-
begl(cee Unmet yt Sajak _(w@+pyy , @+pyy(e+ Py? _ a
= { 1 Tp? ae a err De af {1 Tee + [2}°(4/? ihe i (73)
1 2 2 2 | las
Jp) tm + Jpn) [141 = zUa(a oat) | [2] [4 aren ol enen es a oe ; : . (74).
E,(iz)E,( targa ay Fe—aln tA = Salts pete
pL he — 2 Te Miaalinsen (18)
and a similar form for 2". (Cf. Proc. Lond. Math. Soc., series 2, vol. iii.)
1 yr” .
me) pF RA | 2 Vea ee ae
2(1+p*) .. +p") - (tp)... +p") ora 7A
2 [27 +1]! } (76)
< a [40+ 2] Pane
aa
(Cf. Proc. Edin. Math. Soc., Theorem of LomMst, vol. xxii.)
It is plain that great numbers of such theorems may be found and expressed in
various forms by means of the transformations belonging to H,(«)-, but the examples”
given above will suffice to illustrate the notation.
( 409 )
XVIII.—On Pennella balenoptere: a Crustacean, parasitic on a Finner Whale,
Balznoptera musculus. By Sir William Turner, K.C.B., D.C.L., F.R.S. (With
Four Plates.)
(Read February 6, MS. received February 8, 1905, Issued separately May 26, 1905.)
CONTENTS.
INTRODUCTION . A - : ; : . 409 REPRODUCTIVE ORGANS A ; . : . 424
EXTERNAL CHARACTERS OF THE FEMALE . eA) THe Mae . 5 5 ‘ : ‘ A « AIBAT
CHITINOUS ENVELOPE . 5 : . : 5 othe! CoMPARISON WITH OTHER SPECIES ‘ < . 428
STRUCTURE OF Heap . ; P : F . 414 CONCHODERMA . i : 3 F 4 . 430
ALIMENTARY CANAL . ; F ‘ : . 419 BIBLIOGRAPHY . : ‘ ; 3 ; ~ 4oil
Nervous SystrEmM 3 ‘ ‘ ake _ Abe) EXPLANATION OF PLATES . ‘ é : _ AB?
PENNATE APPENDAGES F i : A AS
INTRODUCTION.
In September 1903 I received a bottle containing twelve specimens of a large
parasite presented to me by Mr Cur. Casrperc, the manager of a Norwegian whaling
company which has established a fishing station at Ronasvoe in the north of Shetland.*
In his letters Mr Casrzere stated that the parasites were attached to a Finner whale,
which, from its size, the mottled character of the whalebone and the pointed head, was
obviously a Razorback—Balznoptera musculus. The parasites were numerous, and were
fixed to the back of the whale, and the attached end penetrated through the skin into
the blubber. Although Mr Casrpere had seen many hundred whales, this is the first
occasion on which he had met with this form of parasite.
From the characters of the specimens I concluded that they were a giant species
of a parasitic Crustacean, of the family Lernzidz, and on further investigation I
associated them with the genus Pennella (Oken).
This genus is now regarded as including those members of the Lernzeidze which, as
studied in the females, have the head stunted and club-shaped, with horn-like arms
radiating from its base ; the body elongated, cylindriform, not bent into a sigmoid shape ;
the anterior part of the body attenuated, but widening further back; a pair of genital
openings with depending ova strings; the terminal part of the body caudate, giving
origin to the characteristic bristle-like pennate appendages ; pairs of minute rudimentary
feet springing from the ventral surface of the body close to the base of the head.
From the time of Aristotle, naturalists had recognised that the Tunny and Swordfish
were infested by worm-like parasites, fastened to the skin near the fin. RoNnDELETIUs,
* I am indebted to my valued correspondent, Mr THomas ANDERSON, merchant, of Hillswick, Shetland, for
putting me into communication with Mr CasTBERG.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 18). 61
410 SIR WILLIAM TURNER
GESNER and SALVIANUS, in their respective treatises, written in the sixteenth century,
described such parasites, and RoNDELETIUS and GxESNER figured specimens from the
tunny.
Boccone published in 1674 an account of parasites found on the swordfish, Xiphias,
implanted in its flesh, which he named Sangsue or ‘“‘ Hirudo cauda utrinque pinnata,”
and he gave a figure. It would seem as if this animal was different from that described
by RonpeLerius and Gesnrr. Boccone had figured a very interesting object, named
by him a “ poux” or “ pediculus,” as big as a pea, attached to the ventral surface of the
parasite, immediately in front of the genital openings. He stated that it was fixed as
firmly to the parasite as a limpet was to a rock. I am disposed to regard this so-called
‘“pediculus” as the male of the female parasite to which it was attached. Its small size
compared with that. of the female, and its position and attachment close to the genital
openings, corresponded with that of the male of the parasitic crustacean, Chondra-
canthus lophii, described and figured by Dr H..S. Witson and myself in 1862.
Linnaus, in the Systema Nature, 1758, classed amongst the Vermes Zoophyta the —
genus Pennatula or Sea Pens, and he named the parasite described by Boccons, which
infests Xiphias, Pennatula filosa. In 1759 J. L. OpHELIus contributed to the Amam-
tates Academice of Linna&vs, a dissertation entitled ‘‘Chinensia Lagerstromiana,’* —
in which he gave the characters of Pennatula sagitta (p. 257, and fig. 13), a parasite
infesting Lophius histrio, the sea-bat of the China Sea. Joun ELuis reproduced in
1764 Bocconr’s figure of P. filosa and OpHELIUS’S figure of P. sagitta. In 1802
Ho.ren recognised a parasite on the flying fish, Hxocetus volitans, which he named —
P. exoceti, specimens of which, burrowing into the abdominal cavity of that fish, have
been recently described, 1901, by Mr ANDREW Scort.
OKEN classed the Lernzeidze amongst the Mollusca, removed these parasites from the
Sea Pens, Pennatula, and placed them in a distinct genus, Pennella, whilst
Dr BLaInvILLE suggested Lerneopenna as the generic name. CuviER and naturalists —
generally had adopted Oxen’s term, though some preferred the spelling Penedla.
Additional species were discovered from time to time. CHAMIsso and HyYSENHARDT —
described Penella diodontis from the branchizee of Drodontis mola, captured in the —
Pacific; DEKkay named P. sagitta as adhering to Diodon pilosus, and von NorpDMANN,
in his description of P. sagitta from Lophius marmoratus, thought that it and DmKay’s
specimen were the same species. ANGuS found a parasite on a species of Coryphena —
near the gills, which Wit11am Bairp named Penella pustulosa. Mitne HpwWaRDs —
stated that Pennella sultana had been found in the mouth of Carenx ascensorwus.
SreENstRUP and LUTKEN gave an account of 2. varians which infested a “ Dolphin,” —
the species of which was not determined. E. Percrvat Wricur described Pennella
orthagorisct from specimens obtained from Orthagoriscus mola caught in Cork har-—
bour in 1869. They were implanted in the skin on either side of the dorsal fin, and the
total length of the parasite from the head to the anal opening was 7 inches. He
* Named after the Swedish Councillor, Magnus LagerstROM.
ON PENNELLA BALAINOPTERA:. All
also stated that Batrp referred a Pennella from a sunfish captured in Cornwall to
P. filosa. G. M. THomson gave an account (1889) of a Pennella found on a swordfish
(Histiophorus herscheli), which he named P. histiophori. Ramsay H. Traquarr has
called my attention to two specimens of Pennella in the Collection of the Royal Scottish
Museum, which he had provisionally named P. orthagorisci. Possibly they may have been
included in the Natural History Museum of the University, which was transferred many
years ago to the Royal Scottish Museum, but nothing definite is known of the animal
on which they were parasitic, or when they were obtained. One specimen was deprived
of the head and arms; the other had a head and two lateral arms, but no dorsal arm,
and it was about 5 inches long.*
Observations on the Lerneidee during the first quarter of the last century induced
naturalists to consider that these parasites were not to be regarded as Worms, Molluscs,
or Zoophytes, but that they had an affinity to the Crustacea. Their position was
finally adjusted in 1832 by ALExanDER von NorpMaANN, who, from the young having
the non-parasitic character of Cyclops, from the segmented structure of the male, which
is a free swimming animal, though it may become attached to the female, and from the
position and characters of the feet, definitely placed these curious animals amongst the
Crustacea, in which they are now generally regarded by naturalists as forming a family
of parasitic Copepoda.
An important extension of our knowledge of the hosts to which different species of
Pennella may become attached was made when it was ascertained that specimens had
been obtained imbedded in the skin of species of whales frequenting the North Atlantic
Ocean. STEENSTRUP and LirKEN published in 1861 a memoir in which a Pennella was
described as attached to a Hyperoodon rostratus captured in 1855 south of the
Faroe Islands ; they named the parasite Pennella crassicornis. They referred to an
observation made some years previously by von Dtpen that a Pennella, species not
named, had been obtained from a Finner whale. In 1866 G. O. Sars stated that
Specimens of a Pennella with the head buried in the blubber were seen attached
to Balenoptera musculus. In 1877 Koren and Dantgtssen published a memoir on a
Pennella found on Balenoptera rostrata, and preserved in the museum at Bergen,
which they had named Pennella balenoptere twenty years previously. Other
specimens from B. rostrata, buried with the head and horn-like arms in the blubber in
the vicinity of the external organs of generation, had subsequently been added to this
museum. VaN BENEDEN, in his memoirs on the natural history of the Cetacea, referred to
these Balzenopterze as serving as hosts for a Pennella; and he further stated, though
without giving very definite authorities, that this parasitic crustacean had also been
found on Balenoptera sibbaldi, and probably on B. borealis.
* Dr Traquair showed at the meeting of the Royal Society at which this memoir was read two dried
specimens of Pennella exocexti, which he had received in November 1904 from Captain Parmr. It appears that when
Captain Pater was on a voyage in the South Pacific a flying fish flew on to the ship ; and deeply rooted in the wall of
its abdomen, behind the pectoral,fin, were the two specimens of Pennella, which he removed and sent to the Royal
Scottish Museum.
412 SIR WILLIAM TURNER
As the memoir of Koren and DANIELSSEN contains a description of the external
characters with observations on the internal anatomy of the female Pennella —
balenoptere, and is illustrated by a plate with nine figures, I have made a careful
comparison of my specimens with their description and drawings.
EXTERNAL CHARACTERS OF THE FEMALE.
As the specimens in my possession, like those studied by Koren and DanteLssEn,
were not uniform in length, | have measured the longest and the shortest in order to
show the variation, and in the following table I have recorded their chief dimensions,
alongside of the corresponding measurements of two of the specimens described by the
Norwegian naturalists.
K. & D. TURNER.
A. B. AS B.
Whole length of parasite : : : 320 mm. 300 294 mm. 206
Length of head ; (3) 6 By ait 4
Breadth of head : : 3 8 on 7 Btn 4
Longest horn-like arm k ; : loom = 33 i 20
Greatest thickness of arm . : : 2 1 2 301 3
Length of thoracico-abdominal part . . 315 1 294 289 1 202 7
Greatest thickness of same : : 6 on 6 45 on 4
Length of pennated abdominal part . : 45 1 42 30 nn 25
It is obvious from these measurements that the females varied considerably in
length ; and as my shortest specimen had a pair of long ova strings attached to the
ventral surface, it may be assumed to be adult equally with the longest. It will be
noticed that neither of the two specimens is so long as the shortest of those recorded by
Koren and DanigtssEN, whilst their longest specimen was 320 mm. (12% inches), —
P. balenopterz is therefore a giant amongst the Copepoda.
The head, both in length and breadth, slightly smaller than in their examples, had :
a stunted, club-shaped appearance. Its colour, that of the arms and of the upper part
of the so-called thoracic region, was brownish-yellow, whilst the lower part of that
region and the entire extent of the abdomen was of a dark purplish hue with a shade
of green, even after the specimens had been for several months in spirit. The head,
arms, and upper part of the thorax were imbedded in the skin and blubber, on the
juices in which the parasite lived. The greenish-purple-tinted part of the body floated
in the sea-water, and was more or less in contact with the skin of the whale. Seen
through the medium of the water, it would approximate to the colour of the skin, and
would furnish an example of protective mimicry.
The summit of the head was studded with numerous shallow, papilla-like tubercles ;
they also surrounded the cleft-like opening of the mouth, which formed a deep
mesial groove extending for a small distance on the ventral surface of the head. A
short groove was present on the dorsal surface, which had, at its upper end, a blunt,
hook-like tubercle at each margin, but in no instance did I see a pair of pointed, claw-
ON PENNELLA BALZINOPTERZ. 413
like antennee, relics of the free Cyclops stage of development, such as are represented
by Koren and DantexssEn in their figure 9, tab. xvi.
From the base of the head three horn-like arms arose, which extended almost
horizontally outwards ; they were the anchors of attachment implanted in the blubber
of the whale. One sprang from the mesial dorsal surface, whilst the others were right
and left lateral. They varied in length in the same specimen, and the dorsal arm was
usually the shortest. They differed also in thickness and were irregular on the surface ;
the free end was blunt (Plate I. figs. 1, 2), and in one specimen a lateral arm was
bifurcated.
The body of the parasite extended from the base of attachment of the arms to the
free end of the pennated portion. It varied materially in thickness in different parts
of its length. Immediately below the arms its transverse diameter was 3 to 4 mm. ;
it was somewhat flattened on both dorsal and ventral surfaces, and on the ventral
surface, close to the mesial line, most of the specimens showed pairs of appendages.
They were so minute as to be scarcely visible to the naked eye. In two specimens
four pairs were seen, as had been figured by Koren and Dantutssen. In others, two
pairs, or even a single pair, only were recognised, and in a few they were not visible.
Their recognition was assisted by the presence of a spot of dark pigment. Four is
without doubt the typical number of these feet-like appendages, though it would seem
as if this number was not always preserved in the process of transformation from the
embryonic cyclopoid form to their retrograde condition in the adult (Plate I. fig. 2).
Hight mm. from the base of the arms the transverse diameter of the body diminished
to 1°5 mm., and fora considerable distance it preserved this diameter ; it was cylindrical
in shape, smooth on the surface, and not unlike in form and colour a steel knitting-
needle. It was an elongated neck-like division of the body, very characteristic of the
parasite, and may be regarded as the thoracic segment.
The body was prolonged into the abdomen, which increased in bulk, measured
4 mm. in breadth, lost its smooth appearance, and was marked by numerous transverse
constrictions, between which minute bead-like projections were arranged in rows.
The abdomen was the widest and most deeply coloured part of the body; as it con-
tained both alimentary canal and the female genital organs, it may appropriately be
named the genito-abdominal segment. At the lower end two genital openings were
seen on the ventral surface, from which depended the pair of ova strings. Immediately
above these openings was a small rounded eminence, to which probably the male
parasite may attach itself when engaged in impregnation.
The ova strings were a pair of very slender threads, yellowish-brown in colour, and
of remarkable length ; in one parasite each string measured 400 mm. (15°7 in.). They
floated free in the surrounding medium; they were sometimes almost straight, but at
others they had an undulating character.
The terminal part of the body was prolonged behind the genital openings from 25
to 30 mm., varying in the different specimens ; it was only 2 mm. in transverse diameter
414 SIR WILLIAM TURNER
and came toa free end. It had a caudate appearance ; but as it contained the intestinal
end of the alimentary canal, it should be regarded as the caudate segment of the
abdomen. ‘The anal orifice was situated in a cleft at its free end. Its dorsal surface
was marked by transverse constrictions, and from its ventral surface a number of
bristle-like structures arose, which gave to the terminal part of the body the pennate
character which has decided the generic name.
CuHITINous Coat.
The chitinous coat of the parasite was translucent, firm, and so tough as to turn
the edge of the razor. It was for the most part homogeneous throughout its substance,
but in places delicate lines, parallel to each other and to the plane of the surface, gave —
it a laminated appearance, as if it had been formed by superposition of layers. It
varied in thickness in different regions, as was seen both in longitudinal and transverse
sections. In the head, this coat was about 4rd of a mm. thick, but at the origin of the ©
arms it was about $rds of a mm. In the arm itself the thickness varied in different parts.
In proximity to the head it formed about 3rds of the diameter of a transverse section, in
the middle of the arm about 4rd, and near the free end about 4. In the attenuated —
thoracic region the proportion was about 4, in the genito-abdominal part it was less,
and it was a little thinner on the ventral than on the dorsal aspect. In the pennated —
abdomino-caudate segment it represented about 4rd of the transverse diameter of the
parasite.
On the outer surface of the chitinous envelope a layer of cuticle was present, which
was usually closely adherent to the chitin, but in places it was partially detached, and
had probably been drawn off in cuttimg the sections. When examined microscopically
it was seen to be striated in a direction perpendicular to the plane of the surface ;
higher magnification showed this appearance to be due to short columnar cells, which
were arranged parallel to each other. In sections where the displaced cuticle had been
turned over so as to expose its free surface, the broader ends of the columnar cells
were seen to be at that surface, and by their close apposition to each other to forma —
continuous layer.
The chitinous wall was lined by a membrane, which in various localities, to be sub- —
sequently referred to, was richly pigmented (figs. 17, 24, 26).
In the papilla-like tubercles, in the parts of the head not occupied by the mnie
in the thickened part of the body immediately below the head and in the arms,
an areolated tissue was situated within the membranous lining of the wall of chitin.
STRUCTURE OF THE Heap.
The internal structure of the head was examined in a series of transverse and
longitudinal sections from its summit to the base of attachment of the arms, The
ON PENNELLA BALZINOPTERZA. 415
papilla-like tubercles formed the most marked feature of the summit. Hach had
a definite chitinous envelope, which inclosed an areolated tissue, the areole of
which varied materially in size, and corresponded in character with the tissue in
the axis of the arms to be subsequently described.
Within the tuberculated summit numerous transversely striped muscular fibres occu-
pied a large proportion of the space dorsally and laterally closed by the chitinous
envelope. They arose from the inner surface of the envelope, which in transverse sec-
tion had a ridge and furrow-like character. The muscular fibres in this region situated
laterally to the mesial plane converged from their origin and seemed to end in
a common tendon, which was attached to the papilla-like tubercles situated on the
side of the cleft which formed the oral aperture (figs. 5, 7, 8). Their apparent
function was to draw the sides of the cleft asunder, widen the aperture, and by
successive contractions and relaxations to convert the cleft into a suctorial mouth.
In transverse sections of the head below the tubercles the muscular fibres were
less numerous; those situated in proximity to the mesial plane converged on the
dorsal wall of the alimentary canal, on which they could act directly as dilators.
The fibres situated further from the mesial plane reached the dorsal aspect of a
pair of bodies, to be immediately described, which stained readily with carmine.
The striped muscular fibres were seen as low down as the origin of the arms,
but they were absent immediately below these appendages, and their place was to
a large extent taken by the areolated tissue.
I have more than once referred to a tissue, which I have named ‘ areolated,’ situated
in the head, in the part of the body immediately below the head, and in the arms
into which it was prolonged at their base of attachment. In a subsequent section I
shall have to call attention to a similar tissue in the abdomen. Koren and
DantEtssEeN described a layer of adipose matter, in most places not very thick,
though it could form isolated fatty agglomerations; in the head, arms and the upper
thoracic division of the body it formed a thick stuffing, and corresponded in its
position to the areolated tissue seen in my specimens: the adipose tissue was composed
of fat cells, which, they say, had one or more ramifications on the cell.
In its general characters the areolated tissue consisted of a meshwork of connective
tissue, continuous with the membranous lining of the chitinous wall of the parasite.
In the strands of this meshwork, more especially in its peripheral part, nucleated
cells were seen in places in considerable numbers, which in size and general
appearance were not unlike leucocytes. The areole of the meshwork varied in
size, the largest being just visible to the naked eye, whilst the smallest required
a magnification of two hundred to three hundred diameters. In specimens taken
from the head, when the tissue was teased with needles and examined in glycerine,
| the areolze were seen to contain rounded or ovoid cells, which, like fat cells, refracted
the light strongly, and showed the characteristic reaction of fat with osmic acid ;
in the act of teasing, many of the fat cells were ruptured and oil globules escaped. In
416 SIR WILLIAM TURNER
sections through the head and arms, which had been treated with nitric acid in
order to soften the chitin previous to making the section, subsequently soaked in
alcohol, and then mounted in Canada balsam, the tissue was modified in appearance.
Although some of the cells retained the ovoid form and to some extent the refracting
character, the majority had more or less irregular outlines, and their contents had
generally the appearance of a granular cell-plasm, not usually staining strongly
with carmine; though sometimes the granules were relatively large, and stained
more deeply with carmine, as if they had a nuclear character. It would seem
as if, with the disappearance of the fat, the cell-plasm had come into view.
In certain localities the areolated tissue showed characters deserving of more
detailed notice. In the arms, where they adjoined the head and where the areolated
tissue was small in proportion to the thickness of the arm, two large areole, each
containing granular cell-plasm with a nucleus, were very distinct (fig. 11). About
the middle of the arm, also, a pair of areolee, containing granular cell-plasm, similar in
size and in close relation to the wall, were present; but as the areolated tissue in this —
part of the arm was much more abundant than near the head, a cluster of large areole
also occupied the central area of the tissue (fig. 12). A somewhat similar appearance
was seen in the relatively smaller amount of this tissue near the tip of the arm.
In some sections the areolated tissue in the arms was modified in a peculiar
manner. Whilst in some of the areole the refracting character of fat cells was dis-
tinctive, many others, especially those of large size, were crowded with nuclei, which
stained deeply with carmine. ‘The nuclei were so closely set that the amount of cell-
plasm associated with each nucleus was extremely small, and the latter dominated in
quantity and distinctness over the cell-plasm. It seemed as if an extensive proliferation
of the nuclei had taken place (fig. 18).
In sections through the head in proximity to the arms, where the areolated
tissue was relatively abundant, the largest areolee with their contained cells occupied
the mid-area of the tissue, whilst the smaller areola formed its peripheral part (fig. 9).
The tissue which constituted the axis of the papilla-like tubercles of the head con-
sisted of the smaller type of areole, though they were not uniform in size, as some
were four or five times larger than others.
It should be noted that the part of the parasite immediately below the arms
had on the ventral surface the pairs of limb-like appendages already referred to.
They were so extremely rudimentary that it was difficult to recognise them with the
naked eye, and sometimes even they were absent. It is within this part of the body
that the areolated tissue was most abundant. Had the limbs been functionally active,
one cannot doubt but that an adequate amount of striped muscle would have been
developed in this region as their motor apparatus ; but, under the changed conditions,
it was no longer required, and its place had been taken by a passive, areolated tissue
containing fat cells.
In addition to the cesophagus, the muscular fibres, and the areolated tissue, the
ON PENNELLA BALZINOPTERZ. A417
chitinous wall of the head inclosed three objects
a pair placed laterally, which
were readily coloured by carmine (fig. 8, g), and one placed mesially next the ventral
surface, which did not take the carmine dye (fig. 8, V).
The red stained bodies were recognised in sections through the head as high
as the sides of the oral chink, and were obviously nerve ganglia. At their upper
end they were separated from each other by the mesial oral chink, the tubercles
connected with its walls and the areolated tissue associated with the tubercles.
Hach was placed close to the common tendon of attachment of the bundle of striped
muscular fibres already described on each side of the head. In the upper part of
a ganglion not more than six to twelve characteristic cells could be seen in the
plane of section, but opposite the lower end of the oral chink the ganglion increased
in size and the cells were much more numerous. Immediately below the oral cleft
the ganglia were relatively large, and were situated partly to the side of the cesophagus
and partly ventrally to it, but they were not continuous with each other on the
ventral surface, as they were separated by the mid-ventral object which did not
take the carmine stain. The ganglia were traced in successive sections as far as
opposite the origins of the arms, but they were not visible in the sections immediately
below the arms, where their place was occupied by areolated tissue. It was noticed
that where each ganglion had a wide transverse diameter, it was not unusual for the
cells in its centre to show signs of disintegration; and sometimes this was so ex-
tensive that a cavity had formed, the wall of which was irregular and showed no sign
of a lining membrane (fig. 8, 9, 9).
When examined under a high magnifying power the structure of the ganglion cells
was readily recognised. The nuclei were large and oval in shape, and as they stained
a deep red with carmine, they were very distinct, and an intranuclear network of
fibrillee was present in them. The cell-plasm was granulated. The best-marked cells
were considerably larger than the motor cells in the lumbar enlargement of the human
spinal cord, though others were very much smaller. The bodies of the cells were
polygonal, and from the angles delicate processes of the cell-plasm projected. As a
rule, the cells were closely aggregated, and it was difficult to trace these processes for
any distance, but they were sufliciently distinct to leave no doubt of the multipolar
character of the cells. In places minute intercellular intervals were visible, and the
outlines of the cells were defined by a distinct wall. Although the relative proportion
of the nucleus to the cell-plasm varied in the cells, it was evident that in the largest
cells the cell-plasm exceeded three or even four times in quantity the size of
the nucleus (fig. 15).
From the character of the cells there can, I think, be no doubt that the red stained
bodies were a pair of nerve ganglia. Their position in the head, their relation to its
ventral surface and to the cesophagus, localise them as cesophageal ganglia, situated
laterally and ventrally to the gullet, though not united to each other on the ventral
aspect of the cesophagus. When portions of these ganglia were removed, teased with
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 18). 62
418 SIR WILLIAM TURNER
needles, and stained with picrocarmine, delicate fibres were seen to lie between the cells
and to emerge from the ganglia, which, from their association with the nerve cells,
were obviously nerve fibres. Some were non-medullated ; others, again, apparently
contained a medullary substance, which had aggregated into little clumps within
the neurilemma.
The mid-ventral object above referred to, when examined in relatively thick sections
and under low magnification, seemed to be a solid cord-like body, lying mesially in the
long axis of the head. It was situated between the ventral aspect of the ali-
mentary canal and the inner surface of the ventral chitinous wall of the head.
In longitudinal sections it was traced as high as the muscles of the head, the fibres of
which arched above it, from their origin from the envelope of chitin to the side of the
oral cleft. Its transverse diameter was greater than the antero-posterior, and it was
bounded by a distinct capsule of fibrous tissue, which gave it a definite outline and
differentiated it from the surrounding structures. The cesophageal ganglia were in
relation to its sides, and in places even encroached on its ventral surface, and their
upper ends were in the same transverse plane as the upper limit of its investing capsule.
Below the ganglia it was bounded by the areolated tissue which was so abundant at
and immediately below the arms. From its position it might have been taken for an
axial nerve cord associated with the cesophageal ganglia, but no fibres could be
detected in it, and it did not stain with carmine (fig. 8, V).
When thin sections were examined with a Zeiss lens x 250 the capsule was seen to be
lined by a layer of rounded cells ; in favourable sections they formed a continuous lining,
but not unfrequently they were arranged in patches, separated by intervals. The cells
were much smaller than the nuclei of the nerve cells in the adjoining ganglia, they were
nucleated, and the cell-plasm was dimly granular. The material generally inclosed by
the capsule had a eranular character, and, as a rule, showed no trace of structure, and
was possibly a coagulated substance. Sometimes, however, nucleated cells of great
translucency were interspersed in the granular material, and fatty-looking globules were
occasionally present.
In sections through the body of the parasite in the thoracic segment the corre-—
sponding arrangement, interposed between the alimentary canal and the ventral
wall of chitin, was the ventral mesial space, so that the mid-ventral object above
described was obviously a prolongation upwards into the head of the ventral space
of the ccelom.
In some of the transverse sections through the parasite made a little above the
attachment of the arms a special appearance was seen. It consisted in the presence
of a band or column of chitin, almost circular in outline, lying in relation to the dorsal
space and interposed between the cesophagus and the inner surface of the dorsal wall
of the chitinous envelope, and apparently quite independent of it. It was difficult to
give a satisfactory explanation of the part which the band played in the economy of
the parasite (figs. 8, 10, Ch).
ON PENNELLA BALAINOPTERZ. 419
ALIMENTARY CANAL.
The canal extended in a direct line from mouth to anus, and had no convolutions in
any part of its course. ‘The oral cleft passed deeply into the substance of the ventral
surface of the head, and was continued at its lower part into a relatively wide cesophagus,
down which a bristle could readily be passed.
In transverse sections through the upper part of the cesophagus, the diameter from
side to side was seen to be much greater than in the dorsi-ventral direction, and the
opposite walls were almost in contact. The ventral wall of the canal was in close rela-
tion with the capsule of the mid-ventral space of the ccelom, which lay between it and
the chitinous wall of the head, the dorsal wall was in relation to the musculature of the
head, and the sides were in contact with the cesophageal ganglia (fig. 8).
In the lower part of the head, where the muscular fibres were replaced by areolated
tissue, the dorsal wall of the canal was separated from the chitinous envelope by the
dorsal space, which contained a granulated material, possibly a coagulum. The space
was bounded by a fibrous membrane, which was lined by nucleated cells, though
frequently they were in patches and did not form a continuous layer. These cells were
about the size of leucocytes, and not unlike them in appearance. The muscular wall of
the alimentary canal was attached to the areolated tissue at its sides by bands, formed
of connective tissue and non-striped muscle, which constituted short lateral mesenteries ;
between these bands were narrow channels, in which blood or other nutritive fluid may
have circulated.
Transverse sections through the body immediately below the arms showed the
alimentary canal in the axis of the section, with a space in relation to both its dorsal
and ventral surfaces. The lumen of the canal was not so compressed dorsi-ventrally as
in the head. Well-marked areolated tissue surrounded the canal with its dorsal and
ventral spaces, and closely packed the whole area between them and the inner surface of
the chitinous wall (fic. 9). As it ethciently supported the canal, the lateral mesenteries
were short and their fibres were continued into the meshwork of the areole, which
again was continuous with the membrane lining the inner surface of the wall. A few
scattered pigment cells were seen in this membrane, though not nearly so abundant
as lower down in the thoracic segment of the body.
In sections through the attenuated thoracic segment the areolated tissue was
no longer present, and the space inclosed by the chitmous wall was occupied by the
alimentary canal and the dorsal and ventral spaces. The canal was in the axis of the
section and was reniform in shape; its lateral angles were in such close relation to the
lining membrane of the chitin that the mesenteries were practically absent (fig. 16). The
dorsal and ventral spaces were proportionally large, almost equal in size, and were situ-
ated between the lining membrane and the corresponding wall of the alimentary canal.
Hach space was inclosed by a definite wall of fibrous membrane, the inner surface of
which was lined by a layer of nucleated cells; the cell-plasm in some was granular
420 SIR WILLIAM TURNER
in character, though in others it was more translucent. The spaces were frequently
devoid of contents, though in some sections irregular fragments, granular in appearance
and possibly a coagulated substance, were present. The dorsal and ventral spaces, not
only in relation to this, but to other divisions of the alimentary canal, formed the
ccelom or body cavity. Koren and DaNnIELssEN named the dorsal space the dorsal
canal, and stated that during life it was full of red thinly-flowing blood.
The chitinous wall was lined by a definite membrane, in which was a layer a large
stellate cells, full of a rich purplish-black pigment.
The alimentary canal and the associated spaces retained the characters just described
as far down the body as where the attenuated thoracic part was continued into the
genito-abdominal segment, in which the chitinous wall also possessed a lining
membrane with large richly-pigmented cells. The alimentary canal was in the axis
of the segment, and its transverse section was almost round, and so capacious that it
may properly be regarded as the stomach. ach lateral aspect was attached to the
adjoiing pigmented membrane by a mesentery. The dorsal and ventral spaces were
relatively small. Between the canal and the sides of the chitinous wall the upper ends
of the two ovaries were situated (fig. 17).
Somewhat lower in the genito-abdominal segment the alimentary canal had a
reniform outline in transverse section. In proximity to the genital orifices it was
compressed dorsi-ventrally, and the opposite walls were almost in contact. In some
sections the canal gave origin at a lateral angle to one and occasionally more diverticular
prolongations, the lumen in which was continuous with that of the canal (figs. 20, 21,
22). At its lateral angles the wall of the canal was attached to the pigmented lining
of the chitinous wall by fibres, apparently non-striped muscle, which formed lateral
mesenteries, and the fibres formed a loose network, in the meshes of which, as well as in
the interspaces of the pigmented membrane, were nucleated cells, some scattered, others
in clusters, many of which resembled leucocytes, though others were elongated, caudate,
and stellate, not unlike the corpuscles of connective tissue.
In the genito-abdominal segment, in relation to the lateral mesenteries and to the
sides of the dorsal space, the areolated tissue was present in abundance, and the cells in
the areolze were distinctly fatty; the pigment of the pigmented lining membrane was
prolonged into the strands of the meshwork, and caused them to contrast strongly with
the light-refracting contents of the fat cells which they surrounded (figs. 25, 26, 27).
In the terminal caudate segment of the abdomen the intestinal division of the
canal had a similar compressed appearance; the wall of chitin was lied by a
membrane associated with characteristic pigment cells; lateral mesenteries and
adipose areolated tissue corresponded with the arrangement described in the
genito-abdominal segment (fig. 32).
In the genito-abdominal and terminal segments the dorsal and ventral spaces
were well marked, and the dorsal was much more capacious than the ventral. The
membrane which bounded them was lined by a layer of cells, sometimes continuous,
ON PENNELLA BALZANOPTER. 42]
though at others in patches, similar in character to those previously described in
the spaces of the thoracic segment, whilst the contents consisted of an indefinite
granulated, possibly a coagulated, material. The existence of these spaces in front
of and behind the alimentary canal permits an expansion of the walls and an
increase in the size of the lumen when the animal is feeding, and their greater
size in the lower end of the intestine leads one to infer that the ejecta accumulate
in it prior to expulsion.
Two coats were readily recognised in the alimentary canal in its entire length
—a muscular and a mucous. In favourable sections an intermediate sub-mucous
coat was seen. The muscular coat consisted of the usual non-striped form of fibre
an external longitudinal and an internal circular or trans-
aitanged in two layers
verse. In the abdominal and caudate divisions this coat was thickened, and had
a crenulated appearance in the sections. When sections were made either longitudi-
nally or obliquely through the canal, to enable one to obtain a view of the free
surface of the mucous membrane, numerous slender, closely-set rugee, lying parallel
to each other, were seen to extend longitudinally along its surface (fig. 6). In trans-
verse sections they were cut across, and they then had the appearance of villous
processes projecting into the lumen. It was observed in these sections that the
sub-mucous coat formed the core of the projections, whilst the free surface was
formed of the mucosa; obviously, therefore, they were not true villi, but were
permanent rugze, like the circular valvule conniventes in the small intestine of the
mammalia. At the lower end of the canal the rugze were more elongated and
thicker than in the thoracic segment of the body. The mucous membrane was
covered by a layer of epithelium, the cells of which in favourable specimens were
seen to be short columns. In longitudinal or oblique sections through the canal
in which the inner surface of the mucous membrane could be seen, the broader
ends of the cells were recognised as forming the free surface of the mucosa. The
lumen of the intestine contained epithelial and other débris.
In proximity to the anus the intestine and the structures around it were specially
modified. A short distance above the anus the intestine in transverse section was flask-
shaped, the stalk of which was attached to the dorsal wall of chitin by a narrow mesial
dorsal mesentery, composed of non-striped muscle, which divided the dorsal space into
_ two lateral halves. The ventral space had not at first a corresponding division. In
addition, muscular fibres on each side passed from the chitinous wall to the sides of the
intestine : these fibres had the form of striped muscle, but were not definitely striated.
The wall of chitin was lined by a strongly pigmented membrane, in which numerous
leucocyte cells were seen, either scattered or in groups. The proper muscular wall of
the intestine was thicker than in the upper part of the caudate segment, and the
parallel ridges of the mucous membrane were closely set together.
A little nearer the anus the section through the intestine was ellipsoidal, with the
long axis directed dorsi-ventrally. The ventral space was now divided into two lateral
422 SIR WILLIAM TURNER
halves by a broad mesial mesentery formed of non-striped muscle. The walls of the
dorsal and ventral spaces were lined by cells like those previously described. Strong
striated muscles were situated laterally to the intestine; they arose from the wall of
chitin, and were inserted by tendinous bands into the wall of the gut. Processes
of the highly pigmented lining membrane passed between bundles of these fibres, and
differentiated them into distinct muscles.
At the anus itself the dorsal and ventral spaces were scarcely to be recognised ; the
lumen of the intestine was small and laterally compressed. The submucous coat was
greatly thickened aud the mucous membrane showed no parallel ridges. The lateral
striped muscles were well marked. ‘The dorsal and ventral mesial bands of non-striped
muscle were prolonged on to the sides of the intestine, external to its proper coat, and
were arranged in an ellipse. At and near therefore the anal orifice the intestine was —
provided with transversely striped muscles, situated laterally, which acted as dilators ;
and with non-striped muscular fibres, distinct from the proper muscular coat, which
formed a sphincter muscle (fig. 19).
No specially differentiated VascuLar SysTEM was recognised, and no structures
that could be regarded as heart, blood- or lymph-vessels. The dorsal and ventral —
spaces associated with the alimentary canal, and the intervals between the bundles
of fibres of the mesenteries and of the lining membrane of the chitinous wall,
provided channels for the distribution of a nutritive fluid.
Nervous System.
In the section on the structure of the head I have described the pair of
cesophageal ganglia, which, from their size, constituted the most important divisions —
of the nervous system. Their relation and structure having already been narrated,
it is unnecessary to repeat them; but it may be stated that the position of the —
ganglia enabled them readily to supply nerve fibres to the wall of the cesophagus —
and to the striped muscular fibres, which formed important constituent parts of
the head. Associated with the ganglia was a relatively large nervous cord, composed
of numbers of delicate nerve fibres.
In transverse sections through the elongated thoracic segment clusters of cells —
were seen at intervals in close relation to the pigmented lining membrane of the —
ventral part of the wall of chitin and to the ventral space. The cells coloured —
readily with carmine, and the nuclei stained deeply and were relatively large. In
some sections at least one process could be seen to arise from the cell body; in
others a process arose from opposite aspects of the cell body, and the cells appeared
to be fusiform or bipolar; other cells, again, were multipolar, and with delicate
processes extending for a recognisable distance. In one specimen a process could
be traced so far undivided as to be obviously the axon of the cell. Hach cluster
of cells formed a small nerve ganglion, the cells in which were smaller than in
ON PENNELLA BALZANOPTERZ. 423
the cesophageal ganglia. From cells of this character being seen so frequently
in the transverse sections, it was clear that a chain of ganglia extended longitudinally
along the ventral aspect of the thoracic segment of the parasite, immediately internal
to the chitinous envelope, and that from the ganglia nerves could readily be
distributed to the wall of the adjoining parts of the alimentary canal.
In transverse sections through the genito-abdominal segment collections of cells
were seen immediately internal to the pigmented lining of the ventral part of the wall
of chitin. They were arranged in a crescentic row, which followed the curvature of the
wall, and the concavity of the crescent was directed towards the cement ducts, but was
separated from them by a definite interval. The cells were nucleated, the cell-plasm
was granulated, and two or three times greater in amount than the nucleus, which,
again, was as big or even somewhat larger than the leucocytes, so abundant in the
lateral mesenteries of the alimentary canal. Some of the cells were globular, others
were elongated and rounded at the ends; occasionally I saw a multipolar cell, or one
with a single pole, and frequently the cells were fusiform, with attenuated poles. From
the position of the groups of cells in relation to the ventral wall of the parasite, and
from their size and general character, | am of opinion that they form the abdominal
chain of the nervous axis, and are engaged in the innervation of the organs contained
in the genito-abdominal segment.
In many of the sections a cell was situated beyond the termination of each horn of the
erescent, which was greatly elongated, and its outer pole was prolonged as far as the
wall of the cement duct, which protruded a pointed process to meet it. In some
sections I observed that this pole bifurcated, and its limbs embraced and were prolonged
into the wall of the cement duct. This cell was placed at the side of the ventral space
and seemed to be in its wall.
PENNATE APPENDAGES.
These appendages, which constituted one of the most characteristic features of the
genus, grew from the ventral surface of the terminal caudate segment of the abdomen,
whilst an occasional one sprang from the sides of the genito-abdominal segment near
the genital openings. They formed a closely-set brush-like arrangement, the bristles
of which varied in length and projected from 4 to 7 mm. from the base of their
attachment, which was continuous with the wall of the segment, and had the character
of a papillary outgrowth of the wall. Branches arose from the stunted basal papille,
and these almost immediately again divided, so that from six to ten secondary branches
might proceed from a common stem. Lach branch had a pigmented core, inclosed in a
translucent wall of chitin (Pl. I. fig. 4).
In sections made through the caudate segment the knife sometimes passed through
the chitinous wall at the spot where the base of a papilla sprang from it (fig. 18).
The chitin of the segment was prolonged into the wall of the bristles, and the
pigmented membrane lining the wall of the segment was continued directly into their
424 . SIR WILLIAM TURNER
axis, and thence into the branches. In transverse sections through the bristles the |
pigmented core was frequently partially or wholly divided into two portions, which
were either close together, or were partially fused and formed a dumbbell-like figure.
REPRODUCTIVE ORGANS.
Koren and DANIELSSEN, in their account of Pennella balenoptere, figured a dis-
section of the genito-abdominal segment. They described as present in it a pair of
ovaries with oviducts, a pair of cement glands with excretion canals, the latter of
which were nearer to the ventral surface than the oviducts, and two short canals. No ;
mention is made of the receptacula, and the ova strings were wanting in most of
their specimens.
Ovaries.—The ovaries were situated in the upper part of the genito-abdominal
segment. At and near its junction with the thoracic segment, where the alimentary
canal was dilated, and the dorsal and ventral spaces were relatively small, short lengths
of a divided tube were seen in transverse sections to occupy a relatively large region on
each side of the canal, dorsal to the lateral mesentery, and laterally to the dorsal space ;
the portions of each tube were scattered in the region, and were, I believe, the upper end
of the ovary, for they were occupied by nucleated cells which resembled rudimentary
ova. The oviducts and cement ducts were not present (fig. 17).
In sections a little lower down the parts of the divided ovary were in greater lengths
and more continuous with each other, the tube was cylindriform in shape, and had
reached or almost reached the mesial plane of the parasite, so as to lie immediately
internal and parallel to the pigmented lining of the chitinous wall, but separated from
the alimentary canal by the dorsal space. The part of each tube which lay next the
wall followed its curvature. Somewhat lower down the wall of the tube next to the
dorsal space bulged into diverticula and lost its cylindriform character. Whilst each
ovary was in many sections situated entirely on its own side of the mesial plane of the
parasite, in others the inner ends of the tubes from the opposite sides crossed the mesial
plane and slightly overlapped each other. In all these sections the oviducts and cement
ducts were present and were transversely divided (figs. 20, 21).
The wall of the tube was formed of a delicate membrane, and the lumen contained un-
fertilised ova (fig. 24). In many instances they were so closely packed together that the
outlines of the individual cells were obscure. The ova were larger and more precisely
differentiated when in proximity to the wall of the tube, which, from its surface being
slightly crenulated, and from the passage of slender processes from the membranous:
wall into the lumen, seemed to be partially divided into compartments, in each of
which an ovum was lodged. Each ovum contained a relatively large, well-defined
germinal vesicle, situated at or near the centre of the cell-plasm, and in each vesicle,
about its centre, was at least one germinal spot; not unfrequently two spots were
present, and in some instances I saw three spots in a germinal vesicle.
ON PENNELLA BALAANOPTER. 425,
Cement Glands.—The pair of cement glands were situated in the upper part of
the genito-abdominal segment. In a considerable part of their extent they were
alongside the ovaries, and corresponded in their general relations; but in some of
the transverse sections ovarian tubes were present without adjoining cement glands,
and in others portions of the cement glands were seen with no ovarian tubes in
proximity tothem. The ovaries and the cement glands were therefore not quite equal in
extent. When both were present in the same transverse section the ovaries lay across
the mesial plane, between the two cement glands, the latter of which were placed in
close relation to the dorsal surface of the lateral mesenteries. When the cement glands
alone were present they lay close to the mesial plane of the parasite, and were separated
from each other by a prolongation of the dorsal space (figs. 22, 23).
Hach cement gland consisted of a coiled tube inclosed in a membranous capsule,
from the inner surface of which fibrous processes passed between the coils of the tubes.
Lying close to the outer surface of that part of each capsule which was next the inter-
posed dorsal space, well-marked nucleated cells, which possessed one or more processes,
were seen; and as similar cells were present in the membranous wall of the space where
it was next the pigmented lining membrane of the chitinous envelope, these cells should
be regarded as belonging to the wall of the space rather than to the capsule of the
cement gland. The coiled tube of the cement gland, in making the section, had been
cut into short picces, transversely, obliquely and longitudinally. It had a well-defined
wall, which was lined by a layer of short cubical cells. The lumen of the tube con-
tained a dimly granular substance which stained with carmine and with hematoxylin.
No sign of an ovum could be seen in the tube.
Oviducts, Cement ducts, Receptacula, Ova strings.—HKach ovary and cement gland
had a characteristic duct. In the numerous transverse sections made through the
genito-abdominal segment, except at the highest part of the ovary, an oviduct and a.
cement duct were seen on each side of the mesial plane. They were placed ventrally
to the lateral mesenteries, and in relation to the sides of the ventral mesial space.
They had evidently emerged near the upper ends of their respective organs, and had
passed forward into the ventral region of the segment, down which they ran to the
receptacula. The cement duct on each side was in front of the oviduct, and was
separated from it in the upper part of their course by a slight interval. A slender
intermediate band passed from the wall of one to that of the other, and at its junction
with the cement duct the wall of that duct was much thinner than im other parts of its
circumference. Lower down in the segment the walls of the two ducts came in contact
with each other and fused together. Before their lumina became continuous with each
other, the oviduct diminished in its calibre, and the cement duct became elongated
antero-posteriorly. The intermediate part of the common wall then disappeared, and
the receptaculum was formed a little above the genital openings (figs. 20-23, 25, 26).
The ducts were readily distinguished from each other, both by their relative
position and their characters. The wall of the oviduct was much the thinner, and was.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 18). 63
426 SIR WILLIAM TURNER
generally cylindriform, though it showed in each transverse section from four to ten or —
twelve bulgings on the outer surface of its wall. In many sections each bulging
seemed to contain a nucleated cell, but under higher powers this was not so evident.
In some sections a sharp line, apparently the lining membrane of the duct, was con-
tinued round the wall, as if to shut off the bulgings with their contents from the lumen.
In others, again, the bulgings projected into the lumen, and were not shut off by a —
lining membrane. When the wall of the oviduct had fused with that of the cement
duct, a layer of nucleated cells was traced from the outer surface of one duct to
that of the other. In some transverse sections through the oviducts the lumen
contained a delicate network of fibres which radiated from the centre to the periphery.
The wall of the cement duct was several times thicker than that of the oviduct,
except at the spot where it was joined either by the intermediate band or by the
wall of the oviduct. The lumen of the cement duct, especially near its lower end,
frequently contained a plug of cement which almost filled the tube (figs. 20-23).
Receptacula,—Lach receptaculum seminis was situated at the side of the ventral
space near its anterior part. Its antero-posterior diameter was longer than the trans-
verse, and the wall lying next the ventral space was sometimes thinner, at others
thicker, than the opposite wall; the anterior part both of wall and lumen had frequently
a tortuous appearance, as if slightly convoluted, and from its lower end a short canal
arose, which ended in the genital orifice. The lumen almost invariably contained a
plug of cement, antero-posteriorly elongated like the receptaculum itself (figs. 29, 30).
Associated with the lower part of the genito-abdominal segment was a distinct
muscular arrangement, the fibres of which were transversely striped, but in: addition -
some bands belonging to the lateral mesenteries consisted of unstriped fibre. The
striped muscles arose from the chitinous wall, some bundles ventral to the mesentery,
others within its substance; they passed downwards and inwards, and in the trans-_
verse sections the fibres were usually cut through transversely or obliquely. Some
fibres were attached to the wall of the oviducts; but the greater number reache
the posterior end and outer wall of the receptacula, to which they were attached
by tendon-like structures (fig. 28). Owing to this arrangement, the wall could be
drawn outwards and the lumen of the receptaculum made larger, a condition which —
doubtless prevailed when the ova, the cement, and probably the spermatic fluid also,
passed into it.
Ova strings.—These were about the thickness of fine sewing-thread. They began
at the genital orifices and floated in the sea in which the animal lived. The outer part
of each string was formed of cement, and the space which it inclosed would have contained
the ova had they been ripe for extrusion. When examined microscopically, transverse
lines closely set together were seen to pass from one to the other side of the inclosing
cement. In my specimens I saw no ova in the ova strings. The ovarian ova were
unripe, and there was an absence of ova in the oviducts and receptacula. When
sections were made through the ova strings, the space inclosed by the cement was seen
ON PENNELLA BALANOPTERZ. A27
to contain a quantity of minute fatty particles, the products of degeneration. It
should be remembered that the parasites were taken in the autumn, after they had, in
all probability, shed a crop of ova, and before the next crop was ripe for impregnation.
THe MALE.
It is well known that in the parasitic Copepoda the male is insignificant in size
as compared with the female. In Chondracanthus and some other genera it has been
ascertained that the male is attached to the female, close to the apertures for the
ova strings. I consequently made a close examination of the ventral surface of the
body of all my specimens of Pennella, with the object of observing if a male were
present in any of them, but I failed to recognise one. Koren and DanNrIELSSEN
stated definitely in their memoir on P. balenoptere that they had not seen any
males attached to their specimens, so that the male of P. balenopterx is as yet
unknown. It would, indeed, appear that the recognition of the male in any species
of Pennella is a rare occurrence. I have stated in the introductory section that
Bocconz, so long ago as 1674, figured, firmly affixed to the Pennella, which is now
regarded as P. filosa, a small object which he spoke of as a “‘pediculus” or louse. I
have no doubt, from its relative size and the place of attachment, that it was the male
of the species. Boccons, therefore, should have the credit of being the first to see and
figure a male Pennella, though he did not realise its sexual significance. In Pennella
exoceti and in P. varians the male has also been recognised and figured.
The habitat of the male Copepod, as in the case of Pennella, when not attached
to the female, is uncertain. In a species like Lernwa branchialis affixed to the gills
of the Gadidez and flounders, males have been found within the gill-chamber, some
attached independently to the branchize, others to the bodies of the females. In
P. balenopterx the females were affixed to the extensive surface of the smooth back
of a great whale, to which they had doubtless attached themselves in the Cyclops phase,
through which the female passes before she becomes adult and assumes relatively gigantic
proportions, though in many respects retrograde characters. If the males of Pennella
be provided with hooked antennz, like those found in the male Lernzea, as there is no
adjoining chamber for their lodgement, they may become directly attached to the skin
of the whale in proximity to the females, until the time arrives when they are required
to affix themselves to the females for the purpose of fertilising the ova when these are
ripe for impregnation. If the male Pennella, as is very probable, is insignificant in
size, when unattached though perhaps in close proximity to the female, it would easily
be overlooked.
In considering the question where and when the ovarian ova are impregnated
in the parasitic Copepoda, it has to be kept in mind that whilst the female is fixed to
its host, the male retains for a considerable time the character of a free swimming
Crustacean, though subsequently it affixes itselfin many of, and possibly in all, the species
428 SIR WILLIAM TURNER
to the female, close to the genital openings, with probably the power of again detaching
itself when insemination is completed. It is possible, as has been shown by ANDREW
Scorr in Lerneea, that fertilisation of the female may take place in the Cyclops stage
when she has become attached to the host. Naturalists have expressed different opinions
on the locality where the spermatic fluid comes in contact with the ova and im-
pregnates them. Some have thought that as they pass out of the genital openings —
the proximity of the male, from its attachment close to the openings, allows the sperm —
to bathe the wall of the ovum and the spermatic threads to penetrate it. This, how-
ever, is doubtful, as the sea-water in which the parasite lives would, possibly, in such a
case have washed away the sperm and impeded or prevented impregnation.
Others, again, consider that the sperm enters the genital orifices, passes into the ©
receptacula, distends them and ascends the ovarian ducts, so as to meet the ova in their
descent. It is obvious that penetration of the ovum by the sperm filaments, which is
essential to impregnation, must occur before the ovum meets with the cement and is
coated by it. This can only take place in the oviduct, for the secretion of the cement —
gland flows into the receptaculum and can envelop the ova as they enter it. The
observations recorded in this memoir show that the receptaculum and its short excretory
canal, even in the unimpregnated female, contained cement, so that the ova could have ~
been coated by it before they had passed out of the genital opening to form, along with
the cement, the ova string. It would seem, therefore, that fertilisation of the ovum 3
must occur in the oviduct. The non-attachment of males to my female specimens
should be associated with the unripe condition of the ova, and the consequent impossi-
bility of fertilisation being effected at the time when the parasites were collected.*
CoMPARISON WITH OTHER SPECIES.
A careful comparison of the characters of my specimens, with the description and
figures by Koren and DaANIELSSEN in their excellent memoir, has satisfied me of their —
identity with the species which they have named Pennella balenoptere. This species ©
therefore infests both Balenoptera musculus and B. rostrata.
I have not seen the species which StEENSTRUP and LUrKeEn described and delinearam
as found on Hyperoodon rostratus, and which they named Pennella crassicornis. —
Koren and Dantexssen, however, after comparing original specimens, considered that 4
their Pennella balenoptere was quite distinct from Pennella crassicornis, as it was half
as long again; had a broader and longer head; the horns were nearly horizontal and
very slender, whilst in Pennella crassicorms the dorsal horn was inclined almost —
perpendicularly downwards.
When compared with the species of Pennella infesting fish, P. balenoptere is very —
much longer. ODHELIUS regarded the length of P. sagitta as equal to the breadth of
* Ova which had developed to the nauplius stage were seen by H. S. Winson and myself in Chondracanthus
lophit collected in August, and in Lerneopoda dalmanni collected early in the year. See our Memoirs in Trans. B.S.
Edinburgh, 1862.
ON PENNELLA BALZAANOPTER. 429
the thumb. Drxkay’s specimen of P. sagitta was little more than half an inch long
but it is obvious from his figure that the head and arms had been torn off: the length
was probably one inch. V. Norpmann stated (Heft 2, S. 122) that P. sagitta found on
Lophius marmoratus was only ten lines long, and with the ova strings 1 inch 4 lines.
Sreenstrup and LUrKeN measured nine specimens of P. varrans and found them to
vary in length from 18 to 27°5 mm. (0°7 to 1*1 inch). These species are the most
diminutive known. Boccone stated that his specimens were usually about 4 inches
long. Bairp gave 4 inches as the length of his Penella pustulosa, CHamisso and
EYsENHARDT’S specimen P. diodontis, THomson’s P. histiophori, and also P. exoceti,
were about the same length. PrrcevaL WricHt’s specimen, P. orthagorisci, was
7 inches long.
Species differed in the number of horn-like arms which radiated from the base of the
head. In Bocconu’s figure neither head nor arms were depicted, and I am disposed
to think that they had been broken off in the process of detaching the parasite from
the Swordfish, in the flesh of which they were buried; the abdominal segment of the
body was shown to be longer than the short thoracic segment. In OpHELIUs’ figure
of P. sagitta neither head nor arms were represented, probably for the same reason.
In the Pennella sagitta described by von Norpmanny, and in P. pustulosa, diodontis,
and orthagorisci, two arms were said by their respective describers to have been present.
THomson states that P. histiophor: had two lateral arms, but projecting between them
posteriorly was a rounded protuberance ; which, without doubt, was a rudimentary dorsal
arm. P. sultana, exoceti, crassicorms; and balenoptere had each three arms. In
eighteen specimens of P. varians examined by Sreenstrup and LUTKEN, one-third
were said to have had three arms, two-thirds only two arms. The lateral arms were
constant, but the dorsal arm was variable in the same species. ‘The presence of a
dorsal arm is not therefore a constant element in the establishment of specific differ-
ences. A specific character, which is obviously of importance, is the relative length of
the thoracic and genito-abdominal segments. In P. balenopterz the thoracic was twice
the length of the conjoined genito-abdominal and caudate abdominal segments, and
nearly three times the length of the genito-abdominal segment. By way of contrast
in von Norpmann’s P. sagitta and in THomson’s P. histeophori the thoracic and genito-
abdominal segments did not seem to be distinctly differentiated from each other ;
in PercevaL Wricut’s P. orthagorisci and in P. exoceti the genito-abdominal and
thoracic segments were about equal in length, and in Cuamisso and EysENHARDT’s
P. diodontis the genito-abdominal segment was nearly twice the length of the thoracic.
Although there seems to be no doubt that P. balenoptere is a species quite distinct
from those that are parasitic on fish, it is difficult to say definitely, in the absence of
the type specimens for comparison, if all the fish-infesting forms of Pennella that
have been described by different specific names have a true claim to this distinction,
though it is, I think, probable, if a careful comparison were made, that the number of
_ So-called species would be diminished.
430 SIR WILLIAM TURNER
CoNCHODERMA.
Several naturalists have observed that species of Pennella have occasionally attached
to them animals belonging to the sub-class Cirripedia. CHamisso and HKysennarpr
seem to have been amongst, if not the first naturalists to describe a Cirriped attached
to a Pennella. In 1821 they stated that a Lernxa (Pennella) diodontis, from the
branchie of Diodontis mola, captured in the Pacific, had Lepas anatifera affixed to
it. G. O. Sars described, 1865, a Pennella, with the head buried in the blubber of
Balenoptera musculus, to which Cineras vittata (Conchoderma virgata) was attached.
Koren and DaNIELSsEN figured two specimens of Conchoderma virgata affixed close
to the genital orifices of Pennella balenopterx, and they stated that in another —
example as many as seven specimens were attached to the thin thoracic part. Paun —
Meyer saw in the collection at Naples six examples of a Pennella from Xziphias
gladius, to one of which Conchoderma mrgata was affixed: owing to the Pennella
being imperfect, the species was not determined. To one of the examples of Pennella
orthagorisct in the Royal Scottish Museum, already referred to, three specimens of —
Conchoderma virgata were cemented at or near ‘the junction of the thoracic and
abdominal segments. Also the P. exoceeti in the same museum were similarly infested.
It is interesting to note that cases have been recorded of a direct attachment of
Conchoderma to the skin of whales. Thus, CHartes Darwin, p. 66, stated that he had
seen the basal end of the peduncle of Conchoderma aurita sunk into the skin of
Cetacea. G. O. Sars had described the same species attached to the humpbacked whale, —
Megaptera boops, and a similar attachment had also been noticed by Soprus Hauras.
One of my specimens of P. balenoptere had an example of Conchoderma virgata
cemented at the junction of the thoracic and genito-abdominal segments (Plate I. fig. 3),
It is unnecessary to describe the generic characters of Conchoderma, or the specific
characters of C. virgata, as they have been so fully narrated in the classical treatise of
CHarites Darwin; but in order to identify the species, I may briefly refer to the ~
external appearance of my specimen. It measured 46 mm. (1°8 in.) in extreme length, —
15 mm. in the greatest dorsi-ventral diameter, and 15 mm. in greatest breadth. Though
the peduncle blended with the capitulum they could be differentiated, and the former
was found to be slightly longer than the latter. The dorsal carinal plate was 16 mm.
long and 3 wide, and reached the anterior end of the capitulum. The scutal plate was —
three-lobed and 7 mm. in length. The tergal plate was 5 mm. long and only 1 mm.
in width. The interval between the upper lobe of the scutum and the carina was 8 mm.,
and between the anterior lobe of the scutum and the tergum 6mm. The coat in the
intervals between the plates was not calcified, and was yellowish-grey in colour, with —
three purple bands on each side extending antero-posteriorly. The highest band on each —
side reached the dorsal border behind the carina, where it blended with its fellow. The
other bands ran independently the whole length of the animal, and did not branch, A
pair of stunted processes at the anterior end of the carina represented the pair of ear-
ON PENNELLA BALZNOPTER. 431
like appendages so characteristic of Conchoderma aurita. My specimen in general
form and characters resembled that figured by Darwin in plate iii. fig. 2, but it had
_ three, and not four, purple stripes in the mantle.
In conclusion, I would express my acknowledgments and thanks to Mr Joun
Henperson, Assistant Keeper of the University Anatomical Museum, for the aid which
he has given me in preparing the numerous sections examined in the course of my
research, and for photographing those which illustrate the internal anatomy of the
parasite, many of which have been reproduced in three of the plates.
BIBLIOGRAPHY,
Bairp, W., ‘‘On a new Species of Penella,” Annals and Magazine of Natural History, vol. xix. p. 280.
1847.
Bairp, W., “‘ Natural History of British Entomostraca,” Ray Socdety. London, 1850.
Bassert-Smiru, P. W., ‘‘ Systematic Description of Parasitic Copepoda found on Fishes,” Proc. Zool. Soc.
Lond., p. 482. 18th April 1899.
Van BeEnepen, P. J., “ Animal Parasites and Messmates.” London, 1876.
Van Benepen, P. J., “ Histoire naturelle des Balénoptéres, Mémoires couronnés et autres Mémoires,” Acad.
Roy. de Belgique, vol. xli. 1887.
De Buaryviniz, “ Mémoire sur les Lernées,” in Journal de physique, de chinvie et @histotre naturelle, vol.
xev. p. 372 and p. 437, plate. 1822.
De Buainvitte, Art. Lernea, Dict. d. Scien. Nat., vol. xxvi. p. 112. 1823.
Bocconz, “Recherches et Observations naturelles de Monsieur Lboccone, Gentilhomme Sicilien,” figure
opposite p. 284. Vingt-cinquieme Lettre. Amsterdam, 1674.
Burmeister, H., ‘ Beschreibung einiger neuen oder weniger bekannten Schmarotzerkrebse,” Nova acta
physico-medica Acad. Coes. Leop, Carol., vol. xvii. p. 269. 1835.
Cuamisso and Eysennarpt, /enella diodontis in Nova acta physico-medica Acad. Coes. Leop. Carol.,
vol. x., pl. xxiv. fig. 3, p. 350. 1821.
Cuavs, C., Elementary Teat-book of Zoology, translated by A. Sepewick and F. G. Heatucots. London,
1890.
Cuvisr, Les Pennelles. (Pennella, Oken.) Le Régne animal, vol. iii. p. 256. 1830.
Dexay, J. E., Observations on the Pennatule fléche (P. sagitta of La Marck) in the cabinet of Dr Mitchill.
Silliman’s American Journal of Science, vol. iv. p. 87. 1822.
Exuis, Joun, P. filosa and P. sagitta in Philosophical Transactions, vol. liii. fig. 16. 1763.
Gerstazcker, A., “ Crustacea Spaltfiissler,” in Bronn’s Thier-reichs, Bd. v. lst Abth. Leipzig and Heidel-
berg, 1866-1879. Figured in Tab. vii., Penella sagitta and Penella varians.
Guurin, Iconograph. Zooph., pl. ix. fig. 3, quoted by Basserr-Smiru.
Houten, Acta danica, Naturhist. Skrifter, 136, pl. iii. fig. 83. Holmie, 1802.
Koren, J., and Danietssen, D. C., “ On Pennella balenopterx,” in Fauna littoralis Norvegiz, 3rd part, plate
xvi. p. 157. Bergen, 1877.
Kroyer, H., “ Systematische Uebersicht der Schmarotzer Krebse,” Oken’s Isis, 1840, p. 702 e.s.
Linyaus, C., Systema Naturx, 10th ed., vol. i. p. 819, 1758; also a later edition, vol. i. parts vi., vii.,
pp. 3864, 3865.
Meyer, Pau, Mittheil. aus der Zoolog. Station zw Neapel, vol. i. p. 53. Leipzig, 1879.
Minyz-Epwarps, Penellus. Crustacés, vol. iii. p. 522. 1840.
. Movzsr, Acta Suecica, 1786, p. 256, P. sagitta and filosa, quoted by von Nordmann.
432 SIR WILLIAM TURNER
Norpmann, A. von, Mikrographische Reitrage zur Naturgeschichte der wirbellosen Thiere, zweites Heft.
Berlin, 1832. Penmnella sagitta, p. 121, pl. x. figs. 6, 7, 8.
OpHeE.ius, J. L., Chinensia lagerstromiana, published in a collection of Theses entitled ‘ Amoenitates
Academice of Linneus,” vol, iv. p. 257, fig. 3. Holmie, 1759. He gives a description of P. sagitta.
