20

Library of the Museum

COMPARATIVE ZOOLOGY,
AT HARVARD COLLEGE, CAMBRIDGE, MASS.

Founded by private subscription, tn 1861.

NIALTESESEITIL TEE SE

EE

|

ARCHIV

FOR

Matnenarik OG NATURVIDENSKAR

UDGIVET
AF

AMUND HELLAND, SOPHUS LIE, G. 0. SARS og $. TORUP

ATTENDE BIND

KRISTIANIA
ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

1896

OM

DIRECTIONENS ANALYTOKE BETEGNING

ET FORSØG,
ANVENDT FORNEMMELIG
TIL
PLANE OG SPHÆRISKE POLYGONERS OPLØSNING

AF

CASPAR WESSEL, LANDMAALER.

Med en Fortale af Sophus Lie.

>» KRISTIANIA
ALB. CAMMERMEYERS FORLAG
(LARS SWANSTRØM)

CENTRALTRYKKRRIET — KRISTIANIA 1896

H'ortale.

Norske Mathematikere har indtil den sidste Tid staaet i den
Formening, at den høiere Mathematik i Norge begyndte med Niels
Henrik Abel. Hans udødelige Undersøgelser aabnede, som alle ved,
nye udstrakte Felter, hvis Bearbeidelse gjennem Decennier har lagt
Beslag paa Aarhundredets første mathematiske Kreefter.

Nu viser det sig imidlertid, hoist mærkelig, at der for Abel
har været en norsk Mathematiker, der et fjerdedels Aarhundrede
tidligere fremsatte grundleggende Ideer, som utvivlsomt vilde vere
blevet banebrydende, om de ikke vare blevne upaaagtede.

I 1796 indleverede Nordmanden Caspar Wessel, en Broder af
Digteren Johan Herman Wessel, til det danske Videnskabernes
Selskab denne Afhandling!) som indeholder en klar og fuldstændig
Fremstilling af den geometriske Imaginærrepræsentation, som først
senere antydedes, om end kun implicite af den store Gauss, hvis
høit berømte Doktorafhandling (1799) dog kun for en ringe Del
dækker sig med Caspar Wessels Arbeide. Fuldstændigere indfortes
Theorien af Franskmændene Argand (1806) og Mourey (1820) af Eng-
lænderen Warren (1821) samt af Italieneren Bellavitis. Disse Mathe-
matikere synes, da ingen nævner sine Forgjængere, at have arbei-
det uafhængig af hverandre og af Caspar Wessel. I Cauchy’s og
Riemanns Hænder er disse Ideer blevet det formelle Grundlag for
vort Aarhundredes Funktionstheori, blandt hvis Grundlæggere Abel
indtager den første Plads ved Siden af Cauchy.

Caspar Wessels Arbeide indeholder imidlertid foruden Imagi-
nærtheorierne mærkelige Betragtninger, som den danske Mathe-

1) Afhandlingen foreligger trykt i Ny Samling af det Kongelige Danske Videnska-
bernes Selskabs Skrifter, Kjøbenhavn 1799.

4 Fortale.

matiker Juel?) med rette betegner som Forløber til Englænderen
Hamiltons berømte Quaternioncaleul.

Hvis Caspar Wessels Arbeide var kommet til sin Ret, saa vilde
han forlængst have vundet et fuldt saa stort Navn i Mathemati-
kens Rige som hans Broder Johan Herman Wessel inden den nor-
diske Litteratur og som hans Onkel Petter Wessel (Tordenskjold)
vandt som Kriger.

Caspar Wessel er, saavidt vides, ikke tidligere blevet omtalt
af nogen, det være norsk, dansk eller fremmed Mathematiker,
forend Overlerer Christensen i Odense i sin Doktorafhandling (1894)
gav et sandsynligvis meget fuldstændigt Referat af danske og norske
mathematiske Arbeider i forrige Aarhundrede og ved denne Anled-
ning ogsaa omtalte Caspar Wessels Arbeide. Herved blev den
danske Mathematiker Juels Opmærksomhed først henledet paa
samme og han erkjendte dets Værd.

Det er nu Norges Sag at gjøre, hvad der bør gjøres for at
denne mærkelige Mands Minde kan fremdrages af Glemselen og
hans Navn finde sin rette Plads inden Mathematikens Historie.
Foreløbig reproducere vi her Caspar Wessels originale Afhandling
i Archivet.

Kristiania, 15de September 1895.

Sophus Lie.

2) Dansk mathematisk Tidsskrift 1895.

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVII. Nr. 1.

Om Directionens analytiske Betegning, et Forsøg,
anvendt fornemmelig til plane og sphæriske
Polygoners Opløsning.

Af

Caspar Wessel, Landmaaler.

Nærværende Forsøg angaaer det Spørgsmaal, hvordan
Directionen analytisk bør betegnes, eller hvordan rette Li-
nier burde udtrykkes, naar af een eneste Ligning mellem
een ubekiendt og andre givne Linier skulde kunne findes et
Udtryk, der forestillede baade den ubekiendtes Længde og
dens Direction.

For nogenledes at kunne besvare dette Spørgsmaal,
lægger jeg til Grundvold to Sætninger, der synes mig uneg-
telige. Den første er: at den Directionens Forandring, der
ved algebraiske Operationer kan frembringes, ogsaa bør ved
deres Tegn at forestilles. Den anden: at Direction er ingen
Gienstand for Algebra, uden for saavidt den ved algebraiske
Operationer kan forandres. Men da den ved disse ei kan
forandres (i det mindste efter den sædvanlige Forklaring),
uden til den modsatte, eller fra positiv til privativ, og om-
vendt: saa skulde disse to Directioner alene kunne betegnes
paa den bekiendte Maade, og i Hensigt til de øvrige Pro-
blemet være uopløseligt. Dette er vel ogsaa Grunden, hvorfor

6 Caspar Wessel.

ingen dermed har befattet sig) Man har uden Tvivl holdt
det for utilladeligt at forandre noget i Operationernes een-
gang: antagne Forklaring. Og derimod er intet at indvende,
saalænge Forklaringen anvendes paa Størrelser i Alminde-
lighed; men i enkelte Tilfælde, naar Størrelsernes egen Natur
synes at indbyde til Operationernes nøiere Bestemmelse, og
denne med Nytte kan anvendes, bør samme vel ei kaldes utillade-
lig; thi gaaer man fra Arithmetiken over til den geometriske
Analysis, eller fra Operationer med abstracte Tal til dem
med rette Linier, faaer man Størrelser at betragte, der vel
kan tage imod samme, men ogsaa imod langt flere Relatio-
ner, end de, som Tallene kan have til hinanden; om man
derfor nu tager Operationerne i en vidtløftigere Mening, og
ei, som før, blot indskrænker dem til den Brug, at kunne
foretages med Linier af samme eller modsat Retning, men
udstrækker nu deres forrige indskrænkede Begreb noget vi-
dere, saa at det bliver anvendeligt, ei alene i samme Fald,
som før, men ogsaa i uendelig mange flere Tilfælde; jeg siger
om man tager sig denne Frihed, og dog ei derved overtræder
de sædvanlige Operationsregler, saa modsiger man jo ikke
derfor den første Lære om Tallene; men man udfører den
kun videre, lemper sig efter Størrelsernes Natur, og iagt-
tager den Methodes Regel, der fordrer, lidt efter lidt at gjøre
en vanskelig Lære fattelig. Det bliver altsaa ingen urimelig
Fordring, at Operationerne anvendte i Geometrien tages i
en vidtløftigere Mening, end den man i Regnekunsten gav
dem; man vil ogsaa let tilstaae, at det paa den Maade maa
være mueligt at frembringe uendelig mange Forandringer i

Liniernes Retning. Men just derved opnaaes (som siden

1) Uden det skulde være Magister Gilbert i Halle, hvis Priisskrivt
over Calculus Situs maaskee indeholder en Forklaring over
dette Æmne.

Forsøg til Directionens analytiske Betegning. 1

skal bevises) ei alene, at alle umuelige Operationer kan
undflyes, og den paradoxe Setning, at det Muelige maa
undertiden søges ved umuelige Midler, kan oplyses, men
ogsaa at Directionen af alle Linier i samme Plan kan ud-
trykkes ligesaa analytisk, som deres Længde, uden at Hu-
kommelsen bebyrdes med nye Tegn eller Regler. Og da det
synes upaatvivleligt, at geometriske Sætningers almindelige

Rigtighed ofte bliver lettere at indsee, naar Directionen ana-

lytisk kan betegnes, og underkastes de algebraiske Opera-

tionsregler, end naar den ved Figurer, og kun i enkelte

Tilfælde, skal forestilles: saa synes det ogsaa ei alene tilla-

deligt, men endog gavnligt, at betjene sig af Operationer,

der udstrækkes til flere Linier, end de ligestilte (de af samme

Retning) og de modsatte. Paa Grund heraf søger jeg

I. Først at bestemme Reglerne for saadanne Operationer;
II. Dernæst vises ved et Par Exempler deres Anvendelse,
naar Linierne er i samme Plan;

III. Derefter bestemmes Directionen af Linier i forskjellige
Planer ved en ny Operationsmethode, der ikke er alge-
braisk;

IV. Ved Hielp af denne udfindes derpaa saavel plane som
sphæriske Polygoners Opløsning i Almindelighed;

V. Tilsidst udledes paa samme Maade de i den sphæriske
Trigonometrie bekiendte Formler.

Dette er Hovedindholdet af denne Afhandling. An-
ledningen dertil var, at jeg søgte en Methode, hvorved de
umuelige Operationer kunde undgaaes, og da denne var fun-
den, anvendte jeg samme, for at overbevises om nogle be-
kiendte Formlers Almindelighed. Disse første Undersøgelser
havde Hr. Etatsraad Tetens den Taalmodighed at gjennem-
læse, og denne navnkundige Lærdes Opmuntringer, Raad og

8 Caspar Wessel.

Veiledning skylder jeg, saavel at dette Skrivt nu frem-
kommer mindre ufuldkomment, som og at det er værdiget,
at optages i Samlingen af det Kongelige Videnskabers Sel-

skabs Skrivter.

I.
Paa hvad Maade af givne rette Linier ved de algebraiske
Operationer formeres andre, og fornemmelig hvad Retning
og Tegn disse skal have.

Der gives homogene Størrelser, hvilke, naar de faae
Sted hos samme Subject, forøge eller formindske hinanden
paa den Maade alene, som Incrementer og Decrementer.

Der gives andre, som i samme Tilfælde kunne forandre
hinanden paa utallige flere Maader. Af dette sidste Slags
ere rette Linier.

Saaledes kan et Puncts Afstand fra et Plan paa utal-
lige Maader forandres derved, at Punktet beskriver udenfor
Planet en meer eller mindre inclineret ret Linie.

Er nemlig denne Linie perpendicular, det er, gior Pune-
tets Vei en ret Vinkel med Planets Axel, saa bliver Punctet
i Planets Parallel, og dets Vei har ingen Virkning paa dets
Afstand fra Planet.

Er den beskrevne Linie indirect, det er, giør den en
skiev Vinkel med Planets Axel, saa bidrager den et mindre
Stykke end sin egen Længde til Afstandens Forlængning
eller Forkortning, og kan paa uendelig mange Maader for-
øge eller formindske Afstanden.

Er den direct, det er i Linie med Afstanden, tillægger
eller fratager den samme sin hele Jengde, og er i første

Fald positiv, i andet privativ.

Forsøg til Directionens analytiske Betegnirg. 9

Alle de rette Linier, som af et Punct kan beskrives,
ere altsaa, i Hensigt til deres Virkning paa Punctets givne
Afstand fra et udenfor Linierne opstilt Plan, enten directe
eller indirecte, eller perpendieulare,!) alt eftersom de tillægge
eller fratage Afstanden saa meget som det Hele, eller en
Deel. eller intet af deres egen Længde.

Da en Størrelse kaldes absolut, for saavidt den ei ved
Relation til en anden, men umiddelbar antages given, saa
kan i foregaaende Definitioner Afstanden kaldes den absolute
Linie, og den relatives Bidrag til den absolutes Forlængning
eller Forkortning kan kaldes den relatives Virkning.

Der gives endnu flere Størrelser end rette Linier, der
kunne tage imod omtalte Relationer. Det var derfor ikke
unyttigt, at forklare disse Relationer i Almindelighed, og at
indlemme deres almindelige Begreb i Operationernes For-
klaring; men da baade Kienderes Raad, dette Skrivts Ind-
hold, og Foredragets Tydelighed fordre, ei at besvære Læ-
seren med saa abstracte Begreb, befatter jeg mig kun med

de geometriske Forklaringer alene, og siger derfor, at

Sal

To rette Linier adderes, naar man forst foier dem sam-
men, saaledes at den ene begynder, hvor den anden slipper,
derefter drager fra de sammenføiedes første til sidste Punct
en ret Linie og antager saa denne for de sammenføiedes Sum

Gaaer f. Ex. et Punct 3 Fod frem, og derefter 2 Fod
tilbage, saa er disse to Veies Sum ikke de første 3 og sidste
2 Fod sammenføiede; men een Fod frem er Summen, for
saavidt denne Vei, af samme Punct beskreven, har samme
Virkning, som begge de to andre Veie.

1) Indifferente var mere passende, om det ikke skurrede for meget

1 uvante Øren.

10 Caspar Wessel.

Ligeledes naar en Triangels ene Side strækker sig fra
a til b, og den anden fra b til c, maa den tredie fra a til e
kaldes Summen, og maa betegnes ved ab + be, saa at ac og
ab + be have samme Betydning, eller ac = ab + be = — ba
+ be, dersom ba er det modsatte af ab. Ere de adderte
Linier directe, stemmer Definitionen fuldkommen overens
med den sædvanlige. Ere de ikke directe, strider det dog
ikke mod Analogien, at kalde en ret Linie to andre sammen-
foiedes Sum, for saavidt den har samme Virkninger, som
disse. Den Betydning jeg har givet Tegnet +, er heller

ikke saa usædvanlig; f. Ex i den Expression,
ba
ab — Gy —= Tab

ba .
er ingen Deel af Summen. Man kan derfor ogsaa sætte

ab + be = ac, uden derfor at tænke sig be som nogen Deel
af ac; ab + be er kun det Tegn, hvorved ac forestilles.

§ 2

Naar flere end to rette Linier skal adderes, folges samme
Regel; de forenes nemlig, saa at forstes sidste Punct sam-
menfoies med det første af den anden, dennes sidste med
tredies første o. s. v., derefter drages fra det Punct, hvor
første begynder, til det, hvor sidste slipper, en ret Linie,
og denne kaldes Summen af dem alle.

Hvad for en Linie der skal tages for den første, og
hvilken for den anden, tredie o. s. v., er ligegyldigt; thi paa
hvad Sted indenfor tre Planer, der gjør rette Vinkler med
hinanden, en ret Linie af et Punct beskrives, har denne
Linie samme Virkning paa Punctets Afstand fra hver af
Planerne; følgelig bidrager een af flere adderte Linier
til Positionens Bestemmelse af Summens sidste Punct lige-

Forsøg til Directionens analytiske Betegning. 11

saa meget, naar den er den første, som naar den er den
sidste, eller hvad anden Orden den har til de andre adderte;
følgelig er Ordenen i rette Liniers Addition ligegyldig, og
Summen bliver alletider den samme, fordi dens første Punct
antages given, og det sidste faar alletider samme Position.

Derfor kan ogsaa i dette Tilfælde Summen betegnes
ved de adderte Linier forbundne med hinanden ved Tegnet
+, Naar i en Fiirkant f. Ex. den første Side er dragen
fra a til b, den anden fra b til c, den tredie fra e til d
men den fierde fra a til d: saa kan sættes ad = ab + be

+ ed.
38

Er Summen af flere Længder, Bredder og Høider — 0,
saa er Summen af Længderne, den af Bredderne, og den af
Høiderne, hver især == 0.

S4

Productet af to rette Linier maa i alle Maader kunne
formeres af den ene Factor, som den anden er formeret af
den positive eller absolute Linie, der sættes — 1, det er:

Først maae Factorerne være af den Direction, at de begge
kan optages i samme Plan som den positive Unitet.
Dernæst maa i Hensigt til Længden Productet forholde
sig til den ene Factor, som den anden til Uniteten; og
Endelig, dersom man giver den positive Unitet, Factorerne
og Productet et fælles første Punct, skal Productet i
Hensigt til dets Retning ligge i omtalte Unitets og
Factorers Plan, og afvige fra den ene Factor ligesaa
mange Grader, og til samme Side, som den anden
Factor afviger fra Uniteten, saa at Productets Direc-
tionsvinkel eller Afvigning fra den positive Unitet,

2 Caspar Wessel.

bliver saa stor, som Summen af Factorernes Direc-

tionsvinkler.

85.

Lad + 1 betegne den positive retlinede Unitet, og + &
en vis anden Unitet, der er perpendicular paa den positive,
og har samme Begyndelsespunct: saa er Directionsvinkelen
ni 0, ar SD a 180, ar EE at 5 ==)"
eller 270°; og i Følge den Regel, at Productets Directions-
vinkel er Summen af Factorernes, bliver (+ 1).(+ 1) = +
Heen ee
eye na. en
= t+ & (+ 5). +J=—1 (Fe) .(=me)=+L (=>)
(— €) = — 1.

Hvoraf sees at ¢ bliver — Y — 1, og Productets Afvig-
ning bestemmes saaledes, at ei en eneste af de almindelige
Operationsregler overtrædes. —

§ 6.

Cosinus til en Cirkelbue, der begynder fra det sidste
Punct af dens Radius + 1, er det Stykke af samme, eller
modsatte Radius, der begynder fra Centrum, og endes per-
pendicular udfor Buens sidste Punkt. Sinus til samme Bue
drages perpendicular paa Cosinus fra sammes sidste Punct
til sidste af buen.

I Følge § 5 er altsaa Sinus til en ret Vinkel = V —1.
Lad sættes | — 1 = &; lad v betegne en Vinkel, hvilken
som helst; og lad sin. v bemærke en rei Linie af samme
Længde som Vinkelen v’s Sinus, men positiv, naar Vinke-
lens Maal endes i første halve Omkreds, og negativ, naar
det endes i den sidste halve: saa følger af § 4 og 5, at
e sin. » udtrykker Vinkelen vs Sinus baade i Hensigt til
Direction og Længde.

Forsøg til Directionens analytiske Betegning. 13

Sø

I Overeensstemmelse med § 1 og 6 er den Radius, som
begynder fra Centrum, og afviger fra den absolute eller po-
sitive Unitet Vinkelen v, saa stor som cos. v + ¢ sin. v. Men
i Følge $ 4 skal Productet af to Factorer, hvoraf den ene
afviger fra Uniteten Vinkelen v, og den anden Vinkelen u,
afvige fra samme Unitet Vinkelen v+u. Altsaa naar den
rette Linie cos. v + e sin. v multipliceres med den rette Linie
cos. u + e sin. u, bliver Productet en ret Linie, hvis Direc-
tionsvinkel er vu. Følgelig kan Productet efter § 1 og
6 betegnes ved cos. (v + u) + e sin. (v + u).

§ 8.

Dette Product (cos.v + ¢ sin. v). (cos. u += sin. u) eller
cos. (v + u) + e sin. (v + u) kan endnu udtrykkes paa en
anden Maade, nemlig ved at addere i een Sum de partielle
Producter, som udkomme, naar hver af de adderte Linier,
hvis Sum udgiør den ene Factor, multipliceres med hver af
dem, hvis Sum udgiør den anden. Saaledes bliver (cos. v +
e sin. v). (cos. u + & sin. U) = cos. v cos. u — sin. v sin. u +
e (cos. v. sin. u + cos. u . sin. v) i Følge de to bekiendte tri-
gonometriske Formler cos. {v + u) = cos. v . cos.u — sin. v.
sin. u, og sin. (v + u)— Ccos.v.sin.u + cos. u.sin.v. Disse
to Formler kan med Nøiagtighed og uden stor Vidtloftighed
bevises for alle Tilfælde, enten hver af Vinklerne v og u,
eller ecn alene er positiv, negativ, større eller mindre end
en ret. De Sætninger, som af samme to Formler udledes,
har følgelig ogsaa deres Almindelighed.

$9.
Cos. v + esin.v er i Folge § 7 en Cirkels Radius, hvis
Længde er = 1, og Afvigning fra cos. 0° er Vinkelen v;

14 Caspar Wessel.

deraf følger at r.cos.v + r.¢ sin. v betegner en ret Linie,
hvis Længde er r, og hvis Directionsvinkel er = v; thi naar
en retvinklet Triangels Catheter blive r gange større, saa
bliver ogsaa Hypothenusen r gange større, og Vinklerne
uforandrede; men Catheternes Sum er i Følge $ 1 saa stor
som Hypothenusen, altsaa er r.cos.v + r .e sin. v =r (cos. v
— esin.v). Dette er altsaa et almindeligt Udtryk for enhver
ret Linie, der ligger med Linierne cos. 0° og e sin. 90° i

samme Plan, afviger fra cos. 0° Graderne v, og har Længden r.

I 10.

Betegne a, b, c, d directe Linier af hvilken Længde som
helst, positive eller negative, og de to indirecte a + eb og
e + ed ligge i samme Plan som den absolute Unitet: saa
kan deres Product findes, endogsaa naar deres Afvigning fra
den absolute Unitet er ubekiendt; man behøver nemlig kun
at multiplicere enhver af de adderte Linier, der udgiore den
ene Sum, med enhver af dem, som udgiore den anden, saa
vil disse Producter adderte udgiore det sogte Product baade
i Henseende til Længden og Retningen; saa at (a + eb).
fe + ed) = ac — bd + ¢ (ad + be).

Beviis. Lad Liniens a + cb Længde være A, og Af-
vigning fra den absolute Unitet » Grader; men Liniens ¢ + ed
Lengde — C, og Afvigning =u: saa er, i Folge § 9, a + eb
— À . cos. vo + A .e sin. v, og c+ sd = C.cos.u + C.e sin. u,
sr SÅG 0) DS AV Sin å GC== (CO. GOS, th U=
sin.u ($ 3); men i Følge § 4 er (a + eb).(c + ed)= A.C.
[cos. (0 + u) + e sin. (0 + u)]= A.C. [cos. v. cos. u — sin. 0.
sin. u + & (os. v. sin, u + cos. u.sin.v)] § 8. Følgelig, naar
isteden for A. CO. cos.u.cos.v sættes a.c, isteden for A.C.
sin.v.sin. u sættes b.d, o.s. v.: udkommer det, som skulde
bevises.

Forsøg til Directionens analytiske Betegning. 15

Hvoraf følger, at skiøndt Summens adderte Linier ei
alle er directe, saa behøves dog ingen Undtagelse i den be-
kiendte Regel, hvorpaa Ækqvationernes Theorie, og den om
hele Functioner og deres Divisores simplices grunder sig,
nemlig at naar to Summer skal multipliceres med hinanden,
da maa enhver af de adderte Størrelser i den ene Sum mul-
tipliceres med enhver af de adderte i den anden. Man kan
altsaa være forvisset om, at naar en ZEqvation angaaer rette
Linier, og dens Radix har den Form a+ eb: da betegnes
derved en indirect Linie Men vilde man multiplicere med
hinanden rette Linier, som ikke begge kunde ligge i samme
Plan med den absolute Unitet: maatte omtalte Regel tilside-
settes. Dette er Aarsagen, hvorfor jeg forbigaaer saadanne
Liniers Multiplication. En anden Maade at betegne deres
forandrede Retning forekommer i det følgende, $ 24— 35.

PA

Qvotienten mnltipliceret med Divisor skal være saa stor
som Dividendum. Det behøver altsaa ikke Beviis, at disse
Linier skal ligge i samme Plan med den absolute Unitet;
thi det følger umiddelbar af Definitionen § 4 Ligeledes
indsees let, at Qvotienten maa afvige fra den absolute Unitet
Vinkelen v — u, dersom Dividendum afviger tra samme Unitet
Vinkelen v, og Divisor Vinkelen u.

Set f. Ex. at A (cos. v + e sin. v) skulde divideres med
B (cos. u + e sin. u): da er Qvotienten — [cos (o —u) +
e sin. (v — u)|, fordi = [cos. (0 — u) + e sin. (v — u)] < B(cos.u
+ e sin. u)= A (cos.v-+ esin.v), i Følge $ 7. Det er, da

A oo Nie
B [cos. (0 — u) + e sin. (o— u)] multipliceret med Divisor

16 Caspar Wessel.

B (cos. u + e sin. u) er saa stor som Dividendum A (cos. v +

Å A :
e sin. v): saa er ogsaa 5; [cos. (0 — u) + « sin. (vo — u)] den

B
søgte Qvotient.

Sa

Ere a, b, ce og d directe Linier, og de indirecte a + eb -
og © + ed ere i samme Plan med den absolute te da er

il er Sil a-eb
ected år da og voue c oe sk a=
ed
(a + cb). 2 Bar
Følge $ 9 kan sættes a+ sb — A (cos. v + e sin. 0), og © + ed
— C (cos.u + es sin. u), altsaa e— ed=Ü (cos. u— ¢ sin. u), 1

= [ac + bd + e(be — adj] :(*+ d?); thi i

Følge $ 3; og da (ce + ed). (c— ed) er =e? + P=C ($ 10):
— ed 1 ced
saa er ee G (cos.u — esin.u) $ 10, eller EE

1 : 1 DES
ECO: po UG een § 11, og naar multipliceres

med a + ch = A (cos. v + ¢ sin. v), udkommer (a + eb)

c— ed A a + eb
peer OL (v — u) + e sin. (v — u)| = su

Indirecte Størrelser af denne Art har altsaa dette fælles

med de directe, at naar Dividendum er en Sum af flere
Størrelser, da giver enhver af disse divideret med Divisor
flere Qvotienter, hvis Sum udgiør-den søgte Qvotient.

§ 13.
v “0
Hvis m er et heelt Tal, frembringer cos. — + = sin. — mul-
m m

tiplicerét m gange med sig selv Potenzen cos. v + esin.v.

Forsøg til Directionens analytiske Betegning. 17

al
5 m v Ha i
($ 7); altsaa (cos. v + ¢sin.v)™ — cos. Fr + esin. om Men i

Folge § 11 er cos. — = + esin. == 1 =
COS + e sin. —
re
= — —(co8.v+esin.v) ,altsaa, enten m er

&

(cos. » esin.v)™
ae : : v PE)
positiv eller negativ, er alletider cos. Fr e sin. — —(cos.u +

1
esin.v) , og derfor, naar m og n begge ere hele Tal, (cos. v

n
m n > il
— esin.v) ==c0s,—v-+ esin. —v,
m m

Herved findes Værdien af slige Expressioner som Va (b
m
+eV—l) eller VY (a+ V(b + cy —1)); saaledes kan f. Ex.

3
V (4V¥3+4VY—1) betegne en ret Linie, hvis Længde er
— 2, og hvis Vinkel med den absolute Unitet maales ved 10°.

$ 14.

Naar to Vinkler have ligestore Sinus og ligestore Co-
sinus, da er deres Forskiel enten 0, eller 4 rette, eller
en Mangefold af + 4 rette, og omvendt, naar to Vink-
lers Forskiel er enten 0, eller 4 rette, een eller flere
gange tagne, da er deres Sinus saavelsom deres Cosinus
ligestore.

§ 15.
Er m et heelt Tal, og t= 360°, saa har (cos. +

1

esin.»)”" kun følgende m forskiellige Værdier:
2 — Archiv for Math. og Naturv. B. XVIII No. 1.
Trykt den 29. Mai 1896.

18 Caspar Wessel.

D TT Sm En 2 v
cos. — sin. 28 COS. __ £ SIN. = , COS. ae
m m m m
2p mel: v
& SIN, ———, , COS ( > a —

am—1)r to,
m p

e sin.
thi de Tal, hvormed x er multipliceret i foregaaende Række,
ere i en arithmetisk Progression 1, 2, 3,4...m—1. Alt-
saa er Summen af hver to — m, naar det ene er ligesaa langt
fra 1, som det andet er fra m—1, og er deres Antal uef-

fent, bliver to Gange det Midterste = m; derfor, naar ad-

(m—mea+v,y M—WT+o
m m

, og denne er i Rekken

m— Dr,
m

deres

m+ ov (m—-n)r--u
m

ligesaa langt fra ger EL fra

2m —u—n Ù 20
saa er Summen = — —— 7! — = ™ 7; men at ad-
m

m
Be er det samme som at subtrahere (lee =) Gr Ne,

ne,

m

dere

og da Differencen bliver 7: saa har, i Folge $ 14,
(m—u)r +o
m

; ligeledes har

(m—n)r+ov.
m Å

samme Cosinus og Sinus som

el samme Cosinus og Sinus som
altsaa giver —m7 ei andre Verdier end.+ 7, Men at ingen
af disse ere ligestore følger deraf: at Forskiellen mellem to
af Rækkens Vinkler alletider er mindre end 7, og aldrig =0.

Der findes ei heller flere Værdier ved at fortsætte Rækken;

thi da bliver Vinklerne 7 + =, x + å = = m+ a "0.8. vs

altsaa i Folge $ 14 Værdierne af deres Cosinus og Sinus
de samme som før. Skulde Vinklerne falde udenfor Ræk-

Forsøg til Directionens analytiske Betegning. 19

ken, blev i Tælleren ei x multipliceret med et heelt Tal, og
Vinklerne vilde da m gange tagne ei kunne frembringe en
Vinkel, der subtraheret fra v gav 0, eller Æ 7, eller en
Mangfoldighed af + x, altsaa kunde ei heller den mte Po-
tenz af slig en Vinkels Cosinus tilligemed Sinus blive

= 008.0 + e sin. v.

$ 16.

Uden at vide Vinkelen, som den indirecte Linie 1 +x

giør med den absolute, findes, naar Længden af x er mindre
mx mm
Te ae

og dersom denne Rekke ordnes efter Potenzerne af m, be-

end 1, Digniteten (1 + x) —_ L x? &e.,

holder den samme Størrelse, og forvandles til I + = --

ale mes
1.23
er en Sum af en direct og en N a. kaldes

xt
+ &e., hvori I san Ar &e., og

den directe a, og den perpendiculare by —1: da er b det

mindste Maal til Vinkelen, som 1 + x gior med + 1, og
sættes 1 + En + 3 —- + &e.— e, kan (1 + x)" eller

212 313 >
m ; må I ma--mby—1,

ee en betegnes ved e

det er (1 +x)” har Længden e™*, og en Directionsvinkel,

hvis Maal er mb, forudsat m at være positiv eller negativ.
Saaledes kan Directionen af Linier i samme Plan endnu ud-
trykkes paa en anden Maade, nemlig ved Hielp af de natur-
lige Logarithmer. Fuldstændigt Beviis for disse Sætninger
vil jeg en anden Gang, om det tilstædes mig, fremlægge.
Nu, da jeg har giort Regnskab for, paa hvad Maade rette

20 Caspar Wessel.

Liniers Sum, Product, Qvotient og Dignitet efter min Me-
ning findes, vil jeg alene give et Par Exempler paa Metho-
dens Anvendelse.

Il.
Beviis for den Cotesianske Læresætning.
S 7.

Jeg forudsætter som bekiendt, at naar Æqvationen x? +
pa se 0 haridem Radices 21h
c...g: da har den hele Function 2" + pz®—! Lqyn—2
+ ...+sz Et de Divisores simplices z—a, z—b, z— c

.Z—g, og er et Product af dem alle.

S 18.

Den af Cotes opfundne Setning er folgende:
Naar Buerne ab, be, ed, de, ea (Fig. 1) ere i Tallet n,

og indeholder Graderne 27 =" og Radius oa sættes = r,

a0=—r, 0P—=z, po = — z, og p er det sidste Punct i Lin-
ierne ap, bp, cp, dp, ep: saa er ap.bp.cp.dp.ep — zu = En
Thi ef § 1 og § 9 følger
at ap = z—r
T EN
bp = z—r (cos. = + ¢ sin. =

:
Dre

DE ne )
r (cos, = ahs sin, ==
n Sig n

ep = Z
IT :

dp = z—r (cos. — + & sin. —
n D-

Ar Makes
ep = z—r (cos, 7 esi. |

Forsøg til Directionens analytiske Betegning. ZA

eller ep —= 7—r (cos. * (n = ee Tales 1 a)

og af 8 15 sluttes, at AEgationens x! —r" = 0 Radices ere

iss r (cos. = sin =}; r (cos, 7 en ae
AE = EE = apps EEE IE)

altsaa bliver i Følge $ 17 zZ —r"=ap.bp.ep.dp.ep. Fol-
gelig er Længden af z" —r" saa stor som Productet af Lin-

iernes ap, bp, ep &c. Længder, § 4.

Om plane Polygoners Opløsning.
SEE)
Folgende af Trigonometrien bekiendte Formler anfører
jeg uden Beviis.
a) sin. (a+b)= sin a.cos. b + sin. b.cos. a.
b) cos.(a+b) = cos.a.cos. b — sin. a. sin. b.
c) sin. 2a — 2sin.a.cos.a.
d) 1+cos.2a—2 cos? a. -
e) 1— cos. 2a— 2 sin? a.
sin 2a
f) tang.a — we
a+b a—b

g) sin.a-+ sin.b=2 sin. —1— . cos.

2 2
; : b ai a—b

h) sin.a— sin. b= 2 cos. zu Sin.
RR G a b . a A b
i) cos. b— cos.a=2sin. a . sin, ;

sin. a + sin. b a+b
k) ane) a

cos. a + cos. b 2

22 Caspar Wessel.

sin. a — sin. b Ve om
== tang. ——.
cos. a + cos. b 83

))

$ 20.

Til Polygoners Opløsning kan det ogsaa være tienligt
at erindre sig: naar et Problem er bragt dertil, at man har
a==bcos.u-+csin.u, og u alene er den ubekiendte, da kan
den qvadratiske Æqvation, hvorved sin u eller cos. u skulde

b
findes, undgaaes ved at sætte = tang. 9, eller oe cot. D.

Derved findes ¢ eller 4, som bliver positiv eller negativ,
og behøver ei at være større end 90°. Er g eller funden
søges derefter u ved en af følgende /Egvationer: sin. (u + ¢)
— à sin. ©: b= acos.¢: ©, og cos. (U—V) = cos, (V —u) =
a COS. D

a sin. ¢ : å : :
5 = 7; Thi naar Ledene i den givne Ævation a

— b cos. u + csin.u divideres med c, eller med b, og der-
: b é
efter isteden for „ sættes dens Verdi tang. 9, eller cot. ¥,

C

b

og isteden for — sættes cot.¢ eller tang. ¥, udkommer:

= tang. 9.cos.u + sin.u — cot. L. cos. u + sin. u, eller

ye oe|e

cos, u-+ cot. 9. sin. u — cos. u + tang. Y. Sin. u.

Følgelig, naar Ledene i den første af disse Ævationer mul-
tipliceres med cos. a, i den anden med sin. 4, i den tredie

med sin. 9, og den fierde med cos. ¥, faaes

a i :
— cos, p= SIN. Y. COS. u + COS. ©. SIN. U,
re

Forsøg til Directionens analytiske Betegning. 23

a. « -
«si. U = cos. d. cos. u + sin. u. sin. ,

ae A .
— Sin. @ = SIN. 9. COS. U + COS. Y. SIN. U,

b

a : å
— cos. ) = cos. L. cos. u + SIN. U. sin. V;

b
altsaa er, i Følge § 19, a, b,

a COS. © asin. d

= sin. (u + 9), = cos. (u — V) = cos. (Y—u),

5 :
= = ? — sin. (u + 9), 2 = T — cos. (u— Y)= cos. (Y—uU).

og

Sal,

Naar i et plant Polygon intet mere gives end alle Vink-
lerne, og Siderne saa nær som tre: da er Polygonet ube-
stemt. Dette er tydeligt nok, hvis alle tre ubekiendte Sider
følger efter hinanden; thi da kan med den ene ubekiendte
Side drages Paralleler, som skiære de to andre ubekiendte
i flere Puncter, og disse tre Sider kan altsaa have utallig
mange Værdier; men deraf følger ogsna, at de tre ubekiendte
Sider kan have ligesaa, mange Værdier, endskiondt de ikke
følge efter hinanden; thi da Sidernes Orden er i Hensigt
til deres Sum ligegyldig ($ 2): saa kan af ethvert Polygon
alletider construeres et andet, hvori Sidernes Længde og
Retning er den samme, men deres Orden alene forskiellig.

8 22.

I et Polygon abed (Fig. 2) antages den ene Side ab for
absolut, og tælles fra a til b, den anden be tælles fra b til
cea trae tlade da fra dal a2 evene Tal it, IV, VI,

24 Caspar Wessel.

vit bemærke Sidernes Længder; de uefne I, II, V, VII,
ere deres Afvigninger fra foregaaende Sides Forlængning
talte positive elier negative; f. Ex. med Solen positive, og

mod Solen negative.

1, IT, V, vil betegne cos. I + esin I, cos.IIT + esin. III,
COS. VE esm.vV 0. 8: v.
T', ur’, V', vir’ betegne cos. —1 + esin. — I, cos. III —

e SIN. III, cos. v—esin.v &c.

Naar dette forudsættes, og man fra a drager Paralleler
med be, ed, da: saa folger,

I) At første Parallel afviger fra ab Graderne 11, anden
Parallel fra ab Graderne m + v, tredie Parallel eller
sidste Sides da Forlængning ae afviger fra ab Graderne
mm + v + vir eller — 1. Derfor bliver alle Vink-
lerne tilsammen — 0, og Maalet til deres Sum bliver
enten 0, eller == 4 rette, eller en Mangefold deraf.

JOP) rv mv oe SE nutes fie vit = Oe
thi ab + be + ed + da =0 ($ 2); men ab = 11, be —
Iv . al (§ 9), ed = vi [cos. (Im + v) + esin. (III +V)],
i Følge foregaaende Numer I og $ 9, altsaa er efter
§ 7 cd = vwr.nr .v, og ligeledes bevises at da er —
VEV Vi.

TIP ane mme ve VIR Ev ev vi Wie aE EVER
=0; thi naar Ledene i foregaaende Æqvation IT divi-
deres med 111 . v . vir, udkommer i Folge $ 12
DTV VI SE va Sv Ne
vill = 0, og da ethvert Led i denne /Egvation, saa
nær som det sidste, er multipliceret med en Cosinus
tilligemed en Sinus, (første Led f Ex. er = 1 [cos.
(111 + v + vit) — esin. (HI + v + val); men Sum-

men af alle de directe Led er ligesaavel = 0, som

Forsøg til Directionens analytiske Beretning. 25

Summen af de Led, der ere multiplicerede med Sinus,
§ 3: saa bliver den totale Sum endnu = 0, endskiøndt
hver Sinus faaer modsat Retning, og naar dette skeer,
forvandles Udtrykket til det, som skulde bevises.

KD rn Ml 2 COS ME SV SE Vo —
2 cos. (I + V), or .v' + ur . V = 2 cos. (III —
vem Sonne — 2 eral OR One ni aaa —
2esin. (+ V), IT .V' — ur’. Vv’ = 26 sin. (II V),

am) — 1 1—(nr'? (mm ”+1
EN EE ane ( DE Pacis =
(ar)? + 1 1+ar')” (am’)? — 1
1 igh > : ER
— & cot. II = al = af hvilke Formler Rigtigheden

1 — (Ir)

! !

let indsees ved at satte isteden for Il, Mr, v’, Vv’
deres Værdier cos. III + ¢ sin. III, cos. III — € sin, III,

cos. V + esin. V, &e.

8 23.

To Æqvationer af den Form som JJ og III i fore-
gaaende Paragraph ere tilstrækkelige til ethvert Polygons
Opløsning, naar kun tre Vinkler, eller to Vinkler og
een Side, eller een Vinkel og to Sider ere ubekiendte;
thi i det sidste Tilfælde har den -ubekiendte Vinkel samme
Cosinus og Sinus, som det modsatte af de øvrige Vinklers
Sum (§ 22 No. J); i de to andre Tilfælde udelukkes af
Ævationerne den ene ubekiendte Vinkel, naar den betegnes
ved I ligesom i $ 22 No. IT og No. IIT: Følgelig inde-
holde /Eqvationerne kun to ubekiendte Stykker. Altsaa kan
findes, hvad Function det ene Stykke er af det andet ved
Hielp af den ene Ligning; denne Function indført i den
anden Ligning befrier samme fra det ene ubekiendte Stykke,
og derved findes tilsidst Værdien af det andet.

Lad f. Ex. i Polygonet Fig. 2. 1, II, VI være ube-

26 Caspar Wessel.

kiendte og Il søges, da eri Følge § 22 No. 11 og No. ITT:

I + Iv.ur À Vie Ve + Vin. .V 0 vir = 0 —
TRE ve ve Ev soi Ev mo Ea AA:
den første Æqvation findes — 11 . 1 .v —1v.v —

VIII . VII = VI, og naar denne Værdie af vi indføres i
den anden /Egvation, efterat sammes „bes er dividerte med

vir, udkommer I . Il. V — Il. de my, AY = my

v + vit. vir’ — vil. vil = 0. i Folge $ 22 No.

IV, 11.e.2 sin. (I + V) + VI.e. 2 sin. V — le. 2 sin. VII
VII, sin. VII — Iv . sin. V

— 0, eller sin. (Im + v) =

II

LI.
Hvordan Directionen af en Kugles Radii kan betegnes
§ 24.

Jeg äntager, at en Kugles to horizontale Radii giøre
rette Vinkler med hinanden, og ere begge perpendiculare
paa en tredie Kuglens Radius. Den ene horizontale sætter
jeg at strække sig fra Centrum til venstre Haand, og at
være=r; den anden horizontale at gaae fra Centrum fremad,
og at være ==.r; men den verticale fra Centrum opad at
være — 7.r, og de modsatte at være —r, —er, —yr. Ved
Bogstaven r betegnes Længden af Radius; Uniteterne e og 7,
ere begge perpendiculare paa + 1, og i Sammenligning med

2

denne maa 7? saavelsom < være =— 1, i Følge § 5.

25.

UN

Drages der et Plan igiennem de fire Radii r, — r, ry,
— mr, og et andet igiennem r, —r, er, — er, da giøre disse

Planer en ret Vinkel med hinanden, og overskiære Kuglen

Forsøg til Directionens analytiske Betegning. DR

i to Storcirkler, af hvilke jeg kalder den igiennem r og ry
Verticalcirkelen, og den igiennem de horizontale Radii r og
er Horizonten.

Buerne i Verticalen og dens Paralleler telles fra det
Punct paa venstre Haand, hvor de overskiæres af Horizon-
ten, opad positive, nedad negative. De horizontale Buer
tælies fra Verticalen med Solen positive, og mod Solen
negative. Naar f. Ex. owyhpi (Fig. 3) betegner Horizonten,
kfsß dens Parallel, okrqno Verticalen, x og n Horizontens

Poler, p og y Verticalens: saa antages co=r, ct——r,
CCD — er cr nr, cn = ge Oy — JU, Op —
— 90°, or=-+ 90", on= - 90°; og Buerne i Parallelen

telles den Vei fra k til venstre positive, og fra k til hoire

negative.

S 26.

Trækkes der fra Kuglens Centrum c (Fig. 3) til et Punct
d i Horizontens og Verticalens fælles Radius en Linie cd
og fra dennes yderste Punct d drages en anden de, som
er parallel med Horizontens Axel mn, og atter fra Enden
af denne trækkes en tredie Linie ef parallel med Vertica-
lens Axel py: da ere disse tre Linier Coordinater til det
Punct f, hvor den sidste Linie ef endtes. Den første cd er
Punctet f’s Abscisse, og betegnes ved x; den er enten af
samme Retning som Radius + r, eller den er negativ som
Radius —r. Den anden og tredie Linie de og ef ere Punctet
fs Ordinater; ved den anden de forestilles Punktet f’s Af
stand fra Horizontens Plan; den betegnes ved my, fordi den
er parallel med yr eller med — yr. Den tredie ef er
Punctet fs Afstand fra Verticalens Plan, og betegnes ved
ez, fordi den er parallel med Radius er eller —er. Den
tredie ef (==z) gior en ret Vinkel med den anden de

28 Caspar Wessel.

(=y), og denne yy giør en ret Vinkel med den første
Gal (en)
§ 27.

En Radius, hvis yderste Punct har de Coordinater x
ny og ez, betegner jeg ved Summen x + yy + ez ($ 2).
x + yy multipliceres med a + nb, og x +ez med a + eb
paa samme Maade som c + dy —1 med a+ by — 11; thi
da Directionsvinklerne af 7 og af = tælles begge fra samme
Radius + 1 ($ 25), saa maa i Følge § 5 saavel 7?, som e?
være — — 1, og altsaa findes Producterne (x + ny). (a + qb)
og (x + ez).(a + eb) efter den Regel $ 10.

3 98

Dersom et Punct rykker frem eller tilbage i en hori-
zontal Cirkels Omkreds Bkfs (Fig. 3) et vist Antal Grader
fs (— III), og dets Coordinater vare ed (= x’), de (= ny), og
ef (==): da bliver Ordinaten ny uforandret, fordi Punctet
beholder samme Afstand fra Horizonten; men Abscissen

ed (= ue) eller x’ forandres til ul(=x"), og Ordinaten
ef (= =z") forandres til Is (= ez"), og Summen af de to nye
Coordinater ul + Is (= x" + ez") bliver (x’ + zz’). (cos. 111 +
esin. 111); thi lad Radius uk kaldes p, Maalet til Vinkelen
kuf kaldes 1, altsaa Maalet til Vinkelen kus = 1 + 111: saa
er i Folge $ 9 ue + ef (=x + &7)=p.(cos. 1 + sin. I);
ligeledes er ul + Is (= x" + ez") = op. [cos. (I + 11) +

e Sin. (I + Im] = p (cos. 1 + e sin. I) . (cos. III + esin. III),
§ 8; og altsaa, naar isteden for p(cos. 1 + esin.1) sættes
x + ez, faaes x" + ez” —(x e7/). (cos. 111 + e sin. Im).

§ 29.

Naar et Punct beskriver i Verticalen eller dens Parallel

en Bue af et vist Antal Grader II, saa forandres Summen

Forsøg til Directionens analytiske Betegning. 29

af dets forrige Coordinater x’ og yy’ til (x’ + yy’). (cos. 11 +
4 sin. It); men den tredie Coordinat <z bliver uforandret,
fordi Afstanden fra Verticalen kan ei forandres, saalænge
Punctet bliver i Verticalens Parallel. Forresten er Beviset
i Følge $ 27 netop som det foregaaende.

$ 30.

Har Kuglens Radius de Coordinater x, ny og ez, da
betegnes denne Radius i Følge $ 27 ved x + yy + ez. Men
forandres dens Direction saaledes, at dens yderste Punct for-
flyttes de horizontale Grader 1: bliver den = ny + (x + ez).
(cos. I + esin. 1) = yy + xcos. I — Zsin.I + ex sin. I +
ez cos. I (8 28), og betegnes ved (x + ny + ez) ,, (cos. I +
e sin. I.

§ 31.

Forandres derimod Directionen af Radius x + ny + ez:
ved at forflytte dens sidste Punct de verticale Grader n,
bliver den = ez + (x + my) - (cos. + 1 sin. II) = ez +
x cos. 11 — ysin, II + nx sin. II + ny cos. ($ 29), og be-
tegnes ved (x + ny + ez),, (cos. + n sin. 1).

8 32.

Hvoraf følger, at (x + ny + ez) ,, (cos. ı + e sin. I) ,
(cos. IT 4 e sin. III) er det samme som (x + y + ez) ,,
(cos. (I + m1) + e sin (1 + ım)); thi enten det sidste Punct af
Radius x + yy + ez gaaer først frem de horizontale Grader
I, og derefter de horizontale Grader 1x, eller det gaaer paa
eengang frem den hele Bue r+ 111: saa bliver Radius fra
Centrum e til sidste Punct i Buen 111 den samme. Lige-
ledes følger, at (x + ny + ez) „ (cos. II + 7 sin. IT) ,, (cos. IV

30 Caspar Wessel.

+ 7 sin Iv) = (x + ny + e2) , (cos. (I1+1V) + n sin. (IT +1V)),
og altsaa x + ny + ez = (x + ny + ez) ,, (cos. I + e sin. 1),
(cos. I — esin.I) = (x + ny + 22) ,, (cos. II + 7 sin. II) „
(cos, II — 7 Sin. IE).

SMS.

Gaaer et Punct frem deels i Horizontens, deels i Ver-
ticalens Paralleler, beskrivende vexelviis en horizontal og
en vertical Bue; men de beskrevne Buers Grader, i den
Orden som de folge hinanden, betegnes ved I, II, III, IV, V,
vi; og Radius fra Centrum af Kuglen (Fig. 4) til første
Punct i forste Bue betegnes ved s; Radius fra Centrum til
sidste Punct i sidste Bue ved S; og cos.1 + & sin.1 betegnes
ved Y, cos. + 7 sin. 11 ved IT, cos.IH + e sin. 111 ved IT
o. s. f.: samt cos.I—esin.I ved I’, cos.11—v7sin. II ved
AND Ch re saa_ ev, ı Holoe Sa) Oe Bl, Saas 0
IV, V » IV, i hvilken Æqvations sidste Led Uniteterne IV,
v', vi, eller saa mange man vil af de sidste, der umiddelbar
følge hinanden, kan borttages, naar deres reciproqve Stor-
relser sammenføiede ved Tegnet (”) i inverteret Orden til-
føles første Led; det er, man kan i Følge $ 32 satte 8,
We piv pity == Spit pie Seles SAVE
Wh IN ar os

Ss 34.

Antages s=S, og sættes s — ır, bliver derfor

LA
s, I = M

-/

ER ren COSI — ISI) SV NC DV —

l IH.CIV.cV.[vI-n.cIv.cvi —e.fni.erv.ev. Le
r.4t+em.fiv.evi —mn.frv.ev.fvr—e. fi. fiv.evr |:
— [rir. fv. fv1 —e.cui.{[v. [VI |

Forsøg til Directionens analytiske Betegning. 31

=—==============————==——————==

PET Im, Ul =r. (1. em — fu. enr €. fir. fin) =
SP VAGLE ip iy ==
ev .ev.Ivr —e. fv. vr+mn.erv.evn |
"V4 fv. evi — 1. fv. ev. [vif

ES 10, 1; „IV —

f n-cir.crv — cil. [iv — €. fir. fr)

Pa ==
[Sn fur Jene. ev — i crt, ery j

Jerv vi Sr (CM ivi e iv fyr. n.cvn.

TD) sje
n.eH.civ —cu.[Iiv.ev —.e.en.[iv.fv |
r .4+ Én. enr.crv — fr. enr. civ eV —e.frr.enr.crv.[v
em ve 5 tr ev |

= SPE rn ev a),

8 35.

Sættes s — S = er, faaes folgende Ædqvationer:
; g a

I) S,I'—=r.(¢.cl— 1) =8, vi", Vy IV", IT =
e.CII.CV cu. eV —nm. fr. fr. ev |

r.j—s.fi.erv.fv + er.er.erv. fv — 1. fir. ert.crv.f |
— [ir VIN —mn.en. fv. iv

ID) s,r,1'=r.(- fr. er —m. fr. frr +e.cn —
DD NS, VAL, I —

ES Gat GY —m. DV. IV + fin. ev |
r. .
mn ev [by + ent. crv. fv]

JUG SA Le, ME
— fr. cm. ett — e. fr. em. firt — 4. fr. fr)
r ==
-— CI. {11 — €. CL. CII j

S, vi‘, Vi LV —r.(.cv- civ. fv — 1. f1v.1V).

32 Caspar Wessel.

IV) Spy MOE „ut Th —

e.cI.cHl -- IT.et.err.erv — 4%. fr. frr. civ
r .J—e.fr.cir.fri — er. ft. —n.[1.cıL.caL[Iv
+ fr.fir.frv ——nmn.e. fin. fiv

— pr „wi, (65 ov SE liv),

IV.
Om sphæriske Polygoners Oplesning.

$ 36.

Et sphærisk Polygon er den Figur, som paa en Kugles
Overflade (eller Yde) fremkommer ved at sammenføie flere
end to Storbuer saaledes, at den følgende begynder der, hvor
den foregaaende slipper, og den sidste ophører hvor den
første begynder. Polygonets Sider ere de Storbuer, hvoraf
det er sammensat; Vinklernes Maal ere de Grader, som hver
Sides Plan afviger fra Planet af foregaaende Sides Forlæng-
ning. Naar Radius er — 1, betegnes Polygonets Sider og
Vinkler (Fig. 5) i den Orden, som de følge hinanden, ved 1,
II, III, IV, V, VI &e.; de uefne Tal bemærke Vinklerne, og
de efne Siderne; ır er f. Ex. den Side mellem 1 og I, mm

den Vinkel, som Siden tv afviger fra Forlængningen af 11.

8 37.

Dersom et Polygons Vinkler og Sider ere bekiendte,
saa nær som een Vinkel og to Sider, eller saa nær som to
Vinkler og een Side, eller tre Sider, eller tre Vinkler: da

bestemmes det ubekiendte ved følgende Ædqvation,

SJT NAP SITI TVs Vie py VI NIS,

Forsøg til Directionens analytiske Betegning. 33

i hvilken s er ubestemt, og kan antages enten for Horizon-
tens og Verticalsirkelens fælles Radius r, eller s kan sættes
= er, som er Kuglens horizontale Radius, der er perpedi-
cular paa r, eller s kan sættes = yr, som er don verticale
Radius, der er perpendicular paa r og paa er. €? ligesaavel
som 7? er — — 1, i Følge § 27. 1'— cos. 1 + e sin. I, 1' =
cos. II + Sin. IT, Il‘ = cos. II + € Sin III, .. «y, N'==cos.N
I I

ASIAN, OF — ; Dr - 0.
aa COS. I + ¢sin.1’ COS. II +17 sin. H

Teegnet (”), hvorved s, 1", 1 &e. ere forbundne, bemærker

SV.

at s først skal multipliceres med 1', dernæst s ,,1' med I
saa S ,,I', II‘ med II‘, 0. s. v.; men dog med den Ind-
skrenkning, at den af de adderte Linier i Multiplicandum
bliver uforandret, som ligger udenfor Planet af Cirkelbuen
i Multiplicators Mærke, saa at 7 ,, (cos. 1 + & sin. 1) =1,
e , (cos. II + 7 sin. 11) — €, (x + ny + zz) ,, (cos. HI + e sin. I)
= ny + (x + ez). (cos. II + esin. 111), ligesom allerede til-
forn er sagt $ 28—32.

Hvordan omtalte Æqvation (s,, I' ,, IT' ,, IN" , IV"... N
— s) kan tiene til et sphærisk Polygons Oplosning, indsees
af følgende:

Lad Kuglen qhow (Fig. 6) kunne væltes om Axelen zen
af den horizontale Storcirkel hpow, | og om Axelen pcy af
den verticale Storcirkel qrov, uden at disse to Cirklers Po-
sition derved forandres, og lad samme Kugle

1) Stilles saaledes, at i Polygonet ı 11 II IV v VI den

sidste Sides sidste Punct falder i Horizontens Pol x,

og samme Sides Forlængning falder i Verticalens Qva-

drant xo Fig. 6.

2) Lad derpaa Kuglen væltes om Horizontens Axel ren
de horizontale Grader 1, saa falder Siden 11 i Veticalen

mellem 7 og o, ligesom Fig. 7 forestiller.
3 — Archiv for Math. og Naturv. B. XVIII. No. 1.
Trykt den 29. Mai 1896.

34

Caspar Wesssel.

3)

4)

Naar nu Kuglen væltes om Verticalens Axel per de

verticale Grader 11, da gaaer hele Siden 11 igiennem
Horizontens Pol 7, og Kuglen faar Positionen Fig 8.
Væltes den nu atter om Horizontens Axel de horizon-
tale Grader 111, kommer derved Siden rv til at ligge
i Verticalbuen mellem o og 7 (Fig. 9).

Og bliver man saaledes ved at omvælte Kuglen de ver-
ticale Grader IV, de horizontale v, de verticale vi &e.:
faaer den tilsidst samme Position som den allerførst
havde No. 1, Fig. 6.

I det at Kuglen omvæltes vexelviis paa Horizontens
og Verticalcirkelens Axel, beskriver ethvert Kuglens
Punct først en horizontal Bue, som er Maalet til Poly-
gonets første Vinkel; dernæst en vertical Bue af saa
mange Grader som Polygonets første Side; saa atter en
horizontal, der maaler den anden Vinkel, o. s. f. lige
til at Kuglen igien er kommeni første Position, og hvert
dens Punct, efterat have beskrevet ligesaa mange hori-
zontale Buer, som Polygonet har Vinkler, og ligesaa
mange verticale, som det har Sider, er kommet tilbage
til samme Sted, hvorfra det udgik.

Følgelig naar et Polygons Vinkler og Sider tilsammen
ere af Antallet N, og i Kuglens første Position (Fig. 6)
et af dens Puncter, hvilket som helst, havde til Coordi-
nater de tre Linier, som udgiøre Summen x + ny +

MS) AE COMMISE Sv

"ye ++ N. Endnu maatte agtes

a) At paa Overfladen af Kuglen er, medens den om-
væltedes, af det faste Punct p afridset et Polygon,
hvori første Side er = Vinkelen 1, følgende Vinkel
— Siden 11. følgende Side — Vinkelen nr, o. s. V.;

thi naar Kuglen væltes om Horiozntens Axel, og

Forsøg til Directionens analytiske Betegning. 35

dens ydderste Dele stryge det faste Punct p forbi,
tegner samme Punct paa Kuglens Overflade Poly-
gonets Sider, og, naar den væltes om Verticalens
Axel, faaer hver foregaaende Side sin Inclination
til den følgendes Forlængning, hvilket just ikke er
vanskeligt at forestille sig, skiøndt Polygonet har
maattet udelades af Figurerne 6, 7 &e, for at ei
den ene Linie skulde falde i den anden, og alt blive

utydeligt.

b) Af det faste Punkt o er aftegnet et andet Polygon,
hvis Vinkler ere deels — 90°, deels + 90°; Siderne
ere I, Il, HI, IV,..., N, og Polygonets Æqvation er
Sp In (== Sty IE på pp WO (=D gy EV Sy eco HEG)
» Nye=s. Dog herom maa vere nok sagt, da
denne Æqvation ei i det folgende er brugt. Jeg
maa nu vende tilbage igien til den Formel, som
jeg eengang har lagt til Grund for alle de ovrige,

nemlig:

De en VO NIE Denne; Formel kan

(oa)

forandres paa mange Maader; thi da s er Summen af
Coordinaterne til et bestemt Punct, saa kan isteden for
s sættes hvad for en Linie det skal være, følgelig ogsaa

& 1, nr eller er.

I Formlens første Led kan af de Uniteter, som følge
efter s, hvilken man vil antages for den forste, naar
den folgende tages for den anden, nestfolgende for
den tredie, o. s. f, foregaaende for den sidste, næst-
foregaaende for nestsidste, o. s. v. Antages f. Ex.
første Led at begynde med s,, 11, da bliver Fig. 8
Kuglens første Position, Fig. 9 den anden, Fig. 7 den

næstsidste, og Fig. 8 den sidste, saa at i Følge $ 33,

36

Caspar Wessel.

