !) found at 99°.4 the following:

K Cl (4, = 348)2).

0/) increase of —— 9/9 increase of 7
| P Fa E
Concentration | Mo!- conductive power in the : in the
3 concentration interval concentration interval
1—1/,, gr. mol. 1—1/,, gr mol,
L 240.0 ) 1.69 )
29 Mee)
Ug 309.9 j 1.89 | §
|
K NO; («= 340).
il 205.8 ) 1.605 )
38.5 14.6
Vig 985.1 j 1.84 | §
NaCl G@z= 36):
1 204.4 | ) 1.65 )
oll 12.0
Wig 268.1 | 1.85 | J
Na NOs (“= 309).
1 173.7 | ) 1.56 | )
45.4 16.6
a 252.5 | j 1.82 | j

1) Zeitschr. f. Physik. Chem. 5, 8. 250 (1890).
2) Instead of uo here is taken seyo9, but it is easy to demonstrate, that for our
purpose this manner of acting is permitted.

( 721 )
In these tables it is assumed, that for the concentration given the
; £ Bee et!
quotient ies represents the degree of dissociation.

«o
It appears, however, from JAHN’s investigation that this is not
the case even for very small concentrations.
The mobility of the K and Na ions appears to increase very
perceptibly with the concentration, so that for liquids, which are

- : fe . eae Ae
not excessively dilute, —— is greater than the degree of dissociation,
“4

Me
while the difference is continually increasing with the concentration.

All the values of ¢ occurring in this table ought, therefore to be
diminished by a certain amount which should reach a maximum
for the greatest concentration.

If we now started from the supposition that the corrections, which
ought to be applied in the case of the above mentioned salts in
order to get the true degree of dissociation, exercise about the same
influence on the progressive change of 7, it would follow from this
table that in the case of K NO; and Na NO; the degree of dissocia-
tion and consequently the theoretical value of 7 (from the conducti-
vity) diminishes much more rapidly with the increase of the con-
centration than in the case of K Cl and NaCl *).

Should this be confirmed by more accurate determinations of the
degree of dissociation of more concentrated solutions it might provide
an explanation of the fact, that the experimental 7 (from the decrease
of vapour tension and increase of boiling point) increases with the
concentration in the case of not very diluted solutions of K Cl and
Na Cl whereas the reverse happens with K NO; and Na NOs.

The change of the experimental 7 is due not only to the change
of the dissociation, but also to the influence of the deviation from
the diluted condition. Researches on non-electrolytes render it pro-
bable that this last influence will cause the experimental 7 to increase
with the concentration and will, therefore, possess a sign opposite
to that of the influence of the dissociation change.

As one of the influences increases the experimental values of 7
and the other one tends to reduce them, the final result will depend
on the relative magnitudes of the two influences.

If then the dissociation in the case of one salt diminishes much

1) Zeitschr. f. Physik. Chem. 33, 545 (1900).
2) The corrections cannot as yet be deduced from Jaun’s research, as these have
been determined for greater dilutions only.

( 25

less rapidly with an increase of the concentration than in the case
of another salt, it is possible that, while in the one case a very
slow increase of the experimental 7 is observed (K Cl, Na Cl), the
reverse may be the case with the other (K NO;, Na NOs).

In conclusion it may be remarked that the results of the freezing
point determinations of not very dilute solutions have not been
discussed in this paper because some doubt has been thrown on
them by their disagreeing with those obtained by the determination
of the vapour tensions and boiling points.

Amsterdam, Chem. Lab. University, March 1901.

(May 18, 1901).

Q Akademie van Wetenschappen,

57 Amsterdam. Afdeeling voor
ALS de Wis~— en Natuurkundige

Ve3 Wetenschappen

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