In the references which I have seen to this species it is made to appear as if it had been described by
Linneeus himself, and the name of his pupil Odhelius is not given,
Oxen, Lehrbuch der Naturgeschichte, 1815, part iii. Allgemeine Naturgeschichte, vol. v. part i. p. 564;
oder Thierreich, vol. ii. 2nd part. Stuttgart, 1835.
Sars, G. O., “ Beskrivelse af en ved Lofoten indbjerget Rerhval (Balenoptera musculus),” Forhandlinger 7
Videnskabs-selskabet i Christiana, p. 280. 1866.
Scorr, ANDREW, “ Lepeophtheirus and Lernea,” Memoirs of Liverpool Marine Biological Committee.
London, 1901.
Sregnstrup and LirKen, Om Slegten Pennella, in Dansk. Vid. Selsk. Skriv., vol. v. p. 408, pl. xiv. 1861.
Tuomson, G. M., “‘ Parasitic Copepoda of New Zealand,” Trans. New Zealand Inst., vol. xxi. p. 353,
pl. xxviii. fig. 2, 1889. Describes Pennella histiophort.
Turner, Wa., and Wirson, H. §., “On Chondracanthus lophit,” also “ On Lernzopoda dalmanni,” Trans.-
Roy. Soc. Hdin., vol. xxiii. p. 67, pl. iii. and p. 77, pl. iv. 1862.
Wricut, E. Percevat, “ On a new species of the Genus Pennella,” Ann. and Mag. Nat. Hist., 4th series,
vol. v. p. 43, plate i. 1870.
CoNCHODERMA.,
Darwin, C., Monograph on the sub-class Cirripedia. Part 1. The Lepadide. ay Soc. London, 1851.
Hatuas, Sopuus, Vidensk. Medd. fra den Naturhist., vol. ix. Copenhagen, 1868.
Meyer, Paut, “Carcinologische Mittheil.,” p. 53. Mittheilung. aus der Zoolog. Station zu Neapel, vol. i.
Leipzig, 1879.
Hosgx, P. P. C., “ Account of Conchoderma Virgatum, var. chelonophilus, obtained from the carapace of a
Chelone,” Challenger Reports, part xxv. p. 55, pl. ii. figs. 13-15. 1883.
Sars, G. O., Forhandling. i Vidensk, Selsk., p. 280, Christiania, 1866, also 1880.
EXPLANATION OF PLATES.
Prats I.
The drawings in this plate were made from nature by Mr James T. Murray.
Fig. 1. Pennella balenoptere seen from its ventral surface. Natural size.
Fig. 2. Head, arms, and upper part of thoracic segment, to show the four pairs of rudimentary feet-like
appendages ; enlarged.
Fig. 3. Abdomen, showing the attachment of Conchoderma virgata to the upper end of the genito-
abdominal segment. Natural size.
Fig. 4. Pennate bristles detached from the caudate abdominal segment. x10. p. 423.
Puate II.
Fig. 5. Longitudinal dorsi-ventral section through the head and upper end of the body of Pennella.
The arrangement of the striped muscles s,m. in the head, the relations of the csophagus CE. to the mid-
ventral space V., to an cesophageal ganglion g. and to the areolated tissue ar. are shown. x8. p. 419.
Fig. 6. A more highly magnified section through a part of the esophagus CZ., in which a portion of the
free surface of its mucous lining with the longitudinal folds parallel to each other, also the fibres of the non-
striped muscular wall, x.m., passing into the surrounding areolated tissue, ar., and forming mesenteries, are
shown. x14. p. 421.
ON PENNELLA BALAINOPTER. 433
Fig. 7. Transverse section through the upper part of the head. The oral cleft on the ventral surface,
the tubercles and the arrangement of the striped muscles are shown. x13. p. 415.
Fig. 8. Transverse section through the head below the oral cleft, showing the relation of the alimentary
canal A. to the midventral and dorsal spaces, the pair of cesophageal ganglia, each of which has a cavity in
the centre, and the striped muscles. Ch. marks a transversely divided column of chitin, lying in relation to
the dorsal space. x13. pp. 418, 419.
Fig. 9. Transverse section through the parasite close to the origin of the arms. The relations of the
alimentary canal with the ventral and dorsal spaces and the large amount of areolated tissue are shown.
cao. p. 416.
Fig. 10. An oblique section through the parasite at the origin of an arm, showing the relations of the
alimentary canal to the dorsal and ventral spaces, and to a mass of areolated tissue. The position of the
inner column of chitin, Ch., is also shown. x13. p. 418.
Fig. 11. Transverse section through the arm close to its origin to show the two large areole and those
of smaller size. x13. p. 416.
Fig. 12. Transverse section through the arm about its middle. x13. p. 416.
Fig. 13. Another transverse section through the arm, in which many of the areole were crowded with
nuclei, x13. p. 416.
Fig. 14. Transverse section through the body a short distance below the arms, showing the areolated
tissue which surrounded the alimentary canal and dorsal and ventral spaces. x13. p. 419.
Puate III.
Fig. 15. Section through an cesophageal ganglion, showing the nucleated nerve cells. p. 417.
Fig. 16. Transverse section through the attenuated thoracic region, showing the alimentary canal and
the dorsal and ventral spaces. x13. p. 419.
Fig. 17. Transverse section through the body at the junction of the thoracic and genito-abdominal
segments. The upper end of the pair of ovaries can be seen at the sides of the alimentary canal, the mucous
lining of which was torn off in making the section. x13. p. 420.
Fig. 18. Transverse section through the caudate abdominal segment, showing the relation of the
alimentary canal to the dorsal and ventral spaces and the origin of one of the pennate bristles. x13. p. 423.
Fig. 19. Transverse section through the intestine at the anal orifice. On each side of the gut is a pair
of large transversely striped muscles; on the ventral aspect a pair of non-striped muscles which form a
sphincter arrangement around the intestine. x50. p. 422.
Fig. 20, Transverse section through the upper part of the genito-abdominal seyment, showing the two
ovaries placed dorsally, with a cement and an oviduct on each side of the ventral space, separated from each
other by an interval ; also the alimentary canal with its foldings or diverticula. x15. p. 423.
Fig. 21. Transverse section through the same region, showing the same parts, but with a less complicated
alimentary canal, x 13.
Fig. 22. Transverse section through the upper part of the genito-abdominal segment, showing ovaries
and cement glands in the same plane, also oviducts and cement ducts. x15. p. 425.
Fig. 23, Transverse section through the genito-abdominal segment, showing the pair of cement glands
at the sides of the. dorsal space; the cement ducts and oviducts are near the ventral space: the walls of
the ducts on each side are connected by an intermediate band. The pigmented lining membrane has shrunk
away from the wall of chitin. The alimentary canal is reniform in section. x13. p. 425.
Puate IV.
Fig. 24. Section through an ovary, showing the contained ova. p. 424.
Fig. 25. Transverse section through the lower part of genito-abdominal segment, no ovaries or cement
glands, but the walls of the oviduct and cement duct on each side are in contact: bundles of striped
muscles, s.m., are also seen. x13. p. 425,
Fig. 26, A similar transverse section, showing fusion of the oviduct with the cement duct. x 13.
Fig. 27. A similar transverse section, where the two ducts on each side are blended, and form a
receptaculum, A loop-like arrangement across the mesial plane connects the two receptacula. x 13.
TRANS. ROY. SOC. EDIN. VOL. XLI. PART II. (NO. 18). 64
il
434 SIR WILLIAM TURNER ON PENNELLA BALZAANOPTERA.
Fig. 28. A transverse section a little above the genital openings. Striped muscles are attached by
distinct tendons to the outer wall of each receptaculum.
x 9.
p. 426.
Figs. 29, 30, 31. Three transverse sections in succession from above downward in proximity to the
genital openings. They show the receptacula, each containing a plug of cement. In 29 is also seen the
short canal of the receptaculum which leads to the genital opening; and in 30 the opening itself is visible
with a plug of cement protruding through it.
Fig. 32. Transverse section through the upper part of the caudate abdominal segment. The origin of a
pair of bristles is seen and the pair of ova strings lie ventrally to the segment. x 13,
Lettering of Plates II., IIL, IV., the figures in which are reproductions by Messrs M. & T. Scorr
of photographs of sections through Pennella.
A. Alimentary canal.
ar. Areolated tissue,
C. Cement gland.
c.d. 5 duct.
Ch. Chitin.
D. Dorsal space.
g. Esophageal nerve ganglion,
g.o. Genital opening.
m. Mesentery.
n.m, Non-striped sphincter muscle.
n. Nerve cells.
O. Ovary.
oa. Ova.
. Oviduct.
. C&sophagus.
. Oral cleft.
. Ova string.
. Pinnate bristles.
. Pigmented lining membrane.
. Receptaculum.
. Striped muscles.
. Tubercles.
. Ventral space.
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(4350)
XIX.—On the Histology of the Blood of the Larva of Lepidosiren paradoxa.
Part I]. Hematogenesis. By Thomas H. Bryce, M.A., M.D. (With Four Plates.)
(Read July 18, 1904; MS. received October 15, 1904. Issued separately May 6, 1905.)
INTRODUCTION.
In the first part of this memoir I described the structure of the corpuscles at a
stage of larval development when the red cells were actively dividing and the blood
contained several varieties of white cells. During the course of these more strictly
eytological observations, it was impressed upon me that the great size of the elements
and their very marked histological characters, combined with the simple character of
the organisation of the animal, made Lepidosiren a very favourable case for the study
of the first principles of Hzematogenesis. I was specially interested in what may be
termed a middle phase in the history of the blood. I refer to a period after the primi-
tive corpuscles have acquired hemoglobin and there are leucocytes present, but before
the blood-forming organs are unfolded. This stage lasts a relatively long time in
Lepidosuren up to the differentiation of the spleen, as the liver takes no part in blood-
formation at any period.
Since Bizzozero first discovered that heemoglobin-containing cells divide by mitosis,
and emitted the hypothesis that the red cells are a stirp kept up only by division, it
has been largely held that all forms of the coloured corpuscles are descendants of those
first laid down.
The admission of a non-hemoglobin-containing element into the erythrocyte series
(Lowir and Denys) only pushed back the argument from the ‘hematoblast’ of
_ Neumann to the ‘erythroblast? of Lowir. If the erythrocyte series constitutes a
“tissue ’ su generis, when does it cease to be laid down ?
We know from observations on the characters of the corpuscles at various stages of
development that in all vertebrates the elements are at first identical, but that their
characters change, and the adult corpuscles are different in character from those which
first appear. It is sometimes assumed that the adult nucleated erythrocytes of the
lower vertebrates correspond to the nucleated discs of mammals, but in the Lepidosiren
larva the erythrocyte series shows all the stages seen in the higher forms. There
are ‘erythroblasts’ without hemoglobin; ‘hzmatoblasts’ with hemoglobin; young
erythrocytes with reticular nucleus; and mature or old forms with vesicular nuclei.
All forms save the last divide by mitosis, and the last is probably only a hemoglobin
carrier like the mammalian red blood corpuscles.* Thus, though the outward form of
* Of. Laaunsse, Journal de lV Anat., T. 26, 1890.
TRANS, ROY, SOC. EDIN., VOL, XLI. PART ITI. (NO. 19). 65
436 DR THOMAS H. BRYCE ON
the elements is rather different, the essential problem is the same in both lower and
higher animals. The heterogeneity of the erythrocyte series through the whole larval
life, and the fact that all the elements except the mature erythrocyte multiply by
mitosis and after their kind, seems a presumption in favour of continued new formation.
If this were so the erythroblasts would necessarily bear a relation to some less
specialised cells. Analogous facts in other forms have led to the theory, in all its
varieties, of the origin of the red cells from the white elements.
From the theory that the vascular and lymphatic systems are formed in the
mesenchyme (ZIEGLER), whatever view may be taken of the actual channels and spaces,
it follows that the cells, fixed and free, red and white, are all homologous, having the
same parentage. Further, the theory gives room for the acceptance of continuous
formation of free cellular elements, at any rate up to the completion of histological
differentiation, and of the genetic relation in some sort between the red and white
corpuscles.
On the other hand, if the vessels arise 7 setu but the blood has a restricted local
origin in one part of the embryo from which the corpuscles are dispersed—as pointed to
by the works of Rtckerr, Rasy, Zwinck, SwaEn and BracuetT—and the sites of origin
are not also those of the germs of the connective tissue, the blood and the lymph may,
from the embryological and morphological point of view, require to be distinguished
(Ferrx, Swaen and Bracuer). The two classes of corpuscles might then belong to
two separate stirps, multiplying by division and having no mutual relationship.
The origin of the first leucocytes has not yet been demonstrated beyond doubt, but
the almost universal opinion has referred them to the mesoderm (mesenchyme). This
is ZIEGLER'S* view, and in this country it has been specially maintained by GULLAND.
They are ‘ wandering cells’ formed outside the blood stream; and as they appear at a
later stage of ontogeny than the primitive blood corpuscles, they belong to a different
category.
In recent years, however, there has been a tendency to derive the lymphoid cells
direct from the endoderm. KOLLIKER first described the epithelial cells of the thymus ~
as becoming converted into lymphoid cells; PRenant, ScuuLttzn, Maurer, NussBauM
and Prymak, and Brarpy{ have come to a similar conclusion, and the last named
claims for the gland that it is the sole source of the leucocytes.
A similar conversion of the epithelial cells of the gut into the lymphoid cells of
the intestinal glands has been described by Rerrerer, RupincER, Daviporr, and
Kraatscn, but it has been denied by Stour and Koiimann.t
In the matter of the spleen there has also been a question of the endoderm providing
the cells of its rudiment. This view has been put forward specially by Maurer and —
Kuprrer, but the older view that it is formed from the mesoderm as a mass of
* Ber, der Naturforsch. Gesellsch. zw Freiburg, Bd. iv., 1889. Verhandl. d. deutschen Zool. Gesellsch., 1892.
+ Zool. Jahrbucher Abt. f. Anat., vol. 17, 1903. For a historical account of histogenesis of thymus and references
to literature this work may be consulted.
t For critical review and references, see KonLMaNn, Archiv f. Anat., 1900.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 437
mesenchymatous cells, maintained by Lacuxrsse, has been upheld by most of the
recent workers, especially by Tonxorr, Kotumann, KerpBet, and PIpEr.*
My observations on the blood of Lepidosiren have not included the first origin of
the blood and vessels, but have been directed specially on the later phases, for the
study of which Lepidosiren presents very favourable opportunities. I have, however,
made an exhaustive examination of the blood corpuscles of all the early stages, so that
my observations extend over the whole history of the blood, from the time the first
corpuscles appear in the heart onwards. I have necessarily studied the histogenesis
of the spleen, and the development of the lymphoid tissue, so called, in the kidney,
and have made incidental observations on the thymus gland. On this last head I shall
have little to say, as [ hope soon to study the development of the gland in detail.
For the purpose of the research, I have had the opportunity, through the kindness
of my friend Professor GRAHAM Kerr, of going through the whole of the larval stages.
This has involved the exhaustive examination of more than twenty series—up to stage
No. 38 of the sequence, when the larva is already practically a small adult Lepidosvren.
I have also examined sections of the modified filamentous hind limb of the male during
the degeneration which ensues after the breeding season, when the tissues are crowded
with leucocytes.
As the result of these more extensive observations, I have not much to add in regard
to the structure of the fully evolved elements.
The erythrocytes in the adult and later larval stages have almost invariably a
vesicular nucleus, and the few corpuscles that have a nucleus with the coarse reticulum
of the earlier phases are to be regarded as young erythrocytes. ‘The equatorial band
is less distinct in the adult corpuscles, and the reticular structure of the disc is more
doubtful. The adult material is unfortunately not sufficiently well fixed to enable me
to determine whether the reticular appearance of the adult corpuscle is wholly an artifact
or not; but as the granular, irreeularly reticular appearance of the disc closely resembles
that of the reticulum of the early corpuscles in a badly fixed condition, I think it
probable that the larval and adult elements resemble one another in this respect also.
I make, however, the same reservations in regard to this structural feature as I did in
my previous communication. | find that the leucocytes of the adult and late larval
Stages present no essential differences from those of the earlier stages described in
Part I. I must add to that account, however, that I find forms with basophile granules.
The cells containing these do not differ in general character from those with eosinophile
granules, and, as in them, the granulation is either fine or coarse. I shall reserve what
I have to say on the general morphology of the leucocytes until I have described their
development.
Before proceeding to the record of my observations, I must refer to certain general
points.
_* Complete historical accounts are given by CHoronscuHiTzky, Anat. Hefte, Bd. 13, 1900; and Piper, Diss. Med.,
Freiburg, 1902. See also specially Konumann, Archiv f. Anat., 1900.
438 DR THOMAS H. BRYCE ON
A description of the external characters of the embryo and larva of Lepzdosiren and
a general account of the affinities of the animal will be found in Professor GraHam
Kerr’s original memoir in the Transactions of the Royal Society, B., vol. excii., and
an account of the early stages of development in his paper in the Quarterly Journal of
Microscopical Science, vol. xlv. part 1.
The egg is markedly telolecithal, but the segmentation is holoblastic. The ex-
cessive lading of the cells with yolk, and the consequent large dimensions of the
primitive yolk cells, impresses characters on the development remarkable in certain
respects. Among the secondary features due to this cause, the one that chiefly affects
the present study is the long postponement of the formation of the alimentary canal.
Hven at the stage numbered 31, the pharynx, gill clefts, and alimentary tract are
solid, showing in no part an epithelial disposition of the cells. As a further con-
sequence of this, the splanchnic mesenchyme is long in being differentiated. The
splanchnic mesepithelium rests on a layer of smaller yolk-laden cells, in which blood-
vessels form, but which is not separate from, or to be distinguished from, the general
mass of the yolk cells. It is only when the alimentary canal commences to be differ-
entiated that a layer of mesenchyme and a layer of definitive epithelial hypoblast cells
can be distinguished.
The general mesenchyme is differentiated much earlier. It arises, GRaHam KERR
states, for the most part by a proliferation from the mesoderm, at about the level of
the nephric rudiment, very much as in the Selachians, partly directly from the sub-
notochordal region of the hypoblast.
The history of the blood corpuscles may be divided into three phases. The first
phase extends over the period from their origin up to stage 30, when the alimentary
canal commences to be cut off. It is comcident with the laymg down of the heart and
main vessels. While the phase lasts, the corpuscles, like the rest of the tissue cells,
are laden with yolk; and though they vary much in character according to the
amount of yolk borne, are at first all of one type, though very soon two kinds are to
be distinguished.
The second phase is coincident with the formation of the alimentary canal and
the differentiation of the splanchnic mesenchyme. ‘The blood corpuscles, now free of
yolk, like all the tissue cells save the hypoblast, are heterogeneous. There are
erythroblasts, young erythrocytes in active division, and mature red cells, while,
further, there are white elements belonging to different categories. The rudiment of
the spleen appears at the beginning of this phase, and during its persistence is under-
going its histogenetic changes.
As the phase advances the erythrocytes become almost all of the mature variety,
and the third phase is initiated, during which the permanent conditions are established.
The great mass of the red cells are now mature, young corpuscles are sparsely dis-
tributed, while the erythroblasts seen here and there in the vessels are densely crowded
in the spleen pulp, and to a lesser degree in the venous sinuses of the kidney
howl
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA, 439
(mesonephros). The leucocytes, in their several varieties, are coursing in the blood
stream or wandering among the tissues, especially in the walls of the alimentary
tract; they are also crowded in the spleen and, as will afterwards be shown, along a
tract around the kidney.
Though I have thus divided the history of the blood corpuscles into three phases,
it is not to be understood that they are sharply marked off from one another, but that
they overlap and merge into one another imperceptibly.
PuasE I.
The Primitive Blood Corpuscles.
With the actual primary origin of the blood corpuscles, and the development of the
heart and vessels, this paper will not concern itself, nor will it deal with the general
question regarding the morphological relations of the blood in terms of the germ layers.
This will be dealt with by Mr Granam Kerpr himself in a future memoir.
I begin at a stage, No. 26, when the rudiment of the heart is laid down. In it there
are free cells, not to be distinguished by any of their characters from the fixed cells
forming its wall. In the middle line, below the notochord, the aorta appears like a cord
of cells, identical in general characters with the cells of the developing general mesen-
chymatous tissue. The same is true for the cardinal vein.
On the surface of the mass of yolk cells, immediately beneath the fused somatic and
splanchnic layers of mesepithelium, there are groups of free rounded cells, in spaces
which later become definite vessels (fig. 1, Pl. I.).
As I have said, I have not actually studied the origin of these various free rounded
cells, but from certain incidental observations, and from later phases of the develop-
ment of the corpuscles, I may express my belief, subject to the revision of Mr GraHam
Kerr's future researches, that the corpuscles have a multiple origin im situ from the
general mesenchyme in connection with the developing blood-vessels, and from an
irregular layer of smaller yolk-laden cells lying beneath the splanchnic mesepithelium,
on the exact provenance of which I do not wish to express an opinion. I make this
statement with every reserve, and only make it at all because of its bearing on later
stages.
The characters of the primitive blood corpuscles (figs. 1 and 2, Pl. I.) are deter-
mined by the size and number of the yolk masses in the protoplasm. In fig. 2 is
represented at one pole of the nucleus an area free of yolk, including a spot I have taken
for the centrosome, and from it, radiating among the yolk grains, there are delicate
threads of protoplasm reaching the periphery of the cell. The nucleus is rounded or
slightly oval, and sometimes shows a notch. The chromatin is collected into rounded
karyosomes, from which delicate processes ramify to join those of other karyosomes to
complete the reticulum.
Ina stage older, No. 27, the appearance of the corpuscles is considerably altered
440 . DR THOMAS H. BRYCE ON
This is due in some measure to different methods of treatment, the earlier stages being
celloidin sections stained with safranin, while these are paraffin preparations stained with
iron hematoxylin.
Two kinds of corpuscles are to be recognised. The first, evidently the direct
derivatives of the corpuscles of the previous stage, have a large round or slightly oval
body, measuring 50 « to 60 , and a round nucleus which has the same general features
as described for that of the earlier elements.
The protoplasm round the periphery of the cells has undergone a transformation
into a broad band of delicate concentric fibrils. Within this the protoplasm has a
delicate alveolar structure and contains large yolk grains, and im some corpuscles clear
vacuoles. In the particular cell drawn (fig. 3, Pl. I.) there was a homogeneous area at
one pole of the nucleus which I take to represent the centrosomal area of the earlier
corpuscles, but there is no distinct centrosome, nor is there a radial sphere. Most of
these cells are round, but a few are oval in shape (fig. 4, Pl. I.).* The cell of this
class drawn has only a few yolk grains, the alveolar disposition of the protoplasm is
distinct, and at each end of the elongated body there is a group of minute darker-
staining granules, which I interpret as the cross sections of the peripheral fibrillze of
the other cells, and which, as will appear later, in more advanced corpuscles come to
occupy this situation in profile sections.
The second kind of corpuscles are smaller cells, about 39 « in diameter (figs. 5 and
6, Pl. I). The nucleus is notched or lobed, but has otherwise the same general
characters as that of the larger corpuscles. The protoplasm is either uniformly alveolar
or vacuolated. There is a distinct sphere and centrosome, and the peripheral band is
absent.
The vacuolation of the corpuscles at this and later stages is evidently connected
with the using up of the yolk. It is seen in the general tissue cells also. The fibrillar
hand is seen only in the blood corpuscles, and is clearly the first stage in the con-
version of the primitive blood corpuscles into the passive hemoglobin carriers of later
phases.
It seems to be a fibrillar transformation of the peripheral layers of the protoplasm,
and not a mere disposition of an alveolar meshwork; and as none of the corpuscles
have yet the biconvex disc shape, it is not the mere consequence of the shape of the
cell.
While the mass of the corpuscles are thus assuming a passive role, certain remain
as free mobile elements, constituting the second type of cell described, with its
sphere and centrosome, and the lobing of its nucleus somehow associated with the
activities of the cell.
While one cannot at this stage, when there are yet no hemoglobin-bearing cells,
call these elements leucocytes, it is to be noticed that in general morphological
* Jt is probable that these are profile sections of the circular disc-shaped forms.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 441
characters they are identical with the later leucocytes. I may also remark that the
general mesenchyme cells show in certain instances all the characters of these free cells
in the blood, and that some even have definitely polymorphic nuclei.
The next three stages may be described together, as there is no marked difference in
the general characters of the blood. They are numbered 28, 29, and 30.
The large ringed corpuscles have increased greatly in number, partly by active
division, partly by new formation. That new formation is proceeding, I conclude,
because both in the earlier stages and in those now in review there are appearances in
the developing vessels under the mesepithelium over the mass of undifferentiated yolk
cells which indicate the budding off of free elements from the superficial layer of
smaller yolk-laden cells, and it seems to me probable that the opening out of the
cardinal veins in the mesenchyme round the nephric ducts is also associated with the
setting free of elements into the blood stream. ‘The enormous amount of yolk in all
the cells at this stage, and the consequent large size of the cells (each cut through, in
10 « sections, at least three times), make it very difficult, however, for one to satisfy
one’s mind regarding this.
Some of the yolk-laden blood corpuscles are at this stage of enormous dimensions.
These giant corpuscles (fig. 6, Pl. VII.) are either round or oval. The round cells are
about 60 « in diameter; the ring is very broad and distinct, enclosing the yolk grains
and vacuolated protoplasm, from which it is sharply marked off. The large oval cells
(fig. 7, Pl. I.) attain a length of 80 » to 90 4; I have met with individuals even more
than 100 win length. In the smaller célls of earlier stages, as far as | can make out,
the layer of superficial fibrillar protoplasm surrounds the greater part of the corpuscle,
but in the elongated corpuscles it is massed at the ends, z.c. at the equator of the oval
dise. The nucleus of all the corpuscles is of the ‘leucoblast’ type. It is spherical in
the great majority of these large cells, but numbers have lobed or even multiple
nuclei, and these often of very unequal size (fig. 11, Pl. I.). In the earlier stages of
these three series under consideration mitotic figures are numerous; in the later
they also occur, but less frequently, and the question arises whether the multiple
nuclei arise by direct or indirect division.
I have little doubt in referring to direct division certain cases in which the nucleus
is a regularly shaped dumb-bell, and in explaining them as antecedent stages of cells
with two equal nuclei lying side by side. In other cells of a smaller variety, to be
mentioned immediately, the nucleus is irregularly lobed, and there are sometimes
detached free portions, which must be produced by direct fragmentation. On the other
hand, certain instances may be the result of indirect division of the nucleus without
division of the yolk-laden body. The mitotic figures are not numerous enough to
enable me to obtain a complete series without much labour, so that I have not followed
this point out to a judgment. For the same reason I have been unable to determine
the relation, if any, to the multiple and unequal condition of the nuclei, of a number of
instances observed of irregular mitoses, some of which were multipolar.
4492 DR THOMAS H. BRYCE ON
Up to this stage none of the corpuscles contain heemoglobin, as I have been able to
ascertain, at least for the youngest of the series, by staining with methylene blue and
eosin ; but in the next following stage, between which and stage 30, however, there is a
small hiatus, the corpuscles contain hemoglobin, and the megalocytes have disappeared.
The giantism of the corpuscles can hardly, however, be related to the hemoglobin
formation, because there are other hemoglobin-free cells in the blood, very different
in character. These are much smaller cells, and belong to several different categories.
First, there are elements having all the characters of the later red corpuscles, except
that they have round nuclei (figs. 8 and 9, Pl. I.), which have precisely the same
characters as those of the large yolk-laden corpuscles. As all intermediate stages are
observed between these corpuscles and the large ones, there is reason for believing
that they are simply the large cells in which all the yolk is used up and the coarsely
vacuolated protoplasm has been reduced to a fine alveolar condition. To the same
category, cells with lobed nuclei like that in fig. 15, Pl. I. probably belong. On the
other hand, there are, second, still smaller elements (fig. 12, Pl. I.), with smaller rounded
nuclei. These must arise in some other way. They are found in the heart, but
perhaps more frequently in the cardinal veins and in the vitelline vessels.
The appearance represented in fig. 16, Pl. I. seems to point to one mode of formation.
A large yolk-laden cell has apparently divided unequally, the larger moiety remaining
among the yolk cells, and forming part of the layer of smaller cells still incompletely
separated from the larger yolk cells, while the smaller portion, consisting merely of a
nucleus and a small zone of yolk-free protoplasm, is budded off to become a free cell.
I have also observed one instance suggesting that a multinucleated cell is being
resolved into a number of elements; but as I have been unable to discover another, |
cannot speak definitely regarding this possible source of these small corpuscles. That
these small elements become young erythrocytes is indicated by the occurrence of such
cells as figured in figs. 13 and 14, Pl. I.
The first change in the conversion is the appearance of a delicate layer of fibrille
in the protoplasm, forming an ill-defined rig when the corpuscle is seen on the flat,
and showing as the group of apparent granules in profile view (fig. 14, Pl. L.).
Third, still another type of free cell also occurs (fig. 17, Pl. I.) in which the
nucleus is polymorphic. The protoplasm is exceedingly homogeneous, and shows only
very indistinctly any reticular or alveolar disposition, while there is an exquisite radial
sphere and large single centrosome. These cells occur very rarely. They are in
general aspect the same as the elements of an earlier stage (fig. 10, Pl. I.). I have
said above that these latter possibly represented the earliest mobile stage of the blood
cells, or that they were the earliest representatives of the free mobile white corpuscles.
I have little hesitation in naming such a corpuscle at this stage an early leucocyte,
both from its characters and because it is arising from the district of the potential
mesenchyme, in which, in the next phase, the leucocytes begin to appear in large
numbers.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 4438
Passe II.
As already stated, the alimentary tract up to stage 30 is represented by a solid
mass of heavily yolk-laden cells, which can only be distinguished into central large
and peripheral smaller cells. In no part is there any epithelial disposition of these
primitive hypoblast cells. Immediately after this stage the gut begins to be cut off
from the mass of yolk cells, at first as a solid cord with a palisade grouping of its
cells. This cutting off of the alimentary tract is associated with the differentiation of
a layer of splanchnic mesenchyme round it. I am not here concerned with the details
of the process, nor with its general significance, but only with its special significance
regarding the history of the blood. The only point I desire to state is that the
splanchnic mesenchyme of that part of the alimentary tract from the pharynx to the
region in which, later, the pancreas rudiment lies, is laid down as a direct derivative of
the layer of smaller yolk-laden cells which seem simultaneously converted into the
definitive hypoblast and the mesenchyme. The two layers are at first absolutely
continuous, the line of demarcation being indicated only by the retention in the
hypoblast for a longer period of the yolk grains. Later, however, they are sharply
marked off by the rounded hypoblast elements assuming the form of epithelial cells.
Up to this point I think the evidence is fairly clear that the blood corpuscles increase
in number both by direct division and also by new formation. This new formation
ean only be from two sources—from the somatic mesenchyme as the vessels are formed
in it, or from the layer of yolk cells lying beneath the splanchnic mesepithelium. Both
probably before, both almost certainly now, share in contributing to the blood; but as
the definitive hypoblast and the splanchnic mesenchyme are now differentiated, a new
phase is inaugurated.
I shall first enumerate the different types of free cells met with in the blood, and
then refer to their seats of origin.
Four stages (— 31, 31+, 32, and 32+) may be taken together for the classification of
the types, though in referring to their origin I shall have to discriminate between 31
and 32. As stage 32 was the one selected for the study of the cytological characters of
the corpuscles, I must refer to the plates published with Part I. of this memoir for
most of the illustrations.
Ist. Hrythrocytes.
All the giant corpuscles have now disappeared from the blood. The corpuscles have
assumed their definitive disc shape (figs. 1 and 2, Pl. L, Part I.). They now contain
hemoglobin. Three varieties occur, differing in the characters of the nuclei. The great
majority have oval nuclei with a very coarse homogeneous chromatin reticulum, which
takes the orange dye from the mixture of Ehrlich; a certain proportion have round
nuclei and a relatively small cell body, while many have vesicular nuclei. As the
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 19). 66
444 DR THOMAS H. BRYCE ON
vesicular condition of the nucleus is characteristic of the great mass of the erythrocytes
in all the later stages, we may take it that the corpuscles with this character are the
mature elements. I may here remark that after stage 32 the number of dividing
erythrocytes gradually diminishes, until in later phases they are very rare except in the
spleen, where it is only the young erythrocytes which are dividing. I believe that the
mature erythrocyte is probably incapable of division. Those with the oval nuclei
showing a reticulum are therefore young corpuscles, and at the stages under considera-
tion they are in very active division. Those with round nuclei are probably transi-
tional forms between the erythroblast and the young erythrocyte; they are also in
active division.
2nd. Hrythroblasts.
These are small cells with a round or oval nucleus and small cell body, which,
though basophile, has a delicate concentric fibrillation. Such cells are represented in
figs. 18, 19, Pl. I., and fig. 24, Pl. ILI). There are two stages in the fibrillation of
the protoplasm. The cell drawn in fig. 24, Pl. III. has only a narrow zone of proto-
plasm and the fibrillation is extremely fait. In fig. 18 there is a distinct marginal
band, with a zone of apparently alveolar protoplasm round the nucleus; when seen in
profile section (fig. 19, Pl. I.) the band shows at the extremities of the oval body as a
series of fine dots.
The characters of the nucleus are very important. Compared with the mononuclear
cells of this stage and with the young red cells of the blood at stage 30, it is seen that
the chromatin nucleoli are larger, massed closer together, and the intervening reticulum
is coarser, so that the nucleus stains more deeply. These cells apparently correspond to
what Gicxio-Tos * calls ‘thrombocytes,’ after DEKHUYZEN. He regards them, not as
stages of the red corpuscles, but as special elements derived from leucoblasts, and distin-
guished from the erythroblasts by several characters, one of which is the concentric
disposition of the fibrillee of the protoplasm, while in the erythroblasts the filaments are
radially arranged. It is just the concentric fibrillation of the protoplasm, leading up
to the fibrillar band, which determines in this case the nature of these cells.
3rd. Large Mononuclear Cells.
I have given this name to these elements because of the large simple nucleus, which
is either round or notched (figs. 24, 25, Pl. IIL, Part L.). It is distinguished from the
erythroblast by the more purely basophiie reaction of the protoplasm, which is never
fibrillar, showing only an extremely delicate reticulum. The nucleus has its chromatin
nucleoli rather widely scattered ; they are relatively small, and the intervening reticulum
is very delicate and filamentous. It is to be specially noticed that all the corpuscles
up to stage 30, when the hemoglobin appears, have nuclei of this type. The mono-
* Arch, [tal. de Biol., T, xxix., 1898, and Mem. a. R. Accad. delle Sc. di Torino, s. ii. t. xvii.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 445
nuclear cells vary in size, some being smaller and also showing sometimes a deepish
eleft (fig. 25, Pl. III.).
The contrast between the nuclei of the mononuclear cells and the erythroblasts is
important. It corresponds, in general terms, exactly with the contrast between the
erythroblast and leucoblast in higher forms, as established by Lowrr and then Denys,
and more recently, still further elucidated by PapPpENHEIM.*
Ath. Small Mononuclear Cells.
These have a small round or notched nucleus, with a relatively dense disposition of
the chromatin and a narrow zone of delicate hyaline basophile protoplasm.
5th. Leucocytes proper.
These are found sparingly in the blood, but crowded in the spaces of the mesen-
chyme. Outside the blood stream they are simply free wandering mesenchyme cells.
They vary greatly in size; the nucleus shows all degrees of polymorphism; there is
always a large centrosome and sphere; the protoplasm is either hyaline and basophile,
or granular in various degrees, from a few scattered extremely small granules to larger
bodies filling the whole cytoplasm, when the cells have all the characters of eosinophile
leucocytes. In a few instances the granules have a basophile reaction, taking the blue
instead of the eosin from a methylene blue and eosin stain.
In the succeeding section the origin and inter-relation of these various elements will
be considered.
The four stages under consideration present a gradual unfolding of the conditions
which characterise the second phase in the development of the blood.
The disposition of the splanchnic mesenchyme at stage 31, may be gathered from a
section, passing through the liver just behind the pharynx and heart. The solid cord of
cells which represents the future stomach is seen passing down on the left of the liver
to be continuous below with the still undifferentiated yolk cells. Surrounding it, and
passing below over the surface of the yolk, is a very cellular tissue, which also here
surrounds the solid rudiment of the bile duct, and passes along it into the liver.
This mesenchyme is a loosely arranged tissue, everywhere permeated by irregular
Spaces containing red blood corpuscles, but without definite endothelial walls.
The component cells (fig. 2, Pl. II.) are both free and fixed. The latter seem to be
elongating to form spindle-shaped elements, while the former appear to lie free in the
intercellular spaces. These free cells are already of more than one variety. The
majority are large mononuclear cells, but there are also cells with metamorphosed nuclei,
and some even are distinctly granular. The layer is directly continuous with the under-
lying hypoblast, in which mitotic figures are observed.
* Archiv f. path. Anat., vol. 151, 1898. PappENHEIM gives a very extensive bibliography. His theses, summarised
at the close of his paper, agree in respect of these blood cells closely with those of this paper,
446 DR THOMAS H. BRYCE ON
In the vessels in the liver there are numerous cells identical with the free mesenchy-
matous elements, and it is to be noticed that the spaces in the mesenchyme are continuous
with the venous spaces in the liver.
Turning to the somatic mesenchyme *—there is round the pronephric duct and
mesonephric=tubules a specially cellular tract (fig. 21, Pl. II.), which is becoming
canalised, as it were, from before backwards, to form irregular venous spaces round the
tubules, as I shall show immediately. The section drawn (fig. 21) is far back in the
SSS ine
fr
L..
Y
Fic. 1,—Section through larva, stage 82+, behind heart, but in front of undifferentiated yolk cells. 33d.
A, aorta; L, lung; Li., liver; Pr., pronephros; G, glomerulus: S, gullet; P.V., vena advehens of liver;
H.V., vena revehens of liver ; Y, mesenchymatous tissue covering anterior surface of mass of undifferentiated yolk cells.
series, and the tissue is not yet here penetrated by spaces containing blood corpuscles,
but some of the cells seem to occupy spaces in the protoplasmic meshwork, and a few
have polymorphic nuclei. The venous spaces naturally communicate with the cardinal
vein, and these vessels contain cells, having again all the characters of the free elements
in the mesenchyme. ‘This tract of mesenchyme is the rudiment of the lymphoid tissue,
so called, of the kidney. This has long been well known as a seat of blood formation in
* While it is quite legitimate to call the cellular tissue round the gut and on the mass of yolk cells mesenchyme,
it is perhaps not strictly correct to use the term as applied to this tissue. I use it in quite a general sense as 4
convenient word to indicate the young connective tissue. Through the whole larval stages the so-called lymphoid
tissue is mesenchyme in this sense, with free cells in its meshes.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 447
the Teleosteans (B1zzozERo, ZIEGLER, LAGUESSE, FELIX, and others). Inthe Lepidosiren
larva the tissue is not true lymphoid tissue, as we understand the term in higher forms,
and there are no glands. It consists simply of a tract of branched connective-tissue
cells, with wide intervening spaces in which there are free lymph cells. Throughout
the whole of larval life it has much the appearance of the mesenchyme at its first
Fic, 2.—Section through larva, stage 32+, further back than figure 1, through liver ducts. x33 d.
A, aorta; L, lung; Pr., pronephros; G, glomerulus; S, stomach; H.V., vena revehens of liver; Y, mass of
undifferentiated yolk cells ; M, mesenchyme covering mass of yolk cells.
appearance, and is, as it were, a tract of that tissue which has retained its undifferentiated
characters.
Feix * shows that in Salmonide it is not true lymphoid tissue, and he uses the term
‘pseudo-lymphoid’ tissue. The tissue in the Teleosts, as described by him, differs both in
appearance and development from the corresponding tract in Lepidosiren. To this I
shall return later.
At stage 32 the general disposition of parts is indicated in the diagrams in the
text. In figs. 1 and 2 the still solid gut is seen lying dorsal to the liver; further back
* Anatomische Hefte, Bd. 8.
448 DR THOMAS H. BRYCE ON
it descends on the left of that organ, and, as in stage 31, the cord passes into the general
mass of the yolk cells.
Round the cord of cells the mesenchyme forms a layer, differing from the general
somatic mesenchyme in being composed of rounded cells closely packed together.
Traced back, the layer sweeps over the yolk, surrounds the vessels and ducts entering
the liver, passing with them to join the general connective tissue of that organ.
The very anterior edge of the ventral mass of yolk cells is indicated in fig. 1. As
we shall see later, this tissue is composed entirely of mesenchyme, and it passes into the
liver round the portal vein,
Behind the point where the definitive hypoblast of the solid gut joins the general
mass of yolk cells, a mass of the mesenchyme projects free (text fig. 3) into the body
Fie, 3.—Section of larva, stage 32+, through posterior edge of liver, behind point where the solid gut rudiment becomes
continuous with undifferentiated yolk cells. x 38d.
A, aorta; LL, lungs; Y, mass of undifferentiated yolk cells: M, mesenchyme on surface of mass of yolk cells;
N, specialised tract of mesenchyme along pronephric duct.
cavity to the left of the hinder end of the liver. On each side this fades away into the
general mesendodermic layer of the yolk, while behind this point the splanchnic
mesenchyme, as such, is absent (text fig. 4), until again posteriorly it surrounds the
solid hind gut which is being differentiated from behind forwards (text fig. 5). The
general somatic mesenchyme is at this stage formed of widely separated stellate or
fusiform cells, but the tract adjoining and surrounding the pronephric duct, the
pronephric funnels, and mesonephric tubules has quite special histological characters.
This tract can be followed all along the body of the embryo.
Before proceeding to describe the minute characters of the splanchnic mesenchyme
and of this specialised tract of the somatic mesenchyme,* it may be observed, as a fact
* See note, p, 464.
THE HISTOLOGY OF THE BLOOD OF LARVA OF ZEPIDOSIREN PARADOXA, 449
of possible significance, that this specialised tract corresponds in situation to the original
seat of origin of the ‘sclerotome’ from the mesoblast;* while the splanchnic mesen-
chyme is the differentiated representative of a previously undifferentiated mass of
primitive hypoblast cells which had certainly an important share in the contribution
of the early blood corpuscles.
I must also state that I have searched more than once every section through the
pharynx and gill clefts at this stage for thymus ‘placodes’ giving origin to leucocytes,
as described by Brarp.+ I cannot identify any thymus rudiment, nor have I seen
any appearances like those figured by Brarp. Moreover, though leucocytes occur here
JO
5 oO
30
Fie. 4.—Section through larva, stage 32+, behind liver. x88 d.
A, aorta; C.V., cardinal vein ; N, specialised tract of mesenchyme in region of mesor ephros,
and there in the general mesenchyme in that region, and also in the aortic arches, I do
not happen to have seen a single one in the anterior cardinal vein.
Splanchnic Mesenchyme.
It has already been observed that this tissue surrounding the isolated portion of
the gut is composed of rounded closely packed cells. There are numerous spaces in it
containing red blood corpuscles, and here and there free elements with characters
similar to those of the cells immediately to be described.
Dorsal to the gut, a tract is showing the first stages of differentiation from behind
forwards, which will convert it into the spleen. The layer on the yolk which is in
direct continuity with the undifferentiated hypoblast has, however, very special
characters. Ifa section be taken at Y in text fig. 1 it will be seen that the tissue is
composed of loosely arranged fusiform or stellate cells, with many free elements in the
* I find a remark almost in the same terms as this was made by ZEIGLER (Arch, mikr. Anat., Xxx., 1887),
referring to the similar tract in Teleosts. See also Lacussss, loc. cit., p. 364.
+ Loc. cit.
450 DR THOMAS H. BRYCE ON
spaces between them. These are either of the mononuclear type or, more frequently,
show various degrees of polymorphism, and a large number have their protoplasm filled
with granules. Further back, the tissue over the surface of the yolk has the same
characters, and in certain situations, as at the point marked M in text fig. 2, it has
the appearance represented in fig. 22, Pl. II. Above is the line of the mesepithelium,
below and to the left is the yolk-laden hypoblast. Directly continuous with this the
mesenchymatous tissue is composed of a network of protoplasmic threads, in the meshes
of which are cells showing all degrees of polymorphism in their nuclei, while in the
deeper layers near the hypoblast there are numerous cells with the protoplasm laden
Fic. 5.—Section through larva, stage 32+, at level of the hind-
limb buds,
A, aorta ; C.V., cardinal vein ; Pr., nephric duct between
Pr. and A, the tract of mesenchyme lettered N in preceding
figures ; G, solid hind gut.
with fine granules. The nuclei of the cells forming the framework are widely
separated, and are thus apparently fewer in number than the free cells. They are
elongated like the nucleus above and to the left (bounding here a space containing
two erythrocytes), or rounded like those below, between the two horseshoe-shaped
nuclei.
In other portions of the tissue the general characters are the same, but the poly-
morphic metamorphosis of the nuclei is not everywhere so pronounced, and large
mononuclear free elements are more numerous. Throughout this tract of mesenchyme
mitotic figures are of frequent occurrence.
,
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA, 451
Somatic Mesenchyme.
In the tract above mentioned the appearances differ according to the degree to
which the tissue round the nephric ducts is opened out into venous spaces communi-
eating with the cardinal vein.
In the region of the pronephros (fig. 25, Pl. III.) the duct is surrounded by an
irregular sinus, interrupted here and there by delicate protoplasmic strands, belonging
to cells of an endothelial character, with elongated nuclei. The sinus is crowded with
dividing erythrocytes and with large mononuclear cells, with round, pitted, or notched
nuclei. Here and there, there is a free polymorphonuclear corpuscle, either with
hyaline protoplasm or with various degrees of granulation. Within the spaces of the
trabecular framework are many polymorphonuclear cells, in some cases having all the
characters of eosinophile leucocytes.
Further back (fig. 23, Pl. I1.), in the angle between the cardinal vein, aorta, and duct
‘(text fig. 5), the tissue is not so much opened out, the framework is closer, and in its
meshes are massed free elements with round, notched, or polymorphic nuclei and various
degrees of granulation. In the actual blood spaces the great majority of the cells are
of the large mononuclear variety.
In the region of the mesonephros the general characters of the tissue round the
tubules is similar, as will be gathered at once by reference to fig. 26, Pl. III. -
The individual free cells outside the blood stream vary greatly in size, without any
further indication of discriminating characters. Mitoses are frequent, but there is
nothing to indicate that one type of cells is dividing to give origin to another. They
seem to divide at various stages in the metamorphosis of the nucleus, and all after their
kind. In fig. 24, Pl. III. there is drawn a cell in one of the venous spaces, which
from its more crowded nuclear reticulum and the indication of a faint fibrillation of its
protoplasm is to be regarded as an erythroblast, while outside the blood stream is a
mononuclear cell of the largest variety, which in general dimensions is equal to the
erythroblast.
The cardinal vein, compared with the aorta, contains a disproportionate number of
white to red elements, and a preponderating number of mononuclear cells.
Thus in 112 sections the white elements were distributed between the two vessels
thus :—
Small Mononuclear. Large Mononuclear. Polymorphonuclear,
Aorta, 8 He, 8 othe 6
Cardinal vein, 14 Fon 100 ae 26
The cardinal vein, however, being much larger than the aorta, it was necessary to
arrive at the proportion of the white to the red elements in each. This was arrived at
prop
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 19). 67
452 DR THOMAS H. BRYCE ON
by counting the erythrocytes and white cells in every third of the 112 sections. The
figures were as follows :—
Erythrocytes, White Cells.
Aorta, 1003 ate pp
Cardinal vein, 2634 wa 140
The proportion of red cells in the aorta compared with the cardinal vein was thus
less than 1 to 3, while the proportion of white cells was nearly 1 to 7.
I have used the term ‘ white cells’ rather than ‘leucocytes’ here because the counts
include the large mononuclear cells, which are not necessarily all true leucocytes. Those
in the spaces of the mesenchyme outside the blood sinuses are certainly in great part
‘leucoblasts,’ in the sense that all the polymorphic and granular cells are derived from
them by metamorphosis of the nucleus and by the deposition of granules in their
protoplasm ; but what is the relation of those within the blood stream to the non-
heemoglobin-containing erythroblasts ?
As one has, unfortunately, no opportunity of actually seeing one form of cell change
into another, this question can only be answered in terms of probability.
A careful scrutiny of these intravascular mononuclear cells in the cardinal vein and
the spaces communicating with them shows that certain of them have rounder and
larger nuclei than others, though identical in general characters.
Several considerations point to the probability that these cells are progenitors of
the erythroblasts.
1st. The polymorphism of the erythrocyte series is in favour of the view that the
blood is at this stage receiving new formed elements. There seems no reason why
certain corpuscles in the general blood stream should retain, under the same conditions,
their primitive generalised characters if all the corpuscles are survivors from earlier
stages.
2nd. If new elements are being added, the fact that erythroblasts are never found
outside the blood stream indicates that they must be derived from less specialised cells
in the blood stream, which in turn should have the characters of cells outside the blood
stream. The large mononuclear cells fulfil the conditions and complete a logical chain.
But the question arises as to the relations of the cells without and within the blood
stream. Numerous cases prove that cells are passing from the spaces in the mesenchyme
into the blood stream, or vice versa, but it is not possible absolutely to say in which
direction they are moving.
The fact that these mononuclear cells occur in disproportionately large numbers in
a vessel,* the current in which would carry them away from this locality, indicates
that in all probability they do arise in this tract of mesenchyme, and are there set free
* The sections in which the above count was made were behind the liver, a long distance posterior to the point
where the hepatic vein joins the cardinal.
THE HISTOLOGY OF THE BLOOD OF LARVA OF ZEPIDOSIREN PARADOXA. 453
in the blood stream. From the evidence available, it seems to me justifiable to
conclude for this stage—
Ist. That new elements are being added to the blood stream. These belong either
to the erythrocyte or leucocyte series.
2nd. In regard to the leucocyte series, all the cells free in the blood which can be
ealled leucocytes are derivatives of the mesenchyme; certainly of the splanchnic,
almost certainly of the nephric tract of somatic mesenchyme.
._ 3rd. In regard to the erythrocyte series—the erythroblast without heemoglobin is
derived from an intravascular ‘mononuclear element,’ which is in turn derived from
the mesenchyme, probably from both splanchnic and somatic mesenchyme.
Ath. The two series arise from a common mother cell—the mesenchyme cell. The
ehanges which convert the mother cell into an erythrocyte take place in the blood
stream, while its metamorphosis into a leucocyte is brought about in situ, in the spaces
of the mesenchyme outside the blood stream.
Before leaving this stage I must refer to the character of the granulation in the
oranular leucocytes. In some instances, as I have already stated, these cells have all
the characters of eosinophile cells. It would take me out of my direct way to go into
the general question of the meaning of the granulation of leucocytes; and I would here
merely remark, in regard to these particular cells, that the granulation may be merely
yolk material in fine division, for I have observed precisely similar eosinophile granules
in the yolk cells, and the yolk itself has strong affinity for eosin. At this stage I find
the granular cells crowded together only in the splanchnic mesenchyme and in the
tract of the somatic mesenchyme so frequently alluded to. It at once suggests itself,
in the case of the cells near the yolk, that this may be the source of the material which
constitutes the granulation ; and in regard to those in the neighbourhood of the nephric
duct, it is worth mentioning that the cells forming the wall of that duct are filled with
yolk grains long after they have disappeared in the neighbouring tissues. It seems to
me not impossible that these early leucocytes may be concerned in the distribution of
yolk food. Were this the case, the granules would necessarily differ from those of the
leucocytes of later stages, but I see no inherent improbability in the suggestion, which,
if well founded, has a bearing on the nature of granulation in leucocytes generally.
Puase III.
After the second phase, as I have ventured to define it, is fully established at stage
82 or 33, the general conditions are maintained for a time, during which the histogenesis
of the spleen is gradually accomplished and the atrophy of the pronephros completed.
It is with the complete differentiation of the spleen as a hemopoietic organ that what
I call the 3rd phase in the history of the blood is established, and the renewal of the
blood corpuscles is confined to that organ, and to the pseudo-lymphoid tissue round the
kidneys, and possibly also round the gut. It is presumably the adult state of things
454 DR THOMAS H. BRYCE ON
that is thus established. At no stage does the liver take any part in blood formation.
The part taken by the spleen and the lymphoid tissue of the mesonephros and gut in
the process will now be considered.
Histogenesis of the Spleen.
As already mentioned, the rudiment of the spleen appears in the splanchnic
mesenchyme dorsal to the gut. It is simply a differentiated tract of that tissue. The
hypoblast takes no direct share in its formation, but it must be observed that it takes
form in the mesenchyme very shortly after that tissue is itself differentiated from the
primitive undifferentiated mass of yolk cells.
The first sign of its formation is the appearance of a column of large rounded or
oval cells, round which the remaining cells of the mesenchyme group themselves con-
centrically (fig. 28, Pl LV.). The nuclei of the investing cells are oval or elongated,
and their long axes are arranged in a general way parallel to one another, and con-
centrically to the central tract. As elsewhere, this tract of mesenchyme is permeated
with spaces having no definite endothelial walls, but containing red blood corpuscles.
These spaces are at first irregular, but in the second stage (fig. 29, Pl. IV.) they run
together so as to form a peripheral smus surrounding the central tract, or island as it
appears in sections, isolating it in great measure from the peripheral layers of investing
cells. These latter become the investing connective-tissue coat of the spleen. The
central tract is permeated by cleft-like spaces which communicate with the peripheral
sinus. Both spaces and sinus contain red cells, and in the sinus are seen a number of
_ leucocytes, evidently wandering in from the general mesenchyme. In the central mass,
here and there are seen cells with simple nuclei surrounded by a layer of free protoplasm.
Numerous mitotic figures occur among the cells of the central tract, which by multi-
plication of its constituent cells increases in size, while at the same time its spaces are
opened out until (fig. 30, Pl. IV.) it is converted into a system of cellular columns or
trabecule. The peripheral sinus is now less definite in its arrangement, because the
spaces between the outer ends of the columns have enlarged and become continuous
with the lumen of the sinus. The peripheral investing cells are now all flattened
connective-tissue elements, and the capsule of the organ is complete.
The sinuses at this stage are full of red cells, nearly all of the mature variety. There
are few erythroblasts, the phase contrasting in this respect markedly with the next, in
which the sinuses are filled with young erythroblasts.
The cellular columns are composed of cells of various dimensions (fig. 3, Pl. IV.).
Some have smaller and irregular nuclei, but the great majority have round or oval
nuclei of large size. In the spaces within the trabecule there are numerous white
elements (fig. 31, Pl. IV.). These have either simple nuclei and hyaline protoplasm,
or polymorphic nuclei and hyaline or granular protoplasm. The polymorphic nuclei
have a closer arrangement of the chromatin nucleoli than the cells with the simple
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 455
nuclei, so that they take a deeper coloration. The shape of the nucleus varies, but
is most frequently horseshoe-shaped, and the protoplasm is either hyaline or granular
in different degrees. Though it is true that at the earlier stages leucocytes are
wandering in from without, I think there is little doubt that these cells are being
formed at the expense of the cells of the columns or trabecule, which, after all, have
exactly the same origin as the remainder of the mesenchyme, in which we have seen
the cells being transformed into similar elements.
The mononuclear cells have certainly a local origin. They are seen crowding the
splenic vein (fig. 27, Pl. III.). They are of varying dimensions, and are indistinguish-
able from the cells with simple nuclei first observed in the blood at stages 31 and 32.
The problems regarding them are exactly the same as presented themselves at the
earlier stages, but I shall postpone discussion of the point until I consider the next
stage, as I have had the opportunity of staining a series of sections freshly cut from
that stage with stains specially suited for discriminating between the different types
of cells.
At stage 37 the spleen is an elongated organ, overlapping the pancreas behind and
extending forwards along the whole length of the liver to a level close behind the
point where the lung comes off from the pharynx. It is broad behind, but tapers in
front, and it is in this anterior part that the general structure can be most easily
determined (fig. 32, Pl. IV.).
Surrounding the central artery there is an axial mass of cells with small irregular
nuclei. From this to the periphery extend radiating trabecule, with small oval or
elongated nuclei. Between the trabeculz are large sinuses packed with cells belonging
to different categories, and in the meshes of the framework immediately round the
central area are large and round nuclei, which sometimes, it is quite clear, have a zone
of free protoplasm round them, while in other cases they seem imbedded in the general
protoplasmic framework. In the apex of the organ the structure is simple because this
zone is much reduced, but posteriorly it is more extensive and more loosely arranged,
so that the picture is more complicated. It is a matter of great difticulty to say some-
times whether the large round nuclei with which this zone is studded belong to the
trabecular framework or to cells in its meshes.
In the peripheral sinus, and the larger sinuses between the outer ends of the
trabecule which are continuous with it, there are great numbers of hemoglobin-
containing erythroblasts. These and the erythrocytes give to the outer zone of the
spleen characters which would justify the application to it of the name of ‘ pulpe rouge’
used by Lacunssz,* while the central portion is the ‘ pulpe blanche.’
The free cells in the spleen pulp belong to several different categories, and the
discrimination between them is a matter of difficulty, as all the nuclei stain blue with
hematoxylin, and the only differences are those of intensity of staining, associated
with a difference in the disposition of the chromatin. I was unable, except in a
* Jour. de? Anatomie et de la Physiologie, T. xxvi., 1890.
456 DR THOMAS H. BRYCE ON
general way, to identify the elements in a series stained with this dye and counter-
stained with eosin.
On a new series I tried many stains, but owing to some factor in the fixative,
presumably the acid, I found the tissue would not stain with any basic dye. I had
recourse, therefore, to Mann’s double acid mixture of methyl blue and eosin, but
found that for this particular material I got much more vivid differentiation by staining
with the two dyes successively, first for three minutes in a saturated watery solution of
eosin, and then, after rising in water, in a saturated watery solution of methyl blue
for one or two minutes. The results varied according to the proportion in which the
two dyes were held; and although there was some variation in the colorisation, the
conclusions were not vitiated, because the picture was always a relative one.
The general effect depended partly on a difference in the reaction of the protoplasm,
but chiefly on the relative proportions in the nuclei of bodies with different affinities
to the two dyes.
In my most successful stainings I obtained the following results :—
A. Fixed Cells.
The protoplasmic trabeculze stain pure blue, and the nuclei have a general blue tint
owing to the general reticulum of the nucleus selecting the blue dye, but the nucleoli
(chromatin) stain a violet-red colour. The central parts of the karyosomes stain
yellowish-red. The violet colour is given by an outer covering or coating, as it were, of
the blue staining general linin reticulum.
B. Free Cells.
1. In the meshes of the trabeculee there are large numbers of cells with a large
nucleus and a small amount of blue-staiming protoplasm. The nuclei are round and
vary In size, but roughly they may be divided into two classes—those with a diameter
about 24 » and those with a diameter of about 18 u Many have smaller nuclei,
but as there are frequent mitoses they may be considered young cells. The nuclei
are characterised (fig. 33, Pl. IV.) by the large amount of blue they select, the general
fine reticulum taking up the methyl blue, while the chromatin nucleoli, which are
relatively few in number, stain reddish-violet. The characters are thus exactly the
same as the nuclei of the reticulum.
2. Distinguished from these cells are others which have nuclei of the same dimen-
sions as the largest of the cells of the last category, but which react differently to the
stain (fig. 33, Pl. IV.), their general tint being reddish-violet. This is due to a difference
in the disposition of the chromatin. The nucleoli are larger and are more closely opposed,
and the blue-staining reticulum between them is reduced, and has a violet, not a pure
blue tint. These cells are very frequently seen dividing, and are distinguished during
division by the red-violet colour of their chromosomes. The daughter cells have
THE HISTOLOGY OF THE BLOOD OF LARVA OF ZEPIDOSIREN PARADOXA, 457
naturally smaller nuclei, but are distinguished by the reaction of the nuclei. The
protoplasm has an open reticulum, but is relatively small in amount. The outer layers
_ are frequently seen to be fibrillar, the fibrillee bemg arranged circumferentially. There
are also fine reddish granules in many of the cells, which, I take it, would correspond
to GieLi0-Tos’s hemoglobigenic granules.
3. The next class of cells is found only in the large sinuses. The nucleus is of the
same dimensions as that of the cell just described ; it is round or oval, and selects only
the eosin; the colorisation is reddish-yellow, the nucleoli are closely packed, and
joined into a coarse reticulum by bars staining yellow like the rounded masses of the
nucleoli. ‘The mitotic figures, which are very numerous, belonging to this class of cell,
are distinouished by their yellow chromosomes. The protoplasm varies in amount ; it has
an indefinite warm tint, and many of the cells have yellow granules. The peripheral
layer is fibrillar, and round the nucleus the protoplasm shows a wide-meshed reticulum.
Looking at these three varieties of cell, it is clear that the third is an erythroblast
containing hemoglobin. It is almost equally clear that the second is a stage of the
third—that, in fact, it is a primary erythroblast. The spleen, therefore, is a seat of
origin of the erythroblasts, but do they arise by multiplication of erythroblasts which
have entered the organ from without, or by new formation from the spleen cells? I
conclude for the latter alternative, for the following reasons.
While it is possible that the erythroblasts having nuclei characteristic of heemoglobin-
containing corpuscles might be derived by division from the red blood corpuscles in
the sinuses of the previous stage, it is not possible that cells with nuclei which do not
show that reaction should be derived from heemoglobin-containing corpuscles. They
might arise, however, by division from non-hemoglobin-containing erythroblasts
derived from without, but their numbers are far out of proportion to the number of
mitotic figures, so that one is driven to believe them to be a further phase of the larger
cells of the first category. As a matter of fact, in cells with all the characters of these,
here and there one occurs with a definite concentric fibrillar condition of the protoplasm
(fig. 33, Pl. IV.), which I take to be the first stage in the conversion of the cell into an
erythroblast.
I think, again, that itis reasonable to derive these cells of the first category from the
mesenchyme of the original rudiment. It is very hard to say at this stage whether
their protoplasm is actually free, or part of the general protoplasmic framework ; and as
this is the last stage of the series available, I am unable to say whether any part of the
original cellular columns is retained in its primitive form, to give rise continuously to
new budded-off elements; or whether the cells are all set free in the meshes of the
reticulum, and give rise by continuous division to new elements.
It seems justifiable to conclude that the original spleen cells, by a series of changes
in the protoplasm and nucleus, become converted first into non-hemoglobin-containing
erythroblasts, and that these, in turn, acquire hemoglobin and become the young red
cells, and that the cells I have described represent the stages in the process.
403. . DR THOMAS H. BRYCE ON
Besides the erythrocyte series, there is a large leucocyte contingent in the spleen.
The fully unfolded leucocytes are of two main classes. 1st, Small cells, with horse-
shoe or lobed nuclei, with rather closely packed chromatin nucleoli, and a small cell body
composed of hyaline blue-staining protoplasm, though sometimes it contains granules.
2nd, Large cells, with polymorphic nuclei and a large cell body, im which the centro-
some is always surrounded by a well-developed radial sphere and aster. The proto-
plasm is either hyaline and blue-staining or granular, and the granulation is either fine
or coarse. The fine granules stain in some cells blue, in others red, and the coarse
granulation of the eosinophile cells is not always of the same size.
Compared to the erythroblasts, the leucocytes are in relatively small numbers, but
in the spaces and sinuses there are many of the cells which have all the characteristics
of leucoblasts (fig. 33, Pl. IV.). The nuclei vary in size, but generally speaking are
smaller than those of the largest spleen cells (18 » against about 24 «), but have
otherwise the same character and reaction.
The protoplasm is reduced to a very narrow zone, is hyaline, and stains pure blue.
Many nuclei are deeply notched (fig. 33, Pl. IV.), as if beginning to undergo poly-
morphic metamorphosis.
As leucocytes in all varieties are abundant in every tissue of the body, and
especially round the kidney tubules and gut, as I shall presently describe, it is much
less certain whether they are actually formed in the spleen at this stage than that the
erythroblasts are rising there.
The great difficulty is, that it is impossible to distinguish a leucoblast from a
primitive spleen cell. We have here repeated the same problem dealt with before in
connection with the origin of the two classes of corpuscles from the mesenchyme cells;
and considering that the spleen is merely a tract of mesenchyme, which may be ~
supposed to retain its primitive potential characters, the same general scheme may not
unreasonably be considered to apply, which would derive from the primitive cells of
the rudiment both classes of corpuscles by specialisation along different lines. My
observations on the spleen are thus in strict accord with those of LacuussE* in his
classical work. My large mononuclear cell takes the place of his noyau d’origine, a
term borrowed from Poucuer,*+ who first formulated the general scheme here adopted
from his work on the blood of Triton.