9)

10)

11)

12)

og paa samme Maade, som før er viist, Ædqvationen

maa livers). eller AVE EVE al. No us

De to nys omtalte Forandringer af /Æqvationen s ,, I’ ,,
II',, t',,...,,N'==s have den Nytte, at hvilken man
vil af Uniteterne r', 11", 111‘, . . ., N' kan elimineres; skal
f. Ex. m1‘ skaffes bort, da forandrer jeg Æqvationen til
Smed SV ENE ss deremersswebten
jeg s— nr, hvorved s ,, 1° bliver = yr efter $ 28
Skal ry‘ udelades, forandres /Eqvationen til s „ IV', Vv’
SNE NE 3, ons sttesı — sr hvorved
s,1IV' bliver efter $ 29 saa stor som er.

Das mr EE NE saaker 1 øse Sone
JV VE Oe Vie Su ll Tree, eller inane ean
Almindelighed borttage af Ædqvationens første Led saa
mange som man vil af de sidste Uniteter, naar alene de
borttagnes reciproqve Storrelser i omvendt Orden sam-
menfoies indbyrdes ved Tegnet (”), og derefter ved
samme Tegn ” forbindes med det andet Led s.

Herved kan i et af Æqvationens Led hvilken Unitet,
som forlanges blive den sidste, og følgelig en Ligning
udbringes, hvori denne Unitet ei findes. Naar f. Ex. i
EVO AUN Nesey MORN INN VIS NW, EO EVE
hele det første Led er = x + ny + ez, men det andet
Led er =ry-+ yy + 43: da er i Folge § 3 ez — 6 1
hvilken Ligning ei findes tv‘; thi iv‘ = cos. IV + qsin. IV,

altsaa, da der mnltiplicertes i første Led med ıv', blev
ez uforandret, § 29.

Den Æqvation, som man finder for den sogte ube-
kiendte u, efterat have paa anførte Maade elimineret de
to andre ubekiendte, som ikke søges, har den Form:

a=hbcos.u-+csin.u; thi man seer let, at den aldrig

Forsøg til Directionens analytiske Betegning. 37

kan indeholde cos.u.sin. u, eller Potenzer af cøs. u og

sin. u. For at oplose denne ZEqvation, kan sættes»
ligesom tilforn er viist ($ 20), = = cot. 1, og cos. (u— V)
__asin.Ÿ acos.v
merc Viena

13) Er Kuglens Radius r uendelig stor, og det sphæriske

Polygons Sider uendelig smaa Dele af Peripherien, da
forvandles det spheriske til et plant Polygon, hvis
Sider ere Sinus af Siderne i det spheriske multiplicerte
med Kuglens Radius. Oplosningen passer altsaa baade

til spheriske og plane Polygoner.

V.

Nu vil jeg forsoge at udlede af samme ZEqvation

($ 37 No. 6)
de sphæriske Trianglers fornemste Egenskaber.
§ 38.

Da Triangelens Æqvation er s ,,1 ,,1T' ,.-., VI =5
($ 37 No. 6), og Progressionens Begyndelse er ubestemt
(§ 37 No. 8): saa kan den begynde med r' eller 11' eller
v', hvis dernemlig antages at første Unitet skal ligge i Hori-
zontens Plan, eller at den skal være cos. + esin. Jeg be-
tegner derfor de Linier i Progressionen, som følge efter vI'
BEE RVs Xe XT Beh SA ab 1, | VAR I x blive
Synonyma, ligesaavel som 11", vir, XIV‘ 0. s. v. Denne
Maade at tælle paa kan ikke forvilde; thi hvilken i Ordenen
Linien er, naar ei tælles længere end til vr. findes ved at
subtrahere VI saa ofte som mueligt fra de dette Tal over-
stigende Nummere. Denæst sætter jeg den Vinkels cos. +

38 Caspar Wessel.

= sin., hvoraf Progressionen begynder, at være (n 11), og
lader n være ubestemt, uden for saavidt at den enten be-
tegner 0, eller et effent Tal. Triangelens almindeligere Æqva-
tion bliver derfor i Følge denne Benævning og $ 37 No 8:

s(n + 1) 5 (0 +17), (0 410) OH IV) s (n+ V)Y »
nm va)’ =.

Forandres denne Æqvation i Overensstemmelse med $ 33 til

Sy (n + 1) ” (n == Im)‘ =8% (n 5 VL ie ” (n + vr D
a unge

findes, i Følge § 35 No. IT, og § 3,

I) cos. (n + 1) — cos. (n + 111). cos. (n + V) — sin. (n +17).
cos. (a +1V). sin. (n + v).

sin. (n + Iv). sin. (n + V)

sin. (n +11) 5
Forandres den til e,„n+n',„e-+m'„(n-+ım)',,
(n Liv) =«, @+vij‘, @+v)', udkommer en
Egqvation liig den $ 35, No. IV, alene at n er tilfoiet
Tallene 1, 17, mr &e., og r antaget—ı. Altsaa, naar

II) sin. (n +1) =

denne Æqvations Led, der indeholde 7, divideres med
sin. (n + 1), bliver:
cot. (n -+ IV). sin. (n

sin. (n + III)

III) — cot. (n +1) = U) IE Gos (ne

III). cos. (a +11).
Forandres den til n,,(n +1) 4 (a +17)" ,, (n + 117)! =
(n+ viy',(a+vy', (n+1V)*, giver den i Følge
SPA No. 77.
IV) cos. (n +11) = cos. (n + Iv). cos. (n + VI) — sin (n + Iv)
. cos, (n + v).sin. (n + vi)
sin. (n + v).sin.(n + vi)
sin. (n + I) å

V) sin. (n + 11) =

Forsøg til Directionens analytiske Betegning. 39

Og endelig naar den forandres til 7 ,, (a + 1)',, (an + 11)!
» (n+111)', (n+1V)', (n+ v)' = 7, (n-++ vi‘, faaes
af det Led, som indeholder =, $ 34, No. IV,
cot (ari): sine (ner)
VI) — cot. (n +11) = or + cot. (n +

IV). cos, (n + 111).

8 39.

I de foregaaende sex /Egvationer forudsættes, n at be-
tegne Nul, eller ethvert positiv effent Tal; men ved at sam-
menligne de tre første med de tre sidste, vil man finde, at
i de første tre kan ogsaa isteden for n sættes n +1, eller
ethvert ueffent positivt Tal; altsaa kan i de tre første
Æqvationer n bemærke Nul, eller ethvert positiv heelt Tal.
Der kan ogsaa isteden for n sættes n + et positiv heelt
Tal, hvilket som helst; man kan f. Ex. sætte isteden for n:
0+3, 1+3, 2+3, 3+3, og saa videre, altsaa n +3.
Hvoraf følger: at, naar i Æqvationen III, § 38 isteden for
n sættes n + 111, forvandles den til

cot. (n + vir). sin. (1

sin. (n + VI)

mv)
. cos. (n + v).

— cot. (n + 1V) =

Folgelig er

th __ cot. (n +1V). sin. (n+ vi) a é
cot. (n + I) = fm) _ cot, (n +V)
. cos, (n + VI),
og denne Æqvation sammenlignet, med /Egqvationen III,
§ 38, giver følgende dobbelte Udtryk af — cot. (n + 1).

: II
cot. (n + Iv).sin. 2 å
I) — cot. (n + 1)= eat (a Hay) in Sty) ie )

- (n-+ iil
ott (ky)
cos. (> ru }
Rae nr VI

40 Caspar Wessel.

efter hvilken Formel -— cot.(n-+ I) faar samme Værdie,
enten man bruger kun de øverste, eller kun de nederste
af de dobbelte Tal.

Ligeledes naar i /Eqvationen IT, $ 38 sættes n + II

isteden for n, udkommer:
sin. (n + VI). sin. (n +1)
sin. (n + IV)

sin. (n + 111). sin. (n + Iv)
sin. (n + VI)

sin. (n + 111) = , altsaa

sin. (n +1) =

af hvilken Æqvation og den $ 38 No. IT følger:
. N an (n+l
sin. (n + IV). sin. (ee
: (nt vi
sin. e he )
Sættes der i /Egqvationen 7, § 38 Tallet n +11 isteden

for n, faaes:

IT) sin. (n +1) =

cos. (n + VI). cos. (n a II) — cos. (n + IV)
sin. (n + vi). sin. (n +11) Å

8 40.

III) cos. (n +1)=

Ved samme Substitution faaes af samme Ædqvation

cos (n + Iv) = cos. (n + VI) cos. (n + II) = sin. (n + vi).
cos. (n+ 1). sin. (n +17),

eller

— cos. (n +1v) + == ae al an) . sin. (n-} Iv) =

sin, (n-+-vI).sin.(n—+-1I).cos.(n--T).

Altsaa, naar denne Æqvations sidste Led kaldes a, cos. (n +1v)

sættes — cos.u, — I = b, og
cos. (n + VI). cos. (n +11)
sin. (n + Iv)

=c: kan i Følge § 20 antages

Forsøg til Directionens analytiske Betegning. 41

cos. (n + VI). cos. (n +11)
sin. (n + Iv) ve
cos. [(n +19) — 4]

cos. V. sin. (n + vI). sin. (n +17)

tang. ) = —

cos. (n + 1) = —

S 41.
Æqvationen I $ 38 er

a u b
ae —— —— —===
cos. (n + I) cos. (n + III).cos. (n + v)
== ===" === ———=" N ——
a b u
u c
å — ——= HET ee
— sin. (n + 111). cos. (n + IV). sin. (n +V),
ee” — —
e u

og naar dennes Termini benævnes ved de under eller over
skrevne Bogstaver a, b, ec, u: da findes, i Folge $ 20,
cos. (n +1) ved følgende formler:

— cos. (n + Iv). tang. en) fe ) Le

sin. Ware a Å ) En Ge DÅ

; o' |
N i
sin. (+
å

cos. (n + I) =

I Følge § 39 No. I er

cot. (n +1V). sin. (å Å =)

5 n—v
Sim: (i > Å

cot. Er . COS. (å ii a

— et. (n + 1) =

42 Caspar Wessel.

cot. (n + Iv) n-+ VI a
sin. ary a x a6 = a
oul Gh

og ZEqvationen sammenlignes med den § 20, da vil let ind-

og naar — cot. (n +1)=4a

sees Rigtigheden af følgende Formler:

tang. (2) = tang.(n + IV). cos. MD:

— cot. (n 4-1) = = (at: SE: 2) cos (0)

=

§ 43.
Sættes der i de to sidste Æqvationer $ 41 n +11 iste-
den for n: bliver

cot. ¢ = — cos. (n ++ vi). tang. (n + v), og
À COS. (n + UI). sin. ©
sin. (a + + = rn

Men sættes n +1v isteden for n, bliver
cot, 9 = — cos. (n + 11). tang. (n + III) og

sin. (a +2) + p)= EE an a

Altsaa

COS. N
ee,
ie (at | Je COS. (mun) aa

DNS ae n + III
cot. )=— COS. (pumas) tang. re)

Forsøg til Directionens analytiske Betegning. 43

8 44.

Ved at sætte n +v isteden for n i de to sidste Æqva-
tioner § 42, faaes

sin. [(n + 1) + 9] = — cot. (n + vi). tang (n + 1).sin. 9, og
tang, © = tang. (n + III). cos. (n +11);

Men ved at sætte n +1 isteden for n, udkommer:

sin. [fn +1) + 9'| = — cot. (n +11). tang. (n + vi) . sin. 9', og
tang. © = tang. (n + v).cos. (n + vi);

hvoraf folger:
à (n +1) + 9! n +11 ae)
sin, ke en ae cot. Å I) «tang. |, Um)
sin. es ), og

2 | PRÉSENT n + VI
tang. ie ) = tang. & ae å . COS. G dog )

Sin.” I (n I 1)=
sin.2|(n +11) + (n+Iv) + (n+v1) |. sin. [fn +11) +(n+v1)—1-+)],
sin. (n +11). sin. (n+ vi) ?
cos.(n+-VI).cos.(n+ II) — cos.(n+IV)

sin. (n + vr). sin. (n + 1)
og 2 sin? 1 (n +1)—1—cos.(n +1), $ 19 e. Altsaa

thi cos (n+1)—

, 839 No III,

Pee nda) ad cos (n--vI) . cos (n+11) —cos.(n-+-Iv)

sin. (n + vI).sin. (n +11)

, eller

2 sin.” 4 (n + 1) =
sin.(p+vi).sin.(n+11) — cos.(n+VI).cos.(n+II) + cos.(n+1v)
sin. (n + vi).sin.(n +11)
eller, i Folge § 19 8,

44 Caspar Wessel.

__ cos. (n + Iv) — cos, (a + vi) + (1+n))
sin, (n + yi). sin. (n +11) Å

og da cos. b— cos. a=2 sin. å (a +b). sin. å (a — b),
§ 19 7: saa bliver
sin.? 4 (n +1) =
sin.1 [(n+1v) +(m+v1) +H(o+17)] . sin} 1 (m+v)-Hn+n)-(n+v 1
sin. (n + v1) . sin. (n +11)

8 46.
Cos.? I (n +1) =
sin.d[(n+Iv)+(n+1)—(n+vI)]. sin.3[(n-H1v)- (nt) tat],
sin. (n +17). sin. (n + vi) é
thi 1 + cos. (n+1)=2c0s2?1(n+1), § 1 9 d; men efter.
Æqvationen III § 39 er

1 + cos. (n +1) =
sin.(n +17). sin. (n+ vi) + cos (n+11).cos.(u +vr)— cos. mer i)
sin. (n + Ir). sin. (n + vi)

altsaa
2cos.21(n +1)= cos. |(n +11) — (n--v1)| — cos.(n+1v)

sin, (n + 11) . sin. (n + vi)

, 8195.

Følgelig, da cos. b — cos. a=2 sin. å (a + b). sin. å (a — b)
SIR), aa rer
cos? I (n +1) =
sin} (ari) +(n+1v)— (n+v1)] . sin.4|(n-+Iv)—(n-F)+(n-+V1) I
sin. (n —+- II). sin. (n +v1)

SAT

— tang. å [(n +1) — (n+ ım)] = == : ce = på 7 a = =

tang. L(n + v), og

Forsøg til Direktionens analytiske Betegning 45

m +19) — (n + wm]
yaw) + +)

— tang. 3 [fn +) + (+ me?

pol ij

hvilket kan bevises saaledes

tang. I (n + vy),

I) Ved at addere og subtrahere sin. (n+ 1), forandres
Æqvationen

5 sin. (n
sin. (n + IIT) =

— 1). sin. (n + vr)
sin. (n +1V) Zu

til de to folgende
a) sin. (n + 7) — sin. (n + 111) =
sin.(n—+1).. sin. (n+1v) — sin. (n+1). sin. gt)
sin (n + Iv)
b) sin. (n + 1) + sin. (n + 11) = |

OG
og

sin (n+1). sin. (n+1v) + sin. (u+1). sin. mV)
sin, (n + Iv)

Af Æqvationen I, § 39 udkommer, ved at sætte nr
isteden for n, Æqvationen

am cos. (n Maes + v) a
sin. (n + IV). cos. (n + vi)
a sin. (n + v). sin. (n + vi)

Naar dennes Led multipliceres med Ledene i Æqvationen

name ge et SR bliver

cos(n+1v). sin(n+v1). sin(n+1). cos(n+v)
een) sin. (n + Iv).sin.(n+v) Er
cos (n-+ vr). sin. (n +1)
men da

sin. (D + v) ©

46 Caspar Wessel.

em) __ cos. (n + vi) eee) . sin, (n +1) a
sin.(n + vi) cos.(n + ty). sin. (n + 1)
sin. (n +1Vv). sin. (n +V) AS

saa er Summen

— cos. (n + 1) — cos. (n 4+ 111) =
[cos.(n+v) + 1]. sin.((n+ıv)+n-+vn]| sin (n+1,
sin. (n + Iv) 3 sin. (n+V)

C

DE

og naar divideres Formelen q@ med Formelen c, faaes:

Slim, (in 951) GNT (=
cos. (n +1) + cos.(n + nn)
sin. (n +v) sin. (n + Iv) — sin. (n + vi).
1 +cos.(n+v) * sin. [(n +19 + (n+ vn] ’

sin. (n +1) — sin. (n +17) _
N cos. MEN) cose (a em) ee
tang. I [fn -)— (n+ım], $ 19 I,

ee eee ce
°8 1 + cos. Gas) mn Te SAV) RS LY jie

Altsaa — tang. 1[(n +1) — (n + 117) |=
tang. I (n + v). [sin. (n + Iv) — sin. (n + vr)]
sin. [(n + Iv) + (n + vn]

’

og da sin.(n + Iv) — sin. (n + vi) =
2cos1 [m+ıv)+(n+vr)] A sind[m+v)- (n+vn)], $ 19%,

, 20c0s.5[n +19) tar Vy
og sin. [(n + 1v) + (n + VI)| ==

1 \ *
ep

Forsøg til Directionens analytiske Betegning. 47

saa er — tang. F[(n +1) —(n +11) |=
tang. $(n + v).sin 3[(n +1v) — (n +vn)]
sin. Ha + 1v) Fa Fv]

IT) Ligeledes findes ved at dividere Formlen d med Formlen ç:

sin. (0s Dia sin (AF)
eos, (n +7) + cos.(n +11)

sin. (n + v) sin. (n -- Tv) Sin. mn vi)
1+ cos.(a+v)° sin [n+1v + (0 +vn]

— tang $[(n 41 +(n +n0)$ 19 %

sin. 7
og naar isteden for Sean De sættes tang.4(n-+-V),

1+ cos. (n+ v)
§ 19 f, og isteden for sin, (n + tv) + sin. (n + vi) sættes

2 sin. F[(n +1v) + (n + vn]. cos. L{(n +1v) — (n + vn],
§ 19 g, udkommer

tang. I (n + v).
2 sin. F[[n+1v) + (n+vn].cos.4[(n+ıv) —(n+vr)]
sin. [(n + Iv) + (n+ vi)]

— tang. }[(a++ + (+m);

2sind(n tw) +(n + vo] _
sin. [[n +19) +(0+ vn]
1
cos. å [(n + Iv) + (a+ vi)]

men da

u Daleeıs 197e:

saa er — tang. 3 [(n + 1) + (n 1 111) =

JO en). Gen)
u cos. 1 [(n + 1v) + (n+ vn]

48 Caspar Wessel.

§ 48.

Fre alle tre Vinkler i en sphærisk Triangel oivne, findes
Siderne ved hvilken man vil af folgende Formler, naar n
antages — 0, 11, eller mv.
cos. (n + I). cos. (n + IT) — cos. (n + vy)

sin. (mn + 1). sin. (n +111) <
$ 39 Æaqv. HL.

D'cos (na m)=

cos: [n n+ v)— |
[eos (n+11) = cos.).sin.(n--1).sin (09-11)? > og N
en Cos | 8 40.
ne dæ oe (n + 1). cos. (n EI)
| a sin, (n + v) Å

ITT) sin? 1(n +1) =
sind [(n+111)+(n+v)+(o+1)]. sind [mH + (nt) (n+v)]

sin. (n + 111). sin. (n + 1) ;
§ 45.

Sættes i den første af disse tre Formler

a) n + 1 = 90", bliver cos.(n ++ 11)=
— cos. (n + V): sin. (n + I).
b) n+11=90", bliver cos. (n + 11) = |
—- cos. (n + v): sin. (n +1).
c) n + v = 90°, bliver cos. (n + 11) =
cot. (n +1). cot. (a + II).
§ 49

Af to Vinkler og deres fælles Side givne bestemmes
A) Den givne Sides modstaaende Vinkel med Formlen IV,
eller V, naar settes n—0, eller 11, eller rv.
cos(n +11). cos(n-V)— sin(n-FI1I).cos(n--TV) .

sin, (n + v)
$ 38 ZEgvationen I.

I V)cos(n + 1)=

: Forseg til Direktionens analytiske Betegning.

a i 49
. ((nt+n)+0' n+v
all ie . COS. Ga)
cos.(n-+1) = Say > ,
V) sin. (6 ) S 41.

S
co! nv
[oot. (å ) = — cos. (nv). tang. (ea): |
1 Æqvationen IV giver

a) n + 11= 90°: cos (n + 1) =
: — cos. (n + Iv).sin.(n + v).
b) n+ v = 90°: cos.(n +1) = |
— cos.(n + IV). sin. (n + 111).
6) n-+ vi= 90°: cos. (mn 1) —
cos. (n + II). cos. (n + v),
B) De to andre Sider findes ved hvilken som helst af føl-

gende Formler, hvori ligeledes

maa antages n=0
eller 11, eller ıv.

VI) — cot.(n+11) =

cot.(n+v). sin. (ir)
sin.

| n—Iv nr
eot. 6) . COS. ( nr \ § 39, Æqv. 1.

a eg
—cot.(n+11)— = cot ("7") ‚og
VII) sin ( a) § 42.

= (2) = tang. (nv). cos. (ae).

4 — Archiv for Math. og Naturv. B. XVIII No. 1.
Trykt den 29. Mai 1896.

50 Caspar Wessel.

—tang (pu) av) Aa +1)]
sin.3{(n-+-v)—(n-++1
bang EV na av) OE)

— tang. 3 (a +1) +a+1v)] = Å

VII):
nm san]
tang.5(n vi). 2H) ++)

Er i den VIte Formel
d) n + 111= 90", bliver — eot. (n + 0) =
cot. (n + v): sin. (n + Iv).

e) n + = 90°, bliver — cot. (n + 11) =
cot. (n + v). sin. (n + Im).

f) niv =90", bliver — cot. m 4 11) =
n-+v n +I
co Å a. ). en «Å al un):
g) n +1 = 90°, bliver — cot. (n 4 1) =
cot. (n + V) : sin. (n + vi).

h) n + vi= 90°, bliver — cot. (n + I =
cot. (n + v). sin. (n +1).

§ 50.
Af een Vinkel og to Sider, hvoraf den ene staaer lige
over for den givne Vinkel, findes
A) Den tredie Side ved følgende 7ZXde Formel, naar sættes

n==(, 11, eller rv.

en
cos er
nn Ct ee

IX) 8 43.

Forsøg til Directionens analytiske Betegning:. 51

2 naar seettes
1 Noloe .
Er bliver i Følge nan

a) n +111= 90°, cos. (n + 11) =

cos. (n + VI)
cos, (n + Iv)’ NG a Ne

b) n+1 = 390", cos. (n + 11) =

cos. (n + Iv)
cos. (n + vi)’ § 49 ” n HII.

c) n+ 1v= 90", sin. (n + 11) =

cos.(n+ vi) 4
cos.(n +11) > pe

d) n+ vi= 90°, sin, (n + 11) =

cos. (n + Iv)
cos. (n +1) , 9 £9 a, n=- IM,

B) De to givne Siders indsluttede Vinkel udledes af følgende

Formel X, naar sættes n—0, 11, eller tv.

tr EE Li (ag

(n+1)+¢ n-+ VI
SEN ol por
x) tang. nl sin. o) og; 8 44,
nv n+yI
tang. Ee ) = tang. Re) . COS. can N
; å naar for
Er bliver LO EG

e) n+-111=90", cos (n+r) =
— cot.(n+vi).tang(n+11), $49/,n+1v.
f) n+v= 90", cos.(n+r) =
— eot.(n+11). tang(n+v1), $49/.
g) n+v1=90", sin.(n+1)=
— cot (n +11). tang(n+v), S49,
h) n+11= 90°, cot.(n+1) =
— cot.(n+v) cos(n-+vi), $49 /, n+-117.

52 Caspar Wessel.

C) Den anden givne Sides modstaaende Vinkel sluttes af
Formelen XI.
n + =)

sin. (n + Iv). sin. >
XI) sin.(n +1) = | (nr)

Sn Wi
sin. n IL ie:
§ 39, Æqvationen II.

8 51.

Naar i de tre foregaaende Opgaver, § 48, 49, 50 isteden
for Sider sættes Vinkler, og isteden for Vinkler sættes Sider,
oploses de ved at antage i de anforte Formler, n at vere

— 1, eller 111, eller v, § 39.

8 52.

Er i en sphærisk Triangel Siderne mindre end to rette
og positive, da kan ogsaa Vinklerne antages at være af
samme Beskaffenhed; thi at den første Vinkel kan tælles
positiv, at være mindre end to rette, viser $ 37, Fig. 6;
men at de to andre Vinkler er af samme Art som den

ferste, sees af Formlen

å ou
Sin. IV. SIN. ( à
S50 TE

sin. I =

I det følgende forudsættes Vinkler og Sider at være mindre
end 180°.

8 53.
En sphærisk Triangel bestemmes fuldkommen, hvis

Siderne ere mindre end to rette, af tre givne Vinkler; tre

Forsøg til Direktionens analytiske Betegning. 53

givne Sider; to Vinkler og disses fælles Side; eller to
Sider og indesluttede Vinkel, hvilket sees af Formlerne
$ 48, 49, og Sætningen $ 51.

8 54.

Af foregaaende Formler følger ogsaa, at ligestore Vinkler
staae lige over for lige store Sider, og omvendt; f. Ex. naar
i Formlen IV § 49 sættes 1=111, da er Iv=v1I; thi cos. 1=
COS. III . cos. V — sin. IIT. COS. IV. Sin. V, Og cos. III = COS.V.
cos, I — sin. v.cos. VI. sin. 1. (Den sidste Æqvation faaes af
den første ved at forøge Tallene med 1).

$ 55.

Den større Vinkel modsættes den mindre Side, og om-
vendt. Følger af Formlen $ 47
sin, :

— tang. I (I — 111) = tang. IV. ae

(Iv — vi).

(iv + v1)’

thi naar I - III er negativ, maa Iv — VI vere positiv,

wie | Lo}

§ 56.

Hver to Sider ere tilsammen større end den tredie, og
alle tre Sider tilsammen mindre end fire Rette; thi i Følge
§ 45 og 46 er

sin. (Iv +11 — VI). sin. em å
sin. II. Sin. VI

sin. I (Iv +11 + vn). sin. dt

sin. VI. sin. IT

eos * (1) —

sin.?4 (1) =

men sættes 1 første Æqvation vI > IV +11, saa maa ogsaa
IT være større end Iv + vi; thi ellers blev cos? $(1) negativ;

54 Caspar Wessel.

men det er umueligt at vi kan være større end 1v +11, naar
ı > rv + vi; ej heller kan vi være = 1v +11; thi da blev
cos.*1(1)=0. Følgelig maa vi være < Iv +11, og i Almin-
delighed to Sider større end tredie Side; altsaa er i anden

/Eqvation sin. ] (vr + II — Iv) positiv; altsaa ogsaa sin. Å (Iv +

aoe < 180° (§ 52), og 1v+

1 + vi) positiv; følgelig

I + yr er mindre end 360°.

§ 57.

Ligeledes bevises at de to Vinkler ere tilsammen storre
end den tredie, og Summen af alle tre mindre end fire Rette,
hvilket ogsaa folger af § 37, No. 6 a, og § 56.

§ 58.

Naar man paa en Halvkugle fra et Punct C (Fig 12)
mellem Grundeirkelens Pol P og dens Omkreds trækker
Storbuen CB ned til Grundens Peripherie!), da er CB mindst,
naar den endes i r, hvor Perpendicularen PC forlænget skiær
Grundcirkelens Omkreds; derefter voxer den fra Cr til at
den bliver = 90"=r1Q = CQ, og endnu derefter lige til at
den bliver = 180° — Cr (= 0), saa at B falder under QR,
naar CB er stump; men er CB spids, falder B over QR.

Thi lad CBq betegnes ved 1, Hypotenusen BC ved 1,
Catheten Cr ved 1v, og rB ved vr: saa er i Følge $ 49 ¢
(nemlig naar sættes 1 isteden for n) cos.II= cos. IV. cos. VI,
eller cos. BC — cos. Cr. cos. rB, hvoraf Paastandens Rigtighed
letteligen indsees.

1) Rastners Matlrematikens Begyndelsesgrunde, oversat af Hr. Pro-
fessor Wolf. Den sphæriske Trigonometries anden Sætning,
Pag. 517.

Forsøg til Directionens analytiske Betegning. 55

Imedens rB voxer fra 0 til 90°, og CB fra Cr til CQ
(— 90°), voxer Vinkelen CBq fra 90° til 180°—Cr; men
derefter, naar rB voxer fra 90° til 180°, og CB fra 90° til
180° — Cr, aftager CBq fra 180°— Cr til 90°; thi naar i
§ 49 h isteden for n sættes v, bliver v — 90°, og — cot 1 —
cot.Iv Å sin vi, eller — cot. CBq = cot. Cr.sin. rB, af hvilken

Formel sætningens Beviis er let at udlede.

$ 59.

Antages en Triangels Sider (1, Iv, vi) at være mindre

sin. IV . Sin. V

($ 50

end to Rette, og i ZÆqvationen sin.1= :
sin. II

XI) Buerne tv, v, IT ere skieve: da viser folgende Tabel,
i hvilke Tilfælde den sogte Vinkel ı er spids, stump eller

tvetydig.
Er nemlig

et < 180° — Iv tvetydig
of V stump, Iv stump, og IT > 180° — Iv)? saa er I spids ib
3 à £ > 180° — iv tvetydig
iy vspids, Ivspids, I <4 180° — 33) - -1 a
4 vstump, Iv spids, II sn) - -1I ENE)

F 7 tydi

| vspids, Ivstump, II te a Pr Mo)

Nr ny, og dajer1= v
10) 11+ 1v = 180", - 1—=180" — v.

Beviis. Da ingen af Siderne i Triangelen ABC (Fig.
13—18) ere større end 180°, saa falder hele Triangelen paa
en af de Halvkuglers Overflade, som afskiæres ved Planet
af Siden AB (=v1), og da Siderne 11 og tv ere skieve, saa
modes de i et Punct C udenfor Grundeirkelens ABD Pol P.
Man kan altsaa fra Polen P uddrage Storbuen PC til begge

56

Caspar Wessel.

Sider, og ligeledes dens Perpendicular QPR, til at begge

naae Grundeirkelens Omkreds. Disso to Halveirkler fore-

stilles i Figurerne 13—18 ved de to rette Linier rq og QR.

1) Fordi 1v er stump og 11 spids, falder A (Fig. 13) under

QR, og B saavelsom det yderste Punct D af Halv-
cirkelen ACD falder over QR, $ 58. Men da Buen
180° — 1v (= CD) forudsættes at være større end 11
(= CB): saa maa denne falde imellem Cr og CD, eller

: ogsaa imellem Cr og CQ, § 58, og maa paa begge

=]

—

—

—

Steder kunne have samme Størrelse. I det ene Til-
fælde bliver 1 spids, i det andet stump; altsaa er I
tvetydig. |

Da Buen 11 antages > 180°— 1v, eller 11 > CD (Fig.
14), saa er CDR < CBA (§ 55), eller v< 180° —1;
men v antages stump, altsaa er I spids.

Iv er spids og 11 stump, følgelig falder A (Fig. 15) over,
men B under QR. Og da Buen 11 > 180° — 1v, kan
den i Følge $ 58 have samme Størrelse, saavel mellem
CD og Cq, som i ligestor men modsat Afvigning fra Cq.
I kan altsaa være spids eller stump, $ 68.

Efter Betingelsen er 11 < 180° — 1v, eller 11 < CD
(Fig 16); altsaa er i A CBD CDQ > CBA, eller v >
180° — 1 ($ 55); men v er spids, altsaa 1 stump.

IT og IV antages begge spidse; altsaa ere B, A og C
(Fig. 17) paa samme Side af QR (§ 58); og da antages
II < 1v, saa kan B falde paa begge Sider af Cr; paa
den ene Side bliver 1 stump, paa den anden spids ($ 58),
altsaa er 1 tvetydig.

) 11 > Iv, altsaa v < 1 ($ 55); men v er stump, altsaa

I stump.
Da 11 og 1v ere begge stumpe, saa overskiære de Per-
pendieularen QR (Fig. 18) imellem Puncterne Q og R

Forsøg til Directionens analytiske Betegning. 57

($ 58). Og da 11 > 1v, saa kan Buen 11 enten ligge
imellem Iv og Cq, eller paa den anden Side af Cq.
Altsaa Vinkelen 1 enten være spids eller stump ($ 58).
8) Naar 11 < Iv, er v > I (§ 55), altsaa, naar v er spids,
bliver ogsaa I spids.
9) n=nv giver v=1 ($ 44).

10) 11 +1v= 180", giver 1= 180" — v, fordi Supplementerne
til 11 og Iv dame tilligemed AB (Fig, 19) en anden /\
ABC' hvis Vinkler og Sider ere saa store som de i
/\ ABC (§ 53).

8 60.

Forudsættes der ligesom i foregaaende $ 59 at Tri-
angelens Sider (II, Iv, v1) ere <j 180°, men i /Eqvationen sin, 1 =
sin. IV. Sin. v :
EE ($ 50, XT) to af de givne Stykker (vy, Iv, II)

er rette: da er

1=180" — ıv, hvis v og 11 ere rette, (Fig. 19).
D DUT, MEN Orvik erefrette
OR 22 117 op it ere rette.

Er derimod kun et af de givne Stykker ret; da er enten

>} vret og IV | Zu) hvoraf følger ı er ( a) eller
if v spids, tv ret, og II ke Zr (ea)
À v stump, Iv ret, à og II Pee ices Teneo ae }
IR spids, Iv (ia) ogure, - - - Ier en)

10) vstump, IV el OS TEE = - I er aaa

58 Caspar Wessel.

Beviis. No. I og 2 følge deraf, at den større Side
staaer lige over for den mindre Vinkel (§ 63).

No. 3 og 5 ere umuelige; thi naar Iv er ret, kan v og
11 hverken være begge spidse, eller begge stumpe, fordi
— cot. I= cot. v sin. III ($ 49 e).

I 7, 8, 9, 10 ere 1 og v af forskiellieg Slags, fordi naar
11= 90" er — cot. 1v=cot.1. sin. 111, hvilket følger af § 49 h,
naar antages n—II.

No. 4 og 6 kan bevises saaledes: Enten ir er stump
og v spids, som i No. 4, og i /\ ABC Fig, 20, eller 1 er
spids og v stump, som No. 6, og i /\ACB': saa kan der
formeres af 11 tilligemed Supplementerne til ıv og vI en
anden /N A'BG, eller A'B'C, hvori 11, 1v og v beholde samme
Størrelse; men Vinkelen 1 forandres i sit Supplement.
Følgelig kan der af samme Data 11, Iv, v dannes to for-
skjellige Triangler.

S 61.

I Følge $ 37 No. 6 a kan enhver Triangel forvandles
til en anden, hvori Vinklerne ere den forrige Triangels Si-
der, og Siderne den forriges Vinkler, Ordenen forresten
uforandret. Følgelig naar af vi, v, 111 givne skal findes 11
sin. V. sin. VI

efter Formlen sin, 11—= :
sin. III

: kan det Givne og Søgte

betegnes ligesomi § 59, 60, og de der anførte Regler ogsaa

i dette Tilfælde anvendes.

8 62.
Da Formlerne LY og X § 50 ere udledte af en Æqva-
tion, den indeholder baade Cosinus og Sinus af den søgte

Bue: saa kunde formodes at de ikke skulde, som Æqv. XT,

Forsøg til Directionens analytiske Betegning. 59

$ 50, give det Søgte nogen positiv Værdie, som var mindre

end 180°, og ei stemte overens med Triangelens Data, naar

disse vare alle positive og mindre end to Rette; men for

herom fuldkommen at overbevises, sætter jeg:

1) At n+ © er positiv, mindre end to Rette, og en Værdie

==

af n +11, der ved Hielp af Æqv. IX, § 50 er beregnet
af de Data: n— 111, n+1v, n+vr. Dernest slutter
jeg, at i en Triangel, hvori gives W--ır, n+ nr og
n—-ıIv, og hvori det som staaer lige over for n+ 1
kaldes n + vr, er i Følge $ 49 I Vde /Egv. cos. (n +vr)=
cos. (0 -+ Ir). cos, (n + Iv) — sin. (n +11) . cos. (n + II.
sin. (n + Iv); men den samme Værdie faaer sos.
(n + vi), naar i Æqvationen sin. [m +11) + 9] =
eh sin o ($ 50 LX) Sinus til Summen ud-
trykkes ved Parternes Cosinus og Sinus, derefter divi-
deres med sin. +’, og tilsidst sættes — cos. (n + 111) K
tang. (n —- Iv) isteden for cot.¢'. Følgelig bliver n + VW =
n-+ vr, og altsaa kan den beregnede Værdie n + IT,
og de givne Stykker n +11, n + 1v, n + vr tilhøre en
og den samme Triangel.
Ligeledes antager jeg i Xde Æqv. $ 50 at n +T er en
Værdie af n Lt, tillige at den er positiv, mindre end
180°, og beregnet af de Data n+, n + v, n + vi;
derefter slutter jeg i Følge $ 49 Æqvat. VI, at i en
Triangel hvori gives Wr, n+ v og n--v1, og hvori
det n+v modstaaende Stykke betegnes ved n+, er
Au nn u) + cot. (n + vi):
cos.(W-+T), eller ved at dividere med cot. (n+ vi),
cot.(n+v). sin. +T) |
~ cos. (n + VI) |

— cot. (n- IE) =

— cot m ir). tang. (n + viy=

60 Caspar Wessel.

cos. (n--T); men denne samme Formel udkommer for cot.
(n + 11), naar i Æqvationen X $ 50 sin. +1) + 9"
udtrykkes ved Cosinus og Sinus af n+r og af 9,
der-efter divideres med sin. ¢’, og tilsidst sættes isteden
for cot. %' dens Værdie; følgelig er n+ 11 =n +11, og
altsaa høre nr, n+un, n+v, n+vwr til samme

Triangel.

§ 63.

Saaledes kan der ogsaa construeret en Triangel, hvis
Sider og Vinkler ere mindre end to Rette, af to i hver af
/Eqvationerne, c, d, g, $ 50 givne Stykker tilligemed det
Sogtes Værdie, naar denne kun er positiv og under 180°;
tillige kan bevises, at det tredio givne Stykke ogsaa tilhorer
den construerede Triangel, følgelig at det Søgtes beregnede
Værdie alletider kan bestaae med de givne Stykker; f. Ex.
i Folge $ 50 c er n+1v = 90°, og sin. mn
lad nu nLir være det Sogtes Verdie, og af n+,
n—+1v og n-+11 lad construeres en Triangel, hvori det som
staaer lige øver for nr kaldes n+ vr: saa er cos.
(n + vr)=— sin. (1 +17). cos. (n +11) § 49 b; men cos.
(n+ vi) er ogsaa ——sin(n +17).cos.(n +11), $ 50 c;
altsaa n + vin + vr.

Jeg tilføier endnu følgende, for at vise, hvordan de i
30te og 3lte § antagne Directionstegn kunne anvendes til
at udtrykke en Ædqvation for retlinede Polygoner, hvis Sider
udstrækkes i forskiellige Planer,

Forsøg til Directionens analytiske Betegning. 61

8 64.

Et Polygon af omtalte Beskaffenhed er ubestemt, naar

det har fire Sider af ubekiendt Længde.

Beviis.

1) Lad de fire af Længde ubekiendte Sider følge efter

hinanden, og vere ab, be, ed og de, Fig. 21. Hvis
da Puncterne a, b og ce ere i en ret Linie, kan ab for-
kortes, og cb ligesaa meget forlænges, uden at disse
to Liniers Direktion, eller de ovriges Direction og
Længde paa nogen Maade forandres. Altsaa ere de to
Polygonets Sider i dette Fald ubestemte.

Er hverken abe eller cde en ret Linie, men abe er
i samme Plan som ede; da kan i dette Plan udenfor
Punctet c, drages med be og ed Paralleler, som skiære
ab og de. Altsaa er ogsaa i dette Fald Polygonet
ubestemt.

Er Triangelen abe ikke i samme Plan som Tri-
angelen cde; da maae dog disse Trianglers Planer
skiære hinanden i en ret Linie dragen igiennem Punctet
c, og fra Puncter i denne Linie, udenfor c, maae kunne
trækkes med ed og be Paralleler, som skiære ab og de.
Altsaa bliver endnu Polygonet ubestemt.

Siderne af ethvert retliniet Polygon kan man give
hvad Orden man vil, uden derved at forandre deres
Sum, Direction og Længde, $2. Altsaa, dersom ab, be,
ed og de ei følge efter hinanden i uafbrudt Orden,
ligesom i de foregaaende Beviis er antaget: da kan
man forestille sig et andet Polygon, hvori Siderne ere

de samme, men de fire af Længde ubekiendte ere i et

62 Caspar Wessel.

sammenhængende Følge. Og da nogle af disse fire
kunne i denne Orden have uendelig mange Værdier
efter første Beviis: saa maa de ogsaa kunne have
ligesaa mange, naar de igien omsættes 1 forrige
Orden, § 2.

S 65.

I ethvert retliniet Polygon, hvori Siderne ei ligge alle
i samme Plan, forudsættes, hver Side at begynde der, hvor
foregaaende ophører, hvorfor ogsaa Summen af dem alle
bliver — 0 1 Følge § 2. Dernest antages, at Længden af
første, anden, tredie, , . ., mte eller sidste Side betegnes

ved et Mærke af samme Orden i Rækken la, (Tv, iv,

viv, ..., (2m—n)v, og Siderne selv i den Orden, de
folge hinanden, ved de uefne Tal 1v, mv, vv, vouv,..,.
(2m—1)" med en tilfoiet Toddel øverst til høire Haand
for at skille Siden fra Vinkelen, som Planet igiennem samme
Side og foregaaende gior med Planet igiennem hiin og fol-
gende Side,; thi disse Planernes Vinkler betegnes ogsaa
ved Tallene)1, 1, v, ... ., 2m); saa at © (Rig 22)Fer
de to Planers Vinkel, der overskiære hinanden i Linien 1,
eller Vinkelen mellem Planerne CDA og DAB; 11 Vin-
kelen mellem dem, der overskiære hinanden i Linien nm,
eller Vinkelen mellem Planerne DAB og ABC, o. s. f.

(2m-—-1) er Vinkelen, som Planet igiennem sidste og første

Side gior med Planet giennem sidste og næstsidste.

End videre antages, at Vinkelen, som hver Side af
viger fra foregaaendes Forlængning, betegnes ved det efne
Tal 11, Iv, VI, . . ., eller 2m, hvilket er een Unitet større

end foregaaende Sides Tal; 11 er nemlig Vinkelen, som

Forsøg til Directionens analytiske Betegnins. 63

wiv afviger fra Forlængningen af 1°; ıv er Vinkelen, som
vy afviger fra Forlengningen af mv, 0.8. f, 2m er Vin-
kelen, som første Side ıv afviger fra sidste Sides (2m—1)v
Forlængning.

S 66.

Alle disse saavel Planernes som Sidernes Vinkler kan
man antage for positive, og efter eget Tykke fastsætte, om
en Sides Afvigning fra foregaaendes Forlængning skal tages
for større eller mindre end to Rette. Men efterat dette er
fastsat, bliver det ei længere ligegyldigt, hvordan Planernes
Skraahed skal maales, om ellers Reglerne for disse Poly-
goners Opløsning skulde giælde for alle Tilfælde.

8 67.

Skal Planernes indbyrdes Hældning efter een og den
samme Regel maales, maa man forestille sig tre af Poly-
gonets Sider, der følge i sammenhængende Rad efter hin-
anden, ligesom i Fig. 23 Linien fra a til b, den fra b til c,
og den fra e til d; derefter drage fra midterste Sides be
sidste Punct e en Parallel cf med foregaaende Side ab;
beskrive om samme Punct ¢ som Centner fra Parallelen cf
til midterste Sides Forlengning eg en Cirkelbue fg, der
maaler den Vinkel cbe, som midterste Side afviger fra fore-
gaaendes Forlængning be; ligeledes om samme Centner og
* og med samme Radius en Cirkelbue gi fra midterste Sides
Forlængning cg til følgende Side cd. Den spæriske Vinkel
igh, som den sidst beskrevne Bue gi afviger fra Forlæng-
ningen gh af den første Bue fg, bliver da saa stor som

Vinkelen, Planet igiennem midterste og følgende Side af-

64 Caspar Wessel.

viger fra Planet igiennem midterste og foregaaende, eller
saa stor som Planets bed Afvigning fra Planet abe. Og
denne Vinkel maales paa den Maade, at, naar man paa
Sphæren følger Buen fg, og kommer fra f til g, saa gaaer
Vinkelens Maal fra Forlængningen af fg til venstre Haand.
Saaledes kunne disse Vinkler bestemmes, naar man i et
Polygon vil vide nogle af dem, for at kunne beregne de

øvrige.

8 68.

Men er Sidernes Directioner i et Polygon Fig. 22 paa
lidet nær bekiendte, kunne dets Vinkler tydeligere fore-
stilles, naar fra Centret c af Kuglen wpho (Fig. 24) drages
de Radier «X, cB, «G og cD af den Direction, at hver for
sig bliver parallel med Siden af samme Orden i Rækken
Iv, II, vv, VIT”, Fig. 22; thi da faaes ved at drage Stor-
buerne AB. BE, CD og DA et sphærisk Polygon AS CD,
hvoraf Siderne maale det retliniede Polygons Vinkler m,
IV, VI, VII, og de sphæriske Vinkler ere de samme som
Planernes Vinkler 1, 11, v, vir i den retlinede Figur 221).
For et saadant Polygons Vinkler har man altsaa samme
/Eqvation som for et sphærisk Polygon, memes, zu,
ie si in) SU (8 O1) is kan nae loeiacma Gn=
hver ret Linie, og 2m er det retlinede Poligons sidste

1) Efter Tegningen Fig. 24 og Reglen § 67 ere Vinklerne 1! og
vil større, men Vinklerne ı og v mindre end 180°. Atv falder
under Projectionsplanet, gjør at Siden vi synes at ligge til
Høire, da den dog falder til Venstre for den, der paa Sphæren
følger Buen ty fra 9 til ©.

Forsøg til Directionens analytiske Betegning. 65

Vinkel, eller første Sides Afvigning fra den mte (det er
den sidste Sides Forlængning.

8 69.

Nu setter jeg, at Awyhp (Fig 24) er Horizonten, Yrqu
er Verticalcirkelen, A er begge Cirklers fælles Nulpunct;
de horizontale Buer tælles positive til Venstre, og de ver-
ticale positive opad; Radius U= +1, y=s, (r=, og
hver to af disse Radier indeslutte en ret Vinkel, ligesom
tilforn er antaget § 24 og 25. Jeg setter endnu, at Spidsen
af Polygonets XBCD første Vinkel 1 falder i Horizontens
og Verticalens fælles Nulpunct X, og at Forlængningen af
den sidste Side vi falder i Verticalen %v under Hori-
zonten. Dette forudsat, er Radius cv = 7 ,, IV‘, Tr‘, 11°,
r‘,,(—7), og i Almindelighed, hvis det sphæriske Polygons
sidste Side 2m er vertical, og endes i Nulpunctet 9, men
gaaer forlenget under Horizonten, og i denne Kuglens
Position drages Radius c(n+1) til Spidsen af Vinkelen
(m+1), eller til sidste Punct af Polygonens Side n: saa
er samme Radius c(n-+1) = m, 14", (n— 1)", (np —17)*,,

Tepe AT gl ss Å

For at bevise denne Sætning antager jeg den hori-
zontale og den verticale Cirkel for ubevægelige, ligesom i
8 37, og lader Kuglen fra omtalte Position (Fig 24) først
omvæltes 90 verticale Grader, derefter de horizontale Grader
I, saa de vertisale 11, dernæst de horizontale 111, o. s. f,
tilsidst de verticale Grader n. Derved forflyttes Spidsen
af Vinkelen (n +1) saa mange Grader, som Kuglen er
omvæltet, og 1 Følge § 33 forandres derved Radius c(n+1)

5 — Archiv for Math. og Naturv. B. XVIII. Nr. 1.
Trykt den 3. Juni 1896.

66 Caspar Wessel.

først til c(n +1) , 7 derpaa til c(n +1) , n ,, I dernest til
en Em, Lis Wie saa enn Fors
omsider forandres den til c(n +1) , 1, I» Il» OT. >. yy
(n —1)',, n’, og bliver saa stor som n, fordi det sidste Punct
af Siden n, og altsaa det sidste af Radius c(n +1), falder
nu i Horizontens Pol x. Af Aögvationen c(n-+1) ,, 7»
jg SS ge 1 MGS 355
einen) — nr, oe Se NES hyilker
var det som skulde bevises.

8 70.

Efter foregaaende Formel er derfor i Figur 24 c1=1,
en) 5 ESN EET py MIT ET)
o. s. f. Desuden er, efter Betingelsen 8 68, c1 parallel med
Tv, cli med mv, cv med vv, &c., Fie 22. Altsaa er 19 —
c1. 19, mv =o. [119, vv=cv.|vv &e. og (2m—1)9 =
c(2m —1) X (2m — Dy, $ 65, (ved (2m—1)" forstaaes det
retlinede Polygons mte og sidste Side. Videre, da 1v +
mv ve LE . . . + 2@m—n»=0, § 2: saa er ogsaa |1v +
mem vev One). (em nn) 0%0e
naar i denne Ædqvation isteden for Radii crit, cv, cvIL...,
c(2m —1) sættes deres Verdier efter $ 69 og derpaa det
yderste Punct af hver Radius forflyttes 90 vertioale Grader,
udkommer Ægqvationen |1v. 7 + ke gg
TR LEE Ge ct vor. N TI iat
Ma 4, Omen (2m — 11)* „ (2m --111)" „

. 3 11, 1‘=0, hvoraf endnu, om skulde behøves, kan
udelades r' paa den $ 33 omtalte Maade.

Forsøg til Directionens analytiske Betegning. 67

caval

Man har ogsaa for ethvert retlinet Polygon, hvori
Siderne ei lige i samme Plan, følgende to Ædqvationer:

SEE D TE) ely Ve em). == 15, 8 68, og

5) Po g Sent TE PE ine ee
HT gl ae |
. + (@m—ıI)v.n,„ (2m — 11), (2m—11)" ,, ...,

Ten, TR tent Op ore CO?

VAD såg VO AY ay IN ag OO Ay a es

At disse Æqvationer maa kunne forstaaes uden Hielp
af det foregaaende, vil jeg her igientage Tegnenes Be-
tydning.

Siderne tælles saaledes at den foregaaende ophorer der,
hvor den folgende begynder.

Polygonets første, anden, tredie, . . ., mte eller sidste

Side betegnes efter Ordenen ved 1°, IHv, vv, VII", . ..,
(2m —1)’, Fig. 22. |

Siderues Længder ved lıv, ze, Bee,
en

Hver Sides Afvigning fra foregaaende Sides Forlæng-
ning ved et effent Tal 11, tv, vi, ..., eller 2m, som er
een Unitet storre end det uefne, der tiener til foregaaende
Sides Meerke.

Vinkelen, som Planet igiennem den midterste og fol-
gende af de tre sammenhængende Sider, afviger fra
midterste og foregaaende Plan, betegnes ved det uefne Tal
I, IH, v, &e, eller (2m — I), der tilhører den midterste Side.

Alle Vinklerne ere positive. Om de skal være større
eller mindre end to, Rette, sees bedst af § 66 og 67.

68 Caspar Wessel.

Vinklerne I, IV, VI . . ., 2m maales i Verticalen,
eller i en Cirkel, der staaer sænkret paa Horizonten, hvori
Vinklerne 1, II, v, VIL, . . ., (2m — I) maales, $ 25. Begge
Cirkler overskiære hinanden i Radius + 1.

Sinus til 90 Grader, eller Y—1 (§ 6), betegnes i den
verticale Cirkel ved 1, og i den horizontale ved ¢; =? saa-
velsom 72 er =— 1, i Folge § 5.

mSetter man at ner — 11, iv, 100 feler em dames
il

teones cos.n +nsin n vedn, og ————
= aig RE cos.n +17 sin. n

ne S Ce

Fr n=ı In, v,..., eller (2m — 1), da betyder n'

det samme som cos. n 4 esin. n, og nm’ det samme som

iL
cos.n + esin. n° 3%

Cos.n og sin.n ere i forste og tredie Qvadrant lige-
stilte (af samme Retning), men i anden og fierde mod-
satte, $ 6.

Tegnet ” har kun halv den Betydning som det sæd-
vanlige Multiplicationstegn; thi den Linie i Multiplicandums
Udtryk, der ligger udenfor Planet af Cirkelbuen i Mul-
tiplicators Mærke, bliver ved Operationen uforandret; naar
f. Ex. 2, 3e og 47 ere rette Linier, da er (2 + 3e +47) ,,
11‘ det samme som 3¢-+ (2 +41). (cos.11-++ ysin. 11); lige-
ledes er (2 + 3e +47) „ I det samme som 414 +(2 + 3e).
(cos. 1 +e sin. I).

Desuden maa iagttages, at Operationen skeer i den
Orden, som Factorerne følge hinanden fra Venstre til
Høire; saaledes maa man f. Ex, naar Værdien af (2 +
3e +47) , 1°, 11° skal findes, forst soge Værdien af (2 +

Forsøg til Directionens analytiske Betegning. 69

5 =4 2 cos.I-+ 2esin. I
Je +47) ,, I | Den og derefter Vær-

44 +2008.1+2 esin. I
dsen af ( TRE DIE

s kan betegne en ret Linie af hvad Længde og Direc-
tion man vil; saaledes kan man i Ædqvationen A sætte
isteden for s et Led af Æqvationen B, og derved for-
andre Ledets Udtryk; Er f. Ex. s = |". n , 11", I =
det andet Led i B, da forvandles Ægqvationen A til [inv .
ev, En NN 8 32.

Videre har jeg ikke gaaet i disse Polygoners Under-

søgelse.

Vo

DEVELOPMENT OF

ESTHERIA PACKARDI,

AS SHOWN BY ARTIFICIAL HATCHING
FROM DRIED MUD.

BY

G. O. SARS.

WITH 4 AUTOGRAPHIC PLATES.

D KRISTIANIA OG KJØBENHAVN
ALB. CAMMERMEYERS FORLAG
(LARS SWANSTRØM).

KRISTIANIA — CENTRALTRYKKERIBT 1896.

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVII. Nr. 2.

Development of Estheria Packardi,
Brady, as shown by artificial hatching
from dried mud.

With 4 autographic plates.

By G. O. Sars.

Introduction.

At the commencement of June this year, I received,
through the kindness of Mr. Whitelegge, several samples
of dried mud collected by him in the early days of April
from shallow pools in the neighbourhood of Sydney, and I
have thereby been enabled to continue my hatching experiments
also during the past summer. From 2 of the samples, ta-
ken, according to the label, from pools «off Botany Road,
‘near Waterworks Bridge», besides the usual Entomostraca,
a considerable number of larve of a Phyllopod also devel-
oped. This Phyllopod turned out to be the Estheria
Packardi, Brady, described from alcoholic specimens by the
author in a previous paper inserted in these Archives, together
with several other Australian Phyllopods. Having now
had an opportunity of studying the whole larval and post-
larval development of this form, I propose, in the present
paper, to give a short account of my observations concerning
that part of the biology of the said interesting Phyllopod. In

4 G. O. Sars.

another paper, to be published shortly, I intend to treat of
the other Entomostraca raised from the mud.

Although a considerable number of larvæ were suc-
cessfully hatched in my aquaria, it was only a comparatively
small number of them that accomplished their whole develop-
iment, and but very few specimens grew to their full size. Not-
withstanding this, all the developmental stages, both larval and
postlarval, have been carefully studied, and numerous draw-
ings from living specimens executed, the most instructive
of which are reproduced, by the autographic method, on the
accompanying Plates.

In a previous paper, inserted in the Transactions of
the Scientific Society of Christiania for 1887, and containing
a description of the remarkable Phyllopod, Cyclestheria
Hislopi (Baird), which I succeeded in raising from mud col-
lected near Rockhampton, the development is also treated
of in detail. But the development of this form is very
different from that in other Phyllopods, the brood being, as
in the Cladocera, kept within the shell of the parent until
their full development, whereby any true metamorphosis in
this form is excluded.

Now it appears to me rather interesting to compare
therewith the development of the present Phyllopod, which,
like most other forms of the sub-order, passes through a very
pronounced larval metamorphosis On the whole, the develop-
ment of the present form agrees very closely with that of
Limnadia lenticularis Lin., which also I have had an op-
portunity of studying in detail.

Development of Estheria Packardi.

| on

I. Larval stages.

The larval development may conveniently be divided
into 6 successive stages, to be described below, each
of the stages being characterised by several well-marked
changes in the organisation of the larva. During this period,
which comprises about 4 days, the larva casts off its skin
several times, though the stages here described do not in

every case seem to be accompanied by a true exuviation.

First larval stage.
(Pla testa G2):

The recently hatched larva is very small, scarcely ex-
ceeding in length 0,20 mm. It exhibits all the characters
of a true «Nauplius», being even somewhat simpler
than the well-known typical Copepod-Nauplius, in so far as
one of the 3 pairs of limbs characterising the Nauplius-
stage, viz, the antennule, are quite rudimentary.

The body is divided by a median instriction into 2
divisions of nearly equal size, the anterior one representing
the cephalon, the posterior the still quite simple and unseg-
mented trunk. The anterior division is very convex above,
and, as it were, bulbously inflated, being obtusely rounded
in front; the posterior one exhibits a regular oval form and
has posteriorly a very slight notch.

Quite anteriorly, just within ‘the frontal part, a very
conspicuous, purplish red pigmentary patch, of a somewhat
irregular quadrangular form, is seen. This is the simple eye
or ocellus. Of the compound eye, on the other hand, not
the slightest trace is yet to be detected.

6 G. O. Sars.

The head is produced ventrally (see fig. 2) into a large,
shield-like plate extending posteriorly beyond the limit of
the 2 body-divisions, and representing the greatly developed
anterior lip or labrum. It covers over the place, where the
oral opening is to be formed, and exhibits a regular oval
form, with the edges evenly curved.

Ot the 3 pairs of Nauplian limbs, as above stated, those of the
anterior one, the antennulæ, are still quite rudimentary, only
forming, on each side of the frontal part, a very small, knob-
like prominence tipped by a slender and delicate sensory
bristle. The 2nd pair of Nauplian limbs, the antenne, are,
on the other hand, very largely developed, constituting the
chief locomotory organs of the larva. They originate from
the sides of the {anterior division, and are extended later-
ally as a pair of powerful arms, but being very mobile,
they admit of being bent, now anteriorly, now posteriorly,
and it is indeed by such movements that the animal is
propelled through the water. The proximal part of these
limbs forms a rather thick and very flexible scape, from the
base of which, somewhat ventrally, a conical process issues,
pointing posteriorly, and tipped by a single, spine-like bristle.
At the end of the scape, moreover, a strong posteriorly
curving seta is seen to originate. ‘The distal part of the
limb is represented by 2 unequal rami issuing close together
from the tip of the scape. The outer ramus is the larger,
and of a somewhat fusiform shape, being provided with 4
strong sets, 2 of which issue from the tip, the other 2 from
slight notches on the inner edge. The inner ramus is nearly
cylindric in form, and carries on its tip 3 strong sete ac-
companied by a small, dentiform process.

The 3rd pair of Nauplian limbs, the mandibular feet,

originate on each side of the median instriction of the body

Development of Estheria Packardi. 7

from a rounded prominence, which represents the mandibular
body, and are, like the antennæ, extended laterally, pointing
generally obliquely behind. They are scarcely more than
half as long as the antennæ, and form each a simple stem,
movably articulated to the above-mentioned prominence, and
divided into 3 imperfectly defined segments. It is provided
with 6 short, spiniform appendages, 3 of which issue from
the tip, the other 9 from the inner edge, 2 of the latter
being placed close together on the lst segment.