The leucocytes, in their several varieties, are found in the blood-vessels and scattered
in every tissue, but are specially crowded in the wall of the gut in the mesentery and in
the tissue surrounding the tubules of the kidney.
Pseudo-lymphoid Tissue of Kidney.
The tract described at stage 32 has disappeared in front with the atrophy of the
pronephros, but it can be identified in the region of the kidney, and the general
* Loe. lt. t+ Gaz. Méd. de Paris, 1879.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 459
appearances are much like those figured at stage 32 in the region of the mesonephros
fie, 26, Pl. IIT.). ,
The tubules are imbedded in what is practically a huge sinus; in the blood stream
a great variety of elements occur. There are numerous erythroblasts, many mono-
nuclear cells, and numbers of leucocytes, while in the pseudo-lymphoid tissue there are
large quantities of leucocytes of various kinds, but the polymorphic and granular
varieties preponderate. The general impression when a section is compared with a
section of the spleen is, that while in the latter the primary erythroblasts and secondary
erythroblasts are greatly in the majority, the reverse is the case in the kidney.
I have made some attempts to arrive at some estimation of the relative numbers of
erythroblasts and leucocytes in the renal-portal and cardinal veins. As the vessels are,
in the greater part of their course, unequal in size, any count, to be a reliable index of
the part taken by this tissue round the kidney, in contributing new elements to the
blood, would require to be one relative to the number of erythrocytes. This I found
impracticable, on account of the corpuscles being unequally distributed. I therefore, to
reduce the balance in a rough way, counted in every fourth section of a continuous
series of 200 the erythroblasts and leucocytes in one renal-portal, and put them against
those in the two cardinals. I have not sufficient confidence either in the method or
the figures themselves to submit them in detail, or to found a definite judgment on
them, but I may say that the general result was in favour of the renal-portal as regards
both erythroblasts, large mononuclears, and leucocytes ; and that while erythroblasts and
large mononuclears of the type seen issuing from the spleen pulp were very common
in the renal-portal along the whole length of the kidney, they were practically absent
in the cardinal. The possible explanation is, that in the ‘backwater’ formed by the
great kidney venous sinus, the erythroblasts and their mother cells undergo their
further transformation into erythrocytes.
Thus, though I have shown that it is highly probable that both orders of corpuscles
are produced along this tract at an earlier stage, it seems doubtful whether in the later
phases the pseudo-lymphoid tissue of the kidney is concerned in the new formation
of red cells. I have shown how the spleen, at first distinctly lymphoid, becomes
later more specially concerned in the formation of the erythrocytes, and there is some
reason for believing that the kidney tract is differentiated in the opposite sense.
The development of this pseudo-lymphoid tissue, according to my account, is very
simple. It is nothing more than the mesenchymatous tissue round the nephric duct
and tubules, canalised, as it were, by venous spaces which communicate with the
eardinal vein. From the first the cells are fixed and free; the fixed cells form the
general connective-tissue basis; the free cells are either derived from the primitive
mesenchyme cells of the tract itself, maintained by constant division, and set free in
the blood stream by their own amceboid movement, or they wander to this site
from the splanchnic mesenchyme. I have shown reasons for a belief in the first.
alternative. . ;
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 19). 68
460 DR THOMAS H, BRYCE ON
This account is different from that given by Frtix* of the development of the
corresponding tissue in the Salmonidee. He derives the tissue from proliferation from
the wall of the vein, and he describes and figures trabeculee of epithelioid cells which —
give rise to the tissue, the cells in places becoming converted into both white and red
elements. I have not seen appearances like these in Lepidosiren. In the early stages
there is no sharp separation of the tract laden with lymphoid cells from the general
mass of the mesenchyme, and all the indications are in favour of the view that it is
merely a tract of the general mesenchyme in the spaces of which, for physiological
reasons, the lymph cells are congregated. §
This lymphoid tissue in the larval kidney is the rudiment of a very remarkable
mass of lymphoid tissue in the cortical part of the adult kidney. It forms a thick cap,
so densely filled with pigment that the structure is quite concealed, but it can be seen
that it is thickly studded with leucocytes. t
Lymphoid Tissue in Gut Wall.
The fact that G1cL10-Tos { describes the spiral valve as the hemopoietic organ in the
lamprey directed my attention specially to that structure in the later larval stages.
I find that the fold is occupied by a denser tissue than that investing the gut. The
small elongated nuclei proper to the tissue are more closely packed, while the free
lymphoid cells or leucocytes are much less numerous.
The tissue of the spiral valve does not then differ in kind from the general investing
tissue of the gut wall, and so far as the larva is concerned there are no appearances
suggesting that it has a special hemopoietic function.
The number of leucocytes in the connective tissue investing the gut is very great.
They lie in the meshes of a loose alveolar reticulum, and belong to all the different
categories. There are large numbers of mononuclear cells, here in every probability,
leucoblasts. Mitotic figures occur frequently. Cells with all degrees in the meta-
morphosis of the nucleus, and with granules of all the varieties already mentioned, are
very plentiful. Just as in the case of the kidney, this tissue represents, doubtless, the
early stage of the lymphoid tissue surrounding the gut and occupying the spiral valve
of the adult animal. This tissue is probably purely lymphoid—or, rather, the free cells
are probably all lymphoid elements. There are no vessels to be seen crowded with
erythroblasts, such as one would expect to find if the tissue had any relation to the
formation of red cells.
Before closing the descriptive part of my paper, I must refer to the condition of the
thymus gland at this stage. I have not studied the early stages of its development,
but I now find it as a small organ, cut up into lobes by the passage through it of
muscular fibres and a nerve cord. The cells of the gland are now free from the
* Loc. cit. + See paper by Granam Kerr, Proc. Zool. Soc., 1901-2.
£ Arch. Ital. de Biologie, vol. xxvii., 1897. § Cf. ZinGLER, loc. cit., 1892, note, p. 21,
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA, 461
hypoblast, and though differmg from the cells lining the gill clefts and pharynx, in
respect of their limited protoplasmic envelope they have a definitely epithelioid
appearance. The nuclei are closely packed, are round or oval, and in no single
instance fissured, horseshoe-shaped or lobed. In the whole gland I have detected
only one leucocyte—an eosinophile, and therefore a mature variety. The appearance of
the cells is wholly different from that of any class of the leucocytes; and while these
elements occur in their thousands round the gut in the spleen and kidneys, and
scattered in every tissue, only one or two occur in the neighbourhood of the gland.
The so-called lymphoid transformation of the epithelial cells described in various
forms by Ko.iiker, Prenant, Maurer, Scuuitzze, Nusspaum and Prymak, and
BrEaRD cannot, so far, have taken place. Up to this stage, then, the thymus can have
no share in contributing leucocytes to the blood, unless on the impossible assumption
that the epithelial cells have become lymphoid, gone off as leucocytes, and become again
replaced by epithelial cells.
I hold this observation to be ample proof that the leucocytes in Lepidosiren do not
originate in the thymus in the larval stages, but I have in preparation a note on the
Thymus which will bring the matter to a perfectly conclusive issue.
GENERAL REMARKS.
The divergence of opinion as to the first origin of the blood is so great that it is
difficult to reconcile the various accounts. My results are suggestive in this con-
nection, for they show how both primitive hypoblast and mesenchyme may, under
certain conditions of development, share in blood formation. As in the later phases
there is, in the nature of things, a degree of uncertainty, I shall attempt to summarise
my facts in the strictest terms of accuracy, and then draw together such conclusions
as | think they may reasonably bear.
SuMMARY OF Fact.
(1) The primary corpuscles, the first origin of which I have not studied in detail, are
all alike in characters.
(2) At a stage sometime before there is any suspicion of hemoglobin being present,
there are two classes of corpuscles, one with a distinct circumferential equatorial
fibrillation of the superficial layers of the protoplasm and without attraction sphere,
the other without such modification of the protoplasm, but with distinct centrosome
and sphere.
(3) In all later stages these two kinds of corpuscles coexist, but at stage 32 there
is a sudden great increase in the proportion of the active type of cell.
(4) At stage 30, which is critical, there are (a) corpuscles presenting the features of
intermediate stages between the large ringed yolk-laden bodies and an oval, disc-shaped,
462 . DR THOMAS H. BRYCE ON
ringed yolk-free corpuscle with a round nucleus; (b) small cells with a small amount of
protoplasm formed (?) by budding (unequal division) of larger yolk-laden cells, and (c)
similar cells with slight concentric fibrillation of the protoplasm.
(5) In all stages up to 30 the nucleus in every variety of corpuscle is identical
except in size. In the arrangement of the chromatin it agrees with that of the large
mononuclear basophile elements of all later phases.
(6) The cells from which the smaller elements are derived are located certainly in
the mass of yolk cells under the splanchnopleuric mesepithelium, possibly in the somatic
mesenchyme in the neighbourhood of the developing cardinal veins.
(7) From stage 30 onwards the active cells appear in progressively greater numbers
up to stage 32+, in which they are very plentiful.
(8) From stage 30 onwards there are always cells with nuclei of the erythroblast
type, and fine concentric fibrillation of a basophile protoplasm. Side by side with these -
are hyaline cells with small amount of basophile protoplasm and simple nuclei of the
leucocyte type, identical with the nuclei of the earlier young red cells.
(9) The mass of yolk cells immediately under the splanchnopleuric mesepithelium
begins at stage 30 to become differentiated with the growth of the liver, and isolation
of the gut rudiment, into definitive hypoblast and splanchnic mesenchyme.
(10) At stage 31 the splanchnic mesenchyme is a cellular tissue with spaces
containing blood corpuscles and free elements of two kinds: (qa) cells identical with
the large mononuclear cells appearing in increasing numbers in the blood; and (b)
polymorphonuclear cells, with either hyaline or granular protoplasm. The nephric tract
of somatic mesenchyme also contains a few free mononuclear and polymorphonuclear
cells, but in smaller numbers than occur in the very cellular splanchnic mesenchyme.
Mitoses are frequent in both tissues.
(11) At stages 32 and 32+ the splanchnic mesenchyme holds in its spaces numbers
of mononuclear basophile cells, and in parts is composed almost wholly of polymorpho-
nuclear cells, with hyaline or granular protoplasm. The whole perinephritic tissue has, 7
massed in the spaces between its stellate cells, very large numbers of mononuclear
basophile cells, with nuclei becoming transformed into every grade of lobing, and their
protoplasm acquiring every degree of granulation. The portal and hepatic veins, and
the cardinal vein and spaces communicating with it, contain white cells of different
categories, the mononuclear preponderating. The cardinal vein contains three times as
many erythrocytes as the aorta, but seven times as many white elements. The
mononuclear outnumber the polymorphonuclear by four to one in the cardinal vein,
while in the aorta they occur practically in equal proportions.
(12) The splanchnic mesenchyme retains its primitive characters in part, round the
gut along its whole length, forming the so-called lymphoid tissue of the adult.
(13) The nephric tract of the somatic mesenchyme also retains its primitive
characters and forms the so-called lymphoid tissue of the adult kidney.
(14) The spleen rudiment is a tract of, at first identical, closely packed mesenchyme
THE HISTOLOGY OF THE BLOOD OF.LARVA OF ZLEPIDOSIREN PARADOXA, 463
cells. ‘he outer cells, later, form the capsule; the central cells give rise to cellular
trabecular tissue, which in part becomes the connective tissue of the fully formed organ,
in part gives rise to free cells.
(15) In the earlier stages the splenic vein is full of mononuclear cells, with nuclei of
the leucocyte type, identical with those in the blood at stage 32, before the spleen has
differentiated. There are also in the vein a few polymorphonuclear cells, and these are
in large numbers in the spaces of the trabecule.
(16) In later stages the spleen pulp contains fist basophile cells, with the leucocyte
type of nucleus. In some parts the remains of the basophile cellular trabecule are seen
containing nuclei of the same type; second, similar cells with concentric fibrillation
of the basophile protoplasm ; thord, cells with nuclei of the erythroblast type and con-
eentric fibrillee in the protoplasm; fourth, cells with nuclei of the erythrocyte type,
and yellow granules in the ringed cell-body ; fifth, mature erythrocytes; sixth, mono-
nuclear leucocytes with basophile protoplasm ; seventh, polymorphonuclear leucocytes,
small and large, in all their varieties. The members of the erythrocyte series seem
greatly to outnumber those of the leucocyte series in the spleen.
(17) The leucocytes are in great abundance before the thymus rudiment appears,
and at the end of the larval series examined, the gland is still a mass of epithelial cells,
showing no resemblance to. the lymphoid cells in other tissues. There are practically no
leucocytes in its substance, and no special grouping of them, either in the surrounding
mesenchyme or in the veins.
SUMMARY OF INTERPRETATION.
The study of the early corpuscles shows that they are at first all alike—probably
wandering cells, such as those first described in the living Teleost embryo by WrENcKE-
BACH.~ Almost immediately a change sets in, which leads to the adoption by most of
them of a passive role, while others remain free mobile elements, with centrosome and
sphere.
The latter have all the morphological characters of leucocytes, and exactly similar
cells occur in the somatic mesenchyme. As this is long before hemoglobin is developed,
the cells are never at any stage wholly heemoglobin-containing corpuscles; and if these
leucocyte-like cells are the successors of the early corpuscles, mobile elements are never
absent from the blood. It is possible that we should call the early corpuscles them-
selves ‘leucocytes.’ This may seem an unwarrantable use of the term, but I believe it
might bear examination. ‘The leucocyte is generally admitted to be the phylogenetically
older cell. In the Dipnoi the blood is extraordinarily rich in leucocytes, and they
appear at a very early stage. The postponement of the appearance of the leucocytes in
Ontogeny, supposed to exist in all vertebrates, has, it might be considered, only
* Journal of Anat, and Phys., vol, xix., 1885 ; Archiv f. Mikr. Anat., Bd. 28, 1886,
464 |. DR THOMAS H. BRYCE ON
partially taken place in Lepidosiren. PARKER™ says that in Protopterus the leucocytes
bear a larger proportion to the red cells than in any other vertebrate, except in patho-
logical conditions. It is a possibility that in Lepidosvren we have a stage in which the
blood vascular and the lymph vascular systems are not sharply marked off from one
another. Perhaps we see in the blood the division of labour going on, which makes one
primitive corpuscle a respiratory, another a lymph cell. The phenomena of phase 2
support such a supposition.
Up to stage 30, when the hemoglobin appears and phase 2 sets in, all the cor-
puscles, active or passive, have nuclei of the leucocyte type; the chromatin is collected
into karyosomes, rather widely scattered, with a fine filamentous intervening reticulum.
The erythroblasts in the following stages have the erythrocyte type of nucleus, richer in
chromatin, with large closely-set chromatin nucleoli, jomed by a coarser and more dis-
tinetly reticular intervening substance. (Compare figs. 13, 14, 15, 19, Pl 1.) At
stage 31, and better marked at stage 32, the place of the earlier cells with nuclei of the
leucocyte type is taken by the large mononuclears. These have either a single or a—
double origin. It may be that they are all derived from the splanchnic mesenchyme,
and that they wander from thence, especially into the nephric tract of the somatic mesen-
chyme., The distribution of cells in the cardinal veins is, however, against this, and I
am disposed to believe that they arise in both situations. The point is not very
material—they are mesenchymatous in origin in either case.t
Exactly similar cells to those mononuclears in the blood stream become outside the
blood stream leucocytes of the several varieties. From the larger number of those
mononuclears in the blood, compared to the number of polymorphonuclear cells, while
the opposite proportion prevails outside the blood stream, and from their identical
characters with the basophile cells of earlier stages, I believe it is a logical induction,
not an assumption, that they become converted in the blood into the heemoglobin-
containing elements. Mitoses are frequent in those cells outside the blood stream, but
they do not occur in the blood stream itself. This inference is confirmed by the observa-
tions on the spleen; and thus I conclude that from common mother cells added to the
blood during phase 2 from the mesenchyme, and in phase 38 especially from the spleen
(a derivative of the mesenchyme), are derived two families of cells, one undergoing their
metamorphosis in the blood to form the respiratory erythrocytes, the other undergoing
their metamorphosis outside the blood stream in the connective tissue, v.e. lymph spaces,
to form the typical wandering polymorphonuclear leucocytes. }
* Trans. Roy. Irish Academy, vol. xxx. part iii. p. 168.
+ I am here assuming that the facts justify me in concluding for a continuous new formation, at least up to the
end of phase 2, The statement in the text is perhaps too sweeping. If it were possible to establish that all the
colourless cells were derived from the splanchnic mesenchyme, and that they wandered thence, it would be a fact of
great significance, as it is derived directly from the primitive hypoblast, and it might be held that the free cells im it
were directly derived from that layer. I think this would be a strained interpretation, and difficult to reconcile
ee described regarding the nephric tract of the somatic mesenchyme, but it is a possibility which must not
{An objection might here be raised that the nuclei of the polymorphic cells may regain their simple form in the
blood, but as there are many polymorphs in the blood this objection would not have much force.
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA, 465
This may be expressed in the following scheme :—
Puase I.
Primitive blood cells
Primitive erythroblasts Primitive leucocytes
Puase II.
Mesenchyme cells
Mononuclear cell Mononuclear cell
rythsoblase Parhiat
Young erythrocyte | Hyaline, Basophile, Painarphesale leucocyte |
Mature ee | Granular cells in a their varieties |
As I have already said, LacurssE adopts a scheme very closely similar to this, and
the origin of both red and white corpuscles from a common mother cell in the blood
was first suggested by Povcurr in 1879. ‘The same sort of scheme was set forth by
Giext0-Tos in his account of hematogenesis in the adult lamprey. My large mononuclear
mesenchyme cell would also represent the embryonic form of the parent white cell
postulated by PappenHerIm as the forerunner of the erythroblast, while from an
embryological point of view my results in a general way agree with those obtained
by SaxeErR, according to whom the red cells in the mammalia are derived from
polymorphic mesenchyme cells, while the leucocytes are derivatives of similar cells
at a later stage of development.
DESCRIPTION OF PLATES.
All the drawings were carefully traced with Abbé’s drawing apparatus (Zeiss). The lenses used were
the 3 mm. 1°40 N.A. apochromatic lens or the 4 mm. 0°95 N.A. apochromatic lens of Zeiss with com-
pensating oculars 4, 6 or 8. The substage condenser was the achromatic combination 1:0 N.A. of Zeiss.
The following lettering in the figures used to indicate the different catagories of free cells :—
s.m., small mononuclear ; 7.m., large mononuclear ; 0.p., basophile polymorph ; g.p., granular poly-
morph ; f.g.p., finely granular polymorph ; ¢.g.p., coarsely granular polymorph ; ery., erythro-
blast.
Puate I,
Fig. 1. Group of free cells in a space between the mass of yolk cells (hy) and splanchnic mesepithelium
(spm). x 500. Stage 26. Som., somatopleure.
Fig. 2. Primitive yoke-laden blood corpuscle from heart tube; safranin, Stage 26. x 800,
466... DR THOMAS H. BRYCE ON
Fig. 3. Corpuscle from heart with fibrillar ring. Yolk stained black with iron hematoxylin. Stage 27, —
Series 84B. 2. x S00.
Fig. 4. Corpuscle from vessel on surface yolk in vertical section. Stage 27, Series 84B. 5. x 800.
Fig. 5. Corpuscle with centrosome and sphere from heart; fibrillz of ring appear as equatorial groups of
granules. Stage 27, Series 84B. 2. x 800.
Fig. 6. Large vacuolated ringed corpuscle from heart. Stage 30, Series 93C. 3, x 800.
Fig. 7. Giant corpuscle in vertical section from heart. Stage 30, Series 93C. 3. x 800.
Fig. 8. Small ringed yolk-free corpuscle with alveolar protoplasm and round nucleus. Stage 30, Series
93C,3. Ses00!
Fig. 9, Same in vertical section. Stage 30, Series 93C. 3. x 800.
Fig. 10. Corpuscle from heart, with centrosome sphere and lobed nucleus and without ring. Stage 30,
Series 84B, 2. x 900.
Fig. 11. Giant apparently multinuclear cell from heart. Stage 30, Series 910. 13. x 500.
Fig. 12. Small eorpuscle with alveolar protoplasm faintly fibrillar. Stage 30, Series 93C. 9. x 800.
Figs. 13 and 14. Small corpuscles in vertical section, showing groups of granules at equatorial points.
Stage 30, Series 93C. 5. x 800.
Fig. 15. Large cell with lobed nucleus. Stage 30, Series 93C. 5. x 800.
Fig. 16. Small cell apparently being budded off into vascular space (v.) on surface of yolk cells (hy).
Stage 30, Series 93C. x 800.
Fig. 17. Cell with polymorphic nucleus centrosome and sphere in space on surface of yolk cells (hy).
Stage 30, Series 93C. 4. x 500.
Fig. 18. Erythroblast with basophile protoplasm, and faint circumferential fibrillation. Nucleus with
some closely-grouped, larger, and darker-staining karyosomes, and more distinct intervening reticulum. Stage
32+, Series 113C. 24. x 800.
Fig. 19. Same in vertical section. Stage 32, Series 113C. 35, x 800.
The character of the nucleus in both these cells is markedly different from that of the nucleus of the
similar elements of earlier stages, figs. 13 and 14.
Puate II,
Fig. 20. Portion of splanchnic mesenchyme near its developing edge. Stage 31+, Series 106C. 11.
x 400. Below is mass of yolk cells (hy) with nuclei and yolk grains, and very indistinct cell outlines ;
above, the mesenchyme consisting of fixed and free cells, and showing spaces filled with blood corpuscles.
Fig. 21. Section, through the mesonephros and adjoining parts. Stage 31+, Series 106C. 35. x 400.
To right, the notochord (N.), aorta (A.),-and cardinal vein (C.V.); to left, the inner outline of the
muscle plate (m.p.).
Fig. 22. Section of the splanchnic mesenchyme at point M, text figure 2. Stage 32+, Series 1130, 29.
x 500. Below and to left is mass of yolk cells (hy), above is the line of the mesepithelium (spm.).
The free cells of the mesenchyme have almost all become polymorphonuclear, and a number are coarsely
granular.
Fig. 23. Section through the mesenchyme between aorta and pronephric duct dorsal to cardinal vein
(cf. text figure 4). Stage 32+, Series 1130.34. x 700. To left, outline of pronephric duct (P.D.); the
section passes through an opening from the venous sinus round the duct into the cardinal vein (C.V.).
Puate III.
Fig. 24. Another portion of nephric tract of mesenchyme. Stage 32+, Series 113C. 34. x 600.
Below, a typical erythroblast (ery.); above and to the right, a large mononuclear (/m.), contrasting in size
with the smaller polymorphonuclear cells, ;
Fig. 25, Section through payt of venous sinus round pronephric duct in region of pronephros. Stage 32+
THE HISTOLOGY OF THE BLOOD OF LARVA OF LEPIDOSIREN PARADOXA. 467
Series 113C. 24. x 700. Below and to right is pronephric duct (P.D.) The sinus is crossed by delicate
protoplasmic strands with elongated nuclei. In the meshes of this reticulum, polymorphonuclear granular
leucocytes (yp.). In sinus space itself many large mononuclear cells, also erythrocytes drawn in outline,
some of them in division.
Fig. 26. Section through mesonephros. Stage 32+, Series 113C. 40. x 500. A, aorta; C.V.,
cardinal vein; P.D, pronephric duct. The nuclei of the tubules have not been filled in. The meshes of
the reticular tissue are filled with leucocytes of all varieties.
Fig. 27. Section through splenic vein. Stage 36, Series 139. 19. x 300. a, outline of stomach
wall; }, spleen; e, liver. In vein, a polymorphonuclear leucocyte and four mononuclear cells.
Puate LV.
Fig. 28. Section through spleen rudiment. Stage 32+, Series 113C. 22. x 400. Below and to
right, outline wall of stomach.
Fig. 29. Section through spleen rudiment. Stage 33, Series 108.11. x 300. Below and to night,
wall of stomach, with its nuclei represented in outline. a, a, a, peripheral blood sinus,
Fig. 30. Section of spleen ; Stage 37; Series 139. 20. x 200. 5S, outline wall of stomach.
Fig. 31. High-power view of portion of same section, showing cellular trabecule and spaces containing
red blood corpuscles and white cells of different varieties. x 700.
Fig. 32. Section of anterior end of spleen. Stage 39, Series 137B. 11. x 400. Above and to
left, vein (spv.) ; in centre of spleen, artery (a).
Fig. 33. Portion of same. x 850. a, central artery; 0, peripheral sinus, Four large cells in a row :
to left, two large mononuclear spleen cells, ¢; to right, secondary erythroblast with hemoglobin, d; in
centre, primary erythroblast, e. Cells f and g were introduced from a neighbouring section ; f has a nucleus
like the spleen cells, c, but the basophile protoplasm shows delicate concentric fibrillation; g has a similar
but deeply notched nucleus, and the protoplasm is very delicate and hyaline. It is probably a leucoblast.
TRANS, ROY. SOC. EDIN., VOL. XLI, PART II. (NO. 18) 60
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XX.—Supplement to the Lower Devonian Fishes of Gemiinden. By R. H. Traquair,
M.D., LL.D., F.R.S., Keeper of the Natural History Collections in the Royal
Scottish Museum, Edinburgh. (With Three Plates.)
(Read December 19, 1904. Given in for publication April 14, 1905. Issued separately May 13, 1905.)
Since the publication, about a year ago, in the Transactions of this Society, of my
paper on the Lower Devonian Fishes of Gemiinden,* a review of it has appeared in the
pages of Science by Professor Basnrorp Dean, of New York. In this review Professor
DEAN endeavoured to throw doubts on the correctness of my orientation of the elements
of the dermal skeleton of Drepanaspis Gemiindenensis, in the following words : t—
“Thus, his grounds seem inadequate for distinguishing dorsal and ventral sides.
In no specimen figured is the relation of the dorsal lobe of the tail shown convincingly
to be continuous with the so-called dorsal aspect ; moreover, the eyes occur on the side
which Traquair regards as ventral. Unless additional evidence is forthcoming, it would
accordingly seem to me more probable that the ‘labial’ { of TRaquarr was the ‘rostral’
plate, a structure which appears constant in Heterostracans. ‘This interpretation would
permit the eyes to be seen at the sides of the dorsal armoring, as indeed they occur in
Pteraspis, and would enable us at the same time to locate the greater number of the
larger plates on the dorsal side. This conclusion is the more satisfactory on com-
parative grounds, since there is not an instance in the chordate phylum in which the
eyes and the most complete part of the armoring appear on the (morphological) ventral
side. And I doubt whether, on the present evidence, we can assume, with Professor
Patren, that Drepanaspis might have evaded the law of vertebrate orientation by
swimming on its back. Dr TRaquarr has attempted to solve this dorso-ventral difficulty
by suggesting that either the orbits are ‘sensory’ pits, 7.e. not orbits, or that, ‘since the
specimens are all crushed absolutely flat, it is by no means certain that in the original
uncompressed condition the openings did not look out to the side.’”
The tail of Drepanaspis being heterocercal, the dorsal aspect of the caudal fin, in
accordance with the universal condition of such tails among fishes, will be that along
which the prolongation of the body-axis proceeds, as shown by its greater extent, by
the squamation, and more especially by the larger size and (usually) greater number of
the ridge scales or “fulcra.” In the above-quoted criticism Professor BasHrorp DEan
gave it as his opinion that I had failed to prove that this dorsal aspect of the tail was
coincident with that aspect of the carapace which I described as dorsal, and which he,
* “The Lower Devonian Fishes of Gemiinden,” Trans, Roy. Soc. Edin., vol. x1., Part iv., October 1903.
t Science, N.S., vol. xix., No. 471, January 8, 1904.
{ The plate here meant is in my memoir termed mental, and not “labial.”
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 20). 70
470 DR R. H. TRAQUAIR ON
from other reasons, thought much more likely to be ventral. In other words, I had
turned the fish upside down.
It was, however, satisfactory to read in the same periodical, a few months later, the
following counter-criticism by another eminent American paleeichthyologist, Dr C. R.
Hastman, of Cambridge, Massachusetts :—
‘Whatever may be thought of Traquarr’s figures, though his Plate II. seems to us
conclusive enough, there can be no question about the originals, and those who have
examined them attentively are compelled to admit the correctness of the Scottish
author’s interpretations. The dorsal ridge-scales are larger than the ventral and form
a more extended series, beginning further forward and continuing further back than the
ventral fulera, Several specimens in the Edinburgh Museum have been pointed out to
the present writer by Dr Traquarr in which this row of prominent ridge-scales can be
traced continuously from a point shortly behind the median dorsal plate to the tip of
the dorsal lobe of the tail. The extent to which the caudal lobes are covered with
fulcra is well shown in Plate IV. and Plate [. fig. 1 of the memoir in question, and
their connection with upper and lower systems of body-plates appears tolerably
distinct.” *
For my part, I certainly hold that the relations of the heterocercal tail to the
two surfaces respectively of the carapave were quite satisfactorily proved in the plates
plus text of my former paper. The great median plate of the surface on which
the mouth and supposed orbits are placed, I described as being different from the one
on the other side (see Plates I., II., and IV.) by being bilobate in front, and having
behind a peculiar raised longitudinal fold continuing the direction of the posterior
notch a little way forwards. It is true that I did not, among my plates, reproduce a
photograph of an entire specimen of this plate, the one shown in Pl. III. being
deficient posteriorly, but in the text-figure 3, p. 729, I “ restored its contour from other
specimens” (p. 728). And in the specimen, of which a good photograph is given, in
Pl. V. fig. 1, the line of smaller fulera, situated on the presumably ventral margin of
the tail, is exhibited with absolute clearness running up to the posterior (cloacal) notch
of that plate, which, as shown by its prominent median fold, is as undoubtedly the plate
described by me as ventral.
But as Professor DEan’s remarks have been widely circulated in so well-known a
periodical as Sczence, I shall in this “Supplement” go over the subject of the orienta-
tion of the exoskeleton of Drepanaspis once more, this time illustrating by specimens
not figured in my previous memoir, though one of them (Pl. I.) was before me
when it was written.
The depressed and flattened carapace of Drepanaspis shows in front a wide mouth-
slit, which, though nearly terminal, is not quite so, and consequently is seen only on
one aspect of the creature, which may meanwhile be called the oral one. It
* Science, N.S., vol. xix., No. 487, April 29, 1904, p. 704.
THE LOWER DEVONIAN FISHES OF GEMUNDEN,—SUPPLEMENT. A71
‘is this aspect, represented in Pl. III. of my former memoir, which I have de-
noted “ventral,” and on which we find two median plates, the anterior and
smaller of which bounds the mouth behind, while the larger one has posteriorly
a conspicuous median notch (cloacal), the direction of which is continued forwards
for some little distance im the middle lie by the longitudinal fold to which I
have already called attention. In this side of the creature are also seen the “ orbital”
or sensory plates, the anterior and posterior ventro-laterals, and a narrow ex-
ternal marginal portion of the postero-lateral on each side. In the specimen to which
_ [have just referred the posterior extremity of the great median plate is deficient, but
this deficiency I now remedy by figuring the one shown in Pl. I. of this Supplement,
and I may say that this is the specimen which enabled me to complete the restoration
of the plate in question, as seen in text-figure 3, p. 729 of my previous paper. Of this
example an accurate photograph is given in PI. |. of the present communication, and on
comparing this figure with Pl. III. (former paper) it will be at once seen that the
creature presents to us the same oral surface ; for though the front part with the mouth
is lost, there is no mistaking the “ orbital” of one side («.), the anterior ventro-laterals
(a.v.l.), the postero-laterals (p.l.), and the posterior ventro-lateral of one side. In the
centre of the specimen we see the great median plate (m.v.) of this surface, considered
by me as ventral, in a state of nearly absolute completeness, though obliquely deformed
like the rest of the specimen. With perfect clearness we see the bilobate front of this
plate, the re-entering angle thereby formed being occupied by a portion of the mental
plate (m.), while posteriorly the median fold, terminating on the notch behind, is shown
with absolute distinctness. Then, below this, the hinder portion of the median plate
(m.d.) of the opposite side is seen from its inner or visceral aspect, being brought into
view by an oblique backward thrust.
The aspect of the carapace to which the last-mentioned plate (m.d.) belongs is seen
in Plates I. and II. of my former memoir. On it the mouth-slit is never visible,
and consequently the term aboral may be temporarily applied to it. It shows
only one large median plate, which differs strikingly from the corresponding one
on the oral aspect in its proportionally narrower shape, in not being emarginate
or bilobate in front, in having its posterior notch smaller, pointed in front and
filled up by a narrow plate, and finally in the total absence of the median fold
which is so conspicuous on the posterior part of the great median plate of the oral
surface. We also recognise the aboral surface by the much greater extent to which
the postero-lateral plates are visible, by the greater number of small polyoral plates
surrounding the median one, by the fusion of some of these little plates into what I
have called the rostral plates in front, and by the two shallow pits, one on each side of
the front of the head, caused by the compression of one of the small plates over the
ning-like thickening round the margin of the orbital or sensory opening internally.
Having now made sure of the two surfaces of the carapace, the details of which are
put together in my restored figures (pp. 726 and 729 of my previous memoir), it now
472 DR R. H. TRAQUAIR ON
remains to settle accurately the relation to those surfaces of the two margins of the
caudal fin. ,
In fig. 2, Pl. V. of my previous paper, a tail is represented which, though truncated
behind, shows clearly that on one margin the fuleral scales are much larger than on the
other; and an additional difference is, that those of the smaller series are, in front,
peculiarly short and erect. Then, an inspection of fig. 1, Pl Il. of the present
Supplement shows that the caudal fin, though not bilobate, is unsymmetrical above
and below, and projects further back on that aspect on which the larger fulcra are
placed ; moreover, we observe that the lateral scales which clothe the fin are, under the
line of larger fulcra, also larger. In other words we have, to all appearance, a normal
piscine heterocercal tail, of which the longer margin, provided with the larger fulcra, is
presumably the dorsal one, and it now remains to prove with which aspect of the
carapace this margin of the tail coincides. This question, I maintain, was already settled
by the specimen represented in Pl. V. fig. 1 of my previous memoir, in which the line
of smaller fulcra is traceable to the apparent cloacal opening at the posterior extremity
of the median fold of that plate, which is certainly the median plate of the oral aspect
of the carapace.
But a still more complete demonstration of these relations is afforded in Pl. ILI. of
the present Supplement. Here we have a specimen seen from the oral side, as shown
by the form of median plate (.v.) with its posterior fold, the presence of the sensory
plate x. with its orbital (?) perforation, and of the plates a.v.l. and p.v.l., designated by
me anterior and posterior ventro-lateral respectively. It may also be noted that the
median plate (m.d.) of the aboral side, seen from the internal surface, is shown displaced,
and projecting from below the root of the tail. A considerable part of the caudal fin
with the fulera on both margins is shown, and, with absolute clearness, the line of
smaller fulcra (v,f:) is seen to proceed forwards and end at the posterior extremity of
the great median plate of the oral surface of the carapace. Compare this figure with
the two in Pl. V. of my former memoir.
It is therefore proved, beyond all possibility of doubt, that that margin of the
caudal fin which carries the row of smaller fulcra is coincident with the oral aspect of
the carapace ; and conversely, that the other margin, which projects further back, carries
the large fulcra, and presumably contained the caudal body-prolongation, is coincident
with the aboral one. If, then, the tail is constructed according to the normal piscine
heterocercal type, the aboral surface of the carapace is the dorsal, and the oral one ts
the ventral surface.
But it may be asked whether in Drepanaspis the heterocercy might not have
been reversed as in the reptilian Ichthyosaurus, by the caudal prolongation of the
body axis having passed down along the ventral margin of the caudal fin, instead of
along the dorsal one. In that case I should still be in the wrong as regards the
orientation of the two surfaces of the carapace !
In the first place, we know of no such case among fishes. For, though the lower
THE LOWER DEVONIAN FISHES OF GEMUNDEN,—SUPPLEMENT. A73
lobe of the caudal fin in the Angel-fish (Squatina) is larger and projects further back
than the dorsal one, there is no downward bend of the vertebral axis, which proceeds
straight backwards. Nor has the greater size of the lower caudal fin lobe in the
teleostean homocercal Flying-fish (Hxocetus) any bearing on the question.
Another circumstance which cannot be overlooked is the position of the mouth.
This, as I have already shown, is not truly terminal, but is situated on that aspect of
the carapace which is coincident with the shorter margin of the fin and the apparent
eloacal opening. Now, although the mouth may appear to look upwards in such a
peculiarly specialised bony fish as the recent Angler (Lophius), yet, judging from the
analogy of other Ostracoderm types, such as Pteraspis, Cephalaspis, and Asterolepis,
the dorsal side is not the one on which we would expect to find it in the case of
Drepanaspis.
But of really crucial importance is the position of the cloacal opening or vent. It,
at least, we cannot expect to find on the dorsal aspect of the tail of a fish or fish-like
vertebrate, unless we should take upon ourselves to deny the presence of a notochordal
vertebral axis in those creatures. Now if we look at Pl. II. of my former memoir, which.
represents the aboral surface of the fish, we find no trace of any such opening, although
the scales of the middle line, between the posterior margin of the great median plate
and the fulcra of the tail, are in complete order and well preserved. The aboral side
of the fish is therefore not ventral; and if it be not ventral, then it is dorsal, and the
oral side is the ventral one, in accordance with my original description.
Turning now to this oral side,—in the specimen represented in fig. 1, Pl. V. of my
former memoir, the position of the cloacal opening seems to me to be distinctly marked
just in the notch which follows the prominent posterior median fold of the great central
plate, in front of the first fulcral scale in the middle line. Again, in the specimen
represented in Pl. III. of the present Supplement, we have the great median plate
(m.v.) of the aboral surface distinctly shown, as is also its median fold behind and the
notch ¢., though one margin of the latter is broken away. It is this notch c. which, in
my opinion, marks the position of the cloacal opening, in perfect accordance with the
appearances shown in the figure just referred to, and also represented in the restoration
of the ventral surface in text-figure 3, p. 729 of my previous memoir. It is, however, to
be noted that in this specimen (PI. III.) the anterior extremity of the first (ventral)
fuleral scale is slightly displaced, or shoved to one side, so that it no longer closes the
cloacal notch (c.), which is consequently left open behind.
I submit, therefore, that I have amply shown—
First.—That the aboral aspect of the carapace of Drepanaspis is coincident with
the apparent dorsal “lobe” or aspect of the caudal fin.
Second.—That the absence of a cloacal opening on the aboral aspect of the
commencement of the tail, and its apparent presence on the oral one, is equivalent to a
proof that the aboral margin of the tail, consequently of the entire creature, zs the
dorsal aspect. Conversely, the oral aspect is the ventral; and my previous orientation
474 DR R. H. TRAQUAIR ON
of the creature is correct, no matter on which side of it the openings supponay to be
orbits are placed.
No one will question the sensory nature of these openings, but that they really are
eye-orbits, however possible or even probable that may be, is by no means certain.
Their position is, however, analogous to that of the supposed orbits in Pteraspis ; and
I can only repeat that, situated as they are so near to the right and left edges of the
vertically flattened carapace, they might well, in the living and uncompressed condition
of the animal, have enjoyed a considerable amount of lateral outlook.
Scales of the tail-pedicle-—I have already in my previous memoir (p. 731) alluded
to the fact that on that part of the tail which lies between the carapace and the caudal
fin there is at least one longitudinal row of scales, which are considerably higher than
broad, and which are seldom well seen, owing to that part being usually obscured by
pyritous deposit. As the form of these scales can only be expressed in a direct lateral
view, they could not be properly represented in my restored figures, in which the tail-
pedicle is depicted as seen from above and from below.
However, in fig. 2, Pl. Il. of this Supplement the tail-pedicle is seen free of pyrites,
and here two. rows of such vertically elongated scales are clearly visible. At the caudal
fin they pass into smaller scales of a rhombic form, which become very small on the
fin-membrane.
This specimen is also interesting in this respect, that, while lying on its ventral
surface, that is to say, back upwards, the median dorsal plate has dropped out and the
visceral aspect of the median ventral one has come into view, this plate being at once
recognisable by the prominent emargination of its anterior border. This condition is
the reverse of what more commonly occurs, for, as I have already stated, it is not at all
rare to find in a specimen lying on its back that the median ventral plate has been lost,
and the inner surface of the median dorsal one shown in consequence. See my previous
memoir, Pl. [V., and explanation, p. 738.
In sonclaein: I may remark that up to the present I have not been able to — in
Drepanaspis any trace of a lateral sensory canal system.
THE LOWER DEVONIAN FISHES OF GEMUNDEN,—SUPPLEMENT. 475
EXPLANATION OF THE PLATES.
All the figures in the following plates have been reproduced from photographs taken from specimens from
the Lower Devonian Roofing Slate of Gemiinden in the Royal Scottish Museum.
m.d., median dorsal plate. p.l., postero-lateral.
m.v., median ventral. f.p.l., right postero-lateral.
m., mental. L.p.l., left postero-lateral.
Z., SENSOTY. d.f., dorsal fuleral scales of tail.
a.v.l., anterior ventro-lateral. v.f., ventral fulcral scales of tail.
p.v.l., posterior ventro-lateral. ¢., position of cloacal opening.
PuaTE I.
Ventral surface of a carapace of Drepanaspis Gemiindenensis, somewhat deficient in front and on the left
side. The specimen is strongly obliquely deformed, so that the lateral plates on the right side are shoved in
advance of those on the left. Here we have an exceedingly good view of the median ventral plate (m.v.)
with its posterior median fold and notch, and the anterior emargination in which the hinder portion of the
mental plate (m.) is seen to be lodged. Owing to oblique displacement of parts, the hinder portion of the
internal surface of the median dorsal plate (m.d.) is also seen below and behind the median ventral.
Compare this figure with that on Plate III. of my previous memoir.
Puate II.
Fig. 1. Tail and caudal fin of Drepanaspis, to show the oblique heterocercal configuration, and the
greater size and strength of the fulcra on the upper or dorsal margin. The lateral scales of the tail-pedicle
in front of the caudal fin are covered with pyritous deposit, and the commencement of the row of dorsal
fulera is also not exhibited. Natural size.
Fig. 2. Specimen of Drepanaspis somewhat deficient on the left side, lying on its ventral surface, but
with the median dorsal plate wanting, so that the zmmer surface of the median ventral is exposed. At the
antero-external corner of the carapace the small rounded pit formed by the compression of one of the external
dorsal polygonal plates over the internal ring-like thickening of the opening in the sensory plate is well
marked ; behind this, the outer margin of the carapace and its postero-lateral angle are formed by the
postero-lateral plate. The median row of dorsal fulcra is seen from its commencement, and the two rows of
vertically elongated scales on the side of the tail-pedicle are unusually well shown. The ventral fulcra are
not seen, having been cut off by the broken edge of the stone, but a great part of the expanse of the caudal
fin, covered with small rhombic scales, is visible, One-half natural size. j
Puate III.
Specimen of Drepanaspis Gemundenensis lying on its back, and showing the greater part of the outer
surface of the median ventral plate (m.v.) with the posterior mediag fold, and the notch c. marking the
position of the cloacal opening. ‘This notch is followed by the line of rfedian ventral fulcral scales (v.7.), the
first of which is slightly displaced in front, so that its anterior margin no longer completes, as it ought, the
notch into an opening. ‘The dorsal fulcra (d,f.), of obviously larger size, are seen on the opposite side of the
tail, the anterior ones being slightly confused. The scales of the beginning of the tail-pedicle are, as is
commonly the case, obscured by pyritous deposit, but those further back and on the caudal fin are clearly
exhibited. Portions of the left sensory plate (x.), of the left anterior ventro-lateral (a.v.l.), and of the left
postero-lateral (L.p./.) are seen at the top of the figure ; a portion of the right postero-lateral (A.p.l.) is also
seen below, removed from the rest of the fish, and turned right over so as to show its dorsal surface. Lastly,
the median dorsal plate (m.d.) is so displaced from the rest of the body as to be seen almost in its entirety,
—seen, of course, from its internal or visceral aspect.
a Roy. Soc. Edin! Wola:
Dr R. H. Traquarr on Fossit Fisoes oF GEMUENDEN, SUPPLEMENT——PuiaTE I.
Reduced by One-fourth.
M‘Farlane & Erskine, Edinburgh.
iS
M'Farlane & Erskine, Edinburgh.
One-half Natural Size.
NDEN, SUPPLEMENT—PLatTE [J].
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Tins. Roy. Soc. Edint- | Viole xm,
Dr R. H. Traquair on Fossit Fisues or GEMUENDEN, SuppLEMENT—Prate III.
Reduced by Two-sevenths.
M‘Farlane & Erskine, Edinburgh.
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TRANSACTIONS
OF THE
OVAL SOCIETY OF EDINBURGH.
L UME XLI. PART Il].—FOR THE SESSION 1904-5.
CONTENTS.
PAGE
| Contribution to the Freshwater Plankton of the Scottish Lochs. By W. Wsst,
dG. S. West, M.A., F.L.S. (With Seven Plates), . , ; hk all
f (Isswed separately 15th June 1905.)
ibranchiata of the Scottish National Antarctic Expedition. By Sir Cuartes ©
K.C.M.G., 5 : : ‘ = BES
(Issued ith 9th Were 1905. )
‘ernal Structure of Sigillaria elegans of Brongniart’s “ Histoire des végétaua
By Roserr Kinsron, F.R.S.L. & E., F.G.S. (With Three Plates), . ~ "633
og * (Issued separately 30th June 1905.)
ture of the Series of Line- and Band-Spectra, By J. Haum, Ph.D., . ee 3!
(Issued separately 3rd July 1905.)
ydrodynamical Theory of Seiches. By Professor CurystaL. With a Biblio-
ul Sketch, , ‘ : : ; ; ; - oh B99
(Issued separately 3rd July 1905.)
of Linear Differential Equations of the 2nd Order, 6 Rae! Professor /
Seiche-equations. By J. Harm, Ph.D... ; : =) (GOL
(Issued separately 31st Jay 1905.)
ada of the Scottish Lochs. By Jamus Murray. (With Four Plates), Js BTL
P (Issued separately 20th July 1905.)
ains in the Scottish Peat Mosses, Part I.—The Scottish Southern Uplands,
J. Lewis, F.L.S. (With Six Plates), . ; , é = 2) GDS
_ (Issued. ereeeecie August 1905.)
iv B.Sc. (With Twelve Plates), . ’ : PRS
‘4 (Issued separately 30th August 1905.)
aph on. the general Morphology of the Myxinoid Fishes, based on a study of
_ Part I.—The eae! of the Skeleton. 7 Frank J. Cour, B.Se. Oxon.
hree Plates), ; : : ‘ sD
_ (Issued separately 25th Bapdebaile 1905. )
story of Xenopus levis, Daud. By Epwarp J. Buss, B.A., B.Sc., Assistant
at the University of Glasgow. (With Four Plates),
i (Issued separately 8th November 1905.)
EDINBURGH:
& NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON.
- MDCCCCVI.
Prive Forty-five Shillings.
ii CONTENTS. ae
XXXII. Calculation of the Periods and Nodes of Lochs Earn and Treig, from the Bathyme
Data of the Scottish Lake Survey. By Professor CorystaL and Ernest Macpac
Wepperzsurn, M.A. (With Two Maps),
(Issued separately Tth November 1908. )
XXXII. The Aleyonarians of the Scottish National Antarctic Bupedition, By Professor J. Art
Tuomson, M.A., and Mr Jamus Rircuiz, M.A. (With Two Plates), :
(Issued separately 18th January 1906.)
Tur CouNvIL OF THE SOCIETY,
ALPHABETICAL List OF THE ORDINARY FeLLoWs,
List or Honorary FELLows,
List oF OrpINARY aND Honorary FELLows eee DURING duane 1904- 1905,
FeLttows Dsceasep, 1904-1905, ; : : ; ; ; : a
LAWS OF THE SOCIETY, ; ;
Tue Kaira, -MakpouGALL-BRISBANE, Neo AND Danis wannceae ae Peis,
Awarps oF THE KerrH, MaKpouGaLL-BrisBaNne, AND Newitt Prizes rrom 1827 ro 1904, ax
THE GUNNING VICTORIA JUBILEE Prizm From 1884 to 1904,
PROCEEDINGS OF THE STaTUTORY GENERAL Muztine, 1904,
InpEx, : ; : : L : : : P ; sia
ERRATUM. .
Vol. XLI., Part III., No. XXII., p. 529, figs. 11 to 14, for Tritonia antarctica read Tritonia
(Gyeaaee)
.—A further Contribution to the Freshwater Plankton of the Scottish Lochs.
By W. West, F.L.S., and G. S. West, M.A. F.L.S. Communicated by
Professor I. B. Batrour, F.R.S. (With Seven Plates.)
(MS. received January 26, 1905, Read March 6, 1905. Issued separately June 15, 1905.)
CONTENTS.
PAGE PAGE
I. Int oduction, . : . 477 | III. Systematic Account of the more important
[. Detailed Account of the Bleaicon we the iow Alge of the Plankton, . : . 496
. ‘investigated, c : - : 5 . 478 | IV. Gaul Remarks on Scottish ERptoplanicont . 509
J. INTRODUCTION.
On first investigation of Scottish plankton in 1901-2, although only tentative and
what meagre, was sufticient to show that, as regards the phytoplankton, the lochs
e west and north-west of Scotland were probably richer than any lakes previously
ed. Owing to the extraordinary richness of the few collections then examined, it
msidered eminently desirable that the investigation should be further extended.
e have been enabled to do by means of a third successive grant from the Royal
, and the present paper is one of the results of a visit to the north-west of Scot-
July, August, and September, 1903.
terial was collected from more than twenty of the lochs in Perth, Inverness, Ross,
Outer Hebrides, and its examination has been most gratifying. The collections
made in the ordinary manner by silken tow-nets, about 9 inches diameter at the
1, and the material was mostly preserved in 4 p.c. formalin. It is to be regretted
much of this material could not be examined in the living state, as there is every
to believe from the preserved samples that some at least of the lochs were rich
Heliozoa.
In Perthshire, Loch Tay was investigated during the month of July along a great
its length, and a number of collections were also made from the River Lochay.
Inverness, six lochs were investigated during August, viz., L. Bairness, L. na
Sgoilt, L. na Criche, L. Gorma, L. Morar, and L. Shiel. Of these, the two latter
the best material.
In Ross, material was collected during September from L. Luichart and L. Rosque.
In Lewis, nine lochs were investigated during August. The plankton of most of
se lochs was distinctly rich, especially that obtained from Loch Fadaghoda, which
unrivalled for the abundance and diversity of its Desmid-flora.
Harris, three lochs were examined, viz., L. Diracleet, L. a Mhorghain, and L.
_ TRANS. ROY. SOc. EDIN., VOL. XLI. PART III. (NO. 21). 71
478 MR W. WEST AND MR G. 8S, WEST ON
In our previous contribution to Scottish freshwater plankton we recorded a number |
of algze from Loch Tay, Perthshire, and from Loch Laxadale, Harris; and for the sake ‘
of better comparison these records have been included in the tabulated account of the: |
plankton, along with additions obtained by subsequent collections from these lochs. j
We have also included in this same table the results of an examination of some —
material forwarded to us by Mr J. Murray, of the Scottish Lake Survey (Pullar Trust),
from Lochs nan Cuinne, Ghriama, and Ruar, in Sutherland, and from Loch Morar, in
Inverness. We obtained permission from Sir Jonn Murray to utilise these results to
the best advantage, and we have therefore tabulated them alongside the other plankton —
records. The material from Loch Ruar was both rich and interesting, and consisted —
principally of Desmids and Diatoms. The Desmids were almost as abundant and con-—
spicuous as those from Loch Fadaghoda, but were not nearly so diversified in character. —
The Diatoms, however, were especially noticeable, and constituted fully one-half of the —
plankton. a
In preparing this paper we have largely made use of photomicrography. An |
inspection of photomicrographs, especially those taken under a magnification of 100 —
diameters, greatly facilitates the comparison of plankton from different lochs, and —
renders more manifest the distinguishing features of the material. In preparing the
plankton-material for photography, it is absolutely essential to remove the larger
animals, such as the Entomostraca, otherwise the thickness of the film of water is
too great to allow of obtaining a reasonable focus of the majority of the floating objects.
The photographs used for purposes of illustration are principally of material from Lochs
Ruar and Fadaghoda, as they indicate very clearly the differences between the Scottish
plankton and that of most of the lakes of continental Europe.
Mr Lemmermann, of Bremen, has kindly reported upon the Persdinew and some |
other flagellate organisms from certain of the lochs.
II. DetaiteD Account oF PLANKTON OF LOCHS INVESTIGATED.
Plankton has been examined from the following twenty-four lochs and from the
River Lochay. The date refers to the date of collection.
1. Loch Tay, Perthshire, July 1903.—The loch is about 12 miles long and 290 feet
above sea-level, and is situated in the vicinity of mountains which reach a height of —
4000 feet. The collections were made from the western part of it during very fine
weather. Desmids and Diatoms were abundant in the plankton, and there was also
an abundance of Celospherium Kiitzingianum.
2. River Lochay, Perthshire, July 1903.—The collections were made from the lower
reaches of the river before its entrance to Loch Tay. Diatoms were very abundant.
3. Loch Bawrness, Inverness, Aug. 1903.—This is a small loch situated among very
rocky surroundings in Moidart. The plankton contained numerous Desmids and a great
abundance of the Rotifer Anwrea cochlearis, Gosse.
THE FRESHWATER PLANKTON OF THE SCOTTISH LOCHS. A79
4,5, and 6. Lochs na Cloiche Sgoilt (alt. 800 feet), na Criche (alt. 700 feet), and
Gorma (alt. 800 feet), Inverness, Aug. 1903.—Small lochs in Moidart, with rocky
‘surroundings, the largest one being barely a mile in length. A long-spined form
of Ceratiwm hirundinella and Crucigenia irregularis were very abundant in Lochs
na Cloiche Sgoilt and Gorma. The plankton of Loch na Criche was remarkable for
the enormous quantity and large size of the colonies of Kirchneriella lunaris (Kirchn.),
Mob.
7. Loch Morar, Inverness, Aug. 1903.—This loch is 114 miles in length, and at its
widest part is only a mile and a half in breadth. It is a little more than 30 feet above
the sea-level, and is one of the deepest lakes in Europe. It has a maximum depth of
1017 feet, and only seven of the lakes of continental Europe exceed this depth—four in
Norway and three in Italy. The temperature of the surface-water in July 1902 was
55°2° F., and the temperature at the bottom 42'2° F.*
Three collections of plankton were examined from this loch. All were remarkable,
owing to the quantity of Stagonema minutum, Hass., St. mamillosum, Ag., Calothrix,
sp., and Gleocapsa Ralfsiana (Harv.), Kiitz., they contained. These alge are not
plankton-forms, and had most probably entered the lake by mountain torrents during
heavy rains.
8. Loch Shiel, Inverness, Aug. 1903.—This loch is about 18 miles in length,
and one of the narrowest in Scotland, presenting a close resemblance to a Norwegian
fjord. For much of its length it lies between high mountains, and its altitude is only
15 feet above sea-level. The plankton was mostly obtained from towards the western
extremity, and species of Mougeotia and Zygnema were very common init. Rhizopods
Were not uncommon, one species of Nebela being hitherto undescribed.
9. Loch Lwmchart, Ross, Sept. 1903.—This loch is above 4 miles in length, and is
280 feet above sea-level. It is situated in a valley between rocky hills, the lower
slopes of which are thickly wooded. The plankton contained quantities of Mesoteniwm
macrococcum (Kiitz.), Roy & Biss., in small gelatinous colonies, and also an abundance
of Clathrulina elegans, Cienk., and Diplosigopsis frequentissima (Zach.), Lemm.
10. Loch Rosque, Ross, Sept. 1903.—A loch about 3 miles in length, 508 feet
above the sea-level, and situated between high mountains. The plankton contained
quantities of Clathrulina elegans, Cienk., and was rather remarkable for the scarcity of
Peridiniex. It contained numerous specimens of a Rhaphidiophrys, probably R. viridis,
Arch., and Diplosigopsis frequentissima (Zach.), Lemm.
11, 12, and 13. Lochs nan Cuinne, Ghriama, and Ruar, Sutherland.—Loch nan
Cuinne is about 3 miles in length; 390 feet above sea-level, and is situated among a
number of low hills of north-east Sutherland. Lochs Ghriama and Ruar are much smaller
lochs. The plankton was collected from these three lochs by Mr James Murray, of the
Scottish Lake Survey (Pullar Trust), and samples were forwarded to us for the investi-
* Bathymetrical Survey of the Freshwater Lochs of Scotland, part v.—Lochs of the Morar Basin—by Dr T. N.
Jounston, The Scot. Geog. Mag., Sept. 1904, vol. xx., No. 9.
480 MR W. WEST AND MR G. S. WEST ON ;
gation of the alge. The material was in every case fairly rich, that from Loch Ruar~
being especially rich in Desmids and Diatoms. |
14. Loch east of Cearnabhal, Lewis, Aug. 1903.—This was a small deep loch, about
200 feet above sea-level, and situated amongst rocky bog-land. .
15. Loch Cuthaig, Lewis, Aug. 1903.—A small loch among rocky and bogey land,
about 200 feet above sea-level. The plankton contained many Desmids, the most
abundant of which were forms of Arthrodesmus Incus (Bréb.), Hass., and Stawrastrum
lunatum, Ralfs, var. planctonicum.
16. Loch Fadaghoda, Lewis, Aug. 1903.—This loch is about 2 miles long, with a
very irregular contour. It contains several rocky islands, and its margins are both
rocky and bogey. The plankton was well investigated, and the material collected was
the richest we have ever examined. The Desmids were in great quantity, and also in
great variety. Many species of great rarity and interest occurred in abundance in this —
plankton, and the investigation of this material has extended the geographical range of
quite a number of Desmids. Stawrastrum Ophiura, Lund, and Sphexrocystis Schroeteru,
%
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Chod., were especially noticeable.
17. Loch Langabhat, Lewis, Aug. 1903.—A loch about 8 miles in length and about
200 feet above the sea-level. The plankton contained large numbers of Mallomonas
caudata, lwanoft.
18, 19, 20, 21, and 22. Lochs Rownebhall, an Sgath, Shubhaill, Stranabhat, and an
Toman, Lewis, Aug. 1903.—These lochs are all of small size and are similarly situated,
none being at an altitude of more than 300 feet above sea-level. The plankton obtained
from them was of a somewhat uniform character, that from Loch Stranabhat being
undoubtedly richer than the others. Loch an Sgath was remarkable for the great
abundance of Rotifers. L. Roinebhall contained Mallomonas longiseta, Lemm., and —
M. producta (Zach.), Iwanoff.
23. Loch Diracleet, Harris, Aug. 1903.—A small loch south of Tarbert, with rocky -
shores, and situated very little above sea-level. The plankton was characterised by the —
great abundance of Stawrastrum jaculiferum, West. 4
24. Loch a Mhorghan, Harris, Aug. 1903.—A small loch among the hills 5
miles north of Tarbert; its altitude is 480 feet. The plankton had no distinguishing
features, although Asterzonella gracillima, Heib., occurred in considerable quantity.
25. Loch Laxadale, Harris, Aug. 1903.—This loch is about 15 miles in length, a
quarter of a mile in breadth, and is 40 feet above sea-level. It is situated near Tarbert,
in the midst of high rocky mountains. The plankton was somewhat varied in character,
and contained an abundance of Staurastrum paradoxum, Meyen, and St. jaculiferum,
West. Seven species of Rhizopods were observed in this plankton. LLEMMERMANN also
records Mallomonas caudata, Iwanoff, and M. longiseta, Lemm.
481
OF THE SCOTTISH LOCHS.
THE FRESHWATER PLANKTON
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TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 21).
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MR W. WEST AND MR G. 8S. WEST ON
Ceratium hirundinella, O. F. Miiller.
The abundance of this organism is one of the most conspicuous features of the Scot-
tish plankton, but suttcient observations have not been made to decide definitely the
time of its maximum period.
The length and divergence of the antapical horns are exceedingly variable.
LEMMERMANN gives the following measurements :—
Tenecice Length of | Length of | Length of Total | —
Locality. a ae |Ist Antapical] 2nd Antapi-| 3rd Ant- Length of | —
pical Horn. :
Horn. cal Horn. | apical Horn. Body. |
Loch Cuthaig, i 103u 68-5 44. 15p 2345p
Loch Roinebhall, Lewis, 96-1096 | 72-85p 33-42 Tp 212-245°6y |
Loch Shubhaill, f : 105-124 60-93 37-545 py 4-15 py 2105-281!
Loch Diracleet, : 103-lllp 82-104u 34-49 15-234 238-291u |
Loch a Mhorghain, Harris, 101-153p 86-1204 45-60 15-30 251-357
Loch Laxadale, : 105-120°54 | 73-103u 40-45 15-31°54 | 237-304p |]
To these we add two others—
Loch Ruar, Sutherland, 86 46u Qhp 0 1984 |
Loch Fadaghoda, Lewis, 118-129 67-82 60-67 31-38 235-260u |
In the specimens from Loch Ruar there was a complete absence of the third (short)
antapical process, and in those from Loch Fadaghoda the three antapical processes were
nearer a uniform development than in any other specimens examined.
Fig. 1.
A, from Loch Ruar, Sutherland ; B, from Loch Asta, Shetlands; C,
Ceratium hirundinella, O. F. Miiller.
from Loch Fadaghoda, Lewis; D, from Loch Beosetter, Bressay, Shetlands.
horn ; at,, at,, ats, the three antapical horns.
(All x 200.) ap, apical
In fig. xylogr. 1, A, the third antapical horn is absent, but in fig. 1, D, it has reached
its maximum development (at,). _LEMMERMANN has figured a large number of different
THE FRESHWATER PLANKTON OF THE SCOTTISH LOCHS. 495
forms of this species from the plankton of Sweden (wde Lemm. in Archiv f. Bot.,
Bd. ii., No. 2, t. 2, f 1-49). We have found all these forms in the Scottish plankton,
and cysts occur plentifully. Figs. xylogr. 1, B and D, are from specimens observed in
plankton from the Shetland Islands. Fig. 1, B, shows the first appearance of the third
antapical horn (at,), and fig. 1, D, shows the maximum development and divergence of
the three antapical horns.
Peridinum Westw, Lemm., sp. n.
Body nearly globular, at sie posterior margin slightly sinuate, 44-45 long and
42°5-59u broad, in the girdle-view (fig. xylogr., 2, C and D) nearly reniform, divided by
the transverse furrow into two nearly equal halves. Transverse furrow disposed in a
conspicuously spiral manner (vide fig. 2, A). Longitudinal furrow reaching a short
distance into the apical half and downwards as far as the posterior margin of the body,
in the posterior part much dilated, and in the middle of the left margin with a blunt
papilla. Membrane ornamented with irregular, undulating, and sometimes ramified
ridges.
Plates BE Aianly developed, in the lower part of the body much larger than in
the upper part. Hpivalve (fig. 2, C) with a transversely elongated rhomboidal plate ;
equatorial plates seven, the dorsal one much larger than the others; first apical plate
quadrangular, dilated outwards ; second apical plate pentagonal, nearly as long as broad ;
third apical plate on the dorsal side of the first dorsal plate, forming part of an apical
eirele of plates; fourth apical plate irregularly quadrangular ; first dorsal plate nearly
triangular, situated at the apex of the upper part of the body; second dorsal plate
trapezoid ; apex wanting. Hypovalve (fig. 2, D) with two antapical plates, of which the
right one is the larger; suture between these plates running from the middle of the
ventral margin obliquely towards the left dorsal side.
Intercalary strips of the carapace very variable, in old cells sometimes very broad.
Hab.—Lochs Bairness and Shiel, Inverness ; Loch Rosque, Ross; Loch Shubhaill,
Lewis, Outer Hebrides.
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Fie, 6.—Branchia. Fic. 7.—Portion of edge of jaw. Fic. 8.—Median tooth.
Fies. 6 to 8.— Tritonia appendiculata.
The sheaths of the rhinophores are 3 mm. high and 3°5 mm. broad ; the margins are
jagged. The rhinophores are thick clubs, surrounded by about ten simply pinnate or
bipinnate plumes, white, with greenish tips, and hard to separate from one another.
The dorsal margin is distinct, 3 mm. broad, and starts from the back of the rhinophore
sheaths, to which it is attached, giving them a somewhat elongated appearance
behind,
On each side are nineteen branchie (fig. 6) of various sizes, but those on the left are,
on the whole, rather larger than those on the right. ‘They are scanty, and not foliaceous.
The smaller are simply bifid; the larger consist of three processes set on a common
prominence; each process is twice bifurcate. The anus is 22 and the genital orifice
15 mm. from the anterior end of the body. The former is just under the dorsal
margin, the latter half-way up the side of the body and surrounded with ample folds.
There is no tail separate from the body. The foot is rounded and grooved in front,
where it is thickened by a layer of what appear to be glands.
The pericardium and heart are as usual. The central nervous system is large, but
no eyes were found. The ganglia are yellow and smooth, showing no signs of grannla-
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. Spal
tion. The pedal ganglia are round, the cerebro-pleural elliptical, with traces of a
division into two parts.
The jaws are strong, horny, elongate, yellow, with black edges. They are 10 mm.
- long and 4°3 wide at the broadest part. The region of the hinges is straight and flat.
The rest of the jaw curves outwards and is convex. The edge (fig. 7) itself is smooth,
but behind it are about six rows of stout denticles, which are blackish in the jaw and
yellowish on the short (1°5 mm.) masticatory process. Behind them are about fifteen
rows of flatter, roundish prominences, not amounting to denticles. The radula is of the
type usual in Tritonia, with a formula of 29 x about 50.1.1.1.50. The median (fig. 8)
tooth is tricuspid, the central cusp, pointed, those at the side blunt. The first lateral
(fig. 9) is of the usual clumsy shape: the rest (fig. 10) are hamate, moderately stout
Fic. 9.—Ist lateral. Fre. 10.—Laterals.
Fras. 9 and 10.—Tritonia appendiculata.
and moderately curved. The tips are often broken off, particularly near the middle of
the radula.
The salivary glands are 8 mm. long, thin, ribbon-shaped above, slightly flocculent
below. The cesophagus is at first narrow, but rapidly broadens out and enters the thin
membranous stomach. About half of the stomach is surrounded by the brownish-
yellow liver, which is itself surrounded by the hermaphrodite gland. The intestine
leaves the stomach at the point where it emerges from this covering of liver and gland.
lt is strong and thick, and turns to the right after a slight bend forwards. Both the
stomach and the intestine were filled with blackish matter, with which were mixed some
bright red spiculous animal fragments.
The hemaphrodite gland consists of bright pale-yellow bodies set in colourless jelly.
The mucous and albumen glands are large, both greyish-yellow. The spermatotheca is
elongate, with a short duct. The vas deferens is convoluted. The verge is broadly
conical at the base, with a thin pointed top.
This species offers many points of resemblance to 7. challengeriana (Bergh,
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 22.) 78
528 SIR CHARLES ELIOT ON. THE NUDIBRANCHIATA
Challenger Reports, Nudibranchiata, p. 45), but the veil is different, and the grooved
tentacles are, as preserved, below it; there are more tubercles on the back, and the
branchiz are fewer in number. The tentacular prolongations of the lips are also
remarkable. Rudiments of such formations may be seen in other species, but here they
are unusually distinct.
Though I hesitate to refer the specimen to TZ. challengeriana, it is quite possible
that the two species may not really be distinct.*
Tritoma pallida, Stimpson. Stimpson, Proc. Acad. Philadelphia (1854), p. 388.
One specimen, with the label ‘8 m. N. of Dassen Island in 35 fath.” (Cape Colony.)
The animal is perfectly smooth and white; the yellowish viscera can be seen
through the semitransparent integuments. It is somewhat bent and measures 35 mm.
in length, equivalent to at least 40 if it were straightened out. The breadth is 14 and
the height 12°5 mm., the foot is 12 mm. broad.
There appears to be no tail distinct from the body. The back is bordered by a
distinct dorsal margin, projecting about 2 mm., and bearing seventeen branchial plumes
on each side. The foot also has an expanded lateral margin and is rounded in front.
The middle of the anterior margin is drawn up towards the mouth, but not notched.
The branchial plumes are of various sizes. The largest are the third, fifth, ninth
and thirteenth on the right, and the fourth, seventh, eighth, ninth and eleventh on the
left. The two or three foremost and hindmost are quite small. The largest plumes
stand out from the back about 4 mm., and measure 6 mm. across. The primary axis is
bifureate ; each bifurcation bears two to four secondary branches, and these branches in
their turn bear irregular, simply pinnate projections. The smaller branchiee are from a
quarter to half the size of the larger ones and simpler, generally consisting of a short
bifurcate stem, bearing on each side two or three simply pimnate plumes. The genital
orifices are not conspicuous, and are situated under the fourth plume on the right side,
rather high up. The vent les just under the dorsal margin, between the sixth and
seventh plumes.
The frontal veil (fig. 11) is of moderate size, about 8 mm. wide and projecting 3 mm.
from the head, not counting the appendages. There are four of these on each side,
digitate, and about 3 mm. long. The veil is divided into two halves by a central curve
inwards, in the middle of which is a very small papilla. There are only slight and
uncertain traces of a tentacular groove on the outermost process.
The rhinophore sheaths are wide and open, 2 mm. high and 3 wide, with irregularly
erenulate edges. The club of the rhinophores is quite simple and surrounded by about
ten plumes, united at their bases and of various sizes, simply pinnate or bipinnate, and
occasionally imperfectly tripinnate.
* Since writing the above I have examined the type specimens of 7. challengeriana in the British Museum.
They are almost smooth, whitish, and, in addition to other differences, the branchiz are more numerous, finer, and
more elaborately ramified than in T. appendiculata.
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 529
The central nervous system is much as in Candiella lineata. The ganglia are
smooth and yellowish ; the nerves white. There is a large common commissure. The
cerebro-pleural ganglia are pear-shaped, and show signs of a division into two halves.
~The pedal ganglia are round, and separated from the cerebro-pleural more clearly
than in C. lineata. The eyes are black and very small. The pericardium is white, and
as usual in the genus.
The buccal mass is rather elongate, measuring 12 mm. by 5:5, and strongly
muscular. The inner parts and the radula have a faint yellowish tinge. The jaws are
yellow, about 7 mm. long and 4 broad in the widest part, somewhat curved outwards.
The edge of the jaw and the masticatory process bear five rows of very distinct denticles
of somewhat varying shape. The radula consists of forty-one rows. Those in front
are much worn and incomplete. The longer rows contain forty teeth or slightly more
on each side of the rhachis, so that the formula is about 41 x 40.1.1.1.40.. The central
tooth (fig. 12) is tricuspid; the first lateral (fig. 13) of the usual clumsy shape; the
shay ,
Fic. 11.—Frontal veil. ee
/3
3
4 : 5
2
Fic, 12.—Median tooth. Fie, 13.—First lateral. Fic. 14.—Other laterals.
Fries. 11 to 14.—T7ritonia antarctica.
remaining laterals hamate, and slightly curved at the tip. None of the teeth bear any
| denticles, and the bases are not large.
The salivary glands are 5 mm. long, white and flocculent. The cesophagus is rather
broad, 12 mm. long by 3°5 wide, with rather thin walls, irregularly laminated internally.
It dilates into a stomach of moderate size, the greater part of which is enclosed by the
liver. The liver is greyish, and surrounded below as well as above by a thick layer of
the hermaphrodite gland, which consists of pale yellow bodies set in a colourless jelly.
There is no trace of stomach plates. The stomach is filled with a yellowish mass,
containing numerous black particles.
The spermatotheca measures 5 mm. by 3, and is yellowish, slightly striated, and
apparently empty. Its duct is 5 mm. long. The albumen and mucous glands are
moderately large and both white. The vas deferens is longish, not much convoluted ;
the verge conical, sharply pointed, unarmed, with a coiled duct inside.
I think that this specimen may be identified with Tritonia pallida, Stimpson, from
Table Bay, Cape of Good Hope. Differences are not wanting : the white line mentioned
530 SIR CHARLES ELIOT ON THE NUDIBRANCHIATA
by Srumpson is not visible, and the arrangement of branchie is not quite the same. But_
though Srimpson’s description is very slight and superficial, the similarity m colour and —
in the structure of the frontal veil seems suthciently great to warrant identification m
specimens from the same coast.
This form offers resemblances to Tritonia (candiella) australis and imgolfiana, but —
both of these have the first lateral tooth denticulate, and differ in other details.
Tritonvopsis, gen. nov.
The teeth of this form seem to differ from those of Tritonia too decidedly to allow
of its being included in the same genus. Whereas in Tritonia the median tooth is broad,
and the first lateral lower and of a more clumsy form than the others, in Tritoniopsis
the median tooth is narrow and pointed, without wings or accessory cusps. The first
lateral does not differ markedly from the others, but the outer laterals are very long and
almost filamentous in appearance.
In the only known species there is one longitudinal and several transverse ridges
on the back; the rhinophore sheaths bear appendages resembling branchie.
I have dedicated the species to Mr Brucz, leader of the Expedition.
Tritomopsis brucei, gen. et spec. nov.
Three specimens. The label says “ April 22, 1904. Fathoms 10. Temperature
55 H ‘Gough Island.” 40> 200559" S6OW:
The animals are of a innispanen white (in one specimen with a slightly bluish
tinge), allowing the yellow viscera to be seen through the integuments.
Fie. 15.—Branchia. Fic. 16.—Frontal veil from below.
Fias, 15 and 16.—Tritoniopsis brucei.
The largest specimen is much bent, but would measure about 22 mm, in length if
stretched out. The breadth is 8 mm., the height 8:5. The others are slightly smaller.
In all the shape is high and rather narrow, rising up from the head to the centre of the
back, and then sloping down to the tail.
On the dorsal margin, which does not project, are twelve to fourteen branchial tufts
(fig. 15), of which the alternate ones are larger and set more inward, whereas the smaller
are directed outwards. The longest do not project more than 2 mm. from the body and
are stout, but not at all arborescent or foliaceous. They consist of two or three stems,
arising from a prominence which hardly amounts to a common stalk. Hach of these
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 531
stems is bifurcate, more rarely trifurcate, and each of these secondary (neti ends in
three (sometimes only two) small blunt points.
Down the middle of the back runs a low distinct ridge, sending off side ridges to
the large branchiz but not to the small ones. There are two branchiz on each side
before the first of these ridges. There are four of the transverse ridges in the anterior
part of the body, but in the posterior portion both the longitudinal and transverse
ridges become obliterated.
The veil (fig. 16) is ample, not bilobed, 9 mm. wide and projecting 2°5 from the head
without the processes. It bears at each end a grooved tentacle of the shape usual in
Tritonia, and twelve to fourteen digitate appendages, large and small, alternating with
fair but not absolute regularity. The larger measure 2 mm., the smaller are about
half the size.
The rhinophore sheaths are rather low (2 mm.), fairly wide, with a wavy margin.
| 6
3 5
Zz
2 18 19 4 20 (4)
I7
Fic. 17.—Central tooth, Fic. 18.—Central tooth, Fics. 19, 20.—Lateral teeth. 4 is nearergthe rhachis
from the side. from above. than 5 and 6.
Fics. 17 to 20.—Tritoniopsis brucei.
In front they carry two or three appendages, each bearing three points, and suggesting
that a branchia is fused with the sheath. The club of the rhinophore is smooth and is
surrounded by about twelve appendages, many of which are quite simple, while others
bear a few pinne.
The orifices are not at all conspicuous. In the specimen in which they can be seen
best the genital orifices lie below and between the fifth and sixth plumes, and the anus
between the seventh and eighth, rather sigue up but some distance from the dorsal
margin.
The central nervous system resembles Bereu’s figure of this organ in Atthila
ingolfiana (Nud. Gasteropoda of the Ingolf. Exp., pl. v. fig. 12). The four ganglia
are all of much the same size and round. They are mottled and apparently granulate.
The cerebro-pleural ganglia are not pear-shaped or larger than the pedal, and show no
signs of a division into two halves. The buccal ganglia are rather large. No eyes are
visible.
The jaws are yellowish, fairly hard and strong, rounded, not elongate, very convex.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 22.) 79
532 NUDIBRANCHIATA OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION.
The edge is smooth, and there seems to be no masticatory process. The radula is
colourless and transparent. Seen from above, the median teeth (fig. 18) appear as
simple, straight, pyramidal spines, rising from broadish bases; seen from the (fig. 17)
side they are slightly bent downwards towards the tip, and somewhat resemble the
teeth of Favorinus. They are quite smooth. The first laterals (fig. 19) are rather
stouter than the others, but not of a different shape, as in Tritonia. The remaining
laterals (fig. 20) are very long ahd thin, sometimes almost like filaments. They vary
somewhat in shape: those nearer the rhachis are more distinctly hamate, those in the
outer half of the row have a wavy or almost straight outline. They are difficult to
count, as they seem to lie in sheaves, but the number on each side does not much
exceed thirty at most.
The short and broad cesophagus leads straight into a rather small membranous
and fragile stomach, almost entirely covered by the liver, and with no trace of
plates. The liver is of a pale yellowish colour, covered with a thick layer of the
hermaphrodite gland, which is of much the same hue, but still lighter. The albumen
and mucous glands are greyish and of moderate size. The spermatotheca is yellow,
roundish, small, with a long duct. The vas deferens not much convoluted. The verge
is long, pointed, not armed ; as preserved, it is curved at the end.
Scyllaea pelagica, L.
Ten specimens, captured on Ist July 1904, off floating gulf weed, 33° 53’ N., 32° 27’ W.
They vary in length from 7°5 mm. to 13°5 mm. The colour is semitransparent
white, with occasional minute spots of opaque white and a certain amount of yellowish-
brown pigment, found chiefly on the margins and bases of the appendages, and differing
in intensity and quality in the different individuals.
In some specimens there is nothing that can be called a caudal crest, the tail being
merely rudder-like, and not raised above the level of the dorsal surface; but this
peculiarity is not accompanied by any anatomical variation from the type, and passes
into the normal form through intermediate stages.
( 533 )
XXIII.—On the Internal Structure of Sigillaria elegans of Brongniart’s “ Histoire
des végétaux fossiles.” By Robert Kidston, P.R.S.L. & E., F.G.S. (With
Three Plates.)
(MS. received February 23, 1905. Read May 1, 1905. Issued separately June 30, 1905.)
INTRODUCTION.
Before giving a description of the specimen which forms the subject of this
communication, it seems desirable that a brief summary of the literature dealing with
the internal structure of Srgillaria, and some general remarks on the classification of
the genus, should be given. ;
More for the purpose of convenience than on scientific grounds, the genus Srgillaria
is usually divided into four groups. ‘These groups were originally supposed by their
founders to be of generic value, but experience has shown that the characters on
which they were founded are more or less common to all four divisions, and in some
cases the distinctive divisional characters even occur on the same specimen.
Group I. RHYTIDOLEPIS, Sternberg, 1823.
Stem ribbed, furrows distinct, straight or slightly flexuous. Leaf scars more or less
distant, as wide as, or narrower than, the rib.
Group II. FAVULARIA, Sternberg, 1823.
Stem ribbed, furrows flexuous. Leaf scars with prominent lateral angles, and
occupying the whole width of the rib. The lateral angles project slightly, and, alter-
nating with those of the neighbouring leaf scars, impart a zigzag course to the furrows.
Group III. CLATHRARIA, Bronegniart, 1822.
Stem without ribs. Leaf scars placed on contiguous rhomboidal, slightly elevated
cushions, which are separated by deep oblique furrows. .
Group IV. LEIODERMARIA, Goldenberg, 1857.
Stem without ribs. Leaf scars distant and unprovided with cushions.
Groups I. and II. pass into each other; and though in a few cases one can refer
certain species to the Favularia section, such as Srgillaria elegans, there are others
which so combine the characters of groups I. and II. that in practice it is impossible to
treat them as members of distinct groups.
TRANS. ROY. SOC. EDIN. VOL. XLI. PART III. (NO. 23). 80
534 MR ROBERT KIDSTON ON
In the same manner, groups III. and IV. run into each other; and though some
species appear to possess only the characters of the Clathrarie, as Sigillaria discophora,
Konig, sp. (= Ulodendron minus, L. & H.), and others those of the Levodermarie, as
Sigillaria camptotenia, Wood, sp., still typical specimens of the groups Clathraria
(Sigillaria Brardi, Brongt.) and Lewodermaria (Sigillaria spinulosa, Rost, sp.) have
been found more than once organically united on the same example.*
A transition from the Clathraria to the Favularva can also be seen in Sigillaria
semipulvinata, Kidston.t
It is therefore evident that, although the outer surface of the stems of Sigillaria
differs in being ribbed or smooth, and in the leaf scars being distant or approximate,
all these forms are closely connected by intermediate links; and though the larger
division of ribbed and non-ribbed stems is generally very distinctive, still a case is not
wanting to show how closely even these two groups stand to each other.
There are, however, differences in the structure of the vascular system of those
stems of Sigzllarza whose internal organisation is known, and though these differences
are only variations of a single type of structure; they may hold a definite relation
to the group of which the species is a member ; so it is not without interest to consider
this point in connection with the group to which the species belongs. Stems of
Sigillamva showing their internal structure and the outer surface of the bark, and
thus permitting of a specific determination, are, however, very rare.
The earliest description of the internal structure of Sigularia is that given by
BRONGNIART in his well-known memoir, ‘“‘ Observations sur la structure intérieur du
Sigillaria elegans comparée a celle des Lepidodendron et des Stigmaria et a celle
du végétaux vivants.” { It is rather remarkable, however, that the plant Broneniart
identified as Sigularia elegans in this memoir is, as ZEILLER§ has pointed out, —
the Sigillaria Menardi, Bronet.,|| and therefore a member of the Clathrarian
section.
In 1872 Wituiamson described some Sigillarian remains which he referred to
Favularia, but his specimens were very imperfect, and threw little additional
light on the subject.4]
It was not till the publication of RenauLt and Granp’ Eury’s memoir, “ Etude sur
*Wuiss, Zeitsch. d. deut. geol. Gesell., 1888, p. 566. ZEILLER, Bull. Soc. géol. d. France, 3° sér., vol. xvii. p. 608, pl.
Xiv., 1889. ZEILLER, Flore fossile, Bassin houiller et permien de Brive, p. 88, pl. xiv. fig. 1, 1892. Kinston, Proc.
Roy. Phys. Soc. Edin., vol. xiii. p. 233, pl. vii. fig. 1, 1896.
+ Trans. Roy. Soc. Edin., vol. xxxix. p. 57, pl. ili. figs. 1-5, especially figs. 1, 2, 1897.
t Archives du Muséum, vol. i. p. 405, pls. xxv.-xxviii., 1839, Paris. See also Renavtt, “Structure comparée de
quelques tiges de la flore carbonifere,” Nouvelles Archives du Muséum, ii., 2° sér., 1879, p. 262, pl. xi. fig 13. RenavLt,
Flore fossile, Deux. part, Bassin howiller et permien d’Autun et d’Epinac, fase. iv. p. 200, pl. xxxvi. figs. 8-11, pl. xxxvii.
figs. 3-7, 1896.
§ Ann. d. Screnc. nat., 6° sér., Bot., vol. xix. p. 259, 1884. Wauuss, Sitz. Bericht. d. Gessell. naturforsch. Freunde zu
Berlin, 1886, No. 5, p. 70.
|| Hist. d. végét. foss., pl. clviii. fig. 6 ( ? non fig. 5).
J “On the Organisation of the Fossil Plants of the Coal Measures.” Part II. Lycopodiaceze : Lepidodendra and
Sigillarie. Phil. Trans., 1872, p. 197.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 535
le Sigillaria spinulosa” * that any real advance was made in our knowledge of the
structure of Sigillarian stems. This important memoir is a worthy companion to
Bronenrart’s “ Observations,” and is one of the most valuable contributions which
have been made to the subject.
Sigillaria spinulosa, Rost, sp., is the Leiodermarian condition of Sigillaria Brardi,
Brongt., and is the type of the section Lesodermaria. Probably there are species
of Sigillaria which possess a Leiodermarian type of cortex in all stages of their
growth, but unfortunately the internal structure of none of these is known.
RENAULT gives some additional details of the structure of Sigillaria (Clathraria)
Menardi, Bronet., and Sigillaria (Leiodermaria) spinulosa, Rost, sp., in the Bassin
houiller et permien d’Autun et d’Epinact and also in the same work describes a
Sigillarian axis under the name of Stgillaria xylina. {
All the Sigillarian specimens whose structure was known previous to 1899 belonged
to the non-ribbed members of the genus, but in that year Professor BERTRAND read an
account of a ribbed Sigillaria (S. elongata, Brongt.) before the Botanical Section
of the British Association at Dover. An abstract of this communication appears
in the Annals of Botany, vol. xiii, 1899, p. 607. This paper gives the first clear
account of the structure of a mbbed Sigillaria, and embraces all we know of the
structure of this group, with the exception of a short account given by Dr Scorr
of a transverse section of a Sigillaria (Rhytidolepis) type, § and a note by WILLIAMSON, ||
with a few explanatory remarks, where he refers the Diploxylen of his Memoir II.
to Sigillaria reniformis, Brongt. 1 This identification by WiLLIaMson is improbable,
as Sigillaria reniformis has never, as far as | am aware, been found in so low a
horizon as that from which WILLIAMSoN’s specimen came—the Lower Coal Measures.
The above brief sketch contains a note of the papers and works dealing with
original investigations on the structure of undoubted stems of Szgzllaria as far as known
to me,** but before passing from the literature of this subject I wish to refer to a stem
which has been described by Professor F. E. Weiss as “‘a biseriate Halonial branch of
Lepidophloios fuliginosus,” t+ and which I think more probably belongs to the
Ulodendroid group of Clathrarian Sigillaria than to Lepidophlovs. I have come to
* Mem. présentés par divers savants a ]’Acad. des Sciences de l’institut national de France, vol. xxii., No. 9, 1875,
Paris, pls. i—iv., pl. vi. figs. 33, 34. See also Renavtt, “Structure comparée de quelques tiges de la flore carbonifére,”
p- 264, pl. xi. figs. 17-21, pl. xii. figs. 1, 2, 1879. “Notice sur les travaux scientifiques de M. Bernarp RENAULT,”
Autun, 1896, p. 132.
+ Fase. iv. part ii., 1896, pp. 200, 208, pl. xxxvi. figs. 8-11, pl. xxxvii. figs. 3-7 and fig. 40 (Sig. Menardi), pl. xxxvi-
figs. 2-5, pl. xli. figs. 4-11, 18-21, 23-26 (S. spinulosa).
t Lc, p. 237, pl. xxxviii. figs.1-3. § Studies in Fossil Botany, p. 207, fig. 80, 1900.
|| General, Morphological, and Histological Index to the Author’s Collective Memoirs on the Fossil Plants uf the Coal
Measures. Part I]. Mem. and Proc. Manchester Lit. and Phil. Soc., Session 1892-93, p. 35, 1893.
| Pl. xxviii. figs. 33, 34.
_ ** See, in addition to references already given, RENAULT, Cours d. botan. fossile, vol. ii., 1881. Poronih, Lehrbuch
der Pflanzenpaleontologie, 1899. Zer~LER, Eléments de Paléobotanique, 1900. Soums-LavBacu, Fossil Botany (English
translation), Oxford, 1891. Kupston, “Carboniferous Lycopods and Sphenophylls,” Trans. Nat. Hist. Soc. Glasgow,
vol. vi., new series, p. 101, 1891.
tt Weiss, Trans. Linn. Soc. London, 2nd ser., Bot., vol. vi. part 4, pp. 217-236, pls. xxiii.—xxvi., 1903.
536 MR ROBERT KIDSTON ON
this conclusion after a very careful examination of the specimen which was collected
by the late Mr G. Wixp, and sent to me for identification by Mr James Lomax, into
whose possession it had come.
The following are my reasons for adopting the opinion that the more probable
systematic position of this fossil is with the Ulodendroid Sigillarize :—
I. The only carboniferous genera possessing biseriate cone scars, which have been
definitely identified from the presence of leaf scars on their bark, are Lepidodendron,
Sigillaria (Ulodendroid section), and Bothrodendron.
II. The specimen under discussion differs from the biserial Lepidodendra in the
closely placed cone scars, and from Bothrodendron (B. punetatum, L. & H.) in the cone
scars possessing a central vascular cicatrice, which in Bothrodendron is eccentric.
III. That in the position of the cone scars and their vascular cicatrices, and the
distance arrangement of the leaf vascular cicatrices, it agrees entirely with specimens of
Sigilaria discophora, Konig, sp.* (= Ulodendron minus, L. & H., sp.), when partially
decorticated.
IV. That every Halonial (fruiting) branch of Lepidophloios which has shown the
leaf scars, and so admitted of an undoubted identification, has had more than two rows
of cone scars on the fully developed fruiting portion, and these are spirally arranged.
V. Dr Hoyts, Director of the Manchester Museum, has very kindly sent me for
examination the specimen figured by Professor Weiss on his pl. xxii. figs. 2, 3. In
comparing these figures with fig. 1 of the same plate, it should be remembered that
fig. 1 is natural size, and that figures 2, 3 are only 2 natural size.
With the exception of a few places, the outer bark is removed from the Manchester
Museum specimen (Weiss, l.c., figs. 2, 3), and what remains is converted into bright
coal. These coaly patches have the appearance of downward imbricating scales or |
cushions, but what their real structure has been cannot be clearly made out. Their
lower ends are terminated by a fracture, and no leaf scars are shown.
The upper part of the fossil shows the two stumps of a bifurcation. On fruiting
branches of Lepidophloios (Haloma) the fructification is frequently borne on the two
forks of the stem immediately above the bifurcation. Below the fork the fructification
sometimes begins as a single or double row, but when it extends to the forks the true
multispiral arrangement is developed. This was pointed out many years ago by Dr
(now Professor) J. M. MacrarLane.t
The part represented by the specimen in the Manchester Museum may very prob-
ably represent a similar condition to that described and figured by Professor MacraRLaNg,
but as the two arms of the dichotomy are broken over on the example figured by Professor
Weiss, the true spiral series which would naturally have occurred on the two arms is
wanting. Had only a similar portion of Dr Macrar.ane’s specimen been preserved, there
would have been here a so-called “ biseriate” Halonia, but that term cannot be applied,
* Konia, Icones fosstlium sectiles., London, pl. xvi. fig. 194.
+ Trans. Bot. Soc. Edin., vol. xiv. pp. 186, 190, pl. vii.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 537
as the “biseriate” Halonia—in this case at least—is only the beginning of the usual
and typical multiseriate Halonia. It is quite possible that the specimen figured by Pro-
fessor WEIss is a fragment of a Halonial branch of Lepidophiloios, though the state of
_ preservation of the specimen makes it quite impossible to affirm this positively ; but
though this point cannot be settled, I am perfectly satisfied that the fossil which forms
the subject of Professor Weiss’ figures 2, 3, pl. xxiii., does not represent the same
species as that of which he describes the structure, and of which a figure is given,
natural size, at fig. 1 of the same plate. The disposition of the cone scars shows this.
The specimen also figured by Professor Wriss on his plate xxiv. fig. 5, which is con-
tained in the Williamson Collection, British Museum, No. 19458, has very kindly been
sent me for examination by Dr A. Smrra Woopwarp, F.R.S., Keeper of the Geological
Department. Of this specimen Professor Wuiss says, “The leaf bases are perfectly
distinct over the whole surface, and their broad and fimbriating nature mark them out
as belonging to Lepidophlows, as indeed was recognised by Williamson.”* The
characters here given as distinctive of Lepidophlovos are not those which distinguish the
genus, and afford no data for a generic identification. They would apply equally
to most of the other genera of the Carboniferous Arborescent Lycopods if the leaves
were forcibly broken over at a point above their attachment to the leaf cushion, as
they appear to have been on this specimen.
This example, as I interpret it, is given in Professor Wetss’ figure in inverted position.
The smaller end, which he places downwards, [ think is the upper end of the fossil.
The outer surface bears the broken-over portions of the lower part of the leaves—not
the persistent portion, which forms the leaf cushion on which the leaf scar occurs, but
parts of the leaf while still attached to the cushion ; hence no leaf scars are seen on the
specimen. ‘The fossil is too imperfectly preserved for a satisfactory determination, but
in all the characters it shows they agree perfectly with those of Srgillaria discophora ;
and if I am correct in thinking that Professor Wrrss has inverted the specimen in his
figure—a view which I think his figure seems to bear out—then the “ fimbriating” leaf
bases point upwards. As already stated, from such imperfect material as that under
discussion, it is extremely difficult, if not impossible, to arrive at any certain conclusion
as to the nature of the fossil, but the fossil does not appear to me to show any of the
characters of Lepidophloios, Sternberg.
The reference to Professor WILLIamson’s figs. 27 and 28 of Memoir II.t throws no light
on the point in question. WILLIaMsoNn describes his specimen as a Ulodendron, and at
that date that was the genus into which specimens of Sigillaria discophora (= Uloden-
dron minus, L. & H.) would be placed ; and, as far as can be learned from WILLIAMson’s
figures and description, the specimen might as well belong to Sigillaria discophora
as to Lepidophlowos fuliginosus, Williamson.
Tam further indebted to Dr A. SmirH Woopwarp for specimen No. 1949a of the
Williamson Collection, and a transverse section cut from it (slide No. 1949), to which
* Loc. cit., pp. 220-221. + Phil. Trans., 1872, p. 209.
538 MR ROBERT KIDSTON ON
Professor Weiss also makes reference. My thanks are also due to Professor Bowsr
for the loan of another transverse section from the same block, which he received from
the late Professor WILLIAMSON.
The remaining portion of the block from which these slides were made (No. 1949a)
is about 14 inches long, and shows a subepidermal surface with a single tubercle. The
leaf cushions have been removed, so it thus possesses no external characters for a generic
determination.
Part of a section made from this specimen is figured by WILLIAMSON in his Memoir
XIX., on pl. iv. fig. 30.*
When one examines the remains of the original specimen and the slides made from
it, itis dificult to interpret the relation of the parts to each other. One difficulty in ex-
plaining the relationship of the parts is, that if the two sides of the specimen represent the
subepidermal surfaces of the original stem, how does the portion figured by WILLIAMSON
come to hold the position that it does? Again, the pressure to which the specimen,
and especially the vascular axis, has been subjected, makes a critical examination of its
structure very difficult. These circumstances have prevented me from arriving at any
conclusion as to the true position of this fossil.t
My thanks are due to Dr A. Smrrx Woopwapp, F.R.S., Keeper of the Geological
Department of the British Museum, for kindly giving me the opportunity of examining
the specimens in the ‘“‘ Williamson Collection,” and to Dr Hoye for sending me the one
contained in the Collection of the Manchester Museum.
VI. That the vascular axis of the specimen described by Professor Wess belongs
to the same type of structure as the vascular axis of Lepzdophlows fuliginosus is
beyond dispute. The stems of these two plants are closely related in anatomical
structure, but I do not think they are identical. Professor Weiss in his paper —
points out some slight differences, but what I regard as three important differences
seem to be passed over in his description as of too little value for a separation of
the two plants. The first is the very prominent and continuous (except where
broken by the presence of leaf traces) band of tissue described by him as phloem.
‘This layer is very much more developed in the specimen under discussion than in
typical Lepidophloios fuliginosus. The second distinguishing point is the greater
number of leaf traces given off by the vascular cylinder of Professor WHiss’
specimen, while the third distinctive character is the presence of a well - defined
pericycle.
The leaf traces are generally composed of a larger number of elements than
those of Lepidophloios fuliginosus, and therefore appear more prominent, and are
frequentiy larger in transverse section. From these causes, and the fact of the
leaf traces being more numerous, they form a much more distinct ring of leaf traces
surrounding the axis than do those of what I regard as the true Lepidophloios
* Phil. Trams. vol. clxxxiv. p. 20, 1893.
+ Another portion of this specimen (Williamson, 19494) is in the Wild Collection, Manchester Museum.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 539°
fuliginosus of Wituramson. If I am correct in my opinion that the specimen
described by Professor Werss belongs to Sigidlaria discophora, the leaf traces should
be more numerous than those given off by Lepidophloios fuliginosus, for in Sigillaria
discophora the leaf scars are smaller, and consequently more numerous in a given
space than those of Lepidophlows, and the close position of the leaf scars is very
clearly seen in tangential sections of the specimen described by Professor WEIss,
of which I possess a fine series of sections. The same character and their quad-
rangular arrangement are also seen on the outer surface of the specimen as figured
by Professor Weiss on plate xxii. fig. 1.
These differences are slight, and even if they did not exist within the two
stems the arrangement of the cone scars is sufficient to separate the Ulodendroid
Sigillaria from Lepidophloios; and in a group containing so many closely allied
genera as are known to exist amongst the Carboniferous Arborescent Lycopods, one
must expect to find in the internal structure of their stems a great similarity.
VII. In regard to the specimen under discussion, and which has been referred
to Lepidophloios fuliginosus by Professor WEIss, it appears to me that the external
characters of the fossil point more strongly to its belonging to Sigillaria discophora
(=U. minus) than to Lepidophloios ; and further, that its internal structure, though
of the same type, is not identical with that of Lepidophloios fuliginosus of WILLIAMSON.
In concluding this criticism, I wish clearly to state that I do not say that a
“hbiseriate Halonia”—that is, a Halonial condition of Lepidophloios, on which the
cones are arranged in two rows, “ Ulodendroid” fashion—does not exist; but what
I do maintain is, that if there is a Lepidophloios which bears its cones in two
opposite and vertical rows, and in this mode alone, proof of its existence has still
to be given.
DESCRIPTION OF SPECIMEN.
Sigillaria elegans of Brongniart’s Histoire des végétawx fossiles, vol. i. p. 438, pl. cxlvi. fig. 1, pl. elv.,
pl. elviii. fig. 1.
As some botanists doubt the identity of Broneniart’s Sigillaria elegans with the
Sigillaria (Favularia) elegans of SrernBerG,* | have adopted BRONGNIART’s name as my
authority for the species whose structure is about to be described, as my specimen agrees
in all respects with the descriptions and figures given in the Hist. d. végét. foss. On
the other hand, I believe that BronenrarT was quite correct in identifying his specimen
with Favularia elegans, Sternberg; for if SrERNBERG’s figure be inverted and so
“brought into its natural position, and if a very slight allowance be made for the
delinquencies of the artist, it is difficult to see how there can be any real difficulty in
Trecognising the specific identity of BRonaNrIaRT’s and STERNBERG’S specimens.
* STERNBERG, Essai flore monde prim., vol. i. fasc. 4, pp. xiv, 48, pl. lii. fig. 4, 1826.
t See also ZurnuER, Flore foss. Bassin howil. d. Valenciennes, p. 582, pl. lxxxvii. figs. 1-4, Atlas 1886, Text 1888.
540 MR ROBERT KIDSTON ON
General Description of Specimen.—The specimen was contained in one of the well-
known coal balls from the Halifax Hard bed near Huddersfield, Yorkshire (Lower Coal
Measures), and was found by Mr W. Hemineway, by whom it was communicated to me,
and to whom my thanks are due for the opportunity of describing the specimen.
Through a fortunate fracture in the stone, part of the outer surface of the specimen
was exposed, showing a well-preserved row of leaf scars. This surface of the specimen
is shown natural size at fig. 1, Pl. I, and enlarged two times at fig. 2.
With the exception of the row of leaf scars, the remainder of the surface of the
specimen exposes the layer which lies immediately underneath that on which the leaf
cushions sit. Its surface shows the leaf traces surrounded below by the parichnos,
x
J. 4.
oo
OKA
SRR KER XR oeclst
X OY
”, LX eee.
S
ep
KRACK)
at 7
(fT CMT
Texr Fic. 1.—Sigillaria elegans, Sternberg, sp.
A. Transverse section of the specimen showing the vascular cylinder and portion of the cortex. The ribs are
numbered I. to XIX. x 4.
B, Transverse section of the vascular cylinder. The furrows on outer margin of primary wood are numbered 1 to 28,
x9. Protoxylem, pra. Primary xylem, 2’. Secondary xylem, x”. Leaf traces are shown in the furrows
marked with a x. Slide No. 964,
which form a semicircle, Pl. I. fig. 2. At this point the parichnos do not seem to com-
pletely surround the leaf trace. Between the narrow ridges on which the leaf trace scars
are seen, the exposed surface is striated with close, slightly flexuous longitudinal ridges.
An outline sketch of a transverse section of the specimen is shown at text fig. 1,
A, enlarged four times. Towards the right is seen the vascular cylinder, the two sides of
which are pressed together, and only a small part of the pith-cavity is seen.
—————— OO
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 541
The complete zone of cortex bore twenty-eight ribs, of which nine are not seen in the
section, but the figure allows one to estimate the proportional size of the vascular
cylinder to that of the circumference of the stem.
The stele, which measures slightly under 13 mm. in its longest compressed diameter,
consists of a perfectly continuous ring of primary wood, «’, which is surrounded
by a zone of secondary wood, 2”,
The pith and the tissue which originally composed the inner portion of the cortex
and all remains of the phloem elements, have been entirely destroyed. The only other
remaining portion of the stem in which the structure is preserved is the outer layer of
the cortex on which the leaf cushions are situated. The structure of these parts may now
be considered in detail.
The Primary or Centripetal Xylem.—At fig. 3, Pl. L, is shown a transverse section
of the vascular cylinder, enlarged about 43 times. ‘The ring of primary xylem «.’ is
quite continuous, and is about 0°70 mm. thick. As seen in fig. 4, Pl. L, its outer margin
is deeply and regularly undulate or crenate, so as to form a number of blunt ridges
alternating with as many intervening furrows. The inner margin of the xylem ring is
very uneven, sending irregular toothed projections into the now empty pith-cavity (PI. I.
me. 4, w.’ and p.c.).
The main mass of the primary xylem consists of large tracheides, more or less
hexagonal in transverse section, and without any intervening parenchymatous cells.
They diminish slightly and gradually in size towards without, but just underneath
the ridges a decrease in size takes place somewhat abruptly, and the ridges themselves
are composed of much narrower elements, that are to be regarded as constituting the
protoxylem (Pl. I. fig. 4, prx. Text fig. 1, B, pra.).
At the inner margin of the primary xylem a certain amount of thin-walled parenchy-
matous cells are to be found between the tracheides, and a few of the latter may even be
surrounded by parenchyma, and separated from the rest of the mass. Some especially
narrow tracheides also occur here and there along the inner margin.
Radial longitudinal sections, Pl. II. figs. 6 and 8, show that all the, elements of the
primary xylem, both protoxylem (Pl. II. fig. 7, prx.) and metaxylem (Pl. II. fig. 9, x.’),
are elongated scalariform tracheides with pointed ends (fig. 7, pre., fig. 9, .’), except a
few of the innermost tracheides bordering on the pith, which are quite short, blunt-ended,
‘and irregular in shape, but still scalariform. So far as observed, no spiral or annular
elements at all were found at any point in the primary xylem, not even in the
protoxylem.
The protoxylem elements are seen in radial section at prz., figs. 6 and 8, Pl. II.
They are long and narrow, and terminate in an elongated conical point (PI. II. fig. 7, pra.).
Secondary or Centrifugal Xylem.—This forms a zone of varying thickness surround-
ing the primary xylem, and attaining at its widest part a breadth of about 0°75 mm. (Pl.
I. figs. 3, 4, and 14, x.”). Its inner margin follows the crenulate outline of the primary
xylem. The outer margin exhibits the same crenulations, but to a slightly less degree.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 23), 81
542 MR ROBERT KIDSTON ON
The tracheides of the secondary xylem are arranged in radial rows (Pl. I. figs. 3, 4, —
and 14, «.’’), interspersed at intervals by numerous medullary rays which run unin-
terruptedly through the whole thickness of the secondary wood.
The number of rows of tracheides at the inner margin of the secondary wood is
greater than at the outer margin, so that many of the rows begun at the inner edge
come to an end after running a certain distance, their loss being compensated for
by the increased size of the tracheides in the rows which persist.
At figs. 6 and 8, Pl. IL, are radial longitudinal sections of the stele, which show that
the tracheides of the secondary xylem are elongated and scalariform, with pointed
ends, similar to those of the main body. of the primary xylem (metaxylem), only some-
what smaller in diameter.
The tracheides are of the same size throughout the secondary xylem, there being
no difference between those opposite the ridges and those opposite the furrows.
Occasionally one or two thin-walled cells intervene between the primary xylem |
and the inner tracheides of the secondary xylem, but frequently the primary and
secondary xylem are in direct contact.
The medullary rays (Pl. L. fig. 14, m.r., Pl. III. fig 10, m.r.) are usually one cell wide,
rarely two, and are formed of thin-walled cells, slightly elongated radially. Their walls
sometimes bear delicate scalariform thickenings (PI. I. fig. 14, m.r.). Similar cells have
been figured by Wr1Li1aMson.*
In tangential section (Pl. I. fig. 28, m.7.) the medullary rays are seen to vary much
in height, and may consist of from one to nine superposed cells. In many cases the
cells have become decayed, and their position is only indicated by a larger or smaller
lenticular space.
Leaf traces.—The leaf traces arise from the periphery of the primary xylem, and |
invariably at the base of the furrows, never from the tops or sides of a ridge (text fig.
1,B; PIL. fig. 4,22; Pl IL. figs. 11, 12, 13,72); and as the leaf traces appear to keep
in the same vertical plane in their course through the cortex, the furrows on the
primary xylem must correspond in position to the ribs on the surface of the stem.
In text fig. 1, B, the vascular cylinder is enlarged about nine times. This shows
twenty-eight furrows, so there must have been twenty-eight vertical rows of leaves ; and
although text fig. 1, A, only shows nineteen, before the specimen was cut, the full
number was actually present as already mentioned.
When the leaf trace is about to become free from the metaxylem at the bottom of
the furrow it consists of a group of about a dozen small tracheides, arranged radially
around the smallest of the group, which lies approximately in the centre (Pl. IL. fig.
11, /.t.). Followed downwards, these small tracheides are seen to spread out over the
surface of the furrow, and finally die out below (PI. IL. fig. 17, /.t.).
When the leaf trace becomes free from the primary xylem it first runs upwards
and slightly outwards (Pl. II. figs. 12 and 13), then bending abruptly outwards, passes
* Memoir XIX., Phil. Trans., vol. clxxxiv. (1898), p. 33, pl. iv. fig. 38.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 543
out through a medullary ray in an almost horizontal direction. Once free of the
secondary xylem it suddenly bends upwards again (Pl. Il. fig. 15, /..).
By the time the leaf trace emerges from the secondary wood one or two additional
rows have been added, mostly on the side next the axis, but a few may have been
added to the opposite side, and the leaf trace now shows a distinct mesarch structure
(Pl. IL fig. 15, /.¢.). On another leaf trace, which is slightly further removed outward
from the axis, a greater number of.tracheides have been added, and the increase seems
to have been more equally placed on all sides of the primary group (PI. IL. fig. 16, /.t.).
_ The course of the leaf traces through the xylem, and their behaviour on their
emergence from it, seems to be similar to that so well represented in the figure of the
radial section of Sigillaria Menard: given by Renavu.r.*
It was impossible to discover any annular or spiral tracheides in the leaf trace, but
their structure is very much effaced in their passage through the secondary xylem.
Sigillaria elegans does not show any secondary wood in connection with the leaf
trace up to their entrance into the inner cortex and in the outer layer of the bark (the
only portion of the cortex preserved) ; the leaf traces are too imperfect to permit of their
structure being made out.
Cortex.—The only part of the cortex which has been preserved is that formed
by the ribs, which must probably be regarded as composed of the confluent persistent
leaf bases and a small portion of the underlying periderm.
Fig. 18, Pl. I., shows the outer surface of a specimen of Sigillaria elegans,
collected by Mr W. Hemineway from the Yorkshire Middle Coal Measures. In
this condition the leaf cushions are usually compressed. ‘They are arranged on
the ribs in vertical rows, the leaf scars of one row alternating with those on the
contiguous rows. The leaf scars are subhexagonal, with prominent lateral angles,
which alternate with those of the neighbouring leaf scars, and thus impart a zigzag
course to the furrows between the ribs. The cones are borne in a verticil formed
of a single row, and some of the cone scars are seen in the figure at c.s.
In the uncompressed condition the leaf cushions slope outwards, and their lower
margin becomes considerably elevated. This is shown on Pl. III. fig. 19, which
is a radial section through a rib of Sigillaria elegans. The leaves are attached
to the sloping surfaces, s.a. This figure is from a specimen received from Mr
JamMEs Lomax, and was derived from the Halifax Hard bed.
The surface of the leaf scar is formed of a stratum of dark broken - down
parenchymatous tissue. The main body of the leaf cushion below this consists of
fairly thick-walled parenchyma, the cells of which are more or less oval, with their
longest diameter directed outwards. Towards the upper adaxial side of the cushion
these cells become smaller, and seem to contain a dark-coloured material, which causes
_ the tissue in this region to become opaque (PI. III. fig. 5). The lower margin is also
formed by similar small opaque cells, but not developed to the same extent.
* Flore fossile, Bassin howiller et permien d Autun et d’Epinac, Deux. part, Atlas, pl. xxxvii. fig. 6, 1893.
544 MR ROBERT KIDSTON ON
At lt., fig. 5, Pl. IIL, is seen the opening through which the leaf trace has
passed to the leaf. The leaf cushions are attached to a continuous zone of under-
lying periderm (Pl. III. fig. 19, pd.), formed of very dense elongated fibres of small
diameter, with fairly thick walls. In longitudinal section this tissue is usually very
opaque, and seldom shows its structure distinctly. In transverse section (Pl. UI.
fic. 21) the fibres are seen to be arranged in close radial rows.
If a transverse section of cortex with several attached leaf bases be examined,
it will be seen that some of the leaf bases have only a narrow band of dark dense
tissue, as at Pl. I. fig. 3, l.c., whereas others seem to be entirely composed of it,
as at fig. 3 lc.’ This is explained by reference to fig. 5 and fig. 19, Pl. ILL
the section passes through the lower part of the cushion the greater part of the
section will show transparent parenchyma, whereas if the section passes through
the upper part of the cushion it will be composed of dense opaque tissue.
A leaf cushion in transverse section is given on Pl. III. fig. 20, The dark
broken-down margin is reduced here in thickness (p.p.), while the more transparent
parenchyma occupies at this position the greater width of the cushion. At pd.
are seen some fragments of the periderm.
The cause of the flexuous striations on the surface of the stem (Pl. I. fig. 2)
where the leaf cushions have been removed is not very clear, but they seem to
be formed at the point of union of cortex and periderm, and are probably caused
by the projecting teeth of the latter (see Pl. III. fig. 20, pd.).
A section of a cushion approximately parallel with and a short distance below
the outer surface is given on Pl. III. fig. 22. The two parichnos (par.) are seen,
but the delicate tissue with which they were filled has mostly decayed. The leaf
trace lying between them is too imperfectly preserved to admit of a detailed description.
The parenchyma of the groundmass is here well preserved (Pl. IL. fig. 24).
Cone Scars.—On the specimen showing the outer surface of the bark given on
Pl. I. fig. 18 part of a verticil of cone scars is seen at c.s.
In one of the tangential sections of the cortex of the specimen shown on Pl. L
fig. 1 two vascular strands belonging to cones are cut through. This specimen is
shown enlarged eight times at fig. 23, Pl. III, where the branches going to the cones
are lettered c.s. and c.s.’
The cone axis ¢.s.’, fig. 28, Pl. III., is seen enlarged on PI. III. fig. 25. |
The peripheral zone of cortex, b, which has accidentally separated off from the rest, —
is too much disorganised to show the structure, but probably corresponds to the
periderm. ‘The space lettered d is a mechanically produced rupture.
The rest of the cortex consists of fairly thick-walled and apparently parenchymatous
cells, which increase in diameter as they are traced inwards (PI. III. fig. 26). This
tissue, which undoubtedly belongs to the cortex, is separated from the solid axis of the
cone by a clear empty zone (Pl. III. fig. 25, g, and Pl. I. fig. 27, g), which was
probably occupied by some delicate tissue.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 545
The cells of the innermost layer of cortical tissue lining this zone consist of
smaller cells, roughly tabular in transverse section, and have very much the appearance
of an endodermis (PI. II. fig. 26, e; Pl. I. fig. 27, e).
Within the clear zone is a central mass of xylem (PI. III. fig. 25,4; Pl. I. fig. 27, 4),
surrounded by a fairly stout zone of comparatively large thin-walled cells, separated from
the xylem by a dark line of disorganised material (Pl. I. fig. 27, h). The xylem is too
badly preserved for detailed description, but it is quite clear its development is
centripetal. The smallest elements are at the periphery, and there is a gradual increase
in size towards the centre. ‘There is no trace of any secondary thickening.
The zone of thin-walled tissue surrounding the xylem possibly represents the so-
ealled phloem of Lepidophiowws, but the preservation is so imperfect that a definite
decision as to its true nature is not permissible.
Remarks.—The structure of Sigillaria elegans, Brongt., is very similar to that of
Sigillaria elongata, Brongt., the only other ribbed Sigilaria of which any detailed
account of the structure has been given, but the short abstract of his paper given by
Professor C. Ec. BerTRAND scarcely enables one to make a critical comparison between the
structure of the two species.* He has, however, very kindly favoured me with some
photographs of his specimen, and the general agreement in structure between the two
plants is very striking.
They both have a continuous circle of primary wood, with a distinct corona. In
the Hardinghen specimen the projecting teeth of the protoxylem are pointed, while in
the Yorkshire example they are rounded and contain a greater number of elements.
The secondary xylem seems to offer no special point of difference.
On my specimen the leaf traces rise as a single strand directly from the base of the
furrows of the primary xylem, and they may differ somewhat in their mode of origin
from those described by Professor Berrranp;t but until the full description of the
Hardinghen specimen is published, it is undesirable to institute any critical comparison
between the anatomy of Srgillaria elongata and Sigillaria elegans.
In comparing the organisation of the various species of Sigillaria of which the
structure has been described, one might be inclined to think that in the genus there
were two types of structure; this, however, is not so. If one takes the Sigidlaria
~Menardi described by Broneniart, with its isolated strands of primary xylem, and
Sigillaria elongata or Sigillaria elegans, with their continuous circle of primary wood
and prominent corona, they at first sight look very distinct. But in Sigillaria
spimulosa, which normally is supposed to possess the same type of structure as Sigillaria
Menard, Soums-Lavpacu has pointed out that the separate bundles of primary wood
Sometimes coalesce, and in part form a continuous ring.{ This character of the
Goalescence of the primary bundles of Stgillaria is also well seen in the figures of
Sigillaria spinulosa given by Dr Scorr.§ In Sigillaria xylina, Renault, the same
* Annals of Botany, vol. xiii. p. 607, 1899. + Loc. cit., p. 608. t Fossil Botany, English ed., p. 252, fig, 29, 1891.
§ Studies in Fossil Botany, p. 201, figs. 77-78, 1900.
546 MR ROBERT KIDSTON ON
character has been observed.* It is therefore seen that the isolated strand type of |
primary wood, and that even in the same specimen, passes into the continuous type, and —
that there is between the two forms an unbroken chain which connects them together.t
If the structure of Sigillaria elongata or Sigillaria elegans be compared with the
structure of the large specimen of Lepidophloios described by SEwarp and Hitz, and
which they believe to be the Lepidophlowos Harcourti, Witham, sp., or with any of the
Lepidodendroid stems whose primary wood is provided with a corona, the great
similarity in structure is very apparent. The corona on the stems of Lepidophlovs,
though less prominent than in Sigilaria, is most distinctly present, and is also formed
by the protoxylem elements. The leaf traces are also given off from the dividing bays,
and the difference between the corona of many of the Lepidodendrex and the Sigillariz
is only one of degree. If a series be arranged, beginning with Lepidophloios Har-
courtt, followed by Sigillaria elongata, and concluding with Sigillaria elegans, it will
be seen that by a gradual increase of the size of the teeth of the corona you pass
insensibly from the Lepidophlovos structure to that of the Sigillarzz which possess the
continuous ring of primary wood. The distinction at one time supposed to exist between
the Srgillariz and the Lepidodendrex, of the former possessing secondary wood in con-
nection with the leaf trace, is now found not to hold, for a considerable development of
secondary wood takes place in the leaf traces of Lepidophilowos.§ On the other hand, no
development of secondary wood on the leaf traces of Sigillaria elongata or Sigillaria
elegans has yet been observed.
Whether we are justified in classing all of the Lepidodendrex with a corona on the
primary xylem with Lepidophloios may be open to question, though it is certain that
some Lepidophioios had primary wood so formed ; and though on some stems of Lepido-
dendron the primary wood has an even contour, still in other Lepidopendra and in Both- |
rodendron || the primary wood has a slightly undulating outline, so that in the Car-
boniferous Lycopodiacee there is a continuous chain of structure variation in the
arrangement of the protoxylem elements which binds closely together all the genera of
the Carboniferous Arborescent Lycopods. Between no two genera is there any out-
standing character in the structure of the vascular cylinder which sharply separates
them from each other. It seems, therefore, highly probable, as suggested by ZErLume,
that the Carboniferous Arborescent Lycopods have descended from a common stock.1
In their fructification and certain other points, however, these ancient lycopods differed
from each other in several important characters.
I am inclined to regard the Arborescent Lycopods as a group which has left no
* Renavtt, Bassin howiller et permien d’Autun et @Epinac, Flore fossile, Deux. part, p. 238, 1896.
+It might be mentioned that Renavunr has described a Lepidodendron (L. Jutiert) in which the vascular system is
formed of a circle of separate bundles. “Structure comparée de quelques tiges de la flore carbonifere ” (in Now.
Archives du Mus., ii., 2° sér., 1879, p. 258 ; also Runavtt, Cours d. bot. fos., vol. ii. p. 28, 1882.
{ Trans. Roy. Soc. Edin., vol. xxxix. p. 907, pls. i—iv., 1900. § Sewarp and Hitt, l.c., p. 914.
|| From the discovery by Mr Jamms Lomax of a specimen showing the outer surface of the bark, it has been shown
that the Lepidodendron mundum, Williamson, is a Bothrodendron.
{ ZuitLER, Eléments paleobotanique, p. 178, 1900.
THE INTERNAL STRUCTURE OF SIGILLAKIA ELEGANS. 547
descendants except in the case of Szgillaria, the structure of whose cone shows some
similarity with the fructification of Jswtes. Our other modern lycopods (Lycopodium
and Selaginella) seem to have descended from the Carboniferous genus Lycopodites,
with which they show much in common.
The geological distribution of the Szgillaria whose structure is known also brings
out an interesting point ; and though the evidence may not be sufficient for any definite
conclusions, still it indicates changes which deserve recognition.
The following table gives the age of the rocks which have yielded Sigillaria, showing
their internal structure, and also indicates a few of the more prominent characters of the
species discovered.
TABLE.
Lower Permian Sigillaria Menardi, | Stem without ribs Primary xylem a circle of
Brongt. (Clathraria section) separate bundles.
Secondary xylem forming a
centrifugal zone.
Do. Sigillaria spinulosa, | Stem without ribs Primary xylem a circle of
Rost, sp. (Clathraria and Leio- separate bundles, some of
(= Sigillaria Brardi, dermaria sections) which frequently coalesce.
Brower) Secondary xylem forming a
centrifugal zone.
Upper Carboniferous No specimens show-
Upper Coal Measures ing structure from
this horizon
Middle Coal Measures | Sigillaria elongata, | Stem ribbed Primary xylem in form of a
(= “ Westphalian Brongt. (Rhytidolepis section) closed ring.
partes”) Secondary xylem forming a
centrifugal zone.
Lower Coal Measures | Sigillaria elegans, | Stem ribbed Primary xylem in form of a
Brongt. (Favularia section) closed ring.
Secondary xylem forming a
centrifugal zone.
The non-ribbed Sigillariz are more characteristic of higher horizons and the ribbed
Sigillariz of the lower horizons, but neither group is restricted to either series.
The genus Sigillaria also extends into the Lower Carboniferous, where it is, however,
very rare, but no specimens showing structure have yet been recognised from these
rocks. In the following list I only mention the British species :—
Lower Carboniferous.
Carboniferous Limestone Series.
Sigillaria Youngiana, Kidston : 2 Stem ribbed.
Sigillaria Canobiana, Kidston ‘ ; Stem ribbed.
Sigillaré h Stem without ribs.
igillaria Taylori, Carr., sp. . ; : (Ulodendroid Clathraria.)
Calciferous Sandstone Series.
Sigillaria Taylori, Carr., sp. . | Oa ae
(Ulodendroid Clathraria.)
548 MR ROBERT KIDSTON ON
The lowest horizon from which I have seen the typical Clathrarian Sigillarie is
the Lower Coal Measures, but from this horizon I have only seen a single example.
The non-ribbed Sigillarie of the Ulodendron-Clathrarian group (Szgillaria disco- —
phora, Konig, sp. = Ulodendron minus, L. & H., and Sigillaria Taylori, Carr., sp.)
extend into both divisions of the Lower Carboniferous, but the ribbed Sigillaria, —
although they occur in the Lower Carboniferous, do not, as far as I know, extend to
the base of the Carboniferous Limestone Series.
If I am correct in believing that the stem whose structure has been described by ©
Professor WeIss as “a Biseriate Halonial Branch of Lepidophloios fuliginosus” is the
Sigillaria discophora, Konig, sp., with which Sigidllaria Taylori, Carr., sp., is very closely
related, then the probability is that Srgillaria Taylor also possessed primary wood of
the continuous ring type, and the same may be presumed for the two-ribbed Sigillarie
from the Carboniferous Limestone Series.
If it is permissible to assume these probabilities—and the assumption is not without
some support from the known structure of the Middle and Lower Coal Measure species
of Sigillaria—then it is probable that the continuous ring of primary xylem is the older
type of Sigillarian stem structure, and that the circle of isolated strands which form the
primary xylem of the Clathrarian Sigillarize of the higher geological horizons has
originated by a splitting up of the continuous ring type of bundle; and, as already
mentioned, even in the few Clathrarian Sigillarize from the higher horizon of which the
structure is known, the actual transition from the one type to the other can be observed.
The Lepidodendra form, however, an older genus than Szgillaria, and extend to
the base of the Carboniferous Formation. In beds not far above the base and low down
in the Calciferous Sandstone Series specimens of Lepidodendron showing structure have
been found; and of two of these occurring in the same bed, one species shows the ~
continuous ring of primary wood, while the other possesses a solid cylinder of primary
wood without any trace of pith ; and although there occur here the two types of primary
wood, side by side, still the solid cylinder type seems to be more common in the lower
than in the upper horizons of Carboniferous Rocks, and the sequence of changes in the
development of the primary xylem of the paleeozoic Arborescent Lycopods seems to
point to the sold vascular cylinder as the oldest type, from which has been derived the
medullate cylinder with a continuous ring of primary wood, and this continuous ring of
primary wood has, in turn, broken up to form the zsolated strands of primary wood
found in the Clathrarian Sigillarizx.*
I wish to express my thanks to Mr D. T. Gwynnz-Vaucuan, Glasgow University,
for much kind criticism and advice while preparing this paper.
* See note on p. 546 (Lepidodendron Jutiert, Renault).
BE fig.
q. 1,
16 2
I 3.
I 4,
1g 5
Il. 6
IL 7
II. 8
Il. 9
il. 10.
oe - il
Mm 12
m 613
I 14,
i «= 15.
om @6«=—«éd‘«’.
mm. 17.
am 6«(18.
Il. 19.
foe §8=s 20.
THE INTERNAL STRUCTURE OF SIGILLARIA ELEGANS. 549
EXPLANATION OF PLATES I-III.
Sigillaria elegans, Brongt. (Sternb., sp.).
Portion of outer surface of the specimen from near Huddersfield. Halifax Hard bed, Lower
Coal Measures. Natural size. To the right is seen a row of leaf scars. Specimen No.
3497.
Part of the same specimen enlarged two times. To the right is seen the vertical row of leaf
scars, and to the left the surface of the cortical layer which bears the leaf cushions.
Transverse section of the vascular cylinder and part of the cortex x 44. Primary xylem, ~.'
Secondary xylem, 2.” Leaf cushions, J.c. and /.c.’ Slide No. 964.
Portion of vascular cylinder x 35. Protoxylem, prx. Primary xylem, x.’ Secondary xylem,
x.” Pith-cavity, p.c. Slide No. 964.
Longitudinal (radial) section of leaf cushions x 20. Spongy transparent parenchymatous
tissue, p. Dense tissue of smaller cells, p.p. Leaf trace opening, /.t. Very dense tissue
at upper left corner of figure, periderm. Slide No. 841.
Radial section passing through xylem x 95. Protoxylem, prx. Primary xylem, x.’ Secondary
xylem, w.” Slide No. 967.
Radial section passing through xylem x 170, At pra. is shown the termination of a tracheide
belonging to the protoxylem. Slide No. 967.
Radial section passing through xylem x 95. Protoxylem, pra. Primary xylem, x.’ Secondary
xylem, 2.” Slide No. 968.
Radial section passing through primary xylem x 95, At.’ is shown the termination of a
tracheide. Slide No. 970.
Transverse section of secondary xylem x 95. Showing medullary rays, mr. Slide No. 964,
Transverse section showing leaf trace x 85. Protoxylem, prx. Primary xylem, x.’ Leaf
trace, l.t., which is about to become free from the metaxylem. Slide No. 961.
Transverse section showing leaf trace x 85. Lettering as before. The leaf trace has just
become free from the metaxylem. Slide No. 966.
Transverse section of leaf trace x 85. Lettering as before. The leaf trace has moved
outwards and is becoming suddenly bent to pass out through a medullary ray. Slide No.
964.
Transverse section of secondary xylem, showing cells of medullary ray with spiral thickening
mr. x 115, Slide No. 962.
Transverse section showing leaf trace at outer margin of secondary xylem x85. Medullary
ray, m.r. Secondary xylem, x”. Leaf trace, /.4. The leaf trace has bent upwards after
emerging from the secondary xylem, and is cut through at approximately right angle.
Slide No. 962.
Transverse section of leaf trace quite free from the outer margin of the secondary xylem x 85.
Slide No. 962.
Transverse section of xylem x 95. Primary xylem, 2.’ Secondary xylem, «.” At .t, is seen
the narrow spread-out base of the leaf trace shortly before it dies out. Slide No. 964.
Outer surface of a specimen showing the leaf scars and portion of a circle of cone scars, c.s.
Natural size. From Wombwell Main Colliery, near Barnsley, Yorkshire. Horizon,
Barnsley Thick Coal, Middle Coal Measures, Collected by Mr W. Hemingway.
Specimen No. 989.
Radial (longitudinal) section passing through six leaf cushions x 4. Periderm, yp.d.
Surface to which leaf was attached, s.a. Opening through which leaf trace passed, J.t.
The cushion marked /.t. is enlarged at fig. 5. Slide No. 841.
Transverse section of cushion x 14. ‘Transparent parenchymatous tissue, p. Broken down
margin of cushion, pp. Periderm, pd., pd.’ The part marked pd.’ is enlarged at fig. 21.
Slide No. 962.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 23). 82
MR ROBERT KIDSTON ON SIGILLARIA ELEGANS.
Transverse section of periderm x 50. The part enlarged is seen on fig. 20, pd.’ Slide
962. —
Section of leaf cushion approximately parallel with the surface x 14. Position of leaf trac
lt. Parichnos, par. Transparent parenchymatous tissue, p. Slide No. 973. -
Section approximately parallel with outer surface of stem x 8. Free portions of leaf cushion
lc. Cone pedicels, cs., cs.’ Slide No. 972. |
Portion of transparent parenchymatous tissue of the leaf cushion shown at fig. 22, p., x 60. —
Slide No. 973. , .
Transverse section of cone pedicel x 20. Slide No. 972. See description in text, page 54
Portion of the cortex shown at fig. 25, c.,x 35. Slide No. 972. "
Transverse section of vascular strand of cone pedicel x 70. Thin-walled disorganised tiss
h. Vascular strand, &. Endodermis-like structure, e. Slide No. 972. :
Tangential section through secondary xylem x 95. Medullary rays, m.r., cut throug]
right angles. Slide No. 969.