The body of the larva is of a greyish white colour,
being filled with an opaque granular matter, partly extend-
ing into the bases of the limbs. Of inner organs, besides
the ocellus, only a very faint trace of the intestine is dis-
cerned in the axis of the body. On the whole, as yet only
at very slight differentiation of the tissues seems to have
taken place.
| The motions of the larva in this stage are still rather
imperfect and abrupt. At times it certainly moves the antennæ
violently; but, as their setæ are still without cilia, the
body cannot at any regular rate be propelled through the
water, but very soon sinks again to the bottom. It is only
after the Ist exuviation has taken place, that the motions
acquire that regular and rhythmical character that dis-
tinguishes the larva in the succeeding stages. By this
exuviation the larva passes immediately into the next stage.

Second larval stage.
(Pl. I, figs. 3 & 4).

In this stage the body of the larva has become rather
more elongated, attaining now a length of 0,34 mm.

8 G. O. Sars.

The form of the anterior division is nearly unaltered,
whereas the posterior one has changed from the original
regular oval form to an almost cylindrical shape, and now
considerably exceeds in length the anterior. It terminates
in 2 short, juxtaposed projections (the furca), separated
by a small sinus, in which the anal orifice has been formed,
but is otherwise quite simple, without any trace of segment-
ation or of true appendages. As in the preceding stage, it
is for the greater part filled with an opaque granular mat-
ter, whereas the anterior division has become considerably
more transparent.

The ocellus, as also the antennulæ, both in this and in all
the succeeding larval stages, does not exhibit any changes
whatever.

The antennæ, on the other hand, appear somewhat more
fully developed, all the sete being now densely plumose.
Moreover each of the rami has acquired an additional seta,
the number of the sete being accordingly on the outer
ramus 5, on the inner 4, the latter issuing all close together
from the tip of the ramus. The basal process has assumed
the form of a strong falciform seta, originating with a
thickened base from the lower face of the scape, and having
its outer part densely ciliated. The seta at the end of the
scape has also become considerably stronger, and is likewise
distinctly ciliated.

The mandibular feet have preserved their form and
size unaltered; but the short spiniform appendages found
in the preceding stage are now transformed into bristles, those
issuing from the inner edge being densely ciliated. The
mandibular bodies are more distinctly developed, with their
masticatory part in process of formation.

The labrum (see fig. 4) exhibits a similar shield-like

Development of Estheria Packardi. 9.

shape to that found in the Ist stage, and is now to a cer-
tain extent mobile, admitting of being somewhat raised and
again bent in against the body. Immediately inside its
terminal edge, several very large and distinctly nucleolar cells
are seen, apparently of secretory nature.

The alimentary tube appears now rather distinctly in
the axis of the body, being filled with yellowish contents,
which become dark brown in its posterior part. It is con-
siderably dilated in front, and exhibits here on each side a
short auricular expansion, the first intimation of the richly
ramified liver found in the adult animal. Posteriorly it
terminates with a very distinctly defined, and rather narrow
rectum, from which delicate muscular fibres radiate to the
walls of:a surrounding cavity.

- The larva now moves rather quickly through the water
by rhythmical strokes of the powerful antennæ. By every
stroke the basal faleiform process is seen to be thrown in
between the labrum and the body, towards the now formed
oral orifice, and it is therefore very probable that this
process is of essential service for bringing nourishing
matter to the mouth, for which reason it may properly be
termed the masticatory process of the antenne.

Third larval stage.
(Pl. I, fig. 5).

This stage immediately succeeds the preceding one,
being however rather sharply marked off from the same by
a previous complete exuviation of the larva, whereby some
very conspicuous changes have taken place.

The form of the body appears still more elong-

10 G. O. Sars.

ated than in the preceding stage, and the posterior
division has now assumed a more conical form, being con-
siderably tapered in its outer part. At the base, it exhibits
on each side a rather conspicuous swelling, indicating the
place where subsequently the lateral parts of the carapace
are to be formed, but is otherwise as yet quite simple. The
furcal projections have however become considerably more
elongated than in the preceding stage, forming 2 pointed
lappets separated by a deep sinus.

As to the limbs, at least one very conspicuous change
has taken place. This change affects the masticatory pro-
cesses of the antenne, which now appear considerably
stronger, and have divided at the end in a fork-like manner
into 2 somewhat unequal and densely ciliated points. It
is evident that this modification renders these processes still

more suitable as auxiliary organs for the procuring of food.

Fourth larval stage.
(PL. I, figs 6 & 7).

Though this stage does not appear to be marked off
from the preceding one by any true exuviation, it is, how-
ever, pronouncedly distinguished by the first apparition of
the carapace and of the anterior pairs of legs, these parts
having developed inside the larval skin.

The carapace, or rather the first intimation of such,
presents itself as a rather small, semilunar fold extending
dorsally over the most anterior part of the trunk, and having
its posterior edge deeply emarginated in the middle (see
fig. 6). The lateral parts of this fold represent the valves
of the shell in the adult animal, and are not yet defined

Development of Estheria Packardi. vil

fr om each other, but are confluent dorsally. They exhibit each
a distinct, narrow linguiform marking, which is the first
trace of the shell-giand. Behind this rudiment of the shell
appear on each side a regular series of 4 bud-like promin-
ences, which constitute the first trace of the 4 anterior pairs
of branchial legs. They are, as above stated, like the de-
veloping shell, enclosed within the larval skin, which passes
over them without any interruption.

In the Nauplian limbs no perceptible change has taken
place, and the labrum, the ocellus and the alimentary
tube also exhibit the very same appearance as in the 2 pre-
ceding stages. |

The body has, however, now become very transparent,
and the differentiation of the tissues has proceeded, so as
to show rather distinctly the several muscles moving the
antennæ and mandibular feet (see fig. 6). The length of
the larva in this stage is 0,42 mm., and accordingly but very
little greater than in the preceding stage.

Fifth larval stage.
(Pl. IT, figs. 1—é&—2).

This stage is rather sharply marked off from the pre-
ceding one, a complete exuviation of the larva having taken
place, whereby both the carapace and the lateral pedal buds
now become freely exposed. |

The carapace has somewhat increased in size, covering
a greater part of the trunk, and advancing over the anterior
pair of pedal buds, its posterior emargination having at
the same time become distinctly angular.

The fureal processes have likewise increased in length,
2 — Archiv for Math. og Naturv. B. XVIII No. 2.
Trykt den 6te Juni 1896.

12 G. O. Sars.

and exhibit each at the base dorsally a small secondary
denticle not found in the previous stages. This denticle
represents the strong, spiniform inferior corner of the tail-
plates in the adult animal, whereas the terminal part of the
furcal processes becomes converted into the caudal claws.

In this stage, moreover, the first trace of the compound
eye is seen above and somewhat in front of the ocellus.
It appears as 2 widely separated, and very small pigmentary
patches, each surrounded by a pellucid area, in which the
visual elements are in process of development. This organ
in the larva is accordingly double, whereas in the adult
animal the 2 halves are so completely fused together as to
constitute a simple mass.

Finally, in this stage another organ has made its/first appear-
ance, viz., the heart, which is rather distinctly traceable in the
anterior part of the trunk dorsally (see fig. 1), exhibiting
already some irregular pulsations.

In the structure of the Nauplian limbs, no perceptible
change has taken place, and the larva moves through the
water in the very same manner as in the previous stages.

The length of the larva in this stage has increased to

0,52 mm.

Sixth larval stage.
(EL 106 eek 9,4 SL

This stage is chiefly distinguished by the progressive
development of the carapace and of the branchial legs;
otherwise it nearly agrees with the preceding one, no exu-
viation having apparently taken place between the two.

The carapace has now considerably increased in size,

and is rather broad and expanded, obtecting, like a mantle,

Development of Estheria Packardi. 13

the dorsal face of the trunk in more than half its length.
The lateral parts are of rounded form, and advance over
the greater part of the developing legs. Dorsally, they still
. pass immediately into each other, but posteriorly they are
separated by a deep incision. Anteriorly the carapace is
also well defined, and between it and the anterior division
of the body a rather deep impression occurs (see fig. 3).
The shell-gland is best seen in the lateral view of the
larva (fig. 3), and has nearly assumed its definitive structure.

The anterior, or cephalic part of the body is scarcely
half as long as the posterior, and has the dorsal face still
strongly convex above. Ina lateral view of the larva (fig. 3),
it appears almost transversely truncated in front, with the
anterior edge somewhat flexuous, exhibiting a slight bulging
at the place inside which the compound eye is developing.
The lower corner, in front of the antennule, is somewhat
projecting, but no trace of a true rostrum is as yet to be
detected. The posterior division, as in the preceding stages,
is gradually narrowed distally, and has the furcal pro-
cesses more fully developed, with the secondary denticle
larger. At some distance in front of the latter is seen
dorsally a slight angular prominence, and below it the caudal
sete are about to grow forth.

The ocellus, labrum and Nauplian limbs are, on the
whole, unchanged, except that the outer ramus of the an-
tenne exhibits a trace of an articulation.

The branchial legs, of which, in the preceding stage,
only 4 pairs of bud-like rudiments were found, appear now
more fully developed. They have, moreover, increased to
6 pairs, rapidly diminishing in size posteriorly, the last pair
being still rather small. On all the legs the 3 chief parts,
the exopodite, endopodite and epipodite, may now be

14 G. O. Sars.

discerned, and small bristles are already seen growing forth
from the tip and inner edge of the endopodites, The coxal
.lobes are likewise well defined, and easily observed, when
the larva is viewed from the ventral face (fig. 5), all of
them curving inwards. Still, however, the legs are quite
immovable and densely crowded, all pointing behind. The
length of the larva has now increased to 0,65 mm.

This is the last larval stage, and the young animal is
now about to cast its skin, before entering into the next
phase of its development, the postlarval one.

II. Postlarval stages.

The postlarval development is of very long duration,
as compared with the larval one, and indeed rather more
than a month would seem to be needed for its full accomplish-
ment. It comprises numerous succeeding stages, each being
marked off by an exuviation of the animal, whereby, how-
ever, only the inner coating of the shell is cast off, the valves
being kept in their place, and only supplied with a newly-
formed peripheric area. In this manner the characteristic,
concentrical lines of growth are formed, the number of which
indeed indicates the number of successive exuviations, which
have taken place. Among the most prominent features
distinguishing this phace of the development from the larval
one, may be mentioned, besides the transformation of the
mantle-like carapace of the larva into a true bivalve shell,
the complete loss of both the masticatory processes of the
antennæ and of the mandibular feet, and finally, the functional
evolution of the branchial legs.

Development of Estheria Packardi. 15

As the postlarval development on the whole proceeds
rather gradually, without any strongly marked changes, only
some few stages need be described in detail.

First postlarval stage.
(Pl. II, fig. 1).

Though this stage immediately succeeds the last larval
one, being only marked off from it by a single exuviation,
very considerable changes have taken place in the orga-
nisation of the animal, which now presents itself under a
rather different appearance. Whereas in the larval stages,
owing to the lateral extension of the antennæ and mandi-
bular feet, the animal, when brought under the microscope
in a small quantity of water, invariably turns its dorsal or
ventral face to the observer, it is now found to assume a
lateral attitude, it being rather difficult to get a dorsal or
ventral view of the animal. This is chiefly due to the
transformation of the carapace, as also to a somewhat diffe-
rent direction of the antenne. On the whole, the animal
now exhibits a more compressed form, whereas in the larval
stages it looks on the contrary ‘somewhat depressed. Of
exclusively larval organs some remnants are still found, though
in process of degeneration, Thus the antennæ exhibit at the
base posteriorly a conical projection, not found in the suc-
ceeding stages. This projection is the rudiment of the
peculiar bifurcate masticatory process, mentioned in the larva
as a most efficient auxiliary organ for alimentation.
Moreover, a rudiment of the mandibular feet is still found
appended to the outer side of the mandibles, but both
these appendages are now quite useless, and have therefore
lost their bristles, being also greatly reduced in size.

16 G. ©. Sars.

The carapace has now been transformed into a distinetly
bivalvular shell, obtecting the trunk not only dorsally but
also laterally, so as to include between the valves both the
oral parts and the legs. It is, however, still of inconsider-
able size, as compared with that in the adult animal, for
which reason, the anterior and posterior parts of the body
remain uncovered, projecting considerably beyond it, without
being enabled to withdraw themselves into the shell.
Seen laterally, it exhibits a rounded triangular form, its
antero-dorsal corner being somewhat projecting. The dorsal
edge, where the valves are connected, appears rather short
and nearly straight, joining the free posterior edges of the
valves at an obtuse angle. In the anterior part of each
valve the shell-gland may be very distinctly traced as an oval
coil of closely crowded canals. Otherwise the shell is quite
smooth, without any trace of concentric lines, and highly
pellucid.

The anterior, or cephalic part of the body is still
strongly convex above, and is defined dorsally from the ad-
joining part of the trunk by a distinct, though not very
deep depression, from which a transversal suture passes on
each side to the insertion of the mandibles. The frontal
part of the head is now produced downwards to a distinct,
though not very prominent, acute rostrum, and has the an-
terior edge somewhat irregularly flexuous. Ventrally, the
head is prolonged into the posteriorly pointing labrum, the
form of which now nearly agrees with that in the adult
animal, being somewhat compressed, not, as in the larval
stages, shield-like.

The compound eye is still double, and has the pigment
rather poorly developed, the visual elements being not yet
distinctly formed. On the other hand, the ocellus, located

Development of Estheria Packardi. 7

at some distance below the eye, is very conspicuous, and
exhibits much the same appearance as in the larval stages.

The antennulæ, issuing from the ventral face of the head in
front of the labrum, are well defined, though still rather short
and claviform in shape, without any trace of segmentation
or lateral lobules.

The antennæ exhibit a structure somewhat intermediate
between that in the larve, and that characteristic of the
adult animal. As in the latter, the scape is bent anteriorly,
exhibiting an almost elbow-shaped flexure at the base, and
from this flexure the above-mentioned rudiment of the
masticatory process is seen to issue. At the end the scape
exhibits several imperfectly defined joints, not found in the
larva, and from the anterior side of them several small,
spine-like bristles are seen growing forth. Posteriorly a
single, rather short, ciliated bristle occurs, which is easily
recognized as the remnant of the strong, falcate seta origin-
ating from the same place in the larva. This bristle be-
comes subsequently lost altogether, as also the basal pro-
cess, which latter becomes replaced by a bundle of ciliated
sete, The rami are still rather short, though some-
what more fully developed than in the larva. The outer
ramus is the larger, and is divided into 5 or 6 articula-
tions, the 2 middle of which have each anteriorly a single
short spine. The last articulation has a similar spine and 2
ciliated setz, and each of the 3 preceding articulations a
somewhat longer seta posteriorly. The number of natatory
setæ on this ramus is accordingly the very same as in the
larva. The inner ramus has retained its original simple
cylindric form, though a slight trace of segmentation is visible
in the middle; and it carries only 3 apical sete, the 4th seta

18 G. O. Sars.

oceurring in the larva being replaced by a very small denti-
form projection.

The branchial legs are now so fully developed, as to
admit of being moved in the rhythmical manner character-
istic of the adult animal. Behind the 6 pairs already found
in the last larval stage, 2 additional pairs have developed,
the total number of legs being accordingly 8 pairs.

The pedigerous part of the trunk in this stage shows
the first trace of segmentation, and from the segments the
dorsal, hairy protuberances are seen growing forth, their
number being, in this stage, only 4.

The caudal part, or tail, is still but little deflexed, and
thereby less conspicuously marked off from the adjoining
part of the trunk, It is, however, constructed in essentially
the same manner as in the adult animal, the caudal claws
being now well defined and movably articulated to the an-
terior corner. Each of the caudal plates is produced at the
lower corner to a strong spiniform projection, and between
this projection and the knobs carrying the caudal setæ, only
a single denticle is as yet developed on each plate. Just
above the caudal sete, as in the adult animal, a pair of
dentiform projections occur, and in front of them there are
traces of another pair.

Of the inner organs, the alimentary tube is very con-
spicuous by its yellow contents which turn to dark brown in its |
posterior part. Anteriorly, it has on each side a well-defined
cecal appendage, which is slightly bilobed and forms the
commencement of the liver. The heart is also distinctly
observable within the anterior part of the trunk dorsally. It
is rather elongated, and exhibits on each side 4 venous
fissures,

The body is still highly transparent and almost colour-

Development of Estheria Packardi. 19

less. Its length, measured from the tip of the rostrum to
the end of the caudal claws, is 0,65 mm, or about the same
as In the last larval stage. The length of the shell scarcely
exceeds 0,40 mm.

As to the mode in which the animal moves through the
water, it looks very different from that observed in the
larva. Whereas in the latter, by rhythmical and not very
rapid strokes of the antennæ, and partly also of the mandi-
bular feet, a rather slow and somewhat jumping motion is
effected, it has now more the character of an even run, the
animal being propelled by very rapid strokes of the outer
part of the antennæ alone. At times the animal is also seen
affixing itself with its back to the walls of the aquarium,
but both in this case and during swimming, the branchial
legs are found to be in an uninterrupted swinging motion.

Second postlarval stage.
(Pl. III, fig. 2).

This stage is chiefly characterized by the appearence on
the shell of the Ist line of growth. This line is nothing
less than the edges of the primitive valves, which, as it
were, are superposed on the newly formed ones, so as to
leave only the peripheric part of the latter exposed. This
part is rather narrow, and has the edges throughout fringed
with delicate bristles, not found on the edges of the primitive
valves. By the said additional peripheric area, the shell has
increased considerably in size, so as now to allow the animal,
by a strong flexion of its anterior and posterior parts, to
be completely withdrawn into the shell. Its form is, how-

ever, nearly unaltered.

20 G. O. Sars.

As to the animal, the rostral part of the head has be-
come considerably produced, terminating in a very acute
point, whereas its dorsal part is somewhat less convex than
in the preceding stage.

The compound eye is more fully developed, and its 2
halves are about to join in the middle.

The antennule are still rather short and claviform.

The antenne have quite lost the basal process, as
also the seta found in the preceding stage at the end
of the scape posteriorly, whereas the spine-like bristles in
front are more fully developed. The rami are now subequal
in length, the outer one resembling that in the preceding
stage, except that the 2 middle joints have each 2 spines, instead
of a single one, anteriorly. The inner ramus is divided
into 5 well-defined articulations and, like the outer, is provided
with scattered natatory sete, both at the tip and on the
posterior edge.

The number of branchial legs is apparently the same
as in the preceding stage, though perhaps a 9th pair is in
process of formation. The pedigerous part of the trunk is
more distinctly segmented, and the hairy dorsal protuberances
have considerably increased in number.

The tail appears more deflexed, but otherwise exhibits
an appearance very similar to that found in the preceding
stage. ;

The length of the shell in this stage measures 0,70 mm,
its height bemg 0,56 mm.

Third postlarval stage.

In this stage, which is not figured in the plates, 2 lines
of growth have appeared on the shell, which has thereby

Development of Estheria Packardi. Dil

increased considerably in size, measuring now 0,86 mm. in
length. The enclosed animal does not much differ from that
in the preceding stage, and is still highly pellucid, with only
a very faint yellowish tinge, the shell being, as in that
stage, almost colourless.

Fourth postlarval stage.
(Pl. II, fig. 3).

The shell in this stage masures 0,93 mm., and exhibits
3 lines of growth, the outer 2 being, like the free edges ot
the valves, fringed with delicate bristles. Its form has be-
come somewhat more elongated in proportion to its height,
but is still rather unlike that of the adult animal.

Of the several appendages, the antennule have some-
what increased in length, but are still quite simple, without
any distinct segmentation or lateral lobules. The rami of
the antenne have likewise become more elongated, and are
each divided into 7 well-defined joints. Of branchial legs,
10 pairs are now distinctly developed, and on the caudal
plates 3 denticles have appeared above the spiniform lower
corners.

As to the inner organs, it is only to be noted, that the
cecal appendages of the intestine have commenced to divide
in a dichotomic manner, to form the complicated liver-masses
fillmg up, in the adult animal, a great part of the inner
cavity of the head.

Seventh postlarval stage.
(PL IV, fig. 1).

In this stage the shell exhibits 5 well defined lines ot
growth, and measures in length 1,70 mm. The primitive

22 G. O. Sars.

ud

valves now occupy only a comparatively small part of the
shell, and their edges, forming the lst line of growth, are
concentrically encompassed by the 4 other lines, which all,
like the free edges of the valves, are densely setiferous.
The form of the shell is still somewhat more elongated than
in the 4th stage, more approaching that in the adult animal,
though the umbonal part appears far less prominent.

The enclosed animal (not drawn in the figure), which
now exhibits a clear yellowish orange hue, has developed
its appendages more fully, the antennulæ being considerably
more elongated, and each of the rami of the antenne having
become 8-articulate. The branchial legs have increased in
number, 12 pairs being now distinctly developed, and behind
them there is, moreover, a slight trace of 2 other pairs in
process of formation. The tail does not differ from that in
the preceding stages, except by a somewhat increased number
of denticles on the concave edge of the terminal plates. The
cecal appendages of the intestine have now divided into
numerous lobes, and exhibit a clear yellowish hue.

Ninth postlarval stage.
(Pl. IV, fig. 2).

The length of the shell in this stage has increased to
2,25 mm., the height being 1,55 mm. and its form is now
rather similar to that of the adult animal, though some-
what more compressed. The lines of growth are 8 in each
valve, being all, except the Ist, like the free edges of the
valves, fringed with bristles, which, however, are shorter
and more densely crowded than in the stages previously
described. The Ist line of growth now only encompasses a

Development of Estheria Packardi. 23

very small part of the shell, and it is easily seen that the
primitive valves become at last restricted to the tip of the
umbones, where, on a closer examination, they can be dis-
cerned even in full-grown specimens.

The enclosed animai (not dravn in the figure) has now
assumed a light brownish hue, but is still rather transparent,
so as to admit of the alimentary tube being very distinctly
traced in its whole length. Also the shell-gland, which in
the adult animal is very difficult to observe, appears rather
distinctly inside the umbonal part of the valves. Of branchial
legs may now easily be counted 16 pairs, and behind them
some other pairs are apparently in process of formation.

Subsequent postlarval stages.

The succeeding stages, which are rather numerous, I
do not find it neccessary to describe in detail, They are
characterized by a very gradual increase both of the shell
and animal, the lines of growth at the same time augmenting
in number, and the several appendages assuming gradually
the appearance characteristic of the adult animal. In most
of the stages the setous armature of the lines of growth and
of the free edges of the valves could be discerned; but the
bristles gradually become shorter and partly broken off,
so as at last, for the most part, only to leave their insertions.
The peculiar radiating striation of the shell described in my
previous paper, is undoubtedly due to these bristles, or more
correctly to their former insertions on the edges of the several
superposed valves.

24 ‘ G. O. Sars.

IT. Adult form.
(BIE VA es onan):

The full-grown animal of both sexes has been described
in detail by the author in his previous paper, from alcoholic
specimens. I shall therefore here only give some notes on the
colouring and the habits of the animal, as observed in my
aquaria, and add 2 figures of the largest specimen reared,
representing the animal within its shell viewed from the side
and from above, in the attitude it generally assumes when
brought under the microscope in a suitable quantity of water.

The specimen, which was of the female sex, measured in
length about 7 mm., and may be supposed to have attained
its full size, as the lines of growth were no less than 24 on
each valve, or as many as in the largest specimen formerly
examined, The shell was horn-coloured and semi-transparent,
whereas the enclosed animal exhibited a very dark brownish
red colour, turning, on the ventral face and on the legs, to a
vivid and deep blood-red. The alimentary canal could be only
faintly traced through the shell, and on its sides the greatly
developed, opaque whitish ovaria could be discerned, in the
form of elongated, twisted bags (see fig. 3).

As to habits, the animal showed itself to be on the
whole rather sluggish, being often found for a rather long
time resting on the very same place, more or less deeply
burried within the loose bottom deposit. At times, however,
and especially in clear weather, it made some abrupt ex-
cursions through the water, moving rather rapidly, and at a
perfectly even rate up along the walls of the aquarium, some-
times up to the surface of the water; but it very soon sank
back to the bottom, assuming again its quiet attitude, The

movements, as in other bivalve Phyllopoda,seem to be exclusively

Development of Estheria Packardi. 25

effected by the aid of the antennæ, the outer part of which,
together with the head, being extruded from the shell anter-
iorly, and the rami violently moved sidewards. Not infrequetly
the animal was seen to move in this manner rather slowly
along the bottom, the back upwards, whereby the muddy
particles were whirled up around it and partly thrown inside
the shell. This proceeding being often repeated, it would
seem that it was effected chiefly for the purpose of feeding.

In the same aquarium, in which the above-mentioned
female specimen occurred, two male specimens were also
reared, both apparently attaining to their full size, though
being somewhat smaller than the female. They were often
seen eagerly pursuing the female, and in one case one
of the ınales got a rather firm hold on the female by inserting
the strong claws of his 2 anterior pairs of legs inside the
shell of the latter, at its upper posterior corner. The 2
sexes remained for rather a long time locked together in this
manner, but wether a true copulation thereby took place, I
could not ascertain. The specimens, after having been sub-
jected, to a closer examination under the microscope, were
replaced in the aquarium, but they did not live long after-
wards, and their empty shells were subsequently found on
the bottom of the aquarium

Explanation of the plates.

BIER

Fig. 1. Recently hatched larva (Ist larval stage), viewed
from the dorsal face; magnified 120 diameters.

»

»

»

Fig.

CXS fre 12

G. O. Sars.

Same, ventral view.

Larva in the 2nd stage, viewed from above; >< 120.
Same, ventral view.

Larva in the 3rd stage, viewed from the ventral
face; X 120.

Larva in the 4th stage, viewed from above (left
antenna and mandibular foot not fully drawn)
>< 120,

Same, ventral view.

let Ol,

Larva in the 5th stage, viewed from above (left
antenna and mandibular foot not fully drawn);
>< 120:

Same, ventral view,

Larva in the 6th or last stage, viewed from the right
side: 120:

. Somewhat more advanced larva of same stage

viewed from above (left antenna and mandibular
foot not fully drawn); + 120.

Same, ventral view.

EPST

Young Estheria in the 1st postlarval stage, viewed;
from left side; magnified 120 diameters.

Å specimen in the 2nd postlarval stage, the shell
having acquired the Ist line of growth, viewed from
right side; magnified 95 diameters.

Another specimen in the 4th postlarval stage, with
3 lines of growth, exhibited from right side;
x 80.

Development of Estheria Packardi.

IND
=!

PI TV.

Fig. 1. Shell of a young Estheria in the 6th postlarval stage,

with 5 lines of growth, viewed from left side;
x 42.

» 2. Shell of another specimen in the 9th postlarval
stage, with 8 lines of growth, viewed from left side;
32.

» 3. Fully grown female, drawn from life, and viewed
from left side, magnified about 10 diameters.

» 4, Same, dorsal view.

ON FRESH-WATER

ENTOMOSTRACA

FROM THE NEIGHBOURHOOD
OF SYDNEY,

PARTLY RAISED FROM DRIED MUD.
BY

Cy, ©. SARS

WITH 8 AUTOGRAPHIC PLATES

år KRISTIANIA

ALB. CAMMERMEYERS FORLAG
(LARS SWANSTRØM).

KRISTIANIA — CENTRALTRYKKERIET 1896.

INTRODUCTION.

Ås is well known, our earliest knowledge of Australian
fresh-water Entomostraca is due to the Rev. R. L. King,
who in the «Papers and Proceedings of the Royal Society
of Van Diemen’s Land» has published some interesting
treatises on that part of the fauna. His investigations were
chiefly restricted to the environs of Sydney, and showed
indeed that part of the country to be rather rich in Ento-
mostraca, some of which exhibited a very close relationship
to well-known European species, though the greater number of
them were regarded as specifically distinct. As the descrip-
tions and figures given by Mr. King do not always admit
of our fully recognizing the species, I was very anxious to
obtain some of the native forms for a closer examinination,
and for this purpose applied to two well-known natura-
lists of the country, Prof. Ramsay and Mr. Th. Whitelegge.
Both these gentlemen readily complied with my request,
and furnished me with a rather interesting material, the
working out of which has been of great interest to me. In
1888, Prof. Ramsay kindly sent me a tube containing a
sample taken from the Waterloo swamps near Sydney,
and in the succeeding year, I published in the Transactions

4 G. O. Sars.

of the Scientific Society of Christiania a short account of
the contents of the tube. Some years afterwards, severa]
additional samples preserved in spirit were kindly for-
warded to me by Mr. Whitelegge, who collected them from
several places in the neighbourhood of Sydney, and recently
a number of samples of dried mud have also been kindly
sent to me by the same gentleman. With this mud I have
made, in the course of the past summer, a series of hatching
experiments, and have thereby been enabled to examine the
greater part of the species also in the living state. Of the
Phyllopoda I have already in this Journal given a detailed
account accompanied by autographic plates, and propose
now to give a similar account of the other Entomostraca.
The number of species examined amounts to no less than
42 in all, 26 of which have been examined in the living
state. As several of these species have already been de-
scribed and figured in detail by the auther in previous papers,
some from the northern part of the country, some trom
New Zealand, these forms will be only briefly mentioned in
the present paper, whereas descriptions and figures will be
given of the remaining species.

The plates accompanying this paper have been prepared
with the greatest care by the autographic process, and
I am glad to see that the printing of the plates has been
more successfully accomplished than has been the case with

the plates of some of my recent papers.

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVIII. Nr. 3.

Cladocera.
Fam. Daphnidee.
Gen. Daphnia, Miller.

1. Daphina carinata, King.
(PL 1.)

Daphnia carinata, King, Papers & Proceedings Roy.
Soc. Van Diemen’s Land, Vol. IT, Part. II, p. 246, PL I,
mess PL VI: Å.

Specific Characters.—Q Shell, seen laterally, some-
what varying in shape, being in some specimens oblong oval
and narrowed posteriorly, in others comparatively broader,
rounded quadrangular, spine generally rather long and more
or less obliquely upturned, denticles of the dorsal margin
extending nearly to the cervical region. Head distinctly
carinated throughout, the carina being more or less developed,
and thereby causing the lateral aspect of the head to be
somewhat variable, though it always appears rounded in front;
rostrum acute, not deflexed; fornix terminating on each side
in a spiniform corner. Eye of moderate size. Antennulæ
very small, scarcely projecting beyond the shell of the head.
Tail conically tapering, with the posterior edge perfectly
straight, anal denticles about 12 on each side, rather small

6 G. O. Sars.

and subequal; terminal claws comparatively short, without
any secondary denticles. Ephippium produced anteriorly to
a narrow stripe, egg-ampullæ obliquely disposed. Length,
without the spine, from 3 to 41/2 mm.

Remarks. The present form, first described by
Mr. King, is closely allied to the New Zealand species
D. Thomsoni, G. O. Sars, though differing in some parti-
culars, so that it should more properly be regarded as spe-
cifically distinct. As Mr. King observes, it is, however, a very
variable species. The crest of the head, from which the
species has been named, seems indeed to vary considerably
in development, thereby giving the head a somewhat diffe-
rent appearance in specimens from different localities, as
shown in the figures here given. Mr. King has figured
a very extreme variety, in which the crest even forms
a strongly curved lamina projecting from the cervical
region. The shape of the shell itself would also seem
to be subject to some variableness, according to local-
ity, perhaps also according to the season. Notwithstand-
ing this great variableness, there are to be found certain
characters common to all the varieties, by which this spe-
cies may be readily distinguished from the New Zealand
form. Thus the rostrum is never, as in that form, deflexed,
but forms always the immediate continuation, of the ventral
edge of the head. The shell-spine in all the individuals I
have examined, is considerably longer than in D. Thomsoni,
and, as a rule, also more upturned. Moreover, the denticles
of the dorsal margin of the shell are continued in front as
far as the cervical region, whereas in the New Zealand form
they are restricted to the posterior half only of this margin.
Finally, the tail is more regularly conical in form, and the

terminal claws comparatively much shorter.

On Fresh-water Entomostraca. 7

Description of the female.
a. Typical form.
(Wei al, anise’. Ig)

This form, or variety, agrees closely with that described
and figured by Mr. King as the «common form», and is
probably derived from the very same locality as the latter.

The length of the largest specimens examined measures,
without the spine, 4,70 mm.; but the greater number of the
specimens are considerably smaller, though ovigerous.

The form of the shell, when seen laterally (fig. 1), is
oblong oval, and considerably narrowed posteriorly towards
the base of the spine, with the dorsal margin evenly convex
in the middle, and forming anteriorly, in the cervical region,
a very slight concavity. The spine, which issues from
near the middle of the posterior extremity, is rather elong-
ated, exceeding half the length of the shell, and is perfectly
straight, but somewhat upturned.

The head appears considerably narrower than the shell,
and somewhat irregularly rounded in front, with a slight
indication of an angle in the ocular region. Its ventral
edge is somewhat oblique, and forms a perfectly straight
line as far as the tip of the rostrum, which is accordingly
not deflexed, though terminating in a very acute point.
The dorsal crest, the limits of which are shown by the
insertion of the muscles moving the antennæ, is not very
largely developed, though distinct all round the head. The
fornix appears, in the lateral view of the animal, as a curved
elevated line extending from the ocular region to the point
where the valves take their origin, and in this place pro-
jecting as a spiniform corner. The posterior half of the free
edges of the valves is closely denticulated, the denticles

8 G. O. Sars.

being continued, as usual, along the lower edge of the shell-
spine to its tip. The spine, moreover, exhibits 2 lateral and
one dorsal row of similar denticles, the dorsal row being
continued in front along the dorsal margin of the shell as
far as the cervical region. The sculpture of the shell is the
usual one, consisting of 2 sets of curved striæ crossing each
other at nearly right angles.

The eye is of moderate size, and placed somewhat
within the anterior edge of the head, at its junction with
the ventral one. It exhibits a number of distinct crystalline
bodies projecting from the dark pigment. The ocellus is
extremely minute, punctiform, and located at some distance
behind the eye, at the inferior end of the cerebral ganglion.

The antennule, as in D. Thomsoni, are very small, and
searcely project beyond the shell of the head, except with
their apical bundle of olfactory papillæ.

The antenne are constructed in the usual manner, and
have the natatory sete densely plumose.

The tail exhibits dorsally the usual curved lappets, and
has the terminal part (see fig. 2) comparatively short and coni-
cally tapering distally, with the posterior edge perfectly
straight and densely hairy in its upper part. The anal den- .
ticles are rather small and of uniform length, about 12 on each
side. ‘The terminal claws are comparatively much shorter
and stouter than in D. Thomsoni, and are destitute of any
trace of secondary denticles, though a delicate ciliation may
be observed along their concave edge.

The cæcal appendages of the intestine are of moderate
size, and but slightly sigmoid.

The ova in the matrix, in large specimens, are very

numerous and of comparatively small size.

On Fresh-water Entomostraca. 9

b. Var. intermedia.
(Fig. 3).

In this variety, which is of somewhat smaller size, mea-
suring in length, without the spine, 3,35 mm., the head appears
comparatively larger in proportion to the shell, with the
dorsal crest more developed. The shell is less narrowed
posteriorly, and the spine issues considerably above the
longitudinal axis, being obliquely upturned.

All the specimens of this variety, which I have had
an opportunity of examining, were provided with ephippia,
and accordingly belonged to the later generations.

The ephippium is rather narrow and, seen laterally, of
a somewhat fusiform outline, with the anterior extremity
prolonged into a narrow stripe extending along the cervical
part of the shell and, like the whole dorsal margin, densely
denticulated. The egg-ampulle are rather small and obliquely
disposed, exhibiting a very dark hue, whereas the remaining

part of the ephippium is opaque whitish.

ce. Var. magniceps.
(Fig. 4).

This variety, which attains a length, without the spine,
of 31/2 mm., differs considerably in its outward appearance
from the two preceding ones, though evidently belonging to
the same species. The shell is comparatively shorter and
broader, and exhibits a rounded quadrangular form, with
the dorsal margin nearly straight, and not defined from the
head by any perceptible sinus. The spine, which issues
far above the longitudinal axis, is considerably upturned, and
about half the length of the shell. The head is exceedingly

10 G. C. Sars.

large, fully as broad as the shell, and has the dorsal crest
strongly developed, its inner limit being well indicated by
the insertion of the antennal muscles. The edge of the head
forms a quite even and uninterrupted curve from the cerv-
ical region to the tip of the rostrum. The specimens
examined were laden with numerous small eggs in the
matrix, and would accordingly seem to have belonged to
the earlier generations. In the structure of the fornix, tail
and various appendages, no differences could be detected
between this and the 2 preceding varieties.
Observations. Some few specimens of the present
species were successfully hatched in my aquaria from the
mud received, but none of them arrived at full maturity,
apparently owing to the excessive increase in the same
aquaria of another form, a species of Moina. I am there-
fore not able to say into which variety these specimens
would have developed. ‘The specimens, which had the
spine of the shell very much elongated and somewhat up-
wards curved, were watched for some time in the aquaria.
They kept themselves constantly near the bottom, moving
along it in the usual somewhat jumping manner.
Occurrence. According to Mr. King, the present
species is rather common in the environs of Sydney. The
localities for the typical form ere not enumerated, whereas
for the 4 varieties he figures, none of which agrees with
thoes here described, the localities were recorded. Of the
typical form several well-preserved specimens were con-
tained in the sample first sent me for examination by
Prof. Ramsay. This sample was taken on the 13th August,
1888, from the Waterloo swamps. The variety inter-
media was found in a sample taken by Mr. Lea from
some ponds «Near Hay». Finally, the variety magniceps

On Fresh-water Entomostraca. 11

occurred, though rather sparsely, in a sample taken by
Mr. Whitelegge from Waterholes off Bourke Street, Wa-
terloo. Out of the continent of Australia, this species has
as yet not been recorded.

Gen. Simocephalus, Schoedeler.

2. Simocephalus australiensis (Dana).

Daphnia australiensis, Dana, United St. Expl. Exp.
Crust. II, p. 1271, Pl. 89, figs. 4, a—e.

Simocephalus australiensis, G. O. Sars, Addit. Notes
on Austral. Cladocera raised from dried mud, p. 15, PI. 2,
figs. 1—5.

Of this form, described and figured in detail by the
author in the above mentioned paper, some specimens were
collected by Mr. Whitelegge from the Marubra Swamp
near Sydney. ;

Distribution. Queensland, Knysna (G. O. Sars).

3. Simocephalus Hlisabethe (King).

Daphnia Elisabethe, King. 1. c. p. 247, Pl. II.

Simocephalus Elisabethæ, G. O. Sars, 1. c. p. 22, Pl. 2,
figs. 6, 7.

‘As pointed out in my above mentioned paper, Mr. King
has most probably confounded this and the preceding spe-
cies. It is therefore not possible to decide with certainty
the localities where the present species was found by that
author, A few not very well preserved specimens of
this form were found in one of the samples sent me

12 G. O. Sars.

nd

by Mr. Whitelegge. It was taken from a pond off Botany
Road, near Waterworks Bridge, on the 6th April. 1895.
Distribution. Queensland (G. O. Sars).

4. Simocephalus acutirostratus, (King).
(Pl. 2, figs, 1—3).

Daphnia Elisabethe, var. acutirostrata, King, 1. c. p. 254,
JE NIE (Ge

Specific Characters. Shell, seen laterally, oblong
oval, terminating posteriorly in a rather prominent, obtusely
conical prominence, slightly denticulated at the tip, and
extending somewhat above the longitudinal axis, dorsal
margin forming a perfectly even curve throughout. Head
comparatively small, procumbent, with the front produced into
an acute deflexed projection, ventral edge straight, ob-
liquely ascending, rostral projection small, deflexed. Eye of
moderate size; ocellus very small, punctiform. Tail rather
broad, forming, above the anal sinus, a gibbous expansion,
anal denticles about 12 on each side, terminal claws with
a series of well-marked secondary teeth. Length attaining
3 mm.

Remarks. This form has been recorded by Mr. King
as only a variety of his Daphnia Elisabethæ. It is, how-
ever, quite certainly, as justly pointed out by Mr. Schoe-
deler, a very distinct species, exhibiting, as it does, several
well-marked differences from all the other known species
of the genus, The specific name acutirostratus is somewhat
inappropriate, since it is not the rostrum, but the front,
which is acutely produced. According to the laws of prior-
ity, however, this name, as the older one, must be preferred
to that proposed by Schoedeler, viz., paradoxus.

On Fresh-water Entomostraca. 13

Description of the female.

The length of the largest specimens examined is about
3 mm., and this form accordingly grows to a rather large
size, as compared with the other species of the genus.

The shell, as in the other species, is rather tumid, and
somewhat navicular in shape. Seen laterally (fig. 1), it ex-
hibits an irregular oval, or oblong sub-rhomboidal form, with
the posterior extremity remarkably produced, and forming
a rather large, obtusely conical prominence extending some-
what above the longitudinal axis of the body. The pro-
minence is not defined above by any distinct sinus, and
exhibits at the tip a number of small appressed denticles.
The dorsal margin of the shell is quite evenly convex
throughout, and continuous with that of the head, though,
as usual, a small indentation may be traced between the two
in the cervical region. ‘The inferior edges of the valves are
greatly bulging in front, and posteriorly join the obliquely
ascending posterior edges by an even curve.

The head (see also fig. 2) is comparatively small and
procumbent, and is highly distinctive by the production of
the front into a very conspicuous acute, deflexed projection,
resembling a rostrum. Behind the latter, the ventral edge
ascends obliquely and quite evenly to the small, deflexed,
true rostrum. The fornix is moderately prominent, and of
the usual appearance, joining the valvular part of the shell
at a very acute angle.

The shell is sculptured in the usual manner by oblique,
partly anastomosing striæ, running parallel to the posterior
edges; and exhibits inside, at some distance from the inferior

edges, a ciliated ridge.

14 G. O. Sars.

The eye (see fig. 2) is not very large, and exhibits a
number of well-defined crystalline bodies projecting from
the dark pigment.

The ocellus (ibid.) is very small, punctiform, and occurs
near the insertion of the antennulæ.

The latter appendages (ibid.) exhibit the usual structure,
and this is also the case with the antenne (see fig. 1).

The tail (fig. 3) is remarkably broad, and differs from
that in other species by the production of the posterior
edge, above the anal sinus, to a nearly rectangular gibbous
expansion, The anal sinus itself is defined above by a
rather small, obtusangular corner, and is armed on each
side with about 12 denticles, successively rapidly increasing
in length distally. The terminal claws are nearly straight,
and each armed in their basal part with a regular, comb-
like series of well-marked secondary teeth.

The number of eggs in the matrix is often very great,
amounting to more than 50 in all. i

Young specimens have the acute projection of the front
as distinct as in the adults, and only differ in their smaller
size, and in the dorsal margin of the shell not being con-
vex, but nearly straight.

Occurrence.—Mr. King found this form in ponds at
Denham Court. In one of the gatherings kindly sent me
by Mr. Whitelegge, and taken from Waterholes at Bourke
Street, this species occurred rather abundantly, and it was also
found in another sample probably from the same locality.

Though some ephippia apparently of this form were
detected in the mud sent me from the said place, I did not
succeed in hatching this form in my aquaria, As, however,
the spirit-specimens sent were in a very good state of pre-

servation, a minute examination could be instituted, especi-

On Fresh-water Entomostraca. 15

ally by mounting the specimens in canada balsam, whereby

a sufficient transparency of the body could be obtained,

5. Simocephalus gibbosus, G. O. Sars, n. sp.
(Pl. 2, figs. 4-6).

Specific Characters—Y Shell, seen laterally, ob-
liquely oval, widening posteriorly, and terminating with a
comparatively short and blunt median prominence; dorsal
margin for the greater part of its length, almost straight,
posteriorly, however, abruptly curved, forming a large and
very conspicuous, gibbous expansion just above the median
prominence, edges of the expansion closely denticulated.
Head of moderate size, less procumbent than in the prece-
ding species, front narrowly rounded, ventral edge scarcely
ascending, and slightly convex in the middle, rostral projec-
tion almost obsolete. Eye comparatively larger than in the
preceding species; ocellus prolonged anteriorly into a narrow
stripe. Tail less broad, posterior edge above the anal sinus
searcely expanded; anal denticles 10—12 on each side ;
terminal claws quite smooth. Length of adult female 2 mm.

Remarks.—This new species is allied to the European
S. vetulus, and has a similarly formed ocellus, but is at once
distinguished by the very conspicuous gibbous expansion of
the dorsal face posteriorly, which gives. the shell a peculiar
oblique shape. This expansion is even traceable in quite
young specimens.

Description of the female.

The length of fully adult, ovigerous specimens does not
exceed 2 mm., and this form is accordingly rather inferior
in size to the preceding one.

2 — Archiv for Math. og Naturv. B. XVIII No. 3.
Trykt den 9de Juni 1896,

16 G. O. Sars.

Seen laterally (fig. 4), the shell exhibits a somewhat irregu-
lar, obliquely oval form, being gradually expanded posteriorly,
and terminates in a well-defined, though rather short and blunt .
prominence, which extends in the direction of the longitudinal
axis of the body. The dorsal margin appears, throughout
the greater part of its length, almost straight; but quite
posteriorly it makes an abrupt bend, so as to form here a
greatly projecting gibbous expansion, extending just above
the median prominence, and defined from it by a well-marked
sinus. The edge of the expansion is coarsely denticulated,
the denticles being also continued around the median pro-
minence. The inferior edges of the valves appear somewhat
less bulging in front, and join the oblique posterior edges
by a greater curve.

The head (see also fig. 5) is comparatively larger than
in the preeeding species, and less procumbent, being, as
usual, defined from the shell above by a small indentation.
Its dorsal margin is slightly curved, and joins the ventral
edges immediately, without any intervening frontal projection,
the front itself being narrowly rounded. The ventral edge
is slightly convex in the middle, and scarcely ascending,
and the rostral projection is rather indistinct, and not, as
usual, deflexed. The fornix exhibits the usual appearance.

The eye (see fig. 5) is comparatively somewhat larger
than in the preceding species, and located just within the
front.

The ocellus (ibid.) exhibits an appearance similar to
that found in S. Elisabethæ, and in the European species
S. vetulus, being drawn out in front to a narrow stripe.

The tail (fig. 6) is not nearly so broad as in S. acu-
tirostratus, the posterior edge above the anal sinus not

being, as in that species, gibbously expanded, but only very

On Fresh-water Entomostraca. 17

slightly convex. The defining upper corner of the anal
sinus is, on the other hand, more prominent and nearly
rectangular. The anal denticles are 10--12 on each side,
increasing, as usual, rapidly in length distally. The terminal
claws are perfectly smooth, without any trace of secondary
teeth.

The ova in the matrix are comparatively larger than
in the preceding species, though sometimes present in a
rather considerable number.

Occurrence.—Of this pretty species a number of spe-
cimens were collected by Mr. Whitelegge in the Centennial
Park, near Sydney.

Gen. Moina, Baird.

6. Moina propinqva, G. O. Sars.

Moina propinqva, G. O. Sars, On some Australian
Cladocera raised from dried mud, p. 29, Pl. 5, figs. 4, 5;
1216. =

Of this species, which in its general appearance strongly
recalls the European M. braciata, some few specimens were
collected by Mr. Whitelegge from waterholes off Bourke
Street.

The same form was also raised in one of my aquaria,
from mud derived from the same locality. It did not,
however, multiply to nearly such an extent as the 2 suc-
ceeding species.

Distribution. — Queensland (G. O. Sars).

18 G. O. Sars.

7. Moina australiensis, G. O. Sars, n. sp.
(PL 3.)

Specific Characters.—Shell of the usual appearance,
varying in female considerably in form, according to the
degree of distention of the matrix. Head in female not
very large, and somewhat procumbent, being evenly vaulted
above, with a very slight, though distinct sinus above the
eye, front not much produced and obtusely rounded, ventral
edge but very slightly convex at the insertion of the anten-
nule. Head in male comparatively much larger, sub-erect,
and less strongly vaulted above, frontal part obtusely trun-
cated, ventral edge straight. Eye of moderate size. Anten-
nulæ in female comparatively short, subfusiform, in male
about the length of the head, and armed at the tip with 4
strong claws. First pair of legs in female with the sub-api-
cal seta simple, ciliated; those in male having, in addition
to the usual claw, an unguiform spine and a long terminal
seta. Caudal claws quite smooth. Ephippium with 2 egg-
ampullæ placed obliquely transversally. Body pellucid, in
female with a more or less distinct orange hue. Length of
adult female 1,30 mm., of male 0,30 mm.

Remarks.—This form exhibits several points of agree-
ment with the European species M. paradoxa, Weismann, and
indeed at first I belived it to be the very same species. Being
however acquainted with another Australian species, which ex-
hibits a similar agreement, and having instituted a closer com-
parison between the European species and these 2 Australian
forms, I am now induced to regard them as being speci-
fically distinct. From M. propinqva, the present species is
easily distinguished by the rather different form of the head,
the structure of the Ist pair of legs in the male, and by the

ephippium having 2, instead of a single egg-ampulla.

On Fresh-water Entomostraca. 19

Description of the female.

The largest specimens examined attain a length of 1,30
mm., and this form accordingly grows to a somewhat larger —
size than M. propinqua, which, as a rule, does not exceed
a length of 1 mm.

The general form of the body (see fig. 1) is that cha-
racteristic of the genus, the head being very sharply marked
off from the shell by a deep dorsal depression.

The form of the shell appears rather variable, according
to the degree of distention of its dorsal part with ova or
embryos. Sometimes this part is quite enormously distended,
so as to form an almost globular expansion, sharply defined
from the valvular part of the shell, and this is gener-
ally the case with all the individuals of the earlier gener-
ations. The valvular part of the shell, however, preserves
its shape unaltered, in all specimens being comparatively
_small, so as not fully to obtect the tail, a greater part of
which is always seen to project freely beyond the shell
posteriorly. At the junction between the dorsal and valvular
parts, the shell projects posteriorly as a short and obtuse
prominence, below which the posterior edges appear slightly
incurved. The inferior edges of the valves are nearly
straight, and join by a perfectly even curve both the anterior
and posterior edges. They are clothed with small marginal
hairs, which are more distinct in the anterior part, gradu-
ally disappearing behind.

The head is comparatively small and somewhat pro-
cumbent, without any trace of a dorsal crest, being evenly
vaulted above. Just above the ocular region, a slight sinus
may be traced, but this sinus is not nearly so pronounced
as in M. propinqva. The frontal, or ocular part is but slightly

20 G. O. Sars.

prominent, and is evenly rounded; and the ventral edge of the
head forms only a slight convexity at the insertion of the
antennulæ, without being defined by any perceptible notch
from the base’ of the labrum. Of the fornix, only a slight
trace is found as a somewhat elevated ridge above the base
of the antenne.

The eye is of moderate size, and provided with a
number of well-defined crystalline bodies. The ocellus, as
in the other species of the genus, is wholly absent.

The antennule (fig. 2) are comparatively short, scarcely
exceeding half the length of the head, and exhibit a some-
what fusiform shape, being distinctly dilated in the middle.
They are, as in the other species, freely mobile, and are
clothed posteriorly with delicate cilia. Anteriorly each
antennula carries a single sensory bristle, occurring somewhat
nearer to the base than to the tip, and the latter has a bundle
of very small olfactory papillee.

The antenne are powerfully developed, and of the_
structure characteristic of the genus. The scape is very
massive and strongly muscular, and is provided near the
base outside with 2 juxtaposed and rather long sensory
bristles, which, especially in the dorsal or ventral views of
the animal, are very conspicuous; at the end, another sensory
bristle is seen projecting between the bases of the rami.
Both the outer part of the scape and the rami are densely
hairy, and the natatory setæ finely ciliated.

The 1st pair of legs (fig. 3) are constructed in the very
same manner as in the European species, M. brachiata, and
differ markedly from those in M. paradoxa, by the sub-
apical seta being quite simple and finely ciliated, like most
of the other sete, whereas in A. paradoxa, according to

On Fresh-water Entomostraca. Pil

the statement of Prof. Weissmann, this seta is very strong,
spiniform, and coarsely denticulated anteriorly.

The tail agrees in its structure with that in most other
species, its outer part beyond the anal opening (fig. 4) being
conically tapered, and provided on each side with 10—12
denticles, the outermost of which is bidentate, whereas the
others are extremely delicate, squamiform and finely ciliated
on both edges. The terminal claws are perfectly smooth,
without any trace of secondary teeth.

The ephippium (fig. 5) is of an oval or somewhat
semilunar form, and has the surface very coarsely reticulated.
It contains, as in M. paradoxa, 2 egg-ampulle, which are
somewhat obliquely disposed, the one behind the other.
Before the ephippium is detached from the shell, jhowever,
the 2 winter-eggs occupy a rather different place, being, as
shown in the succeeding species (see PI. 4, fig. 2), juxtaposed
in the anterior part of the matrix; and in a lateral view of
the animal it therefore appears as if only a single ovum
were present.

The adult male (figs. 6, 7) is rather inferior in size
to the female, scarcely exceeding a length of 0,80 mm., and
exhibiting a very different appearance.

The shell is much narrower, its dorsal part not being
at all expanded; and the posterior extremity appears, in the
lateral view of the animal, obtusely truncated, forming above
almost a right angle. The inferior edges of the valves are
densely clothed with fine hairs, which, in their anterior part,
assume a fur-like appearance.

The head looks very different from that in the female,
being much longer and more erect. It gradually tapers
towards the front, which appears obtusely truncated and
defined above by a very slight sinus. The inferior edge of

2 G. ©. Sars.

the head is perfectly straight and horizontal, whereas the
upper one is obliquely ascending- and, but very slightly
convex.

The antennulæ, which issue from the most anterior part
of the head, are greatly developed, being fully as long as
the head. They are very mobile, but, as a rule, extended
obliquely anteriorly, with the terminal part more or less
incurved (see fig. 7). Near the base they each form a some-
what genicular bend, and at this place 2 unequal sensory
bristles are seen to project anteriorly. The outer part of
the antennule is rather narrow, and nearly cylindric, and
terminates with 4 strongly curved hooks, between which a
small bundle of olfactory papillæ is traceable (see fig. 8).

The Ist pair of legs (fig. 9) are, as usual, transformed
into powerful grasping organs. They closely resemble in
structure those in the male of M. paradoxa, as figured by
Prof. Weismann, each having a rather long, setiform appen-
dage extending beyond the claw, and terminating in a fine
hooked point. In addition, a thin lamella is seen projecting
inside the claw, having 3 apical bristles, the anterior of
which is curved in a hook-like manner, and devoid of cilia.

The tail does not seem to differ essentially in structure
from that in the female.

The testes (see fig 6 & 7) are confined to the posterior
part of the trunk, appearing as 2 somewhat twisted bags,
which extend along the sides of the intestinal tube. They
are each continued into a narrow duct, which enters the
tail, and debouches at the sides of the anal orifice. Viewed
by a high magnifier (fig. 10), they are found to be filled
with clear rounded cells, very densely accumulated in the
anterior, dilated part of the bags. It often happens, when .

a male specimen is examined for any length of time under

D

On Fresh-water Entomostraca. 2

t

IV

the microscope, that some of the zoosperms are poured out
from the genital openings, and in such cases I have always
found them to be simple, rounded, cellular bodies (fig. 11),
never showing any approach to the peculiar vermiform
shape deseribed by Prof. Weismann in the male of M.
paradoxa.

In living specimens of both sexes, the body is very
pellucid, and in the male almost colourless. In the female,
it generally exhibits a more or less distinct orange tinge,
and this would seem to be invariably the case with
individuals of the earlier generations, whereas those of later
generations, as a rule, become more pale in colour.

The «summer-eggs» are at first, when received in the
matrix, very small and nearly colourless, with only a very
small quantity of nutritive yolk. They, however, rapidly
increase in size during the development, imbibing, as first
stated by Prof. Leydig, a nourishing fluid contained in the
cavity of the matrix, and secreted from a dense cellular
layer on the back of the parent animal. The «winter-eggs»
are considerably larger, and of a brick-red colour.

Observations.—Of the present form, numerous speci-
mens developed in my aquaria, and in some of them multi-
plied in quite an astonishing manner, so as at last to fill
up the aquaria with myriads of individuals. The earlier
generations consisted exclusively of female specimens; but
after the lapse of some time, the characteristic ephippial
formation was beginning, and at that time male specimens
made their appearance in rather large numbers. After the
ephippia were deposited, some of the females again became
laden with summer-eggs, though generally not in such
great numbers as in the individuals of the earlier gener-
ations. From that time, the males gradually diminished in

24 G. O. Sars.

numbers, and at last scarcely a single male specimen was to
be detected, though the females were still present in great
numbers, multiplying in the usual parthenogenetical manner.
In some of my aquaria, a 2nd bisexual period was observed,
and thereby the «polycyclar» character of this form ascer-
tained.

In habits, this form agrees with the other species of
the genus. The movements of the animal are rather rapid,
and effected by short abrupt jerks, whereby the body gener-
ally assumes a somewhat prone attitude. The males, as
usual, are still more agile, and were often seen eagerly to
pursue the females. I also happened several times to
observe the male getting a rather firm hold of the female
embracing with his powerful antennule the lower part of
her shell, and at the same time inserting his prehensile 1st
pair of legs within the edges of her valves.

Occurrence.—The mud, from which this species was
raised, was taken by Mr. Whitelegge from waterholes at
Bourke Street, opposite Lachlan Street, and off Botany Road,
near Waterworks Bridge. A spirit sample taken from
the same localities likewise contained numerous specimens
of the same species. Moreover, the greater number of the
specimens contained in the sample first received from
Prof. Ramsay, and taken from the Waterloo Swamps, turned
out, on a closer examination, to belong to the said species.

8. Moina tenuicornis, G. O. Sars, n sp.
(PL. 4)
Specific Characters.—Very like the preceding spe-
cies, but differing rather markedly in the shape of the head,
which does not exhibit any trace of a sinus above the eye,

and moreover in the female, forms below, at the insertion

On Fresh-water Entomostraca. 25

a

of the antennulæ, a very conspicuous, rounded prominence,
defined from the labrum by a deep notch. Eye compara-
tively larger than in that species. Antennule in female
- comparatively much longer and narrower, sublinear in form;
those in male considerably exceeding half the length of the
body. First pair of legs in both sexes of a simular structure
to that in the preceding species. Terminal claws of tail
armed at the base with a well-marked, comb-like series of
secondary teeth. Ephippium with 2 transversely disposed
egg-ampullæ. Length of adult female 1,20 mm., of male
0,70 mm.

Remarks.—Though very nearly allied to the preceding
species, as also to the European M. paradoxa, this form
may at once be distinguished from both of them by the
form of the head in the female, the remarkably elongated
and narrow antennule, and finally by the terminal claws of
the tail being distinctly denticulated at the base, like those
in M. brachiata.

Description of the female.

The length of the largest specimens is 1,20 mm., and
this form is accordingly but little inferior in size to the
preceding one.

The general form of the body (see fig. 1) agrees rather
closely with that in M. australiensis. On a closer com-
parison, however, the head is found to differ very markedly
in shape, being quite evenly vaulted dorsally, without
exhibiting any trace of a sinus above the eye The front
is obtusely rounded and, as in the preceding species, but
little prominent. On the other hand, the inferior part of
the head is produced, at the insertion of the antennule, to a

rather conspicuous, rounded prominence, which is defined -

26 G. O. Sars.

behind by a deep notch, giving the head, in a lateral view
of the animal, a physiognomy rather different from that in
M. australiensis.

In the form and structure of the shell, scarcely any
essential difference is to be found from that in the said
species, excepting that perhaps the inferior edges of the
valves are more densely setiferous.

The eye is comparatively larger than in M. australiensis,
almost completely filling up the frontal part of the head,
and the crystalline bodies seem also to be more numerous.

The antennulæ (fig. 3) are distinguished by their
unusual length, being comparatively nearly twice as long as
in the preceding species. They are very narrow, sublinear
in form, and provided behind with scattered, delicate hairs.
The sensory bristle of the anterior edge occurs much nearer
to the base than to the tip, being placed at about the end
of the first third part of the length of the antennula.

The antenne do not exhibit any essential difference
from those in the preceding species; the Ist pair of legs
(fig. 4) too are constructed in the very same manner, the
subapical seta being, as in that species, quite simple.

The tail (fig. 5) likewise looks rather similar. But, on
a closer examination, the terminal claws are found to differ
essentially in being each provided at the base with a well-
marked, comb-like series of secondary teeth (see fig. 6).

A similar armature, as is well known, is found in
M. brachiata, whereas in the other European species, M.
paradoxa, the claws are quite smooth, as in M. australiensis
and M. propinqva.

The ephippium (fig. 7), as in the preceding species,
always contains 2 egg-ampulle, which in this form, however,

are placed more transversely, or in a manner similar to that

On Fresh-water Entomostraca. oT

figured by Prof. Weismann in the ephippium of M. para-
doxa. Before the ephippium is detached from the shell,
the 2 winter-eggs occupy (see fig. 2) a similar juxtaposed
situation in the matrix to that observed in the preceding
species.

The adult male (fig. 8) scarcely exceeds a length of
0,70mm., and on the whole closely resembles the male of
M. australiensis, though the antennule appear still more
elongated, considerably exceeding half the length of the
body. The Ist pair of legs are constructed in the very
same manner as in the male of the said species, and the
zoosperms in this form also are represented by simple, clear,
nucleated cells.

As in the preceding species, the body in both sexes is
highly transparent, especially in the male. In the female
generally a faint bluish violet tinge, more rarely changing
to reddish, may be observed. The winter-eggs are brick-red.

Observations.—This form was also raised in con-
siderable numbers in some of my aquaria, and was watched
during numerous succeeding generations. All the specimens
exactly agreed with each other, as to the form of the head,
the slender antennulæ, and the denticulated claws of the
tail. Its habits are much as in the preceding species.

Occurrence.—The mud that yielded this species, was
taken by Mr. Whitelegge from a pond at the corner of
Bourke Street and Botany Road. A spirit sample from
the same place contained numerous specimens of the same
species, exactly agreeing with those raised here in Chris-

tiania.

28 G. ©. Sars.

Gen. Moinodaphnia, Herrick.

Syn. Paramoina, G. O. Sars.

9, Moinodaphnia Macleayii (King).

Moina Macleayii, King, 1. e., p. 251, Pl. V.

A solitary, somewhat imperfect female specimen, ap-
parently of this form, was found in a sample taken by
Mr. Whitelegge from the Marubra Swamp. Mr. King col-
lected this form in a pond near Elisabeth Ray.

Fam. Lyncodaphnidee.

Gen. Macrothrix, Baird.

10. Macrothrix spinosa, King.

Macrothrix spinosa, King, 1. e. p. 256, Pl. VIE.

Macrothrix spinosa, G. ©. Sars. Additional Notes on
Austr. Cladocera raised from dried mud, p. 25, Pl. 3.

Some specimens of this form, described and figured in
detail by the author in the above-quoted paper, were found
in a sample taken by Mr. Whitelegge from a pond near
Sydney.

Distribution.—Queensland (G. O. Sars).

Gen. Ilyocryptus, G. O. Sars.

11. Ilyocryptus sordidus (Liévin).
(Pl. 5, figs 1—3).
Acanthocercus sordidus, Lievin, Die Branchiopoden der
Danziger Gegend: Neueste Schriften der naturf. Gesellsch.
in Danzig, p. 34, Pl. VIII, figs. 7—12.

On Fresh-water Entomostraca. 29

In one of my aquaria there developed several specimens
of an Ilyocryptus, which I am unable to distinguish from
the well-known European species I. sordidus, Lieviu. In
order to show the identity of both forms, I have given on
the accompanying plate a figure of a full-grown female spe-
cimen, together with more highly magnified detail figures of
one of the antennulæ and of the tail. The specimens, which
exhibited a blood-red colour, did not exceed a length of
0,57 mm.

As in most other species of the genus, the shell is not
completely cast off by the several exuviations of the animal,
and in fully grown specimens (fig. 1), therefore each valve
has the appearance of being composed of a more or less
considerable number of superposed valves of different sizes,
most of them still exhibiting their marginal setous armature.
It is chiefly on this account that the animal is generally found
so densely covered with mud as to be scarcely recognizable.
Indeed, the mud adheres so firmly to the numerous rows
of bristles, that it is a matter of great difficulty to cleanse
the shell sufficiently for a minute examination. The speci-
mens were only found on the bottom, more or less deeply
buried in the loose muddy deposit, through which they
moved very slowly by the aid of the antenne and the
powerful tail. I have never seen the animal make even
the slightest attempt to lift itself from the bottom, and in
this respect it differs rather markedly from the 2nd Austra-
lian species, I. longiremis, which is by no means devoid of
swimming power.

Occurrence.—The specimens were raised from the
same parcel of mud, which yielded the above-described
Moina tenuicornis. As above stated, this mud was derived
from a pond at the corner of Bourke Street and Botany

30 G. O. Sars.

Road. In a sample taken by Mr. Whitelegge from another
pond off Botany Road, near Waterworks Bridge, some few
specimens of the same form were contained. Moreover, the
author has raised this species from mud collected in China.

Fam. Lynceidee.
Gen. Chydorus, Baird.

12. Chydorus Leonardi, King.
(PL 5, figs. 4, 5).

Chydorus Leonardi, King, |, e. p. 258, Pl. VII C.

Syn.: Chydorus minor, Lilljeb. M. 8.

This form, first described by Mr. King, is undistinguish-
able from a small Chydorus, which is rather common in
Norway, as also in Sweden, and for which Prof. Lilljeborg
has proposed the name of Chydorus minor. Ås shown by
the figures here given, it is very nearly allied to C. sphæ-
ricus (Mill.), but is of much smaller size, and without any
trace of the reticulation of the shell characterising that
species. The specimen here figured, which measured in
length 0,25 mm., was picked up from a sample taken from
the Waterloo Swamps, near Sydney.

Of the same form numerous specimens also developed
in some of my aquaria, and continued to live and propagate
during the whole season, They were rather active, moving
about in the water in a somewhat revolving manner, at
times affixing themselves to the walls of the aquarium or
to the plants growing in it.

Occurrence.—Mr. King found this form in several

places around Sydney: near Wavely Mills; the waterfall,

On Fresh-water Entomostraca. BIL

St. Leonard’s; South Creek; Denham Court. To these local-
ities may now be added the followings: Waterloo Swamps;
pond opposite Lachlan Street; off Botany Road, near Water-
works Bridge.

In all probability, the species is distributed all over
Europe, Asia, Africa and America, being a true cosmopolite.

13. Chydorus globosus, Baird.
(Pl. 5, figs. 6—7).

Chydorus globosus, Baird, Brit. Entomostraca, p. 127,
eV he. 7.

Chydorus augustus, King, L ce. p. 258, Pl. VII B.

There cannot, I believe, be any doubt that this is the
true Chydorus augustus of King. This form however, as
shown by the figures given on the accompanying plate, is
undistinguishable from the well-known European species
C. globosus of Baird, and, as the name given by Baird is
much the older of the two, it ought to be retained for the
species. The solitary specimen here figured, which measured
0,65 mm. in length, was found in a sample from the Centennial
Park. Mr. King collected the species from a pond on the
Road to Botany Bay,

Gen. Pleuroxus, Baird.

l4. Pleuroxus inermis, G. ©. Sars, pn. sp.
(PL 5, fies. 8, 9).
Specific Characters—Y Shell, seen laterally, of an
irregularly rounded form, and narrowly truncated posteriorly,
dorsal margin boldly curved, ventral somewhat protuberant

in front, and nearly straight behind, infero-posteal corners
3 — Archiv for Math. og Naturv. B. XVIII No. 3.
Trykt den 10de Juni 1896,

32 G. O. Sars.

rounded off, and without any trace of denticles. Head
strongly procumbent, terminating in a long and sharply
pointed rostrum. Surface of valves smooth, except in their
anterior part, where they are sculptured with 10—12 very
conspicuous, curved, transverse striæ, inferior edges densely
ciliated. Ocellus much smaller than the eye. Tail nearly
of uniform breadth, and obtusely truncated at the tip,
posterior edge somewhat flexuous, post-anal angle very slight,
ante-anal denticles extremely small, hair-like, terminal claws
strong and curved, each with 2 secondary denticles at the
base. Colour light corneous. Length of adult female 0,60 mm.

Remarks.—In a previous paper!) I have wrongly
identified this species with Chydorus augustus of King,
which, as above stated, is identical with C. globosus, Baird.
The present form, which is a true Pleuroxus, is very closely
allied to the European. species P. aduncus, Jurine, and exhi-
hits a very similar sculpturing of the valves, but differs in
the more rounded form of the shell, and very markedly in
the rounding off of the infero-posteal corners of the valves,
where there is no trace of the denticles found here in all

the other known species of the genus.

Description of the female.

The length of adult specimens measures 0,60 mm., and
this form is accordingly of about the same size as the Euro-
pean species, P. aduncus. |

The shell is moderately tumid, and, seen laterally
(fig. 8), of a somewhat irregularly rounded form, the greatest

breadth being but little inferior to the length, and occurring

1) On a small collection of Fresh-water Entomostraca from Sydney
(Chr. Vid. Selsk. Forh. 1889) p. 5.

On Fresh-water Entomostraca. 33

somewhat in front of the middle. It is narrowly truncated
posteriorly, and strongly vaulted above, the dorsal margin
forming a bold and rather even curve until the tip of the
rostrum. The inferior edges of the valves are somewhat
protuberant in front of the middle, and join the anterior
edges by an abrupt curve; behind, they appear nearly
straight, or very slightly convex in the middle, and ascend
obliquely to the infero-posteal corners, which are evenly
rounded off. The head is very procumbent, and, as in
the other species of the genus, to a certain degree mobile,
admitting of being bent in against the anterior part of the
valves. It terminates in a long and sharply-pointed rostrum,
which curves somewhat posteriorly, and projects considerably
beyond the free edges of the valves. The fornix appears
as an elevated sigmoid ridge, which joins the valves at a
very acute angle.

The surface of the shell appears, in its greater part,
quite smooth, without any perceptible reticulation. In the
most anterior part of the valves, however, a very conspi-
cuous sculpturing is traced, consisting of from 10 to 12
curved, transverse striæ, which run parallel to the ante-
rior edges, and are very sharply marked. The inferior
edges of the valves are throughout fringed with delicate
bristles, which, especially in their posterior part, are rather
conspicuous and finely ciliated. The infero-posteal corners
are quite smooth, without the slightest trace of the strong
denticles occurring here in other species.

The eye is of moderate size, and occupies its usual place.

The ocellus is scarcely half as large, and occurs much
nearer to the eye than to the tip of the rostrum.

The antennule are short and thick, extending scarcely

beyond the middle of the rostrum.

34 G. ©. Sars.

The antennæ are comparatively short, and of the usual
structure.

The tail (fig. 9) is of moderate size, and almost of uni-
form breadth throughout, being obtusely truncated at the
tip, with the posterior corner rounded off. The post-anal
angle is but little prominent, and is obtuse. The posterior
edge below it appears very slightly flexuous, being some-
what convex in the middle. The ante-anal denticles are
very small, almost hair-like, and occupy the outer half of
the edge, being continued around the distal corner. The
terminal claws are rather strong and curved, having each 2
distinet secondary denticles at the base, not found in the
European species P. aduncus.

As in most other Lynceidæ, the matrix never contains
more than 2 ova or embryos, which are generally juxtaposed.

The body in living specimens is semi-pellucid, thus
showing through the integuments several of the inner organs,
especially the dark-coloured and twisted intestinal tube. It
generally exhibits a yellowish or light corneous hue.

Observations.—Of this species some specimens were
found in one of my aquaria, all of them females. They
did not, however, multiply to any greater extent, and in the
latter part of the summer, this form wholly disappeared.
The animal is rather agile, moving quickly through the water
in much the same manner as the species of Chydorus. Very
often it was also seen clinging to the wall of the aquarium
or to the plants growing in it.

Occurrence.—The mud, from which I raised this spe-
cies, was taken by Mr. Whitelegge from a pond opposite
Lachlan Street, Bourke Street; and in a sample from the

same locality, a considerable number of specimens was con-

On Fresh-water Entomostraca. 35

tained. It also occurred in the sample first received from

Prof. Ramsay, and taken from the Waterloo Swamps.

Gen. Alona, Baird.
15. Alona Whiteleggii, G. O. Sars, n. sp.
(Pl. 6, figs. 1, 2).

Specific Characters.—Y Shell, seen laterally, oval
quadrangular, but very slightly widening behind, dorsal
margin evenly arcuate, ventral nearly straight, hind extremity
somewhat obliquely truncated, with the upper corner obso-
lete, lower rounded off. Head somewhat procumbent, ter-
minating in an acute rostrum. Surface of shell striated
longitudinally, inferior edges densely ciliated. Ocellus almost
as large as the eye. Tail rather large, lamellar, though
searcely widening distally, being obtusely truncated at the
tip, post-anal angle almost obsolete, posterior edge below it
very slightly convex, of ante-anal denticles about 15 pairs, each
accompanied by a squamiform lateral denticle, terminal claws
each with a rather strong secondary denticle at the base.
Length of adult female 0,63 mm.

Remarks.—This form is somewhat intermediate in
character between the European species, A. qvadrangularis
and oblonga, without being referable to either of them. In
size and sculpture it more resembles the first-named species,
but the form of the shell and that of the tail is rather dif-
ferent, and agrees more with that found in A. oblonga. I
have much pleasure in dedicating this beautiful species to
Mr. Whitelegge, to whom I am indebted for the greater
part of the material here treated off.

36 G. O. Sars.

Description of the female.

The length of the specimen examined, which is a fully
grown ovigerous female, measures 0,63 mm., and is accord-
ingly somewhat inferior to that of both the above-named
European species.

Seen laterally (fig. 1), the shell exhibits an oval quad-
rangular form, with the greatest breadth about in the middle.
The hind extremity is obliquely truncated, and not nearly
so broad as in A. qvadrangularis, and with the inferior corner
the more prominent. The dorsal margin forms a perfectly even
curve until the tip of the rostrum, and joins the hind edge
without any distinct intervening angle. The inferior edges
of the valves are nearly straight and horizontal, though
slightly ascending in front to the anterior corners. Behind,
they join the posterior edges by a rather sharp but perfectly
even curve. The head is somewhat procumbent, not nearly
so erect as in the 2 European species, and terminates in
an acute, somewhat hooded rostrum.

The surface of the shell is sculptured with well-marked,
and rather closely set, longitudinal striæ, about 20 on each
side, These striæ are more conspicuous in the posterior
part of the shell, disappearing gradually in front. The infe-
rior edges of the valves are throughout fringed with deli-
cate bristles.

The eye is well developed, exhibiting some few very
conspicuous crystalline bodies.

The ocellus is comparatively large, almost attaining the
size of the eye, and occurs somewhat nearer to it than to
the tip of the rostrum

The antennulæ are rather narrow and sub-fusiform, and do

not quite extend to the tip of the rostrum. They are pro-

On Fresh-water Entomostraca. 37

vided at the tip with a bundle of somewhat unequal olfactory
papille, and have, moreover, each a delicate sensory bristle
projecting from the anterior edge about in the middle.

The antennæ are well developed, and exhibit the normal
structure.

The lamellar expansion of the labrum is of moderate
size, and exhibits the usual securiform shape, its edge being
quite smooth.

The tail (fig. 2) is rather large, lamellar, and almost of
equal breadth throughout, or but very slightly expanded
distally, being obtusely truncated at the end, with the pos-
terior corner rounded off. The post-anal angle is rather
indistinct, nearly obsolete, and the posterior edge below it,
very slightly convex, exhibiting a double row of well-defined
denticles, about 15 in each row. Somewhat within the edge,
moreover, occurs on each side a lateral row of very deli-
cate, somewhat squamiform denticles, corresponding in num-
ber with the marginal ones. The terminal claws are rather
strong, and each armed at the base with a comparatively
large secondary denticle.

Occurrence.—The above-described specimen, the only
one I have seen, was found in _a sample taken by Mr.
Whitelegge from the Centennial Park, near Sydney.

16. Alona pulchella, King.
(Pl. 6, figs. 3, 4).
Alona pulchella, King, 1. c. p. 260, Pl. VIII B.
Specific Characters.—Shell, seen laterally, oblong
quadrangular, not widening at all behind, posterior extremity
obtusely truncated, with the lower corner rounded off, dor-
sal margin evenly arcuate, ventral straight. Head sub-erect,

38 G. O. Sars.

terminating in an acute rostrum, Surface of shell faintly
striated longitudinally. Ocellus much smaller than the eye.
Tail comparatively short and of uniform breadth, trans-
versely truncated at the tip, with the posterior corner well
defined, postanal angle distinct, though obtuse, posterior
edge below it perfectly straight and armed with a double
row of very delicate denticles, in front of which there is
on each side a lateral series of still more delicate, squami-
form spinules, terminal claws rather elongated, each with a
distinct secondary denticle at the base. Length of adult
female 0,58 mm.

Remarks —This is, as I believe, the form originally
recorded by Mr. King under the above name. It is closely
allied to another Australian species described by the present
author from the northern part of the country as A. levissima.
But in the latter form, as indicated by the specific name, the
shell is perfectly smooth, whereas in the present species it
exhibits the usual longitudinal striation.

Description of the female.

The length of adult, ovigerous specimens does not
exceed 0,58 mm., and is accordingly rather inferior to that
of the preceding species.

The form of the shell, when seen laterally (fig. 3), is
oblong quadrangular, being scarcely wider behind than in
front. The posterior extremity appears obtusely truncated,
with both the upper and lower corners rounded off, the
latter being the more prominent. The dorsal margin is
quite regularly arcuate until the tip of the rostrum, and
has its greatest curvature about in the middle, whereas the
ventral one appears almost straight and horizontal. The
head is less procumbent than in the preceding species,

On Fresh-water Entomostraca. 39

and terminates in an acute rostrum, somewhat shorter than
in that species.

The surface of the shell is sculptured with distinct,
though not very sharply marked, longitudinal striæ, which
are less closely set than in the preceding species, their
number being from 14 to 15 on each side. The inferior edges
of the valves are, as usual, densely ciliated.

The eye is well developed, with distinct, though small
erystalline bodies.

The ocellus is much smaller than the eye, and plac:d a
little nearer to it than to the tip of the rostrum.

The antennule exhibit the usual narrow subfusiform
shape, and do not extend to the tip of the rostrum.

The antenne are less powerful than in the preceding
species.

The lamellar expansion of the labrum is rather large,
and has the edge perfectly smooth.

The tail (fig. 4) closely resembles that in A. levissima,
being comparatively short, and of uniform breadth. It is
transversely truncated at the tip, with the posterior corner
well defined and somewhat produced. The post-anal angle
is distinctly marked, though not very prominent, and
the posterior edge below it appears perfectly straight, car-
rying a double row of very small, hair-like denticles, 10 —12
in each row. As in the preceding species, there is on each
side an additional lateral row of extremely delicate, some-
what squamiform spinules. The terminal claws are con-
siderably elongated, and each exhibit at the base a well-
marked secondary denticle.

Occurrence.—Some few specimens of this form, all
of them females, were found in the sample at first received
from Prof. Ramsay, and taken from the Waterloo Swamps.

40 G. O. Sars.

Mr. King collected the species at Varroville, near Denham
Court, and also at St. Leonards, near Sydney. In the
samples taken by Mr. Whitelegge, this species did not occur.

17. Alona abreviata, G. O. Sars, n. sp.
(Pl. 6, figs. 5, 6).

Specific Characters.—X Shell comparatively short
and stout, and, seen laterally, of irregular quadrangular form,
broadest in front of the middle, posterior extremity trans-
versely truncated, dorsal margin abruptly curved in front,
ventral slightly convex anteriorly. Head somewhat flattened
above, semi-erect, terminating in a rather prominent, acute
rostrum Surface of shell sculptured in its posterior part
with obliquely longitudinal lines, which are somewhat flexu-
ous, so as to form an indistinct reticulation, anterior part
of valves transversely striated, inferior edges ciliated.
Ocellus smaller than the eye. Lamellar expansion of the
labrum with a distinct notch anteriorly. Tail short and
stout, obtusely truncated at the end, with the posterior
corner evenly rounded, and armed on each side with about
10 well-defined denticles, post-anal angle rather prominent,
and occurring at about the middle, terminal claws of moder- _
ate size, and each armed with a small secondary denticle.
Colour pale corneous. Length of adult female 0,37 mm.

Remarks.—This form, at the first sight, looks very
like the New Zealand species, A. macrocopa, described by the
present author in another paper, but differs, on a closer com-
parison, in the somewhat different sculpture of the shell,
as also in the minor development of the antenne. Both
these species form, as it were, a transition to the genus

Alonella, though being distinguished from the species of

On Fresh-water Entomostraca. 41

that genus by the immobility of the head, as in the other
species of Alona.

Description of the female.

Fully adult, ovigerous specimens do not exceed a length
of 0,37 mm., and this form is accordingly of very small size.

The shell is unusually short and stout, exhibiting, in a
Jateral view of the animal (fig. 5), a somewhat irregular
quadrangular form, with the greatest breadth somewhat in
front of the middle. The posterior extremity appears trans-
versely truncated, with the upper corner well marked, the
lower rounded off. The dorsal margin is boldly arched,
forming an abrupt curve at the junction with the head,
whereas the ventral one appears straigther, though exhi-
biting a slight convexity in front of the middle. The head
is semi-erect, and has the dorsal face somewhat flattened, its
upper edge being almost straight and declining towards the
rostrum; the latter is rather prominent and, when seen later-
ally, acuminate.

The surface of the shell is very distinctly sculptured,
exhibiting in its posterior part a number of obliquely
longitudinal lines, which appear somewhat flexuous, thus
forming an indistinct reticulation. These lines, in the
anterior part of the valves, are crossed by a set of curved,
transverse striæ, running parallel to the anterior edges, and
rather sharply marked. The inferior edges of the valves
are, as usual, densely ciliated.

The eye is of moderate size, and in its usual situation.

The ocellus occurs somewhat nearer to it than to the
tip of the rostrum, and is of very interior size.

The antennule exhibit the usual structure, and do not
extend to the tip of the rostrum.

42 G. O. Sars.

The antennæ are of normal appearance, not being of
any unusual size.

The lamellar expansion of the labrum is rather large,
and exhibits in front a distinct notch not found in the
other known species.

The tail (fig. 6) is short and thick, on the whole
resembling in shape that in A. macrocopa, though having
the tip less obliquely blunted, and the rounded posterior
corner more prominent; around the latter, a double series
of from 8 to 10 well-defined denticles occur. The post-anal
angle, as in A. macrocopa, is rather prominent, and placed
nearly in the midåle of the posterior edge.

The colour in living specimens is yellowish, or pale
corneous.

Observations.—This form developed rather plenti-
fully in one of my aquaria, and during one period of the
season, it occurred in such numbers, that I was almost sure
to get some specimens, on taking up, by the aid of a dip-
ping tube, a very small portion of the loose bottom deposit,
and examining it in a watch-glass. In the latter part of the
summer, however, it almost wholly disappeared, and no male
specimens were for this reason secured. It moves through
the water in the very same manner as most other species
of the genus, the movement being quite even and somewhat
tremulous, not, as is the case with the New Zealand spe-
cies, by abrupt jerks.

Occurrence.—The mud from which this form was
raised, was taken by Mr. Whitelegge from a pond at the
corner of Bourke Street and Botany Bay. ‘The species also
occurred in a sample from the same locality, but in a very

limited number.

On Fresh-water Entomostraca. 43

Gen. Alonella, G. O. Sars.

18. Alonella diaphana (King).

Alona diaphana, King, I, e. p. 360, Pl. VIII C.

Alonella diaphana, G. O. Sars, Add. Notes Austr. Cla-
docera, p. 47, Pl. 5, figs. 5—7.

This form, described and figured in detail by the present
author in the above-mentioned paper, developed in the same
aquarium as Alona abbreviata, but did not occur in any
considerable number. It was, moreover, found in a sample
taken by Mr. Whitelegge from the Centennial Park, though

rather scarce.

19. Alonella clathratula, G. O. Sars, n. sp.
(Pl. 6, figs. 7, 8).

Specific Characters.—X Shell, seen laterally, oblong
oval, greatest breadth in front of the middle, posterior
extremity narrowly truncated, with the lower corner well
defined, simple; dorsal margin evenly arcuate, ventral some-
what flexuous and convex in front. Head procumbent, pro-
duced to a sharply-pointed rostrum. “Surface of shell very
distinctly sculptured, exhibiting posteriorly a rather regular
reticulation, anterior part of valves striated transversally.
Ocellus much smaller than the eye. Tail rather narrow,
not widening distally, post-anal angle well-marked, tip nar-
rowly truncated, ante-anal denticles very small, hair-like,
terminal claws of moderate size, each with a well-marked
secondary denticle at the base. Length of adult female
0,36 mm.

Remarks. —This form is somewhat nearly allied to the
European species, A. excisa, Fisher, but differs in the more

44 G. O. Sars.

elongated form of the shell, and in the infero-posteal corners

being simple, not excised.

Description of the female.

The length of fully adult, ovigerous specimens does not
exceed 0,36 mm., and this form is accordingly of rather
small size.

The form of the shell, when seen laterally (fig. 7), is
oblong oval, with the greatest breadth about in the middle,
and the posterior extremity narrowly truncated. The dorsal
margin is quite evenly arcuate, and forms with the posterior
one a distinct, though somewhat obtuse angle.

The inferior edges of the valves are somewhat flexuous,
being rather convex in front, but posteriorly assuming a
straighter course. They are defined from the posterior
edges by a distinctly projecting corner, which sometimes
terminates in a sharp point. No notch, however, like that
generally occurring in 4. excisa, is ever found above this
corner.

The head, as in most other species of the genus, is
rather procumbent, terminating in a long, acuminate, some-
what posteriorly-curving rostrum.

The surface of the shell is very conspicuously sculp-
tured, exhibiting in its posterior part a rather regular reti-
culation, the meshes being disposed in oblique rows, whereas
anteriorly, each valve exhibits a number of sharply-marked,
curved, transverse striæ. The inferior edges of the valves
are densely fringed with delicate bristles.

The eye occupies its normal place, and is of mode-
rate size.

The ocellus occurs much nearer to the eye than to the

tip of the rostrum, and is of very inferior size.

On Fresh-water Entomostraca. 45

-

The antennulæ are comparatively short and thick,
searcely extending beyond the middle of the rostrum.

The antennæ are rather small, and of the usual structure.

The tail (fig. 8) is comparatively narrow, and somewhat
resembles in form that in A. excisa, not being at all
expanded distally, and having the tip narrowly truncated.
The post-anal angle is well defined, though not very pro-
minent, and the ante-anal denticles are very small, almost
hair-like, and present to the number of about 10 pairs.
The terminal claws are not very strong, and have each a
minute secondary denticle at the base.

Occurrence.—Some specimens of this small Lynceid
were picked up from a sample taken by Mr. Whitelegge
from the Marubra Swamp, near Sydney. The specimens

were of a very dark grey hue.

Gen. Camptocercus, Baird.

20. Camptocercus australis, G. O. Sars, n. sp.
(PL. 6, figs. 9, 10).

Specific Characters. — Y Shell highly compressed
and, seen laterally, of oblong form, broadest in front, poste-
rior extremity narrowly rounded, dorsal margin evenly con-
vex, ventral bulging anteriorly, straight behind. Head rather
large, crested, terminating in a deflexed, blunt rostrum.
Surface of shell longitudinally striated; inferior edges cili-
ated in the middle and not exhibiting any trace of denticles
at the infero-posteal corners. Eye small; ocellus still
smaller, both occurring at a rather considerable distance
from the anterior edge of the head. Tail very slender and

elongated, conically tapering distally, post-anal angle well-

46 G. O. Sars.

marked, ante-anal denticles about 20 pairs, terminal claws
slender, each with 2 distant secondary denticles. Length of
adult female 0,74 mm.

Remarks.—This form looks very like the well-known
European species, ©. macrurus, Müll, but is at once distin-
guished by the total abscence of the denticles found at the
infero-posteal corners of the shell in that, as also in the
other known species of the genus.

Description of the female.

The body, as in the other species, is highly compressed,
and provided with a distinct crest, extending along the
dorsal face of both the shell and the head. Seen laterally
(fig. 9), the shell exhibits an oblong form, being broadest in
front, and narrowed towards the posterior extremity, which
appears obtusely rounded, without any angle below, and
with the upper corner almost obsolete. The dorsal margin
forms a rather even curve until the tip of the rostrum,
whereas the ventral one appears somewhat flexuous,
being rather protuberant in front, and assuming behind a
more straight course. The head is rather large and some-
what procumbent, terminating in a blunt, deflexed rostrum.
The fornical edge is but very slightly curved, and joins the
shell on each side at a very acute angle.

The surface of the shell is sculptured with well-marked
longitudinal striæ, about 18 on each side, and exhibits
besides, in the most anterior part of the valves, a number
of closely set, curved transverse lines. The inferior edges
of the valves are fringed with delicate bristles, which suc-
cessively diminish in length behind, and disappear altogether
at some distance from the posterior extremity. Not even

the slightest trace of any denticles is found behind the

On Fresh-water Entomostraca. 47

bristles at the infero-posteal corners of the shell, which
appear perfectly smooth, and evenly rounded off.

The eye is rather small, and located at a considerable
distance from the anterior edge of the head. This is also
the case with the ocellus, which is much smaller than the
eye, and occurs somewhat nearer to it than to the tip of
the rostrum.

The antennule are rather slender and elongated, though
not extending beyond the tip of the rostrum, except by
their apical papille, which latter are rather fully developed,
and of somewhat unequal length.

The antennæ are comparatively short, and of the usual
structure.

The lamellar expansion of the labrum is not very large, but
of the usual securiform shape, with the edge perfectly smooth.

The tail (fig. 10) exhibits the structure characteristic of
the genus, being very slender and exceedingly mobile. It is of
a narrow conical form, tapering gradually towards the end,
which does not exhibit any notch or projecting corner
behind the base of the terminal claws, The post-anal angle
is well defined, and not far removed from the base of the
tail. The posterior edge beyond the anal orifice is armed
with a double 10w of about 20 well-defined denticles, the
outermost of which is placed at some distance from the tip.
The terminal claws are rather strong, and nearly straight,
each having a well-defined secondary denticle at the base,
and another somewhat smaller one about in the middle of
the posterior edge.

Occurrence.—A solitary, but well preserved female
specimen of this form was found in a sample taken by Mr.
Whitelegge from the Centennial Park, near Sydney.

4 — Archiv for Math. og Naturv. B. XVIII No. 3.
Trykt den 15de Juli 1896.

48 G. O. Sars.

Ostracoda.

Fam. Cyprididæ.

Gen. Cypria, Zencker.
21. Cypria pusilla, G. O. Sars, n. sp.
(Pl. 7. fig. 1, a—b).

Specific Characters.—X Shell much compressed and,
seen laterally, almost semicircular in form, anterior extremity,
however, lower than the posterior, dorsal margin boldly
arched, ventral nearly straight; seen dorsally narrow oblong,
both extremities somewhat blunted. Valves rather unequal,
the right one being much the larger, and considerably over-
lapping the left in the middle of the dorsal face, as also
anteriorly. Surtace of shell smooth, but dotted all over
with brownish pigment; both extremities clothed with deli-
eate hairs. Length of adult female 0,58 mm.

Remarks.—This form is nearly allied to the European
species, C. ophthalmica (Jurine), but of much smaller size,
and, moreover, distinguished by the very conspicuous inequal-

ity of the valves.

Description of the female.

The length of the shell in fully grown specimens does
not exceed 0,58 mm., and this form is accordingly of very
small size as compared with the European species.

The shell is highly compressed and, viewed from the

side (fig. 1 a), of a somewhat semicircular outline, with the

On Fresh-water Entomostraca. 49

greatest height about in the middle. The anterior extremity
is somewhat oblique, and much lower than the posterior,
which is broadly rounded. The dorsal margin forms a bold,
and rather even curve, joining the anterior and posterior
edges, without any intervening angle. The ventral margin
appears almost straight, though there is a slight approach
to a median sinus. Seen from above (fig. 1b), the shell
appears narrowly oblong, with the lateral contours nearly
parallel, and both extremities somewhat blunted, though the
anterior is somewhat narrower than the posterior.

The valves are very unequal, the right one being much
the larger, and projecting considerably beyond the left along
the middle of the dorsal face. Anteriorly it overlaps the
left valve by a thin hyaline border, and a similar, though
much narrower border is also seen at the infero-posteal corner.

The surface of the shell is perfectly smooth, without any
distinct sculpturing. It is, however, dotted all over with a
reddish brown pigment, similar to that found in ©. ophthal-
mica. At each extremity the shell is clothed with very
delicate hairs, somewhat more densely crowded together
anteriorly. The eye may be pretty well traced through the
shell, and the muscular pits in the centre of each valve
are also rather conspicuous.

Occurrence.—Of this small species, solitary specimens
were picked up from a sample taken by Mr. Whitelegge
from the Waterloo Swamps.

Gen. Cypris, Mill.

22. Cypris bennelong, King.

Cypris bennelong, King, Proc. Roy. Soc. Van Diemen’s
kand 11855, -p. 63, Pl Xx As

50 G. O. Sars.

Cypris bennelong, G O. Sars, Fresh-water Entomo-
straca of New Zealand, p. 24, Pl. IV, figs. 1, a—d.

Syn. Chlamydotheca australis, Brady.

Of this characteristic form, described and figured by the
present author in the above-quoted paper, numerous specimens
were tound in 2 different samples taken by Mr. Whitelegge
from waterholes at Bourke Street. It is rather singular,
that not even a single specimen of this species developed
in my aquaria, though empty shells were not uncommon in
the mud, with which these were prepared.

Distribution.—New Zealand (G. O. Sars).

23. Cypris sydneia, King.

Cypris sydneia, King, 1. ec. p. 65, Pl. X. M.

Cypris sydneia, G. O. Sars, Fresh-w. Ent., N. Z., p. 27,
Pl. IV, figs. 2, a—e.

Syn. Cypris ciliata, Thomson.

This form, which exhibits so close a relationship to the
European species, C. incongruens, developed rather plenti-
fully in some of my aquaria, and grew to a much larger
size than the specimens raised by the present author from
New Zealand mud. It was also found in great numbers in
some samples taken by Mr. Whitelegge from waterholes at
Bourke Street, and in addition to these, a single, young
specimen occurred in the sample first received from Prof.
Ramsay, and taken from the Waterloo Swamps.

Distribution.—New Zealand.

24. Cypris leana, G. O. Sars, n. sp.
(Pl. 7, figs. 2, a—d).
Specific Characters.—Shell large, seen laterally, oval

reniform, greatest height in the middle, anterior extremity

On Fresh-water Entomostraca. 51

evenly rounded, posterior subtruncate and scarcely broader
than the anterior, dorsal margin almost angularly bent in
the middle, ventral but very slightly sinuate; seen dorsally
oblong cuneiform, gradually tapering in front, anterior extre-
mity acuminate, posterior obtuse. Valves nearly equal,
left one having the edge minutely tuberculated in front and
behind; inner duplicatures not very broad. Surface of shell
remarkably smooth and polished, being clothed at both extre-
mities with minute hairs. Caudal rami rather slender and
slightly flexuose, narrowed distally, outer claw about half
the length of the ramus. Length of shell 2,70 mm.

Remarks.—The present species is allied to C. sydneia,
but is evidently distinct from it, being nearly twice as large and
having the shell higher in proportion to its length. It is
named in honour of its discoverer, Mr. Lea.

Description of the female.

The length of the shell measures 2,70mm., and this
form accordingly grows to a very large size.

Seen laterally (fig. 2a) the shell exhibits a somewhat
irregular, oval reniform shape, with the greatest height,
which about equals 3/5 of the length, occurring in the middle.
The anterior extremity is quite evenly rounded, whereas the
posterior one appears somewhat obtusely truncated, and is
scarcely broader. The dorsal margin is boldly arched, being
almost angularly bent in the middle, and slopes at about
the same angle both anteriorly and posteriorly. The ventral
margin appears nearly straight, though a slight sinus may
be traced in the middle.

Seen from above (fig. 2 b), the shell exhibits an oblong
cuneiform shape, with the greatest width, which about equals
half the length, occurring far behind the middle. Anteriorly

52 G. O. Sars.

it is gradually narrowed to a somewhat twisted acute point,
whereas the posterior extremity is more obtusely rounded.

The valves, at first sight, appear nearly equal. On
a closer examination, however, the left one is found to be
somewhat larger than the right, overlapping it anteriorly by
a narrow, hyaline border; and below the posterior extre-
mity a similar projecting rim may also be traced. As in
C. sydneia, the right valve exhibits at the anterior edge and
at the posterior part of the ventral one, a series of small
knobs or tubercles, giving the edge a minutely crenulated
appearance. The inner duplicatures are rather narrow, though
ihe anterior one is somewhat broader than the posterior.

The surface of the shell is remarkably smooth and
polished, without any perceptible sculpturing, except the
usual small dots; and it is only at each extremity that it is
clothed with very small hairs. The muscular pits in the
centre of each valve are fairly conspicuous, and resemble
those in C. sydneia.

The colour of the shell could not be ascertained, as
the specimens were discoloured by long immersion in spirit.

The caudal rami (fig. 2c) are of moderate size and
rather slender, tapering somewhat distally, and exhibiting a
slight flexure. They are armed in the usual manner, each
having at the end 2 unequal claws and 2 bristles. The claws
are rather slender, the outer one being half the length of
the ramus.

Occurrence.—A rather considerable number of this
pretty species were contained in a sample taken by Mr. Lea
from a pond «Near Hay».

Ot

| Go

On Fresh-water Entomostraca.

25. Cypris lateraria, King.
(Pl. 7, figs. 8, a—c).

Cypris lateraria, King, 1. c., p. 65, Pl. X G.

Specific Characters.—Shell ventricose, seen later-
ally, clavate in form, much higher in front than behind,
anterior extremity broadly rounded, posterior subtruncate,
dorsal margin subangular above the eye, and gradually
sloping behind, ventral deeply sinuated: — seen dorsally,
regularly ovate, with the greatest width fully equalling the
height, and occurring behind the middle, anterior extremity
more pointed than the posterior. Valves very unequal, the
left one being much the larger, and overlapping the right
both anteriorly and posteriorly. Surface of shell of a dull
appearance, being distinctly granular all over, and also
armed with scattered tubercles, more conspicuous towards
both extremities, which are densely hairy. Caudal rami
moderately strong, nearly straight, outer claw not attaining
half the length of the ramus. Colour of shell uniformly
yellowish green. Length 1,05 mm.

Remarks.—This is a very distinct species, and un-
doubtedly that recorded by Mr. King under the above
name. In outward appearance it somewhat resembles the spe-
cies of the genus Jlyocypris, and, indeed, I at first believed
it to belong to that genus. A closer examination of the
several appendages has, however, shown it to be a true

Cypris.

‘Description of the female.

The length of the shell, in fully grown specimens, but
little exceeds I mm., and this form is accordingly of rather

small size.

54 G. O. Sars.

Seen laterally (fig. 3 a), the shell exhibits a pronounced
clavate form, being much higher in front than behind, with the
greatest height equalling about half the length. The anterior
extremity is broadly rounded, whereas the posterior one
appears somewhat obliquely truncated, with the lower corner
more prominent than the upper. The dorsal margin has its
greatest curvature just above the eye, where it exhibits an
almost angular bend, and from thence slopes evenly, and at
a nearly straight course, to the hind extremity. The ven-
tral margin is deeply sinuated somewhat behind the middle,
and joins the posterior edge by an abrupt curve.

Seen from above (fig. 3 b), the shell appears very tumid,
the greatest breadth, which occurs considerably behind the
middle, fully equalling the height. It exhibits a rather
regular ovate form, with the side-contours evenly curved,
and the anterior extremity somewhat more pointed than the
posterior,

The valves are very unequal, the left one being much
larger than the right, and overlapping it considerably along
the whole anterior extremity, as also posteriorly. The inner
duplicatures are not particularly broad.

The surface of the shell is of a dull appearance, and
often covered with muddy particles. It appears closely
granular all over, exhibiting, as it were, a squamous
sculpture. Moreover, a number of well-defined obtuse tubercles
may be traced on each valve, being more conspicuous
towards each extremity. Both anteriorly and _ posteriorly
the shell is densely hairy.

The colour of the shell, in living specimens, is a rather
uniform yellowish green.

The several appendages agree on the whole in their
structure rather closely with those in the typical species of

On Fresh-water Entomostraca. 55

Cypris, both pairs of antennæ being provided with very
long natatory sete, and the masticatory lobes of the Ist
pair of maxillæ exhibiting the usual narrow, digitiform shape.

The caudal rami (fig. 3 c) are moderately strong, nearly
straight, and but slightly narrowed distally. Their armature
is the usual one, the outer claw being the longer, though
not attaining half the length of the ramus.

Observations.—Some few specimens of this form
developed in one of my aquaria, and were watched for some
time. They did not, however, multiply to any great
extent, and after the lapse of some months, no specimens
were to be found in the aquarium. The animal is rather
active, moving about through the water with great speed,
at times affixing itself to the walls of the aquarium.

Occurrence.—The mud from which this species deve-
loped, was taken by Mr. Whitelegge from ponds and ditches
at Bourke Street. Several well-preserved specimens also
occurred in a sample taken by that gentleman from the
same locality. Mr. King collected the species from a pond
in a brickfield, near Sydney.

Gen. Candonocypris, G. ©. Sars.

22. Candonocypris candonoides, King.

Cypris candonoides, King, 1. c., p. 66, Pl. X F.

Herpetocypris stanleyana, G. O. Sars, On some Ostra-
coda and Copepoda raised from dried Australian mud, p. 35,
Pl. II, figs. 1—2, Pl. V, figs. 5—7.

This form, whose identity with Cypris candonoides
of King, I have stated in my paper on the New Zea-
land Entomostraca, developed rather abundantly in several

of my aquaria, and was also found in great numbers in some

56 G. O. Sars.

of the samples sent by Mr. Whitelegge, and taken from
ponds and ditches at Bourke Street.
Distribution. — Queensland, New Zealand, Knysna

(G. O. Sars).

Gen. Ilyodromus, G. O. Sars.

27. Ilyodromus varrovillius, King

Cypris varrovillius, King, 1. c., p. 66, Pl. X D.

Ilyodromus varrovillius, G. O. Sars, Fresh-water Ento-
mostraca of New Zealand, p. 41, Pl. VI, figs. 1, a—c.

In some of my aquaria this beautiful form developed
rather plentifully, and continued to live and multiply during
the whole season. It also occurred, though rather rarely,
in the samples sent by Mr. Whitelegge, the locality being
the same as that from which the preceding form was derived.

Distribution.—New Zealand (G. O. Sars).

28. Ilyodromus viridulus, Brady.

Cypris viridula, Brady, Proc. Zool. Soc. London, 1886,
Dy Ssh EL VIG hass 10 2

Herpetocypris viridula, G. O. Sars, On some Fresh-
water Ostracoda and Copepoda raised from Australian mud,
prAL.BI. WM, figs. 3,4; Pl. V tes, Se

As observed in my paper on the New Zealand Ento-
mostraca, this form ought to be referred to the genus Jlyo-
dromus, as characterised by the author in that paper. It
developed in the same aquarium as the preceding species,
and was likewise found occasionally in the samples se>t by
Mr. Whitelegge.

Distribution.—Queensland (G. O. Sars).

On Fresh-water Entomostraca. 57

29. Ilyodromus substriatus, G. O. Sars.

Ilyodromus substriatus, G. O. Sars, Fresh-water Entom.
N. Zeal., p. 45, Pl. VI, figs. 3, a—e.

Some few specimens of this form were found in the
samples sent from Mr. Whitelegge. It did not, however,
develop in my aquaria.

Distribution.—New Zealand (G. O. Sars).

30. Ilyodromus ellipticus, G. O. Sars, n. sp.
(Pl. 7, figs. 4, a—c).

Specific Characters.—Shell much compressed, seen
laterally, regularly oblong or elliptical in form, both extre-
mities nearly equal and evenly rounded, dorsal margin but
very slightly convex, ventral almost straight: — seen from
above, narrow oblong, anterior extremity somewhat nar-
rower than the posterior. Valves nearly equal and having
the inner duplicatures very broad. Surface of shell very
faintly striated longitudinally, and clothed at each extremity
with scattered hairs, those of the posterior one being parti-
cularly long. Colour of shell transparent yellowish, each
extremity, but especially the anterior one, being tinged with
deep green. Caudal rami rather strong, and of the structure
characteristic of the genus. Length 1,18 mm.

Remarks.—The present new species is somewhat allied
to J. substriatus, exhibiting a similar faint longitudinal stria-
tion, but it may be at once distinguished by the rather different
shape of the shell, which is more regularly oblong or ellip-
tical than in any of the other known species.

Description of the female.
The length of the shell in fully grown specimens does
not exceed 1,18 mm., and this form is accordingly somewhat
inferior in size to I. substriatus.

58 G. O. Sars.

Seen laterally (fig. 4 a), the shell exhibits a very regular
oblong, or rather elliptical form, with the greatest height
attaining not nearly half the length. Both extremities appear
evenly rounded and nearly equal. The dorsal margin is but
very slightiy convex, without forming any trace of angle at
the junction with the anterior and posterior edges. The |
ventral margin appears almost perfectly straight, the usual
median sinus being quite obsolete.

Seen from above (fig. 4 b), the shell appears very much
compressed, the greatest width scarcely exceeding 1/3 of the
length. Its form is very narrow oblong, with the side-
contours but slightly convex, and the anterior extremity
somewhat more pointed than the posterior.

The valves, at first sight, appear nearly equal. On
a closer examination, however, the left valve, as in the other
species, is found to be in reality a little larger than the
right, overlapping it anteriorly by a very narrow hyaline
rim. The inner duplicatures, especially the anterior ones,
are very broad and shelf-like, and their defining edge may
be pretty well traced through the shell.

The surface of the shell is indistinctly striated longi-
tudinally, the striæ being very delicate, and in some cases
only with great difficulty traceable. At both extremities it
is clothed with delicate hairs, which on the posterior extre-
mity are particularly long and far apart.

The colour of the shell in living specimens is trans-
parent yellowish, allowing the cecal appendages of the
intestine and the opaque whitish ovarial tubes to be seen
through rather distinctly. At each extremity it is tinged
with deep green, this colour being especially very conspi-
cuous anteriorly, where it occupies a rather broad, semilunar

area inside the edge.

On Fresh-water Entomostraca. 59

The eye is very large and conspicuous, exhibiting in
the living animal a brillant iridescent lustre.

The several appendages closely agree in their structure
with those in the other species of the genus.

This is also the case with the caudal rami (fig. 4 c),
which are very strong, of a light corneous hue, and of about
uniform breadth throughout, They are, as usual, armed
at the end with % strong claws, successively increasing in
size distally, the outermost one being, however, scarcely half
the length of the ramus; just in front of it, the usual small
bristle occurs.

Observations.—This form developed in some of my
aquaria, but only in one of them did it multiply to any great
extent. In habits, it agrees with the other species, moving
with great dexterity through the loose bottom deposit, but
being wholly devoid of swimming power.

Occurrence.—The mud from which this species deve-
loped, was taken by Mr. Whitelegge from waterholes at
Bourke Street, and from a sample taken in the same place
some few specimens. of this form were also picked up.

Gen. Cypridopsis, Brady.

31. Cypridopsis minna, King.
(Pl. 7, figs. 5, a—c).

Cypris minna, King, 1. c., p. 64, Pl. X B.

Cypridopsis minna, Brady, Proc. R. 8. London, 1866,
p. 91, Pl. X, figs. 1—3.

Specific Characters.—Shell moderately tumid; seen
laterally, exceedingly high, of a rounded trigonal form, with
the dorsal margin boldly arched and abruptly bent in the
middle, ventral slightly sinuated, both extremities rounded

60 G. O. Sars.

and nearly equal; — seen from above broadly ovate, greatest
width not exceeding the height, anterior extremity obtusely
pointed, posterior evenly rounded. Valves rather unequal,
the right one overlapping the left considerably in the middle
of the dorsal face, as also anteriorly. Surface of shell
smooth, or very slightly granular, moderately hairy, with a
narrow, transversely-striated, marginal area just within the
anterior edge of each valves. Colour yellowish, variegated
with dark green, partly anastomosing patches. Length ot
shell 0,92 mm.

Remarks.—This is undoubtedly the true C. minna of
King, and the form described by Brady also belongs quite
certainly to the very same species. On the other hand, the
form described by the present author under this name from
New Zealand is specifically distinct, as will be shown farther
on. The present species may be easily recognized from any
of the other known forms by the extraordinary height of the

shell, which gives it,in a lateral view, nearly a trigonal shape.

Description of the female.

The length of the shell in fully adult specimens mea-
sures 0,92 mm., and accordingly somewhat exceeds that of
the said New Zealand form

Seen from the side (fig. 5 a), the shell exhibits a some-
what unusual form, being exceedingly high and almost tri-
gonal in outline, with the greatest height not very inferior
to the length, and occurring in the middle. Both extremi-
ties appear somewhat obliquely rounded, and nearly equal.
The dorsal margin is very boldly arched, exhibiting an
almost angular bend in the middle, and from thence sloping
rather steeply both anteriorly and posteriorly. The ventral

margin is but very slightly sinuated in the middle.

On Fresh-water Entomostraca. 61

Seen from above (fig. 5 b), the shell appears less tumid
than in the New Zealand form, and exhibits arather regular
rounded ovate form, the greatest width not exceeding the
height. The anterior extremity is obtusely pointed, whereas
the posterior one appears quite evenly rounded.

The valves are rather unequal, the right one being the
larger, and overlapping the left not only along the anterior
extremity, but also in the middle of the dorsal face. Some-
what below the centre of each valve, the muscular pits are
observed, and just within the anterior edge, as in some
other species, there is a narrow, very dark-coloured, marginal
area, which exhibits a number of very conspicuous, light,
transverse striæ.

The surface of the shell is smooth, or very slightly
granular, being clothed all over with delicate hairs, which
at each extremity are more densely crowded together.

The ground-colour of the shell in living specimens is
yellowish and semi-transparent; but along the edges of the
valves, as also in their centre, several dark-green. patches
occur, which are partly confluent, so as to form irregularly
ramified bands.

The several appendages do not seem to differ in any
manner from those in other species of the genus; the caudal
rami too (fig. 5 c), exhibit the characteristic, very narrow
linear form, with the claws extremely slender and almost
setiform.

Observations. — This form developed rather plenti-
fully in some of my aquaria, and cont'nued to live and
propagate during the whole summer. In habits, it exactly
agrees with the other species of the genus.

Öceurrence.— The mud from which this species deve-
loped, was the same parcel, that yielded most of the other

62 G. O. Sars.

Cypridide here treated off, having been taken by Mr. White-
legge from waterholes at Bourke Street. A sample taken
from the same place, also contained numerous well preserved

specimens.
32. Cypridopsis turgida, G. O. Sars, n. sp.

Cypridopsis minna, G. O. Sars, Fresh-water Entom. of
N. Zeal. p. 20, Pl. IV, figs. 3, a—d.

As above stated, this form is evidently specifically
distinct from the preceding one, with which I have wrongly
identified it at an earlier date. It must therefore have
another name, and I propose to call it C. turgida, on account
of its extremely tumid shell.

This species too, developed in great numbers in my
aquaria, and could at once be distinguished from the pre-
ceding one by its more tumid shell, and more uniform
colouring, It was also found in the sample sent by Mr.
Whitelegge.

Distribution.—New Zealand, Knysna, China (G.O. Sars).

Gen. Candonopsis, Vavra.

9

33, Candonopsis tenuis, Brady.
(Pl. 7, figs. 6, a—d).

Candona tenuis, Brady, Proc. R. S. London, 1886,
fos BA Te 5.910:

Specific Characters.—Shell much compressed, and
of slightly different shape in the 2 sexes, being, however, in
both, when seen laterally, more or less oblong reniform, with
the hind extremity rounded and broader than the anterior;
ventral margin distinctly sinuated, the sinus in female being

median, in male, occurring somewhat in front of the middle,

On Fresh-water Entomostraca. 63

dorsal margin in female almost straight, with an indication
of angle both anteriorly and posteriorly, in male evenly
arched throughout: — seen from above, narrow oblong,
more pointed in front than behind. Valves equal, smooth,
semi-pellucid, of whitish colour, hairy at both extremities.
Caudal rami very narrow, almost straight, and terminating
with 2 somewhat unequal claws, each having beyond the
middle a distinct secondary denticle, dorsal bristle wanting.
Length of female 0.90 mm., of male 1.00 mm.

Remarks.—This, I believe, is the form briefly
described and figured by Prof. Brady as Candona tenuis.
It certainly belongs to the genus Candonopsis, as recently
characterised by Mr. Våvra in his Monograph of the
Ostracoda of Bohemia, and is nearly allied to the typi-
cal form C. Kingsleyi, though differing somewhat in the
form of the shell, and apparently also in the structure of
the caudal rami.

Description.—The length of the shell in adult female
specimens scarcely exceeds 0.90 mm.; that of male specimens
is somewhat greater, measuring 1.00 mm,

The shell in both sexes is highly compressed and, seen
laterally (fig. 6a, 6 b), of an oblong reniform shape, the
greatest height scarcely exceeding half the length, and occur-
ring behind the middle. Both extremities are rounded, and
the anterior one is considerably narrower than the posterior,
which appears somewhat compressed in its inferior part.
The dorsal margin in the female (fig. 6 a) is nearly straight
in the middle, with an indication of an angle both in front and
behind, whereas in the male (fig. 6 b) this margin appears
quite evenly arcuate. The ventral margin is in both sexes
distinctly sinuated, but the sinus occurs in the male (fig. 6 b)
somewhat in front of the middJe, whereas in the female

8 — Archiv for Math. og Naturv. B. XVIII No. 3.
Trykt den 16de Juli 1896.

64 G. O. Sars.

(fig. 6 a) it is almost median. On the whole, the posterior
part of the shell in the male (fig. 6 b) appears broader and
more expanded than in the female (fig. 6 a), and the ante-
rior extremity more produced. Seen from above (fig. 6 c),
the shell in both sexes appears very narrow oblong, with
the anterior extremity somewhat more pointed than the
posterior.

The valves are nearly equal, and rather thin, are
semipellucid, and clothed at each extremity with delicate hairs.
The inner duplicatures are rather broad, especially the ante-
rior ones, and their defining edges may be fairly well traced
through the shell.

The surface of the shell appears quite smooth and
polished, though exhibiting, when examined under a strong
magnifier, an extremely delicate reticulation.

The colour of the shell in living specimens is trans-
parent whitish, permitting several of the inner organs to be
fairly well traced through it.

The eye is very small, and, it would seem, devoid of
the usual dark pigment, being on that account rather difficult
to trace.

The structure of the several appendages seems exactly
to agree with that described by Mr. Våvra in the typical
species, C. Kingsleyi.

The caudal rami (fig. 6 d), as in that species, are rather
narrow, sublinear, and lack all trace of the usual dorsal
bristle. They are, however, in the present species straighter,
and each of the terminal claws has beyond the middle a
very conspicuous secondary denticle, not found in the typical
species.

In the male (fig. 6b—c) the very large «mucous

glands», or more correctly the «zenckerian organs» are

On Fresh-water Entomostraca. 65

distinctly traced through the shell, both in its lateral and
dorsal views, appearing as 2 large, juxtaposed bags extend-
ing through the posterior half of the shell, and exhibiting
within from 5 to 6 verticils of bristle-like radiating pro-
cesses. Also the spermatic tubes contained within the 2
lamellæ of the valves may be fairiy well discerned.

Observations—An adult male specimen of this form,
the one here figured, was by a mere chance found in one
of my aquaria, on taking up, by the aid of a dipping tube,
a small quantity of the bottom deposit. It was at once sub-
jected to a closer examination under the microscope, and
its habits studied. Though subsequently very closely exa-
mining the bottom contents of this aquarium, I did not
succeed in detecting any more specimens. In habits, this
form agrees with the typical species, as also with the species
of the genus Jiyodromus, as it moves rather quickly through
the loose bottom deposit, but is wholly devoid of swimming
power.

Occurrence.—The mud, from which this form deve-
loped, was taken by Mr. Whitelegge from waterholes at
Bourke Street. Numerous specimens of the same form,
both males and females, moreover, occurred in a sample
taken by that gentleman from the Marubra Swamp. The
specimens examined by Prof. Brady were derived from
Condong, Tweed River, New South Wales.

66 G. O. Sars.

Copepoda.

Trib. Calanoidea. Fam. Diaptomidee.

Gen. Boeckella, Guerne & Richard.

34. Boeckella triarticulata (Thomson).

Boeckia triarticulata, Thomson, Proc. N, Z. Inst. Vol.
KAPP Val fies! 112209.

Boeckella triarticulata, G. O. Sars, Fresh-water Entom.
N. Zeal., p. 49, Pl. VII & VII.

Of this species, described and figured in detail by the
author in the above-quoted paper, some few specimens,
exactly agreeing in every detail with the New Zealand form,
were found in a sample taken by Mr. Whitelegge from
some pond near Sydney.

Distribution.—New Zealand (Thomson).

35. Boeckella robusta, G. O. Sars, n. sp.
(Pl. 8, figs. 1—4).

Specific Characters.—Anterior division of body in
female rather thick and swollen, oblong oval in form,
broadest in front of the middle, and slightly narrowed
posteriorly, lst segment about the length of the 4 succeeding
ones combined, front narrowly rounded; lateral expansions
of last segment scarcely divergent, extending beyond the
ist caudal segment, outer lobe large, broadly lanceolate,
inner lobe very small, acute triangular. Tail, including the

caudal lamelle, not nearly half the length of the anterior

On Fresh-water Entomostraca. 67

division, 1st segment moderately tumid and slightly asyme-
trical. Caudal lamelle nearly as long as the last 2 seg-
ments combined. Anterior antennæ scarcely exceeding in
length the anterior division of the body; right prehensile
antenna in male about as in B. triarticulata. Last pair of
legs in female, with the terminal joint of the outer ramus
shorter than the preceding joint, and armed with 7 spines,
the outer apical one being rather strong; those in male, of
the structure characteristic of the genus, inner ramus of
right leg conically tapered, with a small curved seta inside
the base, left leg without any serrated lamella at the base
of the inner, extremely small ramus. Length of female
3.20 mm. |
Remarks.—In the comparatively robust form of the
body, this new species somewhat resembles the South Ame-
rican form DB. brasiliensis, Lubbock, as recently described
by Messr. Poppe and Mråzek. It is, however, of much
larger size and, moreover, differs rather markedly in some
of the anatomical details. From B. triarticulata it is also

very easily distinguishable.

Description of the female.

The length of the body, measured from the front to
the tip of the caudal lamellæ, is 3.20 mm., and this species
accordingly grows to a very considerable size.