Vol. XLI.
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SIGILLARIA ELEGANS. PLATE I
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XXIV.—On the Structure of the Series of Line- and Band-Spectra. By J. Halm,
Ph.D., Lecturer on Astronomy in the University of Edinburgh.
(Read July 4, 1904. MS. received October 14, 1904. Issued separately July 3, 1905.)
In a preliminary note read before the Society on July 4, 1904, 1 drew attention to
the fact that a number of line-series, forming a group which includes the first series
of Hydrogen, can be represented by an equation of the form
1
Vo —Vv
=am?+b,, (1)
where v denotes the wave-frequency of any line of the series, v. that of the so-called
“tail” of the series (m=), and a, 6, constants depending on the nature of the
emitting substance ; the frequencies of successive lines being obtained by substituting
successive integers for m. We see at once that this equation is a generalisation of
Batmer’s formula, into which it is transformed by equating }, to zero. In the same
note I also pointed out the existence of another group represented by an equation of the
same form, if (m+) is substituted form. As a special case (b,=0) this group contains
the second Hydrogen series discovered by Professor PickERING in the spectrum of
¢ Puppis. Subsequent investigations convinced me, however, that, although a consider-
able number of line-series may be classified into these two groups, there are numerous
instances where the more general formula
oS 1 = a,(m + p.)? + b, (2)
Vo = VV
must be employed, in which u represents various fractional numbers. Also, in studying
more thoroughly the literature on the subject, I found that the equation, in the last-
mentioned form, is merely a modification of a mathematical expression already employed
by Professor Tu1rLE in his investigations on the band-series of the carbon spectrum
and on the line-series of Helium. But, convinced as I was from my own computations
of the accuracy and general importance of this equation, I was surprised to find it
rejected by Professor THIELE, on the ground that it did not sufficiently represent
the observed wave-lengths. This statement appeared to be so far from acceptable,
that I resolved to demonstrate, by an exhaustive examination of all the known series,
not only the general applicability of equation (2), but also its great superiority over
any other formula hitherto proposed. The demonstration of this fact will be the first
object of the present communication. It will be shown that the equation represents not
only all the line-series hitherto known, but also the band-series, with an accuracy which
leaves nothing to be desired. But far more important even than the demonstration
of equation (2) as an empirical formula of practical usefulness are certain con-
clusions which may be drawn from the character of this equation and the numerical
values of its constants. For instance, we shall see that equation (2) can be represented
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24). 83
’
552 DR J. HALM ON
in a geometrical form, by means of which we are enabled to collect all the line- and
band-series into one single diagram revealing a community of properties between the
two classes of spectral regularities and their individual members. This new geometrical
connection between the series appears to be of theoretical importance, inasmuch as it
shows a striking similarity between the vibrations of a radiating system of atoms
and the nodal vibrations of elastic bodies. From this point of view an im-
portant relation has been discovered between the wave-frequencies of the “tails” of
line-series and the atomic volumes of the emitting elements. In the course of this
paper we shall have frequent opportunities of observing regularities in the constants
of equation (2), and of drawing from them conclusions which cannot but be of some
importance, however small, in connection with the theory of the phenomena of spectral
regularities—a region into which the speculative mind has so far vainly attempted to
penetrate. The outcome of the investigation must, I think, be to convey the impression
that equation (2) is to be considered as more than a merely empirical formula, and that,
if it does not represent the physical law itself, it 1s at least a remarkably close
approximation to it, sufficiently reliable, perhaps, to guide the theorist in his search
for the ultimate cause of the spectral regularities here considered.
Before entering upon the first part of our investigation, viz. that dealing with the
question how far equation (2) is capable of representing the observed wave-frequencies,
it will be useful to derive other forms of this equation, which we shall employ later on. —
First of all, we see at once that (2) may be expressed by the following series :
l by b?
~a,(m+p)2 a,*(m + p)4 x a,3(m + p)® zh
V =Vo
and we notice that in this form it represents a more general case of RyDBERG’s formula,
into which it converges, for b,=0. In order to express the fact of its belonging to this
type, and at the same time to distinguish it from Rypsere’s more special equation, I
propose for it the name “ Rypperc-THIELE” equation, recognising thereby Professor
THIELE’S merit in having first introduced its present form into spectroscopic science.
Equation (2) assumes a simpler and in some cases a more convenient form by intro-
ducing v), the wave-frequency corresponding to m+m=0. In most cases there is no
line referring to this special value of », which obviously must lie close to the “ head” of
the series. But for the sake of convenience we may be permitted to speak of vp in the
following formulze as the wave-frequency of the “beginning” of the series. Introdue-
ing v), we find from (2) :
A=)
=,(Ve —Vy). (M+ p)?=a,(m + p)?. (3)
Vo —V
Similar equations are at once obtained if wave-lengths are substituted for wave-
frequencies :
1
A— Xx
ea Bae ie ae 2
soy ed ae ee a,(m + 1) + B,
(4)
Xr -- Neo
PWS veces. x2 (m +)? =a,.(m + ph)?
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 553
Still more convenient for computation are the following transformations, in which »,
and A,, the wave-frequency and wave-length of the xth line of the spectrum, are
introduced :
1 mi 1 y a 1 1 ds ;
Vov, \vo—v,/ a, (m+pyP—(e@+pe* ve—v, (m+pyP—-wtePet 8
(5)
1 ( de) 1 1 1 as
aie eS: a Gal eae we Gee eee te
The advantage of using these two formule lies in the fact that we may choose for
y, or X, the wave-frequency or wave-length of any observed line of the series, whereas
in the preceding equations »), v» and Ay, A» are quantities not directly obtainable from
the observations. The arithmetical process of evaluating the other three unknowns is
thereby greatly facilitated. Lastly, we may write
er, 1 a eh b
V—=V Ay(Ve — v)*(m +p pet ve fo vy (m+ py? :
(6)
it ae one 1 a,
; = == Gea Sea
equations which will be specially useful in the investigation of the band-series.
In comparing first our formula with the observed wave-frequencies of line-series,
we shall make use of equation (2), and apply it in this form to all the series
mentioned in Professor Kaysrr’s Handbuch der Spectroscopie, vol. u. I may state
at once that in all cases the constant « was found to be a proper fraction, the
denominator of which is represented by an entire multiple of 5, or, expressed in
algebraic symbols , De p and q being integers. As unit of wave-length the
tenth-metre or Angstrém unit was adopted, while for » the value 108-1 was taken, in
accordance with Kayser and RunGE and others. When not mentioned otherwise, the
wave-lengths and oscillation-frequencies are reduced to the Rowland scale.
A. Ling-SEries.
Group of Alkali metals.—There are two distinct kinds of series of spectra in the
elements of this group: the “ principal ” series, consisting of strong and sharply defined
lmes—the principal lines of the spectrum—which are easily reversible, and one or two
fainter “subsidiary” series represented by hazy lines, with little or no tendency to reversal.
These lines have been observed with very different degrees of accuracy. Kayszr’s tables
contain a column indicating the estimated probable limits of the observational errors
expressed in units of wave-length. These limits are given in the last columns of the
following tables, but in units of wave-frequency. Although the estimated uncertainties of
the observed wave-lengths cannot be considered as quite reliable, they may nevertheless
convey an approximate idea of the accuracy to be expected in our comparison.
554
1, Lithium.
PRINCIPAL SERIES.
log a, = 495920 — 10
« <-) = 43498'5
log b, = 3:55776 — 10
er Se ince
| Obee= imts o
dt bs. comp. : Error of
(m+ p) | v obs v comp Comp. oa
1:95 | 149071 |149070] +01 | 0-4
2°95 30933°2 | 30932°8 +0°4 0:3
3°95 36477°8 | 36475°7 +271 0-4
4°95 39022°9 | 39022°5 + 0°4 0:5
5°95 40401°9 | 40399°1 = DS} ey
6°95 41227°8 | 41226°0 +1°8 18
7:95 417617 | 41761°5 + 0:2 3°5
8:95 42124°8 | 42127°7 - 2-9 2
9°95 42383°7 | 42389°2 —5°5 q
1. SUBSIDIARY SERIES.
] = 4:95899 — 10
Se Gree oe ear ya = 28594-7
log b= — co
| | Limits of
| Obs. —
(m+p)\ vobs. | vy comp. | Error of
Comp. | Obs.
30 16383°3 | 16383°3 0-0 0-1
4°0 DG ATos) |) DL Bae |) as Deo 0°5
50 24198°8 | 241986 |} + O-2 ey
6°0 ayes) |) Aves) || == (0533 1:3
7:0 26351:°2 |26351:8 | — 0:6 34°5
8:0 268897 |26877°5 | +12:2 36°5
9:0 | D243 NATO) |) se AG 38:0
2. SUBSIDIARY SERIES.
og a, = 4°96060 - 10 ua :
log b, = 3°48865, — 10 ey
| Limits of |
(m+p),\ v obs, vy comp. ae Error of |
P. Obs.
2°6 12304:0 | 12304:0 0-0 1
3°6 PAD ONL 0:0 0:4
4:6 23400°4 | 23400°3 | + O'1 1+]
56 25088'2 | 25087:9 | + 0:3 ee)
6°6 26053°2 | 26067'°5 | —14°3 AND)
DR J. HALM ON
2.
Sodium.
PrincipaL SERIES (1st Component).
log a, = 4°95369 — 10
log b, = 4°43154,, — 10 er a
One Limits of
(m + ph) v obs. vcomp. | G : Error of
2°2 16960°2 | 16960-2 0:0 cfd
3:2 302749 | 30274-9 0:0 0:3
4-2 35051°9 | 350517 +0°2 0°6
5-2 37307°0 | 37307°2 — 0:2 13
6:2 38550°8 | 38550°9 — 01 1°5
72 39310°5 | 39309°2 +1:3 15
8-2 398053 | 39804°8 +0°5 3:2
1. Sussipiary Serres (1st Component),
log a, =4'95740 — 10
log b, = 3°16660,, — 10 v0 ae
Limits of
(m+p)) — v obs. v comp. ee ~ | Error of
| Pe) Obst
3'0 12202°9 | 12202-9 0-0 4
4:0 17580°1 | 17580-2 -0O1 05
5:0 2006671 | 20066°1 0-0 0:8
6:0 21416°0 | 21415°7 +0°3 2°2
7:0 22222°2 | 22229°3 -7T1 4-9
8:0 22759°9 | 22757°2 +2°7 q
9-0 23117-7 | 231192 — 15 q
2. Supsipiary Series (1st Component).
log a, = 4°95369 — 10
o = 24490°4
log b, = 4:29709, — 10
| Limits of
Obs. —
(m+ p) vy obs. vy comp. Error of
| Comp. Obs.
Eo a = = Br.
Be 16230°7 16230°8 = il 0°3
4-7 19403°5 19403°4 +0°1 0-4
Dee 21042°9 | 21042°7 +0:2 0°6
6:7 21997°2 | 21999°8 — 2°6 1:0
ears 22605'°5 | 22607-0 —1°5 q
8:7 23021°8 | 23020°3 +15 2
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA.
3. Potassium.
PrincipaL SERIES (1st Component).
Jog a, =4°94821 — 10
log b, = 4:75966,, — 10 A ak Ana
Limits of
Obs. —
(m+ p) v obs. y comp. Soran ae e
2°4 12988:2 | 12991-:0 -2°8 8°5
3°4 94707°5 | 24705-2 + 2°3 0-2
4:4 29006°6 | 29009-2 — 26 0:3
5-4 31077°5 | 31078-6 -1'1 0:3
6°4 BrZoo 4 | o2200°2 —1°8 1:0
T4 32949°6 | 32947°9 +17 11
8-4 334188 | 33418°5 +0°3 16
9:4 33746°2 | 33745:4 +0°8 2°4
10°4 33981:2 | 33982°1 —0°9 11°6
‘
1. Supsrprary Serizs (2nd Component).
log a, = 493963 — 10
2 = 22049°8
log b, = 4'86438,, — 10 ‘ s
Limits of
| Obs. —
(m+p)| vobs. = vy comp. Error of
Comp. Obs.
4:0 | 144693 | 14469°3 0-0 1-0
5:0 17293:0 | 17293-0 0:0 0-2
6:0 18784°5 | 18781°5 + 3:0 0:5
7:0 19667:°7 | 19663-7 +4:0 0:8
8:0 20230°2 | 20230-4 — 0:2 4:2
9-0 20616°9 | 20616°3 +0°6 4
10:0 20883°8 | 20890:9 =i q
2, Sussipiary Series (1st Component).
555
4. Rubidium.
PRINCIPAL SERIES Ga ; Component ) .
es fF eareee —10
ol ) 4:92935 — 10 _ j 33762°6
loo b. — § 4799618, — 10 ‘ns 3387547
aes 4:98695, - 10
W@iee Limits of
(m+ )| — v obs, v comp. | Gom Error of
mP | Obs.
2-6 j 12577°9 | 12578-1 - 0°2 05
12810°7 |! 12810°7 0:0 0°38
3-6 23720°7 | 23720-9 — 0-2 0-2
23798°3 | 237982 +01 0-2
46 27841:7 | 27840°9 +0°8 0-4
27876°7 | 27876°8 —0O1 0-4
56 { 298416 29841°8 —0°2 0:5
| 29860:9 29860°9 0-0 0°5
Supsipiary Series (2nd Component).
log a, = 490803 — 10
log b, = 4°76895,, — 10
Veo = 21203°3
Limits of
| |
Obs. — Error of
v obs. | vy comp, Comp
(m +p)
0 1S1L1-9 | T3119 0
0 16111°6 | 16111°9 -—0
0 17704°8 | 17699°6 +5°
0 18646°5 18643°2 +3
0 19250°0 19250°0 0
0 19662°6 1
19663°6 =
5. Cesium.
PRINCIPAL SERIES one | Component ).
noeeey® 3 4:90783 — 10
Sel ' 491436 —10
Jog a, = 492834 — 10 31525°6
wo = 2 c =
log b, = 4'76493,, — 10 SR ad loo b, = § 3'15453, — 10 a | 314965
— —— acne =? 8 °1— 1 513949, — 10
| | Limits of rai |
| Obs. — | Limits of |
ee) 7 obs. Be ial i@ orp. | ae ee (m+ )| — v obs, v comp. ae | Error of |
Ss. omp. Obs |
| D. |
BO | 171461 [171462] - 01 | 0-2 eres Peta eatin aces |
60 | 186571 |186571| 00 | 0% 28 i
70 | 19559:2 |19555'3) + 34 | 0-8 3°8 ieee A onl les
80 | 201390 |201341) 4+ 49 9 41 aE aera aoa tne
90 | 205322 |205984| +38) 7% ome Ise lene hae
100 | 207969 | 208093 | —12-4 ? SOE eee Wer a culis oe
M0 | 210111 /210166| — 55 1 Slo ran ale eeaie eros Mace
| 27686-7 |27685-'7 | +1:0 | 1°6
556 DR J. HALM ON
5. Cxesium—continued.
Sussiprary Series (1st Component),
log a,=4'90651 — 10
log b, = 521884, — 10 al ca
Limits of
(m+p)| v obs. v comp. one ~ | Error of
ig Obs.
4:0 10855°6 | 10855 °6 0:0 0:8
5:0 14339°2 | 14343°1 -3°9 10:0
6:0 16094°2 | 16094 3 — O01 1:3
7:0 17108°4 | 17106-0 +2°4 15
8:0 17745°9 | 177456 +0°3 16
9-0 18175°5 | 18176°7 -—12 q
10:0 18481:°2 | 18481°4 - 0:2 q
11:0 18705°9 | 18705-0 +09 q
I have omitted the second subsidiary series of Rubidium, of which only three lines
are known, the series being thus insufhcient for determining all the constants. It 1s,
I think, obvious, and scarcely requires to be mentioned, that the principal series of
Rubidium and Cesium, in which the four unknowns of our equation had to be
computed from the only four lines available, can tell us nothing of the accuracy of the
formula employed. But for obvious reasons I have made it a rule to compute every
series from which all the four constants may be obtained.
Let us now, before we proceed to other groups of elements, investigate the residuals
given in the columns [Obs. — Comp. ], by comparing them with those of the hitherto best
empirical formula, that proposed by KaysEr and RUNGE:
108\-l=a4+6m-2+em-4.
This equation apparently contains three unknown constants, a, b, and ¢, and seems
therefore to possess in this respect an advantage over ours, which has four unknown
quantities. But it is well to consider that a fourth unknown is implicitly involved in
Kayser’s formula, viz. the value of m for the first lime of the series, which we may
call m,. Strictly speaking, the difference between Kayser’s formula and the one here
proposed is therefore this, that the fourth unknown m, in the former is an integer,
while in the latter it is a compound fraction. But let us grant to Professor Kaysmr’s
equation the full advantage of having one unknown less than ours. If it would
represent the observations equally well, it would doubtless be the superior formula.
This condition, however, is far from being fulfilled. Let us, for instance, consider the
principal series of Potassium. Professor Kayser has computed the three unknowns
of his equation by the method of least squares, and has found the residuals, expressed
in units of wave-lengths, which are given in the first column of the following table,
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 557
while the second column contains, in the same units, the residuals computed from the
Rypserc-THIELE formula :
SEM esate an 8 sacl gahe} ey?
-36. | -04 | 0-0 0-0
Some 0°38 0-0 0-0
+ 1:3 +0°1 0-0 -01
+0°8 +02 +03 +01
—0°3 20: % + 0°2 0-0
— 0-4 00 | O(n i) waeOs4:
Po 10:5 Ost" | +1:0 +08
2 0s O11, amecets! +11
| |
A comparison of the two columns shows the considerable superiority of the
Rypserc-THiELte formula. Indeed, the representation of the observed wave-lengths
by Kaysrr’s formula appeared to Professor Kayser himself so little satisfactory that
he abandoned this method of computing the constants. In order to obtain more reliable
values of these, he disregarded the first line and computed his equation from the second,
third and fourth lines only. The residuals in this case are given in the third column.
In another calculation, the result of which is represented in the residuals of the fourth
column, he computed the constants from all the lines except the first. We observe
that in both cases his endeavour to improve the shorter wave-lengths was defeated,
notwithstanding the sacrifice of the first line, which shows an enormous discordance. The
computations demonstrate clearly that KaysEr’s formula cannot be made to represent
the observed wave-lengths nearly so well as the RypBERG-THIELE equation, although the
discrepancies of this latter, in the special case considered, are much greater than usual.
But it may be urged that the introduction of another unknown in Kayssr’s formula
might improve matters. To decide this point, let us consider the more general
equation
10®’“!=a+bm-2+em-*+dm-6,
I have computed the numerical forms of this equation for the principal series of
Li, Na and K, by using first the 1., 3., 5. and 7. lines of the series, and obtained the
following equations :
Li: 108A-1 = 43552-5 — 130802 m-2 — 1156838 m-4+ 124237 m-6
Na: 108A-1=41516°7 — 128378 m-2— 829617 m-4 — 36437 m-§
K: 108\7!=35075°6 — 126522 m-2— 618583 m4 — 287275 m-6
The residuals, expressed in units of wave-frequency, are shown in the subjoined
table under the heading K-R, while those of the RypBERG-THIELE sougul: are repeated
from the preceding tables and given under Ry-Th.
558 DR J. HALM ON
| Li. Na. | K.
| KR. RyTh K-R. By-Th.| KR. Ry-Th.
O00) Stl |). 000 400 00 28
| + 44:4 +04 +431°5 0:0 + 26:0 +2°3
00 +421 0-0 +02 00 -26
Bee Ree ee) a] SS
QO E26) 80-0 | or 00 -18
208; Sl Gaghece D4 ue salen, |e oo Meee
00 +402 0-0 +05 0:0 +03
| =4q) 29:9 -2:0 +08
-~88 —55 E63). 209
The enormous discrepancies in the second lines show that Kayserr’s formula is
still far from representing the actual phenomena, and hence, even in this extended
form, is inferior to the Rypserc-THIELE equation. To give full justice to the
former I have repeated the computations by excluding the first lines, but I have come
to the conclusion that while the fourth constant produces on the whole a slight
improvement in the shorter wave-lengths, the discrepancies in the first lines are even
increased. All these computations have convinced me that no general improvement
can be expected by adding a further term to Kayssr’s formula.
But besides we find other facts which speak in favour of the equation here employed.
There exists a certain empirical law, first pronounced by RypBERG and Kaysmr, that
if for a given element two or more subsidiary series exist, these series converge into one
common tail. This law has now been confirmed approximately in so many instances,
that we may accept its correctness. The presumption is warranted, therefore, that —
the better formula should also bear out this law more precisely. Now let us compare
in this respect KayseEr’s formula with the RypBeRG-THIELE equation. We find for the
wave-frequencies of the tails of the 1st components :
K-R. Ditt, .| Ry-Th: Diff.
Lithium 1. S.S. 28586°7 | 28594°7 |
| | +80°7 =i
De Shs). 28666°7 28583°3
Sodium 1.8.8. | 24492°3 | 24481-2
+ 56'8 +9:2 |
2.5.8 245491 | | 24490:4 zea
Potassium 1.8.8 21991°2 | | 21991°8
| +30°6 +51 |
2s 22021°8 21996-9 |
These ficures leave no doubt that the law is represented much better by our formula
than by that of Kayser and Runar. We shall see later on that this applies to other
spectra as well.
= AS
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 559
A scarcely less convincing test of the superiority of the RypBrrG-THIELE equation
is afforded by the discussion of another empirical law which we owe to Rypsere. This
law may be expressed as follows: (see Kaysmr, H.d./S., p. 557). The wave-frequency
of the first line of the principal series is equal to the difference of the wave-frequencies
of the tails of the principal and subsidiary series. It must be remarked, however, that
if we take the first components [7.e. those of greater wave-lengths] of the subsidiary
series, the law refers to the second components [shorter wave-lengths] of the principal
series. Here are the figures corresponding to the two formule :
KR. k _— Comp.
Ry-Th. Ones Obs. — Comp
Ist Line of
BS, SS, Wittens | es: Sree) erence! _ KR. Ry-Th
Li: 43584 28627 14957 | 43498 28589 14909 14907 Sa eo
Na: 41542 24521 17021 | 41468 24486 16982 16977 eee
K: 35086 22006 13080 | 35030 21994 13036 13045 Bae hao8
Rb: 33762 20919 12843 | 33755 20965 12790 12811 -~32 421
Gs: 31509 19743 11766 | 31496 19748 11748 11726 24g S28
From the last two columns we see that Rypperre’s law is represented in a distinctly
better manner if the Rypperc-THIELEe formula is used. More important advantages
of the latter will, however, appear in a subsequent part of the investigation upon
which we can enter only after having examined the line-series of the other elements.
Of the remaining elements of the first vertical column in MENDELEJEF’s series we
can investigate here only Silver, of which four lines of the 1st subsidiary series are
known. This being the minimum number of lines necessary for computing the
constants of our equation, we must omit those series in which less than four lines
have been observed. Doubtless in some of these cases three lines would be sutfticient,
because we have seen already that in a considerable number of series « =0 or (m+ }
an integer, so that our equation contains only three unknowns. But to decide whethex
the series belongs to this special group we still require at least four data.
6. Silver.
lst Susstprary Serius (1st Component).
log a, =4'96094 — 10
« = 30646°4
log b, = 4'15268, — 10
(m+) v obs. vy comp. | Obs. — Comp.
30 18275°8 18275°8 0-0
4:0 23741:1 | 23741:1 0:0
5:0 26242°6 26242°6 0-0
60 27593-7 27594-0 —0°3
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24) 84
560 DR J. HALM ON
It is of course quite unnecessary to compute the equation for more than one component
in those cases where the subsidiary series consists of double or triple lines, because it is
well known that the difference between the wave-frequencies of corresponding com-
ponents is constant throughout the series. We therefore obtain the equation of the
second or third component from that of the first by simply adding a constant to v0.
We now turn to the elements of the second vertical column of MENDELEJEF’S series.
The tables are computed in the same manner as before, but I have added a column
showing the residuals of KaysEr’s formula which have been taken from the data in
his Handbuch, but have been converted into wave-frequencies. The structure of the
triplets in the 1st subsidiary series is in many cases complicated, especially that of
the first two components. In such instances my computations refer to the simpler
third components :
7. Magnesium. 8. Calcium.
1. Sussrprary Serres (1st Component). 1. Supsrp1aRy Series (3rd Component),
log a, =4°95065 — 10 log a, =4°95797 - 10
2 =39779°3 : » = 34073-0
log b, = 4:34688,, — 10 i c log b, = 4°76493,, — 10 2
|(m+p)| — v obs. v comp. Cea K-R. (m+ p)| vobs. | v comp. Coan K-R. |
2°9 260522 | 260513 +09 , +01 3°2 22595°9 | 225964) - 05) — 03
3°9 32288°7 | 32290°9| —2:2 -0O1 4:2 27592°5 | 27592°5 00] - 05 |
4°9 350651 | 35064:2| +0°9 —3°9 5:2 29900°0 | 29900-0 0:0 00
59 36538'5 | 36537°6| +0°9 0:0 6°2 31155°0 | 311586} - 36/ + 38 |
6°9 37412°6 | 37413°7| -1:1 +3°5 1:2 31886°4 | 31921:4| -—35:0 | -—218
79 | 379776 | 379769| +07 | 49-7 |
2. SuBsipIARY SERIES (1st Component). 2. Sussrprary Series (1st Component).
log a,=4°94696 -10 log a, = 4°94860 —10
o= g » = 34001°7
log b, = 4'81358,, - 10 eae log b, = 4-92942,, — 10 s
(m+ p) v obs. vy comp. one K-R. (m+yp)| — v obs. vy comp. ce K-R
2°5 19290°7 | 19290:2| +0°5 — 198-0 27 16227°4 | 162276} -—0O2 | —158
3°5 29968°6 , 29967°5|) +1°1 + 03 3°7 251641 | 25161:3| +2°8 00
4°5 339881 | 33990°2) -—2:1 — 05 47 28671°3 | 28675:0| -—37 0:0
5°5 35951°4 | 35951°9| -0°5 + 02 5-7 304300 | 30431°9| -19 | - 072
6°5 37058°5 | 370586} -—O'l1 - 15 67 31432°9 | 31440°3) -—74 | — 216
75 37745°8 | 37744:9| +09 | — 38 vferi 320739 | 32072°0| +19 | + OF
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 561
9. Strontium.
1. SussipiaRy Series (3rd Component). 2. Supsipiary Series (1st Component).
7 set : : ero SS aa cae =31077°7
log >, = n— log 6, =5°10018, — 10 Ags
(m+ p)| vobs. | v comp. a K-R. Ole
P- ; (m+ )| — v obs. |v comp. Cam, K-R.
35 20694°3 | 20694°3 O00) 4 07
4:5 25374°7 | 253748} -O-1 - 26 2°9 14142°9 141429 | 00 | -—96-
55 275544 | 275571) -2°7 | -11°7 3°9 225315 , 225301) +14 | + O1
6°5 287580 | 287606); -26 | — 95 4-9 25868°7 | 25868°7 00 | - 22
75 294980 | 29497°5| +05 | + 3-1 59 27559°0 | 275565; +25 | -— Ol
85 29987-9* | 29982-4) +55 | +16°3 6°9 28533°3 | 28533°3 - 0:0%| = 2:2
The enormous discrepancies in the first lines of the 2nd subsidiary series shown
by Professor Kayser’s formula might, as in similar cases before, be considerably reduced
by employing these lines in the computation of the constants. But this would involve
inadmissible residuals in the shorter wave-lengths. It may be shown by easy calcula-
tions that no numerical form of KaysEr’s equation can represent the observed wave-
frequencies with the same accuracy as the Rypperc-THiELe formula. After the
foregoing discussion of the relative merits of the two formule I need not dwell upon
this point any longer. The shortest wave-length of the 1st series of calcium is badly
represented by both equations ; and although Kaysgr’s formula is distinctly better than
ours, neither formula is satisfactory. It is worthy of note that there are two other
instances, viz. the first series of Aluminium and the second series of Thallium, where
both equations distinctly fail.
10. Zinc.
1. Sussiprary SzriEzs (1st Component), 2. SUBSIDIARY SERIES.
log a, = 494561 — 10 log a, =4°93860 — 10
«o = 429186 . «o = 42924:
log b, = 4°43373, — 10 i log b, = 4'84137,, — 10 ‘
Obs. — Obs. —
(m+ )| v obs. COMPS | Comp, K-R. (m+ )| — v obs. v comp. Cane. K-R. |
30 29889°3 | 29889:2} +0:1 +0°7 9°45 20787:0 | 20787:0 0:0 | —251- |
4:0 35701°7 | 35701°6} +01 -0°3 3°45 32550°0 | 32550°5} —-—0°5 0:0
5:0 38333°3 | 38332°0} +1°3 -0:9 4°45 36864:0 | 368631 +09 | -— 02
6:0 39745°5 | 39745-5 0-0 +1:8 5:45 38940°0 | 38939°2} +08 | + 0-2
7-0 40592°7 | 40592:7 0:0 +6°5 6:45 40101:0 | 40101°5| -05 | + 06
80 411400 | 41140°6} -0-°6 ae T:45 40820:0 | 408184) +16 | + 3:3
* The line observed is the first component : v=29408°0.
ar
362 DR J. HALM ON
11. Cadmium. 12. Mercury.
1. Supsiprary Series (3rd Component).
log a, =4°95111 —10
1. Supsipiary Serres (3rd Component).
log a, = 4°95027 —10
= 42450: «= 46582°5
log b, = 4°56211,,— 10 va eee log b, = 4:44885,, — 10 ‘
| | | Obs. —
(m+p)| — v obs, v comp. nae K-R. (m + 4) v obs, vy comp. aan. K-R.
3:0 | 29379°3 | 29379°3 00 | +01 30 | 336985 | 336968) +1:7
4-0 | 352483 | 35248:3 0-0 | +05 40 | 394490 | 39447°5| 41:5
5:0 | 37884:5 | 37884:5 00 | —41 50 | 42045:0 | 42048-9| - 3-9
6-0 | 392945 | 39299°8/ -5:3 | +1-0 6:0 | 434480 | 434464] +1°6
70 | 40137* | 401498: -5:8 | 45:3 f a
2. Supsipiary Series (1st Component).
log a, = 4°93417 —10
» = 40765°7 2. Supsrp1ary Serres (1st Component).
log b, = 492926, — 10 /
; log a,= 494401 —10 Ae
| a log b, = 4°84592,, — 10 oe
(m+ p)| — v obs. v comp. oe K-R.
Obs. —
: ae (m+ p)| — v obs. compe Geant K-R
2°55 19661°9 19661:0} + 0:9 | — 263: |
B 5b i 307448 30746. be 17a ne Onl |
4°55 34863°3 34862°9| + 04) + 0-2 2°45 18311°7 18311°7 0:0 = Nile
5:b5 36864:0 | 36862°7) + 1:3) — 0:3 3°45 29924:'7 | 29923:9) +0°8 + O1
6°55 87989:0 | 37989°3|} -— 0:3 ee 4°45 34182°3 34182°5| -—0:2 —~ OF
7-55 38716°7 38688:3| +28-4 26°3 5:45 36234°2 36232°6| +1°6 - 06
8°55 39141°0 | 39152:1) -11:1 6°45 37380°3 | 37380°3 0:0 =- $4
|
Turning to the elements of the 3rd column of MENDELEJEF’s series, we find Al, In
and Tl each with two subsidiary series. I have mentioned already that unexplained
anomalies exist in the first series of Al and the second series of Tl, and that neither
Kayser’s formula nor the present one represents the observed lines in a satisfactory
manner. Professor Kayser has nevertheless partly reconciled his formula with the
observations by neglecting in each case the first three lines, and by demonstrating that the
remainder could thereby be brought into fairly satisfactory agreement. It might be easily
shown that under these circumstances our formula would render equally good service.
But as long as the nature of these quite exceptional discrepancies is unknown, I consider
such computations as being of little value. Iam inclined to think that the series referred
to are not homogeneous, but are in fact the result of a superposition of several branches,
perhaps two in each case, which coalesce in such a manner as to give the impression of
one single series. We shall come upon such anomalous cases later on when treating of
the band-series, where in at least one instance, viz. the cyanogen-band, the hetero-
* Computed from the 2nd component : »=39594'5,
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 563
geneous character of what to all appearance seems a single series can be proved.
Leaving this point in abeyance for the present, we shall disregard the two discrepant
series.
13. Aluminium. Indium—continued.
2. Supsmpr1ary Series (1st Component). 2. Sussip1aRyY SERIES (2nd Component).
Jog a, = 4°94086 — 10 are ag 2 irene Sie aerons
log 0,=4°82757,-10 9” He GN Sera Re
Obs. == Tea
Oe (m+p)| v obs. PURI ctr K-R.
(m+ p)| — v obs. CORN her K-R.
2°45 24379 24379 0 — 333
2°4 25242°2 | 25242°2 00 — 338° 3°45 36311 36311 0 0
3°4 37587°3 | 37587°8| —0°5 0:0 4-45 40648 40648 0 0
4-4 42043°6 | 42043°9| -0°3 0-0 5°45 42730 42729 + 1 0
54 44172°0 | 44171:4| +06 0:0 6°45 43891 43891 0 - 2
6°4 45356°7 | 45356°8| -—1:0 + 17 7°45 44611 44609 + 2 + 2
8°45 45080 45082 - 2 - 6
9°45 45455 45412 + 43 + 39
15. Thallium.
14. Indium. 1, Supsiprary Series (1st Component).
log a, =4:94304 — 10
1, Sussm1ary Series (2nd Component). ie 7 2 ee Laie Veo = 415117
log a, =4°92091 —10
3) 46 4 |
log b, = 4°41282,, - 10 ee lee a) pee a eee) Ob” aha
les ; i Comp. ;
Obs. —
(m +p) v obs. vy comp. Garant K-R. Be 98339 98339 0 0
4:0 34228 34227 | + 1 + 1
5:0 | 36887 36887 | 0 - 2
3°0 32900 32900 0 0 6:0) | 38316 |) 38314 + 2 0
4:0 39060 39060 0 0 %0 39168 39168 0 + 2
5:0 41847 41847 0 0 8-0 39722 39721 | + 1 + 5
6:0 43350 43345 +5 +11 90 40096 40098 - 2 + 3
7-0 44236 44243 -7 + 2 10:0") 40362," 9+ 408635) a1 - 1
8-0 44825 44823 | +2 +16 11:0 40559 40567 8 - 4
9:0 45224 45220 +4 +20 12:0 40708 40718 | -—10 - 7
10°0 45506 45502 +4 +19 13:0 40824 40836 -12 -1l
11:0 45714 45713 +1 +17 14:0 40916 40929 | -13 -13
12:0 45871 45872 -l +13 15:0 40991 41005 —14 —16
To complete our investigation of the line-spectra we will now discuss the line-series
observed by Runce and Pascuen in the spectra of Oxygen, Sulphur and Selenium
(Astrophysical Journal, vol. viii.), and in the spectrum of Helium (Kayser, Handbuch,
pp. 560-1). The comparison of these series with the RypBERG-THIELE formula is specially
Interesting, not only on account of the extreme accuracy of the observations which
thereby afford a valuable test of this formula, but still more because it had been
564 DR J. HALM ON
found that Kayserr’s formula, in its original form, did not sufficiently sable the
measurements, which had to be represented by an equation of the form
108A-!=a + bm? + em-3,
This modification must of necessity complicate the theoretical aspect of the problem,
inasmuch as the line-series would appear to be of two different types, in which the
structure of the series is seemingly determined by different conditions. But we shall
see now that the series of all these elements are represented by the same type of the
RYDBERG-THIELE equation which we had employed in the foregoing discussion, and
hence that a separation in two different types, such as is demanded by Kayszr’s
formula, is not required. This must be considered as an important advantage in our
equation, which will become more apparent in the later discussion of the results.
16. Oxygen. Oxygen—continued.
lst TrreLet Serigs (1st Component). Ist Parr Serres (1st Component).
log a, = 495404 — 10 Laat Ae 108 eee : vo = 21201-7
log b,=3'80598,-10 igo ain
|
NS, ae v obs, comp. | O2Sam R-P.
(m+) | (reduced to| vy comp. es % I ce 6 ( “I (red. to vac.)} ” f Comp. |(/.c. p. 81),
nota) omp. |(J.c. p. 76). |
38 13781:2 | 137815); —-0°3 — 0:2
40 | 162335 | 162339) —-O+4 0-0 4:8 16533°8 | 165324; +14 | +09
50 18753°6 | 187534) +40:2 — 0:3 5:8 17996'4 | 179965! -0-1 —~0'4
6:0 20119°5 | 201186) +0°9 +0°2 6:8 18865°7 | 188677} —1:3 — Jen
7:0 20941:3 | 209406) +07 + 0:2 7:8 194264 | 19425°5| +09 +0°9
8-0 21473°9 | 214736) +03 +0°2 88 198049 | 19805°6| -—0°7 —0°6
9°0 | 218384 | 218389) -0'5 | -0-2 9-8 20075°9 | 20075°6| +03 | +05
10:0 22099'7 | 22100°1| -—0-4 +0°5
2nd TripLet SERIES (1st Component). 4nd Parr Srrms (1st Component).
log a, =4°95587 - 10
log a, = 4°95750 —10 ee Yo = 21212°7
2 = 23207- log b, = 3°55793,, — 10
pe eeteT6157.= 10. nw oe 3
b ) v obs. Obs, — R-P.
sda Obs. — R-P. (re (red. to vac.)| ” °°™P* | Comp. |(Z.c. p. 81).
(m+ p) | (reduced to| vy comp. CG I 77
vacuum), omp. |(/.c. p. 77).
4:0 14276°8 | 14276°7; +01 +02
3°8 154846 | 15484°6 0:0 -0°3 50 16777°5 | 16777-7; —02 —0°4
4°8 18387°3 | 18387°3 0:0 +1:0 6:0 181343 | 181343 0:0 -0°5
58 19913°6 | 199134; +402 -0:1 70 18951°3 | 18951:'8); —05 —0°8
68 20813°8 | 208140) -0:2 -0°8 8°0 19485°2 | 19482°0; +3°2 +30
78 213896 | 21389°9) -03 —0°2 | 9:0 198463 | 198454) +0°9 +08
88 21780°2 | 21780°3} -0-1 +0°9 10°0 20102°9 | 201054) -2°5 -—2:3
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA.
17. Sulphur.
Ist TRIPLET Series (1st Component).
log a, = 4°96004 — 10
} EO) 5
log b, = 463201 - 10 gee
i
v obs. Obs. — R-P.
(m+ 1) (red. to vac.) LN ae Comp. |(/.c. p. 87).
4°5 14794:6 | 14794:5| 4-0-1 +0:1
5:5 16516°3 | 16517:0| —-0-7 —0°5
6:5 17519°3 | 17519°5| -0-2 +01
io 18153:1 | 18152°9| +0°2 +0°5
85 18578:-2 185782 0:0 +0°1
95 18877°4 | 18877:4 0:0 +02
2nd Tripter SER1Es (1st Component).
log a,=4°95431 — 10
Mmeee45976,-10 =~ 200804
v obs. Obs. - | R-P.
(i+ 1) (red. to vac,)| ” °°™P: Comp. he p. 88)
5:0 15582°6 | 15582°7) -0-1 +0:1
6:0 16973-1 | 16973:2| -0-1 -0:1
70 178062 | 17805°9|} +0:3 +04
8-0 18343°6 | 18344:0| -0-4 +01
18. Selenium.
Ist TRipLer Szrizs (1st Component).
log a, = 4°97128 - 10
log b, = 481092 - 10 wee eeer se
4 v obs. Obs. — R-P.
+ 1) (red. to vac.)| ”°°™P- | Comp. (dc. p. 94).
4°5 141562 | 141564) -0-2 0:0
55 158050 | 158048 +0-2 0-0
65 16769°2 | 16769°8,; -0-6 0:0
75 173796 | 173816) —2-0 —1:2
85 17794'9 | 17793°3| +1-6 + 2°2
9°5 18083-2 | 180830} +0-2 -—0°6
105 18293°9 | 18294-:7; -—0-8 -18
565
Selenium—continued.
2nd Tripter Series (1st Component).
log a, = 4°95145 — 10 19286°2
Vo =
log 6, =3°40040 — 10
(se) v obs, ek Obs, — R-P.
P \(red. to vac.)| ” P- | Comp. |(i.c. p. 95).
50 14818°2 | 14818-2 0-0 0:0
60 16182°4 | 16182°3, +01 0:0
(0) 17005°4 | 17005°3} +0:1 0-0
80 175381 | 17539°5| -1-4 -17
19. Helium.
Ist PRINCIPAL SERIES.
log a, = 495902 - 10
20 = 38465"
log b, = 311561 - 10 é aoe
Obs. —
(m+p)| — v obs. VCE. | Can K-R.
214 25715°3 | 25715°3 0-0 0:0
314 31369-2 | 31369-2 0-0 0-0
4i4 33953°1 | 33953°2,| — 0-1 0-0
_ oF4 35345°8 | 35345°6| +0°2 +0°2
614 36180-°7 | 361805} +0:2 -O1
w44 36720°8 | 36720°2| +06 -01
814 37088°3 | 37089°1| -0°8 -07
9214 37352°5 | 37353:2| -0°7 —0°3
1034 375475 | 375467} —0°8 +0°3
lst Sussrp1ary SERizs (2nd Component).
log a,=4°95913 —10
= 29231:
log b, = 2°60695, — 10 Var seal 6
(m+ p)| — v obs. vy comp. ae K-R
30 17018°8 | 17018°8 0:0 0:0
4:0 22363°5 | 22363°3; +02 0:0
5:0 24836:5 | 24836°3| +0°2 0:0 ©
6:0 26180°0 | 26179:5|; +0°5 -—01
7:0 26989°4 | 26989°4 0:0 —0°3
8:0 97515:0 | 27514:°9) +01 —0°5
9:0 97875:3 | 278752) +0°1 -07
10:0 28133°3 | 28133°0} +0°3 -—1'1
11:0 28323°8 | 283236] +0°2 - 1:0
12:0 98468'7 | 284686} +01 —1:0
13:0 2858173 | 28581:°5) —0°2 -—10
14:0 28670°7 | 28670°9| —0-2 —12
15-0 28743°3 | 28743°3 0:0 -1:2
16:0 28802°7 | 28802°5) +0°2 —1:0
17:0 928851°3 | 28851:°5) —0°2 a i
18:0 288900 | 28892°5) -—2°5 — 3-4
19:0 28927°3 | 28927°3 0:0 -07
566 DR J. HALM ON
Helium—continued. Helium—eontinued.
3rd SUBSIDIARY SERIES,
log a, = 4'95930 — 10
2nd Sussiprary Series (2nd Component).
log a, = 496066 —10
= : = 271/82°
log 6, =3°40436, — 10 Yo = avene ie log 6, = 2°60712, — 10 10
(m+p)| v obs. v comp. ee K-R. (m+ m)| v obs. v comp. Con K-R.
2°7 14153°3 | 14153°7| —0°4 — 48: 3°0 14973°4 | 14973°6| —0-2 0:0
37 21216°7 | 212160) +0:7 0-0 4:0 20316°7 | 20316°5] +02 . 0-0
4:7 242661 | 24267-:0| -—0-9 0:0 5:0 22789:0 | 22788°6| +0°4 0-0
5-7 25855°9 | 25856°6| -—0-7 0-0 6:0 24131-°7 | 24131:-4} +0°3 00
6°7 267881 | 26788:-9| -—0°8 + 14 70 24941:2 | 24940°9| +03 00
(her 27381°2 | 27381:8}' —0°6 + 3:5 8:0 25466°5 | 25466°3) +0°2 +01
8-7 27781-°9 | 27782°2| -—0:3 + 55 9-0 25826°3 | 25826°5| -—0°2 -O
oT, 28065:3 | 28065°3 0:0 a VG 100 26084°4 | 26084:2} +0:2 — 0-2
10°7 28272°7 | 28272-7 0:0 + 9-3 11:0 26274:7 | 26274:7 0-0 — 0:2
117 28429°4 | 28429-3| +01 +10°7 12-0 26420:0 | 26419°7) +0°3 — 03
12°7 28550°7 | 28550°3| +0-4 +12°7 13:0 26531°9 | 265325] -—0°6 — 0-4
13-7 28647°3 | 28645°8| +1:5 +14:1 14:0 26621°9 | 26622°0) -0O-1 - 01
14:7 28722:5 | 28722°5 0:0 + 14:0
2nd Principau SERIES,
log a, = 4-96161 — 10 ee 4th SuBsipiaRy SERIES.
log b, = 3°40531 — 10 ee log a, = 495932 — 10 ye = 27181-7
log 6, =3°67610, - 10
Obs. — 2
m+ v obs. v comp. K-R. |
oD) P| Comp. (m+p)| vobs. | v comp. Coal K-R
3°0 19936°8 | 19936°4| +0°4 0-0
4:0 95221-1 | 25221°1 0-0 0:0 233 13732°8 | 13732°8 0:0 —158
5:0 MAIER) MAGEE || Ors 0:0 312 19810:9 | 19810°77; +02 0-0
6:0 29004°5 | 29004:9; -—0-4 +0:2 473 22534°2 | 22534:6| -—0-4 0-0
7:0 29809°3 | 29808°8} +0°5 +0°7 543 239861 | 23986°1 0:0 0:0
8:0 30331°3 | 38330°8) +0°5 +0°7 632 24849°4 | 24850°1| -0°7 + O04
9°0 30690°7 | 30688°7| +2°0 +1°5 742 25405'°9 ,; 25405°6| +0°3 + 10
10:0 30947°1 | 30944°8| 42°3 +1:8 843 25784°7 | 25783°9| +08 + 13
11:0 31136°4 | 311384°3) +2°1 +2:1 gi3 260537 | 26053°0| +07 + 18
12:0 31280°7 | 31278°4| +42°3 + 2:0 1043 ses ao ae
13:0 te Se a ae 1143 26401°8 | 26401°6| +0-2 + 2°3
14:0 31480°7 | 31479°6| +1°:1 —0-4 1233 265200 | 265181; +19 + 44
Reviewing the results of the foregoing computations, which embrace now all the
line-series so far as known, we must admit that the RypBerc-THIELE formula is in many
cases distinctly better than that proposed by Kayspr and Runes, and is never inferior
to that equation. Its advantages become still more obvious if we investigate more
closely the constants. Let us begin by testing the law mentioned before, according
to which two subsidiary series of the same element possess common tails. In the
following table we give for all cases in which two subsidiary series-have been found,
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 567
the differences of the wave-frequencies of their tails, computed on the one hand by
Kaysir’s formula, and on the other by the RypBerc-THIELE equation :
K-R. Ry-Th. K-R. = Ry-Th.
Ibis + 81 -11 Hg: +58 -13
Na: + 57 +9 In: +20 + 3
K: + 31 + 5 O: —14 = 5
Mg: + 41 + 1. ae qe Jl
Ca: +121 + 83 S: — 9 + 3
Sr: + 35 +18 Se: +20 +28
Zn: + 10 + 5 He: — 26 -— 38
Cd: + 42 +457 - 7 -— l
These figures show clearly that the law in question is more closely represented by
the Rypserc-THieLE formula. [Errors of 10-15 units are possibly accounted for
by the uncertainty of the data from which the constants have been derived, because it
can be shown that an error of only one unit in one of the observed wave-frequencies may
sometimes alter the computed position of the tail by more than ten times this amount.
The discrepancies in the [Ry-Th.] column, except those for Ca and Se, may therefore
be considered as admissible, if the still existing uncertainties of the observed wave-
lengths are taken into account.
With regard to », it has doubtless been noticed that in a considerable number of
eases this constant is zero. Indeed, among the 44 series mentioned above we have no
less than 19 instances of this kind. _We find that, with the exception of Mg,
Ca and Sr, all the first subsidiary series belong to this particular group, which, as has
been already pointed out, includes the first Hydrogen-series. There is also evidence
of the existence of smaller groups, for instance »=0°5 [H, Mg, 8, Se]. Now
in any such group, if we denote by » the wave-frequency of a line of one series
and by n the wave-frequency of a line of another series, since « is the same in both
series, we have the relation
= 5 +5 (7)
where a, and b; are constants while v, and n, are the wave-frequencies of the «th
lines of the two series. This relation obviously enables us to express one series of
lines by means of another belonging to the same m-group. A similar relation obtains
for the wave-lengths :
+B; (8)
It may be of interest to prove the existence of such a relation between the series
of different spectra in some special cases. Let us take, for instance, the group »=0,
and let us assume as the series of comparison the well-known Hydrogen - series
Tepresented by Batmer’s formula. In accordance with the foregoing equations, we
call the wave-frequencies and wave-lengths of the hydrogen-lines n and 1 respectively,
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24). 85
568 DR J. HALM ON
those of the series to be compared vy and A. From the considerable number of series
belonging to this group we select here the following: He, 3rd S.8.; In, 1st SS. ;
(2nd comp.); Tl, 1st 8.8. (1st comp.); Zn, Ist 8.8. (2nd comp.); Li, Ist SS. The
following table contains the results of the comparison. By using equation (8) and
adopting for \, in each case the wave-lengths. which I have bracketed in the table,
we find the following values of log a, and log #6, :
log a;. log B;.
He: 9:99165 — 10 450246, — 10
‘In: 0°43927 6°31899 —10
Tl: 0°35204 6°13701 —10
Zn; 0°39819 625993 —10
Tei © 0:03893 505185 — 10
while the computed wave-lengths as well as their discrepancies (Obs. — Comp.) are given
as follows :
In, Ist 8.8. Tl, Ist S.S. Zn, 1st 8.8. i
ES SGD eHTSES. (2nd Comp.) (1st Comp.) (2nd Comp.) te
6563-07 6678°37 0:00 3039°5 0:0 3529°6 0:0 3302°8 0:0 6103°3 0:0
4861°52 492210 0:00 2560°2 0:0 29216 0:0 2771:0 0:0 4602°4 0:0
4340°63 4388:07 + 0:03 2389°6 0:0 2711:1 —0°3 2582°7 —0°1 4132°3+0:1
4101:90 4143:90 + 0:02 2307:0 —0°2 2610°2 —0°3 2491'7 0:0 3915°14+071
3970°22 4009°41+0-01 2260°2 + 0°4 2553°3 — 0:2 2440:2 —0°3 [3794°9]
3889-20 3926°70 — 0:02 [2230°9] 2517-9 --0°4 [24080] ... 3720°8 — 1:9
3835°53 3871-96 — 0:01 2211°3-0'1 2494-2 —0°2 3671°6 - 1:0
3798 04 383369 + 0:02 2197:5 0-0 [2477-6]
3770°77 3805°88 + 0°02 2187:4+01 2465°44+0°1
3750°30 378501 + 0°02 2179:9+0°1 2456°3 + 0:2
373451 3768:91 + 0°04 2449°2+0°4
3722°08 [3756-24] 2443°7+0°3
3712°11 2439°2 + 0:4
|
Although the method of computation scarcely needs an explanation, I will never-
theless illustrate it by one example. Suppose we want to find the 3rd _helium-line
(from the top). The corresponding H-line is /=4340°63, further \,=3756'24 and
L, = 8722°08, hence
{ a;
X— 3756-24 ~ 434063 — 3722-08 * Ps
= 3756°24 + 631°83 = 4388°07,
= 00015859 — 0:0000032 = 0:0015827
The existence of so remarkable a relation between the line-series of different
elements is a novel and certainly important feature, the discovery of which we owe
to the application of the Rypserc-TureLte formula. In some cases the relation
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 569
between series belonging to different chemical atoms is still closer. If we write our
original equation (2) in the form
il 2 b
= 2 eh IL
a,[(m + p) wel GS (9)
we find that in certain cases the expression within the brackets is the same for two
series. Under this special condition we have obviously
Pas
Vv
= const.
Nao > n
I have found the following four instances of this kind :
(1) Zine, 1st S.S., and Indium, Ist 8.8. Calling the difference (v» —v) in the case of
Zn: |v]z, and in the case of In: [v],, we find from the preceding tables
[van [vin 0-94374[7],,
13029 13807 13030
iy 7647 7217
4585 4860 4587
3173 3357 3168
2326 2471 2332
1779 1882 1776
Hence we have, with suthcient accuracy : [v]z, = 0°94874[7],,.
(2) Zine, 1st 8.S., and Mercury, Ist 8.8.
[Vv] zn [vu | 1:01137[v]y,
13029 | 12884 | 13031
WT | 7134 7215
4585 | 4537 | 4588
3173 3134. 3170
It obviously follows that [v],, = 0°94874[v],, =1°01137[)]z, .
(3) Zinc, 2nd 8.8., and Mercury, 2nd §.S.
ie wives | O0286lvly,
| :
22138 21856 | 22138
10374 10243 10374
6061 5986 | 6063
3985 3934 | 3985
2824 2788 | 2894
570 DR J. HALM ON
(4) Lithium, Ist 8.8., and Hydrogen, Ist 8.S.
[voi [yn
12211 12189
6867 6856
4396 4388
3053 3047
2243 2238
1705 1714
1351 1354
1-00177[¥ Ju
12211
6868
4395
3052
2242
akcalcg
1356
The RypBeRG-THIELE equation in the form given in (9) presents some striking regu-
larities of the constants which deserve to be mentioned.
{by far the most frequent) where b, is negative, we may write the equation in the form;
[vo —v]}*=a,(m+pt+c)(m+p-—c)=a,(m+d)(m+e)
Now it appears that in a certain group of elements, such for instance as the alkalis,
the constants d and e may be represented by common fractions having the same
denominator. Thus we find for the subsidiary series the following numerical equations :
Li 1.88.: [v,-v]}*=[4:95899 — 10}m- in
2, SS: =[4-96101 — 10](m — 3;)(m — 3%)
Na “IEs.S:: = [4°95748 — 10](m+%)(m — i%&
2. 8.8.: = [4°95512 — 10](m+ =3,)(m — 42
Ko) aeSis:: = [4:94046 — 10](m +44)(m— 44
2. Si8i: = [4°92668 — 10](m + 42)(m — 32)
Rb 1sSise = [490881 — 10](m +43)(m — 43
Cs SHEE == [4°90432 — 10](m + 23)(m — 22
The coefficients a, are given as logarithms.
means of these equations leave the following errors in the observations :
The wave-frequencies computed by
If we consider first the cases
14
C.)
(10)
= 28595
= 28580
= 24481
= 24481
= 22049
= 22005
= 21202
= 19746
iL | Li, | Na,
0; + 2 0
ae 2) ||) = al —1
0 0 0
Oo; +1 0
— 1) -13 —8
+12 +3
+ 6 =I
Na, HS K, Rb Cs
0 +1|]+ 41 +1 +2
0 -3 0 —2 —7
+ 1 Oo; + 2 +3 -2
0) +2! 4 3 +1 +2
+ 3 —2 0) a | +1
+10 -l1'! —-16 -2 0
—8 |} —10 +1
+3
These errors are sufficiently small to be explained by the uncertainties of the
measurements; they are indeed of the same order as those previously met with and
considerably less than the corresponding residuals of Kaysmr’s equation. Turning to
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. Oval
the principal series we find that here also the denominator 15 plays an important part.
Thus, considering the first components, the values of ¢ are for Li: 0°199, for Na:
0°548, for K: 0°805, for Rb: 1°083, and for Cs: 1°328, hence very nearly 53, 7%, 13,
“i8and 22. Except Li, the values of c and » form an arithmetic progression. For we
notice that » is represented by the fractions— 3, s45, o%, 33%, 3%, the numerators of
which are obtained from those of the quantities ¢ by subtracting 4. Such regularities
eannot be accidental, although we must confess that at present it is impossible to
assign a meaning to them. Nor are they confined to the group of elements here
considered. Thus we may easily convince ourselves that, for instance, the four series
of Oxygen mentioned before are represented by the equations :
1. Triplet: (ve —v) =[4°95404 — 10][m? — (4)°] yo = 23212'5
2. Triplet : = [4:95750 — 10][(m — 2)? - (4&)"] 23207°3
1. Pair: = [4-96523 — 10][(m — 8)? + (48)'] 21201°7
2. Pair: = [4°95587 — 10][m? - (,2,)°] 21212-7
Similar conditions we find in three of the six Helium-series, viz.,
Ist P.S. : [vo —v] =[4'95884 - 10][(m— 3s)? +(,%)7] v2 = 38466°8
Ist S.S. : = [4:95913 — 10][m?— (2,)°] 29931°6
3d S.S. : = [4:95930 — 10][m? — (25)"] 27182°4
whereas in the other three series the fractions contain the denominator 2 x 15, viz.,
2nd P.S. : [ve -v] =[4:96161 — 10][m? + (.5)°] v2 = 320369
Ond 8.8. : = [4:96066 — 10][(m — 28,)* - (s5)"] 29229-2
4th S.S.: =[4-95943 - 10][(m — 4, )* - (s55)"] 27181-4
The series of the three elements Mg, Ca and Sr, on the other hand, appear to be
well represented by fractions with the denominator 14. 1 have found the following
numerical equations :
Mg st S$.S.: [ve—v] =[4:95105 - 10](m+-5,)(m — 58) va = 39781
2nd 8.8. : =[4-94696 — 10](m+12)(m —-%) 39779
Ca 1st SS: =[4-95797 - 10](m+18)(m - 3%) 34067
Qnd 8.8. : = [4-94622 — 10](m + 24)(m — +4) 34005
Sr 1st S.S.: = [4-93097 — 10](m+28)(m—42 31636
2nd 8.8. : = [4:92352 - 10](m+32)(m— 31079
All these regularities seem to me interesting enough to be mentioned in this dis-
cussion, although [ admit that without a theoretical foundation they are perhaps of but
little importance. Nevertheless the mere fact that the RypBeRG-THIELE equation is
capable of showing so many interesting links between the series of different chemical
elements, of which we see no traces in other formule, speaks highly in its favour,
especially if considered in conjunction with the no longer doubtful property of this
formula, that it satisfies the observations much better than other empirical equations
hitherto proposed. But the chief importance of the RyppeRG-THIELE formula seems to
me to lie in some other properties which we are now to discuss.
572 DR J. HALM ON
It may be shown that an interesting geometrical relation exists between the
line-series belonging to the same m-group. Jf, in fig. 1, the points a,, a. :. am,
are fixed upon the straight line AB so that the distance Aa, =(m+ )?, and if from
any point O outside this line we draw the straight paths Ov, Ov, , Ory... Orn . q
Ov. , through A, a, a... dm... ao, any line-sertes belonging to this particular
group, which has been arranged oe a transversal line CD so that the distane €
Fic, 1.
the spectral lines fall exactly upon the rays Ov, Ov,, Ove... . The proof of this
theorem is very simple. If the dotted line, CH, be drawn parallel to AB, we have:
and generally
CO
Sea en, S
04% =z (17 + )
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 573
On the other hand, from the Rypprrc-THIELE formula (3)
ae 1A) a, (m + p.)? R
Hence, if the transversal CD be drawn in such a manner that
UGE
AKOZOD SE 2’
we find
Cém=Vm—Vo and ¢pD=ve -Vv,, and hence
€)C5 = Vo — Vy 5 Colg—=Vg—Vo, - > + - = CD ve — V9 Q.L.D.
If, now, all the series belonging to the same «-group be arranged in our diagram,
in every case the lines could be made to fall upon the rays Oy, Or, . . . Ove , so that
aN
7 8 9 10..--... oO
Fie, 2.
to an observer stationed at O all these series would seem to coalesce into one. In
virtue of equation (4) the same geometrical property holds good, if we consider wave-
lengths instead of wave-frequencies.
From the above theorem we deduce at once the following corollary :
If we fix upon a straight line, on any arbitrary scale, the lines of a given series in
such a way that the distances between two lines express the differences of the
corresponding wave lengths or frequencies, and if from any point outside we draw
‘Straight paths through these spectral lines, then the lines of any other series belonging
to the same u-group can be represented as the points of intersection of these straight
paths with a certain transversal line.
An illustration of this geometrical relation is given in fig. 2 for some series
>
574 DR J. HALM ON j
belonging to the group «=0. On the lowest horizontal line the wave-lengths of the
first Hydrogen-series (BALMER’S formula) have been drawn on a certain scale (in the {
original drawing 10 t.m.=1 mm.), beginning with m=3 (A,=6563°07) on the left to
m= 0 (Ao = 364610) on the right. The points 3, 4,5, . . . thus obtained were then
connected with a point O arbitrarily fixed in the plane of the paper. If now we draw,
not necessarily but for the sake of convenience, on the same scale, the wave-lengths of,
say, the 1st subsidiary series of Lithium on another straight line, for instance the edge
of a ruler, we can bring this line on our diagram into such a position that its intersections
with the rays O,, O, . . . O» mark precisely the positions of all the lines of the
series. The line is indicated in the drawing by the transversal Li. In the same way
the transversals He, Tl, Zn and In represent the 2nd principal series of Helium
and the Ist subsidiary series of Thallium, Zine and Indium, which, as we have seen
before, belong to this particular group u=0. Obviously the “tails” of all these series
are situated upon the ray Ow, while the “heads” lie upon O, which corresponds to
m=0(. In line-series these “ heads” are of no special interest, because they correspond
to wave-lengths outside the range of observation. Nevertheless, they will be considered
here on account of their great importance in relation to our investigation of the band-
spectra in subsequent pages. The construction of fig. 2 was based on wave-lengths in
order to show that the RypBere-TuHreLe formula may also be employed in the form
given by equation (4). For theoretical purposes, however, an investigation founded on
wave-frequencies must doubtless be preferred. This has been already pointed out
by Rypperc, Kayser, ScHusrEeR and others. ‘We shall therefore now revert to our
formulee referring to wave-frequencies.
Since the position of O is quite arbitrary, we may conveniently choose it so that
the two boundary rays Oy and Ov» form a right angle. In this case the cotangent of
the angle a between the rays Ov and Ov» (fig. 3) is equal to (m+ u)*, if we make
AOQ=1. Let us further call 6 the angle formed by the ray Ov and the transversal
which represents our series. Since cc» =v. —v and < Occ =90° —a—, we have from
triangle Occ :
sin a sina
Voo Te Ob GEG) a cha (OEEB) s (11a)
On the other hand, from triangle Occ, we find
a cosa | cos a (118)
Cos (a +B) cos (a+ 8)
Comparing the first of these formule with equation (2) we see at once that
Oc _ cos B _
The RypBERG-THIELE equation may therefore be written in the form
| yi
sin a
eee. (12)
V—=Viai=
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 575
This is probably the most convenient form for computation. It becomes identical with
BaLMeEr’s formula for «= 0 and 6=0, because we have then tan a=m~* and
—2
V = Ve —Qo. + tan a = Ve — An > mM ¥
If only 8 =0, we find RypBere’s formula
v= Ve —o+(m+p)*
Hence we see that both BaLmer’s and Rypsera’s equations suppose the transversal
to be parallel to the ray 0»), whereas, according to the more general RypBERG-THIELE
formula, the two lines may form any angle 8 with each other.
Now, an important result is arrived at if we investigate more closely these angles .
We notice that while in some cases (6 is small, and hence the transversals are nearly
parallel to Ov), there are also instances where this angle is considerable. The extreme case
B 5)
Fie. 3.
Seems to be represented by Czesium, where 6 is about 64°. Naturally the question
arises, what would happen if 8 should become still greater and should finally be +90”.
In this case the transversal representing our series would be parallel to the ray Ova, and
hence a» would become infinite. But from the equation (116) we find that
v=Vv)F4(m+p)*. (13).
Now obviously this equation is a more general form of Destanpres’ formula for the
band-spectra into which it converges for u = 0, viz.
v=V) Fam,
where », represents the wave-frequency of the first line (the “head” of the band), while
the upper or the lower sign indicates that the band “shades off” towards the red or
the violet side respectively. We perceive, then, that the Rypperc-TH1eLe formula
ineludes as a special case also the DesLanpres formula, and thus opens the prospect of
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24). 86
¥
576 DR J. HALM ON
the two phenomena, the line- and band-series, being comprised under one and the —
same mathematical, and probably also physical, conception.