The form of the body, as compared with that of
B. triarticulata, is very robust, the anterior division being
considerably tumefied, and more than twice as long as the
posterior one. Seen from above (fig. 1), the former division
exhibits an oblong subfusiform shape, the greatest breadth
occurring somewhat in front of the middle, and almost
equalling half the length. Anteriorly it terminates in a nar-

68 G. O. Sars.

rowly rounded frontal part, whereas posteriorly it is but
slightly attenuated. As in other species, this division exhi-
bits 6 well-defined segments, the ist of which is much the
largest, equalling in length the 4 succeeding segments com-
bined. At the sides of this segment, the 2 pairs of antennæ
and to some extent also some of the oral parts are seen
to project. The last segment is deeply emarginated in the
middle, and is produced on each side of the emargination
to a lamellar expansion pointing backwards and extending
somewhat beyond the Ist caudal segment. As in B. triarti-
culata, these expansions are each divided into 2 lobes, the
outer of which is much the larger and of broadly lanceolate
form, terminating in a sharp point, bent slightly outwards.
The inner lobe is extremely small, appearing merely as a
slight acute lappet issuing from the inner side of the outer
lobe. In B. triarticulata these inner lobes are much more
fully developed, and the outer lobes rather narrow, mucro-
niform, and considerably divergent.

The tail is comparatively short, not nearly attaining
half the length of the anterior division, and, as usual, is
much narrower. It is divided into 3 well-defined segments,
the Ist of which, the genital segment, is much the largest,
and somewhat irregularly dilated in the middle, exhibiting
below a rounded prominence, to which the egg-bag, when
present, is attached. The last segment, which about equals
in size the penultimate one, is somewhat dilated distally,
and exhibits at its end the anal opening, partly covered
above by a semilunar ridge. To this segment the caudal
lamellæ are attached. They are comparatively larger than
in BD. triarticulata, attaining about the length of the last 2
segments combined, but otherwise they exhibit much the same

appearance, having each 5 strong and densely plumose

On Fresh-water Entomostraca. 69

marginal sete, and also at the inner corner above, a
simple bristle.

The eye is rather small, though distinct, being placed,
as usual, at some distance from the front and nearer the
ventral than the dorsal face.

The anterior antennæ (see fig. 1) are comparatively
shorter than in the New Zealand species, scarcely exceeding
in length the anterior division of the body, and they are
divided into the usual number (25) of articulations.

The posterior antennæ, the oral parts and the 4 ante-
rior pairs of legs in their structure agree, on the whole, per-
fectly with those parts in BD. triarticulata, and need not
therefore be described in detail.

The last pair of legs (fig. 2) are also constructed in a
very similar manner, being, like the preceding pairs, natatory,
though differing from them in some points. The outer
ramus is rather robust and, as in the other known species,
has the 2nd joint produced inside to a strong conical pro-
cess, coarsely denticulated on both edges. The terminal
joint of this ramus is comparatively smaller than in B. tri-
articulata, being scarcely as long as the preceding joint, and
very much narrower. It is, however, armed with the same
number of spines, viz., 7, 2 of which issue from the outer
edge, 3 from the inner, and 2 from the tip; of the last
the outer one is much the larger and considerably stronger
than any of the others, The inner ramus is but little more
than half as long as the outer, and much narrower. Of its
3 joints, the terminal one is comparatively much smaller
than in B. triarticulata, and carries only 5 sete, whereas 6
such sete are found in the said species. On the other
hand, the 2nd joint has an additional seta inside, not found

in B. triarticulata.

70 G. O. Sars.

The adult male is somewhat smaller than the female,
and exhibits the same difference from it as that observed
in B. triarticulata, being on the whole of much more slender
form and having the last segment of the anterior division
quite simple, without any lateral expansions. Moreover, the
tail appears more elongated, and is divided into 5 well-
defined segments, besides the caudal lamellæ.

The right prehensile anterior antenna (fig. 3) is con-
structed in a similar manner to that in the male of B. triarticu-
lata, the movable terminal part being without any processes
or spines and somewhat shorter than the adjoining tumefied
part of the antenne.

The last pair of legs (fig. 4), as in the other species of
the genus, are transformed into strong grasping organs, both
legs being nearly equally developed, and each terminating
with a slender claw. In the right leg, the outer ramus is
distinctly biarticulate and comparatively more strongly deve-
loped than in the left leg, where it is composed of a single
joint only. In the right leg, moreover, the claw is more
abruptly curved than in the left, the claw of which, on
the other hand, is more elongated and exhibits outside,
near the base, a small secondary spine. The inner ramus
of the right leg is simple and conically tapering in its outer
part, and carries at the base inside a small, curved bristle;
that of the left leg is extremely small, knob-like, and
attached to the inside of a projecting corner of the last
joint of the basal part. Of the serrated lamella occurring
in B. triarticulata inside this joint, no trace is found in
the present species.

Occurrence.--Some specimens of this pretty species
were found in a sample taken by Mr. Whitelegge from some

pools near Sydney. It is most probable, that the species

On Fresh-water Entomostraca. all

has also been observed by Mr. King, and regarded by him
as a species of the genus Diaptomus. But, as no figures
or descriptions are given of the 4 species he enumerates, it
is impossible to decide to which of .them it ought to be
referred.

36. Boeckella minuta, G. O. Sars, n. sp.
(Pl. 8. figs. 5—7).

Specific Characters.—Body much more slender than
in the preceding species, the anterior division exhibiting in
female a narrow oblong or almost cylindrical form, with the
front obtusely rounded; lateral expansions of last segment
less fully developed, not nearly extending to the end of the
Ist caudal segment, outer lobe short lanceolate, inner tri-
angular. Tail nearly as in the preceding species, but with
the caudal lamellæ somewhat smaller. Anterior antennæ
rather elongated, equalling in length the whole body, except-
ing the caudal lamellæ. Last pair of legs in female, with
the terminal joint of the outer ramus extremely minute, and
only provided with 2 unequal apical spines; those in male of
a similar structure to that in the preceding species, but with
the inner ramus in both legs simple eylindrical. Body in
both sexes highly pellucid and nearly colourless. Length
of adult female 1.28 mm.

Remarks.—This additional new species is easily distin-
guishable both from B. triarticulata and robusta, being of
very inferior size, and also differing in the much more
slender body, the less fully developed lateral expansions of
the last pedigerous segment in the female, and in the
somewhat deviating structure of the last pair of legs in
both sexes.

12 G. O. Sars.

Description of the female.

The length of fully adult, ovigerous specimens does
not exceed 1.28 mm. and this form accordingly is very
inferior in size to any of the other known species.

The body is, on the whole, much more slender than in
the preceding species, and in this respect also surpasses :
the New Zealand form. The anterior division exhibits, when
seen dorsally (fig. 5), a very narrow oblong, almost cylindrical
form, the greatest width scarcely exceeding 1/3 of the length.
Anteriorly it somewhat tapers towards the obtusely rounded
front, whereas posteriorly it is scarcely at all narrowed. The
lateral expansions of the last segment are not nearly so
fully developed as in the 3 other species, and extend but
little beyond the middle of the 1st caudal segment. They
are each divided into 2 well-defined lobes, the outer of
which is the larger, and of a short lanceolate form, whereas
the inner is more triangular in shape.

The tail does not attain half the length of the anterior
division, and has the caudal rami somewhat smaller than in
B. robusta, not nearly attaining the length of the 2 pre-
ceding segments combined.

The eye is very conspicuous, the pigment being of a
dark red colour.

The anterior antenne (see fig. 5) are rather elongated,
equalling in length the whole body, minus the caudal
rami. They are composed of the usual number of articula-
tions, and in the living animal are generally extended later-
ally, with a slight curvature at the base.

The last pair of legs (fig. 6) differ conspicuously from
those in the other species in the poor development of the

terminal joint of the outer ramus. This joint is extremely

On Fresh-water Entomostraca.

me
(3

small and of a linear form, carrying only 2 apical spines,
the inner of which is the longer. Otherwise these legs, as
also the other appendages, exhibit the structure charac-
teristic of the genus.

The adult male, as usual, is even somewhat smaller
than the female, and differs from it in the usual sexual
characters.

The last pair of legs (fig. 7) are on the whole con-
structed as in the other species, though, on a closer com-
parison, several minor differences may be found to exist.
Thus, the last joint of the outer ramus of the right leg is

- comparatively narrower than in the preceding species, and

on the left leg this ramus is somewhat attenuated distally,
whereas in B. robusta it is on the contrary, dilated at the end.
The inner ramus in both legs is simple cylindric, being
somewhat larger in the right than in the left leg. In the
latter, the last joint of the basal part projects inside to a
sharp corner, but any serrated lamella, like that found in
B. triarticulata, does not exist.

In the living state of the animal, the body is highly
pellucid and almost colourless, admitting of some of the inner
organs being pretty easily traced through the thin integu-
ments, The ovisac in the female (see fig. 5) only contains
a very restricted number of eggs of a pale greenish colour.

Observations.—Some few specimens of this form
developed in one of my aquaria and were watched for
about a month, They did not, however, multiply, though
some of the females were ovigerous, and in the later part
of the summer they wholly disappeared. In habits it agrees
with B. triarticulata, moving about in quite a similar manner.

Occurrence.—The mud, from which this form deve-
loped, was taken by Mr. Whitelegge from a pond off Botany

74 G. O. Sars.

Bay, near Waterworks Bridge. A rather considerable num-
ber of specimens of the same species were, moreover, picked
up from a sample taken by that gentleman from ponds at
Bourke Street and the Waterloo Swamps.

Trib. Cyclopoidea. Fam. Cyclopidæ.

Gen. Cyclops, Mill.

37. Cyclops australis, King.

Specific Characters.—Y Body moderately slender,
with the anterior division oblong oval, tapering somewhat
posteriorly; none of the segments extant laterally. Tail
about */3 as long as the anterior division, genital segment
not attaining the length of the 3 succeeding segments com-
bined, and moderately dilated in front. Caudal rami narrow,
linear, not diverging, exceeding in length the last 2 seg-
ments combined, innermost apical setæ a little longer than the
outmost, both being much shorter than the 2 median ones,
bristle of the outer edge not far remote from the tip.
Anterior antennæ scarcely exceeding in length the Ist seg-
ment of the body, and 12-articulate, 8th and 9th joints
rather large. First pair of legs with both rami biarticulate,
the 3 succeeding pairs with 3-articulate rami of normal
structure; 4th pair with the outer apical spive of the inner
ramus nearly as long as the inner, 5th pair of legs very
rudimentary, the basal joint not being defined from the
segment, though carrying the usual seta, terminal joint very
minute, with a comparatively short apical seta and an extremely

small lateral denticle. Length of adult female 2.20 mm.

On Fresh-water Entomostraca. 75

Remarks.—Although Mr. King would seem to have
comprised several species under the above name, I think I
am right in restricting the specific denomination proposed
by that author to the present species, all the other forms,
with which I am acquainted, having turned out to be
identical with well-known European species. The present
species is a very distinct one, differing, so far I can judge,
from all the other known forms. For want of room on the
plates, I have not been enabled to give any figure of this
form, but I hope, that the above diagnosis will suffice
for easily recognizing the species.

Occurrence.—This form was found in 4 different
samples, the localities of which are as follows: Waterloo
Swamps, Centennial Park, waterholes at Bourke Street, and

«Near Sydney». It was not hatched in my aquaria.

38. Cyclops albidus (Jurine).
Syn. C. tenuicornis, Claus.
A few specimens of this well-known European species
were found in a sample from the Centennial Park.

39. Cyclops Leuckartii, Claus.

Numerous specimens of this form were picked up from
3 different samples, the localities of which are as follows:
Centennial Park; Bourke Street; Waterloo Swamps; water-
holes at Bourke Street.

40. Cyclops serrulatus, Fischer.

Found rather abundantly in 2 samples, the one from
the Centennial Park, the other from the Waterloo Swamps.

Tt also developed in great numbers in my aquaria.

76 G. O. Sars.

41. Cyclops phaleratus, Koch.

Some specimens of this species occurred in a sample

from the Centennial Park.

42. Cyclops affinis, G. O. Sars.

Very frequent in several samples: Waterloo Swamps;
Centennial Park; Bourke Street; Waterloo Swamps; water-
holes at Bourke Street; opposite the Rope Works; Near
Sydney. It was also found in great abundance in my

aquaria.

Explanation of the plates.
JEG 16
Daphnia carinata, King.

Fig. 1. Typical form: ovigerous female, seen from left
side; magnified 26 diameters.
» 2. Tail of same, more highly magnified.
» 3. Var. intermedia: female with ephippium, seen from
left side; magnified 26. diameters.
» 4. Var. magniceps: ovigerous female, seen from left
side; magnified 26 diameters.

Jed, TU,
Simocephalus acutirostratus, King.

Fig. 1. Ovigerous female, seen from left side; magnified
24 diameters.
» 2. Anterior part of the body, more highly magnified
(antennæ omitted).

ay Abell

On Fresh-water Entomostraca. TUR

»

»

Fig.

10.
te

Simocephalus gibbosus, G. O. Sars.

Ovigerous female, seen from left side; magnified
44 diameters.

Anterior part of body, more highly magnified
(antennæ omitted).

Tail.

PLATE
Moina australiensis, G. O. Sars.

Adult female, with the matrix greatly distended
with embryos, seen from left side; magnified 62
diameters.

One of the antennule, more highly magnified.
Leg of Ist pair.

Extremity of tail.

Ephippium from left side.

Adult male, seen from left side; magnified 79 dia-
meters.

Same, viewed from the dorsal face (rami of the
antennæ not drawn).

Extremity of one of the antennulæ, highly magnified.
Prehensile leg of Ist pair.

One of the testes, with the efferent duct.
Zoosperms very strongly magnified.

BISTV.
Moina tenuicornis, G. O. Sars.
Adult female, with the matrix distended by rather
fully developed embryos, seen from left side;
magnified 62 diameters.

78

G. O. Sars.

Fig.

SUR co

D I ©

(ep)

Another female, with winter-eggs and the ephip-
pium in process of formation, viewed from the
dorsal face (rami of the antennæ not drawn).

One of the antennulæ, more highly magnified.
Leg of Ist pair.

Outer part of tail.

Extremity of same, still more highly magnified.
Ephippium from left side.

Adult male, viewed from right side; magnified 95
diameters.

PL V.
Ilyocryptus sordidus, Lievin.

Adult female, with 7 lines of growth, seen from
left side; magnified 102 diameters.

One of the antennulæ, more highly magnified.
Tail.

Chydorus Leonardi, King.

Adult female, seen from left side; magnified 120
diameters.

Tail of same, more highly magnified.

Chydorus globosus, Baird.

Adult female, seen from left side; magnified 104
diameters.

Tail of same, more highly magnified.

Pleuroxus inermis, G. O. Sars.

Adult female, seen from left side; magnified 104
diameters.

Tail of same, more highly magnified.

|

Fig.

»

Fig.

On Fresh-water Entomostraca. 79

10.

la.

eve
Alona Whiteleggei, G. O. Sars.
Adult female, seen from left side; magnified 104
diameters.

Tail of same, more highly magnified.

Alona pulchella, King.

Adult female, seen from left side; magnified 104
diameters.

Tail of same, more highly magnified.

Alona abbreviata, G. O. Sars.

Adult female, seen from left side; magnified 124
diameters.

Tail of same, more highly magnified.

Alonella clathratula, G. O. Sars.

Adult female, seen from left side; magnified 124
diameters.

Tail of same, more highly magnified.

Camptocercus australis, G. O. Sars.
ç

Adult female, seen from left side; magnified 104
diameters.

Tail of same, more highly magnified.

Jel, VING
Cypria pusilla, G. O. Sars.

Adult female, seen from left side; magnified 45
diameters.

» 1 b. Same, viewed from above.

6 — Archiv for Math. og Natury. Bd. XVIII. Nr. 3.

Trykt den 28de Juli 1896,

80

G. O. Sars.

»

»

»

»

2b.
PIC:

4 b.
4 ¢.

6 c.
6 d.

Cypris leana, G. O. Sars.

Adult female, seen from right side; magnified 24
diameters.
Same, dorsal view.

Caudal ramus, more highly magnified.

Cypris lateraria, King.
Adult female, seen from right side; magnified 45
diameters.
Same, dorsal view.

Caudal ramus, more highly magnified.

Ilyodromus ellipticus, G. O. Sars.

Adult female, seen from right side; magnified 45
diameters.
Same, dorsal view.

Caudal ramus, more highly magnified.

Cypridopsis minna, King. |
Adult female, seen from left side; magnified 45
diameters.

Same, dorsal view.
Caudal ramus, more highly magnified.

Candonopsis tenuis, Brady.

Adult female, seen from left side; magnified 45
diameters.

Adult male, in the same aspect and with the same
magnification,

Same, dorsal view.

Caudal ramus, more highly magnified.

On Fresh-water Entomostraca. 81

ji. VWIUUE
Boeckella robusta, G. O. Sars.

Adult female, viewed from the dorsal face (left
antenna not fully drawn); magnified 35 diameters.
Same, leg of last pair, more highly magnified.
Right prehensile antenna of male.

Last pair of legs of same.

Boeckella minuta, G. O. Sars.

. Adult, ovigerous female, viewed from the dorsal

face (right antenna not fully drawn); magnified 68
diameters.

Same, leg of last pair.

Last pair of legs of adult male.

es ela) LIN

ET BIDRAG

TIL

KUNDSKABEN OM STRANDEROSION

AF

PETER ANNÆUS ØYEN

KRISTIANIA

ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

KRISTIANIA — CENTRALTRYKKERIET 1896.

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVII. Nr. 4.

Skilbotn.

(Et bidrag til kundskaben om stranderosion.)
Af
Peter Anneus Øyen.

Oppe paa Helgelands kyst skjærer Skilbotn sig fra den
for sin Torghat bekjendte Torgo i nordøstlig retning ind i
landet over mod Velfjorden. Af mere fremtrædende punk-
ter har man her inde paa fastlandet Trælnæshatten i syd og
Moakslen i nord. Helt nede fra havet i sydvest har Skil-
botn en ganske flad, svagt stigende dalbund op til den halv-
cirkelformede begrænsning mod nordøst. Nede paa den
flade dalbund helt ind under de noksaa brat opstigende
fjeldsider har man her Skaaren i en høide af 45 m. o. h.
Foruden de to før nævnte fjelde i syd og i nord bør man
mærke sig Ramtind i øst og i vest Tilrumshatten, hvis syd-
ligste del, Havlarstuva, har en høide af 175 m. o. h. De
fjeldrygge, som mere eller mindre sammenhængende forbin-
der de nævnte fire toppe, udgjør den tidligere anførte
begrænsning i nordvest, nordøst og sydøst; den nogenlunde
regelmæssige udvikling lader Skilbotn fremtræde som en
smuk, vid fordybning, der paa grund af de to fra sydvest
indgaaende fjordarme, Skilbotnfjord i sydøst og Trælvikosen
i nordvest, faar fuldstændig karakteren af en fjordbotn.

Mellem Skilbotnfjord og Trælvikosen hæver sig en lav, lang-

4 Peter Annæus Øyen.

strakt fjeldryg, Aunheien, der som selve botnen har sin
længdeudstrækning fra nordøst til sydvest. Aunheien har
præg af et i stor maalestok montonneret klippeparti med
stødsiden mod nordøst.

Paa Tellef Dahlls geologiske kart over det nordlige
Norge er, naar undtages en liden som glacialt eller post-
glacialt betegnet strimmel, det hele herhen hørende parti
betegnet som cambrisk, en afdeling, der jo forøvrig i petro-
grafisk henseende er meget heterogen, men dog hovedsagelig
bestaar af forskjellige krystallinske skifere. Af Corneliussen!)
er bergarterne inden dette omraade henregnet til den af ham
indførte «glimmerskifer-marmor-formation». Jeg har ved en
tidligere anledning?) meddelt endel geologiske iagttagelser
fra dette strøg, og den mikroskopiske undersøgelse har vist,
at det væsentlig er glimmerskifere, snart med biotit, snart
med: muscovit, man her har for sig; overgange findes til
klorit- og kvartsskifere. I det store og hele synes strøg-
retningen at være nordøstlig, faldet steilt; men herfra kan
dog paavises større og mindre uregelmæssigheder. Et karak-
teristisk træk turde fremhæves i de flere hinanden skjæ-
rende lithoklassystemer.

Naar man fra et nogenlunde fritliggende sted, som f. ex.
Havlarstuva eller endnu bedre den store afsats i Ramtinds
sydvestlige del, lader blikket glide ud over Skilbotn, saa

vil en paafaldende skarp og sammenhængende linje udhæve

Skilbotn. 5

sig rundt botnen helt fra den sydlige del, Skilbotnfjordens
sydøstlige side, over til Havlarstuva i vest. Det viser sig
endvidere, at den nævnte linje falder ind i høide netop med
den ovenomtalte afsats i Ramtind, Denne afsats ligger her
110 m. o. h. og viste sig at være en gammel strandlinje i
fast fjeld; det er altsaa tydeligvis et mærke efter en tid-
ligere havstand, man ser tegne sig rundt botnen — en
slutning, som detailundersogelsen fuldstændig bekræftede.
Imidlertid vil mau allerede med det blotte oie opdage
enkelte afvigelser, som ogsaa maalingerne antyder, endskjønt
de kun er anstillet med aneroidbarometer; men disse afvigel-
ser er dog ikke saa store, at de paa nogensomhelst maade
berettiger udskillen af flere særskilte niveautrin.

Saaledes ser man f. ex. i Skilbotns sydlige del paa
_ sydostsiden af Skilbotnfjord etsteds tre forskjellige, men
hinanden ganske nærliggende trin; jeg fik dog ikke her
anledning til at anstille nøiere undersøgelse paa stedet.

Mod syd ser man fra Ramtind et inde i botnen
opragende mindre fjeldparti, der ganske skematisk er gjen-
givet i følgende skisse:

Den udprægede linje, der omkranser partiet, er en
tydelig afsats, som falder ind netop i høide med den linje:
der nogenlunde sammenhiengende strekker sig langs hele
Skilbotns sydøstlige side. Dette fjeldparti har altsaa i sin
tid været en mindre opragende ø i lighed med de mange
man nu har anledning til at se langs den norske kyst. Ved
den ene ende ser man en liden opragende knat adskilt fra

6 Peter Annæus Øyen.

den større; dette er altsaa et forhold fuldstændig analogt
med, hvad man f. ex. ogsaa har anledning til at iagttage
ved Leka i den saakaldte Lekamo (cfr. afbildning, pag. 15
i Mohn’s afhandling?)).

Som allerede for nævnt ligger den store afsats i Ram-
tind 110 m. o. h. og fremtræder meget tydelig som en gam-
mel strandlinje, til og med i fast fjeld. Selve strandlinjen
fremtræder her som en større, ialfald efter øiemaal at
dømme horizontal flade. Til orientering vedfoies en skema-

tiseret skisse:

I den ydre kant rager fast fjeld op over fladens mid-
lere niveau. De saaledes opragende fjeldknauser viser et
tilsyneladende montonneret preg; men der fandtes ingen
typisk glaciale skuringsstriber, ligesom heller ikke stod- og
læ-sidefænomenet traadte frem. Den afrundede form synes
i dette tilfælde nærmest at maatte betragtes som resultatet
af en kombineret vandskvulp- og drivis-indvirkning. Jeg
har ved en tidligere anledning*) hentydet til et lignende
fænomen nær den nuværende havstrand i nærheden af Torg-
hatten; her var det imidlertid iøinefaldende, at kun bølge-
slaget havde andel i dannelsen af den særegne form.

At knauser af fast fjeld saaledes rager op over strand-
linjens flade synes ikke at være et saa sjeldent fænomen
endda. Schiøtz omtaler det samme fænomen fra Vagge og
Hammerfest®); men man faar ingen oplysning, om de op-
ragende partier var afrundede, skurede eller ei. De nævnte

lagttagelser benyttes saa af Schiøtz til argumentation mod

Skilbotn. 7

drivistheorien for strandlinjers dannelse, til argumentation
‘for denudation i ebbe- og flodtid®). Paa samme sted an-
tyder da Schiotz, at kystis maa tænkes som det exporterende
middel. Naar man imidlertid betragter den afbildning, som
Reusch giver af strandlinjen ved Vagge”), saa er det ind-
lysende, at ialfald paa dette sted maa en undersøgelse af
erosionsfenomenet gaa forud for de opragende partiers
anvendelse som bevis mod udskuring ved is. I Stygfjeld
og Grubefjeld siger Hansen, at «de som holmer vpstikkende
skikthoveder i seten selv er afrundede» 8).

Keilhau?) og med ham senere Pettersen!®) og Hansen!)
antog jo, at strandlinjerne var udgravet af svømmende
isflag, og det vilde visselig være at forbise selve kjends-
gjerningerne at fradømme denne theori enhver betydning.
De afrundede, opstikkende fjeldpartier i strandlinjerne kan
saa langt fra benyttes som bevis mod drivistheorien, at de
tvertimod er et meget sikkert mærke efter isens skurende
indflydelse. Det er forresten mærkelig, at man her stilles
ansigt til ansigt med en modbevis- og bevisførelse, der er
fuldstændig analog med en tilsvarende med hensyn til roches
moutonnées, for hvis vedkommende jeg kun henviser til
min tidligere diskussion af sammel*). Naar man videre har
søgt at rykke i marken med beviser, hentede fra analoge
forhold ved den norske kyst nufortiden, som f. ex. Petter-
sen!3), saa er dette vistnok en fuldstændig rigtig fremgangs-
maade; men efter alt, som foreligger, tilhører jo de høit-
liggende strandlinjer langs Norges kyst en tid mere arktisk
end nu, ja «the date of these rock-terraces probably goes
back into the glacial period» 4), og det bliver derfor ogsaa
mere tilsvarende at hente de analoge beviser fra nuveerende
arktiske egne. Feilden og de Rance omtaler havisskuring
fra Smith’s Sound), og jeg har selv i Smeerenburg Bay

8 Peter Annæus Øyen.

(Spitzbergen) havt anledning til at se, hvilke ismasser en
arktisk strom kan sætte i bevægelse, hvorledes disse masser :
af drivis kan presses sammen, drives mod land og forsvinde
for atter at give plads for nye skurende masser — det vilde
være i hoi grad besynderlig, om de ikke skulde sette sit
mærke paa kysten, ja til og med et betydeligt mærke, forud-
sat at kystlinjens forskyvning var forholdsvis langsom.

Men man opholder sig heller ikke længe ved en ark-
tisk kyst, før man faar erfaring for, at ogsaa andre faktorer
er virksomme i det nuværende strandbelte: det er den af
hyppig temperaturveksling foraarsagede forvitring, som træ-
der sterkt frem. Det siger sig selv, at hvor flod og ebbe
gjør sig gjældende i udpræget grad, vil denne forvitring
træde endnu sterkere frem, et forhold, som Blytt16) trak i
forgrunden med hensyn til strandlinjers dannelse.

Man vil visselig finde, at flere forskjellige faktorer er
medvirkende ved dannelsen af strandlinjer, snart træder en,
snart en anden mere i forgrunden. Men til at forklare
strandlinjefænomenet i sin almindelighed langs den norske
kyst maa jeg erklære mig enig med Geikie, «that they may
have been due in large measure to the effects of the free-
zings and thawings along the cold «ice-foot», and to the
rasping and grating of coast-ice» 17). Jeg vil i det følgende
faa anledning til efterhaanden at omtale enkelte af de min-
dre fremtrædende faktorer, der ofte er af rent lokal natur.

I strandlinjen under Ramtind var selve fladen ca. 39
meter bred og dannedes for en stor del af myr og mose-
bund. Ved den indre veg var der nederst en mindre ur,
der sikkerlig skyldtes recent denudation; denne maatte for-
resten begunstiges i betydelig grad derved, at fjeldet ved

R. er meget gjennemsat af lithoklaser.

Skilbotn. 9

I den steile fjeldvæg ved R. lykkedes det mig at finde
tydelig vandslidt overflade, karakteriseret ved det glatte
udseende, den uregelmæssig buklede og lappede overflade
og talrige smaa udskulpede erosionshuler. De marker, som
vandskvulpet saaledes præger fjeldoverfladen med, er saa
karakteristiske og er af en saa stor betydning, at det synes
mig fuldt ud berettiget for dette erosionsfænomen at ind-
føre en egen benævnelse. Man gjenfinder det i huler, man
gjenfinder det i strandlinjer — overalt er dette karakteri-
stiske fænomen paa sin side et ligesaa godt mærke som de
isslidte og vindslidte paa sin. Man vil derfor ogsaa finde,
at ved studiet af littoralbeltets erosionsfænomener har ogsaa
dette spillet sin rolle.

Senft gav saaledes f. ex. en ganske treffende, men
kort karakteristik af dette fænomen!*). Reusch foreslog for
dette erosionsfenomen benævnelsen «polstret Fjeld»19), en
benævnelse, som derpaa af Baldauf ganske kritikløst blev
overført i den tyske literatur som «gepolsterte» 2°), men
synes forresten ikke at have vundet nogen videre indgang.

At denne benævnelse «i Lighed med det velkjendte
Roches moutonnées for det isskurede Fjeld»?1) staar langt
tilbage for sidstnævnte i træffende karakteristik, springer
meget snart i oinene; thi man kan trygt sige, det er meget
sjelden, «Udseendet minder — — — om en udstoppet Ryg
i en Sofa eller en Lænestol»*) — overfladen har ikke det
regelmæssige preg. Man finder derfor ogsaa de to strand-
linjeforskere Hansen og Pettersen kun tale om «den eien-
dommelige avglatning, polering»*). Penck gav ganske nylig
en udførlig og træffende karakteristik af fænomenet, men
har ikke fundet sig beføiet til at anvende nogen særegen

benævnelse?4).

10 Peter Annæus Øyen.

Jeg har havt anledning til at undersøge dette erosions-
fænomen paa flere forskjellige steder, seet det optræde i
forskjellige former, alt efter de forskjellige forhold. I
Sjonghelleren fandt jeg den vandslidte overflade meget hem-
met i sin udvikling af de i gneisen optrædende talrige litho-
klaser. I Torghattens gneisgranit viste hullets vægge paa
flere steder typisk skvulpeslidt fjeldoverflade. I en tildels
mere udvisket form finder man det samme fænomen i de af
glimmerskifer bestaaende vægge i Havlarsholet og Monsen,
hvorom mere senere. Det synes idethele at være de mere
haarde og massive bergarter, som leverer de mest typiske
former. Talrige lithoklaser hemmer den typiske udvikling,
idet den almindelige forvitring træder sterkere i forgrunden;
det samme synes i hoi grad at vere tilfældet ogsaa ved
mere skifrige og lose bergarter, endskjont man her paa sine
steder kan finde meget typiske former, naar den senere
denudation ikke har traadt for sterkt i forgrunden.

At finde en benævnelse, der paa sin side med hensyn
til de vandslidte former med alle de forskjellige varianter
indebærer et saa adækvat udtryk som den af Saussure”)
for de isskurede former indførte, er meget vanskelig, for
ikke at sige umulig.

Glatte, afrundede i smaa som i store træk fremtræder
de vandslidte former med en overflade af et snart mere
lappet, snart mere buklet udseende, der ofte faar et nervet
og arret præg ved de talrige snart aareformede fordybninger,
snart mere kopformede eller skaalformede huller af større
eller mindre dybde, med mere ovalformede gjennemsnit eller
mere kredsrunde, hvorved de ofte faar et rent jettegryde-
udseende. Skulde man for disse meget vekslende erosions-

former, hvor ikke det regelmæssige præg spiller hovedrollen,

Skilbotn. 11

men det uregelmæssige, optage nogen fælles sammenbindende
benævnelse, saa vil jeg foreslaa: «roche reniforme» *).

Naar jeg her har foreslaaet indført denne benævnelse,
saa har jeg ikke forbiseet, at Reusch ved en tidligere lei-
lighed har brugt udtrykket «nyreformet overflade» i følgende
skildring fra Bømmeløen: «Granitlandskabet ligner, hvad
dets almindelige karakter angaar, meget den af augitsyenit
bestaaende egn ved Fredriksværn. Man har for sig en
utallighed af smaarygge og smaaknauser. Deres sider er
bratte; oventil er de afrundede med lave bukler, hvorved
en slags «nyreformet overflade» fremkommer. Grunden til
disse klippeformer maa antagelig søges i en forud for is-
skuringen gaaende forvitring»*%). Det fremgaar af den oro-
grafiske skildring, at man i det af Reusch behandlede
fænomen har med et ganske andet at gjøre, for hvilket den
nævnte betegnelse maa ansees for mindre adækvat, og jeg
skal ved denne anledning ikke gaa nærmere ind derpaa —
det er af mere orografisk karakter.

Roche reniforme er et bevis for, at brændingen har
gjort sig gjældende som erosionsfaktor i littoralbeltet. Stu-
derer man imidlertid dette fænomens optræden meget nøie,
vil man snart komme til det resultat, at om end brændingen
har været medvirkende ved strandlinjernes dannelse, kan
den dog ingenlunde, som flere forskere har antaget, forklare
selve strandlinjefænomenets udvikling. Reusch fandt jo, at
det faste fjeld mellem fjæremaalet og flodmaalet, saa høit
som sjøsprøiten naar, var sterkt forvitret, tagget, medens
det saavel lavere som høiere var afglattet eller almindelig

*) Af den lighed, som nyreoverfladen f. ex. hos hornkvæget ved
sit uregelmæssig lappede, buklede og aarede udseende viser

med den her omhandlede overfladeform.

12 Peter Annæus Øyen.

forvitret 2"), Men det falder ikke vanskelig at paavise, at
selve fjeldlegemets sammensætning og forhold forøvrig, de
petrografiske og stratigrafiske eiendommeligheder ligesaavel
som ikke at forglemme de tektoniske har spillet en stor,
om end ogsaa kun lokal rolle ved erosionen i littoralbeltet
— at de spiller en stor rolle i det nuværende, har jeg havt
anledning til at iagttage paa mangfoldige steder af den
norske kyst.

Kjerulf. antog jo, at°«Strandlinierne ere havets eget
arbeide under strøm i flod og fjære»*), og betegnede dem
ogsaa senere som «horizontale, af havbrynet indgravede
mærker» *), men vedfoier dog ogsaa Keilhau’s forklaring?®).
Mohn3!), Reusch®?), Lehmann?) m. fl. betonede saa med
større eller mindre styrke denne dannelsesmaade; men som
jeg tidligere har udviklet, har man at betragte brændingen som
en bifaktor i lighed med de forskjellige tektoniske forhold.

I Ilsvikens strandlinjer (Trondhjem), om hvilken Cham-
bers allerede 1850 udtaler, at «not the least doubt can
exist, that it is the effect of the working of the sea»®%),
lykkedes det mig ikke at finde sikkert roche reniforme —
nu, jeg fik ikke anledning til at undersoge den hele linje;
men det er dog tilstrækkelig til at vise den lokale fore-
komst af fra dette sted af Reusch omtalt «eiendommelig
tilrunding af fjeldet — — — indgaaende kopformig jette-
gryde»). .

Naar Feilden og de Rance‘) paa den ene side, Knut-
sen?) paa den anden med forskjellig anvendelse af «isfoden»
(the ice-foot) trækker dels dennes passive og dels dennes
aktive betydning frem i forgrunden for at forklare strand-
linjedannelsen, saa tør det være, at deri er «isfodens» betyd-
ning overvurderet — det bliver efter den erfaring, jeg har

fra Spitzbergen, kun det indledende, ikke det afsluttende

Skilbotn. 13

| arbeide, «isfoden» udforer; men den forbereder ganske
naturlig i høi grad terrænet for den skurende drivis, der
samtidig bliver den sterke, udjevnende valse. «Isfodens»
store betydning for temperaturvekslingen er indlysende.

Man ser saaledes, at der foruden de to hovedfaktorer,
drivisskuring og forvitring, ved strandlinjedannelsen ogsaa
gjør sig gjældende flere bifaktorer, der imidlertid samtlige
kun virker paa en mere underordnet maade og tildels kun
rent lokalt.

Paa Skilbotns nordlige side fra Ramtind i øst over til
det mellem Moakslen og Tilrumshatten liggende skar i vest
ser man strandlinjen noksaa tydelig markeret, og i det
nævnte skar selv ser man endnu nogle masser af løst mate-
riale, som trods sin uregelmæssighed dog nærmest maa tydes
som strandlinjeafleiringer. Ret op for Skaaren dannede saa-
ledes linjen en betydelig afsats, ca. 103 m.o.h. — en sump-
agtig mosebund dannede her for en stor del selve fladen, men
efter alt at dømme var linjen selv skaaret i det faste fjeld.

Et karakteristisk træk ved fjeldet paa den nordlige
side af Skilbotn er, at der umiddelbart over strandlinjen
findes flere mindre botnformede fordybninger i fjeldmassen.
Disse «botner» har et fra de glaciale forskjelligt preg —
de har tildels en noget uregelmæssig form, og de tektoniske
forhold viser sig at have spillet en betydelig rolle. Seet i
forbindelse med huledannelsen eier disse botnformede for-
dybninger en betydelig interesse; thi igrunden saa er de
intet andet end begyndende huledannelser; dette sidste for-
hold tydeliggjøres end mere derved, at den store huledan-
nelse Monsen netop fortsætter ind i fjeldmassen fra en af

de her optrædende fordybninger.

7 — Archiv for Math. og Naturv. B. XVII No. 4.
Trykt den 29de Juli 1896.

14 Peter Annæus Øyen.

Paa Tilrumshattens østlige side følges saa spor af en
strandlinje, der fortsætter videre langs Havlarstuva. I den-
nes sydlige del finder man ret ned for den mærkelige hule-
dannelse Havlarsholet en noget større flade, der udgjøres af
en med frodig græsvekst og frodig løvtræskov bevokset,
sumpagtig myrstrækning i en hoide over havet af ca. 112
meter.

I den vestlige side af Tilrumshatten derimod fremtræ-
der ingen tydelig strandlinje; men derimod lykkedes det
mig her at paavise et par andre mærker, som vel afgiver et
ligesaa tydeligt bevis for den tidligere kystlinje. Paa et
sted fandt jeg nemlig her i ca. 110 m. o, h. et par jette-
gryder ganske tæt ved hinanden, og det faste fjeld viste
sammesteds et afrundet udseende, svarende omtrent til det
før omtalte fra den ydre kant af strandlinjen i Ramtind.
De to jettegryder var omtrent af samme størrelse: ca. 2 m.
diameter og 11/2 å 2 m. dybde, hvorved dog maa mærkes,
at der ikke kunde paavises fast fjeld i bunden af nogen; i
den nævnte dybde havde man i den ene græsklædt sand-
bund, i den anden omtrent en halv meter vand, under hvil-
ket bunden syntes at bestaa af sand og løs sten. At man
her har med stranddannede jettegryder at gjøre, antydes
foruden ved det faste fjelds udseende ogsaa ved den ene
ørydes skraastilling. Jeg kan i denne forbindelse gjøre
opmærksom paa, at det ofte ogsaa har sine vanskeligheder
at afgjøre, hvad der er isskuret, og hvad der er vandskuret
fjeld, naar de to erosionsfaktorer har virket samtidig eller
overgribende i hinanden; jeg erindrer ingensteds at have
seet saa illustrerende exempler herpaa som paa den ude i
Kristianiafjorden liggende ø Store Færder. Kommer saa
drivisskuring til, saa vil naturligvis forholdet blive endnu

mere kompliceret.

Skilbotn. 15

Jeg vil saa benytte leiligheden til at gjøre opmærksom
paa et par andre strandlinjer fra ganske nærliggende steder.

Paa sydsiden af den umiddelbart nord for Skilbotn ind-
skjærende Velfjord har man en meget fremtrædende linje,
der synes at have omtrent samme høide over havet som
strandlinjen i Skilbotn. Jeg fik desværre ikke anledning til
noiere at undersoge denne langt sammenhængende og meget
tydelige linje; da jeg kun har seet den fra fjordens nord-
side, er der jo en mulighed for, at det er et andet fænomen,
man her har for sig. I den paa Velfjordens nordside som
en ren fjordbotndannelse indskjærende Andalsvaag har jeg
seet denne omkranset af en strandlinje væsentlig i løst
materiale og, som det syntes, af omtrent samme høide som
foregaaende; ellers kunde jeg ikke opdage spor af strand-
linjedannelse paa Velfjordens nordside her i den ydre del.

Fra Trælnæshatten i syd har Reusch®*) leveret en teg-
ning med beskrivelse, hvorefter der skulde findes en afsats
eller strandlinje paa dette sted, svarende i høide omtrent
til den, jeg nu har beskrevet længere nord. Jeg har ved
en bestigning af Trælnæshatten ikke kunnet overbevise mig
om, åt nogen strandlinje var udviklet paa dette sted. Der-
imod angav jeg ogsaa tidligere %), at Trælnæshatten syntes
i sin helhed opbygget af forskjellige glimmerskifervarieteter,
og jeg er derfor, indtil mere nøiagtige undersøgelser fore-
ligger fra denne egn, tilbøielig til at anse de at Reusch
optrukne meget uregelmæssige linjer ikke som littorale, men
som stratigrafiske grænser.

Jeg skal derpaa gaa over til at levere en ganske kort
beskrivelse af de to allerede i det foregaaende nævnte hule-
dannelser: Monsen og Havlarsholet.

Monsen har i det store og hele retningen sydsydøst til
nordnordvest med en temmelig vid aabning mod sydsydøst.

16 Peter Annæus Øyen.

Hulen har her ved bunden en bredde af 28 meter og en
høide, som jeg anslog til 20 å 25 meter, medens tversnittet

forresten illustreres ved følgende tegning:

Hulens nordøstlige veg har en heldning paa ca 55°,
medens den sydvestlige væg har eu noget større heldnings-
vinkel, saa at hulen, som tegningen viser, tilspidses noget
opad. Indgangen til hulen faar derved nogen lighed med
Sjonghellerens. Hulens bund ligger ved aabningen ca. 124
m. 0. h. Man har her en større ur, som ogsaa fortsætter
videre nedover fjeldskraaningen. Hulens tversnit, der som
nævnt ved indgangen er temmelig stort, aftager efterhaanden
indover og tilspidses inderst inde endog i den grad, at man
ikke selv ved at krybe kan naa helt ind til den inderste
mod nordnordvest liggende ende. Bunden er noget uregel-
meessig, idet den ligger i forskjellig høide og snart dannes
af sand, snart af større og mindre, skarpkantede blokke;
men inderst inde har hulen samme høide over havet som
ved aabningen. For at give en forestilling om hulens

udseende og størrelse skal jeg vedføie nogle paa stedet

Skilbotn. 17

tagne maal: 90 m. fra aabningen maaltes bredden 12 m. og
117,5 m. fra aabningen en bredde af 4,6 m. med efter øie-
maal anslaaet høide ca. Sm. Hulens hele længde er 137,2 m.
Inde i hulen finder man helt indover til den inderste del
væggene forsynet med de for roche reniforme karakteri-
stiske erosionsheller; paa sine steder har dog atmosfæritierne
«øvet sin udviskende indflydelse. Har saaledes end bræn-
dingen utvivlsomt øvet sin indflydelse ved Monsens dan-
nelse, saa fremgaar det allerede meget tydelig af den ved-
foiede tegning, hvor endel af de mest fremtrædende litho-
klaser er angivet, at tektoniske forhold paa en meget
ioinefaldende maade har gjort sig gjældende, et forhold, som
end mere træder skarpt frem, naar man har anledning til
inde i hulen at anstille mere indgaaende detailundersøgelser.

Havlarsholet er en af de mærkeligste huledannelser,
jeg har seet. Fra den allerede før omtalte afsats (112 m.
o. h.) i Havlarstuvas sydlige del fører en skraaning opover,
og man er nu snart oppe i selve hulen, hvis bund er street
med skarpkantede, mindre og større, tildels kjæmpemæssige
blokke. Hulen, der strækker sig fra syd mod nord, har en
temmelig vid aabning mod syd; men væggene trækker sig
-efterhaanden noget sammen mod nord, og bunden stiger,
saa at hulen, om end rummelig, er noget trangere i den
indre del, hvis bund ligger ca. 138 m. 0. h. I den indre
væg ser man endnu et par tilspidsede hulrum, der tildels
er fyldt af nedfaldne, skarpkantede blokke, Inde i hulen
finder man væggene udsirede med de eiendommelige erosions-
furer og erosionshuller, saa karakteristiske for roche reni-
forme. Denne huledannelse, der ikke udmærker sig saa
meget ved sin længde, udmærker sig desto mere ved den
omstændighed, at i den indre del en temmelig vid skakt,
det egentlige Havlarshol, fører helt op i dagen, og det gjør

18 Peter Annæus Øyen.

et eiendommeligt indtryk at skue op gjennem den vide
«skorsten», hvis tversnit, skjønt noget uregelmæssigt i form,
kan sættes til ca. 106m. Den høide, det her gjælder, vil
man kunne danne sig en forestilling om, naar man erindrer,
at hulens bund paa dette sted laa 138 m. o. h., og finder,
at Havlarsholet kommer i dagen i en høide af 150 m. o. h,
altsaa 15 m. under toppen af den til 175 m. o. h. opragende
Havlarstuva. Heroppefra leverer den nedenforliggende græs-
og skovklædte mark seet gjennem hullet et høist eiendomme-
ligt skue. Tyder end det fundne roche reniforme paa bræn-
dingens arbeide og dens indflydelse paa huledannelsen, saa
springer det meget snart i øinene, at paa dette sted har de
tektoniske forhold øvet en afgjørende indflydelse. Man ser
tydelig, hvorledes hulens kontur i alt væsentlig retter sig
efter et omtrent horizontalt liggende og tre steiltstaaende
lithoklassystemer; kun i mindre træk og udviskende har
vandskvulpet ligesom de senere virkende atmosfæritier øvet
sin indflydelse.

Ved de to nu beskrevne huler har jeg gjort opmærk-
som paa, at tektoniske forhold maa betragtes som den for
deres udseende egentlig bestemmende faktor — at imidlertid
ogsaa andre faktorer maa være traadt til, er indlysende, og
af disse er allerede en omtalt. At senere forvitring har
øvet sin indflydelse, er i denne forbindelse af mere under-
ordnet betydning, hvor der er spørgsmaal om den egentlige
genese. I denne forbindelse vil det imidlertid være nød-
vendigt at stille sig de huledannende kræfter overhovedet
klart for øie.

Den store rigdom paa huler langs Norges vestkyst har
tiltrukket sig megen opmærksomhed, og det allerede for-
holdsvis tidlig. Torghatten finder man saaledes f. ex. omtalt
af Pontoppidan4), Hell#!), Thaarup4?). Neumann skrev sin

Skilbotn. 19

«Bjerg-Hulerne i Bergens Stift»*). Det vilde idethele blive
et langt arbeide at gjennemgaa den hele række af denne
klasse huler, og det vilde heller ikke høre hid — de staar
alle i nær forbindelse med en tidligere marin grænse. Men
foruden disse gives der en klasse huler, der gaar ind under
det saakaldte karstfænomen, huler, som man ogsaa finder
talrige repræsentanter for i Nordland. Af nogle gav Cor-
neliussen saavel en geografisk**) som geologisk”) beskri-
velse, ligesaa Vogt4); Vibe beskrev en eiendommelig hule-
dannelse4*) — erosion har ved disse huler været den bestem-
mende faktor; dog sees tydelig, at stratigrafiske og petro-
grafiske, ja vel ogsaa tektoniske forhold har øvet sin
indflydelse.

De to nu nævnte klasser af huler er hver paa sin vis
eiendommelige — hver har de sin forskjellige dannelse.
Det vil imidlertid være nødvendig at tage endnu et led i
huledannelsen med, og paa den maade selvfølgelig se noget
noiere paa en egen klasse huler. Reusch beskrev «En Hule
paa Gaarden Njøs, Leganger Præstegjæld i Bergens Stift» 45)
og fandt, at «ingen af de Dannelsesmaader, man almindelig
hører anføre for Hulers Vedkommende, passer her» 4%); men
at det er «en ganske anden Dannelsesmaade — — —, Forf.
tror at have kunnet læse ud af Forholdene paa Stedet:
under et Jordskjælv er tidligere existerende Sletter blevne
udvidede til Spalter; det opspaltede Fjeld er under Jordeas
Bæven knust, saaledes er Kløften, og hvor eiendommelige
Forhold ved Sletternes Retning traadte til, den overdækkede
Hule dannet»). Den klasse huler, hvortil den her af
Reusch beskrevne hører, er meget interessant; men den her
angivne dannelsesmaade kan ingenlunde betragtes som
væsentlig ny — det er i denne forbindelse tilstrækkelig at
henvise til «coupe théorique, indoquant la maniére dont

20 Peter Annæus Øyen.

ont pu se former certaines cavernes ‘par suite du refoule-
ment, du plissement et de la dislocation des couches de la
surface du globe»®'), I Bykle (Sætersdalen) har jeg i
Kværnhusaasens nordside selv havt anledning til at under-
søge en huledannelse, der gaar ind under denne klasse.
Fra Gauas dalføre beskriver Brøgger talrige sprækkedannel-
ser og antager, «at mægtige Kræfter, ikke langsomt virkende
Agenser»>*) har frembragt dem. Imidlertid har det exem-
pel, jeg anførte fra Bykle, antydet for mig, at man ved
huledannelser af denne art ikke maa lade den af frost-
sprængningen betingede virkning for meget ude af betragtning.

Med de tre nu angivne forskjellige slags huler har man
ihænde midlerne til noiere at undersøge, hvilke de faktorer
er, som især har været virksomme ved dannelsen af de
huler, der i række følger efter hinanden langs kysten. Man
kan gaa ud fra den sidstnævnte art, om hvilken man med
Virlet kan sige, at «les causes premières de l’existence des
cavernes sont les dislocations et les commotions successives
de l’écorce du globe»), og videre: «quand ces éboulemens
se sont propagés jusqu’à la surface, ils y ont donné lieu à
des espèces de cirques d’enfoncement» 5) — (cfr. her hans
tidligere «cirques d’enfoncement ou cavernes à ciel ouvert»).
Den anden art, karstfænomenets huler, interesserer i denne
forbindelse kun forsaavidt, de viser erosionens betydning
for huledannelser paa en tydelig maade. Endriss fandt saa-
ledes, «dass zwischen dem Bau der Hohlråume und dem
Bau der Spalten innige Beziehungen bestehen, dass die
Spaltenziige sozusagen die Grundlage fir die Ausbildung
des Höhlensystems abgaben»56); hvorimod Fraas fandt hule-
dannelser, «die bald ausschliesslich auf Erosion zurückzuführen
sind, bald aber auch mit localen Spaltenbildungen und Zer-

klüftungen des Gebirges in Verbindung gebracht werden

Skilbotn. 2

können — — — Eine grössere tectonische Bedeutung als
die localer Zerkliftungen wird sich aber wohl kaum heraus-
construiren Jassen»5”), Og selv Virlet omtaler «cavernes
qui se sont formées par simples érosions, commes celles qui
se sont creusées le long des rivages de la mer, par l’action
répétée des vagues»). Tektoniske forhold og erosion spil-
ler altsaa gjennemgaaende hovedrollen.

Torghattens hul er et meget instruktivt exempel fra
den foreliggende egn. Mohn gav jo en beskrivelse af
«Torghatten»5°) og gjorde opmærksom paa horizontal- og ver-
tikalsletter samt en tidligere høiere havstand som momenter
af betydning ved hullets dannelse. Ikke desto mindre finder
man senere Kjerulf opstille sin bekjendte dislokationstheori
for Torghatten og Kinnekloven®). Reusch fandt jo som
regel for huledannelsen, at hulerne dannes paa spalter®!), at
spalter og sletter er det bestemmende for deres form), at
de er «et Værk af Havet» ®), og udtalte specielt om Torg-
hathullet, at det «engang er dannet ved Brændingens Arbeide
— — — paa et Sted, hvor der optræder Spalter, som netop
der maa have lettet Bølgeslagets Virksomhed»6). Sollas
betragtede ogsaa Torghathullet som «a sea cave excavated
between two master-joints» og udtalte videre, at «the joints
are the most important factors in denudation» 5). Jeg hen-
viste ved en tidligere anledning‘) for Torghathullets ved-
kommende til de optrædende slettesystemer og havbølgernes
tærende og udmeislende indvirkning.

De huler, der som de to af mig her beskrevne optræder
langs den marine grænse, maa betragtes som en flerhed af
andre huler væsentlig betinget i de tektoniske forhold, hvor-
paa saavel deres forekomst som udseende tyder — det er
de rent lokale forhold, ikke de mere generelle, som har
været det bestemmende. Er end dette paa en vis maade

22 Peter Annæus Øyen.

en passiv betingelse, er den i dette tilfælde ikke desto min-
dre af stor betydning. Som eroderende har man bølgeslaget;
derfor har man bevis i roche reniforme og i hulernes litho-
rale forekomst. At saa foruden disse to hovedfaktorer flere
af mindre betydning spiller ind med, maa ikke forbisees:
seismiske virkninger kan have øvet sin indflydelse ligesaavel
som atmosfæritierne ved senere indvirkning — den af tem-
peraturveksling betingede forvitring maa ikke glemmes, lige-
som for de høitliggende hulers vedkommende kystis kan
have spillet en rolle som transportmiddel.

Reusch angiver, at man ingen sikkerhed har for, at de
havdannede huler tilhører samme tid ifølge sin dannelse
som de øvrige vandstandsmerker®™). Da jeg nu i Skilbotn
inden et forholdsvis snevert omraade imidlertid har paavist
strandlinjer i fast fjeld og i lost materiale, havdannede jette-
gryder og roche reniforme, havdannede «botner» og huler —
alt i nær samme niveau, forekommer det mig, at man ialtald
paa dette sted har med samtidige dannelser at gjøre. At
hulerne ligger noget høiere end strandlinjen, er et noget
afvigende forhold, som jeg senere skal komme tilbage til.
Naar Reusch imidlertid opstiller følgende trinfølge: «Huler,
Tunneler, Kløfter, Skar, Sund» 6) for de littorale erosions-
fænomener, saa maa jeg gjøre opmærksom paa, at denne
trinfølge ingenlunde maa opfattes for bogstavelig — de
stranddannede «botner» antyder, at trinfølgen ogsaa tildels
kan blive en anden, idet de to første led overspringes.

Strandlinjer og huledannelser gav i Skilbotn ligesom
ogsaa ellers paa Norges vestkyst et umiddelbart indtryk af
at være ny i forhold til selve egnens konfiguration. Naar
man ser saadanne over strandlinjen opragende kupper som
Torghatten, Sverresborg, Bremnæshatten og den foran afteg-

nede syd for Ramtind, bestyrkes endnu mere denne opfat-

Skilbotn. 93

ning. Det skulde forsaavidt ikke her være nødvendig at
komme tilbage til den af Sexe opstillede glaciale theori for
strandlinjernes dannelse®), efterat Hansen havde givet sin
treffende kritik af den?9), hvis man ikke selv ganske nylig
havde fundet en efterdønning — Rekstad antager nemlig,
«at en isbræ har gaaet ud efter fjorden, medens dens mæg-
tighed ikke har været stor nok til at fylde den ganske.
Den vilde da blive horizontal og følgelig have horizontale
sidemoræner»"!). Efter det kjendskab, jeg har saavel til nu
existerende br&er som til tidligere existerende bræers
afleiringer, er imidlertid det af Rekstad førte tankeexperi-
ment ikke stemmende med de kjendsgjerninger, som de
virkelige forhold frembyder; kunde de end til en vis grad
tænkes mulige for de i løst materiale optrædende linjer, saa
er det i ethvert fald aldeles utænkelig for de i fast fjeld
optrædende. Men man vilde i dette tilfælde selv for de i
løst materiale optrædende linjer efter Rink's”*) og Hel-
lands”) fremstilling ikke have med en isbræ at gjøre, men
med de fra bræen løsnede blokke og paa den maade være
kommet tilbage til selve drivistheorien. Sexe angav jo, «at
der paa det omkring 300 Fod høie Klippeparti mellem
Dybdal og Mundal fandtes Skuringsmærker fra Istiden
baade der, hvor Linien siges at ligge, og ovenfor og neden-
for samme», og anfører saa videre: «Paa Grund af disse
Skuringsmærker kan den omhandlede Strandlinie ikke være
frembragt efter Istiden» 74), Som det vil fremgaa af, hvad
jeg har meddelt om strandlinjen i Ramtind, maa man være
meget forsigtig med hensyn til de spredte skuringsmærker,
man iagttager i strandlinjer — deres forekomst og udseende
maa studeres særlig omhyggelig; dette har jeg seet et
udmærket exempel paa i Aardalsfjord (Ryfylke); i denne

forbindelse kan ogsaa henvises. til de Skuringsmærker, man

24 Peter Annæus Øyen.

ofte finder i det nuværende littoralbelte. Denne Sexe’s iagt-
tagelse kan derfor ikke tillægges nogen afgjorende betyd-
ning, da det sandsynligvis er drivisskuring, som i dette til-
fælde er forvekslet med glacialskuring. At de strandlinjer,
der her er tale om, er af sen glacial eller postglacial alder,
tor ansees som sikkert. Thi selv om man gik til den ex-
treme yderlighed at benægte en isbræes erosionsevne, at
man tvertimod ansaa isbræen som konserverende, og paa
den maade kunde forsvare den preglaciale existence af
strandlinjer i fast tjeld, saa vilde det dog være aldeles umu-
lig at hævde en saadan opfatning med hensyn til de linjer,
man finder i løst materiale; men man er udentvivl berettiget
til at betragte begge de nævnte arter linjer som samtidige
dannelser.

I denne forbindelse kunde det være værdt at se lidt
paa den, hvortil strandlinjer findes paa den heromhandlede
kyststrekning mellem 65° og 67° n. br. For at begynde i
syd har man Mohn’s angivelse af en horizontal linje paa
sydsiden af Leka 340° og en horizontal linje paa nordsiden
af Leka 341). Torghattens aksler angives af Mohn til
347' 0. h.76). Torghathullet ligger derimod med sin bund —
123 og 144 m. o. h.™), I det foregaaende er strandlinjerne
fra Skilbotn og Velfjord omtalte. I den indre del af Vet-
senfjord angav jeg den høieste strandlinje til 107 m. o. h.
og flere lavere terrasser”®). Fra Mosjøen har jeg seet ter-
rasseformet anordnede grusmasser i syd, men jeg fik ikke
anledning til nøiere at undersøge dem; skulde det vise sig,
at man her har for sig virkelige terrasser høiere end det
fra Vefsenfjorden nævnte, er det sandsynlig, at netop paa
grund af landets eiendommelige konfiguration særegne gla-
ciale forhold her har gjort sig gjældende, saa at man iste-

detfor marine terrasser faar. saadanne, der skriver sig fra

Skilbotn. 25

opdæmmede indsøer — alt dette bliver det imidlertid en
detailundersøgelses-sag at udrede. Fra Tomøen angiver Mohn
en strandlinje paa østsiden 301' o. h.®) og Corneliussen en
huledannelse paa nordvestpynten 87 m. o. h.%). Rekstad
angiver fra Holandsfjord strandlinjer ved Rendalsvik (102
m. 0. h.), Enga (102 m. o. h.), Braset (98 m. o. h.) og Ho-
land (50 m. o. h.)®!); hans forklaring af «strandlinjedannel-
sen» paa dette sted har jeg før gjort opmærksom paa.
Strandlinjerne i Holandsfjord har imidlertid allerede Geikie
tidligere gjort opmærksom paa: «the Norwegian fjord has
its sides marked by the line of a former sea-margin, about
250 feet above the present. This terrace winds out and in
among all the ramifications and curves of the fjord»5). Og
fra Fondalsbree forteller Geikie videre, at «the high terrace
so marked along the sides of the Holands fjord enters this
valley, and extends on the mountain sides as far as, at
least, the foot of the glacier. Hence the gravelly plain and
the moraine mounds that separate the glacier from the
fjord are overlooked on either side by a raised sea-beach» #).
Ved Glomfjorden omtaler Rekstad «en horizontal terrasse i
en hoide af omkring 75 m. o. h.» ved Vasdal — «dens
udseende tyder paa, at det er en morænedannelse», og lige-
saa omtales ved gaarden Glommen «tvende terrasselignende
moræner, den ene 66 m. o. h., den anden 108 m.» 5), Efter
Rekstads egen udtalelse skulde altsaa i dette tilfælde strand-
moræner foreligge; den ubestemte beskrivelse giver heller
ikke anledning til nogen bestemt slutning, skjønt høide-
forholdene taler sterkt for virkelige strandlinjer. Man ser
altsaa, at der paa den omhandlede strækning af den norske
kyst udhæver sig et ganske bestemt strandlinjeniveau i høi-
den 100—110 m. o. h. De forholdsvis faa og ikke absolut
noiagtige maalinger tillader ikke at drage nogen bestemt

26 Peter Annæus Øyen.

slutning med hensyn til linjernes horizontalitet eller ei.
Under dette niveau følger da flere lavere. Et træk af sær-
lig betydning er, at der ved flere huledannelser viser sig
sikre mærker efter brændingens arbeide indtil omtrent 30 m.
over den høieste strandlinje.

Ganske lignende forhold, som de nu her paapegede,
finder man ogsaa paa andre steder, f. ex. i omegnen af
Trondhjem. Chambers omtaler jo her «a terrace of ero-
sion, on the face of the cliffy hill to the west of the city
—- — — it extends for miles along the face of the hill, at
one uniform elevation», som han da ved nivellement be-
stemte til 522 «feet» o. h.%). Denne linje er saaledes ikke
blot beskrevet og maalt efter den af Kjerulf angivne dato%),
men ogsaa før. Jeg har ved et besøg paa stedet havt
anledning til selv at undersøge en del af denne Ilsvikens
berømte strandlinje, og Chamber's beskrivelse er meget
træffende: «on near inspection, we find a deep cut into
the almost horizontally disposed slate-rocks, with a ledge,
flat though rough>%). Der findes imidlertid paa dette sted
ikke blot en, men to linjer. Ilsvikens to strandlinjer blev
beskrevet af Kjerulf%), deres høide af Mohn bestemt til
respektive 512 og 569 fod®®), og ved senere nivellement
fandt kaptein Sejersted respektive 161,1 og 177,8 m.%).
Mohn siger, at Ilsvikens strandlinje er horizontal, og at den
nedre linje, hovedlinjen, viser sig horizontal i flugt med den
horizontale afsats i Sverresborg?!) Men i nærheden findes
ogsaa en hel del lavere terrasser. Hugh Miller angav den
øvre linje til 580 «feet» o. h., svarende til den i Norge
almindelige «marine limit», og meddeler videre, at «above
the Bay of Leangen, two miles east of town and river, and
far beyond all erosive influence of the latter, thirty of these

lines were mapped one above another in the first 300 feet

Skilbotn. ZI

of ascent — — — the number actually mapped was forty-
three, or, with the two rock-terraces, forty-five», og Miller
siger, at «these terraces are all post-glacial» 22).

At man i det første af de her foreliggende tilfælde
over selve hovedlinjen har huledannelser i en høide, der
svarer omtrent til en mindre tydelig markeret strandlinje i
det andet, antager jeg, er et forhold, der, skjønt mindre
paaagtet, er af den største betydning for forstaaelsen af
selve strandlinjedannelsen. Det viser ialfald med sikkerhed,
at den høieste skarpt markerede strandlinje ingenlunde
repræsenterer mærket efter den høieste vandstand. Naar
saaledes Mohn inddelte strandlinjerne i flere grupper og
hver af disse grupper igjen i flere niveauer®) og videre
taler om «de tydelige Sprang mellem disse Niveauer» %),
saa vil den foregaaende fremstilling tilfulde vise berettigel-
sen af en saadan adskillen; men den lader sig ikke derfor
uden videre anvende paa de to her foreliggende tilfælde,
der meget mere tyder paa, at de to nærliggende trin i dan-
nelse væsentlig er at henføre til omtrent samme tid. Den
egentlig strandlinjedannende kraft, drivisen, arbeidede under
havfladens niveau, medens de forskjellige bifaktorer gjorde
sig gjældende med større og mindre-styrke i og over, natur-
ligvis især mellem ebbe- og flodmaal. Derfor fik man egent-
lig et dobbelt mærke for hvert adskilt trin: øverst fik man
mærke efter brænding og forvitring, der fik man utydelige
strandlinjer og huler — men nederst skardrivisen, «a deep
eut», der fremstod den egentlige strandlinje.

Jeg skal ikke ved denne anledning gaa ind paa det
interessante sporgsmaal om strandlinjeforskyvningens kon-
tinuitet eller diskontinuitet, om strandlinjen undergik en
negativ forskyvning i sprang (Kjerulf %), Mohn*)), periodisk
(Hansen), Schiøtz*)) eller kontinuerlig (Blytt®), Petter-

28 Peter Annæus Øyen.

sen100)), Henvisningerne kunde her forfleres; men de an-
førte vil være tilstrækkelige til at vise, at paa dette omraade
vidt forskjellige anskuelser gjør sig gjældende.

Naar Schiøtz paa rent theoretisk grundlag fører et
mathematisk bevis, hvis resultat er, at man ved en kon-
tinuerlig forskyvning af strandlinjen ikke kan faa en hori-
zontal strandlinjeflade!), saa er dette visselig fuldstændig
korrekt, naar man gaar ud fra de forudsætninger, Schiøtz -
gjør. Men som det vil fremgaa af den foregaaende udvik-
ling, maa man efter min mening tillægge drivisen en langt
større betydning, end Schiotz’s forudsætninger gjør, og dertil
kommer som en meget vigtig faktor den omstændighed, at
strandlinjefladen, som jeg har gjort opmærksom paa, ikke
dannes i, men under havfladen, et forhold, som Schiøtz
ogsaa har været opmærksom paa, men tydeligvis ikke har
draget fuldt ud konsekvenserne af!0*). Den følgende udvik-
ling vil klargjøre forholdet tydeligere.

Geikie gav en skematisk fremstilling af et submarint
plan (altsaa begyndelsen til, hvad Ramsay kaldte «a plain
of marine denudation»1%)) med de tilsvarende littoraldan-
nelser: huler, tunneler etc.10). Noget svarende til strand-
linjer ser man ikke; Geikie’s anskuelse om disse er tidligere
anført. Den allerede før meddelte skematiske skizze af
strandlinjen i Ramtind kan vistnok tages som en type paa
et strandlinjetversnit — allerede selve tversnittet antyder,
at den eroderende kraft ikke har virket udelukkende i
samme horizontalniveau. Det er jo forholdsvis sjelden, man
i strandlinjerne træffer det af Geikie fremstillede littorale
erosionsprofil med den udoverhængende klippe over flod-
maalet1%). Reusch afbilder rigtignok et lignende forhold
ved Ilsvikens strandlinje ); men jeg har selv havt anled-

ning til at overbevise mig om, at selv ved Ilsvikens strand-

Skilbotn. 29

linje er dette forhold ingenlunde det almindelige; det sand-
synlige er, at man paa vedkommende sted har med rent
lokale aarsager at gjøre — noget, man forresten ingen
oplysning faar om.

For at anskueliggjøre forholdet ved strandlinjens ero-

sion vil jeg fæste opmærksomheden ved følgende figur:

Lad RCE betegne tverprofilet af et strandlinjeindsnit i
den oprindelige fjeldside RE.

Tænker man sig nu de eroderende kræfter begynde i
R og erosionen fortsætte under strandlinjens negative for-
_skyvning, samtidig med at de eroderende kræfter øges og
naar sit maximum i me, saa vil i dette øieblik ifølge det
foregaaende strandlinjens tverprofil ikke vere Rme, men
Rme', hvor e‘m' vil ligge desto dybere under em, jo ster-
kere isdannelsen i dette øieblik er. Fortsætter nu videre
under strandlinjens negative forskyvning erosionen med
aftagende kraft sit arbeide, saa skulde man ifølge Schiøtz1%)
faa profilet Rm; men ifølge det foregaaende vilde jo efter
den samme fremgangsmaade resultatet være profilet Rm' H
— altsaa en strandlinjeflade Hm‘ med betydelig mindre
heldning end Em. Det er imidlertid indlysende, at selv
profilet Rm‘H ikke er det endelige resultat, naar man efter

8 — Archiv for Math. og Naturv. B. XVIII. No. 4.
Trykt den 11te August 1896,

30 Peter Annæus Øyen.

det i det foregaaende paaviste ikke alene har at betragte
den almindelige denuation som en eroderende faktor, men
efter kjendsgjerningerne at dømme maa tillægge drivisen
en væsentlig betydning. Denne vil nemlig fortsætte sit
arbeide omtrent ligelig over hele strandlinjefladen, saalænge
kun denne flade befinder sig i tilstrækkelig dybde under
vandfladen. Er imidlertid de eroderende kræfter aftaget i
den grad, at de ikke kan holde skridt med strandlinje-
forskyvningen, vil forholdet ganske naturlig blive et helt
andet — da kan denudationen komme til at gjøre sig gjæl-
dende paa den af Schiøtz theoretisk udviklede maade —
deraf den ofte ved Æ iagttagne afplatning af kanten.

Det er langt fra min mening paa denne maade at have
indirekte paavist, at strandlinjerne maa være dannet under
en negativ forskyvning af strandlinjen, da de nemlig kan.
være dannet under særegne forhold i de eroderende kræf-
ters til- og aftagen. Men saa meget vil dog fremgaa af
det nu udviklede, at strandlinjernes udseende ikke kan
tages til indtægt mere for en theori om strandlinjens stil-
stand end for dens forskyvning under dannelsen — det bli-
ver ganske andre forhold, som maa afgjøre, om der har
gjort sig gjældende nogen periodicitet i strandlinjens for-
skyvning. dJeg antager ogsaa, at Schiøtz selv vil være den
første til at indrømme, at ved strandlinjedannelsen saa
mange forskjellige faktorer kommer til at spille sin rolle,
at det vil være meget vanskelig at gjøre en rent theoretisk
mathematisk betragtningsmaade exclusivt gjældende. Selve
strandlinjedannelsen afgiver visselig endnu et særdeles rigt
og interessant studiefelt.

I denne forbindelse, da nu engang spørgsmaalet om
stranderosion foreligger, vil jeg ogsaa i korthed berøre et

andet forhold, som slutter sig temmelig nøie hertil. Det

Skilbotn. 31

var jo antaget, at den skandinaviske halvø steg, og i den
anledning har man ogsaa paa den norske kyst anbragt endel
vandstandsmærker. Naar man har villet knytte disse til
tang- og balangrænsen (cfr. Storthings-Dok. No. 75 og Indst.
No. 164 i 1893), saa maa hertil bemærkes, at disse to greenser
optræder paa en saa uregelmæssig maade, influeret dels af
de petrografisk-stratigrafiske forhold og dels af littoral-
erosionen, at de mærker, der er knyttet til disse greenser,
ingenlunde kan benyttes med nogen sikkerhed til bestem-
melse af strandlinjens forskyvning. Dette er et forhold,
som jeg har havt anledning til i detaljerne at studere paa
en stor del af Norges kyststrækning. Det er imidlertid
indlysende, at her visse strømforhold ogsaa vil gjøre sig i
høi grad gjældende, ligesom tidvandet øver en betydelig
indflydelse. | |

Tidligere antoges det jo ganske almindelig, at strand-
linjerne var dannede langs selve havkanten — i havets
niveau. Imidlertid opstillede Suess sin «Gletscherabschluss-
theorie» 1), der saa af Sandler modificeredes derhen, at
ogsaa glaciale afleiringer ved fjordmundingerne skulde have
været medvirkende; men Sandler medgiver dog, at «eine
Untersuchung von Fall zu Fall» maa afgjøre, om alle strand-
linjer paa den norske kyst kan ansees dannede i saadanne
opdæmmede indsøer10%).

For den mellem Leka i syd og Støt i nord liggende
del af den norske kyst kan imidlertid hverken den af Suess
eller den af Sandler opstillede theori gjøres gjældende i sin
almindelighed til at forklare strandlinjefænomenet — selv-
samme. strandlinjeniveau inde i de dybe fjorde og paa øerne
ude mod det aabne hav er bevis nok.

Det ligger udenfor nærværende afhandlings ramme at
gaa ind paa en nærmere diskussion af det lave forland, der

32: Peter Annæus Øyen.

optræder langs den norske kyst og i omegnen af Torghatten,
optræder paa en meget typisk maade saavel ude paa øerne
som inde paa fastlandet. Jeg skal kun i forbigaaende gjøre
opmærksom paa, at «opdagelsen» af dette lave forland
ingenlunde tilhører det sidste decennium, og at «the views
— — — bear a very striking resemblance to a simple

raised beach » 110),

ee

Skilbotn. 33

Literaturhenvisninger.

Reusch: Det nordlige Norges geologi, Pag. 155.

Øyen: Bidrag til det nordlige Norges geologi, Pag. 13, 14.
Nyt Magazin for Naturvidenskaberne, B. 22.

Øyen: Bidrag til det nordlige Norges geologi, Pag. 11.
Schiøtz: Nogle Bemerkninger om Dannelsen af Strandlinier i
fast Fjeld, Pag. 4, 5.

l. c, Pag. 5—8.

Reusch: Det nordlige Norges geologi, Pag. 95.

Hansen: Om seter eller strandlinjer i store høider over havet
(separataftryk), Pag. 7.

Nyt Mag. for Naturv. B. I, Pag. 231.

Arch. for Math. og Naturv. B. 3, Pag. 222.

Arch. for Math. og Naturv. B. 14, Pag. 294—301.

Oyen: Isbrestudier i Jotunheimen.

Tromsø Museums Aarshefter 3.

Geikie: Geological Sketches at Home and Abroad, Pag. 153.
Qvart. Journ. Geol. Soc., London, Vol. 34. Geological Maga-
zine 1890.

Kristiania Vid. Selsk. Forh. 1881, nr. 4,

Geikie: Geological Sketches at Home and Abroad, Pag. 153.
Senft: Synopsis der Mineralogie und Geognosie IT, 1, Pag. 144.
Nyt Mag. for Naturv. B. 22, Pag. 211 og B. 26, Pag. 80.
Neues Jahrbuch f. Min., Geol. ete. Jahrg. 1879, Pag. 250.

Nyt Mag. for Naturv. B. 26, Pag. 80.

Nyt Mag. for Naturv. B. 22, Pag. 211.

Archiv for Math. og Naturv. B. 14, Pag. 285.

Penck: Morphologie der Erdoberflache B. II, Pag. 472, 473.
Saussure: Voyages dans les Alpes B. II, Pag. 512, 513.
Reusch: Bømmeløen og Karmøen, Pag. 256.

Kristiania Vid. Selsk. Forh. 1874, Pag. 284—285.

34 Peter Annæus Øyen.

28. Kjerulf: Om Skuringsmærker ete. II. Univ. prog. 1872, Pag. 89.

29. Kjerulf: Udsigt over det sydlige Norges geologi, Pag. 15.

BO, IL &, Tar» 116

31. Nyt Mag. for Naturv. B. 22, Pag. 50. Kristiania Vid. Selsk.
Forh. 1870, Pag. 443 flg.

32. Kristiania Vid. Selsk. Forh. 1874, Pag. 284 fig. Nyt Mag. for
Naturv. B. 22, Pag. 205.

33. Ueber die ehemaligen Strandlinien in ausstehendem Fels in
Norwegen. Halle 1879.

34. The Edinburgh New Philosophical Journal vol. 48, Pag. 73.

35. Kristiania Vid. Selsk. Forh. 1890, nr. 7, Pag. 25.

36. Quart. Journal Geol. Soc., London, vol. 34. Geological Maga-
zine 1890.

37. Meddelelser om Grønland B. 9, Pag. 235.

38. Norges geol. undersøgelse, aarbog 1892—93, Pag. 9.

39. Øyen: Bidrag til det nordlige Norges geologi, Pag. 10.

40. Pontoppidan: Norges Naturlige Historie B. I, Pag. 75.

41. Hell: Ephemerides astronomicæ Anni 1791.

42. Thaarup: Mag. for Danmarks og Norges Beskr. B. I, Pag.
144—145.

43. Urda B. I, Pag. 201 fig.

44. Den norske turistforenings aarbog 1875, Pag. 64 flg.

45. Reusch: Det nordlige Norges geologi, Pag. 177—182.

46. Vogt: Dunderlandsdalens jernmalmfelt, Pag. 11—16.

47. Det norske geogr. selsk. aarbog III, Pag. 87—90.

48. Kristiania Vid. Selsk. Forh. 1874, Pag. 275 flg.

49. 1. c., Pag. 278.

10, hy Cony Pace 209.

51. Bulletin de la Société Géologique de France 1833 a 1834, Pag. 347.

52. Kristiania Vid. Selsk. Forh. 1877, nr. 2, Pag. 26.

53. Bull. de la Soc. Géol. de France 1834 a 1835, Pag. 163.

54. 1. c., Pag. 164.

550 De Pag, 158.

56. Zeitschrift d. Deutschen geol. Gesellschaft B. 44, Pag. 57.

57. Zeitschrift d. Deutschen geol. Gesellschaft B. 45, Pag. 1.

58. Bull. de la Soc. Géol. de France 1834 a 1835, Pag. 164.

59. Kristiania Vid. Selsk. Forh. 1870, Pag. 443—453.

Skilbotn. 35

90.

Kjerulf: Stenriget og Fjeldlæren 1878, Pag. 109.

Nyt Mag. for Naturv. B. 22, Pag. 206.

l. c., Pag. 207.

Me Bao: 205.

Nyt Mag. for Naturv. B. 26, Pag. 80.

The Geol. Mag., Londen 1880, vol. 7, Pag. 516.

Øyen: Bidrag til det nordlige Norges geologi, Pag.

Nyt Mag. for Naturv. B. 26, Pag. 168.

l. c., Pag. 85.

Sexe: On the Rise of Land in Scandinavia. — Sexe: Jettegry-
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Naturv. B. 1 og B. 5.

Arch. for Math. og Naturv. B. 14, Pag. 284, 285.

Rekstad: Beretning om en undersøgelse af Svartisen, Pag.
303, 304.

The Journal of the Royal Geogr. Soc. vol. 23. London 1853.
Pag. 152.

Mitth. des Ver. fir Erdk. zu Leipzig 1876, Pag. 31.

Kristiania Vid. Selsk. Forh. 1874, Pag. 187.

Nyt Mag. for Naturv. B. 22, Pag. 14, 15.

es) Bag, 15:

Nyt Mag. for Naturv. B. 26, Pag. 72.

Øyen: Bidrag til det nordlige Norges geologi, Pag. 18.

Nyt Mag. for Naturv. B. 22, Pag. 15, 16.

Reusch: Det nordlige Norges geologi, Pag. 168, 169.
Rekstad: Beretning om en undersøgelse af Svartisen, Pag. 303.
Geikie: Geological Sketches at Home and Abroad, Pag. 137.
l. c., Pag. 145.

Rekstad: Beretning om en-undersegelse af Svartisen, Pag. 294.
The Edinburgh New Philosophical Journal 1850, vol. 48, Pag 72.
Kjerulf: Udsigt over det sydlige Norges geologi. Atlas, pl.
III. — Kjerulf: Merakerprofilet, Pag. 69.

The Edinburgh New Philosophical Journal 1850, vol. 48, Pag. 73.
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Nyt Mag. for Naturv. B. 22, Pag. 10—13.

Kjerulf: Merakerprofilet, Pag. 69.

36 Peter Annæus Øyen: Skilbotn.

91. Nyt Mag. for Naturv. B. 22, Pag. 10—13.

92. Nature Vol. 32, Pag. 555.

93. Nyt Mag. for Naturv. B. 22, Pag. 32—37.

94. 1. e., Page 50.

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98. Kristiania Vid. Selsk. Forh. 1894, nr. 4, Pag. 15.

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102. 1. &, Pag. 13—14

103. Cfr Huxley: Physdography, Pag. 183.

104. Geikie: Class-Book of Geology, Pag. 100.

105. Geikie: Physical Geography, Pag. 152.

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108. Suess: Antlitz der Erde II.

109. Dr. Petermann: Geographische Mittheilungen 1890, Pag. 242
110 The Geographical Journal, London, 1894, Pag. 186.

Trykfeil.

Side 4, linje 3 f. 0. og side 6 linje 13 f. o. staar montonneret, skal

være motttonneret.

STRANDEN JER

GUDBRANDSDALEN

AF

PETER ANNÆUS ØYEN

dn KRISTIANIA

ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

0

à »
È
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Centraltrykkeriet — Kristiania 1896:

DEC 4 1896

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVIII. Nr. 5.

Strandlinjer i Gudbrandsdalen.
Af
Peter Anneus Oyen.

Allerede fra gammel tid af synes bygdens folk at have
været opmærksom paa de i Dovre og Lesje optrædende
«Flaatte»; men disse har dog ikke her spillet en saadan
rolle i den overleverede tradition som f. ex. «Munkevejene»
i Trysil?) og «Fingalian Roads» i Lochaber?).

Den eiendommelige indflydelse, som disse setedannelser -
har saavel i rent topografisk henseende som paa jordsmonnet,
har i disse bygder gjort sig gjældende paa en meget frem-
trædende maade i selve bebyggelsen, og man sporer som
paa flere steder indflydelsen selv i enkelte gaardsnavne.
Allerede Chambers har været opmærksom paa dette eien-
dommelige topografiske forhold til bebyggelsen; thi han
siger: «I could distinctly trace this terrace by its hum-
mocks of water-laid sand, and the farmhouses perched on
its favourable points. A long series of hamlets on the
road to Molde is placed upon it» *),

Naumann, der reiste i Norge i aarene 1821 og 1822,
siger om Dovre, at «sich im ganzen Thale Sand-Anhiufungen
sehr bemerklich machen»*), og han omtaler ogsaa de optræ-
dende setedannelser. Da Naumann’s optegnelse synes fuld-
stændig glemt®), skal jeg hidsætte følgende: «Die ganze

1 — Archiv for Math. og Naturv. B. XVIII Nr. 5.
Trykt den 22de September 1896.

4 Peter Annæus Øyen.

Thalstrecke von Bottem bis unterhalb Mölmen scheint einst
das Bette eines groszen Sees gebildet zu haben, dessen
Spiegel wohl sehr hoch tiber dem des Lessø-Werk-See lag
Nun findet sich aber nach jeder Seite ein gewaltsamer
Durchbruch abwärts, der eine unterhalb Mölmen, der andere
bey Bottem — — — Wenn man die Gehänge jenseits Bot-
tenı von einem hohen Standpunct diesseits mustert, so be-
merkt man ein paar terrassenartige Zonen, die sich hier
und da unterbrochen, horizontal am Gehäng hinziehen und
auf Spuren der ehemaligen Ufer zu deuten scheinen. Wohl
dürfte sich die Höhe der unteren dieser Zonen nicht viel
vom jetzigen Niveau des Lesso-Werk-See abweichend er-
geben» 6).

Denne Naumann’s iagttagelse af strandlinjer i den nord-
lige del af Gudbrandsdalen er selv i og for sig meget
interessant, men bliver det i endnu høiere grad, naar man
ser hen til den omstændighed, at den er gjort kun nogle
ganske faa aar efter, at Mac Culloch ved offentliggjørelsen
af sin afhandling «On the Parallel Roads of Glen Roy»*”)
i aaret 1817 havde indledet den senere saa livlige diskussion
om disse, men dog fuldstændig uafhængig. Det er ligeledes
meget interessant at se Naumann i dette tilfælde erkjende
linjernes lakustrine karakter, ligesom Mac Culloch for lin-
jerne i Glen Roy; men imidlertid synes ingen af dem at
have dannet sig nogen bestemt forestilling om dæmningens
karakter — dog synes tanken nærmest henledet paa grus-
ophobninger.

For Lochaberlinjerne fremsatte saa Darwin i 1839 sin
marine theori8), og det var derfor ikke andet, end man
maatte vente sig, at denne theori ogsaa blev anvendt paa
Dovrelinjerne, da disse senere blev undersøgt af den marine

theoris vigtigste forkjæmper, Robert Chambers.

Strandlinjer i Gudbrandsdalen. 5

Chambers gav derpaa 1850 ved to anledninger?) beskri-
velse af Dovres og Lesjes strandlinjer og hævder ved begge
linjernes marine oprindelse. «I discovered one,» siger
Chambers, «of a much more remarkable character, passing
along both sides of the valley for fully twenty miles, always
at one elevation — — — Ås an object in physical geo-
graphy, in its form, its uniform level on both sides of the
vale, and its relation to the lake at the summit-level, this
terrace precisely resembles the lowest of the Glenroy
terraces as it approaches Loch Laggan»19%). Dermed var
den væsentlige lighed mellem disse to strandlinjeforekomster
præciseret, og det falder derfor ganske naturligt, at studiet
af dem senere for en stor del udvikler sig side om side.

Efter sammen med Buckland at have aflagt et besøg i
Lochaber 1840 fremsatte Agassiz for de der optrædende
strandlinjer sin glaciale theori, som derpaa er meddelt i en
skrivelse til professor Jamieson. Da imidlertid denne skri-
velse fra Agassiz til Jamieson synes glemt eller forbiseet 14),
skal jeg af den hidsætte følgende: «The existence of gla-
ciers in Scotland at early periods can no longer be doubted.
The parallel roads of Glen Roy are intimately connected
with this former occurrence of glaciers, and have been
caused by a glacier from Ben Nevis. The phenomenon
must have been precisely analogous to the glacier lakes of
the Tyrol, and to the event that took place in the valley
of Bagne» 12).

Det varede dog lenge, for den glaciale theori vandt
nogen anvendelse ved Dovrelinjerne. Kjerulf polemiserede
rigtignok mod den marine theori; men hans standpunkt
karakteriseres meget godt ved følgende udtalelse: «Hvad
der netop her umiddelbart har sperret Bassinet, har man
paa Stedet ikke let for at begribe» #), og denne forfatter

6 Peter Annæus Øyen.

syntes at blive staaende ved denne noget ubestemte opfat-
ning, hvis man ikke skulde være berettiget til at trække en
vis slutning af følgende, hvor talen er om terrasser: «i luk-
ket situation — indenfor en fjeldsnævring, f ex. i et bas-
sin» 4), og hvor man finder Dovredalen opfort som visende
indlandsterrasser i lukket bassin). Det er væsentlig den
samme opfatning, som er gjort gjældende af Gumelius, der
ogsaa beskriver Dovres terrasser som indsøterrasser og for-
klarer tømningen ved postglacial erosion i det trange pas
Rosten!®), og efter hans mening skulde jettegrydedannelse
have været en væsentlig faktor ved gjennembruddet!?).

Sommeren 1872 besøgte saa Dakyns Norge og skrev
umiddelbart efter hjemkomsten til England sin afhandling
«High-Level Terraces in Norway», som imidlertid ikke blev
publiceret før i 187718). Her beskrives da strandlinjer fra
Dovre og Lesje, og denne afhandling er saa meget mere mærke-
lig, som den glaciale theori her trækkes i forgrunden til at for-
klare fænomenet, idet Dakyns siger: «One is irresistibly
led to think of the similar case of the parallel roads of
Glenroy, and to speculate on this terrace too having been ~
due to the waters of a gigantic Marjelen See, dammed back
by ice till it overflowed the summit of the pass at Molmen;
and it is significant that I could see no trace of terrace or
water-mark on the Romsdal side of the pass»19).

Hugh Miller iagttog saa disse strandlinjer 1873, men
forst 1886 samtidig med at gjenkalde i erindringen Cham-
bers’s beskrivelse meddeltes en notits derom. Miller siger
imidlertid selv, at han intet har at føie til de af Chambers
gjorte iagttagelser. Miller taler om «the vanished sheet of
water, in which they were formed»; men om det er den
marine eller lakustrine theori, der skal støttes, fremgaar

ikke med sikkerhed?9).

Strandlinjer i Gudbrandsdalen. 7

Med ottiaarene begyndte en livligere diskussion af de
skandinaviske seter. Det kan i denne forbindelse ogsaa
mærkes, at Blytt 1880 saa en strandlinje paa Tønsæt og
udtaler om samme: «Vielleicht ist dieselbe eine Süsz-
wasserbildung aus der Eiszeit, vielleicht inter- oder prä-
glacial» 21). Högbom beskrev strandlinjer fra Jemtland”)
og gav senere fortsatte bidrag til den samme egns strand-
linjegeologi med hidhorende literaturoversigt*). Hansen gav
1885 en beskrivelse af strandlinjer i Østerdalen, men angav
desforuden ogsaa lignende fra Sel, Vaage og Lesje*.
Hansen hævdede den glaciallakustrine theori ved «sammen-
hængende bræmasser, der skyder bræer op gjennem alle
dalene»). At hævde en saadan forskjel, som Hansen‘)
synes at ville gjøre, mellem denne theori og den af Agassiz
opstillede er neppe gjørlig; thi man kan ved talrige exem-
pler fra Grønland, Himalaya og Alperne paavise en række
af overgangsformer — at man har is som opdæmmende
faktor er i dette tilfælde det afgjorende; den kvantitative
forskjel er af mindre væsentlig betydning, og det vil her
være tilstrækkelig i saa henseende at gjøre opmærksom paa
de instruktive exempler fra Martellthal?7) og Alaska*)
ligesom ogsaa de norske forekomster**).

Der udspandt sig nu efterhaanden en diskussion mellem
Blytt, Hansen og Reusch angaaende Østerdalens og Gud-
brandsdalens seteforekomster, en diskussion, som for en stor
del førtes i «den Naturhistoriske forening» (Kristiania). I
et møde 25 januar 1886 holdt Reusch her et foredrag
om Gudbrandsdalens seter®°), Naar der imidlertid i refe-
ratet af den paafølgende diskussion her siges, at Blytt
erklærede sig enig i Hansens theori°!), saa maa dette bero
paa en misforstaaelse fra referentens side; tbi Blytt har
mundtlig meddelt mig, at han aldrig har været enig i Han-

8 Peter Annæus Øyen.

sens theori. En anden ting er, at Blytt saavel ifølge den
allerede ovenfor meddelte udtalelse angaaende Tønsætlinjen
som ogsaa ifølge senere udtalelser®?) indrømmer lokale bræ-
søer med lokale strandlinjeforekomster. Straks efter offent-
liggjorde saa Reusch en ganske kort opsats: «Vieflotten i
Gudbrandsdalen»). Senere har Hansen paa flere steder 34)
omtalt disse strandlinjeforekomster. Ffter Hansen skal de
være undersøgt og nivelleret af Rudolph); men det har
ikke været mig muligt at faa rede paa, om resultatet af
disse undersøgelser endnu er offentliggjort.

Seterne ialmindelighed betragter Blytt som strand-
morener?°), Det var denne forklaring, Melvin®*) og senere
Reusch**) ogsaa søgte at gjøre gjældende. Jeg har ved en
tidligere anledning?) givet den samme forklaring for dan-
nelsen af de seter, man i Gudbrandsdalen træffer syd for
det bekjendte pas Rosten — vel at mærke: i sin alminde-
lighed; jeg angav enkelte undtagelser som lokale forekom-
ster og gjorde desuden specielt opmærksom paa de lavere
trin, der paa sine steder træffes nede i dalbunden. At for-
klare terrassedannelser som strandmoræner er imidlertid
ingen ny theori — det er ikke en theori, som skyldes nogen
af det sidste decenniums forskere; man maa gaa over femti
aar tilbage i tiden. Bowmann offentliggjorde i aaret 1841
en afhandling: «On the Natural Terraces on the Eildon
Hills being formed by the Action of Ancient Glaciers» *°),
at hvilken jeg skal hidsætte følgende: «As the fact of the
former existence of glaciers in Scotland is now exciting
general attention, and will soon, I doubt not, be firmly
established, I might have silently left it to others to con-
sider them at the true cause of these terraces, had not a
recent visit from Prof. Agassiz afforded me an oppurtunity

of giving him the details of my own observations, and of

Strandlinjer i Gudbrandsdalen. 9

hearing from himself that the appearances I described
have often been seen by him on the sides of existing gla-
ciers — — — I feel persuaded that the theory of their formation
by water must be abandoned, and that they must be con-
sidered to be the true morains of ancient glaciers» 4!), Man
ser altsaa, at den store bræforskers navn staar i en noksaa
nær indirekte forbindelse ogsaa med denne theoris oprindelse.

Efter den historiske oversigt over kjendskabet til Gud-
brandsdalens seteforekomster skal jeg saa gaa over til at
betragte disse noget mere detaljeret. Som allerede oventor
nævnt har jeg ved en tidligere anledning omtalt sete-
forekomster syd for Rosten og skal derfor nu forbigaa disse.
I forbigaaende skal dog opmærksomheden henledes paa det
skille, som dette pas danner mellem to omraader, inden
hvilke de løse afleiringer optræder paa en meget forskjellig-
artet maade. Nu maa man naturligvis ikke forbise, at for-
holdsvis nyere denudation, elveudgravning og jordskred
f. ex., paa sine steder kan have øvet en betydelig indfly-
delse; men dette vil dog altid kun være rent lokalt — det
kunde i denne forbindelse være tilstrækkelig at minde om
den store flom, der i aaret 1789 anrettede saa store øde-
læggelser i Østerdalen**), Gudbrandsdalen”) og Valders#*).
Ved Øvrebø (sydvest for Laurgaard, Rosten) hæver sig
over de for sin Cicuta virosa bekjendte, flade og myriæudte
strækninger endel grushauge med tildels afrundede stene,
blandet med sand og ler; morænegruset synes altsaa paa
dette sted sikkert. Den tildels bastionagtige forekomst
kunde imidlertid ogsaa henlede tanken paa terrassedannelse.
Det lykkedes mig ikke at finde noget snit i disse grus-
masser; men en mand paa Øvrebø fortalte mig, at under
den brugte jord er her det grove grus almindelig udbredt,

og naar man ved dybgravninger gaar længere ned, finder

10 Peter Annæus Øyen.

man i forskjellig dybde nede i gruset igjen et lag brugt
jord. Netop her skulde imidlertid et større jordskred have
fundet sted ved flommen i forrige aarhundrede, og som man
ser, stemmer dette meget godt med lagfølgen i de løse
afleiringer og med deres topografiske udseende.

Fra enden af Vaagevandet optræder østover store grus-
afleiringer, denuderet og omleiret bundmoræne. Denne fort-
sætter ogsaa paa overgangen fra Vaage hoveddal forbi Sels-
vand, hvor der findes svære urer, til Sel. Det moutonnerede
fjeld er paa dette strøg mindre tydelig udviklet paa grund
af bergartens beskaffenhed, men dog tydelig nok til at
angive fortsættelsen af den fra Vaage kjendte, østliggaaende
hovedlinje. I Sel har Gudbrandsdalens hoveddalføre et
sækkedallignende udseende, idet med Rosten en tilsyne-
ladende sperring finder sted. Strandmoræneforekomst og
utydelig skuring i selve Rostensnevringen viser imidlertid,
at den ikke er af postglacial alder i sin helhed. Derimod
er det nuværende, temmelig dybe elvegjel sikkerlig af post-
glacial alder; thi i dette saaes ingen isskuring. Om paa
dette sted jettegrydedannelsen, som Gumeelius*) antog, har
spillet nogen fremtrædende rolle, kunde jeg ikke forvisse
mig om — det er ikke usandsynlig, men heller ikke nød-
vendig. Man har nemlig i Søndre Fron ved Harpefossen
et dybt gjel i dalbunden; dette gjel mangler ligesom Rostens
isskuring — det er altsaa ligeledes postglacialt. Ved dette
kan man imidlertid se, at jettegryder har øvet betydelig
indflydelse ved dannelsen, og ved selve Harpefossen har
man en hel del tildels store jettegryder, der har tiltrukket
sig opmærksomhed allerede i forrige aarhundrede46). Paa
den anden side har jeg ved Langglupelven (Ronderne) havt
anledning til at undersøge et ligeledes postglacialt gjel, hvor

ikke jettegryder, men bergartens strukturforhold viste sig

Strandlinjer i Gudbrandsdalen. i

af stor betydning. Det er derfor sandsynlig, at de eien-
dommelige strukturtorhold med de talrige lithoklaser i Rostens
konglomerat for en stor del har lettet elvens gjennembry-
dende arbeide.

Umiddelbart nord for Rostensnevringen optræder saa
med engang svære grusmasser i bastionagtige terrasser. De
er især udviklet i flere mere eller mindre adskilte trin paa
dalens vestside. I et grustag paa den vestre side af veien
saaes her etsteds et snit, der viste en udpræget lagning i
grusmassen med svagt mod nord faldende lag. Lagene har
høist forskjellig tykkelse, fra centimetertykkelse til et par
decimeter. Bestanddelene er snart sand, snart ganske fin
og snart blandet med indtil ertestore stene; snart haves lag
med indtil centimeterstore stene, og snart forekommer ogsaa lag
med noget større, afrundede stene, hvor det imidlertid ikke
lykkedes mig at paavise nogen isskuring. Derefter sees en
tilsyneladende horizontal, men ganske kort terrasse ved
Rusten paa elvens østside; den tyve-tredive meter over
elven liggende terrasse danner grundlaget for gaardens dyr-
kede mark og ligger noget lavere end den næste paa Lau-
gens vestside optrædende terrasse, der synes sammenhæn-
gende og derfor i niveau med den kupperede morænemasse
ved Brændhaugen. Herfra finder man saa videre mod nord
dalbunden opfyldt af betydelige morænemasser, tildels ter-
rasseformig udviklet: først en terrasse paa vestsiden, saa en
noget høiere paa østsiden og derpaa igjen paa Laugens vest-
side et endnu noget høiere terrassetrin, der strækker sig
helt frem til Ilken*”). De her beskrevne grusafleiringer er
tildels meget uregelmæssige i overfladen — det er den
kupperede bundmoræne, det denuderede terrasseterræn, og
erustag blotter paa flere steder en utydelig lagning. De

maa holdes skarpt ud fra de høitliggende.

12 Peter Annæus Øyen.

Ved Ilken optræder nu som fremspringende bastioner
ved Jøndalens udmunding i hoveddalen terrasser tilhørende
de paa Dovre og Lesje optrædende strandlinjer. Man kan
imidlertid her adskille flere trin, mindst tre. Paa stræknin-
gen fra Ilken moa nord til Toftebergene er linjerne tildels
utydelige, paa sine steder derimod meget skarpe; hvad der
her kunde iagttages, lader sig sammenstille i følgende ske-

matiserede profil:

Selve strandlinjefladen kan paa sine steder omtrent for-
svinde, paa andre udvide sig til over hundrede meter. Der
er enkeltvis iagttaget et meterhøit opspring paa strandlinje-
fladens yderkant. Paa sine steder har man ved at følge
midtlinjen anledning til at iagttage saavel et høiere som et
lavere trin, hvert med en afvigelse af indtil efter øiemaal
seks meters niveauforskjel fra midtlinjen. Det er mulig, at
en nolagtigere undersøgelse kunde fremfinde endnu flere
trin. Terrassernes materiale er, forsaavidt det kommer til-

syne, sand og grus, dertil større og mindre stene, som

Strandlinjer i Gudbrandsdalen. 13

fordetmeste er afrundede, delvis ogsaa skarpkantede. Nede
i dalbunden ser man ogsaa paa dette strog denne jevnt
fyldt af moræne- og terrassedannelser, disse sidste for en
stor del af recent oprindelse.

Fra Toftemoen følger nu mod nord et ganske lavt ter-
rassetrin paa Laugens vestside, saa paa østsiden et høiere
trin, der længere nord har sin ekvivalent over igjen paa
vestsiden — det er selve hovedlinjen, veien nu stiger op
paa, idet man nærmer sig Domaas.

Fra toppen af den høide, der tæt ved Domaas hæver
sig 35 meter over den meteorologiske station, har man en
god udsigt over terrasserne paa Laugens sydvestlige side.
I en høide af ca. 685 meter over havet befinder man sig
her noget høiere end hovedlinjen, hvilket bidrager sit til, at
fænomenet bedre kan overskues. Er end strandlinjen paa
sine steder afbrudt, saa kan den dog meget let følges, til-
syneladende i samme horizontalniveau. Særlig skarpt frem-
træder den i bastioner ved de i hoveddalen udmundende
sideelve, f. ex. Djupdalsaaen. I detaljerne ser man imid-
lertid, at strandlinjefladen er meget ujevn tildels, og særlig
bør opmærksomheden fæstes ved, at fladen ofte skraaner
betydelig af udover mod den ydre kant. Et par bitrin, et
lavere og et høiere end hovedlinjen, synes ogsaa her tildels
at forekomme, om end ikke skarpt udviklet. Paa den nord-
østlige side fremtræder i strandlinjehøiden den udprægede
gaardrække.

Ved Hinaaen (nordvest for Domaas) fandtes ved dens
nedre løb en tildels temmelig mægtig afleiring af fin, sand-
blandet ler, der viste sig tydelig laget. Paa sine steder
sees antydning til foldning. De forskjellige lag er som
regel meget tynde og udhæver sig meget skarpt ved sin
snart lysere, snart mørkere farve, der idethele er graa med

14 Peter Annæus Øyen.

et skjær i det brune eller blaa. Ganske enkeltvis finder
man indesluttet afrundede stene indtil halvdecimeterstore.
Hyppigere findes marleker, hvoraf en flerhed itusloges, uden
at fossiler kunde opdages. I denne forbindelse kan det
nævnes, at Kjerulf omtaler marleker fra Lesje, men ogsaa
uden fossiler 5).

Fra Domaas til Holaker synes morænegruset vandslidt,
og ved Holaker har man oppe i dalsiden over veien en
tydelig afsats, der i høide svarer omtrent til strandlinje-
niveauet. Dette gjenfinder man saa nord for Lesje kirke
noksaa udpræget i veiens nærhed. Videre mod vest folger
nu tildels større masser af morænegrus, og det er her iøine-
faldende, at medens de høiere op i dalsiden optrædende
grusmasser viser en fuldstændig morænekarakter, saa er
dalbundens fyldning vandslidt og tildels omlagret. Ved
Laugens udløb af Lesjeskogsvandet findes morænegrus i
store masser, tildels terrasseformig udviklet.

I den sydlige dalside optræder paa Lesje den saakaldte
«viflaat», en udpræget afsats i dalsidens relief. Det er dog
ikke blot en linje, men som allerede af Naumann bemærket
to. Helt fra dalsnevringen ved Bottem*), der ligger ved
enden af det nu udtappede Lesjevand, mod vest til Lora-
elven kan man forfølge to tydelige trin; de er rigtignok paa
sine steder afbrudt, men skimtes dog nogenlunde sammen-
hængende. Det er især paa det sidste stykke, fra ret over
for Lesje kirke til Loraelven, at linjerne er meget afbrudt.
Ved Lordalens udmunding i hoveddalen optræder derpaa
bastionagtige terrasser i to tydelige trin. Foruden de to
hovedtrin, som kan følges langs dalsiden, optræder paa sine
steder ogsaa et par bitrin, muligens flere. Fra Loraelvens
terrasser kan videre mod vest enkelte utydelige og uregel-

meessige linjer i flere trin skimtes i dalsidens relief.

Strandlinjer i Gudbrandsdalen. 15

Langs Lesjeskogsvandet ser man ingen strandlinjer;
men derimod antyder endel flade, tildels myrlændte stræk-
ninger, endel lave, uregelmæssige terrassedannelser og vand-
slidt grus i dalbunden langs vandet dettes tidligere, høiere
vandstand.

Ved Raumas udløb af Lesjeskogsvandet optræder i den
flade, fordetmeste overdækkede dalbund paa flere steder fast
fjeld næsten ud til elven paa begge sider. Morænegruset
synes tildels vandslidt og terrænet for en stor del myrlændt.

Naar man fra nordøstsiden af Jettafjeld følger disse
strandlinjer op til Lesjeskogsvandet, faar man et umiddel-
bart indtryk af, at de maa vere horizontale. Til dette
resultat kom ogsaa Chambers: «when examined with a cor-
rect instrument from its own elevation on the opposite side,
it is proved to be for a great way truly horizontal»30).
Fra Domaas og Holaker har jeg selv havt anledning til at
undersøge disse linjers horizontalitet. Den korte tid, som
stod til min raadighed, gjorde rigtignok, at undersøgelsen
ikke blev saa nøiagtig, som den burde; men den nivellerede
theodolit viste dog, at deres afvigelse fra den horizontale
linje i ethvert fald maa være meget liden, om der over-
hovedet er nogen. Den af Reusch3' og Hansen) forte
diskussion om disse linjers heldningsforhold maa betragtes
som frugtesløs, saalænge den kun er knyttet til et veinivelle-
ment, et foreløbigt jernbanenivellement og maalinger med
aneroidbarometer; er saa dertil ikke i tilborlig grad taget
hensyn til linjernes ujevne karakter og til den omstændig-
hed, at der foruden de to hovedtrin ogsaa optræder bitrin,
saa er derved saa mange muligheder anbnet, at enhver for-
sker af maalingerne næsten kan faa udbragt det for en

opstillet theori nødvendige.

16 Peter Annæus Øyen.

At man her har strandlinjer for sig, turde efter det
foregaaende være indlysende nok. Der bliver ikke spørgs-
maal om rækker nedgledne fra fjeldsiderne, og der bliver
ikke sporgsmaal om gjenstaaende rester af en dalfyldning.
Strandmorænetheorien finder i dette tilfælde ingen anven-
delse -— jeg har havt anledning til at se mange strand-
moræner, saavel under dannelsen ved nu existerende bræer
som fuldt udviklede efterladt af tidligere, men ingensteds
saa jeg en strandmoræne med et profil som det fra linjen
mellem Ilken og Toftebergene skematiserede. Forekomsten
af den fine’ sandblandede, i tydelige lag optrædende ler
taler for afsætning i stillestaaende vand.

En nøiagtig nivellering af disse linjer vilde derfor være
meget interessant, da den vilde kunne konstatere visse eien-
dommeligheder i jordskorpens bevægelse paa dette sted.

At man har at gjøre med en lakustrin dannelse og ikke
en marin, tør ligeledes efter det foregaaende ansees godt-
gjort. Vigtigere er imidlertid sporgsmaalet om denne laku-
strine dannelses udstrækning og om aarsagen til en lakustrin
forekomst paa et sted, hvor det opdæmmende materiale er
saa sporløst forsvundet som her.

Efter det foregaaende optræder strandlinjerne først et
stykke nord for Rostensnevringen. Denne selv er glacial,
og der findes ikke spor efter betydeligere løse afleiringer,
som senere kunde være borteroderet af rindende vand —
det eneste mulige som sperring paa dette sted er is. Paa
denne maade vilde man her faa en indsø, der, saalænge den
sperrende bræ rak til, vilde søge sit afløb over vandskillet
mod nordvest, men tømmes forholdvis hurtig, naar for-
andringer i de klimatiske forhold medførte bræens tilbage-
gang. Om denne bræ var af mere lokal art, eller om det

muligens var en udløber mod sydvest af den store brærest,

Strandlinjer i Gudbrandsdalen. 7,

der lengere mod nordost i lengere tid holdt sig ostenfor
vandskillet — alt dette maa en fremtidig detaljundersogelse
afgjore, I en afhandling «Bidrag til Jotunfjeldenes glacial-
geologi» har jeg søgt at vise, at det er omtrent paa dette
sted, man maa søge det sydvestlige fremspring af den oven-
nævnte brærest. Paa bredderne af denne bræsø kunde man
muligens ogsaa blandt andre istidsformer have seet mam-
muthen??) spadsere omkring.

2 — Archiv for Math. og Natmy. B. XVIII. No. 5.
Trykt den 23de September 18%.

18 Peter Annæus Øyen.
Literaturhenvisninger.
1. Top. Jour. for Norge B. 6, H. 23, Pag. 81—82.

10.
ioe

12.

13.
14.
15.
16.
17.
18.

Statistical Account of Scotland Vol. 17, Pag. 549 (cfr. Trans.
of the Roy. Soc. Edinburgh Vol. 9, Pag. 13).

Chambers: Tracings in the North of Europe, Pag. 105 (cfr.
Nature Vol. 33, Pag. 319).

Gilbert: Annalen der Physik u. Chemie B. 11, Pag. 190.
Naturen 1886, Pag. 83. — Arch. for Math. og Natury. B. 14,
Pag. 267.

Naumann: Beytråge zur Kenntnisz Norwegens B. 1, Pag. 203
—205.

Trans. of the Geol. Soc. London Vol. 4, Pag. 314 flg.
Philosophical Trans. Roy. Soc. London 1839, Pag. 68.

The Edinburgh New Philosophical Journal Vol. 48, Pag. 71—72.
— Chambers: Tracings in the North of Europe, Pag. 105
(reprinted from Chambers's Journal 1850. — Cfr: Nature Vol.
33, Pag. 318—319).

Cfr. Nature Vol. 33, Pag. 318—319.

Nature Vol. 22 (1880), Pag. 69. — Hansen: Om seter eller
strandlinjer i store heider over havet (Sep. Arch. for Math. og
Naturv. B. 10), Pag. 10. — Af denne afhandling findes et uddrag
„On „Seter“, ,Strandlinjer*, or Parallel Roads in Central Nor-
way“ af Hansen i Nature Vol. 33, Pag. 268-269. — Arch. for
Math. og Naturv. B. 14, Pag. 264—265.

The Annals and Magazine of Natural History Vol. 6 (London
1841), Pag. 397. ;

Forh. skandinav. naturf. 10. møde, Chra. 1868, Pag. 661.
Kjerulf: Udsigt over det sydl. Norges geologi, Pag. 11.

Ik os Ike 1h, ;

Geol. Förn. Förh. Stockholm B. 5, Pag. 120.

I GE 1120)

Geol. Mag. London Dee. 2, Vol. 4, Pag. 72—75.

19:
20.
21.
22.
23.
24.

25.
26.
27.
28.
29.
3 ).

SÅ:

O2
Øv bt

Strandlinjer i Gudbrandsdalen. 19

Geol. Mag. London Dec. 2, Vol. 4, Pag. 75.

Nature Vol. 33, Pag. 318—319.

Engler: Botanische Jahrbiicher B. 2, Pag. 25.

Sv. Geol. Unders. Ser. C, nr. 70, Pag. 30.

Geol. Förn. Förh. Stockholm B. 14, Pag. 490 og 561 fig.
Hansen: Om seter etc. (Sep. Arch. for Math. og Naturv.),
Pag. 18. å

ic Bag. 18:

Arch. for Math. og Naturv. B. 14, Pag. 264 —265.
Finsterwalder: Die Gletscherausbrüche des Martellthales.
Reid: Studies of Muir Glacier, Alaska.

Øyen: Dæmmevand (Et bidrag til Hardangerjøkelens geologi).
Cfr. Naturen 1886, Pag. 48. — Nyt Mag. for Naturv. B. 31,
Pag. 304.

Cfr. Naturen 1886, Pag. 48. — Nyt Mag. for Naturv. B. 31,
Pag. 304.

Kristiania Vid. Selsk. Forh. 1892, nr. 4, Pag. 37 flg.

Naturen 1886, Pag. 82—85.

Arch. for Math. og Naturv. B. 14, Pag. 267 og 310—312. —
Norske Geogr. Selsk. Aarbog 1890—91, Pag. 40. — Hansen:
Om beliggenheten av breskillet, Pag. 5 flg.

Cfr. Hansen: Om beliggenheten af bræskillet, Pag. 7.
Kristiania Vid. Selsk. Forh. 1892, nr. 4, Pag. 38.

Edinburgh Geol. Soc. 1885. — Nature, London 1886, Vol. 33,
Pag. 293.

Naturen 1886, Pag. 84—85:

Øyen: Bidrag til Jotunfjeldenes glacialgeologi.

The Annals and Magazine of Natural History, London 1841,
Vol. 6, Pag. 346 flg.

1. €., Pag. 346—347 og 350.

Thaarup: Mag. for Danmarks og Norges Beskrivelse (1802—3),
B. 2, Pag. 305—311. — Budstikken 1824, Pag. 825—832.
Minerva (Juli, Aug., Sept.) 1791, Pag. 424—426. — Top. Journ.
for Norge (1795—96) B. 4, H. 14, Pag. 28—30. — Kraft: Top.
St. Beskr. over Kongeriget Norge (1822) B. 2, Pag. 177—169.
— Esmark: Reise fra Christiania til Trondhjem (1829), Pag.
65 —66.

Peter Annæus Øyen: Strandlinjer i Gudbrandsdalen.

45.
46.

48.
49.

Minerva (Juli, Aug., Sept.) 1791, Pag. 424—426. — Kraft: Top.
St. Beskr. over Kongeriget Norge (1822), B. 2, Pag. 249—250.
Geol. Förn. Förh. Stockholm, B. 5, Pag. 125.

Danmarks og Norges Oeconomiske Magazin (1758), B. 2, Pag.
340—342. — Top. Journal for Norge (1795—96), B. 4, H. 14,
Pag. 16.

Det fra gammel tid hævdede navn synes at være Ilken eller
Jøndalselven (cfr. Top. Journal for Norge (1795-96), B. 4, H.
14, Pag. 17, & Kraft: Top. St. Beskr. over Kongeriget Norge,
B. 2, Pag. 69).

Kjerulf: Udsigt over det sydl. Norges geologi, Pag. 10.
„Denne Gaard har uden Tvivl i fordum Dage hedt Bottenheim,
og faaet Navn deraf, at den ligger ved Enden eller ved Botten
af den lange Søe, som er omtrent en Miil lang, strækkende sig
lige herfra til Lessje Kirke.“ (Budstikken (1820—21), B.2, Pag. :
595—596).

The Edinburgh New Philosophical Journal (1850) Vol. 48, Pag. 71.
Naturen 1886, Pag. 84. — Norges geol. undersøgelse, aarbog
1892—93, Pag. 59.

Arch. for Math. og Naturv. B. 14, Pag. 310—312.

Cfr. Kristiania Vid. Selsk. Forh. 1888, Pag. 13—14 — Nature
Wool, By Pa B70.

MÆRKER EFTER ISTIDEN

I DET NORDLIGE AF GUDBRANDSDALEN

MED 1 KARTSKISSE

2 FOTOGRAFIER OG 3 PROFILER

AF

J. REKSTAD

"KRISTIANIA

ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

å tv EUR Ey 2 L

© Kristiania — Centraltrykkeriet 1896

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVIII. Nr. 6.

Mærker efter istiden i det nordlige af
Gudbrandsdalen.

Med 1 kartskisse, 2 fotografier og 3 profiler.
Af
J. Rekstad.

I sommeren 95 foretog jeg med understottelse af Rathkes
legat en reise i det nordlige af Gudbrandsdalen for at fort-
sætte undersøgelsen af mærkerne fra istiden. Da jeg i dette
tidsskrifts 17de bind har givet en fremstilling) af iagttagel-
ser fra min første reise i Gudbrandsdalen i samme øiemed,
vil jeg herved i tilslutning dertil give en beretning om denne.

Først skal jeg søge at paavise, hvorfra materialet i den
fremtrædende morænevold*), som ligger ved pladsen Sandbo-
vangen kort nordenfor Sandbo paa grænsen mellem Kvam
og Sel, er kommen. Dens bygning viser, at den er afsat
af en overflademoræne. Den danner en omtrent 900 m.
lang vold, der er saa noget nær lodret paa dalens længde-
retning og med temmelig brat forside, og den bestaar om-
trent udelukkende af kantede stene af en lys kvartsskifer.
Denne bergart er saa rent dominerende, at det er en sjel-
denhed at se en sten af andet slags.

1) Bræbevægelsen i Gudbrandsdalen mod slutningen af istiden.
2) Beskreven ibid.

1 — Archiv for Math. og Naturv. B. XVIII Nr. 6.
Trykt den 23de September 1896,

4 J: Rekstad.

Lad os, inden vi gaar videre, se lidt paa overflade-
morænernes beskaffenhed. De er, som navnet udsiger, mo-
ræner, der føres af bræerne paa isens overflade. Stenene i
dem er kantede, medens de er afrundede og ofte med sku-
ringsstriber i de moræner, som føres under isen. Overflade-
moræner deles i side- og midtmoræner. De første af disse
dannes hovedsagelig af grus og stene, der fra bratte fjeld-
sider langs bræerne styrter ned paa isen. Her spredes dette
materiale, eftersom bræen glider nedover, og kommer saa-
ledes til at danne en vold eller banke, der dækker en mere
eller mindre bred stribe af bræen langs bredden, en side-
moræne. Naar to bræer flyder sammen, forener de sammen-
stødende sidemoræner sig til en midtmoræne, saa kaldt, fordi
den ligger langs den midtre del af den bræ, som fremstaar
ved foreningen.

Fra Sels kirke og nordover til Laurgaard er der langs
dalens østside saa bratte fjeldsider, at den fra disse ned-
ramlede ur gaar helt ned til kongeveien, og bergarten her
er ganske lig den, vi har i morænen ved Sandbovangen.
Den samme lyse kvartsskifer har vi 1 de bratte bergvægge
langs den nordøstre side af veien over Vaagerusten fra
Ulsvold og op til Rustepladsen. Her ligger en række ende-
moræner, som viser, at ismasserne, da disse moræner afsat-
fes, fyldte Ottadalen i den grad, at en bræ pressedes over
Vaagerusten og ned i Laagendalen. Hvorledes denne bræ
skridt for skridt har trukket sig tilbage, eftersom isens
mægtighed aftog, afgiver disse moræner vidnesbyrd om.

Den første af de nævnte endemorener har vi ved gaar-
den Hougen, hvor passet eller sidedalen munder ud i Laagen-
dalen. Den bestaar hovedsagelig af lerblandet grus og
runde stene. Omtrent 1,5 km. længere op ved Grote ligger

den næste, en mægtig stenvold, opstablet af store kantede

Marker efter istiden i Gudbrandsdalen. 5

blokke. 1 km. hoiere op støder vi paa den følgende lige
foran Selsvandet. Denne bestaar igjen af lerblandet grus
og runde stene. Ved Bolstad ovenfor Selsvandet er der
atter en endemoræn, væsentlig bestaaende af store kantede
blokke, og herfra ligger der langs veien opover til Ruste-
pladsen morænehaug ved morænehaug. Endelig kommer
den sidste endemoræne oppe 1 det høieste af skaret, 613 m.
o. h. Dens form viser utvetydig, at den er afsat af en
bræ, som er kommen fra vest, thi den er smukt krummet
og vender med sin konkave side i den retning.

De bratte fjeldvægge i Sel med sine vældige urer af
kvartsskifer har kunnet skaffe ned paa bræen materiale nok
til den store moræne ved Sandbovangen. Bergarten er der
fuldstændig lig morænens, og isen har bevæget sig i sydøst-
lig retning nedover dalen, saa alt taler for, at morænen
skal stamme derfra. Afstanden mellem morænevolden og
Sels kirke er omtrent 9 km. og til nordenden af Selsvandet
24 km., saa den veilængde, morænen er ført, i det væsent-
lige ligger inden disse grænser.