From what has been found in the case of the line-spectra it appears now extremely
probable that Drstanpres’ formula represents only a limited number of band-spectra
and is but a special case of our more general equation, just as BaLmer’s formula is a
particular instance of the same equation in the case of line-spectra. A considerable
part of the remainder of the present communication will be devoted to the investigation
of this point. Before entering upon this new side of the question, however, I should
like to discuss briefly, for the convenience of those readers who are interested in the
foregoing computations, a method by which the four constants of the RyDBERG-THIELE
formula may be determined from one of the two equations (5). If »,, vy, v2, ¥» are the
wave-frequencies of any four lines of the series, we have from the second of (5):
i Se ae Se
Ve—vz (2+)? — (e+ pw)?
1 a.
ware rer Bya)
1 a,
Se eS aD c
ian¥y (ey t Dwr)? ()
1 a,
pee tt ee et he aii
Vo — Vz (w +24 2u)(w—2) z
(a)
(=e eee
; (@@4+e4Quje—z)”
(4)
Subtracting (c) from (a) and (d) from (b), and dividing, we obtain after slight
transformations :
(ety t2n)\(z+w+t Qu) _ _(2—2%)(w— y) N@p= va) Wa Ve)
(w+2+2Qu)(ytwt2p) (y- a)(w—2z) (v,—Vz)(V — Vy)
= ¢, say, (e)
or by substituting
y-“=p
2-2=q
wW-x=Pr
[p+2(m+a)[gtr+2(ut+e)]_
[g+2(u+«)|[ptr+2(u+2)]
—— (uta) Pat Wee =9
The positive root of this quadratic equation is the desired value of (u+2). Let us take
as an example the principal series of Sodium and select the 1st, 3rd, 5th, and 7th
observed line for our computation. From the observations we have therefore :
c, and
(m+2)?
Vy = 16960'19 z2-ae2=4 p=2
Vy = Va49 = 35051°93 w—y=4 q=4
yp = vps o8E50780 y -2=2 AG
Vp = Veug= 39805°27 waee
4.4 18091°74 x 1254°47
4:4, 1800174 x 1254'47 _ o.ggurnge
°= 99 * 9159001 x 475334 °
(u +a)? + 6(4+2)-17:992=0; p+a=2°195.
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 577
The remaining computations are now simple. We have
1 1 _ as ae
v—v, 1809174 (4195)? — (21952?
1 a 1 fs a, Li
y, Vv, 21590°61 (6-195)? — (2195)?
and hence
log a, = 6'26686 — 10
log b, = 561075 — 10.
But from (5) and (2) we find
b= 5 A,
1 bg” 1 Ay
(04) — A =
Vo — Vz A,” Vy —Vz (2°195)?
+ bs.
And finally from these relations :
log a, = 4°95464 — 10; log 6, =4°41367, -10; ve=41464'9.
These constants differ slightly from those previously computed under the assump-
tion that x + =2°200, but they represent the observations almost equally well.
It may be remarked that the relation (e) can also be derived from a well-known
geometrical theorem. If, in fig. 1, we take any four points a,, #,, 4, and a, on the
line AB and the four corresponding points ¢,, ¢,, ¢, and ¢, on the transversal CD , so
that w, and c, lie on the same ray Ov,, a, and c, on the ray Ov,, etc., then we know
from geometry that
Cilig Cy Cl
Qa, Wy CC, CyCy
But we remember that a,a,=(y+m)’—(x+ m)? and c,c,=v,—v, etc., so that
Vamavz io as = (y+ bm)? — (x ar p)? ‘ (w ats p)? (z ae p.)?
Vs—Ve Vovy (2th) —(etp)? (wtp)?—-ytp)?
(2 - x)(w -y) : (Vy — Vz) (Vy — Vz) = (2+ yt 2pu)(z2+ wt Qu)
(y ea x)(w 7" 2) (v, = Vz) (Vi) — vy) (x te ts 2u)(y aT 2m) ;
which is identical with (e).
or
B. Banp-SpPEcTRA.
The fact that the Rypperc-THIELE equation represents both line- and band-series is
perhaps most strikingly demonstrated by the following computations where the wave-
lengths of the lines of the Cyanogen-band (see Kaysur, Handbuch, vol. ii. p. 479)
are used for determining the wave-lengths of the first triplet series of Oxygen given
on p. 564. If in equation (8)
yeu ei
we take for / successively the wave-lengths of the 40th, 50th, etc., line of the Cyanogen-
band, /, being the wave-length for the 100th line for instance, and if we further make
log a, = 960800 — 10
log B, = 7°63969, — 10,
578
DR J. HALM ON
we obtain the values (A —A,) shown in the third column of the following table :
1 2 3 4 5 6
Ist Triplet Series Diff
Cyanogen-band. L—l, A-2, d of Oxygen Ons Con
(1st Comp.). ee
Ly = 3866°95 81°53 1634°70 6158-41 - 6158-41 0:00
1, = 3857°82 72°40 80714 5330°84 5330°84 0:00
Igo = 3846°79 61:37 445-31 4969:01 4968-94 — 0:07
1,) = 3833'93 48°51 250°18 477388 477394 + 0:06
Iz, = 3819°36 33°94 131°83 465553 465554 +0:01
Igy = 3803°16 17°74 54:07 4577-77 457784 + 0:07
Ly99 = 378542 0-00 | 0:00 4523°70 4523°70 ii
Adding to each figure of column 3 the constant 4523°70 we find the values of 2 in
column 4. The 5th column, on the other hand, contains the observed wave-lengths of
the first triplet series (1st component) of Oxygen according to the measurements by
RuncE and PascHEN (see p. 564). The very close agreement between 4 and 5 shows
conclusively that the RypBERG-THIELE equation satisfies the conditions of both series,
Instead of the Oxygen-series we might, of course, have selected any series of the
group «=0.
In my introductory remarks I have alluded to Professor THIELE’s investigation
of the third band of the Carbon-spectrum (Astrophysical Journal, vol. viii.
p. 1). I have mentioned that Professor TuiELe found himself obliged to reject
the simple formula here used, although he had been the first to notice some of its
remarkable properties. His contention, however, that the formula does not sufficiently |
satisfy the observations, is not acceptable, as will be conclusively shown in the
computations which follow. Indeed, if we study more closely the conditions under
which Professor THIELE made use of the formula, we come to the conclusion that his
negative result is due not so much to a deficiency in the equation employed, as to a
particular extra demand imposed upon it. For Professor THIELE introduces an assump-
tion which, though it may have some mathematical probability, has certainly so far no
physical foundation. He assumes that all the series of the band should appear coupled
in pairs, and that each pair should be represented by one and the same equation, the
two branches being obtained by assigning to m either its positive or negative value.
This hypothesis necessitates equations of great complexity, involving at least eight
constants. It must appear difficult, if not altogether impracticable, to use cumbersome
formulz such as those obtained by Professor THIELE as a basis for theoretical investi-
gations, nor are they of use as purely empirical expressions of the law of the spectral
structures. But this complexity disappears as soon as we abandon Mr THIELES
assumption. If we consider by itself each of the many series which he has so success-
fully unravelled by his masterly treatment of the Carbon-band here considered, we
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 579
find that the Rypserc-TuizLE formula satisfies the observations well within their
mean errors, the agreement being on the whole even closer than in Professor
THIELE'S computations. I have carried out the necessary computations for ten
“series, viz., for the five pairs a, 8B, y+, J+, and e+, but will present here, for
the sake of brevity, only the results of the first two pairs. Since Professor THIELE
employed wave-lengths in his calculations, I follow his example and use the second of
equations (6) : |
ae) a, " a, 1
Myr — Gm+pype te Gmapy? + Xe
Series : log a, A de
a+ 0:87883 516510 2241°1
a— 0°88016 5165710 2188°5
B+ 0°87840 5165°18 2271°6
B- 0°87973 5165°18 2219-0
In the following comparisons I give now the results for every fifth line of the series :
at; (m+p) d obs. Acomp. O.-C. a—; (m+) X obs. A comp. | O.-C.
5:0 5161°77 81 — 04 4:5 5162°41 43 — ‘02
10:0 5151°87 "94 = 07/ 9°5 5153:21 ‘26 — ‘05
15:0 5135°63 66 — 03 14:5 5137:°62 65 — 03
20:0 511317 ‘17 ‘00 19°5 5115°84 "82 +02
25:0 508480 76 | +:04 24°5 5088°11 ‘05 +06
30:0 5050°86 79) || —- 07 29:5 5054:73 68 +05
35:0 5011°66 67 - 01 34:5 5016°12 “10 +02
40:0 4967°84 87 — 03 39°5 4972°78 ‘78 -00
45°5 491516 20 — 04
B+; (m+p,) Xd obs. A comp. | O.-C. B-; (m+) d obs. Acomp.| O.-C.
5:0 5161°95 88 +07 4°5 5162-60 51 +:09
10:0 5151:97 2-01 —-04 9°5 5153-32 °32 ‘00
15:0 5135-70 “71 =-O} 14°5 5137-72 fl +01
20:0 5113°17 Ol — ‘04 19°5 5115°84 *86 = 02
25:0 5084-80 ‘78 +:02 24°5 5088:11 07 | +:04
30°0 5050-86 “81 +05 29°5 5054°73 69 | +:°04
35°0 5011°66 69 — 03 34:5 5016:12 at, 00
40-0 4967°84 ‘92 —-08 39:5 4972°78 “81 — 03
We notice that all the four series possess “tails,” a result which has already been
obtained by Professor Time. Geometrically speaking, this means that the transversal
representing the series is not parallel to the ray Ove, but intersects this line at a certain
point. We shall see that this is a general feature of the band-series.
580 DR J. HALM ON
In the Astrophysical Journal, vol. xx. No. 2, Mr Lester has recently published
most accurate measurements of the telluric Oxygen-bands of the solar spectrum. We
shall proceed to investigate how far his observations are accounted for by the RypBEre-
THIELE formula. The general structure of the groups A, B, a and a’, may be described
as follows. Each group consists of two series of doublets called by Mr Lester the
first and second band, in each of which he distinguishes the two components as the
first and second series. In the following tables I exhibit the results of my computa-
tions made on some of the series of the three groups A, B, and a. 3
=)
Oxycren-BAND, Agroup. First Band. First Series. B Group. First Band. First Series.
log a,=0°70266,, »= 13168-40 log a,=0°90992,, Ay = 6867°379
log b, = 6°57928,, — 10 log B; = 668740 — 10
fl
(m+ p) v obs. vcomp. | Obs. - Comp. (m+ p) d obs. A comp. | Obs. — Comp. |
0°75 13168-29 "29 ‘00 0°8 6867-458 “458 000
1-75 13167°81 80 +01 1°8 67794 ‘778 +016
2°75 13166-89 90 - 01 2°8 68°337 344 — ‘007
3°75 13165°61 rol ‘00 3°8 69°144 157 - 013
4:75 13163°94 93 +01 4°8 70°220 218 +°002
5°75, 13161°88 "86 +02 58 71°528 ‘527 +001
6°75 13159°39 “40 - 01 6°8 73-078 085 — 007
75 13156°51 ‘54 — 03 78 74-888 "893 — 005
8:75 13153°30 30 ‘00 8°8 76:953 "952 +001
9°75 13149°69 68 +-01 9°8 79°275 266 +:°009
10°75 13145°70 68 +02 10°8 81°80 83 - 03 |
11°75 13141°36 “30 +06 11°8 84°65 66 - 01 |
12:75 13136°58 "DD +:03 12°8 87°75 ‘74 + 014
13-75 1313143 ‘43 00 13°8 91-05 ‘08 - 03 |
14:8 6894-67 69 - ‘02 :
a Group. First Band. First Series.
log a,=0°88746,,
Ny = 6276°79
log 8,=7°25370 — 10
(m+ p) d obs. A comp. | Obs. — Comp.
0-4 6276°81 Sl “00
1°4 77:03 04 -— ‘Ol
2°4 77-52 D4 — 02
3°4 78°29 29 00
4°4 79°31 Biull ‘00
54 80-61 “60 +01
6°4 82°16 15 +01
74. 84:00 3°98 +:02
8-4 86:09 09 ‘00
9-4 88°48 ‘48 ‘00
10°4 6291°14 ‘16 —'02
I must remark here that the determination of » in band-spectra is a somewhat uncertaim
operation. In the first series, for instance, the fraction 0°8 might have been used
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 581
instead of 0°75 without sensibly altering the differences of the last column. In all
eases the agreement between the observed and computed wave-lengths and wave-
frequencies is doubtless sufficiently close to justify the assertion that the RypBERG-THIELE
formula represents the measurements most accurately. The same agreement is shown
in the following calculations, which refer to some of the second bands.
B Group. Second Band. First Series. B Group. Second Band. Second Series.
log a; =0°90992,, dy = 6867-379 log a, = 0°57250,, vy = 14558°57
log B, = 668740 — 10 log B, = 589220, — 10
(m+ ») X obs. Acomp. | Obs. — Comp. (m + ») | v obs, v comp. | Obs. — Comp.
125 6886-004 004 ‘000 1E0 14526°27 ‘27 00
13°5 89183 181 + ‘002 12-0 14520°15 15 00
14°5 92°614 605 + :009 13-0 14513°49 “50 - 01
15°5 96°282 ‘277 + 005 14:0 14506:29 33 — 04
165 ~| 6900°196 196 ‘000 15-0 1449865 "64 +01
175 04°363 366 — 0038 16:0 14490°42 43 - 01
18°5 08785 ‘784 + 001 17:0 14481:70 69 +°01
19°5 13°449 “452 — 003 18-0 14472°45 ‘45 ‘00
20°5 18°365 371 — 006 19-0 14462°72 ‘70 +02
21°5 23°542 545 — 003 20°0 14452°43 ‘41 +02
22°5 28-986 ‘970 +016 21:0 14441°67 63 + 04
23°5 34°669 649 + °020 22-0 14430°37 *35 + 02
24°5 40°584 584 ‘000 23:0 1441853 19) - 02
255 46770 sero - 001 24:0 1440626 ‘26 ‘00
a Group. Second Band. First Series.
log a, = 0°88756,, dy = 627663
log 8B, = 6°36303 — 10
(m + p») X obs. AX comp. | Obs. — Comp.
10:0 6289-60 "62 - 02
11-0 6292-35 ‘36 - 01
12-0 6295°36 37 -01
13:0 6298-64 64 ‘00
14:0 6302718 17 +01
15-0 6306-00 5°98 + 02
16-0 6310°06 05 +°01
17-0 6314-40 “40 ‘00
18-0 6319-02 01 +01
19-0 632392 co +01
20-0 6329°10 ‘08 +02
21:0 6334-55 53 +02
22°0 6340-28 25 + 03
23°0 6346°27 "26 +01
[have purposely computed wave-frequencies in some cases and wave-lengths in others
in order to show that the RypBeRG-THIELE equation may be used in the same form in
582 DR J. HALM ON
¥
both cases. It is not the object of this communication to enter upon a discussion of —
the constants, but merely to show in a number of typical cases the extraordinary
accuracy of our formula. I shall therefore not discuss the other series of the Oxygen-
bands, and reserve this particular investigation for another paper. One point, however,
in connection with the second bands seems to require special mention. It is noticed
that in these bands the index (m + «) of the first visible line is a comparatively high
number. According to the formula other lines before the one which “apparently”
forms the head or beginning should be possible, but these lines are in fact not present
in the spectrum. Instances of such “missing” lines are by no means rare among the
band-spectra. Bands with “hypothetical” heads have indeed already been pointed out
by Professor THIELE in his investigation of the Hydrocarbon-band. It is interesting to’
find at least one similar occurrence also among the line-series. According to Professor
Kayser the first observed double line of the 2nd Subsidiary Series of Potassium should
be preceded by a strong pair at X = 6985, which, however, has not been observed.
Professor Kayser remarks that this is the only case among all the line-series where
computed lines seem to be actually missing. I am inclined to think that we have here
a (so far) unique instance of a line-series with a hypothetical head. Perhaps the lines
are not altogether absent, but are too faint to be noticed. It is quite a common
feature in band-spectra that the intensity, instead of changing gradually from line to
line, sometimes falls off abruptly. This abnormal phenomenon usually occurs in the
tails, but there is no reason why it should not also be possible near the heads. We
shall have to return to this interesting feature later on when we consider the struc-
ture of the Cyanogen-band.
Mr Lester shows that the measured wave-frequencies of the Oxygen-band can be
represented by an equation
v=v,—am—bm?.
He lays particular stress on the existence of a term depending on the first power of m.
Evidently his formula is a first approximation to the RypBERG-THIELE equation, which
may be written :
(m+ p)? Gy)
a1 + Am + )) o
b 6,2 :
V-Vy= ah te) — g(t pw)? eS a 95
4 4
and can therefore be brought to Mr Lesrsr’s form if m be counted from the first
observed line. Thus we find in the case of the second band (second series) of the
B-group from the constants of the RypBeRG-THIELE equation :
whereas Mr Lester has :
v= 14526°27 — 5°86m —0°2611m?.
The examples here given are in my opinion quite sufficient to demonstrate the appli-
eability of the RypBerc-TuHre.e formula to both line- and band-spectra. The difference
between these two types is seen to be solely due to the difference in the constants of our
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 583
equation. Specially striking is the contrast between the values of a, , which for band-
series is always very much smaller than for line-series.
Professor THIELE has pointed out that in a band-series, proceeding from the head
towards the tail, the distances between consecutive lines should first increase and
afterwards diminish, and therefore reach a maximum at a certain point between the
head and the tail. If we differentiate the RypBERG-THIELE equation
=a,(m +p)? +,
Veo —V
with regard to vy and m, we find
dv _ 2a,(m + p)
dm [a,(m+p)?+6,)?
GV x © 2a, | _ 4a,(m + pw)? |
dm? [a,(m+p)? +, }? a,(m+p)?+b,]°
Hence the particular point m,+., for which the distance is a maximum, is found from
the equation
b
y- 2G. +o)? 0: 1}
3 ay
= M, + ps)? =
ACs (m, + 1)
But from fig. 3 we know that 2 tan 6, hence
1
(m,+p)?=t tan B.
We see at once that for a series, whose transversal is parallel to Ov, (e.g. the first
Hydrogen Series) the maximum distance is at m,+"=0, 2.e. at the beginning (head of
the series), since 6 = 0 ; whereas for a series whose transversal is parallel to Ov, [band-
series satisfying DesLANDRES’ special equation], the maximum distance is at m,+"= ©
(tail of the series), since = but that in general it must be at a point between
the head and the tail of the series. Thus we find without difficulty that in the a+
series of the Hydrocarbon-band (see p. 579) the greatest distance between consecutive
lines occurs between the 85th and 86th line.
Quite recently an important paper has been published by Dr JuneBLurH in the
Astrophysical Journal, vol. xx. No. 4, in which the author discusses his exquisite
measurements of the lines of the Cyanogen-band. I take this opportunity, therefore, of
applying the Rypserc-THIELE formula to this very extensive band, which, as Professor
Kayser has shown in his Handbuch, p. 479, seemed particularly inaccessible to a
satisfactory representation by empirical formule. Before the appearance of Dr
JounesLure’s paper I had already attempted to compute the wave-lengths of this band
by means of the formula proposed in this paper. It was found that the RyppERc-THIELE
formula gave excellent results up to about the 80th line, that the agreement could
still be called very satisfactory up to the 140th line, but that further on the
discrepancies increased enormously, and showed the formula to be not applicable
throughout the whole extent of Professor Kayser’s observations. The question
therefore arises, whether the formula, which has done such excellent work in the
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24). 87
584 DR J. HALM ON
shorter band-series, fails to account for the phenomena if they extend over a wider
interval. If this could be proved, the RypBeRG-THIELE equation would certainly lose
much of its value from the theoretical point of view. But there is an alternative. It
is quite possible that the Cyanogen-band discussed by Professor Kayser is not one
single series, but really consists of several distinct parts apparently joined together so
as to give the appearance of one continuous series. We have seen in the case of the
Oxygen-band that two series of the same band need not necessarily exhibit their lines
right down to their common head. It was noticed that while the one series which
starts from the head may almost suddenly drop off on the tail side, the second series
may show the inverse phenomenon, viz. a sudden decrease of intensity on the head-side.
The effect of this peculiar behaviour is that the second series forms apparently the tail
of the first series. Now in the Oxygen-bands both series consist of pairs of lines, but
the distances between the components of the first (or head-) series are considerably
smaller than those of the second (or tail-) series. Besides, in the head-series the distances
decrease slightly towards the tail, while in the tail-series they increase very rapidly.
To show this I subjoin a table giving Mr LEstrr’s wave-lengths of the B-group.
First (Head-) Series. Second (Tail-) Series, First (Head-) Series, Second (Tail-) Series.
HL SHES yy | ORE)
io ojos | Milaa
eo toe | Billa
vos f 089 asge50 f O88 o6a8 | 272
fie } me coon } 3100
7349 f O96 04-36 p O24
roa f O98 05°26 | 55
HS fo ae
7783 ¢ 0% 1438 | 493
SF on Lat
Pop } 0:92 aes 457
Now let us suppose for a moment that the distances between the components are very
much smaller, perhaps 5th only of those actually observed. ‘The effect is that the
first series appears as a single-line band, while the second, with sufficient dispersion,
may still show its double character. Near the point where the two series coalesce, we
would then have the following wave-lengths of the centres of the lines:
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 585.
Single Line Series. Double Line Series.
6877°41
6879°72
6882°26
6885-09 6885°04
688818 6888:08
6891°46 6891°36
689508 689492
6898°70
Here a remarkable phenomenon will be noticed, viz. that the positions of the
s of the double lines in the second series agree very nearly with those of the
ines of the first series. This is not accidental, because the other groups show
same feature. We have, for instance, in the A-group: (LxsreEr, /.c., pp. 88 and 92)
Single Line Series. | Double Line Series.
7615°87
7619°04
7622°49 7622°40
7626°14 7626°04
7630°04 7629°90
: 7633°98
Single Line Series. | Double Line Series.
6284°38
6286°49
6288°84 6288°77
(6291°48) 6291°38
6294:26
Ve notice, then, that at the point where the second series begins the line of the first
alls between the components of the former, and if its intensity is still sufficiently
and the doubles close, the effect of superposition will be that the resulting line
rs as a broadened single line. Hence the lines of the first series, which near the
are thin and sharply defined, will gradually widen out. But since the intensity
[ the first series declines rapidly, their vitiating effect will lessen, the further we
*
586 DR J. HALM ON
proceed towards the tail, so that finally only the double line series will survive. It is
very probable that the interval between the double lines which in the above bands
increases steadily, may in more extensive groups reach a maximum and then decrease
again further towards the tail. Now the feature thus described seems indeed to agree
closely with the phenomena observed in the Cyanogen-band according to Dr
JuNcBLUTH. I may be allowed to quote the author’s own remarks on this important
point, /.c., 241 :—‘‘ Following the series further, another peculiarity appears, which,
strange to say, has not been heretofore observed, though it comes out distinctly in the
first-order spectrum. The lines become gradually broader as they recede from the
head, and each finally separates into two lines when it has reached a breadth of about
0°07 tm. We have now double lines similar to those above and below the second
head. As the series proceeds, the interval between components of the double lines —
increases to 0°09-—0'1 t.m., and then decreases until the components unite again to
form one line. The lines of all the observed series show this behaviour, so that in
certain parts of the band structure, as for example above and below A 3700, we have
only double lines.” He further remarks that this is “‘a noteworthy property and must
be considered in forming any valid theory concerning the origin of spectra.” The most
remarkable feature seems to me to be the coincidence of the centres of the lines in
both series at the point where the second series begins. In consequence of this
agreement the band changes from the single line to the double line type steadily, ze.
without indication of an abrupt change in the positions of the lines, thus giving the
impression of one continuous series. But in fact, as the Oxygen-bands show, the series
consists of two separate branches. The reason why in the Oxygen-bands we see a
marked discontinuity between the two series is obviously that the lines of the first
series fade off too early, v.e. before the beginning of the second series. If the faint
close doubles, which Mr Lesrer calls the continuation of the first series, were more
prominent, the appearance of the Oxygen-bands would agree with that of the Cyanogen-
band, though the intervals between the components are here too great to produce
the impression of widened single lines by the coalescence of the four superimposed
components.
I think that this view explains sufficiently the peculiar behaviour of the lines
pointed out by Dr Juncsiuru. It reveals also a hitherto unknown similarity in the
structure of bands of different substances, which may have a bearing on the theoretical
aspect of the problem. But what interests us most of all at present is the
probability that the first part of the Cyanogen-series consisting of single lines differs
essentially from the second part, the double-line series, just as the first series of the
Oxygen-bands differs from the second. I am inclined to think that there is even a third
branch containing the single lines near the tail, so that in fact each of the four series
given by Dr JuncBLuTH consists of three distinct parts, each of which satisfies a
different numerical form of the RypBeRG-THIELE equation. The correctness of this
view may appear from the following tables, where the three branches of ‘Series L.,”
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA, 587
which I shall call [,, I, and I,, are discussed. or the series I, and I, the computa-
tions have been made on every fifth line, for I, on every second.
la. Id (first component).
“Tog o,=1°98171, ,=3883°50, An =2199°39. log a, = 1°93237 , A, =3876'56, A, =2708°35.
(m+ ») X obs. d comp. On C, (m+ p) d obs. d comp. 0, -C.
5:0 388325 "24 +01 70:0 3823°98 98 00
10:0 3882744 “46 - 02 75:0 3816°33 33 700
15:0 3881°15 ‘16 - 01 80:0 3808-29 ‘27 +02
20°0 3879°33 34 - 01 85-0 3799°82 “82 ‘00
25-0 3876'99 701 — +02 90:0 379101 ‘00 +01
30°0 3874'14 16 -— 02 95-0 3781:83 82 +01
35°0 3870°80 enh) +01 1000 3772°32 “32 ‘00
40°0 3866°94 ‘OF — 03 105-0 3762°52 “51 +°01
45°0 3862°62 ‘64 — -02 110°0 3752°41 ‘41 ‘00
50°0 2857°81 "82 -— Ol 115:0 3742°04 05) - 01
55:0 3852°53 ‘53 ‘00 120°0 3731°44 “45 - 01
60:0 © 3846°79 (el +02 125-0 3720°61 62 - 01
65°0 3840°59 ‘56 + 03 130°0 3709°63 60 +°03
70°0 3833°95 ‘90 +05 1350 3698-50 “40 +10
74:0 3828°32 26 + '06
Te.
log a,=1°53310, AJ=3777'78, Awe =3368°78.
(m+ p») X obs. X comp. O.-C.
64-0 3685-01 4°99 +02
66:0 3680°51 “49 +02
68:0 3676°00 ‘00 ‘00
70-0 3671°49 ‘50 - 01
72:0 3667-00 01 - 01
74:0 3662°52 D4 — 02
76:0 3658°05 ‘06 - 01
78:0 3653-62 62 ‘00
80:0 3649-21 “20 +°01
82:0 3644-83 81 +02
84:0 3640°45 ‘44 +01
The smallness of the residuals in the last columns proves again the applicability of
the Rypperc-THIELE equation, if we admit the suggested subdivision of the series into
three apparently coherent branches. With regard to the other series of the band
mentioned by Dr JuNGBLUTH, analogous structures are apparent, but I have not yet
found time to undertake the necessary computations.
In his paper Dr JuNGBLUTH suggests that the tails of the four series may probably
be represented by four faint bands shading off towards the red at wave-lengths 3579,
3603, 3629 and 3658. This suggestion had been already made by Mr Kine, who
had first observed the peculiar shadings in question. For several reasons I doubt
the correctness of this view, and rather incline to think that Mr K1na’s bands represent
588 DR J. HALM ON
the “‘ heads” of an independent Cyanogen-band distinguished from the others by the
fact that, like the Oxygen-bands, its components shade off towards the red. First we
must admit that the appearance of the bands does not agree with what we should expect
if they were “tails.” On the plate accompanying Dr JuneBLuTH’s paper they by no
means convey the impression of an “infinity” of lines, but appear to be composed of a
limited number of lines at finite distances from each other. This feature is specially
noticeable at A = 3603 and 3629, and certainly agrees better with the supposition
of “heads.” It is also noteworthy that none of the tails of the 1st series computed
above by means of the RypBerc-THIELE formula agrees with any of the four wave-
lengths of Mr Kine’s bands. Our experiences with the formula cannot but give us
now some confidence that the structure of the band should be at least very nearly
represented by it. On the other hand, however, Dr JuNGBLUTH’s view seems to be
supported to a certain extent by two noteworthy relations between the wave-lengths of
the four heads of the series and the supposed tails. He showed that if we form the
differences between the wave-lengths of corresponding ‘heads and tails, we find
3884 — 3579 = 305
3872 — 3603 = 269
3862 — 3629 = 233
3855 — 3658 = 197
36
36
36
It appears, then, that the lengths of the successive series form an arithmetical
progression. Again, if we form the quotients
SESS a aes
3a79 5 ae 0:0105
Bee
3603 0 0:0105
3862 1:0642
3629 -
aaee 0:0103
3658 = 10539
we notice that these quotients also form approximately an arithmetical progression.
Hence a somewhat remarkable connection seems indeed to exist between the observed
heads and the alleged tails. But on a closer view this connection is found to be only
apparent. or it is seen that the same relations exist, if we combine Mr Krine’s
“tails” with the successive heads of the other Cyanogen-bands. Thus we find:
4606 — 3579 = 1027 4216 — 3579 = 637 3590 - 3579 = + 11
52 ‘
4578 3603= 975 4197 — 3603=594 a 3586 -3603=-17 2°
4553-3629= 924 4181 — 3629 =552 as 3584-3629= -45 28
4532 —3658= 874 4168-3658=510 ~—
These figures show therefore that Dr Juyepiuru’s relation indicates not a specific
connection between Mr Kine’s bands and the band at A=3884 only, but a far more
general correspondence between the former and all the bands of the Cyanogen-spectrum.
One might perhaps conclude that Mr Kine’s shadings may represent the common tail of
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 589
all the Cyanogen-bands, but this conclusion is evidently negatived by the last series at
A= 3590 mentioned in the preceding table, where the edges of the corresponding heads
and tails would then be turned towards each other, 7.e. the lines would not be within
the space between head and tail. We notice also that Dr JuncBiury’s relation applies
as well to the differences between the heads of the four Cyanogen-bands when compared
one with the other. Thus:
4606 — 4216 = 390 4216 - 3884=332
7
4578 — 4197 = 381 ; 4197 — 3872 = 325
4553 — 4181 =372 3 4181 — 3862=319 P
4532 — 4168 = 364 4168 — 3855 = 313
The most probable conclusion would therefore be that the alleged relation constitutes
a property of the “heads” of the bands, and that Mr Kuine’s shadings should be con-
sidered as the edges of a new band of the Cyanogen-spectrum, and not as the tails of
the band at > = 3884.
In concluding this section of my investigations dealing with the band-spectra, I may
point out another form of the Rypperc-THieLe formula which, though somewhat more
complicated in appearance, reveals well its significant structure. Using wave-lengths
we may write the equation in the form
je ees (14)
where n stands for (m+) and where y denotes a constant. We notice without
difficulty that for \,=0, 2.e. when
——— (15)
the formula becomes identical with RypBErRGe’s equation for line-spectra, which again, on
the further supposition that n represents integers, assumes the well-known form of
BALMER’S equation. So far, it is true, the observations have shown no evidence of
Series to which the positive sign in the denominator is applicable. In other words,
no line-series have yet been found progressing from the violet towards the red, 2.e.
having their heads on the violet, and their tails on the red side of the spectrum. But
the present investigation points now to the possibility of such regularities, and may
perhaps induce physicists to search for series of this character.
If, on the other hand, we suppose A» = 0, equation (14) assumes the form
r
Ne: Of (16)
n\2
1+(7)
which becomes identical with Drstanpres’ formula for band-series, if we assign to n
integer values. The positive sign expresses that the band shades off towards the violet,
590 DR J. HALM ON
and vice versd. In general, the wave-lengths of the lines of any line- or band-series
appear to be made up by two terms, the one satisfying the Ryppere formula (15) and.
the other the more general DESLANDRES equation (16). This interpretation of the
RyYDBERG-THIELE formula shows perhaps more concretely than any other the fundamental
character of its structure, and also its importance as the universal expression of spectral
regularities.
C. GENERAL CONCLUSIONS.
We are now prepared to enter upon the discussion of some results of a more general
character. The geometrical property of the Rypserc-TureLe formula, as already
indicated, enables us to represent on one single diagram every possible line- or band-
series as a transversal on which the successive lines of the series are indicated by
the points of intersection with the rays Ov. On fig. 4 accompanying this paper I
have indicated the positions of these transversals for a limited number of cases. The
construction of the diagram is made sufficiently clear by the explanations already given,
and therefore requires little additional comment. After the rays O) and Ow had
been constructed at right angles to each other, a line was drawn parallel to Ow, and,
starting from its point of intersection with O,, the successive values of (m+ )*, on a
conveniently chosen scale, were measured off. Through O and the points thus obtamed
lines were then drawn which are marked at their ends in our figure by the correspond-
ing values of (m+ ). Obviously, in order to obtain the true inclinations 6 of the
transversals, the parallel should be drawn at unit distance from the ray Ow. It was
found, however, that under this condition the diagram would occupy too much space
to be conveniently reproduced here, and I therefore decided to draw the parallel
at a distance of 10 units. Consequently the inclinations of the transversals in the
figure, which we may call 6), are considerably smaller, the two angles being in the
relation tan 8,= 75 tan 8. The rays O,, 0,, 03... , which correspond to integral
values of (m+), have been represented by slightly stronger lines. Now, in the lower
part of the diagram we find nearly all the line-series of the group «=0. The chemical
elements to which the series belong are indicated at the two ends of the transversals,
and, where not otherwise stated, the latter refer to the 1st subsidiary series. ‘If on any
of these transversals we measure off the distances between consecutive points of inter-
section, these distances will be found to be exactly proportional to the corresponding
wave-frequencies of the series to which the transversal refers. In this arrangement,
therefore, all the spectral lines lie precisely on the rays O,, O,,... . and all the
tail-ends on the ray O.. Hence, if we imagine these rays to be represented by thin
pencils of light, we may at once obtain the exact arrangernent of the lines in any of
these series by interposing a plane screen in a direction parallel to the corresponding
transversal, since the centres of the luminous dots on the screen must then mark the
true relative positions of the lines in the spectrum. There would perhaps be m0
difficulty in constructing an apparatus for lecture-purposes by which the correctness of
S00. EDIN., VOL XLI. PART III. (NO. 24).
592 DR J. HALM ON
the RypperG-THIELE formula could thus be experimentally demonstrated. Turning to — '
the upper part of the diagram, we find the transversals exhibiting the arrangements
of lines in all the principal series. A smaller scale has been adopted in this case
in order to keep the drawing within convenient dimensions, but otherwise the lines
have been constructed on exactly the same principle as before. With regard to
the intensity of the lines it must be noted as a general rule that the lines are strongest
near the head and gradually decrease in brightness towards the tail, and that this rule
applies to line-series as well as to band-series. Lastly, four specimens of band-spectra
are exhibited by the four transversals nearly parallel to the ray Ow. In these cases,
however, the scale had to be considerably enlarged, since otherwise the transversals
would have been too close to Ow. The four series belong to the group »=0, and the
drawing is so arranged that the points of intersection with the rays O,,0,,0,....
represent the 10th, 20th, 30th . . . . line of the band.
In his researches on the band-series M. DesLanpres points out that the wave-
frequencies of the lines of such a series are arranged in a manner similar to those of the
sound-vibrations produced by an elastic transversely vibrating rod. Indeed we recognise
without difficulty that the series of sound-vibrations are represented in our diagram by
transversals parallel to O.. or it is well known from the mathematical investigations
of Poisson, SEEBECK and others, that the wave-frequencies of the stationary transverse
oscillations in a vibrating rod, with the exception of the two lowest vibrations, can be
expressed by the relation
vy _ (m+p)?
ve (@+ ph)”
where w depends on certain conditions under which the vibrations take place. But
this equation is obviously of the form
Ie a
a Ceo CES “—
and therefore agrees with the first of (5), if we assume v. =o, 1.e. if the transversal is
parallel to Ow». The remarkable analogy between the sound-vibrations of an elastic
body and the light-vibrations of a radiating atom or molecule is at least suggestive,
Is it not, for instance, conceivable that the latter are caused by ‘standing waves” in
the elastic system of electrons which constitutes the atom? If it were possible to find
an elastic body of such shape and internal conditions that its transverse vibrations
would satisfy the equation
1 a
= b, 18
y—v, (m+pp—(@+ pp” io
where b is a constant, instead of the simpler relation (17), which refers to the special
conditions in a uniform rod, the series of transverse sound-vibrations emitted by such a
body would be exactly analogous to the series of light-vibrations emitted by the radiating
atoms of a gas or vapour. We could then, by varying the conditions on which
depends, represent the acoustic analogies to the whole range of spectral phenomena
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 593
from the band-series to the line-series. At present we are, of course, ignorant of the
conditions which lead to the more general equation (18), but at least this remarkable
and highly suggestive feature has been brought out by our investigation, that the
addition of a single constant to equation (17), the acoustic theory of which is well
established, leads to the RypBERG-THIELE formula, which, as we have demonstrated in
the preceding sections, represents so completely all the phenomena of spectral
regularities. .
It is well known that if the three dimensions of the elastic body are altered in the
same proportion, the wave-frequencies of its transverse vibrations change also in the
same but inverse proportion, higher frequencies corresponding to smaller dimensions.
Thus if we compare two rods of the same material, the one of length /, breadth b, and
width w, and the other of length a./, breadth a.b, and width a.w, the wave-frequencies
of their transversal vibrations are in the ratio 1:a, while the volumes are in the
proportion 1:a*. Hence the wave-frequencies are inversely proportional to the cube
| roots of the volumes. Now, it appears that in the case of vibrating atoms a similar,
| although not quite so simple, relation obtains. In each group of chemically related
elements, such as the alkalis for instance, the wave-frequencies of the tails, v», can be
approximately represented by an equation
oe ee (19)
where m and n are constants and v denotes the atomic volume of the element. As an
example, let us take the wave-frequencies v» of the following five elements, referring to
the first components of the subsidiary series :
v 1/v% Veo | Computed.
ie? 118 0-43925 28589 | 28514
Na: 23:7 0°34814 24486 24660
K: 45:0 0:28115 21994 21827
Rb: 56:0 0:26138 20965 20990
Cs: 79:0 0:23306 19748 19792
The values of the last column are those computed from the equation
DS teal
lv
The atomic volumes have been taken from the data given in the article “‘ Chemistry ”
in the Enc. Brit. To expect more than a merely approximate agreement seems
scarcely warranted, considering the uncertainties in the values of v here adopted. In
spite of the doubtless large discrepancies between the values of the last two columns, |
am inclined to think that the asserted relation between the wave-frequencies v» and the
linear dimensions of the atoms expresses a real physical law. The view is supported
by the following interesting fact. In the vertical column of MENDELEJER’S system
594 DR J. HALM ON
which contains the five elements here considered we find also Hydrogen, which with
regard to chemical valency is certainly related to our group of metals. Supposing, then,
that Hydrogen belongs to the same group, we may, since we know the wave-frequency
of the tail of its subsidiary series, compute its atomic volume. With v.=27426 we —
find from the preceding equation
423003
a (52800 te
: (Fa55) ee
Since the atomic volume is defined as the atomic weight divided by the specific
gravity of the substance in the solid state, we conclude that solid hydrogen should be
14 times lighter than water. It is interesting to see that for the specific gravity of ©
the liquid at the lowest attainable temperature the same value was found by Professor
DeEwak in his celebrated experiments on the liquefaction of gases. The close agreement
may perhaps be accidental, especially since we do not know how much the specific
gravity may change in the transformation of the gas from the liquid to the solid state,
but nevertheless it seems that the new relation assigns to Hydrogen spectroscopically its
correct position in the group of elements to which it is chemically related. The
diticulty which appears in the attempt to connect, in this group, the position of the
tails with the atomic weights, no longer comes in when atomic volumes are considered.
In other groups the same relation, with altered constants, is noticeable. Thus we
find :
v 1/v Veg Comp. v 1/v Veo Comp.
Mg: 137 0°41792 39780 39850 | Zn: well 0°47898 42925 42889
Ca: 25°4 0°34019 33919 Bongo) Cd ebe:9 0°42638 40766 40840
Sr: 34°8 0°30629 31060 SLIS0) 4 Hes La 0°40822 40168 40130
Herp Ge Ho = 24298 ee eeee
s/v xv
On the other hand, however, the relation is not fulfilled for the elements Al, In, Tl,
which Professor Kayser considers as a group of the third vertical column of
MENDELEJEF’S system. But whether the three metals are indeed chemically co-
ordinated, and should therefore be grouped together, is still somewhat doubtful.
I am not contending, however, that the existence of the asserted relation between the
wave-frequencies of the tails and the atomic volumes is conclusively proved by the
preceding figures. So far as we may judge from the scanty materials at our disposal,
we can only venture to say that indications in its favour seem to be present among the
observations. Unfortunately it is not very probable that we shall learn more on
this point in the future, as far as observations are concerned. Nevertheless the
suggestion is perhaps valuable from the theoretical poimt of view, and for this reason a
reference to it was thought advisable at this stage of the investigation. With regard to
a
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECIRA. 595
the constant n of equation (19) some evidence may be brought forward which seems to
point to the conclusion that in the various groups n is always an integral multiple of
one and the same number. For instance, we have seen that in the Mg-group n had
almost exactly twice the value of that in the Zn-group. If, in the various groups, we
assume for m (equation 19) the values
Li-group: m=10580
Mg-group : 6536
Zn-group : 23772
the following comparison will show that by assuming n=4 x 10* or 8 x 10* we can
approximately represent the wave-frequencies of the tails of the subsidiary series :
Comp. Comp.
ie (n= 4 x 104) i (n= 8 x 104)
ite: 28589 28150 Mg: 39780 39970
Nal: 24486 24506 Ca: 33919 33752
Ke: 21994 21826 Sry 31060 31040
Rb: 20965 21035
Cs: 19748 19902 | Comp.
Ven (n= 4 x 104)
Zn: 42925 42931
Cd: 40766 40827
He: 40168 40101
Applying the relation (19) to the principal series of the alkali-group, we find for the
two elements of lowest atomic weight Li and Na, n=2 x 10‘, but for the three others
K, Rb and Cs, n =8 x 10%, with the corresponding values of m: 34610 and 12758.
Veo Comp. Veo Comp.
is: 43498 43395 1K 35030 35250
Na: 41468 41573 Rb: 33762 33668
Cs: 31526 31402
Again we have to confess, however, that the materials at our disposal are too
limited to demonstrate the alleged property of the quantity n conclusively, and hence
that it is useless to enter upon further comment. The history of the subject here
discussed must warn us to state such regularities with due reserve, and not to rush to
hasty conclusions, however tempting they may be.
I shall now discuss in a few words some interesting results with regard to the
constant a, of the RypBreRc-TuHieLe equation. It was shown at the beginning of this
investigation that we can write
1 —-2 b \—-4
V=Ve.— —(m+ map ARIIL) a, sucte, ne
a 1) a, 1)
an equation which assumes the form of Ryppere’s formula when b,=0. As is well
596 DR J. HALM ON
known, Professor RypBERG had assumed that the factor = should be a constant for all
1
the line-series. Kayser, however, showed that this assumption had to be abandoned
because it led to quite inadmissible discrepancies in the computed wave-lengths. In
his own formula the value of ie ranges between 109625 for Li and 155562 for Al, and
ah
thus ‘‘ varies only within narrow limits for the various elements” (Handbuch, vol. ii.
p. 516). At another place he remarks that ‘‘ probably in the true formula, which neither
he nor RyppeRG had found, this factor may indeed be a constant.” Let us now see how
far = changes if the RypBerG-THIELE formula is employed. In this comparison
1
between the various elements we must confine our attention to the subsidiary series,
because so far principal series are only known for the elements of the group of alkalis
and for Helium. Now we notice at once that the values of = are certainly not the
1
same for different spectra, since they range between 109575 for Li and 124020 for Cs.
But the variations are doubtless much smaller than in Professor Kayssr’s formula.
Since the a priori presumption may perhaps be admitted that the changes of ~ may
1
be connected with the position of the element in MENDELEJEF’s system, I have arranged
the following table, which shows the constants in this order :
I, II. Til. VI.
}
1. H: 109704
2. In: LO9STS O: 110118
3. Na: 110788 Mg: 112512 Al: 114590 S: 110567
4. K: 116430 Ca: 111363
5. Cu: 109726 Zn: 114265 Se: 109345
6. Rb: 123572 Sr: 117292
7. Ag: 109410 Cd: 114250 In: 117398 |
8 Cs: 124020
9, eae
10.
ie Hg: 112838 Tl: 114015
The system is that published in vol. 71 of Nature, p. 66. In all cases where more
than one subsidiary series is known, I have taken the arithmetical mean of the
constants computed from each series. One interesting fact is at once revealed by the
figures of this table, viz. that the changes are greatest in the first vertical column, the
difference between the largest and smallest values of a being respectively, column I. ;
a
1
14445; column I[].: 5929; column III.: 2808; column VI.: 1022. But another
important feature is shown if we compare the horizontal rows 1, 2,3... 11. In the
odd rows 3, 5,7 and 11 the numbers increase at first, reach a maximum, and then
THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 597
decrease again. In the even rows 4 and 6, on the other hand, there is a rapid decrease
from column I. to column II.
Now, by a course of reasoning upon which I shall not enter here, I have been led
to investigate a phenomenon which curiously shows the same regularities, although at
first sight it may appear difficult to perceive its causal connection with the changes of
our constants. I refer to the effects of pressure on the displacements of the spectral
lines. If we take these displacements from the results of HumpHrey and MoH.eEr’s
well-known researches and arrange them in MENDELEJEF’s system, we obtain the
following table of values, in which the displacements are given in 7,5 th of a tenth-
metre, and correspond in each case to a change of pressure of 12 atmospheres :
I. II. III. IV. Vid lh ole VII. VIII.
<= = ————— |
1
2
Na Mg Al Si
3 25 46 55 43
K Ca Vi V Cr Mn Fe Ni Co
4 130 27/54 19 25 26 23 25 28 24
Cu Zn As
5 33 57 35
Rb Sr Y Zr Nb Mo Rh Pd
6 130 37/65 15 28 34 40 30 33
Ag Cd In Sn Sb ;
af 39 80 88 55 49 |
Cs Ba La Ce
8 160 34/58 32 27 |
9
\ W Os Pt
10 19 19 20
| Au Hg Tl Pb Bi
11 49 81 61 60 49
Hvidently these figures show the same features as the values of = discussed before.
1
The amplitude of the changes is again decidedly greatest in column J., and decreases
rapidly, being quite insignificant in columns VII. and VIII. We notice further that
in the odd horizontal rows 8, 5, 7 and 11 the displacements tend from small values
towards a maximum and decrease afterwards, whereas the even rows 4, 6 and 8 begin
with high figures, which diminish rapidly and asymptotically approach a constant
minimum value. It is also worth mentioning that those cases where two kinds of
displacements have been observed by Messrs Humpurey and Moats, e.g. Ca, Sr, and
Ba, belong to this second class. Are we allowed, then, to conclude that a connection
exists between the displacements of the lines through changes of pressure and the
constants a, of the Rypserc-THIELE equation? Obscure and seemingly unfathom-
able as these phenomena are at present, they cannot but open new vistas of thought
and instigate theoretical research.
598 DRJ. HALM ON STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 4
In my demonstration of the superiority of the RypBERG-THIELE equation over that
of Kayser and Runes I| hope that I may not have conveyed the impression that I
was insensible of the undoubtedly great merits of the latter. Hveryone who has
studied the problem here discussed cannot but recognise how much we are indebted to
Professor Kaysrr and his co-workers for the enormous advance of our knowledge in
this field of spectroscopic research, an advance which without his empirical formula
would not have been possible. Our feeling of admiration and gratitude for this great
physicist’s work in a novel and difficult sphere of optics, to which he has so long and
successfully devoted his high scientific abilities, will doubtless stand unabated even if
his formula should not be finally accepted as the mathematical expression of the law of
those marvellous spectral regularities, the knowledge of which we owe chiefly to his
ingenious investigations.
( 599 )
XXV.—On the Hydrodynamical Theory of Seiches. By Professor Chrystal.
Wir A BIBLIOGRAPHICAL SKETCH.
(Read June 19, 1905. Issued separately July 3, 1905.)
PARE
GENERAL SUMMARY.*
§ 1. The variations of the surface-level of lakes due to the direct action of wind and
rain, and the smaller disturbances caused by surface waves, of small or moderate length,
due to the action of the wind and the movement of boats and animals, must have been
familiar phenomena at all times. The first accurately recorded observation, that lake-
levels are subject to a rhythmic variation, similar in some respects to the ocean tides,
seems to have been made at Geneva in 1730 by Fatio pe DurILuer, a well-known Swiss
engineer. Owing to the peculiar configuration of the Geneva end of Lake Léman,
these variations occasionally reach a magnitude of 5 or even 6 feet; and DvuILLIER
mentions that they were known in his time by the local name of “‘ Seiches,” which has
now been applied to rhythmic alterations of the level of lakes in general.
From Duiuurer’s time onwards various observations and speculations regarding the
seiches of Lake Léman are recorded. It seems to have been J. P. EK. Vaucuer, Pastor,
and Professor successively of Botany and Church History at Geneva, who, in a memoir
written between 1802 and 1804, and published in the memoirs of the Physical Society
of Geneva in 1833, first pointed out that seiches are not confined to Léman, but are
to be found more or less in all lakes; that they may be of all degrees of amplitude up
to 5 feet; and may occur at all seasons of the year, although their occurrence seems to
be affected by the state of the atmosphere. He also pointed out that the amplitude
of the seiches in Léman increases towards its western end; and that the seiches at
its eastern end are not more marked than those observed in other lakes.
These and other early observations of seiches are mentioned by Foret in his great
monograph on the Lake of Geneva, vol. ii. p. 50. In particular, he cites one observed
at Kenmore on Loch Tay in 1784, which lasted several hours, and is said to have had
a period of seven minutes and a maximum amplitude of nearly 5 feet.
A still earlier example is given in the Scots Magazme for 1755, p. 598, from which
it appears that seiches were caused in several of the lakes of Scotland by the great
earthquake of Lisbon on 1st November 1755.
As the source is not easily accessible to everyone, an extract may be printed here :—
* For the convenience of those who are more interested in the observation of seiches than in the purely mathe-
matical theory, I have separated the mathematics, so far as possible, from the general statement of the conclusions
arrived at and the suggestions of further problems to be solved by experiment or observation.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 25). - 89
600 PROFESSOR CHRYSTAL
“On the first of November last, Loch Lomond, all of a sudden, and without the
least gust of wind, rose against its banks with great rapidity, and immediately retiring,
in about five minutes subsided as low, in appearance, as ever it used to be in the
greatest drought of summer. In about five minutes after, it returned again, as high
and with as great rapidity as before. The agitation continued in the same manner,
from half an hour past nine till fifteen minutes after ten in the morning; the waters
taking five minutes to subside and as many to rise again. From ten to eleven the
agitation was not so great; and every rise was somewhat less than the immediately
preceding one; but taking the same time, viz., five minutes to flow and five to ebb, as
before. About eleven the agitation ceased. The height the waters rose was measured
immediately after and was found to be 2 feet 6 inches (76™) perpendicular. The
same day, at the same hour, Loch Lung and Loch Keatrin were agitated in much the
same manner; and we are informed from Inverness, that the agitation in Loch Ness
was so violent as to threaten destruction to some houses built on the sides of it.”
From this clear description there can be no doubt that the phenomenon observed
was a longitudinal seiche of Loch Lomond of exceptional amplitude, having a period of
ten minutes, probably the trinodal or quadrinodal seiche of that lake. The longest
dimension of both Lomond and Ness is nearly in a straight line with the centre of
disturbance at Lisbon, and a plurinodal seiche is the result we should expect. The
greater disturbance in Loch Ness may be due to the fact that one of the seiche periods
of that lake is about nine minutes.
But our really accurate knowledge of the phenomena of seiches dates from the
commencement of ForeL’s own observations at the harbour of Morges, on the Lake
of Geneva, in 1869. He may with justice be called the Faraday of seiches. He
worked at first with a small portable apparatus (plemyrameter), and later (1876)
with a self-registering limnograph installed at Morges, and a portable limnograph
of simpler construction. In 1877 PLanramour established a magnificent self-
registering limnograph at his villa at Sécheron, near Geneva, which has been in
continuous operation since. In 1879 Sarasin devised his portable limnograph, with
which observations were made at Tour de Peilz, Chillon, Rolle, and various other
stations on Léman, and also upon other Swiss lakes. In 1880 the French Govern-
ment engineers also installed a fixed limnograph at Thonon, with which observations
have been made under the superintendence of DeLEBecque, Du Boys, and Lauriot.
During the last twenty years a large number of enthusiastic observers have followed
the lead given by Foret and his fellow-countrymen; and we have now a great mass
of information regarding the seiches in lakes in various parts of the world,* from the
15-hour seiches observed by Henry in Lake Erie, which is 396 km. long, to the
seiches of 14 seconds, observed by ENpR6s in a small pond whose length was only
111 m.
§ 2. The accurate theoretical discussion and co-ordination of the results has scarcely
* See the extension of Foret’s bibliography appended to this paper.
|
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 60T
kept pace with their accumulation. In the main, the original theory of Foren has
been clearly established, viz., that a seiche is a standing oscillation of a lake, usually
in the direction of its longest dimension, but occasionally transverse. In a motion of
this kind every particle of the lake oscillates synchronously with every other, the
periods and phases being the same for all; and the orbits similar (in fact, rectilinear),
but of different dimensions, and not similarly. situated. Taking, for simplicity, a
longitudinal seiche in a lake of uniform breadth and rectangular section, but vary-
ing depth, the horizontal and vertical displacements of any particle on the surface
originally at a distance x from a fixed point of reference would be given by
E=$,(x) sin n(t—T), C=x,(x) sin n(t—7); where ¢ is the time measured from any
fixed epoch, 7 an arbitrary constant determining the phase of the oscillation, and
T=2r/n is the period of the oscillation.
For a Jake of given configuration, an infinite number of different values of n (but:
not any value) are admissible, say n,, n., 23, . . . ; and the functions ¢,(x) and x,,(a)
are determined when 7 is given.
For any given value of n, say n,, the function x, (v) vanishes for v different values
of z. At these points, which are called nodes, the level of the surface is unaltered by
the seiche. Corresponding to v=1,2, 38, etc., we have uninodal, binodal, trinodal,
etc., seiches. Any number of these may coexist; and the total seiche displacement is
obtained by adding these. When only one of these harmonic components is present
we shall call the seiche pure.
For a number of values of « , intermediate between the nodal values, $,(x) vanishes,
and there is no horizontal motion of the surface particles. These points are called ventral
pots. Four times the distance between a node and the next ventral point is called the
wave length. Obviously the wave length is not in general the same at all points of the
lake. When the wave length is large compared with the depth, which is always the
case in a seiche, the wave is spoken of as a long wave; and the hydrodynamical theory
in that case admits, as is well known,* of considerable simplification.
§ 3. When the depth of the lake is constant, the theory of long waves leads to the
well-known result
é=A, sin = sin see) (t{-r),
c= BEA, cos MF sin = VID (tn) ;
where / is the length of the lake, d its depth, 2 the initial distance of the surface
‘particle in question from one end, all measured in feet, and g=322:¢ denotes the
time, and A, and 7 are arbitrary constants (amplitude and epoch),
lt follows that in a lake of uniform depth the period of the uninodal seiche is
-2l/,/(gd); and the periods of the uninodal, binodal, trinodal, etc, seiches are
proportional to the terms of the harmonic series 1,4,4,.... Also the uninode
* See Airy, art, “Tides and Waves,” §§ 187 et seqg., Encyclopedia Metropolitana, 1848.
602 PROFESSOR CHRYSTAL
is given by #,=//2; the binodes by #,=//4, x,=381/4; the trinodes by x, =1/6,
i, — 31/6, %, — 61/6 ;, and so on;
In this case the wave length for each pure seiche is the same at all parts of the
lake; the ventral points are midway between the nodes; and the uninode, middle
trinode, middle quinquinode, etc. are all at the middle of the Jake. In fact, the
periods, nodes, and ventral points follow the same law as the periods, nodes, and ventral
points of the fundamental and over tones of an organ pipe open at both ends.
§ 4. When, however, the depth of the lake varies, this acoustic analogy is in some
important respects misleading. The theory of long waves applied to a longitudinal
seiche in a lake of uniform breadth and rectangular cross section, but varying depth,
leads to the following among other general results.
§ 5. In any given lake, seiches of all degrees of nodality, z.e. uninodal, binodal,
trinodal, ete., are possible; and any actual seiche is either one of these or a super-
position of several of them. Perhaps the most commonly occurring case is what ForuL
calls a dicrote seiche, whose components are uninodal and binodal.
§ 6. The periods of the series of pure seiches are not in general proportional to the
terms of the harmonic series1,3,4,4,.... The ratios of the periods are in
general incommensurable; in general, not even algebraic numbers, although in certain
special cases the periods are inversely proportional to the square roots of integral
numbers. Thus, for a lake of symmetric complete parabolic longitudinal section, we
have T,=7l/,/{»(v+1)gh}; so that the ratios are
TE eT, ae os, = (Lee (cai I oe sae
Indeed, it follows from a result* which I obtained for lakes whose longitudinal
section is part of the quartic curve z= h(1 — a?/a2)" that concave lakes can be imagined
in which T,, T,,T,, ... . all approach as nearly to equality as we please. Hence,
for example, it may very well happen that it is the trinodal, and not the binodal seiche
whose period is half the period of the uninodal,—a result wholly in contradiction with
the acoustic analogy suggested by the consideration of lakes of uniform depth.
§ 7. As this is a matter which seems to have caused some perplexity, it may
be well to give some numerical illustrations. Let us take a quartic lake of the kind
discussed in the paper to which I have referred. The period of the »-nodal seiche
is given by T, = 2al/y,/{gd(4:*0"/k’? +.1)} , where y and & depend on the configuration
of the lake. Suppose that T,/T,=1/2, then we find that we must have 47*/k’ = 3/5.
It then follows that T,/T,=°686. For a lake of this kind we should therefore have
T,:T,:T,;=1:°686:°5. In a communication to the Société Vaudoise des Sciences
Naturelles, Forrn{ mentions that three periods have been determined from observa-
tions on the Lake of Constance, viz., T,=55°8, T,=39°:1, T,=28°1, which give
T,: T,:T,=1:°701:°'504. It would appear, therefore, that the Lake of Constance
* See Proc. Roy. Soc, Edin., vol. xxv. p. 328, Mar. 20, 1905.
+ Hat. Bull. vol. xl. 149, Feb, 3, 1904.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 603
behaves not very differently from a quartic lake of the kind supposed. Of course it by
no means follows that the normal curve* of the Lake of Constance is even
approximately like the quartic curve supposed.¢ The point I wish to make is that,
from the hydrodynamical point of view, there is nothing surprising in the relation of
its periods. Farther investigation of the phases of the seiche at different parts of the
lake will probably show that the seiche a la .quinte, as Foret calls it, for which
T=39’, is really the binodal seiche; and that the seiche for which T=28'1’ is a
trinodal.
§ 8. The formula for the periods of a quartic lake given above may be written
T,=p//(’ +e), where p=hl/y,/(gd), «=+k'/47’, the minus sign corresponding to
convex lakes. As this formula applies to quartic lakes of every variety, concave or
convex, symmetric or asymmetric, it may be conjectured that it will give rough
approximations at least to the periods of any actual lake of fairly regular configuration.
The constants could not be determined w priori without discussing the bathymetric
data for each lake. The ratios of the periods, however, depend only on the single con-
stant e. We have, in fact, T,/T, = ./{(1+¢)/(’+.¢)}. In general the two longest periods
are best known. If we take these as given, the equation T,’/T,’=(1+¢)/(4+¢) gives
the value of «; and then T,=T,,/{(1+¢)/(’+6)} =p/ /(’ +e), where p=T,,./(1+¢).f
For very large values of v, we have approximately T,=p/v; in other words, the periods
of the seiches of higher nodality approximate to a harmonic series. By means of these
formulee—which I shall call the Quartic approximation—the table on p. 604 has been
calculated for a number of lakes whose periods are fairly well determined. _I have
gone in most cases as far as T=4°7’, which is the period found by Forer for the
longest progressive surface waves ever observed on Léman, calculated for infinite depth
of water.
As a control, I have added at the end of the table, under A, B, C, D, the periods for
a complete symmetric rectilinear, semirectilinear, complete parabolic, and semiparabolic
lake respectively, as calculated by the quartic approximation, and as calculated by the
accurate formulee of §§ 27, 34, 49, and 51 below.
* See § 12 below.
+ Nevertheless it is curious to pursue this numerical case a little further. Referring to my paper already quoted,
and calculating & as above, we get k=8'112. If we assume the longitudinal section to be symmetrical, then y=2 tanh
(k/4); and we have y=1:932. Hence r= {1-(7/2)?}?d, gives, if we put d=252™. (the maximum depth of Constance),
7=11™ If then we take a symmetric quartic lake having the same length as Constance, viz., 65*™., the same
maximum depth, and end depths of 1:1™, we find T, = 165 x 105/:966,/{981 x 25200 x 8+5}=56"0, Hence T,=56"0),
T,=38"4, T,=28'. The agreement with the observed periods of Constance is curiously close, and is, no doubt,
partly accidental. It will be of great interest to work out the normal curve for Constance, and calculate the periods
by a rigorous application of the theory, as has been done by Mr WEDDERBURN and myself for Treig and Earn.
f It is interesting to notice that in the case of a concave lake p/,/« is the period of the “anomalous seiche.” See
Proc, R.S.E., xxv. (1905), p. 645.
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ON THE HYDRODYNAMICAL THEORY OF SEICHES. 605
This table must, of course, be used with great caution. In the first place, as we
increase the number of the nodes we trench more and more upon the limits of the
hypothesis that the waves are “long.” Then it cannot possibly represent the case of
convex (2.e. in practice concavo-convex lakes) so accurately as the case of wholly concave
lakes. It will be noticed, for example, that in Geneva and Ness, which are similar in
their seiche-character, there are seiches of 20’ and 8°8’, probably trinodal or quadri-
nodal, which do not fit into the scheme suggested. As the nodality increases, the
periods become more and more nearly equal, and therefore more difficult to distinguish,
either by a rough calculation, or, for that matter, by observation, from one another, and
from progressive surface waves of purely local significance which are not seiches at all.
Subject to these qualifications, the table is very interesting and suggestive. It
shows the greater variety of possible periods in some lakes as compared with others.
It shows that there is nothing surprising, from the hydrodynamical point of view, in the
fact that the three longest periods for Constance are 55:8’, 39°1’, and 28°1’. The
sewche & la quinte of which Foret speaks in the cases of Constance, Garda, and
Starnberg is in all probability simply the binodal seiche ; and the seiche whose period
is approximately half the longest period is a trinodal. Such questions cannot be
finally settled until the phases of the seiches have been determined by simultaneous
limnographic observations at different parts of the lake, as has been done by ENprRos
in his admirable investigation of the seiches of the Chiemsee, Seespiegelschwankungen
beobachtet am Chiemsee, Traunstein, 1903.
I have included in the table as longitudinal seiches some which have been
held by observers to be transversal. This I have done for two reasons. In the
first place, the absolute identification of these by means of phase observations
has not in all cases been satisfactorily accomplished.* Again, it is possible that a
transversal seiche might coexist with a longitudinal one of nearly the same period
throughout a considerable part of the lake. The interference of these at the ventral
points of the longitudinal seiche would produce the phenomenon of seiche beatst at
various points along the shore. At the ends of the lake, which are ventral points for
all the different pure seiches, all these seiches interfere. It follows, equally from
observation and from the analogy of the vibrating string of varying density, presently
to be mentioned, that the average amplitudes of the seiches that occur in nature
diminish rapidly as their nodality increases. Hence the chief features of the limno-
graphic trace at the shallow ends of a lake will in general be the periodic configuration
due to the interference of the uninodal and binodal seiches ; the effect of the others will
merely be to produce an embroidery on the main outline. Also, since the periods
Become more nearly equal as the nodality increases, this embroidery will have an
* See Foren, Le Léman, t. ii. p. 148.