Morænevolden har, som ovenfor anført, en længde af
omkring 900 m., og dens udstrækning lodret paa bræens
længdeakse er ca. 600 m. Heraf kan vi slutte, at den ikke
er dannet udelukkende af en sidemoræne, thi det er ikke
tænkeligt, at en saadan skulde have havt en slig bredde her i en
forholdsvis trang dal. Omtrent 6 km. ovenfor morænen stødte
nu ogsaa Ottadalens ismasser til, hvilket maatte bevirke, at
bræen fra Laagendalen indsnevredes, og følgelig maatte ogsaa
dens sidemoræne blive smalere. Forovrigt har man et afgjø-
rende bevis for, at en midtmoræne har været medvirkende
til frembringelsen af morænevolden, i det stenstrøede felt!)

1) Nærmere beskrevet ibid.

6 J. Rekstad.

(fot. 1), som strækker sig 600 m. nordover fra morænen og
30 m. indenfor østre strandmoræne.

Dette stendække er utvivlsomt resterne af en midt-
moræne, som blev liggende tilbage, da bræen smeltede bort.

Da morænen er uden afbrydelse, ser vi deraf, at side-
og midtmorænen har bredt sig til et sammenhængende grus-
dække paa bræen, noget som ogsaa finder sted ved flere af
nutidens isbræer!), naar der er rig tilgang paa materiale.

Sidemorænen maa, efter hvad vi har set, stamme fra
fjeldsiderne langs dalens østside mellem Sels kirke og Laur-
gaard, medens midtmorænen antagelig er fremkommen, ved
at isstrømmen over Vaagerusten har forenet sig med hoved-
dalens, og de bratte fjeldvægge langs østsiden af Selsvandet
har da skaffet materiale til den.

Lad os nu se lidt paa, hvorledes det forholdt sig med
bræerne her, da morænen ved Sandbovangen afsattes. Is-
strømmen i Ottadalen var saa megtig, at den sendte en
arm over Vaagerusten ned til hoveddalen. Her forenede
denne sig med Laagendalens bræ, og den derved sammen-
satte isstrøm sluttede sig atter til Ottadalens igjen der,
hvor dalene støder sammen.

Da resterne af midtmorænen ved Sandbovangen ligger
temmelig høit oppe i den østre dalside, kan man deraf
slutte, at isbræen fra Laagendalen har været ubetydelig,
sammenlignet med de ismasser, som kom fra Ottadalen og
over Vaagerusten. Høideforholdene gjør det klart, at broen
over Vaagerusten kun har været en arm fra hovedstrømmen
i Ottadalen, thi det hoieste af veien gjennem passet over
Vaagerusten ligger 613 m. o. h., medens Vaagevandet lig-
ger 351 m., og følgelig maa mægtigheden hos Ottadalens

1) Conf. Heim, Gletscherkunde pag. 347.

Merker efter istiden i Gudbrandsdalen. 7

bræ have været mindst 262 m. større end hos armen over
Vaagerusten.

For at faa et begreb om heldningen hos disse bræer
vil vi anstille en liden beregning. Dalbunden ved Sandbo-
vangen ligger 280 m. o. h. og det høieste af passet ved
Vaagerusten 614 m. Afstanden mellem disse steder maalt
paa amtskortet (horizontalprojektionen) er 26 km. Heraf
følger det gjennemsnitlige fald af bræens underlag paa denne
strækning 44’, Udføres en lignende beregning for Otta- og
Laagendalen, finder vi, at faldet der blir mindre end 10.
Selv om vi antager, at isen over det høieste af Vaagerusten
har havt en 300 m. større mægtighed end nede ved Sandbo-
vangen, saa bliver alligevel ikke det gjennemsnitlige fald af
isens overflade mere end 1° 23'. Dette er nok til at vise,
at bræernes heldning paa denne strækning har under dette
afsnit af istiden været omkring 1°. Tidligere, da isens
mægtighed var større, maatte heldningen have været endda
mindre.

Beliggenheden af den betydelige endemoræne ved Kol-
loen i Kvam!) fortæller os, at den er afsat af en bre fra
Hedalen. Om nu denne bræ har endt ved Kolloen sam-
tidig med, at Ottadalens bræ stansede ved Sandbo i Kvam,
kan ikke med sikkerhed afgjores, men meget taler for, at
saa er tilfældet. Isaafald har Hedalsbræen gaaet omtrent
5 km. længere ned i Gudbrandsdalen end Ottadalens.

Nordover fra Sandbo støder man ikke paa nogen ende-
moræne i hoveddalen, før man kommer til Laurgaard i Sel.
Der har man paa vestsiden af Laagen en liden endemoræne,

hvis beliggenhed viser, at den skyldes en bre nordentra

1) Bræbevægelsen i Gudbrandsdalen mod slutningen af istiden.
Archiv for Math. og Naturv. XVII.

8 J. Rekstad.

Laagendalen. Dette bekræftes end yderligere ved de mange
store blokke, som ligger paa morænen kort nordenfor husene
paa Laurgaard, af den konglomeratartede kvartsit, der staar
kort ovenfor paa begge sider af Laagen.

Paa østsiden lidt søndenfor broen over Laagen ligger
der tæt ved veien to betydelige morænehauge, der bestaar
af store kantede blokke med en del grus indimellem.

Den første endemoræne i Ottadalen begynder ved Dale
og strækker sig herfra opover mod Aasoren i lengden om-
kring 4,5 km. Partiet ned mod Dale paa østsiden af elven
er ovenpaa temmelig fladt og bedækket med vældige kantede
blokke. Ned mod Otta staar der en steil grusvæg ca. 30 m.
hoi. Paa vestsiden stiger morænen terasssevis temmelig
høit; nede ved elven bestaar den i overfladen af grus med
lidt ler og enkelte runde blokke, men eftersom man stiger,
bliver blokke mere og mere overveiende. Af bergarter
saaes i denne moræne gl. skifer, kvartsit gneis og gabbro.

Da der nu mellem morænen ved Sandbovangen og disse
endemoræner ikke findes noget trin som mærke efter bræer-
nes stilstand, maa vi antage, at bræen i Laagendalen har
trukket sig tilbage til Laurgaard og Hougen, omtrent 22
km., samtidig med, at bræen i Ottadalen kun har gaaet 8
km. tilbage til morænen ved Dalen.

Den følgende moræne i Ottadalen begynder lidt norden-
for Veggeim og strækker sig nordover til Eierfos. Der er
omtrent 3,5 km. mellem denne og det øverste parti af den
forangaaende moræne. Dens nedre del paa østsiden af elven
er besaaet med kantede blokke, ofte store som huse. Læn-
gere op gaar den over til vestsiden og ved Eide atter over
til østsiden igjen; elven slynger sig altsaa frem igjennem
morænen snart paa den ene og snart paa den anden side.

Mellem Eide og Eierfos viser morænegruset flere steder

Mærker efter istiden i Gudbrandsdalen. 9

lagning, hvilket rimeligvis hidrører fra, at elven har flydt
ud over større partier af morænen, førend den fik skaaret
sit nuværende leie.

Nedover lien, hvor veien til Hedalen gaar op fra
Lalumsbro, ligger der en mængde grus og blokke, og oppe
i skaret støder man paa betydelige moræner paa begge sider
af veien. En bræ har altsaa skudt sig frem igjennem dette
skar og ned i Ottadalen. Ismasserne maa da have fyldt
Hedalen, saa den ikke kunde skaffe afløb nok; en del af
overfloden er bleven presset over her til Ottadalen. Da
isdækkets mægtighed blev mindre, trak denne bræ sig til-
bage og stansede en tid fremme i skaret, hvor den har
afsat en ret betydelig endemoræne.

Blokkene her bestaar hovedsagelig af gabbro, gl. skifer
og kvartsit.

Langs den nordøstre side af Ottadalen staar en bergryg
frem, som begynder ved Øye lidt nordenfor det sted, hvor
veien over Rusten tager op, og strækker sig op imod Sørum.
Ved den sydøstlige ende af denne bergryg ligger der en
betydelig moræne, der hovedsagelig bestaar af kantede og
runde blokke. Morænen viser os, at den sydøstre ende af
ryggen danner læsiden, og at altsaa bevægelsen har gaaet i
sydøstlig retning. |

Omtrent mellem Skedsvold og Svare i Vaage ligger
der langs den øvre side af den vei, som fører forbi Haaken-
stad op til sæteren og videre over fjeldet til Lesja, en række
morænerygge, paa det nærmeste parallele med Finnas leie;
en af de smukkest udviklede har retningen S 76° O retv.
Hovedmassen i dem er grus og runde stene, men hist og
her ligger der store kantede blokke. De bergarter, der saaes
i blokkene, var gneis, kvartsit, gl. skifer og gabbro. Af
kvartsitblokkene kan man se, at isens bevægelse her har

10 J. Rekstad.

gaaet i nordlig retning, thi denne bergart staar kort søn-
denfor moræneryggene, medens den ikke forekommer læn-
gere nord.

Vender vi os til hoveddalen igjen, saa støder vi her
paa en tydelig sidemoræne i den østre dalside lidt norden-
for Laurgaard, ca. 450 m. o. h. Længere nord, omtrent ved
grænsen mellem Sel og Dovre, begynder der langs dalens
vestre side en terrasseformig moræne, som strækker sig op
til Brændhaugen. Ned mod Laagen er den i stor udstræk-
ning dækket af laget grus, men høiere op gaar den over til
typisk moræne, bestaaende af ler, blandet med grus og store
blokke. Paa sydsiden af Ilka, omtrent fra Storeng til
Stampeli, ligger der igjen en terrasseformig moræne, fuld-
stændig lig den sondenfor Brændhaugen.

Høiere oppe ved Ilka træffer man de første af de smukt
udviklede terrasser, som er saa fremtrædende opigjennem
Dovre og Lesja. Ovenfor disse i det nederste af Jetdalen
er der betydelige moræner, hvilket viser, at en bræ er kom-
men frem her fra vest til Laagendalen.

Igjennem en stor del af Lesja er den nordøstre dalside
dækket af tildels mægtig moræne. En mængde blokke, ikke
sjelden store som huse, ligger udover jorderne, og det uagtet
mange maa være blevne sprængte istykker og skaffede bort
af beboerne i tidens løb. Særligt fremtrædende er dette
morænedække ved Nørstebø, fra Holaker til Hattrem og op
for Loftingsmo.

I den nedre del af Lordalen er der betydelige ende-
moræner og foran disse mægtige grusterrasser. En stor
isbræ maa altsaa være kommen efter denne sidedal, som fra
Lesja gaar i sydvestlig retning omtrent 30 km. ind til den

1926 m. høie Skarvdalsegg.

Mærker efter istiden i Gudbrandsdalen. 1

Det betydeligste morænefelt heroppe har vi ved vand-
skillet. Det begynder ikke langt fra skydsstationen Holsæt
og strækker sig efter dalføret til gaarden Bryggen ved
Lesjeskogens vand, saa den samlede længde bliver omtrent
16 km. Paa denne strækning ligger der morænehaug ved
morænehaug, og vi maa følgelig slutte, at iskanten har holdt
sig lenge her. Mest typisk er morænepartiet ved Lesje-
værk udviklet. Her bestaar morænehaugene af grus og
runde stene, sjelden større end et mandsløft, og flere af
disse hauge rager omkring 20 m. op over de omliggende
dele af morænen. Lesjeskogens vand er opfyldt af holmer,
og disse er alle uden undtagelse, saavidt jeg kunde se,
morænehauge. Paa flere steder i dette morænelandskab er
der flade furumoer, hvor gruset ofte viser lagning og med
- enkelte større blokke inde i den lagede masse. Flerheden

af dem ligger omkring 630 m. o. h.

Flytblokke.

De fremmede blokke, som findes spredte om, giver i
forbindelse med skuringsstriberne den sikreste veiledning til
bestemmelse af ismassernes bevægelsesretning. Nedenfor vil
jeg anføre en del iagttagelser af fremmede blokke fra denne
trakt.

Opefter Laagendalen fra Brændhaugen til Dombaas lig-
ger der blokke af Rustens konglomeratartede kvartsit, alt-
saa et utvetydigt vidnesbyrd om, at bevægelsen her har
gaaet opefter dalen.

Blokke af lys granit er heller ikke sjeldne i denne del
af dalen. Om de stammer fra granitgangene i Jettafjeld ?)
eller fra Dovres granit, er ikke let at afgjøre med sikkerhed.

1) Confr. Kjeruf, Det sydlige Norges geologi pag. 25.

12 J. Rekstad.

Isens bevægelsesretning taler til gunst for den første an-
tagelse. Imidlertid kan det nok tænkes, at blokke er bleven
førte sydover af drivis i den store sjø, som har været
opdæmmet i Dovre og Lesja under sidste afsnit af istiden.
Til støtte for den antagelse, at granitblokkene skulde være
komne nordenfra, kan ogsaa anføres, at de optræder adskil-
lig talrigere ved Dombaas end længere syd i dalen. Her
er bergarten gl. skifer, men graniten staar kort nordenfor.

Blokke af blaagraa stribet kvartsit saaes flere steder i
Laagendalen nordenfor denne bergarts nordgrænse i fast
fjeld, saasom 1 Dovre mellem Brændhaugen og Talleraas
bro samt ved Trondhjemsveien ovenfor Dombaas og i Lesja
ved Loftingsmo, Holset og Rise. Dette antyder en bevægelse
i nordvestlig retning.

I Lesja optræder granitblokke af lysegraa farve, som
Dovregraniten, vestover til Hattrem og ved Loftingsmo,
Holsæt og Rise blokke af gl. skifer, hvilket igjen viser en
bevægelse mod nordvest.

Gabbroblokke tildels stribede findes i betydelig mængde
nedefter Ottadalen fra Vaagevandet, og fra Vaagerusten
nedover til morænerne foran Selsvandet har man ligeledes
blokke af denne bergart, undertiden af flere kubikmeters
størrelse. I det nordlige af Laagendalen er de derimod
ikke hyppige. Der forekommer gabbroblokke ved Brænd-
haugen og Dombaas i Dovre og ved Nørstebø, Holaker,
Holsæt, Rise og Dosæt i Lesja, men paa alle disse steder
kun i ringe antal.

Nedefter Ottadalen ligger der talrige gneisblokke, som
maa stamme fra det store gneisfelt ved Vaagevandet; af
mere usikker herkomst er de blokke af gneis og oiegneis,

som optræder ved Dombaas.

Marker efter istiden i Gudbrandsdalen. 13

Nedigjennem Hedalen er gabbroblokke meget hyppige.
Ved Holen, Bjølstad og Heringstad forekommer ogsaa
blokke af stribet granit, gneis, fyllitskifer, krystallinsk kalk-
sten og dolomit. Bloktransporten her maa altsaa have gaaet
i østlig og sydøstlig retning.

Blokke af dolomit iagttoges ogsaa i morænen ved Kol-
loen og ved Ulsvold, ca. 2 km. vest for Laurgaard. Kalk-
sten og dolomit optræder imidlertid paa flere steder i gl.
skiferafdelingen her og da ogsaa i forbindelse med vegsten,
saa disse bergarter er lidet skikkede som ledblokke. :

Skuringsstriber.
Retningen er regnet fra den astronomiske meridian,
idet kompassets misvisning er sat til 12° vestlig.
Dovre prestegjeld:
55 Ved hovedveien ca. 1 km. syd for Dombaas N1° O1)
56 Ved det vestlige af berghammeren ved Dombaas WN 21° W
57 Omtrent 100 m. længere øst paa hammeren . N 15° W
58 Ved Trondhjemsveien 21/>km. ovenforDombaas N21°O
59 = I ee eNO)
Lesje prestegjeld:
60 Ved hovedveien 1/2 km. NW for Lesjeværk . N 72° W
61 - — QT Ne
| Vaage prestegjeld:
62 Ved Lykken lidt ovenfor Aasoren . . . . 87909
63 Omtrent 1 km. W for Lykken ved veien. . 810270
64 2 km. NW for Suerle skydsstation ved veien S44 0
65 Nord for vestenden af Flatningen, 800 m.o.h.. N3°O
66 Ved det nordlige af Bringsfjeld*), 850 m.o.h. NSO

1) Stærk skuring paa skraa bergflader ved den østre side af veien.
2) Her er smukke stødsider mod NW.
3) Bringsfjeld er paa Amtskortet benævnt Ringsfjeld.

2 — Archiv for Math. og Naturv. B. XVIII No. 6.
Trykt den 8de Oktober 1896.

14 J. Rekstad.

Skuringsstribernes retning er for lettere oversigts skyld
indtegnet paa vedfoiede kartskisse.

Af skuringsstriberne, flytblokkene og morænerne kan vi
se, at isen har bevæget sig ud fra landets hoieste fjeldparti,
følgende terrænets indsænkninger. Naar ismasserne har
været for betydelige til at kunne faa afløb nok igjennem
dalene, er en del bleven presset over høidedragene. Her-
oppe har bevægelsen bedre kunnet følge den retning, hvori
trykket virkede, medens nede i dalene terrænets ujevnheder
har havt en stærk indflydelse paa bevægelsesretningen.

Skillet mellem bevægelsen opefter og nedefter Gud-
brandsdalen maa have ligget omtrent ved grænsen mellem
Sel og Dovre, thi som ovenfor anført findes blokke af
Rustens konglomerat førte nordover til Dombaas og sydover

til Laurgaard.

Terrasser.

Naar man kommer opefter Gudbrandsdalen, begynder
der fra Talleraas bro over Laagen en række terrasserester
opigjennem Dovre, særlig langs dalens østside; paa disse
ligger flere af gaardene. De bestaar af ler, mere eller
mindre opblandet med fin sand, og viser særdeles tydelig
lagning, saa det er klart, de maa være udfældte i en sjø.
Smukkest udviklede er de opefter Dovrebygden til opimod
Dombaas, men man har ogsaa lag af det samme slags sand-
blandede ler vestover i Lesja til lidt bortenfor Holsæt. I
høiden gaar det lagede ler paa sine steder op til 550 m.
0. h. Jeg søgte paa flere steder i berglagene efter dyre-
eller planterester, men uden noget resultat.

Omtrent paa samme strækning ligger der temmelig høit
oppe i den vestre dalside en række terrasser, som sees

særdeles godt fra landeveien, som her gaar paa østsiden.

Merker efter istiden i Gudbrandsdalen. 15

De begynder op for Storeng i Dovre og kan følges med
større eller mindre afbrydelser til Lora i Lesja, det vil sige
paa en strækning af omtrent 40 km.

Høiden over havet af disse terrasser maaltes med
aneroid, hvis skala kort iforveien var bleven korrigeret ved
det meteorologiske institut. For yderligere korrektion af
dets variation sammenholdtes det flere gange med stations-
barometret paa Dombaas.

Ved interpolation mellem de daglige observationer paa
Dombaas fandtes barometerstand og temperatur der paa de
tider, lufttryk og temperatur maaltes paa terrasserne med
aneroid og slyngetermometer. Heraf beregnedes saa høide-
forskjellen mellem terrasserne og Dombaas!). Da observa-
tionerne udførtes under rolige veirforholde og ingen i større
afstand end 25 km. fra Dombaas, saa undlod jeg at tage
hensyn til lufttrykkets variation paa de forholdsvis korte
distancer mellem Dombaas og observationsstederne.

Vi skal nu se lidt nærmere paa de enkelte terrasse-
stykker. De første har vi, som før nævnt, op for Storeng
paa sydsiden af Ilka’). Det øverste trin her (684 m. o. h.)
danner en næsten horizontal og temmelig bred flade, bestaa-
ende af grovt grus med enkelte større runde stene. Vesten-
for i Jetdalen og noget høiere har man moræner, og herfra
har antagelig elven taget materialet til disse terrasser. Det
sydvestlige af den øverste terrasse (tilv. paa fot. 2) danner
et lavere trin (675 m. o. h.) med ryggen smukt indskaaret

det høiereliggende parti af terrassen. Gruset er her ikke

saa grovt og de store stene meget sjeldnere.

Høiden over havet af Dombaas station fikjeg opgivet til 648,9 m.
2) Se fot. 2.

16 J. Rekstad.

Endelig ligger der længere nede en grusmasse, der har
horizontal overflade og paa 3 kanter regelmæssig skraanende
sider. Dens fjerde side støtter sig til dalsiden, saa den
faar formen af en afskaaren pyramide med rundede hjørner. .
Dens top ligger 618 m. o. h.

Fra den østre dalside kan man se, hvorledes den øverste
_ terrasse ved Storeng strækker sig nordover til midt for
Toftemoen, kun afbrudt der, hvor Ilka har skaaret sig igjen-
nem den. Den samlede længde af denne terrasse bliver da
omkring 6,5 km. Overfor Dovre kirke kan man tydelig se
to parallele terrasser, som ved maaling fandtes at ligge
672 m. og 652 m. o. h. Altsaa ligger det øverste trin her
12 m. lavere end ved Storeng, hvis man kan stole paa disse
maalinger, der udførtes med to dages mellemrum. Heldigst
vilde det være, om det kunde lade sig gjøre at faa udført
et nivellement langs denne terrasserække igjennem Dovre
og Lesja.

Det lavere trin har her form af en flad afsats, der
bestaar af grovt grus med runde stene. Flere steder gaar
det over til en bredere eller smalere grusryg med en for-
dybning mellem dalsiden og grusbanken. Det øvre trin ser
ud som en typisk sidemoræne med en mængde store blokke
i gruset.

Herfra seet viser der sig en horizontal linie i den østre
dalside fra Angaard og nordover til Einbugaa. Op for
Haugen fandtes dens høide 636 m., og her danner den en
stærkt skraanende flade, bestaaende af morænegrus. Lige
ved paa nordsiden har Dragaa skaaret sig ned igjennem
mægtige masser af moræneler.

Ligeoverfor Nørstebø i Lesja er der atter to tydelige
terrasser i 700 og 665 m. o. h. Den øverste er en typisk

sidemoræne, og ovenfor staar fast berg frem i dagen. Den

Mærker efter istiden i Gudbrandsdalen. 7

nedre danner her en bred flade, hvis indre parti er dækket
af en mængde store blokke, medens dens forreste del hoved-
sagelig bestaar af grus.

Disse to terrasser ender i vest mod en berghammer,
paa hvis anden side der igjen begynder en terrasse omtrent
ligeoverfor Holaker. Den strækker sig vestover gjennem
Bølien et godt stykke. Jeg gik 2,5 km. langs denne terrasse
fra dens østre ende, idet jeg hyppig aflæste barometret.
Det steg paa denne strækning i løbet af 1 time og 10 min.
0,6 mm. Paa samme tid steg stationsbarometret paa Dombaas
i 6 timer 2,6 mm., hvilket giver i 1 time og 10 min. 0,5 mm.
Heraf kan vi se, at terrassen paa disse 2,5 mm. er saavidt
horizontal, saa der ikke med aneroid kunde paavises nogen
heldning. Dens høide over havet er 674 m. Dens østlige
del ser ud som en sidemoræne med flere store blokke;
blandt disse kan nævnes en vældig kantet granitblok og en
af gneis. Fig. 3 A viser et skematiseret tversnit af dette
parti af terrassen. Længere mod vest bliver den bredere,
dens forreste kant, der væsentlig bestaar af grovt grus,
rager lidt op, og indenfor denne er der en myrstrimmel.
Fig. 3 B giver et skematiseret tversnit af. denne del. Det
vestligste af den strækning, jeg tilbagelagde, har form af en
grusryg, der enkelte steder breder sig ud og forgrener sig
til to eller flere rygge. Fig. 3 C giver et skematiseret
> tversnit af dette parti. +

Ved det nederste af Lora har man megtige terrasse-
formige afleiringer af sand, der af elven er fort nedover fra
de betydelige moræner, som ligger høiere oppe i Lordalen.
Her er to udprægede terrassetrin, et ved 632 m. o. h. og
det andet ved 658 m., men laget sand forekommer op til
700 m, o. h. Bortover Lesjeskogen fra Rise til Lesjeværk

18 J. Rekstad.

og langs Lesjeskogens vand er der flere steder grusflader
med lagning i en hoide af omkring 630 m. o. h,

For lettere oversigt er der udarbeidet en grafisk frem-
stilling af terrasserne (fig. 4), idet afstanden mellem de
maalte terrasser er afsatte som abscisser og høiderne som
ordinater. Disse sidste er tegnede i 100 gange større maale-
stok end de første, thi ellers vilde de optrukne linier kun
umærkeligt have afveget fra horizontalen. Vi ser, at de
maalte terrassehøider lader sig indordne i 3 trin; vistnok
er ikke de optrukne linier horizontale, de viser tvertimod
for de to øvres vedkommende et noget uregelmæssigt for-
løb, men dette kan vel for en del skrive sig fra feil ved
maalingerne, som maaske i ugunstigste tilfælde naar op til 10 m.

De maalte terrassehøider.

Øverste trin. Mellemste trin. Nederste trin.

m. m. m.

Ved Jekla 270 070.684 675 618
Mod Dovre kirke . 672 652 —
- Nørstebø . . 700 665 =

= Holaker 900 — 674 —
MeduLora EPO 658 632
Tbesjeskogen =i. — — 630

Den største afvigelse mellem de maalte høider er i
øverste trin 28 m., i det andet 23 m. og i det nederste trin
14 m. Ved den øverste terrasserække kan man ikke vente
fuldstændig horizontalitet, thi dens moræneartede natur tyder
paa, at den er dannet ved isens virksomhed. Hvorledes
forholdet er ved de to nedre trin, kan kun et nivellement
med fuld sikkerhed afgjøre. Naar dr. Andr. Hansen i sit
interessante arbeide?) kommer til det resultat, at terrasserne

1) Strandliniestudier, Archiv for Math. og Naturv. XIV og XV.

Mærker efter istiden i Gudbrandsdalen. 19

sænker sig opefter dalen, saa fremkommer det for denne
trakts vedkommende, ved at øverste trin syd i dalen sættes
i forbindelse med trin, der tilhører et lavere niveau, læn-
gere nord, f. eks. øverste terrasse ved Storeng med den
lavere ved Lora.

Det megtige og udstrakte morænefelt ved Lesjeskogens
vand viser, at iskanten har holdt sig meget længe her.
Bevægelsen hos de ismasser, som da fyldte det nordlige af
Gudbrandsdalen, maatte være forholdsvis ringe, fordi dette
isbassin intet afløb havde, og dets vigtigste tilløb var i
nærheden af enderne, nemlig bræerne gjennem Jetdalen og
Lordalen, Eftersom afsmeltningen skred frem, samlede der
sig mere og mere vand under isen her, thi det sydlige af
Gudbrandsdalen fyldtes endnu stadig af ismasserne fra
Jotunfjeldene. Dette bevirkede, at friktionen mod under-
laget blev mindre. Under saadanne forholde maatte isens
overflade i bassinet nærme sig mere og mere til at blive
horizontal.

Den øverste moræneartede terrasserække maa antages
frembragt ved isens bevægelse langs dalsiderne. Tll støtte
for en saadan antagelse gjælder det at føre bevis for, at
isen 1 et længere tidsrum har holdt sig i nogenlunde samme
høide og havt paa det nærmeste horizontal overflade. De
betydelige moræner ved Lesjeskogens vand afgiver et klart
vidnesbyrd om, at isens megtighed lenge har holdt sig
uforanderlig, og vi har netop seet, der kan anføres flere
grunde for, at isens overflade her har været meget nær
horizontal.

Allerede før den øvre terrasserække dannedes, havde
bræen i Jetdalen trukket sig bagover til morænerne inde i
dalen, og inden det andet trin afsattes, var ogsaa bræen i
Lordalen gaaet tilbage til de før nevnte moræner bag ter-

20 J. Rekstad.

rasserne her. I Jetdalen ligger ogsaa øverste terrasse foran
morænerne, medens det øverste trin mangler i Lordalen,
de tvende lavere findes der nedenfor morænerne. Som
ækvivalent til øverste trin optræder her sandlag i den nord-
vestlige dalside.

Den anden terrasserække har over store strækninger
form af en bred grusflade, hvilket tyder paa, at den maa
være en stranddannelse. Imidlertid viser dens moræne-
artede natur ved Holaker og flere steder, at ogsaa isen har
været med i spillet. Ved tiden for dens dannelse maatte
da afsmeltningen være saavidt fremskreden, at en stor sjø
var fremstaaet her. Dennes overflade havde endnu et
isdække, der trykkedes saa stærkt opover mod den nord-
vestlige ende af ismasserne syd i dalen, at den dæmmedes
op 35 m. over vandskillet, der, som vi straks skal se, laa
omtrent 14 m. høiere end nu. Middelhøiden af anden ter-
rasserække er 665 m., medens nederste trin, der maa an-
tages at svare til høiden af vandskillet ved slutningen af
istiden, ligger 630 m. 0. h. Lesjeskogens vand, det nu-
værende vandskil, ligger 616 m. o. h. eller 14 m. lavere
end nederste trin, og saa meget maa da elvene have skaaret
sig ned her siden istiden. Naar man ser grusvæggene paa
begge sider af Laagen der, hvor den flyder ud af Lesje-
skogens vand, finder man ikke noget urimeligt heri. Da
isen smeltede bort i.det sydlige af dalen, tomtes ikke denne
sjø fuldstændig; der blev et betydeligt parti af den staaende
igjen, særlig i Dovre, og dette tømtes først lidt efter lidt,
eftersom Laagen mellem Laurgaard og Brændhaugen fik
skaaret sin 5 km. lange bergrende gjennem Rusten dybere
og dybere ned. |

Som vi har seet, ligger de fleste af terrasserne i de to

øverste trin langs dalens sydvestre side. Dette kan ikke

Mærker efter istiden i Gudbrandsdalen. 21

være tilfældigt, men maa henge sammen med de forholde,
hvorunder disse terrasser er fremstaaede. Da de dannedes,
dækkede endnu ismasser det meste af landet paa vestsiden
af Gudbrandsdalen, medens landet paa dens modsatte side
var omtrent isfrit, følgelig maatte den større mængde vand
og is fra vest skaffe mere materiale tilveie til dannelse af
moræner og terrasser og saaledes fortrinsvis begunstige
deres fremstaaen paa den side af dalen.

I Hedalen er der en særdeles fremtrædende terrasse
langs dalens østside. Den begynder lidt søndenfor Ekre og
strækker sig opover til Bjølstad i længden omkring 6,5 km.
Jeg gik langs den i hele dens udstrækning, idet jeg ofte
aflæste barometret. Det viste sig herved, at den stiger for-
holdsvis jevnt hele veien, saa den ved Bjølstad er 56 m.
høiere end ved den sydlige ende. Fig. 5 viser heldningen
50 gange forstørret. Afstandene er afsatte som abscisser og
de fundne høider som ordinater. Bjølstads høide over havet
fandtes med aneroid at være 496 m, og herpaa er da den
absolute høideangivelse paa fig. 5 baseret, hvorfor den vel
ikke kan gjøre krav paa nogen stor nøiagtighed. Terrassens
heldning eller høideforskjellen mellem de enkelte punkter
langs den bestemtes derimod, ved at jeg i løbet af to timer
langs efter den aflæste aneroiden, hvorfor feilene i de rela-
tive høider eller i heldningen ikke kan blive af nogen
nævneværdig betydning.

Den sydlige del af terrassen opover til Steinflnsbø be-
staar hovedsagelig af grus og ler, og her har i tidens løb
rindende vand skaaret den op i en række kegleformede
hauge. Fra Ellingsbø nordover til Bjølstad er den mere
sammenhængende, kun gjennemskaaren der, hvor bække
kommer ned. Paa denne strækning optræder der ikke faa
store blokke, undertiden paa flere kubikmeter. Ofte ligger

22 J. Rekstad: Mærker efter istiden i Gudbrandsdalen.

de paa den forreste kant af terrassefladen og nedover den
bratte forside. De fleste gaarde i denne del af Hedalen
ligger langs terrassen, hvis overflade skraaner mere eller
mindre stærkt ud mod dalbunden. Dens stærke heldning
sydefter dalen og de store blokke paa partiet mellem
Ellingsbø og Bjølstad taler tydeligt nok for, at det er en
sidemoræne, vi her har i terrassedragt. Der er imidlertid
flere mærker efter en sjø, der har dækket dalbunden her
ved istidens afslutning. Denne tømtes, efterhvert som Sjoa
skar sin rende ned igjennem bergsnevringen ved Skjerv-
dalen. Hvor hoit den kan have naaet, er ikke godt at sige,
men den synes at have staaet over terrassen.

Oppe i Hedalens skogbygd ligger der grusterrasser
paa begge sider af Sjoa i en hoide af 648 m.o.h. Mellem
disse er der en omtrens 80 m. dyb spalteformet rende, paa
hvis bund Sjoa flyder. Alt taler for, at dalen ved slut-
ningen af istiden her har været fyldt i høide med terras-
serne af bergras. Siden den tid har Sjoa først skaaret sig
ned igjennem et omtrent 60 m. mægtigt lag af morænegrus
og derpaa udhulet sig en omtrent 20 m. dyb rende i det
underliggende berg. En saa betydelig erosion tyder paa, at
istiden ikke kan ligge os saa ganske nær.

Nedenfor er dalbunden helt ned til kirken dækket af
grovt brægrus og større runde stene, som Sjoa har ført

nedover ved udgravningen af sit leie oppe i skogbygden.

ON A NEW

FRESH-WATER OSTRACOD

STENOCYPRIS CHEVREUXI

G. O. SARS

WITH NOTES ON SOME OTHER
ENTOMOSTRACA RAISED FROM DRIED MUD
FROM ALGERIA

BY

G. 0. SARS

WITH 2 AUTOGRAPHIC PLATES

ARCHIV F. MATHEM. OG NATURVIDENSKAB

"KRISTIANIA

ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

Kristiania — Centraltrykkeriet 1896.

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVIII. Nr. 7.

On a new Fresh-water Ostracod, Steno-
eypris Chevreuxi. G. 0. Sars, with
Notes on some other Entomostraca raised from
Dried Mud from Algeria.
With 2 autographic plates.
By G. 0, Sars.

Introduction.

On the 1st August last year, I received, through the
kindness of the well-known French naturalist M. E. Chevreux,
2 tubes with dried mud taken by him from 2 different
localities in the neighbourhood of Bona, Algeria. The one
sample was taken on the 6th July of the same year from the
swamp of »Bon Kamerac, the other on the 8th July, from
that of »Kharezas«. Each sample was moreover accompanied
by some spirit specimens taken from the same localities.
Immediately after the receipt of the samples, I arranged
a number of aquaria, each to receive small quantities of the
mud, and I have been continuing my experiments not only
during the remainder of the summer and autumn, but
also during the whole winter until the present time, the
aquaria having been placed in a room continually heated.

1 — Archiv for Math. og Naturv. B XVIII. Nr. 7.
Trykt den 8de Oktober 1896,

4 G. O. Sars.

By these means, I have been enabled to raise from the mud,
and domesticate, a number of Entomostraca belonging to all
of the 3 leading groups, Cladocera, Ostracoda and Copepoda.
As might be expected, the greater number of the species have
turned out to be identical with well-known European forms.
But, as the localities do not in fact belong to the European
continent, I think it may be of some interest to note the
species briefly, and I shall do so at the close of this paper.
Among the species raised was a rather beautiful Ostracod,
which I cannot identify with any of the earlier known
species, and which I therefore regard as new to science.
The description of this form will be the chief object of
the present paper, and I have much pleasure in dedicating
the species to the distinguished French zoologist, to whom

I am indebted for the mud from which it was raised.

Fam. Cyprididee.
Gen. Stenocypris, G. O. Sars, 1889.

This genus was established by the present author in his
paper »On some Australian fresh-water Ostracoda raised from
dried mud<, and the species S. Malcolmsonit (Baird) was
there described as the type of the genus. At the same
time, attention was drawn to the fact, that the well-
known European form, Cypris fasciata, Müll., ought to be
referred to the same genus, With equal certainty another
European species, Cypris Fischeri, Lilljeborg, may also
be adduced to this genus, and as a 4th species, the Algerian

form described below is now added.

On Stenocypris Chevreuxi. 5

Stenocypris Chevreuxi, G. O. Sars.
(Pl. 1 & 2).

Specific Characters.—¥ Shell, seen laterally, oblong
reniform, height about equalling 2/5 of the length, anterior
extremity somewhat obliquely rounded, posterior obtusely
produced, dorsal margin perfectly straight in the middle,
and subangular above the eye, ventral slightly sinuated in
front of the middle:—seen from above, oblong fusiform,
greatest width about equalling 1/3 of the length and occurring
behind the middle, both extremities obtusely pointed. Valves
very unequal, the left one being much the larger, and over-
lapping the right considerably both in front and behind;
inner duplicatures of moderate size, and somewhat different
in the 2 valves. Surface of shell smooth and polished,
clothed at both extremities with hairs, those of the hind
extremity remarkably elongated and less densely crowded
than on the anterior, Natatory sete of the inferior antennæ
extending to the tips of the terminal claws. Caudal rami
rather strong, though narrower than in the type species, and
perfectly equal, outer half of the dorsal edge divided into
4—5 slight lobes, each armed with a comb-like series of
teeth; terminal claw about twice as long as the other, both
coarsely denticulated on their concave edge, apical seta
rather elongated, that of the dorsal edge very small and
occurring close to the proximal claw. Colour light greenish,
clouded with darker shadows. Length of adult female
2.40 mm,

Remarks.—In its general appearance, this form shows
some resemblance to the well-known European species,
Herpetocypris reptans (Baird), exhibiting a similar elongated
reniform shape of the shell. It cannot, however, even be
referred to the same genus, as the natatory sete of the

6 G. O. Sars.

inferior antennæ are fairly well developed, allowing the
animal to move rather quickly through the water. In this,
as also in other respects, it agrees with the species of the
genus Stenocypris, though exhibiting well-marked specific

differences from any of them.

Description of the female.

In fully adult specimens the shell has a length of
2.40 mm., a height of 1.90 mm., and a width of 0.80 mm.
This form accordingly grows to a larger size than any of
the other 4 as yet known species of the genus.

Seen from the side (Pl. 1, fig. 1), the shell exhibits a
rather elongated, subreniform shape, the greatest height but
little exceeding 25 of the length. The dorsal margin is
perfectly straight and horizontal, joining the anterior margin
by an abrupt, nearly angular bend just above the eye.
Posteriorly it passes by a more even curve into the hind
margin. The inferior margin exhibits, somewhat in front of
the middle, a rather slight sinus, and joins the anterior and
posterior margins without any intervening angle. The
anterior extremity is broadly rounded, and somewhat obliquely
deflexed, whereas the posterior one appears more produced,
and narrowly rounded at the tip.

Seen from above (fig. 2), the shell appears moderately
compressed, exhibiting an oblong subfusiform shape, with
the greatest width about equalling 1/3 of the length and
occurring behind the middle. The side-contours are but
slightly curved, and both extremities appear obtusely pointed,
the anterior one being a little narrower than the posterior.

The surface of the shell is quite smooth and polished,
with only the usual small distant pits, and is densely clothed

with hairs on both extremities, those of the anterior one

On Stenocypris Chevreuxi. i

being very delicate and densely crowded, whereas those of
the posterior extremity appear much coarser and more
distant, some being of very considerable length. In the
centre of each valve, somewhat in front of the middle, the
insertion for the adductor muscle of the shell is easily observ-
able as a number of well-defined clear spots, the 2 anterior
of which lie somewhat apart from the other 4 (see figs. 1, 4).

The valves are very unequal in size, the left one (see
fig. 3) being much larger than the right (fig. 4), and over-
lapping it considerably both in front and behind, as also
along the ventral face (see fig. 1). The form of the two
valves also appear, when isolated (comp. figs. 3 and 4),
rather dissimilar, the left one (fig. 3) having the anterior
extremity rather more deflexed, and the posterior one some-
what broader than the right valve (fig. 4). The inner
duplicatures are rather large, especially that of the anterior
extremity. On the left valve (fig. 3) this anterior duplicature
exhibits the usual semilunar, shelf-like form, and has a
transversely striated peripheric area surmounted by a pellucid
rim. On the right valve (fig. 4), this duplicature has a
rather different appearance, forming inside a rounded ex-
pansion, and entirely without any transverse striation. The
posterior duplicature is comparatively broader on the left
valve (fig. 3) than on the right, and has the peripherie
area striated in a similar manner to that of the anterior
duplicature: the striation may also be traced along the
whole ventral face of the valve. Just within the inferior
sinus, both valves form a short lingular expansion extended
straight inwards, that of the right valve being overlapped
by that of the left, when the shell is closed. As in other
Cypridids, the valves are connected along the dorsal face

2 — Archiv for Math. og Naturv. B. XVIII. No. 7.
Trykt den Sde Oktober 1896.

8 G. O. Sars.

by a sort of hinge, having inside an elastic ligament which
tends to keep the valves apart. By the aid, however, of a
strong adductor muscle, traversing the body and joining
each valve near its centre, the shell admits of being
perfectly closed, in which case all the parts of the animal
are enclosed within the cavity of the shell. Each valve is
composed of an. outer chitinous lamella of a rather firm
consistency, and of a very delicate inner membranous lining
forming the immediate continuation of the skin of the
body. Between these 2 lamellæ some internal organs are
continued, viz., the ovarial tubes and the cæca of the
intestine (see fig. 4).

The shell, in the living state of the animal, exhibits
a yellowish green colour, dotted with darker green, and
has moreover, dorsally, as also at each extremity, irregular
shadows of a much darker hue, forming partly interrupted
transverse bands (see figs, 1 and 2). On each side of the shell,
behind the central muscular area, may generally be observed
a more or less distinct orange tinge, produced by the ripe
ova accumulated within the underlying body, and a dark
diagonal stripe is also seen running from the upper side
of the muscular area obliquely backwards. This stripe forms
the boundary between the ovarial tubes and the ceca of
the intestine, both lying, as above stated, between the two
lamellæ of the valves. :

When the one valve is carefully detached!), the
enclosed animal can be to some extent examined in its natural
situation lying within the other valve (see fig. 3). It is
thereby easily demonstrated, that the body does not nearly fill

1) This may b» best accomplised by previously killing the animal in
boiling water, when the valves will remain wide open, and

the several appendages extended in their natural position.

On Stenocypris Chevreuxi. 9

the inner cavity of the shell, and that sufficient room is
left for all the appendages, when drawn in by the animal
on closing its shell. During the movements of the animal,
however, both pairs of antennæ, as also gene.ally the anterior
pair of legs, and at times the caudal rami are seen
to extend from the shell. The body is attached to the
shell along the whole dorsal face and also laterally by the
great adductor muscle, in such a manner, that only its
hindmost part is freely movable within the shell. In frout
the body appears, as it were, transversely truncated, and
any boundary between the head and trunk does not exist,
nor is the abdominal division defined from the trunk by
any intervening suture or constriction. There is consequently
no distinctly pronounced segmentation of the body, and the
number of segments that originally compose it, can there-
fore only be determined by the number of limbs. This
is rather restricted, being only 7 pairs in all, viz., 2 pairs
of antennæ, 1 pair of mandibles, 2 pairs of maxillæ, and 2
pairs of legs. Quite in front, and at a short distance from
‘the dorsal face, the eye occurs, and may also be fairly well
traced through the shell. Immediately beneath it, the superior
antenne issue, acting, during the motions of the animal,
upwards and backwards. At some distance below them, the
doubly-geniculated inferior antennæ originate, acting in.
an opposite manner to the superior ones, viz., downwards
and backwards. Between the bases of those antennæ the
voluminous anterior lip is seen to project, forming in front
an obtuse prominence. The oral aperture is found ventrally
at a considerable distance from the bases of the inferior
antennæ, and on the sides of it are seen the bodies of the
mandibles, with their masticatory parts wedged in between
the anterior and posterior lips, whereas their distal parts

10 G. O. Sars.

extend up the sides of the body to above the middle. The
strong mandibular palps issuing from the outer faces of
the mandibles extend obliquely forwards and downwards
between the bases of the inferior antennæ and the oral
aperture, their branchail appendage, however, being gener-
ally extended in the opposite direction. Behind the oral
aperture the anterior maxille are easily observed, with their
digitiform masticatory lobes, and the likewise digitiform palp
extending obliquely forwards towards the mouth. To the
outer side of these maxillæ is attached, the large semilunar
branchial plate extending obliquely upwards. Close behind
these maxille the posterior ones may be partly traced,
with their flabelliform reflexed palps. Then follow close
together the 2 pairs of legs, the anterior of which are
generally extended from the shell below, acting anteriorly,
whereas the posterior ones are constantly kept within the
cavity of the shell, and more or less bent up across the
abdominal part of the body. Between the legs and the
insertion of the caudal rami is a rather long interval, of which
the greater part is occupied by the genital lobes. The
caudal rami are very movably articulated to the end of the
abdominal part of the body, and from the articulation a
strong chitinous stripe is seen extending along each side
of that part, strengthening the articulation. When at rest,
the caudal rami are generally extended straight forwards,
being applied against the ventral face of the body. By
the aid, however, of a number of strong muscles running
along the dorsal side of the abdominal part of the body,
and joining their base posteriorly, they can be suddenly
moved downwards and backwards so as to extend in the
direction of the axis of the body, thereby serving as a most

effective propulsive apparatus.

On Stenocypris Chevreuxi. bil

I will now proceed to a more detailed description of
the above-mentioned parts.

The eye (see PI. 1, fig. 3), which undoubtedly, both as
regards place and structure, corresponds to the ocellus in other
Entomostraca, is of a rounded quadrate form, and contains
a very dark pigment. Its lateral faces are highly refractive,
exhibiting in the living animal a very brillant iridescent
lustre, and are apparently each divided into two facets. The
eye is to a certain extent movable, permitting of a slight
revolving motion accomplished by the aid of 2 thin muscles
joining it on each side from behind.

The superior antennæ (Pl. 2, fig. 1) are each composed
of a thick and muscular basal part and a narrow, multi-
articulate terminal part or flagellum. The basal part issues
from the front part of the body by a broad base, and has
the upper face vaulted, the lower nearly plain. It is
composed of 2 joints, the proximal one being much the
larger, and strengthened by several chitinous stripes
anastomosing with each other. From about the middle of
the upper side of this joint issues an anteriorly curving
simple bristle, and at the end below, two other consider-
ably longer reflexed setæ are seen to extend. The rather
short and narrow distai joint is only provided with a very
small bristle anteriorly, and would seem to be rather firmly
connected with the proximal joint. The flagellum, or terminal
part of the antennæ, is nearly of the same length as the
basal part, to which it is very movably articulated, but is
much narrower, and subcylindric in form, It is divided into 5
well-defined articulations, the 1st of which is much the
largest, From the end of the articulations issue long sete,
forming together a dense brush. It is, however, not easy

to count the sete, as they generally lie very close together;

12 G. O. Sars.

but, excepting the Ist articulation, which has only 2
comparatively short sete, each. articulation would seem
to give origin to 4 natatory sete, 2 anteriorly and 2
posteriorly, the former being particularly elongated. The
last articulation, moreover, has 2 or 3 shorter, spine-like
bristles on the tip. During the swimming motions of the
animal, the sete are spread out in such a manner as to
form a broad fan, and as they are all finely ciliated, these
antennæ may act as most effective propulsive organs.

The inferior antennæ (fig. 2) are comparatively more
strongly built than the superior, and pediform in character.
They also consist of a basal and a terminal part, forming
together a strong geniculate bend. The basal part, as in
the superior antenne, is bi-articulate, but the distal joint is
here much the larger, whereas the proximal one is quite
short and less distinctly defined from the body. Both
joints are strengthened by several chitinous stripes curved
in different directions, and between them is a more movable
articulation than between those of the superior antenne.
The proximal joint carries below 2 or 3 short bristles, and
from the end of the distal joint issues posteriorly a slender
reflexed seta, and anteriorly, somewhat inside the joint,
another still longer seta, which curves downwards in front
of the terminal part. The latter, which is very movably
articulated to the basal part, is composed of only 3 joints.
The Ist joint is fully as long as the distal joint of the
basal part, but considerably narrower, and carries at some
distance from the base posteriorly a peculiar sensory appen-
dage terminating in a very delicate cylindric papilla (fig.
2, b). At the end, this joint has posteriorly a single,
strong ciliated seta, whereas anteriorly, and somewhat

inside the joint, 5 or 6 very slender and elongated setæ issue

On Stenocypris Chevreuxi. 13

close together, curving downwards in front of the outer
joints, and extending as far as the tips of the terminal
claws. These sete are finely ciliated, and during the
swimming motions of the animal, are spread in a fan-like
manner, to counterbalance the effect of those issuing from
the superior antennæ. The 2nd joint of the terminal part
is but little more than half as long as the Ist, and also
considerably narrower, forming with the same a more or less
- pronounced geniculate bend. It is provided on each side,
about in the middle, with a fascicle of slender bristles, and
is produced at the end anteriorly to a knob-like projection
carrying 3 very strong claws of somewhat unequal length.
The last joint is very small, and apparently firmly connected
with the 2nd. It is (see fig. 2, a) of simple cylindric form, ©
and carries on the tip 2 unequal claws, and 3 small, hair-
like bristles. The claws are much smaller than those
issuing from the preceding joint, which in fact extend some-
what beyond them.

The anterior lip (figs. 3, 4) is rather voluminous and
produced in front in a hood-like manner, It terminates
posteriorly with a sharpened edge limiting the oral aperture
in front. Within it, several muscles are seen to spread,
which may serve for lifting it to a certain extent; and
a rather complicated system of chitinous stripes anastomosing
with each other, and partly continued around the oral
aperture, may also be distinctly traced.

The posterior lip (ibid. and fig. 5) is in the form of a
thin plate bounding the oral aperture behind, and placed
almost vertically. It is strengthened on each side by a very
strong chitinous rod, which expands at the end to a dark
horn-coloured lamella, divided into 7 or 8 coarse denticles.

This lamella is placed transversally, and is somewhat incurved,

14 G. O. Sars.

so as to meet the one on the other side. Between the 2
chitinous rods, a close striation is observed (see fig. 5),
and along the middle, a funnel-shaped depression occurs,
leading to the cesophagus.

Immediately behind the posterior lip, the ventral face
of the body forms a somewhat prominent carinated plate,
lying between the insertions of the maxille.

The mandibles (fig. 6) each consist of a strongly
chitinized body, and a well-developed pediform palp. The
body is of a somewhat cuneated shape, its upper part being
produced to an acute point, which is apparently articulated
to the inside of the shell. The dark horn-coloured masticatory
part is slightly ineurved, and has exteriorly a small bristle.
The cutting edge is divided into 6 or 7 strong, dark brown
teeth, diminishing in size inwards, and coarsely denticulated
in their outer part, having between them stiff bristles. The
palp is about half the length of the mandible, and is curved
downwards. It consists of 4 well-defined joints, the Ist of
which is rather large, and carries at the end posteriorly 3
very strong and densely ciliated sete. To the outer side
of this joint a comparatively small, recurved branchial
appendage is attached, carrying 6 densely plumous sete, 4
of which issue from the transversely truncated tip, whereas
the 6th is secured to a separate ledge on the outer edge.
The 2nd joint of the palp is rather short, and carries both
anteriorly and posteriorly several slender bristles. The 3rd
joint is much larger, and is likewise provided on both
edges with a fascicle of bristles. Finally, the last joint is
very small and somewhat conically tapered, and carries on
the tip 3 or 4 short, spiniform bristles.

The anterior maxille (fig. 7) each exhibit a thick and

muscular basal part, to the outer side of which is attached

On Stenocypris Chevreuxi. 15

a very large semilunar branchial plate, which in the living
anımal is seen to exhibit rhythmical vibratory movements.
The plate is provided along its outer edge with about 24 :
exceedingly strong and densely plumous sets, of which the 5
inferior ones are curved straight downwards. From the end of
the basal part issue 4 digitiform lobes, the most anterior
of which is much the largest, and is movably articulated to
the basal part. This lobe, which ought more properly to
be regarded as the palp, consists of 2 well-defined articula-
tions, the 1st of which is the larger, cylindric in form, and
provided at the end anteriorly with a number of slender
curved bristles. The distal joint (see fig. 7, a) is rather
short and very slightly expanded at the end, which is
obliquely truncated and armed with about 6 claw-like
bristles. The 3 other lobes, the true masticatory lobes, are
quite simple, diminishing successively in size, and each
carrying at the tip a bunch of strong, partly denticulated
spines.

The posterior maxille (fig. 8) are much smaller than
the anterior, and of a rather different structure. The basal
part is immediately continued as a simple masticatory lobe
extended obliquely forwards, and armed at the tip with a
dense bunch of slender spines, having also inside, at some
distance from the tip, some few similar spines. From the
posterior side of the basal part issues a conically tapering
lappet, which is extended straight backwards and terminates
in 3 setee, of which the middle one is much longer than the
other 2. This lobe ought to be regarded as a peculiarly
modified palp. Immediately above it a small rounded branchial
plate is secured, carrying 6 densely plumous sete.

The anterior legs (fig. 9) are rather strongly built, and
consist each of a short and thick basal part and a more

16 G. O. Sars.

slender, tapering terminal part. The basal part is strengthened
by several chitinous stripes, and seems to consist of 2
imperfectly defined joints, forming together a geniculate
bend, from which a few small bristles are seen to issue.
The terminal part is divided into 4 well-defined joints, the
ist of which is much the largest and about as long as the
2 succeeding ones combined. It contains several strong
muscles joining the very movable outer part of the leg, and
carries at the end anteriorly a simple bristle. The 2 next
joints are firmly connected, though defined by a distinct
transverse suture, and have each at the end anteriorly a
similar bristle to that of the 1st joint. The last joint is
very small, and carries on the tip an exceedingly long and
slender, anteriorly curving claw, at the base of which 2
small bristles are secured.

The posterior legs (fig. 10) are considerably more slender
than the anterior, and are apparently only composed of 4
joints, though a short basal joint may probably exist The Ist
joint is somewhat bent in the middle, and carries 3 slender
setæ, 2 of which issue from near the end, whereas the 3rd
is attached to the middle of the lower edge. The 2nd joint,
which forms with the 1st a strong elbow-like bend, is very
much elongated and narrow cylindric in form, having a
single slender bristle at the end posteriorly. The 3rd joint
is much shorter and also narrower than the second, being
somewhat constricted at the base. It carries, in the middle
of the posterior edge, a slender bristle, and juts out at the
end to a short, thumb-like projection, The last joint is
extremely small, and is produced to a strongly-curved claw
extending backwards, and having at its base a slender bristle
pointing in the opposite direction. The function of these

legs is apparently that of cleansing the inner cavity of the

On Stenocypris Chevreuxi. 7

shell from extraneous matter, for which reason these legs
are generally termed in the German language »Putzfisse».

The genital lobes (see figs. 11 and 12) occurring between
the posterior legs and the insertion of the caudal rami,
constitute. 2 juxtaposed, transversely oval expansions. At
their posterior end the genital orifice seems to occur, and
a number of distinct muscular fibres are seen to converge
to this place. Farther in front, and somewhat inside the
lobes, there is a funnel-shaped hollow bounded by some
strong, curved chitinous stripes, and immediately above it
may be traced, a peculiar orbicular body, which, on a closer
examination, is found to be formed by a narrow duct coiled
up into numerous dense spiral coils, and finally joining the
above-mentioned hollow. Zencker has explained these hol-
lows as the »vulve«, and the coiled duct to be destined
for the passage of the thread-like zoosperms, believing
that the receptacula seminis are in direct communication
with this duct. I am by no means convinced of the correct-
ness of this explanation. In the present form, not the slightest
trace of any »receptacula seminis«, is to be found, and I
should therefore be more inclined to believe that the duct
is in reality destined to secrete a viscid fluid, from which
the egg-shell may be formed.

The caudal rami (see figs. 12, 13) are rather strongly
developed, fully equalling in length the free abdominal part
of the body. They are in the form of 2 juxtaposed
narrow plates, which, however, at the base are united
(see fig. 12). Each ramus is armed at the end with 2
- strong claws, and has the outer half of the dorsal edge
divided into 4 or 5 slight lobes edged with a comb-like
series of strong denticles (see fig. 13 a). Of the claws the

18 G. O. Sars.

apical one is fully twice as long as the other, though not
attaining half the length of the ramus. Both claws are
but very slightly curved, and are finely denticulated along
their concave edge, Just in front of the apical claw issues
from the tip of the ramus a rather long bristle curving
downwards in front of the latter, and another much smaller
one is seen attached to the dorsal edge, immediately above
the other claw.

Inner organs.

In order to examine the inner organs in their natural
situation, it may be convenient to detach the animal
carefully from its shell, and to place it for some time
in absolute alcohol, then either transferring it to oil of
cloves at once, or after having previously stained it very
slightly with hematoxylin or carmine. The animal may
then be mounted in canada balsam either entire or in
parts. Some of the inner organs, especially those contained
within the lamelle of the valves, may however be equally
well examined in quite fresh specimens.

The intestinal canal commences with a muscular cesophagus
ascending perpendicularly from the oral aperture, and join-
ing the intestine proper by a somewhat tumefied part
strengthened, according to Zencker, by several chitinous
lamellæ. The intestine proper (see pl. 1, fig. 3) is very
capacious, occupying a great part of the inner cavity of
the body. It is divided into two very sharply defined
parts, one anterior, the stomach, and one posterior, the gut
these being separated by a strong constriction occurring about
in the centre of the body. The stomachal portion is pro-
duced above to a large rounded sac advancing over the

anterior part of the gut, and sends off from each side,

On Stenocypris Chevreuxi. 19

immediately above the adductor muscle of the shell a
cylindrical cæcum, the so-called liver-sac. The latter
immediately penetrates between the 2 lamelle of the valves,
extending in each of them diagonally to the hind extremity
(see fig. 4). These ceca are lined internally with large
secretory cells, and generally exhibit a more or less brownish
hue. In the living animal at times a rhythmical peristaltic
movement of these cæca may be observed, which caused
Fischer to regard them erroneously as hearts. The posterior
part of the intestine, the gut, is also rather capacious, and
extends through the abdominal division of the body,
terminating in a short rectum, which debouches immediately
in front of the insertion of the caudal rami. It is generally
found to be filled with a dark matter, whereas those of
the stomachal part always appear considerably lighter. The
walls of both the stomachal and abdominal parts of the
intestine are strongly muscular, and during life both parts
are seen to perform rather energetic movements.

The circulatory system is very imperfect. There are
no blood-vessels whatever, and not even the slightest trace
of a central organ, a heart, is to be detected. The colour-
less blood is contained in the interstices between the inner
organs, and is put in motion, it would seem, chiefly by
the movements of the intestine.

The respiratory system is represented by 3 pairs of
delicate, setiferous lamellæ appended to the mandibular palps
and the 2 pairs of maxille. These lamella, which in the
living animal are in rhythmical vibratory motion, are there-
fore generally termed branchial appendages. It is, how-
ever, most probable, that these appendages are in fact
only subservient to the respiration, and that the latter
process (the exchange of gases) takes place chiefly in the

20 G. O. Sars.

delicate inner membrane of the valves. By the rhythmical
movements of the branchial lamellæ, and especially of those
of the anterior maxillæ, a continous renewal of the water
takes place within the cavity of the shell, whereby a
sufficient aération of the blood contained between the two
lamellæ of the valves may be obtained.

The nervous system I have not been able to examine
more closely, nor could Zencker observe it in its total-
ity, owing to its concealed situation, though the upper
æsophageal ganglion, and another larger one lying behind
the oral aperture were to be faintly traced.

Of the genital system, only the female organs can be
described here, as I have never come across a male speci-
men. In all probability males do not exist at all. The
ovaria consist of a slender tube on each side contained between
the lamellæ of the corresponding valve, and extending
immediately above the liver-sac (see fig. 4). This tube
gradually tapers distally, and its ‘blind end forms an abrupt
curve upwards. At nearly the same place, where the liver-
sacs join the intestine, the ovaria pass into the body,
forming in the abdominal part on each side a capacious
cavity, into which the ripe ova are received, Within the
ovarial tubes egg-cells in every stage of development may be
observed (see fig. 4). In the hindmost blind ends, a great
number of simple nuclei are accumulated. Farther in front,
each nucleus has become surrounded with a clear yolk-
matter, and the several cells are here more clearly defined,
being arranged in several series. By the successively increas-
ing size of the cells more anteriorly, only a double series can be
discerned, and at last there is only room for a single series
of egg-cells successively increasing in size. The cells lying

in the foremost part of the ovarial tube become gradually

On Stenocypris Chevreuxi. 21

filled with an opaque orange matter, the nutritive yolk,
and are now nearly ripe. They are successively received
into the egg-cavities of the body, and there often accu-
mulate in rather large numbers, being at intervals expelled
through the genital openings. All the ova contained in the
said egg-cavities are of exactly the same size and in the same
stage of development; and these cavities cannot therefore pro-
perly be regarded as a part of the ovaria themselves, but only
as a sort of reservoir for the eggs. They are still only
surrounded with a very thin, pellucid, vitelline membrane,
without any trace of the strong, coriaceous capsule, which
is found enveloping the deposited ova. This capsule
must accordingly be formed immediately after the ova have
passed through the genital openings,

Biological Observations.

At first only some few specimens of this form made
their appearance in one of my aquaria rather late in the
autumn. They thrived very well, and soon reached maturity,
whereupon they began to deposit their eggs in smail clusters,
chiefly on pieces of weed contained in the mud. The eggs
after some time developed into young ones, which in their turn
became adult, and in the same parthenogenetical manner
as the first hatched specimens, gave origin to a third
generation. The aquarium contained this Ostracod during
the whole winter, and though from time to time a con-
siderable number of specimens were taken out and pre-
served, some specimens yet remain in the aquarium. All
specimens, without exception, were of the female sex, and
I do not doubt therefore, that this form, like several of

its allies, is exclusively partenogenetical in character.

G. O. Sars.

DD
bo

As to habits, it is more generally found on the bottom
of the aquarium, moving about rather quickly through the
loose mud. Now and then however, it is, seen to ascend
the walls of the aquarium in search of food, and at other
times to swim rather rapidly through the water in a similar
manner to that observed in the species of Cypris. It is,
however, on the whole less active than these forms, and in
this respect holds the mean between the species of Cypris
and Candonocypris.

Occurrence,—The mud from which this form was
raised, was from only one of the two samples received,
viz, that taken from the swamp of Bon Kamera.

[pe]

On Stenocypris Chevreuxi.

A Short Account of the various Entomostraca Raised
from the Two Samples of Mud.

Cladocera.

1. Daphnia magna, Strauss.

This well-known form developed in great numbers in
two of my aquaria, both prepared with mud from the
swamp of Bon Kamera. It was watched during 2 or 3
successive sexual periods, and in the one aquarium is still

living.
2. Ceriodaphnia reticulata (Jurine).

This form also developed rather plentifully in one of
my aquaria, but the mud from which it was raised belonged
exclusively to the other sample, viz., that taken from the

swamp of Kharezas.

3. Certodaphnia minor, Lilljeborg.

Of this species, which is very nearly allied to the
preceding one, but of a much smaller size, numerous speci-
mens developed in two of my aquaria, both prepared with
mud from the Bon Kamera swamp.

4. Simocephalus vetulus (Müller).

This well-known form developed very abundantly in
one of my aquaria, and was watched during 2 successive
sexual periods, male specimens being at the close of each
period very numerous. The mud belonged to the sample
taken from the swamp of Bon Kamera.

3 — Archiv for Math. og Naturv. B. XVIII. No. 7.
Trykt den Sde Oktober 1896.

24 G07 Sars:

5. Leydigia acanthocercoides (Fischer).

A single adult female specimen of this Lynceid was
taken up from the same aquarium, in which Simocephalus
vetulus occurred. It was not, however, observed subsequently.

6. Alona lineata, Fischer.

Of this species, very seldom met with in Norway,

countless myriads developed in all my aquaria.

7. Chydorus sphæricus (Müller).

Found rather frequently together with the preceding

species.

Ostracoda.

8. Cypris virens, Müller; var monilifera.
This variety, distinguished by a number of rounded
nodules at each extremity of the valves, not found in the
typical form, developed in two of my aquaria prepared with

mud from the swamp of Bon Kamera.

9. Stenocypris Chevreuxi, G. O. Sars.

Sec above.

10. Ilyocypris australiensis, G. O. Sars.

Several specimens of an Ilyocypris not distinguishable
from the Australian form described by the present author in his
paper »On some Australian Ostracoda and Copepoda«, were
raised in one of my aquaria prepared with mud from the

same locality as the 2 preceding species,

On Stenocypris Chevreuxi. 25

11. Ilyocypris gibba (Rhambdor).

Of this species, easily distinguished from the preceding
one by the gibbous projections of the valves, a few speci-
mens were raised from mud derived from the other locality,
viz., the swamp of Kharezas.

Copepoda.

12. Diaptomus. sp.?

This is a very small species, which I cannot identify
with any of the forms described by M. de Guerne et
Richard, but which seems to come nearest to D. graciloides,
Lilljeborg. It was raised in two of my aquaria prepared
with mud from the swamp of Bon Kamera, and a consider-
able number of specimens preserved in spirit was also sent
me by M. Chevreux from the same locality.

In addition to the above enumerated Entomostraca
some colonies of a fresh-water Bryozo, Plumatella repens,
Lin, also developed in one of my aquaria prepared with
mud from the swamp of Kharezas.

26 G. O. Sars.

Explanation of the Plates.

PETE
Stenocypris Chevreuxi, G. O. Sars.

Fig. 1. Adult female, viewed from right side, magnified 39

diameters.

DD

Same, dorsal view, magnified 39 diameters.

» 8, Left valve with enclosed animal, the right valve
being detached, lateral view; magnified 45 diameters.

» 4. Right valve of same specimen, viewed from the

inner face, and exhibiting the corresponding liver-

sac and ovarial tube; magnified 45 diameters.

PI:
Stenocypris Chevreuxi, G. O. Sars.
(continued).
The greater part of the figures magnified 88 diameters.
Fig. 1. Superior antenna.
» 2. Inferior antenna.

» 2. a. Terminal joint of same, more highly magnified.

» 2. b. Sensory appendage from same, likewise highly

magnified.
» 3. Anterior and posterior lips, seen from below.
» 4. Same parts, exhibited from right side.
» 5. Posterior lip, more highly magnified, and viewed

from the anterior face.

» 6. Mandible with palp.

On Stenocypris Chevreuxi. Dr

Fig. 7. Anterior maxilla with branchial plate.

» 7 a. Extremity of palp, more highly magnified.

» 8. Posterior maxilla.

» 9. Anterior leg.

» 10. Posterior leg.

» 11. Right genital lobe, seen from the outer face.

» 12. Extremity of body, with the genital lobes and the

extended caudal rami, viewed from the ventral face.

» 13. One of the caudal rami, seen laterally.

» 13. a, Outer part of the dorsal edge of same, more

highly magnified.

DE SONET ØM

OF TWO NEW”

PHYLLOPODA

FROM
NORTH AUSTRALIA
BY

G. O. SARS

WITH 6 AUTOGRAPHIC PLATES

ARCHIV F. MATHEM. OG NATURVIDENSKAB

M KRISTIANIA
ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

DEC 4 1896

ARCHIV FOR MATHEMATIK OG NATURVIDENSKAB. B. XVII. Nr. 8.

Description of Two New Phyllopoda from
North Australia. :

With 6 autographic Plates.
By @. O. Sars.

Introduction.

In a previous paper inserted in this journal, I have
given descriptions and figures of 5 species of Phyllopoda
collected by Messrs. Whitelegge and Lea in the neighbour-
hood of Sydney, all of which have been identified with
earlier recorded forms. I now propose to describe 2 additional
Phyllopoda from the northern part of the continent. The
total number of Australian Phyllopoda, including Cyclestheria
Hislopi, Baird, previously described by the present author, and
some forms recorded by Messrs. King, Baird and Brady,
thus amounts to no less than 10 in all; belonging to the
3 leading sections of the sub-order: Anostraca, Notostraca,
and Conchostraca. Of the 2 species described in the
present paper, the one has been observed by myself in a
living state, whereas the other is described from well-
preserved alcoholic specimens. Both of these forms I

regard as new to science.

1 — Archiv for Math. og Naturv. B. XVIII No. 8.
Trykt den 8de Oktober 1896.

4 G. O. Sars.

Section Anostraca.
Fam. Branchipodidee.

Gen. Streptocephalus, Baird.

Remarks.—This genus was established by Baird in
the year 1852, and is chiefly characterised by the peculiar
structure of the male prehensile antennæ. As I have only
found the Australian species described below in the
female sex, I have been somewhat in doubt as to its true
systematic place among the Branchipodids. In its external
appearance it shows, however, a rather close resemblance
to the female of the species Streptocephalus similis from
St. Domingo, and as it seems to differ in some points
rather markedly from the females of other Branchipodid
genera, I have felt justified in referring it provisionally to

the above-named genus.

Streptocephalus Archeri, G. O. Sars, n. sp.
(Pl. I).

Specific Characters—Female. Body very slender,
with the anterior division about the length of the posterior
(excluding the caudal rami). Head exhibiting on the
dorsal face a small, but well-defined rounded quadrangular
and somewhat elevated area. Eyes comparatively large,
pyriform, with the corneal part globularly expanded and

the pigment very dark, Ocellus small. Antennule narrow

Description of Two New Phyllopoda. 5

and elongated. Antennæ about the length of the antennulæ,
applanated, foliaceous, not compressed, and having at the
obtusely rounded tip a very short pointed projection. Legs
apparently of the usual structure, outer part of endopodite
broadly rounded, exopodite lamelliform, much smaller on
the Ist than on the succeeding pairs, basal plate minutely
and regularly serrated. Marsupium rather short and narrow,
scarcely reaching beyond the 2nd caudal segment; enclosed
ova of a very peculiar shape, being each surrounded by a
tetrahedric shell. Caudal rami very much elongated, being
about half the length of the tail proper, and rather narrow,
tapered distally, and fringed all round with strong plumous
sete. Body, in the living state of the animal, highly pellucid,
nearly colourless, caudal rami, however, tinged with a vivid
reddish orange; eggs in the marsupium dark horn-coloured.
Length of the adult female 9 mm.

Remarks.—As above stated, this form shows some
resemblance in its external appearance to the female of
S. similis, as figured by Baird, though being still more
slender, and having the caudal rami comparatively longer.
Moreover, the marsupium is shorter, and the enclosed ova
apparently of a very different shape.

Description of the female.

The length of the solitary adult specimen examined is
about 9 mm., measured from the front to the tip of the
caudal rami, and this form is accordingly somewhat inferior
in size to the other known species of the genus.

The body (see Pl. I, figs. 1, 2) is extremely slender,
resembling in this respect the species of the genera

6 G. O. Sars.

Branchinecta and Artemia. It shows its 2 chief divisions
well defined, both being about of the same length The
anterior division may be subdivided into the head and the
trunk, the posterior one into the genital part and the tail
proper.

The head is not very large, and but slightly deflexed»
carrying in front the 2 pairs of autennæ, laterally the eyes,
and ventrally the oral parts. By a distinct transverse
suture extending dorsally between the upper ends of the
mandibles it is divided into an anterior and a posterior
part, the latter representing the so-called cervical segment.
The anterior part seen from above (fig. J), is almost
pentagonal in form, and exhibits in the middle of the
dorsal face a small, but well-defined, rounded quadrangular
area, which, in a lateral view of the animal (fig. 2), is
found to be slightly protuberant. This area may also be
observed in other Branchipodids, and would seem to answer
to the postocular tubercle in the Notostraca and the affixing
organ in some of the Conchostraca. The cervical segment
carries ventrally the 2 pairs of maxille, and exhibits on
each side a contorted duct, which undoubtedly answers to
the so-called shell-gland in other Phyllopods.

The trunk is somewhat broader than the head, slightly
depressed, and divided into 11 uniform segments, each
carrying a pair of branchial legs. Seen dorsally (fig. 1), it
appears somewhat fusiform in outline, being broadest in
the middle, and slightly tapering both anteriorly and
posteriorly,

The posterior division of the body is considerably
narrower than the anterior. Its first 2 segments form
together the genital division, and are coalesced in the

greater part of their extent, being only distinctly defined

Deseription of Two New Phyllopoda. 7

dorsally. From this region proceeds ventrally the marsupium,
or ovisac, the free end of which is extended backwards in
the form of a somewhat conically tapered tube, having at
the tip a valvular opening, through which the ova are
expelled, when mature. This free part of the marsupium
is rather short, scarcely reaching beyond the 2nd segment
of the tail proper. The latter is very narrow, cylindric in
form, and is divided into 7 well-defined segments, the last
of which is very short, and slightly produced in the middle,
where the anal orifice occurs (see fig. 1). To this segment
the caudal rami are attached, being extended posteriorly
and more or less diverging.

The eyes (see figs. 1, 2, 3) are rather large, and move
freely, extending generally more or less straight laterally,
immediately behind the insertions of the antenne. They
exhibit a pronouncedly pyriform shape, being considerably
constricted at the base, and gradually widening distally. The
eye-ball proper, occupying the extremity of the eye, is
globularly expanded, aud exhibits a very great number of
visual elements radiating from the dark pigment and forming
a clear zone around it.

The ocellus (ibid.) is very small, and occurs in the
middle of the foremost part of the head as a punctiform,
dark red pigmentary spot.

The Ist pair of antennæ, or the antennule (see figs.
1, 2, 3), are rather slender and elongated, in length con-
siderably exceeding the head, and in the living animal are
generally extended anteriorly and somewhat divergent. They
are of a very delicate structure, narrow cylindric in form,
and slightly tapering towards the tip, which carries a number
of small olfactory papille, and a single somewhat longer

sensory bristle.

8 G. O. Sars.

The 2nd pair of antennæ, or the antennæ proper (ibid.),
are in the form of 2 flattened (not as in most other
Branchipodids compressed), foliaceous lamellæ, generally
extended straight downwards. In length they about equal
the antennule, and are about twice as long as they are
broad. The tip is evenly rounded, and exhibits, about in
the middle, a very small pointed projection, Otherwise the
edge is evenly curved, and provided with extremely delicate,
small sensory hairs. Within the base of each antenna
enters from the head a muscular bundle, which soon divides
into numerous fine, diverging branches (see fig. 3). Any
essential significance however, this muscle does not seem
to have, as the antennæ are scarcely movable, and generally
keep their prone attitude nearly unaltered during life.

The anterior lip is easily observable in a ventral or
lateral view of the animal (fig. 2), forming a flap-shaped
expansion covering over the masticatory parts of the
mandibles, though admitting of being somewhat removed
from them ventrally.

The mandibles also appear very distinctly in the lateral
view of the animal (fig. 2), lying like a pair of much bent
bows on each side of the head, at the limit between its
anterior part and the cervical segment, and meeting ventrally
at the place where the oral aperture occurs.

The maxille, in the lateral aspect of the animal, are
hidden by a lobular expansion of the cervical segment,
containing the lower part of the shell-gland (see fig. 2).

Of branchial legs there are, as in all true Branchipodids,
11 pairs, all of a rather uniform structure, though somewhat
diminishing in size both anteriorly and posteriorly. They
are pronouncedly laminar in character, and are extended

downwards and somewhat laterally, with the anterior face

Description of Two New Phyllopoda. 9

more or less vaulted, the posterior, concave. On all the
legs the following parts are to be distinguished: the stem
proper, or endopodite, the exopodite, the epipodite, and the
basal plate, the last 3 issuing from the outer side of
the stem (see fig. 5). The endopodite is rather broad and
laminar, and terminates in a comparatively large, broadly-
rounded lobe, edged with short, ciliated sete. Above this
lobe issue, from the inner edge of the endopodite, 5 other
lobes, the 3 outermost of which are rather small and conical,
and are each tipped with a limited number of slender sets
(from 3 to 6), some of them rather short and curved inwards.
The 2nd lobe from above is somewhat broader and more
evenly rounded at the tip, and the uppermost one is much
larger still and fully as broad as the succeeding 4 combined.
Both these lobes are fringed with a dense and regular
series of slender, biarticulate sete curving inwards and
upwards in a falciform manner. Of the above lobes, the
uppermost would seem to answer to the coxal lobe in other
Plyllopoda, whereas the others represent the so-called endites.
The exopodite forms an oval lamella movably articulated to
the endopodite, outside its terminal lobe, beyond which it
extends considerably, ‘The lamella ig edged all round with
ciliated setæ increasing in length distally, their number being
from 30 to 40. The epipodite is attached at some distance
above the exopodite, and has the character of a vesicular
lamella of a somewhat spongeous structure, and without any
armature whatever. The basal plate issues from the upper
part of the endopodite outside, and is very thin and pellucid,
of a somewhat elliptical form, with the outer edge finely
and regularly serrated. Of the above-described parts, the
epipodite undoubtedly represents the true gill; but we have

reason to believe that respiration takes place also in the

10 G. O. Sars.

other parts of the leg, which all exhibit a very delicate
membranous structure. Inside the endopodite, numerous
muscular bands are seen extending in different direc-
tions. Some of them join the exopodite, which is the
most freely movable appendage, being found now extended
in the axis of the leg, now considerably incurved beneath
the terminal lobe of the endopodite. Between the muscles
a number of opaque, somewhat stellate patches are seen
scattered over the greater part of the endopodite, These
patches are produced by a corresponding number of cross-
bars connecting the 2 lamelle composing the leg, and thereby
a system of internal hollows is formed, in which the blood
circulates. A similar structure may also be found on other
parts of the leg, and especially very distinctly in the epipodite.

The above description applies to the greater number of
the legs. Only the first and last pairs exhibit some minor
ditferences, to be mentioned below.

In the Ist pair the exopodite is considerably smaller
than in the others, not extending at all beyond the terminal
lobe of the endopodite, which appears rather broad in
proportion to its length (see fig. 4).

The last pair of legs (fig. 6) differ from the others in
the fact, that the terminal lobe of the endopodite is some-
what less developed, whereas the exopodite is fully as large
as in the preceding pairs. Moreover, the inner lobes of the
endopodite are considerably reduced in size, and only supplied
with scattered and rather short bristles. The basal plate
is likewise comparatively smaller than on the other legs;
and finally, the epipodite has lost its spongeous character,
and assumed a structure similar to that of the basal plate,
its terminal edge even being divided into a number of

distinct serrations.

Description of Two New Phyllopoda. ll

The caudal rami (see figs. 1, 2) are considerably elongated,
attaining about half the length of the tail proper. They
are rather narrow, gradually tapering distally, and are all
round fringed with strong ciliated setæ, springing off from
distinct ledges of the edge. By the aid of some muscular
bundles joining their bases, they admit of being to a certain
extent spread out and again brought together.

Of inner organs, the intestine is very clearly traced
through the pellucid integuments (see figs. 1, 2), extending
as a cylindric tube through the axis of the body. It is a
little wider in front than behind, and sends off in the head
anteriorly 2 small rounded ceca of apparently quite a
simple structure. The rectum is very short, and confined
to the last caudal segment.

Immediately above the intestinal tube, the very long
vessel-like heart may easily be traced in the living animal,
exhibiting in each segment a pair of venous ostia.

The ovaria were not distinctly visible in the solitary
adult specimen examined, apparently owing to the recent
evacuation of their contents into the marsupium. It would,
seem, however, that they are confined to the posterior
division of the body, as not the slightest trace could be
detected in the trunk, whereas in the tail several scattered
cellular bodies, apparently belonging to these organs, occurred
on each side of the intestine (see figs. 1, 2). At the base
of the marsupium an irregular glandular mass was distinctly
observed, apparently of the same kind as that furnishing in
other Branchipodids the material for the egg-shell.

The ripe ova contained in the marsupium are, in this
form, of a highly remarkable appearance. They are (see
figs. 7, 8, 9) each enclosed within a rather large and firm,

2 — Archiv for Math. og Naturv. B. XVIII. No. 8.
Trykt den 9de Oktober 1896.

12 G. O. Sars.

horn-coloured capsule of a trigonal, or more correctly
tetrahedric shape, exhibiting 4 plane or very slightly concave
faces of exactly the same size and form, and connected by
obtuse, prominent ribs. As far as I know, in no other
Branchipodid has a similar form of the egg-capsules been
observed. In all the previously known forms, the eggs are
simple globular bodies, and it is only in some of the
bivalve Phyllopoda, for instance in Limnadia, that an
analogous structure of the egg-capsules occurs.

The body in the living animal was highly pellucid and
nearly colourless, with only a very faint yellowish tinge on
the branchial legs. The caudal rami, however, exhibited a

most pronounced vivid reddish orange colour.

Biological Observations.

The above described specimen was raised by the present
author in the summer of 1886 from dried Australian mud, and
was watched for some time ina small aquarium, The larval
stages, however, wholly escaped my observation, and the
animal, when first detected, had already attained a rather
advanced stage of development, though still without any trace
of a marsupium. After the lapse of some time, the marsupium
was formed, and a number of the peculiarly formed eggs
soon made their appearance within it. At this time, however,
the aquarium unfortunately became so encumbered with
confervous growth, that the animal was considerably impeded
in its free movements, and as it showed signs of disease,
I hastened to secure it, after having previously made 2
carefully executed and coloured drawings (the ones here
reproduced) from the animal when still alive. Though I
carefully preserved the residue of the aquarium for later

hatching operations, no specimens developed subsequently.

Description of Two New Phyllopoda. We}

Probably the specimen had not yet deposited any ova in
the mud.

When still in its full vigour, the animal was extremely
rapid in its movements, twisting away in all directions, in
most cases with the back downwards. The movements
were effected partly by the aid of the rhythmically swinging
branchial legs, partly by abrupt strokes of the very flexible
tail, in which the densely setous caudal rami seemed to be
of essential service.

Occurrence.—The mud from which the specimen was
raised, was taken during the previous year by Mr. Archer from
a water hole at Cattle Station—salt at high tides—20 miles
from Rockhampton, Queensland. From the same sample of
mud, several other Entomostraca were also raised, and have
been described and figured by the present author in another
paper. Some other specimens, apparently of the same
Branchipodid, but all of them still immature, were recently
received from Mr. Knut Dahl, who collected them together
with the other Phyllopod here described, from a shallow
pool on Mount Showbridge, near Port Darwin, North

Australia,

14 G. O. Sars.

Section Conehostraca.

Fam. Limnadiidæ.
Gen. Eulimadia, Packard.

Eulimadia Dahli, G. O. Sars, n. sp.
(Pl. II-VI).

Specific Characters.—Shell in both sexes of same
appearance, very thin and pellucid, without any trace of
umbones; seen laterally, of a rather regular elliptical shape,
with the height but little more than */3 of the length, dorsal
margin evenly vaulted, and having its greatest convexity
somewhat in front of the middle, ventral margin forming
a perfectly even curve, and joining the anterior and posterior
edges without any intervening angle, both extremities nearly
equal, obtusely rounded at the tip, and having above a
distinct angle:—seen from above, narrow fusiform, the
greatest width in front of the middle. Maximum number
of lines of growth only 4 pairs. Head having in both
sexes the frontal part considerably produced; rostrum in
female very short and obtuse, being only defined in front
by a slight sinus; that of male considerably more prominent,
terminating in an acute point. Antenne and oral parts of
the usual structure, excepting that the posterior maxillæ
are quite rudimentary. Legs 20 pairs, having the epipodites
of considerable size; the 2 anterior pairs in male very strong,
subchelate. Tail with 2 short, juxtaposed dentiform projections

in front of the caudal claws, the latter throughout the

-

Description of Two New Phyllopoda. 15

greater part of their length, fringed posteriorly with long
ciliated sete, caudal plates terminating below in a very
acute, straight corner, and having the posterior edge divided
into 12—16 small denticles; dorsal spines present only in
a single distinctly developed pair. Eggs in the matrix
provided each with a very uneven capsule divided into
depressed hexagonal facets, the angles of which are acutely
produced. Length of shell in female attaining 7 mm., in
male 5.50 mm.

Remarks.—This is a true Fulimadia, exhibiting very
pronouncedly most of the particulars referred to by
Dr. Packard as distinguishing characters between this genus
and that of Limnadia. It is very distinct from the Sydney
species, E. stanleyana (King), described by the present
author in his first paper on Australian Phyllopoda,and the latter
form should perhaps more properly be regarded as the
type of a separate genus, for which I would propose the
name of Paralimnadia. The present form much more
resembles 2 species recently described by the Japanese
zoologist, Mr. Ishikawa, from the neighbourhood of Tokyo,
as E. packardiana and E. braueriana. From both of
these it differs, however, in the more oblong or elliptical
form of the shell, and in the greater number of branchial
legs. The species is named in honour of its discoverer,

Mr. Knut Dahl,

Description of the female.

In the largest specimens examined, the shell attains a
length of 7 mm. a height of 4.40 mm., and a width of
2.0 mm. It is accordingly rather larger than the 2 Japanese

species, but does not nearly attain the large size of the

16 G. O. Sars.

South Australian species, Æ. rivolensis, Brady, a form which
is still, however, very imperfectly known, and perhaps does
not even belong to this genus.

Seen from the side (Pl. 11, fig. 1), the shell exhibits a
rather regular oblong or elliptical form, and does not show
even the slightest trace of any umbones. The greatest
height of the shell occurs somewhat in front of the middle,
and but little exceeds */3 of the length. The dorsal margin
appears rather gently curved, and has its greatest convexity
a little in front of the middle. It terminates both anteriorly
and posteriorly in a well-marked angle, from which the free
edges of the valves take their origin, These are evenly
curved throughout, though anteriorly and posteriorly their
curvature is somewhat stronger than in the middle. Both
extremities of the shell appear obtusely rounded and nearly
equal, or the anterior one very little broader than the
posterior, having also the upper angle somewhat more
pronounced.

Seen from above (fig. 2), the shell is found to
be rather compressed, exhibiting a narrow cuneate or
somewhat fusiform shape. Its greatest width, which does
not attain half the height, occurs rather in front of the
middle, and the posterior extremity appears considerably
narrower than the anterior. |

The valves are exactly alike, and exhibit a smooth
and polished surface, without any trace of hairs or spines.
They each have, however, a number of very delicate con-
centric striæ, the so-called lines of growth. These striæ,
which lie somewhat closer togetherin front than posteriorly,
do not seem to exceed 4 in number on each valve, and
by the innermost a rather large oval area is defined, within

which, somewhat anteriorly, the insertion of the adductor

Description of Two New Phyllopoda. I,

muscle of the shell occurs, and behind it the shell-gland
extending obliquely downwards. The latter is constructed
in exactly the same manner as in the European Limnadia
lenticularis, Lin., though somewhat narrower and lingui-
form in outline.

The semipellucid shell admits of the enclosed animal
being faintly traced through it (see fig. 1); but in order to
examine it more closely in its natural situation, it is neces-
sary to remove carefully one of the valves, leaving the ani-
mal within the other (see fig. 3), when the several parts may
be submitted to a preliminary examination. It is found upon
the whole to be constructed in a very similar manner to that
described by the present author in Paralimnadia stanleyana.
The dorsal ligament, however, by which the body is con-
nected to the shell above, occurs here at a rather consider-
able distance from the anterior extremity, whereas in the
Sydney species it 1s found close to the place where the
free anterior edges of the valves take their origin. For
this reason, the line of junction between the two valves in
the present form is not only visible behind the ligament,
but is continued in front of it to some extent, terminating
at the upper anterior angle.

The anterior division of the body lying in front of the
dorsal ligament, is generally strongly deflexed, though in the
living state of the animal it may have been allowed to
raise itself to some extent. The cervical segment is evenly
convex above, and defined from the head proper by a rather
deep depression, in the bottom of which a transverse suture
occurs joining the upper ends of the mandibles. The head
(see also PI. III, fig. 1) is about the length of the cervical
segment, and has the dorsal face strongly convex, carrying

somewhat in front of the middle a well-defined affixing

18 G. O. Sars.

organ of a claviform shape. The frontal part of the head
is narrowly produced, and its obtusely rounded extremity
is to a great extent filled up with the large compound eyes.
Below the frontal part, the head exhibits a rather slight
sinus, and is produced behind this to a comparatively short
and broad, obtuse-angled rostral expansion.

The trunk (see Pl. II, fig. 3) is more than twice as
long as the anterior division of the body, and is extended
straight backwards, with a very slight curvature downwards
in its most posterior part. It is nearly cylindric in form,
only slightly tapering distally, and is divided into 20 rather
uniform segments, the last of which, however, is imperfectly
defined from the caudal part (see Pl. III, fig. 3). Dorsally,
the greater part of the segments are provided with trans-
verse rows of posteriorly curving spiniform bristles, which
successively disappear on the anterior segments.

The caudal part (see also Pl. III, fig. 3) is rather short
and slightly deflexed, containing anteriorly the terminal
part of the intestine, whereas posteriorly it is produced to
2 juxtaposed, thin lamellæ, the caudal plates, separated by
a deep groove. These lamellæ each terminate below in a
very acute spiniform corner, and have their posterior edge
divided into 12—16 rather uniform, minute denticles. Between
the lamellæ at their uppermost part there is a small tubercle
carrying 2 slender ciliated bristles, the caudal sete. Above
these the dorsal face of the tail forms a heel-shaped
convexity, which is armed with a single pair of strong,
posteriorly curving spines. At the end in front, the
caudal part is produced to two small, juxtaposed, dentiform
projections, and immediately behind them the caudal claws
are movably articulated to the tip of the tail. These claws

are rather strong, somewhat exceeding the length of the

Deseription of Two New Phyllopoda. 19

tail, and are almost straight, with the greater part of their
hind edge clothed with numerous long, ciliated sete. The
outmost part of the claws forms, as it were, a separate
terminal joint, and has at the base a short spine, whereas
its hind edge is throughout very finely denticulated.

The eyes (see PI. III, fig. 1) are rather large and placed
close together, so as to appear, in a lateral view of the
animal, as a single organ. They exhibit each a great
number of visual elements radiating from the dark pigment,
and forming together a clear peripheric zone. Three narrow
muscles pass from behind to each eye and allow that organ
in the living animal to be moved to a certain extent.

The ocellus is placed at a considerable distance from
the eyes within the rostral expansion, to the end of which
it is connected by a short ligament, whereas another much
longer ligament is seen to pass from its upper end and
enter the frontal part, affixing itself to the skin of the
head immediately below the eyes. The organ exhibits a
similar prismatic shape to that found in the European
Limnadia lenticularis.

The antennule (see Pl. I, fig. 4; Pl. III, fig. 1) originate
from the lower side of the head, just in front of the
anterior lip, and are generally extended downwards. They
are rather short, scarcely exceeding half the length of the
head, and are each composed of a short basal part and a
somewhat narrower terminal part, the anterior edge of which
is divided into 6—8 irregular rounded lobules densely set
with small olfactory papillæ.

The antennæ, or oars (Pl. III, fig. 2) issue with a broad
base from the sides of the head in front of the mandibles,
and consist each of a thick, cylindric scape, and two slender,

multiarticulate rami. The outer part of the scape is

20 G. O. Sars.

=

divided into numerous short articulations, the greater part
of which are clothed anteriorly with dense transverse rows
of strong spiniform bristles. The rami are nearly twice as
long as the scape, and are each divided into about 9
somewhat lamellar articulations provided posteriorly with a
number of slender, densely ciliated natatory setæ, anteriorly
with short spines. The number of setæ and spines some-
what varies in the different articulations, being on the whole
greater on the distal than on the proximal articulations.

The auterior lip (Pl. II, figs. 5,6; Pl. III, fig. 1) extends
posteriorly as an immediate continuation of the ventral sur-
face of the head, being only defined at the base by a very
slight depression. It has a convex lower face and a con-
cave upper one, and terminates in a very delicate tentacular
process, finely ciliated in its outer part. Seen from below
(Pl. II, flg. 5), it appears rather broad in its proximal part,
exhibiting at the base of the terminal process on each side
a distinctly projecting corner. Between these corners issues
from the upper face (see fig. 6) an oval, vertical lamella,
which applies itself between the maxillæ, when the lip is
bent in against the oral area. Within the body of the lip
several glandular bodies may easily be traced, as also a
number of transverse muscular bands apparently acting
upon the soft upper part of the lip, and thus assisting in
the process of swallowing.

The mandibles (see Pl. III, flg. 1) appear as a pair of
much bent bows extending on the sides of the head at its
junction with the cervical segment, and meeting below at
the oral aperture. On a closer examination (see PI. II,
fig. 7), the masticatory part is found to be defined from

the upper navicular part of the mandible by a distinct

Description of Two New Phyllopoda. 21

neck-shaped constriction and is strongly incurved, terminating
with a finely fluted, triturating surface (fig. 8).

The anterior maxille (Pl. II, fig. 9) exhibit the usual
structure, being each composed of a thick, muscular basal
part and a thin semilunar Jamella movably articulated to
its end, and fringed with a dense row of incurved, falci-
form setæ.

The posterior maxille (fig. 10) are very small and
rudimentary, forming only 2 simple conical prominences
lying somewhat outside the anterior maxille, and each
tipped with 2 very small hairs.

Of branchial legs there are 20 pairs present, the posterior
of which, however, are so very small as easily to escape
attention. In the two Japanese species, Mr, Ishikawa states
the number to be only 18 pairs, and the same number is
also given by Dr. Packard in the 2 American species, it
being regarded by him as a generic character. In the
North Australian species, however, there is quite certainly
a greater number of legs, and by repeated dissections, I
have constantly found in fully grown specimens 20 pairs,
as above stated. In structure, the legs would seem to agree
exactly with those in the other species of the genus, the
epipodites being of very large size, as compared with those |
in Limnadia and Paralimnadia. On a closer examination,
they are found successively to increase in size from the
Ist to the 7th or 8th pair, where they attain their fullest
development; from thence, they again rapidly diminish in
size backwards (see Pl. II, fig. 3; compare also PI. V, fig. 8).
The endopodite (see PI. III, figs. 4, 5) exhibits the characteristic
narrow form, and has at the base a well-developed, incurved

coxal lobe, terminating in 2 short denticles, and having

22 GRAOMSSr::

inside, an obliquely transversal row of falciform delicate
sete, outside, a longitudinal row of much coarser plumose
bristles (see fig. 6). The 5 endites are all well defined, the
3 upper ones being, however, but slightly prominent, whereas
the 4th, especially on the anterior pairs (figs. 4, 5), is
strongly produced, forming a linguiform lobe reaching almost
to the tip of the 5th endite. The latter is movably articulated
to the end of the stem, and has the form of a narrow
oblong blade edged outside with long plumous setæ. On
each of the preceding endites there is a double series of
more or less strongly curved, thin, biarticulate sete. The
exopodite is divided into a dorsal and a ventral lappet, the
latter being the larger, though in the anterior pairs not
extending quite to the tip of the endopodite. The dorsal
lappet in the Ist pair (fig. 4) is very small, whereas in the
succeeding pairs it is much more developed, though not
extending nearly to the tip of the exopodite. Fig. 1 on
Pl. IV represents a leg of the 8th pair, showing the great
development of the epipodite, which is more than twice as
long as the dorsal lappet of the exopodite, and terminates
in an acute point. In this pair, as also in those immediately
preceding and succeeding it, the ventral lappet of the
exopodite extends considerably beyond the end of the
endopodite, whereas the 4th endite of the latter has become
considerably shorter than in the anterior pairs. In the 9th
and 10th pairs (see PI. IT, fig. 2; Pl. IV, fig. 2) the dorsal
lappet of the exopodite is prolonged to a slender thread-
like lash, tapering to a fine point (fig. 2 a), and extending
upwards into the dorsal cavity of the shell, where it serves
for keeping in place the egg-mass there accumulated. Fig. 3
on Pl. IV represents a leg of the 15th pair magnified to

the same scale as the previously described legs, As shown

Deseription of Two New Phyllopoda. 23

by the figure, this leg, though scarcely half as large
as the anterior ones, exhibits quite a normal structure.
The hindmost pairs, on the other hand, successively assume
a somewhat different appearance, owing to the considerable
shortening of the endopodite, and the consequent dense crowd-
ing together of the endites. Fig. 4 represents a leg of the last
(20th) pair magnified to the same scale as the preceding figures,
and fig. 5, the same leg much more strongly magnified. It
will be seen, that the coxal lobe is still rather well developed,
whereas the endopodite itself is greatly reduced in size,
being scarcely longer than the former, though still exhibiting
all its endites. These are, however, very small and densely
crowded together, for which reason their sete are also much
less numerous than on the other pairs, and of a somewhat
different appearance, not being falciform. The exopodite
is in the form of a rather broad plate extending down-
wards and considerably beyond the endopodite. The plate
carries 9 strong, and rather distant, plumous sete, the
uppermost of which originates from a short conical process
representing the rudimentary dorsal lappet of the exopodite.
The epipodite is of inconsiderable size, and extends straight
outwards, instead of, as in the greater number of the other
legs, upwards. .

Description of the male.
(Pl. V; VI):

The shell of the only specimen examined has a length
of 51/9 mm., and is accordingly considerably smaller than
that of the female, though the specimen appears to have
attained its full size, exhibiting, as it does, the same number

of lines of growth as in adult females.

24 G. O. Sars.

In form (see Pl. V, figs. 1, 2), the shell looks exactly
like that of the female, and has the dorsal margin
curved in the very same manner, so as to be scarcely
distinguishable from that of young female specimens. It
is therefore only by examining the enclosed animal that
the sex is to be ascertained.

Fig. 3 on the same plate represents, more highly
magnified, the whole animal extracted from the shell, and
viewed from the left side. As shown by the figure, the
male character of the individual is at once revealed by the
peculiar structure of the 2 anterior pairs of legs, which
are both transformed into strong grasping organs. They also
both exhibit a very strong curvature, and are extended
somewhat apart from the other legs, being applied with
their proximal part against the lower face of the anterior
division of the body. On a closer examination, some
other well-marked differences from the female may also be
found to exist.

Thus, the rostral expansion of the head (fig. 4) is of
a very different appearance, being produced to a rather
prominent, triangularly pointed projection.

The antennule (ibid. and fig. 5) are much more fully
developed than in the female, equalling the head in length.
In the specimen examined, they were extended straight
behind between the bases of the 2 anterior pairs of legs,
whereas in the female they are, as a rule, found pointing
downwards. As, however, these limbs are to a certain
extent movable, their direction may, in the living animal,
admit of being changed. The lobules of the terminal part
appear much more sharply defined than in the female, and
are very densely clothed with olfactory papillæ (see fig. 6).

They are about 9 in number, and between them, faint

Deseription of Two New Phyllopoda. 25

transverse lines may be traced crossing the stem, thus
indicating a slight articulation of the antennulæ.

The oars and oral parts do not exhibit any essential
differences from those parts in the female.

The 2 anterior pairs of legs (Pl. VI, figs. 1, 2, 5) are,
on the other hand, as above stated, of a very different
appearance. They are both very powerfully built, and
constructed in essentially the same manner, both having
their anterior face strongly curved. On the proximal
division of these legs, can be distinguished the same parts
as in the female, viz., inside at the base, a well-developed
coxal lobe, below which there are 2 or 3 rudimentary
endites, outside, the vesicular, upwards-pointing epipodite
and the exopodite, of which, however, only the dorsal and
ventral lappets are distinct, whereas the median part is
confluent with the stem. The distal division of the legs,
which is connected to the proximal one by a rather movable
articulation, is transformed into a rather complicated, sub-
chelate hand of a somewhat quadrangular shape, having
inside, about in the middle, a slight prominence (see figs,
4 and 6). At the end inside, the hand is produced to an
obtuse, thumb-like projection, against which the strongly
curved terminal claw admits of being impinged. To this
projection is appended a small oval lamella extending
towards the claw, and from the base of the latter another
very delicate, subeylindric appendage is seen to issue,
extending downwards. Of these parts, the claw would
seem to represent the modified 5th endite, whereas the
thumb may answer to the 4th endite in the female. The claw
is articulated to the hand by a rather broad base, to the
inner side of which a very strong muscle is seen to pass,

with its fibres spread in a fan-like manner within the

26 G. O. Sars.

hand. It is suddenly bent inwards, with the outer part
somewhat tumefied and armed, at the place where it comes
in contact with the thumb, with a number of small tubercles
(see fig. 7). From its tip issues a small, stalked sucking-
dise, as in Paralimnadia stanleyana. The thumb is armed
on the obtusely rounded tip with a dense crowd of incurved
denticles, extending for some distance on its posterior face;
and between them issue a number of stiff bristles curved
inwards. The lamella appended to the :humb is likewise edged
with bristles, which, however, are rather small and less densely
crowded together. The sub-apical appendage issuing at
the base of the claw, is generally extended in the axis of
the leg, and consists of 2 joints the ‘st of which carries
at the end inside, a few small spines. The distal joint is
of a very delicate structure, and somewhat claviform (see
fig. 3), terminating in 2 unequal lobular expansions densely
clothed with delicate papille of a similar kind to those
found on the antennulæ. This appendage, which is undoubt-
edly of sensory significance, is, on the 1st pair of legs (figs.
1, 2, 4), about as long as the hand, whereas on the 2nd
pair (figs. 5, 6) it is much more fully developed, being
almost twice as long.

The 3rd pair of legs (fig. 8) only differ from those in
the female in the fact of the 4th endite carrying on the
tip a slender, cylindric appendage of a similar structure to
that of the sub-apical appendage on the 2 anterior pairs,
though here only composed of a single joint. Also on the
4th pair there is a slight rudiment of such an appendage
(see fig. 9).

The succeeding pairs are of exactly the same appearance
as in the female, except that the dorsal lappet of the

exopodite in the 9th and 10th pairs is not prolonged in a

Description of Two New Phyllopoda AT

thread-like manner, but is of the very same appearance as in
the other legs.

The caudal part (see Pl. V, fig. 3) does not exhibit
any essential difference from that in the female, either in

form or armature.

Inner Organs.

Though I have not had an opportunity of examining
the present Phyllopod in a living state, yet it has been
possible to study rather well the chief inner organs in situ
by rendering the body sufficiently pellucid in an artificial
manner. This is best accomplished by transferring the body
to oil of cloves, after it has been previously immerged
in absolute alcohol, and very slightly stained with some
colouring matter (hæmatoryline or carmine) The body
may then be examined, either at once, or after having been
mounted in Canada balsam.

The intestine (see Pl. II, fig. 3; Pl. V, fig. 3) forms
a cylindric tube extending through the axis of the body,
and terminating in the caudal part with a short muscular
rectum, that opens out between the caudal claws. Its
anterior part, in the region of the adductor muscle of the
shell, is suddenly bent downwards, and, immediately in
front of the mandibles, joins the short esophagus, which
passes straight forwards from the oral orifice. Within the
head, a complicated secretory apparatus is contained, appended
to the foremost part of the intestine. This apparatus (see
PI. III, fig. 1; Pl. V, fig. 4), which is generally regarded
as a kind of liver, consists of 2 symmetrical halves, each
debouching by a short duct into the intestine somewhat
laterally. The greater part of the organ occurs in the

3 — Archiv for Math. og Naturv. B. XVIII No. 8.
Trykt den 9de Oktober 1896.

28 G. O. Sars.

dorsal part of the head, forming there a large rounded
mass, obtecting as a cap the foremost part of the
intestine, and consisting of numerous irregular, twisted
ceca, Inferiorly, a distinct lateral branch is sent off from
each organ, extending to the ventral surface of the head in
front of the anterior lip, where it subdivides into a number
of rounded lobules. This apparatus is also constructed in
essentially the same manner in the European Limnadia
lenticularts.

The heart (see Pl. II, fig. 3; Pl. V, fig. 3) likewise
agrees rather closely in structure with that in the above-
mentioned Phyllopod, forming a comparatively short tube
confined to the foremost part of the trunk, and extending
within the hind part of the cervical segment. It is some-
what wider in front than behind, and exhibits 4 pairs of
distinct venous ostia.

Of the nervous system, the part occurring within the
head is not difficult to observe (see Pl. III, fig. 1; Pl. V,
fig. 4). The supra-æsophageal, or cephalic ganglion appears,
in a lateral view of the animal, as an opaque, somewhat
quadrangular body lying immediately behind the ocellus.
It is composed of 2 symmetrical halves confluent in the
middle, and sends off in front 2 juxtaposed, very strong
and elongated nerve-stems, the optic nerves, which each
expand at the end into a claviform optic ganglion. From
this ganglion, numerous fine nerye-fibres are seen to originate,
entering the eyes and joining the several visual elements.
Inferiorly the cephalic ganglion is produced on each side to
a conical prominence, from the tip of which issue the
nerves for the antennule. Just behind these prominences the
great esophageal commissures are sent off, and from the

anterior part of these commissures the strong nerves for

ke

Deseription of Two New Phyllopoda. 29

me

the oars originate. The ventral ganglion chain can only

be observed by dissection, and would seem to agree perfectly
with that in Limnadia, consisting of 2 long, juxtaposed
nerve-stems, which in each segment form a very slight
ganglionic swelling, and are connected at that place by a
double transversal commissure.

The ovaries (see Pl. II, fig. 3) may be faintly traced
through the integuments as 2 somewhat irregularly twisted
tubes extending throughout the trunk on the sides of the
intestine, each sending off ventrally a short oviduct, which
debouches at the base of the 11th pair of legs. By dis-
section parts of the ovary can be isolated and submitted
to a closer examination (Pl. IV, fig. 6), It is then found
that, as in Limnadia, the ova are developed within
follicles springing from the surface of the ovarial tubes.
Such egg-follicles occur on the same ovary in all stages of
development from very small subeylindrie lobules to rather
large globular bodies. In all the follicles 4 cells are
combined (see figs. 7, 8), of which only the distal one
represents the true ovum, whereas the other 2 are so-called
nutritive cells. The latter become at last wholly absorbed
by the true egg-cell, which rapidly increases in size and
becomes filled with an opaque granular yolk-mass. The ripe
ova, when poured off from the ovarial tubes, are accumu-
lated within the dorsal part of the shell-cavity, form-
ing there an irregular mass (see Pl. II, fig. 1, 2). They
are comparatively small and of a rounded form, each being
provided with a rather firm shell or capsule. On a closer
examination, this shell exhibits (see Pl. IV, fig. 10) a very
uneven surface, being divided into depressed hexagonal
facets, the angles of which protrude as pointed projections.
When rendered pellucid by the aid of oil of cloves (fig. 9),

30 G. O. Sars.

each egg-capsule is seen to contain in the centre a com-
paratively small, perfectly globular body, surrounded by a
very delicate pellucid membrane, This is the egg proper,
which is accordingly of very small size, but little exceeding
half the diameter of the egg-capsule itself.

The testes occupy the same place as the ovaries, and
are also of a rather similar form. The follicles, however,
(see Pl. V, fig. 7) are of a more uniform size, and as it
were irregularly twisted. They each contain a cavity,
which is in communication with the central hollow, and
from their inner walls the spermatic elements are developed
in the form of simple small cellular bodies. I have not
been enabled by dissection to state at which places the
vasa deferentia debouch; but in the specimen examined
there was found (see Pl. V, fig. 3) externally, on each side
of the body, just above the bases of the 9th, 10th and 11th
pairs of legs, an opaque granular mass, which had much the
appearance of being coagulated sperm, which might have
been recently poured off from the body. This induces me
to believe, that the sexual openings in the male occur at
the very same places, where they are found in the female,
viz., at the bases of the 11th pair of legs.

Occurrence.—Of this beautiful form a rather large
number of specimens were collected by Mr. Knut Dahl on
the 3rd November, 1894, from a shallow pool on Mount
Showbridge, in the neighbourhood of Port Darwin, North
Australia, By far the greater number of the specimens were
of the female sex, indeed I only succeeded in detecting
among them a single male specimen, the one here described.
This would seem to indicate, that the present form may

at times propagate in a parthenogenetical manner,

Description of Two New Phyllopoda. og

Explanation of the Plates.

AL 16

Streptocephalus Archeri, G. O. Sars.

Fig. 1, Adult, ovigerous female, drawn from life; dorsal

Fig.

wo bo

kr

NS oa

view; magnified 18 diameters.

Same exhibited from left side.

Head with eyes, antennulæ and antennæ; front
view.

Outer part of a leg of Ist pair; magnified 52
diameters.

. Leg of 4th pair; magnified 52 diameters.

Leg of last (11th) pair; magnified 52 diameters.
8, 9. Three different views of an ovum extracted

from the marsupium.

PIET
Eulimnadia Dahli, G. O. Sars.

. Adult, ovigerous female, seen from left side; magni-

fied 14 diameters.

G. O. Sars.

w bo

Ov =

8.

10.

co m

Same, dorsal view.

Another specimen, in which the left valve has
been removed, in order to show the animal more
distinctly; lateral view; magnified 18 diameters,
Left antennula; magnified 48 diameters,

Anterior lip, seen from below; magnified 48 dia-
meters.

Same, exhibited from left side.

Left mandible, seen from the anterior side; magni-
fied 48 diameters.

Lower extremity of same, with the molar surface,
more highly magnified.

(not numbered in the plate) Maxilla of Ist pair;
magnified 48 diameters.

(do.) Maxilla of 2nd pair.

Jeli, JOUE

Eulimnadia Dahli, G. ©. Sars.
(continued).

. Head of female, with part of the cervical segment,

viewed from left side (oars omitted); magnified 35
diameters,

Left oar; magnified 35 diameters.

Tail with the adjoining part of the trunk, seen
from left side; magnified 35 diameters. —

Leg of Ist pair; magnified 48 diameters.

Leg of 2nd pair; magnified 48 diameters.

Coxal lobe isolated; magnified 88 diameters.

>»

»

>»

DD
te

Description of Two New Phyllopoda.

D te

Wo)

10.

Bl IVs
Eulimnadia Dahli, G. O. Sars.

(continued).

Leg of 8th pair; magnified 48 diameters.

Leg of 10th pair; magnified 48 diameters.

a. Extremity of the thread-like upper lappet of the

exopodite from same leg, more highly magnified.
Leg of 15th pair; magnified 48 diameters.

Leg of last (20th) pair; magnified 43 diameters
Same leg, magnified 170 diameters.

Part of an ovary, showing egg-follicles in different
stages of development; magnified 155 diameters.

8. Two egg-follieles isolated, somewhat more highly
magnified.

An ovum, taken from the shell-cavity, and rendered
pellucid, so as to show the central yolk-mass:
magnified 88 diameters.

Another ovum, viewed as an opaque object; magni-

fied SS diameters,

PV:
Eulimnadia Dahli, G. O. Sars.

(continued),

Adult male, viewed from left side; magnified 14
diameters,

Shell of same, seen from below, with the valves
opened; magnified 14 diameters.

Animal, extracted from the shell, and viewed from

left side; magnified 22 diameters,

34 G 0. Sars. — Description of Two New Phyllopoda.
» 4. Head, with adjoining part of the cervical segment,
viewed from left side (oars omitted); magnified
35 diameters.
» 5. Left antennula; magnified 48 diameters.
» 6. One of the papilligerous lobules of same, more
highly magnified.
» 7, Part of one of the testes; magnified 155 diameters.
PI. VI.
Eulimnadia Dahli, G. O. Sars (male).
(continued).
Fig. 1. Left leg of Ist pair, seen from the outer side;
magnified 48 diameters.
» 2. Same leg, seen from the anterior face, and fully
extended. |
» 9. Distal joint of the sub-apical appendage from same
leg; magnified 88 diameters.
» 4. Hand of same leg; magnified 56 diameters.
» 5. Left leg of 2nd pair, viewed from the outer side;
magnified 48 diameters.
6. Hand of same leg; magnified 56 diameters.
» 7. Terminal claw, more highly magnified.
» 8. Leg of 3rd pair; magnified 48 diameters.

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7026 ARCHIV

ATHENATIK OG NATURVIDENSKAR

UDGIVET
AF

AMUND HELLAND, SOPHUS LIE, G. 0. SARS og $. TORUP

ATTENDE BIND, FØRSTE HEFTE

KRISTIANIA
ALB. CAMMERMEYERS FORLAG

LARS SWANSTRØM

JUNI 1896.

BERGENS MUSEUM

Prisbelønning

af

Henrik Sundts legat

til fremme af naturvidenskabelige undersøgelser.

Legatets fundats bestemmer bl. a.: «Af renterne ud-
redes hvert tredie aar en prisbelønning, bestaaende af 500 kr.
for et videnskabeligt arbeide over kemisk fysiologi. Ved-
kommende arbeide maa være forfattet af en norsk eller 7
Norge bosat videnskabsmand og efter udstedt opfordring til
konkurrance i manuskript være indsendt til museets direk-
tion, som enten selv kan overtage bedømmelsen eller ud-
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samme. Det arbeide, som findes værdigt til at erholde pris-
belønningen, udgives med tilhørende illustrationer paa be-
kostning af legatets renter.»

I henhold hertil opfordres norske eller i Norge hosatte
videnskabsmænd til inden 1ste september 1898 at indsende
til bestyrelsen for Bergens museum saadanne arbeider,
der kan komme i betragtning ved den anden uddeling
af denne prisbelønning Saatremt noget af de indkomne
arbeider findes værdigt til at prisbelønnes, finder ud-
delingen sted d. 17de november samme aar.

Afhandlingerne kan være affattede paa et af de nordiske

sprog, paa engelsk, tysk eller fransk, og skal være forsynede
med et motto, samt ledsagede af forseglet brev, betegnet med
samme motto og indeholdende forfatterens navn og adresse.

Bergens museum d. iste januar 1896.

G. A. Hansen.

Brunchorst.

Bind XVIII Hefte 1.

Indhold.

Nr. 1. Om Directionens analytiske Betegning

Af Caspar Wessel . . . . . . . Side 1—69
» 2. Development of Estheria Packardi
AGO Sa SSG ye EET

Archiv for Mathematik og Naturvidenskab udkommer med
1 bind (4 hefter) aarlig. Subskribtionsprisen er 8 kr. pr. bind.

Alb. Cammermeyers Forlag

(Lars Swanstrøm).

BERGENS MUSEUM

- Stipendier

Joach. Frieles og Henrik Sundts legater.

Af Bergens Museums ovennævnte legatmidler kan et
beløb af indtil 2000 kr. uddeles som stipendier til inden-
landske reiser i naturvidenskabeligt øiemed.

Stipendierne uddeles med forpligtelse for vedkommende
til at afgive til museet, hvad dette maatte tiltrænge af det
indsamlede materiale, og at indsende til museet til offentlig-
gjørelse eventuelle beretninger om de ved reisen indvundne
videnskabelige resultater.

Ansøgninger om disse stipendier kan indsendes til
museets bestyrelse inden iste april dette aar.

Bergens museum d. 25de januar 1896.

G. Armauer Hansen.

Brunchorst.

7026 ARCHIV

FOR

MATHEMATIK OG NATURVIDENSKAR

UDGIVET

AF

| AMUND HELLAND, SOPHUS LIE, G. 0. SARS og $. TORUP

| ATTENDE BIND. ANDET HEFTE. —

KRISTIANIA
ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

JULI 1896

ME >

Fe

Bind XVIII Hefte 2.

Indhold.

Nr. 3. On Fresh-water Entomostraca
Af G. ©. Sars
» 4. Skilbotn.

Af Peter Annæus Øyen
Archiv for Mathematik og I dn udkommer med

1 bind (4 hefter) aarlig. Subskribtionsprisen er kr. 8 pr. bind.

Side 1—81

y LES

Alb. Cammermeyers Forlag så

(Lars Swanstrøm).

BERGENS MUSEU M

Prisbelonning

af

Henrik Sundts lecat

til fremme af naturvidenskabelige undersøgelser.

Legatets fundats bestemmer bl. a.: «Af renterne ud-
redes hvert tredie aar en prisbelønning, bestaaende af 500 kr.
for et videnskabeligt arbeide over kemisk fysiologi. Ved-
kommende arbeide maa være forfattet af en norsk eller x
Norge bosat videnskabsmand og efter udstedt opfordring til
konkurrance 7 manuskript være indsendt til museets direk-
tion, som enten selv kan overtage bedømmelsen eller ud-
nævne en komité af tre kompetente mænd til at foretage
samme. Det arbeide; som findes værdigt til at erholde pris-
belønningen, udgives med tilhørende illustrationer paa be-
kostning af legatets renter.»

I henhold hertil opfordres norske eller i Norge bosatte
videnskabsmænd til inden 1ste september 1898 at indsende
til bestyrelsen for Bergens museum saadanne arbeider, der
kan komme i betragtning ved den anden uddeliug af denne
prisbelønning. Saatremt noget af de indkomne arbeider
findes værdigt, til at prisbelønnes, finder uddelingen sted
d. 17de november samme aar.

Afhandlingerne kan være affattede paa et af de nordiske
sprog, paa engelsk, tysk eller fransk, og skal være forsynede
med et motto, samt ledsagede af forseglet brev, betegnet med
samme motto og indeholdende forfatterens navn og adresse.

Bergens museum d. 1ste Januar 1896.

G. Å. Hansen.

Brunchorst.

DEC 4 1896

FOR

MATHEMATIK OG NATURVIDENSKAB

UDGIVET
AF

- AMUND HELLAND, SOPHUS LIE, G. 0. SARS og 5. TORUP

ATTENDE BIND. TREDIE HEFTE.

KRISTIANIA
ALB. CAMMERMEYERS FORLAG

LARS SWANSTRØM

OKTBR. 1896

Bind XVIII. Hefte 3.

Indhold.

Nr. 5. Strandlinjer i Gudbrandsdalen.

Af Peter Annæus Øyen . . . . . . Side 1—20
» 6. Møærker efter istiden.
Arda Rekstad ra ML Se VEERE
7. On Stenocypris Chevreuxi.
MAG ONS ARS NS SSØ ERE

Archiy for Mathematik og Naturvidenskab udkommer med.

1 bind (4 hefter) aarlig. Subskribtionsprisen er kr. 8 pr. bind.

Alb. Cammermeyers Forlag

(Lars Swanstrøm).

&

DEC 4 1896

7026 ARCHIV

—F= m

FOR

MATHEMATIN OG NATURVIDENSKAN

UDGIVET
AF

AMUND HELLAND, SOPHUS LIE, G. 0. SARS og 5. TORUP

ATTENDE BIND. FJERDE HEFTE. —

KRISTIANIA
ALB. CAMMERMEYERS FORLAG
LARS SWANSTRØM

OKTBR. 1896

|

Bind XVIII. Hefte 4.

Indhold.

GE Q

Nr. 8. Description of Two New Phyllopoda.
AE GGSES 2 7. aes a) ee
Arehiv for Mathematik og Naturvidenskab udkommer med.
1 bind (4 hefter) aarlig. Subskribtionsprisen er kr. S pr. bind.

Alb. Cammermeyers Forlag

-— {Lars Swanstrøm).

ÿ Å E =
N > -
> x Få
=
ak :
Er ; 2

"ei ei =
: i a
å Ele)

å 0
‘ a
\ 14

på
ey

===
==