_ + Since this was written I have noticed that EnpR6s, in his able analysis of the seiches of the Chiemsee, cites
examples of variations in the phases and amplitudes of nearly pure seiches, which he regards as due to the inter-
ference of seiches of the same period differing in phase. He suggests, with great probability, that such seiches are
generated by a common but intermittent cause of disturbance.
606 PROFESSOR CHRYSTAL
irregular character, due to the beats of seiches not very different in period. The ends
of a lake are therefore the worst places for distinguishing seiches of higher nodality.
If a lake had three periods 10’, 11’, 12’, the proper place to observe at, in order to
establish clearly the seiche corresponding to the first or last of these periods, would be
at a node of the seiche whose period is 11’. Thus Foret’s argument, that the 10’ seiche
of Léman is a transversal and not a plurinodal longitudinal one, because it is not detected
at Geneva, is by no means conclusive. I may also add, although I have little theoretical
or experimental ground as yet for the opinion, that it seems to me unlikely that any
transversal seiche would be so stable, especially in a lake of the shape of Léman, as the
beautiful records of Foret’s limnograph seem to indicate. Nevertheless, great weight
must be attached to the inclination of so sagacious an observer, who has all the data
before him.
The table also raises many interesting subjects of inquiry. Why, for example, are
no seiches observed in Constance of the periods 22°4’ and 18°3’? Is this an accident,
due to the position at which the limnograph was placed; or are these seiches unstable,
owing to irregularities of the lake-bottom near one or more of the corresponding
nodes ?
§ 9. In a purely concave lake the ratio of the uninodal period to the binodal period
is less than a half. In a purely convex lake, if such a thing could be found in nature,
the corresponding ratio would be greater than a half. In lakes which are neither
purely concave nor purely convex the value of T,/T, will be greater or less thana half
according as the concavity or convexity predominates.
§10. In the case of parabolic and quartic lakes the rule given by Du Boys for
calculating the periods, viz., aT, = (2/r) | dl/,/(gh), where his the depth corresponding
to the element di of the line of maximum depth, gives too high a value for purely con-
cave and too low a value for purely convex lakes ; but it gives in many cases a good first
approximation to the periods. This approximation is better for concavo-convex lakes
than for purely concave or purely convex lakes ; and for purely concave or purely convex
lakes, the approximation is better the higher the nodality of the seiche. For a purely
concave symmetric parabolic lake Du Boys’ rule would be considerably out; in fact,
for such a case gI',/T,=1'414. It may also err greatly in cases where there are great
variations of the breadth of the lake, as the method of applying the formula takes no
account of such peculiarities. *
§11. In a lake of varying depth the uninode is not in general in the middle of the
lake, and the uninode, middle trinode, middle quinquinode, etc. are not coincident.
Also the ventral points are not midway between the nodes; and the wave length varies
from node tonode. Thus, for example, in a symmetric parabolic lake the uninode is of
course in the middle, but the binodes are displaced towards the shallow ends. It
results from the calculations @ priori, made by myself and Mr WeppeErsury, that in
* Dr Enprés has found a striking example in the uninodal seiche of the Waginger See, of which he was good
enough to tell me by letter.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 607
Earn, which is asymmetric, the uninode is very near the middle; but in Treig this is
not so nearly the case: in neither is the trinode coincident with the uninode. In both
these lakes the deep binode is not far from the point of greatest depth; in both the
shallow binode is nearer the end than a fourth of the leneth of the lake ; but, whereas
in Harn the binodes are on opposite sides of the deepest point, in Treig they are on the
same side. In neither lake are the binodes equidistant from the uninode. It remains
to be seen how far these results of theory will agree with observation.
§12. When the breadth and the form of the transverse section of a lake vary as
well as the depth, provided these variations are not too abrupt, it can be submitted to
calculation by introducing two new variables, viz., ¢, which is the product of the area of
the transverse section by the breadth of this section at the surface ; and v, which is the
area of the surface of the lake between the trace on the surface of the transverse section
corresponding to c, and any other similar line chosen for reference. In order to submit
the lake to calculation, its line of maximum depth is taken and laid out straight ; and
practically the lake is treated as if it were a lake of uniform breadth and rectangular
eross section, whose longitudinal section is the curve, the abscissa and ordinate of any
point on which are v ando respectively. This curve | call the normal curve of the
lake. If we may judge by our results for Treig and Harn, these assumptions are
sutliciently correct for ordinary concave lakes at least.
§ 13. In my calculations no account is taken of the dissipative forces which damp
the seiche oscillation. In some cases the damping is hardly sensible during the period
for which a seiche is observed to be pure, or even simply dicrote. Foret quotes an
observation of Puianramour’s, in which a pure uninodal seiche in Léman, whose
maximum double amplitude was about 169™™., lasted for seven and a half days, and
consisted of 148 oscillations. The mean double amplitude of 20 oscillations was at
first 167™™, and at the 140th, 80™™. It was finally disturbed by the appearance of
a binodal component, which turned it into a dicrote seiche ; otherwise Foret calculates
that it might have lasted two days more.* In other cases the damping of some of
the pure seiches seems to be considerable, owing probably to the fact that the lake
is, so to speak, not well tuned for particular periods. This is seen by studying the
form of the limnograph trace, by the elegant method suggested by Sorer.t 4T,. The displacement
of the uninode towards the shallow end and the greater amplitude of the wave there
were also readily demonstrated. The foregoing experiments were made with water
8°18 cm. deep, in a trough of length CH=39°8 cm.; and the periods were T, = 96",
A
s
Iie ale
T,='52". With a depth of 4:1 em. and C H=30°7 em. it was still possible to maintain
a uninodal seiche of period *97", which agrees very well with the formula T = 2//,/(gd)
applicable to a long wave. .
Foret based his theory of seiches in part upon an interesting series of experiments
of this kind made in 1870,t
* To incline the trough, keeping the volume of water the same, is not the same thing.
+ Enpr6s commenced his investigation of the complicated seiche-phenomena in the Chiemsee with a series of
experiments on the oscillation of mercury in a vessel imitating the configuration of the lake, the results of which, on
the whole, were in remarkable agreement with his subsequent observations, l.c., p. &
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 613
EA ae
MATHEMATICAL THEORY.
GENERAL THEORY OF A SMALL LONGITUDINAL SEICHE IN A LAKE
OF VARYING DEPTH AND CROSS SECTION.
§ 20. Let O X be a longitudinal axis in the undisturbed surface of the lake. Obser-
vation seems to show that this axis should be as nearly as possible in the average
direction of the channel of greatest depth. Take OZ vertical, and O Y horizontal and
perpendicular to O X.
Consider any cross section at a distance O P= from the origin. Let the area of
this section be A(x), and its breadth at the surface-b(x). Take a section parallel to
A(x) at a distance dx from A(x). The volume of this slice (S) will be, to the first
order of small quantities, A(x)dz.
Suppose that, after a time, ¢, the slice, S, has moved into a new position, so that the
distance of its posterior face from O is now x+& ‘Then the breadth of S in its new
position will be dx(1+<é/ax); and the part of its volume below the normal level of the
lake will be A(x + &)dx(1 + 0é/dz).
If we suppose the rise in level of the slice to be the same throughout, say ¢, which
involves the assumption that there is no flow parallel to OY, and that all the water
particles in the same transverse vertical plane have the same velocity parallel to the
plane ZO X, then we may take the increment of the slice owing to the rise of the water
above the original level to be o(x)fda(1+<é/éx). In so doing we neglect the effect of the
shelving of the shore ; so that our calculation would certainly not apply in cases where
the seiche causes a large horizontal displacement of the high-water mark.
With these assumptions the equation of continuity is
A(x)dx = {A(x + €) + 0(x)E}dx(1 + d€/ax) :
that is,
Cb(x) = A(a)/(1 + 0&/ax) — A(x + &) : : - : (L)
Since the amplitude of the seiche is small, we neglect vertical and consider only
horizontal acceleration. The difference between the pressures on the two sides of the
slice in its disturbed position will therefore be simply that due to the difference of
level at its two ends, viz., ged per unit of area, p being the density of the liquid.*
The equation of motion for S, regarded as a whole, is therefore
dix(1 +2¢/2z)p- <5 = - gp de
aes) <<: Bere +
* In order that these assumptions may be justified, the square of the ratio of the depth to the wave length must
be negligible at every part of the lake. See Lamb’s Hydrodynamics (1895), § 169.
that is
i
614 PROFESSOR CHRYSTAL i
The amplitudes being small, we shall neglect quantities of the order of ¢,(dé/éz)?
The above equation then becomes
b(x)t= ae -#)—A(@)-é
ait —eh@),
eA)
ax”
or
f-—apli@} . . . nn
and
A(x p= ag Aa) : : .
If we substitute the value of ¢ in (4), we get
A(z) oe = 9Ale) 2 Eee {Awe} |
Now this last equation may be written
oe SEES He) b( = dx 5 | ie) (x) att e yet] ; oF
If we determine new variables u and v by the equations
u= Kee) b= [xt e) Co
then (5) may be written
Cea gAla 2) b(a 21 2? = go Om 9 . . = (7),
where «x is to be determined as a function of v by the second equation of (6); and o(v)
=A(xr)b(x). Also (3) becomes
f=-— . : i .
The curve whose ordinate and abscissa are « and v we shall call the normal curve of
the lake.
Since a seiche is a standing oscillation, £, and therefore wu, is a periodic fanceee of
the time. We may suppose this periodic function analysed into simple harmonic terms,
and write
u= SP sin n(t - 7) , é : ‘ : (9),
where P is a function of v alone and 7 is constant. The values of n admissible depend
on the circumstances of each case: but, in order that (9) may satisfy (7) we must have
2
-v?P= go(v)- = :
The mathematical theory of a seiche of small amplitude depends therefore essentially
on the differential equation
; : (hell eon
= . . . 1 »
dv tg Ci ; ‘ (10)
where «x is determined in terms of v by the equation v= | dxb(x); and o(v) = A(a)b(a).
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 615
As (10) is simply the canonical form of the linear differential equation of the second
order, a variety of cases can be devised in which the seiche problem can be solved in
finite terms; and in any case where A(x) and b(x) are given slowly varying functions,
approximate solutions can be found, with more or less labour.
§ 21. In all the seiche problems considered in this paper we have at the ends of the
lake either A(x)=0 or else £=0; thatisw=0.
Moreover, the equation (7) may be regarded as the equation of motion of a vertical
string vibrating in one plane, the ratio of whose tension to the longitudinal density is
go(v), v being the distance of any point P of the string from one end when the whole is
at rest. The variable u denotes the lateral displacement of the point P at time ¢; and,
in view of the conditions w=0 at both ends of the lake, we may suppose both ends of
the string fixed. We can then deduce the seiche displacements from the motion of the
string by the equations
€=u/A(x), f= —odu/ov.
It will be observed that the nodes of the string correspond to ventral points of the
seiche, and vice versa; and it appears that we could, by experimenting with a string
loaded so that its density is inversely proportional to the product of the area and
surface breadth of the cross section of a lake, roughly determine in the laboratory the
periods and nodes of the pure seiches that might occur in the lake.
It follows from Srurm’s Oscillation theorem™ that in any given lake seiches are
possible which have
ventral points and
nodes respectively.
In other words, pure seiches of all degrees of nodality are possible; and the most
general seiche disturbance is a sum of such pure seiches with arbitrary amplitudes and
phases. We regard the ends of the lake as ventral points because u always vanishes
there, although in most cases the horizontal displacement does not vanish, as it should
do at a ventral point properly so called.
The identification of the seiche problem with the theory of a vibrating string is not
only very instructive from the physical point of view, but is very helpful mathematically.
For example, when we have worked out the periods and nodes of a seiche for any simple
configuration approximately fitting a given lake, we can correct for the divergence of
the actual lake from the assumed mathematical form by means of the beautiful method
described by Lorp RayteicH in his Theory of Sound, vol. i. § 90.
* See RayueEran’s Sownd (1877), vol. i. § 142.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 25). 91
616 PROFESSOR CHRYSTAL
CasE oF A LakE OF CoNnsTANT BREADTH, RECTANGULAR SECTION,
BUT VARYING DEPTH.
§ 22. Let b(x)=b, A(x)=bh(w), where b is the constant breadth, and h(x) the
varying depth.
Then the equations (7) and (8) may be written
Th = gh(2)— : : : . (ae
c=- = ; : ‘ : : (8') ;
where u = h(x).
In the case of a stationary oscillation, we shall have
Eh(x) =u=P sin n(t - 7) : : : : : (9’)
where
2 2
= + Fits) P=0 (10’).
It will be useful in this case to give the displacement ¢, for a point P in the
water not lying on the surface. If the co-ordinates of P be (x, y, 2) before and
(c+&, y, 2+G) after disturbance, € and ¢ denoting as before the displacements of: the
point (x, y, 0) vertically over (x, y, z), then, applying the equation of continuity to a
small parallelopiped reaching from (#, y, z) to the surface and having sides parallel
to the axes, we get, supposing z measured downwards, ¢ and © upwards,
zdudy =(2—, + £)dw( +é/ex)dyl. Therefore, to the order of approximation contemplated,
we have
-4=-¢-28
that is
—6=2 (uaye)— 22
we
ON Oe be : . (i
It follows that
ee h(x) (h(x) -z) d/ P
brio HO =9 202)
_zh'(z) h(x) -2dP
h(a) P dx (12).
Hence as we pass vertically upwards we find all the particles of water oscillating in
rectilinear orbits the inclinations of which vary gradually from tangency with the
bottom to tangency with the free surface of the lake.
§ 23. If we compare equations (7), (8), (9), (10) with (7’), (8’), (9’), (10’), it is at
once obvious that mathematically there is no difference between the general case and
the special one where the breadth of the lake is constant, its cross section rectangular,
and the depth alone varies. We can pass from the one case to the other by obvious
changes in the meanings of the variables and constants involved. We shall therefore in
future confine ourselves to the more special case, of which it is easier to form a clear
mental picture.
ON THE HYDRODYNAMICAL THEORY OF SEICHES, 617
GENERAL SOLUTION FOR A PARABOLIC LONGITUDINAL SECTION.
INTRODUCTION OF THE SEICHE FUNCTIONS.
§ 24. Consider the equation
d?P c :
a hae” . . . . . (i3)e
uming y=+a,v+ugv2+ .... , we find in the usual way
| ¢4+1.2a,=0, ca, + 2.3a,=0,
' (c-1.2A)a, = 3.4a,=0, (BBN -=0,
| (c ae 3)(n— 2)N}a as Naa, =.
nee we have
more c(e — 1.20) 4 e(¢ — 1.2A)(¢ - 3.4A) \
- ee At Wasps esa
2.3 SDB \\ie= 46
$B yel vf oe o coe ek ; as
ere A and B are arbitrary constants. The series in the brackets are obviously
ent if |v|<1/,/|A|; and divergent if ;v|>1/,/|A|. They are also convergent
+1/,/; for the general term, of say the first series, may be written
euo(Q- ga) (oe) eernen
and, since the infinite product
Ee
3 convergent, wv, is ultimately of the same order as 1/n’*.
aa
If we introduce the notation
Pesce c(¢ — 1.2A) 4
C(c,A,v)=1 i” bear ant ER
Sane ew? c(e = 2.3) 4 en ;
ee) Jeo} 1 oat 23x45
e that the functions C and S have certain properties in common with the circular
ons. For example, we have
Cie,A,-v)= Cle,rA,v);
S(c,A, -v)= —S(e,A, rv);
C(c,r,0)=1, S(ce,A, 0) =0.
C(e, 0, v)=cos( fev), S(c,0,v)=sin ( ,/cv) ;
that the cosine and sine are particular cases of the functions just defined.
618 PROFESSOR CHRYSTAL
From EvLer’s identity, viz.
(T2501 Sti oe eee (1 — u,)
=l-u =f enna o-l)+.-
es. (—)Pu,(u,-1)(-1)...... Gee
we see that
-(1_A\(y_ o/s
le; X51} vy=(1 Hel = Lae ad © ;
Je(y c/x _¢/x
SiGe ye (1 Se =) ae ee ME ad w.
In our applications we shall for the most part put \=1, or \=-—1. Then we may
omit the argument A and write
ye oe ce le
Cle, o)=1- Fert et . Cr
Ne ee a ee
S(r,v)=v- yr eee Bay ba ; : : (16).
We shall call C(c, v) and S(c,v) the Seiche-cosine and the Seiche-sine respectively.
Also |
SA eu? ce+l.2) 4 )
= CR UICKCct co) ae ee
S(e,v)= et po aE : : : (18).
These may be called the hyperbolic seiche-cosine and the hyperbolic seiche-sine.
When c has one of the integral values 1.2,3.4,...., C(e,v) reduces) tome
rational integral function of v; and when c has one of the integral values 2.3,
Ae . . , the like happens to S(c, v).
The same holds for &(c, v) and S(c, v) with regard to the negative integral values
—1.2,-3.4,....,and —2.3, —4.5,.... ; but this is of little interest mua
seiche problem, for which the values of c must be positive.
By a well-known property of the solutions of a linear equation of the second order,
we must have C(c,v) S(c,v) — C(c, v) S(c, v) = constant, where the dash denotes
differentiation with respect to v. In the present case this constant is easily seen to
be unity ; and we have
C(c, v) S(c, v) —Ce, v) S(c, v)=1 a F ; (1O}§
Cc, 1)S'(e, ») —Ci(e, v)G(e,v)=1 . : : : (20).
These are the analogues of the relation cos *@+sin °6=1 for the circular functions ; and
they are very useful in seiche calculations. We might also define a seiche-tangent,
seiche-cotangent, seiche-secant, and seiche-cosecant. We shall only have occasion to
use the seiche-cotangent, viz., C(c,v)/S(c,v), which we shall denote by K¢é, »).
These functions have many curious properties more or less analogous to those of the
circular functions: e.g. K’/(c,v)=—1/S%(c,v), but it is needless to encumber the
present paper with details of this description.
:
:
ON THE HYDRODYNAMICAL THEORY OF SEICHES,. 619
§ 25. We have now, of course,
Ce Nate oe ee Cis
S(c, 1)=(1- 51-35) ey. P ad « ; . (22);
Gp (SN a ietieie Sadek tim eiliniiw «2s (289s
Se,‘ =1(1 +55 \1+75) eee Hiiobegnd ; . (24).
We shall have frequent occasion to use C(c, 1) and S(c, 1); and it is convenient
for purposes of calculation to express them in terms of the gamma function.
We have
c\7, 4n?+6n+2-c
Oe =(1-5) enya)
a c\yyimt4(3 + a) } {n+ 3(3 - 2)}
= ==) (n+4)(n+1) ;
where a= ,/(4c+ 1).
Since #(3 +a)+4(3—a)=4+1, it follows by a well-known theorem * that
ce) = (1-$) 4. arena) 4)
Since P(4)=77, P(1)=1, and a’ = 4c +1, we get finally
C@)1) = n= ==) 2 _) ; » G5
and in exactly the same way
Se. 1) = he a iS = =) : I e6).
Tt follows that
K¢e, 1) = ar(? - ae ; re ; ae) ; ' ~— Oy
a formula which has been much used by Mr WeEppERBURN and myself in the numerical
calculation of seiche periods. If we recollect that
rez) 100475),
n(n) =e 5),
we can put (27) into the form
K(c, 1) = —, cos (a = \r : i (C = : ‘ es 28)e.
which is useful for determining the sign of K(c, 1).
* See Whittaker’s Modern Analysis (1902), § 96.
620 PROFESSOR CHRYSTAL
§ 26. By Srurm’s Oscillation theorem, applied to the solutions of the differential
equation (13), we see that for any real value of v not exceeding unity the equations
C(c,v)=0, S(es0)—0, ‘ : : : (29).
C(e,o)=0, Cle, =0, ‘ ‘ : : (30) ,
have each an infinite number of real roots, and that the roots of each equation of either
pair separate the roots of the other equation of the same pair.
In particular, the roots of
Ces 1) — Ob eare.: cs 24 eee £
of
S(¢; l)=S0) are: “eS 223) 400), we eo ;
unfortunately the roots of
G(c,1)=0, G(c, 1)=0
are not commensurable ; and, owing to the slow convergence of the series involved,
they are very difficult to calculate directly. By a very laborious calculation, I find :—
for the smallest root of @(c,1)=0, c=2°'77... .; and for the smallest root of
6(¢,1)=0, c=12°34.... As these figures agree with the approximations given
by Dr Hato in the paper on the seiche functions above referred to, and with calcula-
tions which Dr Burasss, Professor Gipson, and Mr HorssurcH have been kind
enough to make for me, probably they are correct. It would, however, be hopeless to
calculate the higher roots, or even these two to greater accuracy, by direct use of the
series as it stands in (17) and (18).
SEICHES IN A CONCAVE SYMMETRIC COMPLETE PARABOLIC LAKE.
h(x) =hx(1—2a"/a’).
A a 5 oO a A
Hiren 2:
§ 27. The equation for determining P is, by § 22,
o2P n2
des LIES 2S 1)
Ga? * gh(1 — 22 /a2)
;
or, if w—Z/a,
GINO Tors
ape pS
( aya ohir, o,
say,
a2P ;
(1 — et) teP=0, : : : . : (31),
where
c=n?u2/gh , : ; j : ; (32).
»
ON THE HYDRODYNAMICAL 'THEORY OF SEICHES. 621
We have therefore
éh(1 — w?) =u={AC(c, wv) +BS(c, w)} sinn(t-7),
where A and B are arbitrary constants.
Also
= = { AC(c,w)+BS(c, w) } sin n(t =) ;
where the dashes denote differentiation with respect to w.
Since € is finite, we have w=0, when w=+1. Therefore, since C(c,-—1)=C(c, 1),
and S(c ,—1)= —S(c, 1), the following boundary conditions must be satisfied :
A O(c, 1)+B S(c, 1)=0,
A O(c, 1)-BS(c,1)=0.
These are equivalent to
ALO(en I) =0nae BS(e.1) 08
Now we see from the relation
C(c, w)S'(c, w) -—C'(c, w)S(c, w)=1,
that C(c,1) and S(c, 1) cannot vanish simultaneously. Therefore either
BO nC(c al) =O);
or
MeO) Sie) On
mae we have seen, the roots of C(c,1)=0 are -c,=1.2,¢,=3.4,..
Muee=(2s—1)2s,....; and the roots of S(c,1)=0,c,=2.3,¢4=45,....,
€,=2s(2s+1),... . Hence we have the two sets of solutions
E= A C(Co._1 ,w) sin Noo (t 7 T) .
=e See ee
h 1 - 0? : G3):
c= _— 2 CG: wv) sin Mog (t aa: t)
Here O(c,,,,w) is a polynomial of degree 25; and O'(cy_1,w) a polynomial of
degree 2s—1.
Also
= B S(@s ,&) sin N2,(t — 7),
h 1 — w? 5 | ee
C= B S’(¢o5) W) sin 2»,(¢ — 7)
aa
where S(c,,, w) and S’(c,,, w) are polynomials of degrees 25+ 1 and 2s respectively.
*Since the abstract of this paper was published, I have discovered that the solution for the particular case of a
symmetric parabolic basin was given by Lams in the new edition of his Hydrodynamics (1895), § 182. He arrives
at his result by means of LeGenpDR#’s function, which is closely allied to the seiche functions.
622 PROFESSOR CHRYSTAL
In either case, if T, be the period of the v-nodal seiche, we have
T, =22/n, = 27a/,/(¢,gh) ,
=al/ /{v(v+1)gh}, . : ; : . (35) ,
if 7 denote the whole length of the lake.
UNINODAL SEICHE.
§ 28.
¢,=1.2. T, =al/,/(2gh)
C(c,,w)=1-w?, C(c,,w)= -2u.
AS 2An .
— sinn(t-r), l= a sin n,(t—7).
One node
z/a=0.
In this case the amplitude of the horizontal displacement is constant; and the
free surface is a plane which oscillates about the line of the uninode.
If ¢ be the maximum rise of the water at the end of the lake above the undis-
turbed level, then (=2A/a=4A/l. Hence A=/¢/4. Hence the maximum horizontal
displacement of a water particle from its mean position is £=/¢/4h; and the maximum
velocity of the horizontal stream is nlC@/4h=7l@/2hT,. For example, if Loch Ness
were a symmetric parabolic lake, every inch of maximum vertical seiche at one end
would give over 40 inches of maximum horizontal displacement; and a maximum
horizontal stream velocity of over 8 inches per minute.
BINODAL SEICHE,
N 29.
C= 2.3, T, =7l/,/(6gh),
S(c.,w)=w-w>, S'(c.,w)=1- 3w?,
Ba. B(3az2 — a?) .
=e un na(t -T), C= a sin ,(t-7).
Two nodes at
t/aatht fS= +5774... .
The amplitude of £ increases uniformly from the centre to the ends of the lake; and
the free surface is parabolic,
TT: Qi /G= bomen eee
Hence the period of the binodal seiche is greater than half the period of the
uninodal seiche.
Also the nodes are more than half way from the middle of the lake towards the
ends ; 1.e. they are displaced towards the shallows.
If — and ¢ be the maximum horizontal and vertical displacements at the end of
the lake, we find £/(=1/4h, as before, also £/C=27&/T,¢. For Loch Ness we get
ON THE HYDRODYNAMICAL THEORY OF SEICHES, 623
maeA0.: .., E/@=16'4.... As a binodal seiche of 34 in amplitude has been
observed, maximum horizontal displacements of about 12 feet and stream velocities of
about 5 feet per minute may occur near the end of the loch; these would be reduced
in the ratio of °57:1 at the two nodes of the seiche. As the centre of the loch is a
ventral segment, the horizontal displacement vanishes there at all times, and the
value of C is half its value at the ends of the loch. ©
TRINODAL SEICHE.
C,= 0.4 ; T, = 7l/,/(129h) .
C(c, , w) = 1 — 6w? + 5wt,
=(1 =w?)(1 — 5w?) .
C'(c,, wv) = — 12w+ 20w?,
= (a2 5a) sin n,(t — 7) ,
A 5, ;
C= al 12a%x — 20x) sin v(t — 7) .
Three nodes :—a=0, and e/a=+V73/./5=+°7746 ....
Four ventral points :—a#/a = +°4472, +1.
= 93) J12= 5 /6= 4082 a0;
QUADRINODAL SEICHE.
= 4.5; T, = l/ /(20gh) .
S(c,, w)=w— ae + ys :
= (dw — 10w? + 7w’) ,
1 5 5
Sal — w*)(3 — Tw?) ;
Sci.) (3 — 30w? + 351*) .
B 5 ses
E= hai (34 — 7x?) sin n,(t —7) ;
B 4 22 4) gi
C=—(- 3a + 30a7x? — 354) sin n,(t— 7) .
Four nodes :—a/a = +°3400 , +°8621 .
Five ventral points :—a2/a=0, +°6546, +1.
T/T, = J10 = "3162.
TRANS. ROY. SOC. EDIN., VOL, XLI, PART III. (NO. 25). 92
624 PROFESSOR CHRYSTAL
(JUINQUINODAL SEICHE.
a.
G9
bo
corals T,=7l/ ./(30gh) .
C(c, , w) = 1 — 15w? + 35t — 21 v8 = (1 — w?)(1 — 140? + 21 2*) 5
C'(e; , w) = — 30w + 140w? — 1260? .
E= Se — 14022? + 2124) sin m,(t—7) ;
Ma
(=A (30ate — 1400228 + 12625) sin n,(t=7).
a
Five nodes :—a=0 , x/a= +£°5384 , +°9062.
Six ventral points :—w/a = +°2853 , £°7650, +1.
1
T,/T, = 7g V15= 2582.
§ 33. The following conspectus of the numerical distances from the centre of the
nodes and ventral points will give a clear idea of the shortening of the wave length
towards the ends of the lake :—
I, Brnopatu. II. TRInopat.
aa 4X a/a 4X
V “0000 ‘DITA N “0000 “4472
N ‘DTTA "4226 Ww 4472 3274
V 1:0000 N ‘7746 +2254
V 1:0000
III. QuADRINODAL. TV. QUINQUINODAL.
«e/a +r x/ a 4A
V “0000 *3400 N “0000 "2853
N *3400 *3146 Vv "2853 2531
V 6546 2075 N 5384 2266
| N "8621 WB) we ‘7650 1412
| WV 1:0000 | N ‘9062 0938
V | 1:0000
It will thus be seen that the wave length near the centre is greater, and near the
end is less than it would be in a lake of the same length but of uniform depth. All
the nodes and ventral points which are not central are displaced towards the shallows.
As we see from § 8 that the amplitudes of the various pure seiches at the end of
the lake is of special interest, the following table may be given, in which R denotes the
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 625
ratio for any seiche of the amplitude at the end of the lake to the amplitude at the
ventral point at or nearest to the centre :—
SEICHES IN A CONCAVE SEMIPARABOLIC LAKE.
§ 34. Since all the pure seiches in a symmetric parabolic lake have ventral points
at the ends, and the seiches of even nodality have also a ventral point at the centre,
where there is no horizontal displacement, we could build a wall across the middle of
the lake without disturbing these seiches. It follows that the pure seiches of a semi-
0 a A
Fig. 3.
parabolic lake have the same periods as the seiches of even nodality in a complete
parabolic lake of double the length. The nodes and ventral segments will also be the
same as in one of the halves of the complete parabolic lake.
If, therefore, T,’ be the period of the v-nodal seiche in a semiparabolic lake of length
/and maximum depth h, we shall have
T= 2al/ /{2v(2v + 1)gh} - - : ; (36) .
If T, have the meaning of § 27, we find
T,/T.= A(t Viv +3)}-
Hence every period of a semiparabolic lake is longer than the corresponding period
of a complete parabolic lake of the same length and the same maximum depth ; but
the ratio of the periods comes nearer unity the higher the nodality.
The nodes and ventral points for the uninodal and binodal, ete. seiches will be given
by Tables I. and III. of § 33, provided we remember that x is now measured from the
deeper end of the lake, and no longer from the middle, and that @ is now the whole
length of the lake, and not half the length as before.
§ 35. The results for parabolic and semiparabolic lakes are of great use in forming
rough estimates of the constants and periods, either for experimental purposes, or in
order to get first approximations to the roots of the transcendental equations which in.
626 PROFESSOR CHRYSTAL
general determine these constants. We assume, as in general probable, that any
concave lake whose form is not unusual will be intermediate in character between a
complete parabolic and a semiparabolic lake. It follows that the periods, nodes, and
ventral points will be intermediate; and it is found in practice that in many cases a
good first approximation is obtained by taking the arithmetic mean between the two
extreme cases. As an example, we should expect that the distances of the uninode and
deep binode from the deeper end would lie between ‘5 and ‘58, and between -78 and
‘87 respectively.
In this connection we have found the following table of the ratios of the periods
useful :— .
T,/T, | T,/T, T,/T, T;/T, | T,/T, T,/T, T,/T, T/T,
| Parabolic Lake : odd LOS oO 2b Se 218 eel e9 167 149
| Semiparabolic Lake : | ‘548 | 378 | 289 | -234 | -196 | 169 | -1485 | -134
SEICHES IN A TRUNCATED PARABOLIC LAKE.
§ 36. By means of the seiche functions we can readily find the solution for a
parabolic lake which is bounded by vertical cross walls at distances «=p, x=q from
Fic.;4.
f
its deepest point. The formule are, in our previous notation,
Eh(1 — w?) {S(c, p/a)C(e, w) -— Cle, p/a)S(c, w)}sin n(t — 7) ;
be tee
S(«, p/a)
& = we am p/a)C(c, w) —C(e, p/a)S'(c, w)}sin n(t— 7) .
And the values of c are given by the period equation
C(c, p/a)S(e, g/4) — Sc, p/a)C(c, g/a)=0.
In the case of a symmetric lake g= —p; and the period equation reduces to
C(c, p/a)S(c, p/a)=0.
If, further, p= a, we get
O(c, 1)S(e, 1)=0;
and return to the case of a complete parabolic lake already discussed.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 627
SEICHES IN A CONVEX SYMMETRIC PARABOLIC LAKE.
h(x) =h x (1+2’/a’).
A @) G@ 2 A
Fr. 5.
oP n
B- Oe gos py
Ou? zs gh( 1 + «/a?)
w= c/a,
: (a= ; 37
j (l+w ae Os : : (37),
c=a/g, _- : : : : : (38).
e therefore
EA(1 +?) =u= {A O(c, w) + B S(c, w)}sin ne ;
C= ani G'(c, w) +B Sc, w)}sin nt.
ust vanish at the vertical ends corresponding to w= +1, we have, although
erent reason, the same boundary conditions as before, viz.—
A CG(c,w) +B Se, w) =0,
A @(c, w) - BG, wv) =0.
is before, we arrive at the two sets of solutions
Be A G(¢,,_1, w)sin ,,_, ¢
~ fh Leu? ;
(39) ;
C= =U cai 1D) SI Py geal! B
cB Sloss) sin ny,
=F) 1+?
(40) ;
B a .
€ ais S (Eqs W) SIN Nog ;
js, - --- ,m%1,....- are the roots of the equation
O(c. 1)=0;
Mee... - » %, -.. - are the roots of
Sle, 1)=0.
1,W) and G(‘,,,w) are, of course, no longer polynomials, but transcendental
ns of w.
628 PROFESSOR CHRYSTAL
UnINoDAL AND BINODAL SS#ICHES.
§ 38. Since, as has already been mentioned, y=2°77 . . . . and ¢=12°384 78
if T, and Y, be the periods of the uninodal and binodal seiches respectively, we have
bu!
S/S = (2 0 a Bay Aa
The distances of the binodes from the centre of the lake are given approximately by
v/a=°472.
SEICHES IN A CONCAVE ASYMMETRIC BIPARABOLIC LAKE.
Fic. 6,
§ 39. Let the equations for the portions O A and A’O be A(x) =h x (1 —@3/a’) ; and
h(x) =hx(1—2a"/a”). Then, if w=a/a, w’ =a/a’; c=n’a*/gh, c' =n’a"/gh, we have for
the two portions
En(1 — w®) = {A C(c, vw) + B S(c, w)} sin nt,
C =- HA C'(e, w) + BSc, w)} sin nt};
and
E(1 — w?) = {A Cle, w') + BY Sc’, w') }sin nt,
@ = — 1 {A C(¢') +B Se, w')}sin nt
> a
The boundary conditions at A and A’ give
AC(c, 1) Bic, D0
AY Ce, 1) B See 1)— 0;
The conditions =, C=C at O give obviously
Ae wAC
B/a=B'/a.
From these we deduce
a'C(c,J1)S(e’, 1) + aC(c, 1)S(e, 1)=0,
‘ ‘ (41)
a K(c, 1) +aK(e’, 1) =).
which is the equation that enables us to calculate c or c’, if we remember that
cfc =a" a",
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 629
If we put ac =a’! = n’a’a"/gh =z, the equation (41) may be written
1-74, \(1-3%5) ot (i- al ee ay)
af 1.2a? 3.402 9.3a'2 : 4.5a/2
| ef) i Oi my a dethc(4ays
+a( T.2a” 34a? xa) 4 bat )
Then the period of the v-nodal seiche is given by
T,=22/n,=2raa/ j(zgh); . ; 5 ° ; (43) ;
where z, is the corresponding root of (42),
For some purposes it is convenient to put a/a’=p. The equation (41) then becomes
(pK Gaze Dyn ik(eh I) = Oly Ay
and we have
T, = 27a / J (gh)
= 2ml/(1 + p) Vegi), V ; (45).
=2nl/( J+ Jer) J(gh). §
The equations for the seiche displacement in the two portions of the lake may now
be written
ogee 1)C(c, w) - C(e, 1)S(c, w) }sin net ;
(46) ;
© =- afeni St 1)C'(c, w) — Cle, 1)S'(c, w)}sin nt ;
EN a we, HIE Cle, w’) + Cle’, 1)S(¢, w’) }sin ne ;
(47).
€ =- ier aS(¢,1)* (c', YC(c,, w’) + C(c’, 1)S'(¢, w’)}sin nt.
It is obvious from (44) that when p is given the value of c’ is determined. Now p
is the ratio of the distances of the deepest section of the lake from the ends. Hence, if
this ratio remain unaltered, we see that T, is proportional directly to the length of the
lake, and inversely to the square root of its maximum depth.*
In particular, it follows that, if the basins of two lakes be geometrically similar, the
seiche periods are directly proportional to the square roots of the linear dimensions ; a
result obvious by Newron’s principle of dynamic similarity.
A graphic picture of the solution of the equation (44) may be obtained as follows :—
___ If we trace the curves whose equations are y = K(c’, 1), py= —K(p’c’, 1) , c’ being the
common abscissa, then the values of c’ corresponding to the intersection of these curves
are the roots of (44). The latter of these curves is deducible from the former by
diminishing all the abscissze in the ratio 1: p’ and all the ordinates in the ratio 1: p,
and then taking the image of this deformed curve in the axis of c’. It is thus easy to
see by drawing a schematic diagram that the effect of increasing p is to diminish ¢’.
The period depends on the value of (1+p),/c’ or c+ ,/c’; and the effect of the
increase of p upon this is not so easy to trace by direct analysis. Since, however, the
* In the general case A is the maximum value of the product of the area of a cross section by its surface breadth ;
and a and a’ the areas of the lake surface between the corresponding section and the ends.
630 PROFESSOR CHRYSTAL
shifting of the deepest point of the biparabolic lake without alteration of the length or
maximum depth does not alter the whole volume of water, general dynamical considera- _
tions regarding energy would lead us to expect that increase of p would lengthen all
the seiche periods; and, in point of fact, in the semiparabolic lake, which may be
regarded as the limiting case of a biparabolic lake when p=, all the periods are greater
than in the complete parabolic lake, which corresponds to p= 1.
SEICHES IN AN UNSYMMETRICAL LAKE WITH ONE SHALLOW
AND TWO MAXIMUM DEPTHS.
Od DG EB ae
rea Fe
ues fic
§ 40. A good approximation to the form in many cases that occur in nature can be
obtained by piecing together six parabolee, so as to form a continuous curve.
Let s be the minimum; and, fh’ the two maximum depths. D and D’ the points
of inflexion (the depths at which cannot be arbitrarily assigned). Let AB=a,, BD=6,
DO=d, D’/0’=d’, B/D’=0’, A’B’=a,’; then, for the continuity of the curve of
longitudinal section at D and D’ we have the following conditions, the laws of depth
being h(x) =h x (1—a’/a,’) for AB, h(x) =h x (1 —2?/a,”) for BD, A(x) =s x (1 +27/ag*)
for OD, h(x) =s x (1+2°/a’',”) for OD’, ete. :—
hbja? — sd/a.2=0 , hb?/a," + sd?/a,2=h—-s;
h'b'/a’2 —sd'/a'.2=0, h'b?/a',2 + sd?/a'.2=h'—s.
These lead to
a? =hb(d+h)/(h—s) , a,” = sd(d + b)/(h — 8) ; (48)
a2=Nb(d' +0)/(l' =s), a’ 2=sd'(d'+b')/(h—-s). J”
With the exception of a,, d,, d,, a, and the depths at D and D’, the other
quantities may be arbitrarily chosen.
If now
v,=a/a,, Up = 2/ Ay, U3 = %/ds 5
, / , / , ,
Dl an Vp =n > eae Gait
Wy = b/d , Ww, = d/as ;
0, =0' fa, , Ds =O de;
c, =n?a,7/gh, c= na,2/gh , Cc, = NA,"/gh ;
then we have for the various sections A, B, ete.
Eh(1 =v,”) = {A,C(c,, v1) + B,S(c,, v,) }sin n(t-7),
C= ZA) + B,S'(c,, v,)}sin n(t—7) ,
etc.
The origin for x being in each case the vertex of the corresponding parabola.
ON THE HYDRODYNAMICAL THEORY OF SEICHES, 631
The boundary conditions are then as follows :—
A,C(q,, 1) + BS(e,, 1)=0;
A, = Ap, B,/a, = Bo/a ;
AgO(C , Wy) — ByS(¢y , Wy) = AgE(cg , V3) + BsS (cy , Ws),
— A,O'(e,, Wo) + B,S'(¢ » W,) = ae { A,O'(cg , 03) + BaS (eg , 05) ; ;
3
A,= Ay’, B,/a,= By /a,! ;
— Ay’ (6,', 9’) + Ba'S(cq’ , Wg) = Ag G(cg , Wy’) — By’ E(c,’ , We) »
gO (cy, ty’) + ByS(cy’, 10) = 2, | — Ay C(ey’, 124) + BYS'(ey st) } ;
3
Ay’ =A,’, B,'/a,' = By'/ag ;
Ay Ce’, 1)- B/(¢, 1)=0.
m these, since C(c, , W.)S'(Cy , Wo) —C’(ey , We)S(Cy, W) = 1, we derive
dA O(c, 1) + a B,S(e,, 1)=0,
A,= | Sey. My) ECs, 5) + 28(6, 5 Wa) (Cg, Ws) \ As
3
a { S'(Cy , Wy) SG (Cg » Ws) + “28(c Wy) S (Cg , Ws) \ B,,
3
=)AA,+ pB, (say).
By= | O(c 1) E(C 09) + 2C (6a, 25) (ey, 9) | Ay
3
1 ; O'(Cy Wy) G(cg Ws) + “2.0 (C9, Wy) (Cg 5 Ws) } B,
3
=vA, +B, (say).
x A,0(¢,, 1) {AA, + uBs} +.a,S(c, 1){vA; + pB,} = 0,
{a,AC(c,, 1) + a,vS(c, RAS
+ {aqpCO(c, , 1) + aypS(c,, 1}B,=0.
: dy Ao’ O(c)’, 1) - %'B,/S(e', 1) =0
; 4 A= \ S'(co' , Ws )E(Cg , ws’) + “28(cy) 1 Wy )B'(ca’ » Wg’) } A,
3
a = { S'(c,", ws)S(cq , Wy’) + “280, pt (Cy axthy:) \ Baas
3
=)'A,' —y'B,’ (say). :
li { C'(eo' , 5’) O(c’ , ws’, ) + “2,0 (6, wo’ )G'(cz, Ws) \ As’
3
1 { O'(e,' , We’) S(Cy, Ws) + “2,0(¢9 1 Wy )S'(cs’ , wy) } B,’
3
= = —vA,' +B,’ (say).
Gem DNAs = WB hoa s(e,1)(—v'A, # BPO
{a d'C(e,’ 1) + ay'v'S(c,', 1)} Ag’ = {atg'p'C(cy’, 1) + a,'p'S(e,’, 1)}B,' =0.
ince A,’=A., B,’=a,'B,/a,, the last equation may be written
; {a d'C(e,’ , 1) + a,'V'S(c,’, 1) } Ag — a {a9'u'C(cy’, 1) + a,'p'S(e,', 1)} B, = 0.
_ TRANS. ROY. SOC. EDIN., VOL. XLI. PART ITI. (NO. 25). 93
632 PROFESSOR CHRYSTAL
Kliminating A, and B,, we get finally
As {@AC(c, , 1) + avS(e,, 1)}{ag'w'C(e,' , 1) + ay‘p’S(e,’, 1)}
+ Ag{dyN'C(ey’, 1) +.a,'v'S(cy, 1)} {aguC(e,1) + a,pS(e,,1)}=0; . : (49) ;
which is the period equation for the lake. When the lake is symmetrical, that is,
when @,=(;', @,=,, ete., this equation simplifies, and breaks up into the two
following :— .
AyO(C, , 1){a,8'(Cy, W)C (Cg , 03) + AyS(Cy 5 Wy) E'(eg » Wy) } j \ |
+ a,S(e,, 1) {ag0'(ey , we) O (eg, Wg) + A.C (Cy 5 Hy) B'(cy, w,)} =0, | ;
and AO(C,, 1){4g5'(ce , Wy) S(Cy , Ws) + AyS(Cy , Wy) S'(Cy » Wa)} i (ay
+ a,S(¢,, 1){agC’(e,, W_)G(cg, Wg) + AgC(Cy , My) S'(cy , wz)} =O |
ALTERNATIVE SOLUTION FOR PARABOLIC LAKES.
INTRODUCTION OF THE LAKE FUNCTION.
§ 41. For certain purposes a modification of the solution for parabolic lakes is
convenient. This is obtained by shifting the origin to the positive end, and, for
convenience, halving the scale of the new variable; that is, we put w=1—2z. The
equation
(1- ALE P=
dw? ;
then becomes
Ga PaO . oon
= ;
If we attempt to solve this by the assumption
PHA + AyztAge?+ -- +--+ 5
we find in the usual way that we must have
A=0,
cA, +1.2A,=0,
(c-1.2)A,+2.3A,=0,
(c—2.3)A,+3.4A,=0,
(c_w=2.m—1)A, j+n—1.n7A,=0.
‘Therefore A, = —A ees
=(-1)" ic(e— 1.2)(c-—2.3) . ‘ (e=m=2.n=1)y |
eRe eee ish
‘That is to say, we find
&: Ce we—laye cele mee eee )
oP oe Soe a |
where the series within the brackets is obviously convergent for all real values of 2
between —1 and +1, both included.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 633
We have thus obtained only one synectic integral of (50). A second integral may
be derived in the usual way, but it is not synectic. It has, in fact, an essential
singularity at z=0; and may be expressed in the form P logz+(z), where \(z) is a
power series. It is needless to state the actual result here, as it is of no use for our
present purpose.
Dropping the multiplicative constant, we write
2 5 he 2) 23 plintes =) gt
C7 de= il )z _ ele: 1.2)(c <3) —+ Bee ey : ‘ (51) ;
L Se a
(.2)=*— 9+ T9e2 3 129? 32
or
73
2 :
EC ceo — e(1 -¢/1.2) 3
at
— c(1-e¢/1.2)(1 - ¢/2.3)s i
mae a 6) en eiB: (6,6 - en = Fs a (51’).
The function thus defined will be called the Lake Function. It is obvious that
, P—L(e,2)
is that synectic integral of the equation (50) which vanishes when z=0, 1.e. when
w=1; and it will be valid for 15z 0, that is, for -1 er.
Ci/Cy =a'S(c', 1)/aS(c, 1)= Cle’, 1)/C(e, 1),
ener ia),
=e, 1/2) Tae sl/2) . ; ; (68) .
C/IG=Le, aIL', 3),
=L(e,)0( aeons) | ve,
=L(c, z)(G/G). : . (69),
All irrespective of algebraic sign.
Owing to the want of a simple companion fundamental integral, the Lake Function
is not convenient when the parabolic lake is truncated. In this respect it has the same
defect as the LecENDRE and Brssrt Functions. Its practical advantage is that it gives
highly convergent series at points where the series for C(c, w) and S(c, w) converge
slowly. Unhappily, the corresponding function for a convex lake has an imaginary
argument.
SEICHES IN RECTILINEAR LAKES.
§ 45. If we take the origin of x at a point where the depth is h, then the law of
depth will be /(x)=h x (1—a/a), where a is a constant, positive or negative according
as the lake bottom slopes upwards or downwards in the direction in which increases.
We have, therefore, with the previous notation
Eh(1 -2/a)=u=P sin n(t-7),
Ou ace : . . 70) ,
Gams Boos | Os
where P is determined by
Ciel & n?P
ee =0 . ‘ ° 7] .
dx* ~— yh(1 —x/a) we é ‘
636 PROFESSOR CHRYSTAL
If we transform (71) by putting w=2na,/(1—a/a)/,/(gh), and P = Rw, it becomes
ote lipo, . ll
dw? aw dw
which is a particular case of the Besse, Equation.*
If J,(w) and Y,(w) denote the BesseL and Neumann Functions, as defined in Gray
and MaTHEws’ treatise, the general solution of (72) is
R=AJ,(w)+B Y,(w) .
Hence, with a slight adaptation of the constants, we find
&w={AJ,(w) + BY,(w)} sin x(t- 7); . , (73) ;
2ZajAd Bd :
C= + | eal that) + 2 (w¥y()) } sin n(t—T).
Now, by one of the fundamental properties of J,(w) and Y,(w), we have
1 d 1 Ad , : é x
= wJ,(w) ) oa J q(t), At ale 1) ) = Y,(w) :
Hence
ee J,(w)+BY,(w)} sin n(t—r) : ; ‘ ; : (74).
From (73) and (74) solutions for the following particular cases are readily obtained.
RECTILINEAR LAKE witH Two SLOPES TRUNCATED AT BotH ENDs.
S46. The laws of depth for the two parts will be given by A(1—a/a) and
h(1+«/a’), if we take the origin at the junction of the two slopes, and choose the
standard case to be that where the bottom slopes upwards on both sides of the junction.
NY p ) Dp A
Fie. 8,
Let
w= 2na,/(1 — x/a)/ /(gh), w' =2na’ /(1+2/a’)//(gh) . ; ; ‘ (75) ;
and ;
a= 2a/J/(gh), P= 2an/(1 — p/a)//(9h) ;
a =2a'//(gh), B= 2a /(1 -p'/a’)// (gh).
* Readers unacquainted with the properties of Brsspi Functions will find all that is here required in a few
pages/of the treatise by Gray and Marumws (1895), ch. ii. and pp. 241-292 containing the tables,
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 637
The boundary conditions are, that & vanish at the ends, and that E=&,C=C at O.
These lead readily to the following :—
we=aA weeny We oe hs in n(t—7);
(nF a 28 tage
ea ep
AERO ent
And the period equation is
a2{Y,(n8)Jo(na) - J,(nB)¥ (na) } {V4 (mB")J,(na’) ~ J,(mB')Y (na!) }
+.a2{¥,(mB")Io(na’) — Jy(mB')¥ 4(na")}{ V,(nB)JI,(na) ~ Jy(nB)Y,(na) = 0
UNSYMMETRIC LAKE SHELVING AT Boru ENDs.
§ 47.
es DS 6 p
Fie. 9.
In this case B=0, 8’ =0.
Therefore, since L J,(w)/Y,(w)=0, the equations of § 46 reduce to
w=0
WE = at sin n(t —7),
v_ 2A Jy(w)
“h J, (na)
J,(w’)
we oe ,(na’)
C= _ 207A Jy(w)
~~ sin (t— 7).
h J, (na’)
sin n(t — 7) ;
sin (t —7) ;
: A) re).
Period equation
a?J,(na)J,(na’) + a'23,,(na’)J,(na) =0.
(79).
The nodes are given by *
Jo(w) =0 in the part O A;
AC Ol nee coe eh els
where for the »-nodal seiche
w=na, wW=n,a.
* Roots of the Bessel Functions—In what follows I shall denote the positive roots of the equation Jo(z)~0 by j,,
. aa .; and the positive roots of J, (z)=0 (excluding the zero root j,=0) by jo,Jg,Jg) +++ ++ +++ So that
we have approximately j,=2-405 an 832 , j,=5'°520 , j,=7°016 , j; =8'654 ,j,= 10173, 7,=11° 792 )Jg=13'323 , jy=
14°931 ,j,9>=16°471, etc.
For large values of % , Jn=(2n+1)x/4, approximately : ¢.g. this formula gives j,,=18°064 instead of the correct
Value 18°071 ; so that the error after n=11 is less than ‘1 ae
638 PROFESSOR CHRYSTAL
If ,v, denote the distance from O of the node in OA counting from A to O, and
yt, the like for O A’, we have
1,0 (1 — 2/4) =Jory > Jory <0
Hence
1 = iy (@ = Jor 1 7/4a2e* , Jy <1,08;
seal 2u Tata Ga. nan ee : . (80)
There will be » roots altogether; but the distribution between the two formule will
depend on circumstances. In some cases the nodes are all on one side of O. These
formule lead to some remarkable relations which are true accurately for comple
rectilinear lakes, and approximately for such as are approximately rectilinear. For
example, we have a
(a= ¢:)\a=,) = T/T.) . oa
In other words, the distance from the ends of the lake of the first node of any pure
seiche in a given complete rectilinear lake is proportional to the square of the pena of
the seiche.
Symmetric TRuNcaTED Lake.
§ 48. Here a=a’, 8=6’. The equations can be simplified by the suppression of
unnecessary constants ; and the period equation breaks up into two. We have then —
we = ALY, (nB)J,(w) — J,(nB)Y(w)} sin n(¢—7),
= 228 {YB Solve) =F4(nB)Vy(w) \ sin ne) 5
w/t! = ALY (B)J,(w") — Jy(oB)¥,(w')} sin n(¢ <2),
fe | Y (8) q(2’) — J, (mB) ¥(w") | sin n(é- =). : . Same
The period equation is :—for odd oe _
Y(f2)Tp(na) — J,(nB)Vy(na) = 5
Y,(nB)J,(na)-J,(nB)Y,(ma)=0. : . € 3).
for even nodality,
SymMMETRIC LAKE SHELVING aT Boru ENDs.
§ 49. Starting with the formule of §47, we have to put a=a/=p=p'; and
therefore a=a’. Suppressing unnecessary constants, we may now write
we = AJ,(w) sin n(t- 7),
C= MAT (w) sin n(t - 7) ;
we = AJ, (w’) sin n(t — 7) ;
Cs - =) Jo(w’) sin n(t — 7) ; : : : (84).
The period equation breaks up into . = |
J (va) => 0 ) J ,(no.) =0 fr * . . ° ° (88 ) :
Hence we have a
T,=4ra/j, J(gh). . , (86),
* These formule ire given by Lams in his Hydrodynamics (1895), § 182.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 639
For large values of v, we have
T, = 16a/(2v+ 1) /(gh) . - (D.
And, when 1/2 is negligible, simply
) T,=8a/v J(gh),
=41/v /(gh). : : : ; : (88) .
Hence, as the nodality increases, the periods of the pure seiches tend more and more
to follow the harmonic law; and ultimately are the same as the periods in a uniform
lake of double the length.
If ,2, have the same meaning as before, and ,X, have a corresponding meaning for
the ventral points, we find
1 = ,2,/@ =Joya[j? = T,?/Tors §
in, Xe 72 (27202. ; ; 5 eR
Hence, if we compare the different nodes of the same seiche, the distances of the nodes
from the end of the lake are inversely proportional to the squares of the periods of the
lower seiches of odd nodality.
If we compare nodes of the same order for different seiches, the distances from the
end are directly proportional to the squares of the periods of the corresponding seiches.
It is also easy to see from the above formule that, when the nodality of the
seiche is high, the wave lengths near the ends of the lake increase at first in
arithmetic progression.
If we apply the rule of Du Boys to the present case we get
al i-44/( ()/2 Fone =a"
Since T, = 271/7,,/(gh) , we have
a B= yl 881 5
that is, Du Boys’ rule gives too great a period, as it does in the case of parabolic
or quartic concave lakes: the deviation is even greater than in the case of a
‘symmetric parabolic lake.
As the present case is an interesting one, serving as a standard of comparison for
other cases, I add some numerical data.
Table of Ratios of Periods for a Complete Symmetric Rectilinear Lake.
T,/T, T,/T, T,/T, T;/T, T,/T, T,/T, T,/T, T,/T, T,,/T,
6276 | 4357 | 3428 | -2779 | 2365 | -2040 | -1805 | -1609 | 1460
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 25). 94
640 PROFESSOR CHRYSTAL
Positions of Nodes in one-half of the Lake.
i a0
Dole eee “ ¥ ... |°6057
Bol Oh eee nes af esto?
4 3809 8825
Bil Ol Me ae Wee SBOSO: | a cull loretliea ets “Ie eneeoune
|
Gall Sea learesal, oa. ao be Me ee ee | met
Positions of Nodes when Depth is uniform.
| : |
Lal 30 | |
| |
Pees er s ieay i Osea een eee | a EO EEE
2 ‘5000 | |
Sol Opn vied a bs ee em Gas |
uw«~ | --—-————————_- — es | a | 1). |
4 | +2500 ‘7500 |
| |
Gees ets NP ee rl ——
DallaenOy Ibe bos AO UOK tae Uhm ea Rael le ee, OCD
6) ok (G67 | a | ee | 800041) cee eer el ere
LAKE WITH ONE SLOPE.
§ 50. 0 p A
Fie. 10.
Obviously the seiches are the same as the seiches of even nodality in the symmetric
truncated lake of § 48.
Hence we have Ew = ALY, (na)J,(w) — J,(na)Y,(w)} sin n(t— 7) ;
G = 2A (¥y(na) 5 (w) —J,(na)¥,(w)} sinn(t—7). . * : (90).
The period equation is Y,(na)J,(nB) —J,(na)Y,(nB)=0. . ‘ . (OiiE
For the nodes and ventral points
1- al a Sealy:
1- yXp/Q Sie = dA bcs .
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 641
. LAKE witH ONE SLOPE SHELVING AT ONE END.
“Yl. 6) Dia A
Wie, ul
[ere we have simply to take the seiches of even nodality from the case of § 49.
Ew = AJ,(w) sin n(t - 7) ;
(= AF, (u) sin n(t—7) apts | wi (O2).
eriod equation is
J,(na) =0 ;
T,=4rajjo, /(gh). . : 6 : : (93).
1e nodes are, of course, the nodes of the seiches of even nodality in the right-hand
‘the complete symmetric rectilinear lake discussed in § 49.
following data are useful for reference in lake calculations :—
Ratios of Periods in a Semicomplete Rectilinear Lake.
T/T, T,/T, T,/T, T;/T, T,/T, T,/T, T,/T, T,/T, T/T,
5462 | 3767 | -2883 | -2327 | -1954 | 1684 | 1479 | -1319 | 1190
Positions of the Nodes.
idler .. | 6057
3809 BOC .. | 8825
2
Sas Gai) eEZOBGH| |... \O44
Positions of Nodes for Uniform Depth.
| Meee E5000
1
2a ee e200) ene se 00
3
TOG(gieese. | SO0005)" \.. w» | 8333
642 PROFESSOR CHRYSTAL
SEICHES IN QUARTIC LAKES.
~§ 52. In a paper recently published in the Society’s Proceedings (vol. xxv. p. 688,
May 11, 1905) I gave the solution of the seiche problem for lakes whose normal curve
is a quartic of the form o=A(1=-Fv’/a’). For convenience of reference I recapitulate
the results here, supposing as usual, for simplicity, that the lake has uniform breadth
and rectangular cross section, so that the expression for the depth is h x (a’=Fa2’)?.
ConcavE TRUNCATED Quartic Lake.
The origin is at O over the deepest point (see fig. 12). The length P Q is /.Band
x Q 0 le A
Fie. 12.
P and Q correspond to x=p,x=g. The depths at P, Q, and O are 7, s, d respectively ; _
as rolling 3 se 3n/l-s/9)
m/e} emer
The upper signs correspond to the case figured, where P and Q are on opposite sides
of O.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 643
Then
En(a? - #) =u= A(a?- w?)’sin {2 7 (log ~- log =) \ sin n,(t —7),
ou
CS eet : ; . mn FOD)2
and
=2rl/y /{gd(4v?7r?/k?2+1)}5 ; ; ; (96) ;
where
ACI E EA CEIVED
afitll-a pedal
i y/ ah/ siete ne)
When the end barriers P and Q approach more and more nearly to the infinitely
shallow theoretical ends A and A’, the periods of all the seiches become more and more
nearly equal to each other and to z//,/(gd), which I have called the period of the
anomalous seiche.
(97).
Convex QuartTIc LAKE.
§ 53. The symbols being defined as in § 52, we now have
mili): eral)
ba Aa & eel J 5-2) ) } =ay, say, _ (98).
Eh(a? +27)? = u = (a? + x?) sin ae =— tan” *2) i sin n,(t—T),
a
eas, : ; - , : : (99) ;
On
and Y, = 2l/y J {gd(4v?x?/k? —1)} ; : ‘ : f s (100) ;
Jl OV 4-9
z=2tnr, /(,/2- 1)- tant, /(, /4-1). ; : acy.
§ 54. In constructing a theoretical curve to represent the normal curve of any lake
deduced from bathymetric data we can, of course, combine pieces of parabolas, straight
lines or quartics at will; and the variety of formule above given is probably sutfticient
for most practical purposes, although the labour of the calculation, even in simple cases,
isnot small. To this part of the subject I shall have occasion to return in subsequent
communications to the Society.
where
644 PROFESSOR CHRYSTAL j
PARE Te
A SKETCH OF THE BIBLIOGRAPHY OF SEICHES.
The following list of books and memoirs dealing with Seiches does not claim to be
where I myself have felt the need of help.
What may be called the ancient history of seiche observations is fully dealt with by
of the information for that period. I must also acknowledge obligations to papers by
Haprass, mentioned below, and to Messrs CaumMLEy and Maciacan WEDDERBURN,
both connected with the Scottish Lake Survey, for many of the later references, |
The following abbreviations are used :—
A.G., Archives des Sciences Physiques et Natu- B.V., Bulletin de la Société Vaudoise des Sciences
relles, Genéve. Naturelles. ;
A.H., Actes de la Société Helvétique des Sciénces C.R., Comptes Rendus del Académie des Sciences,
Naturelles. Paris. I
A.Hy., Annalen der Hydrographie. P.M., Petermann’s Mittheilungen.
A.W., Sitzwngsberichte der K.K. Akadenue der Z.G., Zeitschrift fur Gewdsserkunde.
Wissenschaft, Wien. ZL, Zeitschrift fiir Instrumentenkunde.
B.A., British Association Reports.
The Roman numeral indicates the volume, the Arabic the page.
1755. Disturbances of the Levels of Lakes in Scotland and elsewhere caused by the Earthquake of Lisbon,
Scots Magazine for 1755. =|
These notices are interesting, because there is, as yet, little evidence connecting seiches with |
seismic disturbances ; in fact, none at all in the case of ordinary seiches. .
1776. Lapnace. “Sur les Ondes. Suite des Recherches sur plusieurs points du Systeme du Monde,”
§ xxxvii., Hist. de l’Ac. Roy. d. Sc. Paris, Année 1776. '
The modern mathematics of wave motion may be said to date from Lapnacs#’s researches on
the tides. In the memoir quoted he considers waves in a canal of uniform depth to be caus
by the immersion of a given object, and arrives at the expression ,/{g tanh mh/m)} for the velocity
of wave propagation. But, as he does not consider oscillatory waves, the connection of m with
the wave length is not made clear. 1
1781. Lagrance. “ oie la Théorie du Mouvement des Fluides,” Mém. Ac. Berl.
for the elcity of aN hs in a canal of uniform depth, h.
1804. Youne. Lectures on Natural Philosophy, xxiii. Also Works (ed, PEacock), ii. pp. 141, 262.
1815. Caucuy. “Sur la Théorie des Ondes.” Ovwvres, 1° sér., i. 175.
1815. Poisson. ‘Sur la Théorie des Ondes,” Mém. d. l’Inst., i. (1816), etc.
In the works of Caucny and Poisson the mathematics of wave motion has already talent
modern form. Both have Lapnacn’s formula for velocity of propagation, but both are p
occupied with the difficult problem of Lapiacn, and do not consider oscillatory surface way
either progressive or stationary.
1825.
1828.
1837.
1837.
1839.
1843.
1845.
1846.
1873.
1874.
1875.
1875.
1876.
1876.
1876.
1876.
1877.
4
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 645
Weser, W. HE. and E. H. Dive Weillenlehre auf Hxperimente gegrundet, Leipzig.
This treatise is a classic in the experimental part of our subject. Here for the first time
direct observations of the motion of the fluid particles in wave motions are described A great
variety of different cases of wave motion are discussed; and in particular, standing waves in
a canal, of which seiches are a particular example.
Merian, J. R. Ueber die Bewegung tropfbarer Flussigheiten in Gefdssen. Basel.
This memoir was really the first after Lacranex that dealt fully and effectively with the
problem of stationary waves in a canal of uniform depth (h) and length (7). In Merran’s paper
the formula T= ,/{zl/g tanh (zh//)} appears for the first time in connection with stationary
waves. Its relation to the formula of LapLacz, Caucuy, and Porsson for the velocity of propa-
gation is obvious. Unfortunately the memoir attracted no attention when it was published, and
was forgotten until it was reproduced by the author’s grandnephew, Von per Mtut, Math. Ann.,
xxvill. 575, 1885. Meanwhile Mrrran’s results had been rediscovered by other mathematicians.
Russeti, Joun Scorr. His beautiful experiments on canal waves, described in the B.A. Reports
from 1837 onwards, were the starting-point of a long series of English researches by GREEN,
Kennanp, Arry, Stokes, Kervin, Rayieren, and others.
Green, G. “On the Motion of Waves in a variable Canal of small Depth and Width,” Trans. Camb.
Phil. Soc., 1838. Also ib., 1839.
Ketnanp, P, ‘‘ On the Theory of Waves,” 7rans. Roy. Soc. Edin., xiv., 1839. Also 2b., xv., 1841.
Ming, D. ‘On a Remarkable Oscillation of the Sea,” July 1843. Trans. Roy. Soc. Edin., xv. 609.
Airy, G. B. ‘Tides and Waves,” Ency. Metrop.
Stoxes, G.G. ‘‘ On Recent Researches in Hydrodynamics,” B.A., 1846.
Airy’s Article and Sroxss’ Report are classics on the analytical side of our subject.
Forex, F. A. “ Premiére Etude sur les Seiches,” B.V., xii. 213.
Srantpercer. Lbbe und Flut in der Rhede von Fiume, Budapest.
Foren, F. A. ‘ Deuxiime Etude sur les Seiches,” B.V., xiii. 510. Also A.G., liii, 281.
Gururiz, F. “ Periods of Oscillation of Water in Small Tanks,” Proc. Phys. Soc.,i. Also Phil,
Mag., Oct. and Nov. 1875.
Rayueies. “ Periods of Oscillation of Water in Tanks,” Phil. Mag., 5th ser., vol. i. p. 275.
Forgn, F. A. “Les Seiches, Vague d’Oscillation fixe des lacs,” A.H., Andermatt, 157. Also Anm.
Chim. Phys., 1x., 1876.
Forrt, F. A. ‘ Le Limnimétre enregistreur de Morges,” A.G., lvi. 305.
Foret, F. A.‘ La Formule des Seiches,” A.G., lvii. 278.
Airy, G. B. ‘On the Tides at Malta” (Seiches in the Sea at Malta and Swansea), Phil. Trans.,
169, pp. 123-138.
. Puantamour, Pu. “ Notes sur quelques Observations limnimétriques faites a Sécheron,” A.G.,
lvili, 302.
. Gresey. “ Versuch einer Mathematischen Darstellung der Flissigkeitswellen,” Schl. Zedtsch. 7. Math.,
xxii. 133.
. Foren, F. A. “Essai Monographique sur les Seiches du Léman,” A.G., lix. 50.
. Puantamour, Pu. “ Note sur la Limnimétrie, & l’occasion du tremblement de Terre du 8 Oct. 1877,”
A.G., Ix. 511.
. Foret, F. A. ‘‘ Contributions 4 la limnimétrie du Léman,” B.V., xv. 160.
. Foret, F. A. “Les Causes des Seiches,” A.G,, lxiii, 113, 189.
. Foret, F. A. ‘“ Les Seiches des Lacs et leurs Causes,” C.R., lxxxvi. 1500.
. Foret, F. A. “‘ Seiches and Earthquakes,” Nature, xvii. 281.
646
1878.
1878.
1879,
1879.
1879.
LSToe
1880.
1880.
1880.
1880.
1880.
1881.
1881.
1882.
1885
1885.
1885.
1886.
1887.
1887.
1888.
1888.
1888.
1890.
1831.
Soe
1891.
189i:
1891.
1891.
1891.
1891.
PROFESSOR CHRYSTAL
Puantamour, Pa. “Le Limnographe de Sécheron,” A.G., lxiv. 318.
Gavutinr, E. ‘The Seiches of the Lake of Geneva,” Mature, xviii. 100.
Foret, F. A. ‘Le Probleme de l’Euripe,” C.#., lxxxix. 859. Also Za Nature, VIIL., i. 35.
Foret, F. A. ‘Les Seiches, Vague d’Oscillation fixe des Lacs,” A.H., Berne.
PLantamour, Pa. ‘‘Seiche Occasionnée par le Cyclone du 20 Fev. 1879,” A.H., Berne, i. 335.
Sarasin, Ep. ‘‘ Limnimétre enregistreur transportabie, Observations a la Tour-de-Peilz, prés Vevey,”
A.H,, Berne, 1. 724.
Kircnnorr, G. ‘‘ Ueber stehende Schwingungen einer Schweren Flussigkeit,” Wied. Ann., x. 34.
Along with G. Hansemany, ‘‘ Versuche tiber stehende Schwingungen des Wassers,” 2b., 337.
They do not deal with long waves, but it is interesting to compare their results with those
given in § 49 of this Memoir.
Foret, F. A., et Soret, J. L. ‘ Les Seiches Dicrotes,” A.H., Berne, iii. 15.
Foren, F. A. ‘‘Seiches et Vibrations des Lacs et de la Mer” (Seiches on the Sea), C.R., viii® session
Assoc. Fr, pour Av, d. Sc., 493.
Sarasin, Ep, ‘“Tracés Limnographiques dans diverses Stations du Léman,” A.G., iv, 383.
Carrger, S. J. ‘‘ Tidal Phenomenon in Lake Constance,” Mature, vol. xxi. p. 397.
Hann, J. Allgemeine Erdkunde, Prag.
Hicks, W. M. “Recent Progress in Hydrodynamics,” B.A.
MuiaovAns, A. A. Ilepit ris TlaAXipotas tod Hipirov. “Ev AOnvass.
Gtntuer, 8S. Lehrbuch der Geophystk, 1. Stuttgart.
RussELL, H. C. ‘On the Seiches of Lake George, Australia,” Roy. Soc. N.S.W. Ann. Add., 13.
Foret, F, A. “La Formules des Seiches (Les Seiches du Lac George, les Seiches longitudinales du
Léman),” A.G., xiv. 203.
Sarasin, Ep. ‘ Tracés Limnographiques du Lac de Zurich,” A.G., xvi. 210.
Krimugz, O. Handbuch der Oceanographie, Stuttgart.
GREENHILL, A.G. ‘‘ Wave Motion in Hydrodynamics,” Am. Jour. Math., ix.
Kriuuet, O. “Zum Problem des Kuripus,” P.d,, xi. 331.
GtnrHer, S. ‘“ Von den rhythmischen Schwankungen des Spiegels geschlossener Meeresbecken,”
Mitth. d. K.K. Geog. Soc. Wien, 497.
Sigcgr, R. Die Schwankungen der hocharmenischen Seen seit 1880, Wien,
GraBLovitz, G. ‘‘ Ricerche sulle Maree d’Ischia,” Rend. Acc. d’Lincet, 29, 359.
GraBuovitz, G. ‘‘ Le Isorachie della Marea nel Mediterraneo,” Rend. Acc. d. Lincet, 1891, 135.
Mariner. “ Lo Studio delle Sesse nei Laghe Italiani,” Riv. Geog. Ital., vii. 10.
Puantamour, Pa. “ Effets du Cyclone du 19 Aofit 1890 sur le Lac,” A.G., xxv, 302.
Foret, F. A. ‘“ Note sur la Formule des Seiches,” A.G., xxv. 599.
Du Boys, P. “Sur le mouvement de Balancement rythmé de l’Hau des Lacs (Seiches),” C.&., exii.
1202.
Du Boys, P. ‘“‘ Essai Théorique sur les Seiches, avec Appendice par F, A. Forel,” A.G., xxv. 628.
Sarasin, Ep, ‘‘Remarques sur les Seiches Binodales, a propos de lEssai Théorique de M. du
IBowsy0 Al Ga xvas Olle
Ponusapoy. “Sur les changements périodiques en niveau des lacs du district de Bourowitchy,
Gouvernement de Novgorod” (in Russian), Rev. Sct. Nat, 293.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 647
1892. Sarasin, Ep. “ Les Seiches du Lac de Neuchatel,” A.G., xxviii. 356.
1892. Burton, W. K. “Notes on Seiches observed at Hakone Lake,” Trans. Seism. Soc. Japan, xvi. 49.
1892. Horn, A. von. ‘Ueber den Einfluss von Windrichtung und Luftdruck auf den Seespiegel,’ A.Hy.,
xix. 498.
1892. Carson, A. “The Rise and Fall of Lake Tanganyika,” Quart. Journ. Geol. Soc., xlviii. 401.
1892. Grasiovitz, G. ‘“‘Sulle Observazioni Mareographici in Italia e specialmente su quelle fatte in Ischia,”
Att. d. 1° Cong. Geog. Ital.
1892. Stmcer, R. “ Niveauveranderungenan skandinavischen Seen und Kiisten,” Verh. 9th Deutsch Geogr.
Wien, 224.
1892. Brickner, E. “ Ueber Schwankungen der Seen und Meere,” Verh. 9th Deutsch Geographentag, Wien,
1892, 209.
1892. SziKuay, J. “ Oscillations de niveau du lac Balaton, 1890” (in Hungarian), Bull. Soc. Hong. Geog.,
xix. 366.
1892. Finrror, N. ‘‘ Ueber die Schwankungen des Spiegels des Kaspischen Meeres” (in Russian), Russ.
Geogr. Soc., Xx.
1893. Simcpr, R. ‘“‘Seeschwankungen und Strandverschiebungen in Skandinavien,” Zeitsch. Ges. Erdk.
Berlin, xxviii.
1893. Stmczr, R. ‘The Rise and Fall of Lake Tanganyika,” Quart. Jour. Geol. Soc., xlix. 579.
1893. F. A. Foret. ‘“ Die Schwankungen des Bodensees,” Schriften des Vereins fiir Geschichte des Boden-
sees, Xx1i., Lindau.
1893. Parkins, E. A. ‘The Seiche in America,” Amer. Met. Journ., x. 251.
1893. Sarasin, E. “ Des seiches de Neuchatel, A.H., lxxv. 38.
1894. Cuounoxy, E. von. “ Bericht iiber die Ergebnisse des selbstregistrirenden Wasserstandmessers am
Plattensee” (in Hungarian), Féldr Hozl, Budapest, xxii. 148. Abrégé, Bull. Soc. Hongr.
Geogr., xxill. 39.
1894. Bauoxr, W. ‘“ Die Niveau-Schwankungen des Geoktschai-Sees,” Globus, xv. 301.
1894. Utz, W. “ Beitrag zur Instrumentenkunde auf dem Gebiete der Seenforschung,” P.IZ, xl. 213.
1894, Prins, HE. A. ‘‘Seiches in Lake Michigan,” Am. Meteor. Jour.
| 1894-5. Sarasin, E., and Pasquin, L. pu. ‘‘Les Seiches du Neuchatel,” A.G., xxxi. 213, xxxiii, 193;
Bull. Soc. Sci. Nat. Neuchdtel, xxi., xxiii.
1895. Sarasin, E. ‘‘ Les seiches du lac de Thoune,” A.G., xxxiv. 368.
1895. Dawson, W. Betu. ‘“‘ Notes on Secondary Undulations,” Proc. Roy. Soc. Canada, May.
1895. Macraruane, J. H. R. “The occurrence of Seiches in Lake Derravaragh, Co. Westmeath, 1893-4,”
Sct. Proce. Roy. Dublin Soc., N.S., viii. 288.
1895. Lams, H. Hydrodynamics. Cambridge.
1895. Foret, F. A. Le Léman, Monographie Limnologique. Lausanne, t. ii., sixieme partie, pp. 1-288.
These pages form a treatise on Seiches, recording the work of the author and his followers
during a period of more than thirty years; they must always remain the great classic of Seiche
literature.
1897. Denison, F. N. “Secondary Undulations of Tide Gauges,” Proc. Can. Inst., i. 28.
1897. Denison, F. N. “The Origin of Tidal Secondary Undulations,” 70., i. 134.
1897. Duvison, F.N. ‘The Great Lakes as a Sensitive Barometer,” 20., i. 55.
1897. Denison, F.N. “‘Seiches in Lakes Ontario and Huron,” Rep. Brit. Ass.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 25). 95
648
1897.
1897.
1897.
1898.
1898.
1898.
1898.
1898.
1898,
1898.
1898.
1899.
1899.
1899.
1899.
1900.
1900.
1900.
1900.
1900.
1900.
1900.
1901.
1901.
1901.
1902.
PROFESSOR CHRYSTAL
Cuotnoxy, E. Limnologie des Plattensees. Wien, 1897.
Besides giving an account of the seiches in a long and very shallow lake, the paper contains -
observations and conclusions of great importance regarding the non-rhythmic denivellation of a
lake by the wind. It also describes observations of great interest on lake currents ; the first, so
far as I am aware, made with a self-recording apparatus.
SARASIN, Ep. ‘Les Seiches du lac des Quatre Cantons,” A.G., iv. 458.
Foret, F. A. ‘Les Seiches des Lacs et les Variations Locales de la Pression Atmosphérique,” A.G., iv.
Darwin, G. H. The Tides and Kindred Phenomena in the Solar System. London.
Sarasin, Ep. “Les Seiches du lac des Quatre-Cantons,” A.G., v. 389, vi. 382.
Votterra, V. “Sul fenomeno delle seiches,” ZZ n. Cimento (Pisa), viii. 270.
Kuerper, W. ‘“ Studien zur Wasserstandsprognose,” Z.G., i. 10, 129.
Denison, F. H. ‘“ Periodic Fluctuations on the Great Lakes,” Monthly Weather Rev. Washington,
xxvl. 261.
Wueeirr, W.H. ‘‘ Undulations in Lakes and Inland Seas due to Wind and Atmospheric Pressure,”
Nature, lvii. 321.
Hotmsen, A. “‘Seiches i norske Indsjger,” Arch. Math. Naturvid (Kristiania), xx., No. 1, p. 28.
“‘ Steigen des Wasserspiegels im Urmia-See,” Met. Zeitschi. (Wien), xv. 80.
Scnutz, K. Bertrdge zur Kentniss des Gmunden Sees, Gymnasial program, Gmiinden.
Sarasin, Ep. ‘“ Les Seiches du lac des Quatre-Cantons,” A.G., viii. 382, 517.
Foret, F. A. ‘Les Seiches des Lacs,” Verhandl. d. vii. internationalen Geographen-Kongresses im
Berlin, 1899.
Ricuter, E. “‘ Stehende Seespiegelschwankungen (Seichen) auf dem Traunsee,” P.M, xlv. 41.
Evert, H. ‘“ Periodische Seespiegelschwankungen beobachtet am Starnberger See,” Stézwngsberichte
der Math. Phy. Classe der k, bayer. Akademie d. Wissenschaft, xxx. 435.
Starnberg is a highly interesting example of a concave lake (T,/T, =*632, which exceeds the
corresponding ratio for a complete symmetric rectilinear lake). As its configuration is well known
from Ule’s Atlas, it is to be hoped that the Bavarian observers, to whom we already owe so
much, will return to the investigation, work out the uninode and binodes, and also the seiches of
higher nodality, and trace the meteorological conditions under which the various seiches occur.
Berton, P. “Studi Limnografici sulle Sesse del Lago di Garda,” Comm. d. Ateneo d. Brescia.
Futitesorn. “Seiches on Nyassa,” quoted by Forel from Verh. d. Gesellsch. f. Erdkunde, XXViil.,
Berlin, 1900.
Bure, L., and Ianatov, P. “Sur les variations du niveau des lacs en Asie centrale et en Siberie
occidentale,” Russ. Geogr. Soc. St Petersburg, xxxvi. 111.
Henry, A. J. ‘‘Lake Levels and Wind Phenomena,” Monthly Weather Rev. Washington,
Xxviil. 203.
Foret, F. A., et Sarasin, Ep. Les Oscillations des Lacs. Rapport présenté au Congrés international
de Physique. Paris, 1900.
Sarasin, Ep. “Les Seiches du lac des Quatre-Cantons,” A.G., x. 454.
SARASIN, Ep. “Les Seiches du lac des Quatre-Cantons,” A.G., xi, 161, xii. 254.
Expert, H. “Periodische Seespiegelschwankungen,” Sétaungsber. Math.-Phys. Kl. Akad. Wiss.
Miinchen.
Eserr, H. ‘‘ Sarasin’s neues selbstregistrirendes Limnimeter,” Z./., xxi. 193.
Sarasin, Ep. “ L’Histoire de la Théorie des Seiches,” Discowrs d’ Ouverture de la 85 Session Annuelle
de la Soc. Helv. d. Sc. Nat. & Geneve, Sept. 8, 1902.
Pe
q
1902.
1902.
1902.
1903.
1903.
1903.
1903.
1903.
1904,
1904.
1904.
1904.
1904.
1904.
1904.
1904.
1904,
1905.
1905.
ON THE HYDRODYNAMICAL THEORY OF SEICHES. 649
Hatsrass, W. ‘ Stehende Seespiegelschwankungen (Seiches) im Madiisee in Pommern” (2 parts), Z.G.,
v. 15, vi. 65.
This Pomeranian lake is concave (T,/T, =‘566), and of comparatively regular form. Hats-
Fass’s results are of great interest ; and it would be of importance to complete the bathymetric
data, so that the seiche phenomena could be more thoroughly discussed.
Henry, A. J. ‘“ Wind Velocity and Fluctuations of Water-Level on Lake Erie,” U.S. Weather
Bureau Bull. J.. No. 262.
Nakamura, S., and Yosumpa, Y. ‘On the Seiches of Lakes Biwa and Hakone,” Tokyo Phys. Math.
Soc., No. 15, p 115.
Nakamura, S,, and Yosuipa, Y. ‘‘ On the Seiches of Lakes Biwa and Hakone, Tokyo,” A.G., 559.
Enoros, A. Seeschwankungen beobachtet am Chiemsee. (Dissertation.) Traunstein, 1903.
One of the most complete examples of the exact observation of seiches known to me.
Also Z.J., June 1904, 180.
Bruyant. ‘Les Seiches du lac Pavin,” Rev. d’ Auvergne.
Vatentin, J. “Seiches in Riva on lake Garda,” Wiener Anzeiger, 1903, p. 93. Also A. W., April 3,
1903.
Mactacan -WepperRBuRN, E. ‘“ Seiches observed in Loch Ness,” Proc. Roy. Soc. Ed., xxv. 1.
Hauprass, W. “ Seiches oder Stehende Seespiegelschwankungen,” Natwrwissenschaftliche Wochen-
schrift, 11. 881. See also i. 127.
An excellent popular account of the present state of our knowledge of seiche phenomena.
Foret, F. A, ‘Sur les Seiches,” Hat. B.V., xl. 149.
Patazzo, L. “ La Stazione Limnologica de Bolsena,” Boll. Soc. Geogr. Ital., v.
Haxprass, W. “Les Seiches du Madusee en Poméranie,” A.G., xvii. 281.
Hatprass, W, “ Hine bemerkens-werthe Verbesserung des Sarasinschen Limnimetre enregistreur por-
tatif,” P.M, heft v.
Gtnruer, R. T, ‘ The Limnological Stations on the Lake of Bolsena,” Nature, xx. 455.
Enpros, A. ‘“‘ Seiches Kleiner Wasserbecken,” P.M, heft xii, 294.
Curystat,G. “ Some Results in the Mathematical Theory of Seiches,” Proc. Roy. Soc. Ed., xxv. 328.
A brief abstract of part of the present paper.
Crostuwait, H, L. “ Seiches in Lake San Martin, Patagonia,” R. Geog. Soc. Lond., March 1904.
CurystaL, G, ‘Some further Results in the Mathematical Theory of Seiches,” Proc. Roy. Soc. Ed.,
xxv, 637.
Maerini, G. P. “TI Recenti Studi sulle Sesse ; e le Sesse nei Laghi Italiani,” Riv. Geog. Ital., xii.
Pa.
?
—pe
ico)
-XXVI.—On a Group of Linear Differential Equations of the 2nd Order, including
Professor Chrystal’s Seiche - equations. By J. Halm, Ph.D., Lecturer on
Astronomy in the University of HKdinburgh.
(MS. received May 20, 1905. Read June 19, 1905. Issued separately July 31, 1905.)
It is readily seen that the two differential equations
a
(1 -w2) 54 +n(n — ly =0 (1)
1 2 a Uy I 7 =0 92
(1 +07)? Tetn(n + 2)y= (2)
which play an important réle in Professor Curysrau’s mathematical theory of the
Seiches, are special cases of the more general type
d?y dy
el — w?) a ~ (2a+ lw a +n(n + 2a)y=0. (3)
With regard to the first, the Seiche-equation, this becomes at once apparent by writing
a@=-—%. Equation (2), on the other hand, which we may briefly call the Sroxzs-
equation [see Professor CurysraL’s paper on “Some further Results in the Mathe-
matical Theory of Seiches,” Proc. Roy. Soc. Edin., vol. xxv.| will be recognised as a
special case (a = + 1) of the equation
d*y
2)2
(1 +2") da?
d
— (2a -2)0(1 +22) +n(n + 2a)y =0 ; (4)
0
which is transformed into (3) by the substitution x= aaa
It appears, therefore, that the Seiche- as well as the Stoxns-equation belong to the
same family of differential equations whose general form is given by (3). We may
write the latter also
te ay
er 2a tan 27, + n(n + 2a)y=0 (5)
ifwe substitute w=sinz or «=tanz. Corresponding to this equation we have further :
GEO) d
art 2a tanh 2 + n(n + 2a)y=0 (6)
which for w=sinhz and a=-—4 leads to the hyperbolic Seiche-equation :
q2
(1 +102) TS + n(n —1)y=0 (7)
and for «=tanhz and a=+1 to the “hyperbolic” Sroxus-equation :
2 d?y
(1 - x?) Gat Mn+ 2)y=0. (8)
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26.) 96
652 DR J. HALM
From (5) and (6) the solutions of the SroxEs-equation may at once be derived. a
we write, in accordance with Professor Curysrat’s notations, n(z+ 2) = 40 a: and
consider that (5) is identical with
d
ETE ae +1)? [y cos z]= OF,
we find the general solution
Y= = |. cos (202) + D sin (202) if
COS @
or since z= tan~’ x,
y = (1+)? (C. cos (20 tan?) + D sin (20 tan-1 2’) ].
In the same way we find from (6)
d*ly cosh ly,
de
n?—2n—1)[ycoshz]=0,
and, writing n’?+2n—1 = 40’,
Vea ae cos (20z) + D’ sin (2%) |
which, since z= tanh™* «= 1 log 1 +4 i= , becomes
y= (1-28 ¥, cos( 8 fog 1 = + D’sin (2 log a as alk 3 (10)
(9) and (10) are identical with (26) and (i2) of Professor CuRysTaL’s paper quoted
above if - is substituted for z.
It is also at once evident that if we express the Stoxss-functions by means of the
variable w instead of «, we find the general solutions : |
d d dY
W=AT | cos (20 sin w) | ea [sin (20 sin7! w) ] = al , say,
and
dV,
d
=A 55 rp | 008 (2 sinh"? w) [+B Fg | sin (26 sinh™ tw) |= ae
dw
This result is made evident if we consider that Y, and Y, satisfy the well-known differ-
ential equations
PY, a¥,
(1 ~w) =F — w= 4 4eY, =0
aFY, AY
ene ease) ONE ==
+ w ae +4Y,=0,
(1 + w?) ho
which, by differentiation with regard to w, assume the form :
oh pe ee
ayy
yes
(1 ee
(1+ wry TY yop 30 aoe (407 + 1)y,=0,
and become identical with the ane if x is introduced instead of w.
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 653.
Seeing that it is possible to refer the four differential equations of the Seiche-problem to
one and the same general equation, viz., that given under (3), it may be of interest to dis-
euss here the properties of this in many ways remarkable general type, and to derive its
_ particular solutions. The results obtained seem, on the one hand, to be of practical value
in regard to the computations involved in the evolution of the periods and nodes of the
seiches, while, on the other hand, the mathematical investigation here given establishes
an important relation between the Seiche-functions discovered by Professor CHRYSTAL
and other functions frequently used in mathematical and physical problems, notably
those of LEGENDRE, a relation which increases the importance of the Seiche-functions
from the mathematical point of view. It will be recognised at once that equation (3)
is a special case of the hypergeometric differential equation
p I
ol — 0) 55 +[y- (a+ B+1)o] S4- aby =0, (11)
whose solution is represented by the contour-integral
a- -B-1 —a
y=const x [ U "ew: (w—v) du (12)
Cc
C 0 i
Indeed, if we substitute v= == and a=n+2a,8=—1, y=a+4 we have
Belen dy
(_- wo?) 4 —(2a+ Lae + n(n + 2a)y=0 (3)
which, by introducing «= ou under the sign of integration in (12), is satisfied by the
integral
(ue are -4
= const x bai Ae
Jo (t we Wyre
Gin (13)
If we write
w= (il SUP) BeNe
we find easily that Y is a solution of the equation :
ON, aY
(1 — Ww) Fp t 2a - 3) Fp t (m+ 1) (n+ 2a-1)Y=0,
and hence, substituting in (11) and (12) a=n+1, B=1—n-2a, y=3-a:
(1 = Na |
Yeconstx {Gaye t,
‘so that we find as another solution of (3) :
ee (1 — f?)\nt+a-%
y = const x (1 — w?)? Ww o G-upn (14)
For a=4, the integrals (13) and (14) become identical, viz.,
(1 -#)"
y= const x bs (t zs wrth
654 DR J. HALM
This is ScHLAFLI'’s contour-integral of the LEGENDRE-functions, which thus is seen to
satisfy the differential equation :
dy d
(1 = 2) 4 98 n(n On (15)
Our general equation (3) includes therefore also the LecENDRE-functions. If we denote
the solution of (3) by the symbol C,*(w), the Seiche-functions are represented by
C,-(w), the Lecenpre-functions by C,}(w), and the Sroxxs-functions by C,'(w). |
Since (3) is a special case of the hypergeometric differential equation, its integrals
can be at once expressed by hypergeometric series of the type F(a, 8, y¥; w). From
Jacosi’s schematic table of particular solutions given in his “ Untersuchungen tiber die
Differentialgleichung der hypergeometrischen Reihe,” Crelle’s Journal, vol. lvi., we
obtain thus the following 24 possible integrals of equation (3) :—
1+w\i-¢ l-—w
2. aes xF(g-n-a, f+nta,at4; 3")
+ w\-n-2a w—1
3. ee xF(n42a, busta, at; )
2 w+
4. (") xF (=n, k-n-a,ath; ary)
2 w+il
Grove II.
1 — w\-?-24 w+_ti
il. ( 5 ) xP (n+2a, ktnt+a, at+4; e+)
1-w\" w+l
2) = em =
;. ( 2 ) x F( en PO aa w 7)
x ey eam
3 F(u+2a, —N, a+5; 9
4-0 ;
4, i x P(S+n+a, $-n-a, a+}; a
Group ILI.
i (45%) xF(n+2a, d+nt+a, 2n+2a+1; a
2 l-w
=p=Gi= —a 2
2; io (iy x F(1+n, d+atn, 2n+2a+1; )
2 2 l-w
: l+w —n—2u e 1 9 p 2 ) 16 P
3, ( ) x F (n +20, 4+n+a, a comer (16)
a 4-a —n—a-} 9)
ae —— xF(Jtnta, l4n, n+2a41; >)
4
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 655
Group IV.
ite = eyxF(-n, 4-n—-a, 1-2n-2a; Z )
]-—w
Oe) o x F(1-n-2a, £-0-@, 1—2n~ 2a; : )
l-w
as w
n »)
xF (=n, b-n-a, 1-2n-2a ;—— )
l+w
0 — n+a—}
-
LENS FON
—
>
s
Py ‘7 2
x (A-n-a, 1=n—2a, 1—2n -2a; 3)
Groupe V.
lige 2 l-w
aera aes )
ap\4-e a
) x F(1-n-2a, ie eae a
h-a w =e ; w-l1
ae y xF(ftnea, l+n, 3-a; mel
— x F(4 —n—-a, 1-n-2a, 3-a; =)
So
i
bo
PN La ES aN
—
we
=
a. a a
4
aa
—
bo| +
Ss
Group VI.
Ey 1 eer eer mr)
5} 5) w—1
| 7h ipa emeemebanaes
That these integrals cannot all exist at the same time is evident, the convergence
of the F-series depending on the values of n and c. It is easy, however, to find in each
single case those series which represent convergent solutions of the differential equation.
With regard to this point I may refer to Jacosr’s treatise, from which the conditions of
convergence may at once be obtained. We notice that the above solutions may be
arranged in pairs, which differ only by —w being substituted for the positive value.
The necessity of the existence of such pairs is obvious, since the differential equation
(3) remains unaltered if —w is substituted for +w. Since we are also permitted to
write —n—2c for n without changing the equation (3), we have on the whole the
following eight particular solutions, from which the others are obtained by the substi-
tutions just mentioned.
656 DR J. HALM
F(n+2a, -n,at+4; =)
(C4")'F(-n, $—n-a, 1-2n-2a; z )
2 liw
= 4—a n+a—h
(5°) | F(}-n-a, l-n-2a, 1-2n-2a; a) (16a)
eso) * F(Q+n+a, t-n-a, 2-a; ==")
3") (GS) F(1 -n—-2a, l+n, 3-a; =
a ee F(1-n-2a, L_—n-a, 3B_q; 7)
DB} 9 = w+i
Note added on June 30.—The sixth integral in (16a) agrees with Professor
CurystaL’s Lake function, which is obtained by substituting a= —3, n(n—1)=c and
! = =z, so that Lic, z)=z F(n, 1—,2; z). The other corresponding integral is re-
presented by No. 1 of (16a), viz., F(n—1, 7,0; 2), but it belongs to the exceptional
class y=0 of the hypergeometric series, and has a logarithmic form (see Professor
Curystat “On the Hydrodynamical Theory of Seiches,” § 41). The corresponding
solution of the LecENDRE-function (a=4) is F(n+ 17, 1k 7 a well-known ex-
pression for the LecrnprRe-function of the first kind. (See Waurrraker, Modern
Analysis, § 118.) In this case Nos. 1 and 6 of (16a) are identical.
Reverting to equation (11), we notice that it may be transformed into (3) by still
another substitution, viz., by v=w’, a =5+ Gh | -5 , and y=4. Hence we obtain
24 other particular integrals of the following type :—
Group I,
n n
1 F (+a, io 4; w?)
a ln ln
2. (1-w?) xB(5-5-4, ata, 4; w?)
2 Na w
4, (l-w’) x F Ba oe 2 ce 77)
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER.
Group II
4 n Lez w?— 1
1 wr" x FG +a, atta, Rta; Ta )
Ps fm ll @ w?— 1
2 Ww xF(-5 ps Eta; AE )
3 E(j+a, a5: 4 ; (1-w*))
Nh @ 1 3
4 wxF(o +o +a, 9° b+a; (1-%))
Group III
1 wrx F( Sa, t+ Sea, nta+l; 5)
—n— a 1
2 (1 — w2)} xF(14 9 54%, ntatl; :)
-t—a 7% 1 1
3. (1 -w?) * xE(S+a,544, n+atl; =)
SUL epics 1 n nm 1
4, w(1 — w?) 2 7 xF(Zt+$+e are n+a+1; a
Group IV
] wx F(-2, 5 >? L-n-a; 4)
n+2q—1 2\}-a n 1 ee
2. w (1 — w?) xF(1-4 a, 5-4 -a, 1-n-a; =)
eee sea
3 Nes SSG aap eae) l-w
4 ww)? x R(o- 1-2 -a, 1-n-a Z )
) Die 2 2 1 —w?
Group V
I Ww: xE(5 +2 +a, ak, 8; uw?)
2 w(1 — Le ae 14+, 3; w)
1 n OF
3 w(1—-w) ? (Stk es Lae ia)
4 (1—w? B(4-& ee a)
w 2) x BE 1G) b 5} A Oe |
Group VI
1. wht20-1(] — ay2)8-4 ye BF il (eee 3 _w-)
. w (hai ix oe a ee Poa me
aoe ze, 1 2]
= 2. wi" (1 — w?)t eee 1+%, g-a;" 5")
= Liven te
3. (1 — w?)? Mois wa ee)
4 (1 = v2)" x F (1 —— 1+, 3-4; (1- w?))
657
(17)
658 DR J. HALM
The first of Group I. corresponds to Professor CHrysta.’s Seiche Cosine, and the
first of Group V. to the Seiche Sine. Since for the Seiche-functions a= —}, we have
Melson e 2
Seiche Cosine= F (” wise Lae wv?)
Seiche Sine =wF & Ae Ae w?)
Se ta ac ae
or
; meee ue 1) 2 n(n — 1)[ n(n — 1) - 1.2), 4 Un - 1)[n(m — 1) — 1.2][m(m — 1) - 3.4]
Seiche Cosine = 1 — Sea ee eam Lix34x56 wee...
: ¢ pes a = 3 4 Un — 1)[m(m — 1) - 2. 3], 5 — n= 1)[n(m - 1) - 2.3][ n(n — 1) - 4.5), 1
RES ie a Wms i 2.3.x 4.5 2.3% 4.5 x67
or finally, if we write for n(n—1), which is the factor of y in the Seiche-equation, the
symbol c, in accordance with Professor CurysTat’s notation :
; Meee Op OSI) rhe c(c — 1.2)(¢— 3.4)
Seiche Cosine = 1 ie? jes ks i Sa eTaae he te tea
Seiche Sine =w- c¢ Homo re 2.3) ys — he = 2.3) = 4.5) 7 Ae
23° 2-3 x 4.5 2.3x 45x 6.7
Let us denote generally
n n
Cos, ()) = HE +a,-%,4; uv’)
, i o@ 1 : \
Sin, (w) = wF( 5 soy, 5 3; w?) (18)
then we have :
Cos_, (wv) = Seiche Cosine =1 — oie 2 0) w? + (¢+]. O)(e = 1.2) wt — (c+ 1.0)(¢ — 1.2)(¢ - 3.4) wo +.
1.2 x 3.4 1.2 x 3.4 x 5.6
n(n — 1)
Cos, () = Cos(nsinn) = 1 ——— Ba. es Mel (c + 0.0)(¢ — 2.2)(c—4.4) ie
: 1.2x 3.4 1.2x3.4x5.6
c=ne
Cos, (w) = Legendre Cosine = 1 _ (c= 1.0) 1.0) 2 ¢ a LONMe = 3.2) 4 (c— 1.0)(c — 3.2)(¢ — 5:4) w®
12 Roba T2314 516 ‘
c=n(n+ 1)
Cos, (w) = Stokes Cosine = 1 Gee, 24 (EELS ay 4 5 2.0)e7 See eae
12 ORB w! 12x BAX I6 .
— c=n(n + 2) (19)
Sin_,(w) =Seiche Sine = w — (279-4), , (0 0.1)(e— 2.3), _ (0 0.1)(o — 2.8)(e= 4.5)
2.3 2.3 x 4.5 2.3 x 4.5 x 6.7 7; a
c=n(n—1)
Sin, (w) =sin(nsin wy =» CoD es EI) ys Cb (e=8:8)(0- 5.5) 7
n 2.3 2.3 x 4.5 2.3 x 4.5 x 6.7
C=n*
Sin, (w) = Legendre Sine = w _(=2.1) 3 (c- 2.1)(¢- 4.3) Bee (c= 2.1)(c - 4.3)(¢ = 6.5), 7
2.3 2.3 x 4.5 2.3 x 4,5 x 6.7 ow
c=n(n +1)
Sin, (w) = Stokes Sine =o ee, 3 (c- 3.1)(¢-5°3) Bi (¢- 3.1)(¢- 5.3)(¢- 7.5) MGS 53
2.3 2.3 x 4.5 2.3 x 4.5 x 6.7
c=n(n+ 2)
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 659
From (18) we conclude that
PENG ~ 4)
Cos, (1): = —
a Tm Tn (20)
Shea ene ges)
Sin, (1) = 1 oT@)TG- 4)
a 5
*r(i-%-a)r(1+ 2)
Hence
T (T4))? 1 A 1 a T
, — = = H T a — 2s
Cos, (1) COS % 5 i ae G ane i 5 4
5 +5) COS = 7
bo]
|
we vols
Sa Se
|
Sin, (1) = *sinn®
ll
3
=]
Game
pen
| —
iz
a aA aS
eS bo
aN
ts| =
Ney
|
_
i
bo| =
Nee
aw
b| 3
NS
|
ES)
dS! 3 he
which are well-known relations between the [-functions.
From (20) we see at once that
Cos,(1) = 0, if n(n+2a) = 1.(1 — 2a), 3(8- 2a), 5(5-2a)......
Sin,(1) = 0, if n(w+ 2a) = 2(2-2a), 4(4-2a), 6(6 -2ay)......
Applying this result to the Seiche-functions, we find
Cask, (e l= 0 fore 17 dA, t,o
Sime (Gel) =" 0 forie’ = "270i, 4.0 6.7, 2. 2.
[f in equation (3) 1 represents a positive integer, the functions C,“(w) have a
peculiar significance. They are then the coefficients of the powers h” in the series
(1 — 2h +h®)-* = S°A"C,"(w) .
0
Now, according to an important theorem
dt
Waae -" Qari 4 (t= wy )
ChAKOD) Te)! i F(t)
if f(t) represents a function which is regular within the contour C (see WHITTAKER,
Modern Analysis, p. 53). Since we had before (by (13) and (14)) that
(1-#)"+¢-4d¢
c (¢—wyts
(1 — Bere’
e G=ny ~~
C,,"(w) = const x |
= const (1 — w*)-*
we notice that C,”(w) is proportional to
Qrt2a-1
aes { (1 ae ape yeta=t ;
and also to
(le aa | (1 — wy \ ;
We verify without difficulty the following relations :—
a(p) =( —9)r Het (at 2)... . (@+n-1) op fe Solis ee,
ee Gemeente) ae
= — 9)" a(a + 1)(a+ 2) Ce TO (a+n-—1) ae ie }= ory, D)
[) Mem cai eee ae” em
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26). 97
660 DR J. HALM
The Seiche-polynomials C,,~*(w) are therefore represented by the coetticients of tl
ascending powers in the series
1e ;
(1 -— 2hw + h?)t = Dez)
0
where
Bane Sh ee CSO ce epee
(Ole ( v) =, ( 1) pa Ge) dw 24 qd 2) \
Aa ia =) aa |
SG ess eee a ee (22)
The following relations between contiguous C-functions may be mentioned (see
Wauittaker, /.c., p. 236).
tC nr a(t0) — Cona(ta) = Cat)
FE) = 20s) (23)
; Cn" (ew) = 00 'i(«e) =" 20, (0)
nC,,¢(w) =(n — 1 + 2a)wCr_,(w) - fas — w)Cn_3(w).
In the case a = 0 the functions C,°(w) are of course zero, since
(1 — 2hw+h?)?=1
:
But it can be shown that the limiting values of ee (lim a=0) represent the
coefficients in the expansion w
4 log (1 — 2hw +h?),
and we derive the following relation :
oo e Rer-t h 4 d
log /1—2hsinz+h? = Da -1)" ona] SB (2n- 1)z- yy 008 2nz| (24)
n=1 os
w= sinz.
The relations (21) are of particular interest in the Seiche-theory because they lead |
to elegant expressions for the horizontal and vertical displacements € and ¢ If we
write the Seiche-equation referring to a parabolic concave lake
d?P
Spay Efi
(1 wi) 3 + n(n INO)
we have, usine Professor CHRYSTAL’S notations
’ 5 >
uf ‘ 2A Ges { e } 2A a” a)
= Ke 19h See ae ay i ee ee eS — y;2\P-1 = — ap2\n—l
(oe) ee) sin 7,t h(1 — w?) dw? \ a) hn(n—1) dw” { (ae |
cists 2) he BAP (ap
(=1)2.4..... Qn—2) Ry aE (1 -— w?) ;
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 661
UNINODAL SEICHE.
nm=2,n(n—1)=1.2
2
5 ns (1 ~ wu?) \ sin mt, £= 7 sin my
of 2 = (1 — w?) \ sin ft ee ad,
BINoDAL SEICHE.
n=3,n(n—1)=2.3
QA a3 { . (ewe
Dad eee (aay eae t
a Bh dui) (1 — w?) psinn, € 7 tw Sit Ma
2
Dees eB =)? } sin not, € = *(3u? = 1) sin not -
a dw? | 2 a 2
TRINODAL SEICHE.
n=4, n(n—1)=4.3
A 4 { 3 : A z
2.4.6 €= — 6 dwt | (1 — w?) } sin mat; €= — ah — 52) sin not (25)
2A da
2.4.6 f= -
: A :
e aa (1 - w?)" f sin mt; €= ~ gq (12 — 200? )o sin not .
QUADRINODAL SEICHE.
n=5, n(u—1)=5.4
5
2.4.6.8 _— 4 (1 —w?)* } Sin M4 ; g= 5 (Tu? — 8) sin 24t
2 7A © § awe b singe; c= (3508 - 300 +3) sin n,f
2.4.6.8 =. amas — w*) sin ",t ; ba oak dwt — 30w? + 3) sin n,t.
The positions of the nodes are found from the equation ¢=0, and _ hence
| (ql - wy" t =0 for n-nodal seiche, and since this differential-quotient is proportional
to the LecenpRE-polynomial P,,(w) , the nodes are also determined by the equation
P,(w)=0,
where P,,(w) may be defined as the coetficient of h” in the expansion
ore > P,(w)h”.
n=0
Turning now to the hyperbolic Seiche-functions, we obtain convenient expressions
im the form of hypergeometric series by substituting in equation (3) wi for wand ni—a
for n, 7 being the imaginary unit root ./—1. We have then
ay dy 5
(1 +02) 54 + (20+ lw 5 +(n?+a*)y=0, (26)
the particular solutions of which may at once be taken from (17). Most of these series
662 DR J. HALM
are, however, unsuitable on account of the presence of complex factors. The hyperbolic —
Sine- and Cosine-functions are again represented by the first series of Groups I. and V.
These series contain only real terms, as was shown already by Professor Curystat. We
~
find for the hyperbolic Cosine-function :
Oh MG Ch 108, 5
Bet Gy a > 29 a)
2
mn? + a? aig, Ce Eee alae ; (n? + c?) [n? +024 4(a+1)| [72 +0? + 8(a + 2)]
— =< = _ Wr —
ee a. 1.2.34 1.2.3.4.5.6 Ze
The Seiche Cosine is obtained by substituting a= —4} and 17+4=c, hence %
(c+1.2 (c+ 1.2) (e+ 3.4
hyp. Seiche Cosine @(¢, w)=1 — 3 ab ae - wt — a 5 2 S ee ois (27)
while for the hyperbolic Seiche Sine we have
S(e ; Ww) = wE( : ae m1 We . : = v2)
DS a)
De Oe Gree Oa)
= 12a ra ORIEL DSEASIGMI ee ne
Similar expressions are obtained for the corresponding hyperbolic LeGENDRE- and
SroxEs-functions. The series, by which the functions are represented, converge very
slowly. For this reason the theory of convex lakes with parabolic floor has so far
remained incomplete, chiefly owing to the difficulty in determining the roots of the
equations G(¢ , 1)=0 and G(¢ ,1)=0. To avoid this dithculty Professor Curysrat, in
his second communication, proposed a different assumption as to the contour of the floor
of the lakes, by which he was enabled to express the problem by the solutions of the
SroKEs-equation
(ary 4 4 cy =0,
which, as we have seen, are represented by elementary transcendents. In this case,
curiously, the convex lake offers the least difficulty, doubtless owing to the fact that
its equation belongs to the class which also contains the more tractable parabolic
concave lakes. A disadvantage of the Sroxrs-equations, however, is that the quartic
lake profile seems to be a less close approximation to the actual conditions than the
parabolic. Even apart from this, it is certainly of importance to discuss the problem
on at least two different assumptions in order to estimate the influence of the form of
the lake on the periods and nodes. Now the preceding investigation enables us to find
any of the infinite number of roots of the equations G(c , 1)=0 and G(c , 1)=0 with
at least a sufficient degree of approximation, and thus places us in a position to find
also without any difficulty the periods and nodes of the seiches in lakes with parabolie
convex floor.
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 663
_ From equation (26) we see that the Seiche-equation, for which a= —#, lies between
the two equations :
a? dl
(L410?) 4 — wh + (2+ ly =0 e.=n +1)
Be ee 2 a
(l+w Vag t aay t Py = 0 ~ Opa
he particular solutions of these corresponding to the hyperbolic Seiche Cosine and
che Sine are respectively :
€_(w) = - sin [n log (w+ /1+w?)] + /1+w? cos [n log (w+ J/1+ a)
6,(w)
(Jew
n Sy(w)
cos [n log (w+ /1+w?)]
(29)
~cos [n log (w+ /1+w?)] + J1+w? sin [n log (w+ /1+w?)]
ll
sin [n log (w+ /1+w?)]
We may also at once write down the corresponding particular integrals of the two
ther differential equations (a = 1 and 2):
d? d
(1+ 02) 54 + 805" + (n? + 1)y =0 c= 1? +1
(1 +u2/4 TY + bw ne i 0, cC,=n?+4 (30)
G,(w) = (1 + w?) cos [m log (w+ J1 +w*)]
Cy(u) = (14 0%)-# | V1 +0? cos [n log (w+ J1+@)] -= sin [n log (w + i+w }
(31)
— m S(w) = (1+ w*) sin [nlog (w+ J/1+v*)]
(n+ +5) S,(u) = = +0) J/1 +0? sin [n log (w+ J/1+0)] + — cos [n log (e+ Jiu) }
inthe other hand, the solutions (29) and (31) are expressed by the following
eometric series :
(S-FUNCTIONS.
1) a Da eS a wee? 2.4) 96
1.2 Kosa 1.2.3.4.5.6
Gs see 2) Nes Co(Cy + 2.2) (Cy + 4.4) Keak:
Tenino oS esieoiadl 1.2.3.4.5.6 i
pede: supe GNGTe sae 4 _ (+ 4.2)(c, + 6.4), ieee?
1.2.3.4 1.2.3.4.5.6
hes £9 yp 4 Colla + 8.2 2), wes Co(Cy + 6.2) (Cy + 8.4)
Mtb 6 ga
T2 1.2.3.4 (Oe
664 DR J. HALM
©-FUNCTIONS.
y= Vl) g | Ca- Veg $1.8) Ca Le £1 3Ne4+85) 5 | ee an
Riera 2.3.4.5 9.3.4.5.6.7 spear (32)
FVD gy Colt LIM e + 3:3) 95 Cot LIV + 3.30(e + Bry
H aa 9.3.4.5 2.3.4.5.6.7 eae
op GFF), Gt 3G + 5.3), (+ 81NG + 5.3)y + Try
2.3 23.45 9.3.4.5 6.7
_ a+ 51) wey + SING, + 7.3) 5 (Cy + BANG) + T3)ey + 95) rg
73 2.3.4.5 2.3.4.5.6.7
Let us now find the roots of the equations ©,(c,,1)=0 and S,(¢,,1)=0 for the eig t
functions given in (29) and (31). For the 6-functions we have the conditions :
tan [n log (1+ /2)] = 2/2; ¢,=n?+1.
cos[mlog(1+ /2)] = 0 3 =n.
cos[zlog(1+ /2)]}= 0 ;¢ =n?+l1. a
tan[nlog(1+ /2)]=J/2; ¢ = n?+4. ; (33)
and for the G-functions :
cotan [mlog (1+ ,/2)] = —n./2;c,= +1.
sim mloa(i 2) COMME
sinfnlog(1+ /2)|}= 0 3;¢e =n?+I1.
eotan [zlog (1+ ./2)] = —n/2; ¢ =m+4.
From these conditions the roots c, are easily obtained. We find
(S-PUNCTIONS. ©S-FUNCTIONS. ~
e_,=2°35012 ; 27:9681; 78: UOC tae c_, = 12°06756 ; 50°2082; .
Cy) =8°17627 ; 28°5865 ; 79-4068; ... . €) =12°70508; 50°8204;....
4, = 417627 ; 29°5865; 80°4068;. . €4,=13°70508; 51°8204; . ..., (34)
Ci, = 0 DIOLZ OOLIOS Mero TOG. on. C45 = 15°06756 ; 53°2082 ; .
But obviously the roots in each vertical row may be considered as special values of
a certain unknown function of @, so that generally
Ca =f(a) ’
from which equation, if f(a) were known, we would obtain the values c_,, G@, ete. by
substituting a= —1,0, etc. Now, as long as f(a) may be considered as finite and con-
tinuous, the well-known formule of numerical interpolation allow us to find intermediate
values of c from the given data, without knowing the analytical character of f (a),
if a sufficient number of equidistant values of c are at our disposal. We are thus in a
position to determine, at least approximately, the roots c_, of the hyperbolic Seiche-
functions € and © by interpolating between the numbers of the above table (34).
Performing the necessary calculations, we obtain the following roots :
CG a0 p eS 274 5 28251, ote OO
Gi(c,1) SOc =1280 h. .. o0Ow at (35)
;
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 665
function have also been computed directly from the series by Professor CHRysTAL, assisted
by Dr Bourcexss, Professor Gipson, and Mr Horssurcu. They were found to be 2°76
and 12°34, and hence are remarkably close to the values given in (35). The root 28°23
was also verified by Dr Burexss, Professor Gipson, and myself. I have convinced
myself that the exact value must certainly lie between 28°229 and 28°230, so that the
second decimal place of the interpolated value appears to be correct. The method of
interpolation here adopted places us therefore in a position to determine the infinite
number of roots of the two transcendental equations ©_,(¢, 1)=0, and S_,(c, 1)=0,
~ and thus enables us to determine the periods of the seiches in lakes with convex parabolic
floors from Professor CHrysTAL’s equation :—T,=27a/ Jel (see Proc. RS.E., vol. xxv.
p- 332).
A similar method of interpolation may be employed in the calculation of the position
of the nodes. These are found by first forming the equations
d@_(w) 6 AG, (w) B) IG, (w) a AG, (w) 6G
[SS , Saye ? dw J es — | ?
dw du dw
AS_,(w) _ 0 dSo(w) _ 9 AS (10) _ 0 AS,(w) _ 0 (36)
dw ; dw ‘ dw ‘ dw y
and by determining the values of w satisfying these equations under the condition that
¢, has the values mentioned in (85). By interpolating between the w thus obtained,
we find with sufficient approximation the successive values which satisfy the two Seiche-
equations
d@_,(10) =Q0 and dS_,(w) =0
dw dw
?
and which therefore fulfil the required condition that the vertical displacement ¢= 0.
In this way I have found the following positions of the nodes in convex parabolic lakes :
Uninodal Seiche w= 0
Binodal Seiche w= +0°473 ....
Trinodal Seiche w=0; +0°632....
Quadrinodal Seiche w= +0°224....; t0°717....
It is interesting now to investigate the positions of the nodes under the various
lake. From Professor Curystat’s investigations and the preceding discussion we find for
| Lake with poe ao . Trinodal Seiche. — (uadrinodal Seiche.
¢ wR . .
“coneave parabolic floor, . .| w=0 + 577 0; +775 | + -340; + -862
plain horizontal ‘ 0 +500 | 0; + °667 | ae 200 5 “750
‘convex parabolic _,, 0 Ane | dOuved-' 632 QA 4 717 (37)
“Convex quartic, 0 +447 | 0; + :600 + 202; + -684
t |
The figures show clearly that in lakes with curved floors the nodes are always displaced
) towards the shallow water.
666 DR J. HALM
As regards the constants c, which determine the periods of the various seiches, we
have the following values : .
abn eatec Uninodal |. geo eh : Trinodal Quadrinodal
Lake with ene Binodal Seiche. SEane | Seicnel
concave parabolic floor, . 3 2-00 6°00 120 20:0 ;
plain horizontal __,, . | a ine DeSean: 22°25 39 Olam 38)
convex parabolic _,, ; an PaO <- : WOBBLE DSS ae | Oa. (38)
convex quartic Es ; aj Z 00 15-00 | 35°0 | 63:0 ;
and on virtue of the equation T \T, = Were.
TD, Se ee eee
concave parabolic : ada, 408 317 2
plain horizontal : 500 333 250 (39)
convex parabolic : 472 Bie) ‘234 1
convex quartic : ‘447 "293 ‘218
We recognise here, in a more general form, the law found by Professor Curysrat, that
in concave lakes the ratio T,/T, is greater and in convex lakes smaller than the corre-
sponding ratio in a lake with plain horizontal floor
The positions of the nodes may be represented in a convenient graphical form, which
not only shows clearly their dependence on the curvature of the lake, but at the same
time enables us to find the nodes for the curves lying between those here discussed,
which are not amenable to direct analytical treatment. In fig. 1 are shown the halves
of the vertical longitudinal sections of symmetric lakes. OB represents a, the half-
length, and O A the central depth, h, of the lake, whereas A B, AC, A D, and A E signify
the intersections of the vertical plane with the concave-parabolic, the plane-horizontal, th
convex-parabolic, and the convex-quartic floors. Now, on each of these curves the nodes
have been marked by the points B,, B,, B,, ete., in such a way that for instance the
distance of B, from A O agrees with the value of w in (43) which refers to the binodal
seiche in a lake with concave parabolic floor, t.e. w= = =0°577. Inthe same way H, is
drawn at a distance 0°447 from A O, thus representing the position of the binode in a
convex-quartic lake. Having secured the corresponding four points on each of the
curves A B, AC, AD, and AE, we draw the curved lines B, H,, B,; Ez, and B, Ky, and
these lines are obviously the doce of the nodes. We recognise at once in all cases the
displacements of the nodal points towards the shallow water, a phenomenon specially
marked in concave lakes. Let us now take, for instance, a convex lake whose depth is
Pee Le:
Hee
represented by h,/1 +’ and is indicated in our diagram by the dotted curve AF. The |
solutions of the corresponding differential equation
a
NEL Tyee h ty = =0
are not known, and hence we are not in a position to compute the nodes and periods of |
these particular seiches by analytical methods. But approximately the nodes may he
now directly found from the diagram, being represented by the points of intersection |
between the Joci BE and the curve AF. It would seem, therefore, that by the preceding |
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 667
investigation we have gained considerable freedom in the selection of curves representing
the curvature-conditions of the lake floors, so that we may, by the suggested interpola-
method, assign approximate values to the nodes, and by means of (38) also to the
| ods, even under conditions which are unmanageable from the rigorous mathematical
point of view.*
Fie, 1. E
' the advantage of the preceding analysis of Professor CurysTat’s Seiche-equations lies
» fact that they belong to a class which includes cases where the solutions are
ible by means of simple transcendents. If we write the general differential equa-
in their most symmetric form :
Py dy ( -
Ae) iz ade 2_ I \y — (0)
Gea Gy ets (n2+T)y 2)
dw? dw 4
* In § 45 of his Hydrodynamical Theory, Professor CHRys?aL investigates the case of a rectilinear lake, the floor
ch would be represented in the above diagram by the straight line AB. The directions of the nodal loci E B in
suggest that the nodes in rectilinear lakes should be more displaced towards the shallow water than in any
ses here considered, and this conclusion is indeed supported by the numerical results given in § 49 of Professor
[RYSTAL’S paper.—(Note added on June 30.)
TRANS, ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26). 98
668 DR J. HALM
we may say quite generally, that the solutions can always be expressed by simple tran-
scendents if y is an even integer. The Seiche- and LecENnpre-functions, on the other
hand, belong to differential equations of the same class for which y is an odd integer,
Hence each equation of the latter class is included between two equations of the former,
and we have seen that through this remarkable property we were enabled, by studying
the behaviour of the neighbouring simple transcendents, to form conclusions with regard
to the far more difficult Seiche-functions.
In the theory of lakes, the floors of which are composed of two or more parabola
with different parameters, the evaluation of the two functions C(c,1) and S(c,1) for
any given value of c becomes important. The calculation of the series
c(e-2) ee ~ 2)(e— 12)
1.2.3.4 1.2.3.4.5.6
€ , e-6) _e-6)(c~ 20)
“73 9345 ) OE eye”
Cle, l)=1-,5+
sé, e=1
is always an exceedingly troublesome process, especially for great values of c. In many
cases even the calculation of 100 terms is not sufficient. But the foregoing investiga-
tion immediately suggests a rigorous and extremely simple method of computing these
quantities. Reverting to equations (18) and (20) we find for the two Seiche-functions
(a = —4) the relations :
But considering that
In 7Z
we find
Die G) oS
oe
Sis we 5 wa a ie | af
te ae 7
These expressions are very convenient for computation. Let us take, for instance,
c= 105°0176, to which corresponds n= 10°76. We have
(105-0176 ; 1)= - T(5'38) sin 68°-4
T(5'88) Ja
1°38 x 2°38 x 3°38 x 4:38 T(1°38) | sin 68°°4
~ 1°88 x 2°88 x 3°88 x 4°88 T(1'88) Jr
S(105-0176 ; 1)= 2 1°88 x 2°88 x 3°88 x 4°88 I(1°88) cos 68°°4
105-0176 1°38 x 2°38 x 3°38 x 4°38 T(1°38) Jr ;
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 669
| and, since
| log P(1:38) =1:94868 log I'(1-88) = 1-98004,
| we find (105-0176 ; 1) = — 0-231467 ; S(105:0176 ; 1)= +.0:008964
I need scarcely say that in this case a satisfactory calculation by means of the series
is quite impossible. For smaller values of c the computations are of course still more
convenient. If, for instance, c= 14°96, or n=4'4, we have
sin 36°
(14-96 ; 1) = na = 028654.
T(2:2) sin36°_ 12 T(1-2
TT) jean paleniGr
We notice also the relation
1
n(n —1)C(e, 1) -
S(c, 1)= _ Sin tr (42)
Note added on June 30.—The relations (41) and (42), which follow here immedi-
ately from a well-known property of the hypergeometric series F(a,8,7; 1), were
originally derived by Professor CurystaL from a different point of view. (See §§ 25
and 41 of the Hydrodynamical Theory.) His important relation (53) in § 41 may be
also obtained from the equation
Le, =Fin,1—m, 2; =U +nyna—nm= — a,
Mn — T
and, in consequence of (42) :
L(e, 1)=Ci(e, 1). Sé, 1).
aaa
At the request of Professor Curystrau I subjoin tables from which the numerical
values of C(c,1) and S(c, 1) may be taken for any value of c. If we write
aa bth yerd
Oe T(a) sin ar
T(ia+4) are to be taken from the following Table I.
670 DR J. HALM
Terns lh
a @(a) a O(a) a Q(a) a @(a) a O(a)
1:00 0:00000 1°20 — 0°33511 1°40 — 0:49501 1:60 —0:45815 1: 80 — 0:26474
1:01 — 0:01988 1:21 —0°34769 1:41 —0°49775 1°61 —0°45163 1°81 — 0°25237
1:02 — 0:03949 1:22 —0°35984 1°42 — 0:49999 1:62 —0°44471 1°82 — 0:23983
1:03 — 0:05884 1:23 — 0°37152 1:43 —0°50171 1:63 — 0:43741 1°83 — 0:22712
1:04 — 0:07790 1°24 —0°38271 1°44 — 0:°50294 1°64 —0°42975 1:84 — 0°21430
1:05 - 0:09666 1°25 — 0°39346 1:45 — 0°50366 1°65 —- 042171 1°85 — 0°20133
1:06 —0:11512 1:26 — 0°40370 1:46 — 0°50391 1:66 — 0°41332 1°86 — 0°18824
1:07 — 0713326 1:27 -0 41347 1:47 — 0°50365 1:67 — 0°40457 1°87 —0:17505
1:08 — 0°15106 1:28 — 0°42275 1:48 — 0°50292 1°68 — 0°39552 1°88 — 0°16177
1:09 — 0°16852 1:29 — 043153 1:49 —0°50171 1:69 — 0°38612 1°89 — 0°14842
1:10 - 0718563 1°30 — 0:43982 1°50 — 0:50000 1°70 — 0°37643 1:90 — 0:13499
LST = O20 D7 1°31 — 0°44762 1:51 — 0°49785 1:71 — 0:36641 1°91 — 0712151
1:12 — 0°21874 1°32 — 0°45490 1°52 — 0:°49520 1°72 — 0°35612 1°92 —0°10800
ats 0:234 16 1°33 — 0°46170 1:53 —0°49211 1°73 — 0°34555 1:93 — 0:09445
1:14 — 0°25032 1°34 — 0:46798 1:54 — 0°48858 1:74 — 0°33472 1:94 — 0:08090
1:15 — 0:26551 1°35 — 0°47375 1°55 — 0°48458 1:75 — 0°32362 1°95 — 0:06734
1:16 — 0°28029 1°36 — 0-47902 1°56 — 0:48014 1:76 — 0°31228 1:96 — 0:05380
1:17 —0°29464 1°37 — 0°48378 1:57 —0°47527 1:77 — 0°30071 1:97 — 0:04028
1:18 — 0°30855 1°38 — 0:48804 1:58 — 0°46998 1:78 — 0°28892 1:98 — 0:02680
1:19 — 0:32206 1°39 —0:49177 159 — 0:46426 1:79 — 0°27692 1:99 — 0:01337
a a) a X(a) a (a) a 3a) a Xa)
1:00 + 0°50000 1:20+0°45171 1:40 + 0°18899 1:60 — 0°20419 1:80 — 0°57178
1:01 + 0°50281 1:21+0°44336 1:41 +0°17133 1:61 — 0:22463 1°81 — 0:°58638
1:02 +0°50510 1:22 + 0°43447 1°42 + 015336 1°62 — 0:24499 1°82 — 0°60047
1:03 + 0°50687 1:23 + 0°42503 1:43 + 0°13507 1°63 — 0:26525 1:83 — 0°61406
1-044 0°50811 1:24 +0:41505 1444 0:11649 1°64 — 0°28536 1°84 — 0:°62708
1:05 + 0°50880 1:25 + 0°40453 1°45 + 0:09765 1:65 — 0°30533 1-85 — 0°63956
1:06 + 0°50894 1:26 + 0°39347 1:46 + 0:07855 1°66 — 0°32513 1:86 — 0:65148
1:07 + 0°50853 1:27 + 038190 1:47 + 0:05921 1°67 — 0°34473 1:87 — 0°66279
1:08 + 0°50758 1:28 +0°36982 1:48 + 0:03966 1:68 — 0:36410 1:88 — 0°67348
1:09 + 0:°50604 1-29 + 0°35723 1:49 + 0:01992 1:69 — 038325 1°89 — 0°68355
1:10 + 0°50396 1°30 + 0°34416 1:50 0:00000 1:70 — 0:40213 1:90 — 069303
1-11 +0°50130 1°314+0°33060 | 1°51 —0°02007 1:71 — 0°42072 1:91 — 0:70183
1:12 +0°49807 132+0°31657 | 1:52-—0:04028 1:72 — 0°43901 1:92 — 0°70998
1:13 +-0°49428 1°33+0:30207 | 1:53-—0°06060 1:73 — 0°45697 1:93 —0°71744
11440-48991 1:34 + 0°28716 1:54-—0:08101 1:74 — 0°47456 1:94 — 0°72423
1:15 +0-48496 1°35 +0:27179 1:55 — 0°10149 1:75 —0°49181 1:95 — 0°73032
1:16 +0°47946 1°36 + 0°25601 1:56 — 0°12203 1:76 — 0°50866 1:96 —0°73570 _
1:17 +.0°47335 1:37 + 0°23982 1:57 — 0:14259 177 —0°52511 1:97 — 0:74037
1:18 +0:46671 1°38 + 0:22324 1°58 — 0°16315 1:78 — 0:54111 1:98 —0:°74432
1194 0°45948 1:39 + 0°20630 1:59 — 0°18369 1:79 — 055667 1:99 — 0:74755
between O and 30:0.
More convenient, however, for practical use may be Table II., from which the
numerical values of C(c,1) and S(c,1) are directly obtained for values of ¢ included
The intervals chosen are sufficiently close to permit an easy
ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 671
interpolation of these functions for intermediate values of c. If required, the table
may be extended by means of Table I. and the preceding formule.
Tasue II.
c Cie, 1) S(c, 1) C Ce, 1) S(e, 1)
0:0 + 1:00000 + 1:00000 5:6 — 1°50392 + 0:02851
0:2 + 0°86568 + 0:94030 5:8 — 0°50292 +0:01375
0:4 + 0°74008 + 6°88215 6:0 — 050000 0:00000
0°6 + 0°62247 + 0°82674 7:0 — 0°46052 —0:°05615
0:8 + 0°51257 + 0°77390 8:0 - 0'38976 — 0:09397
1:0 + 0:41034 + 0°72302 9-0 — 0:°29986 — 011695
iy + 0°31593 + 0°67440 100 — 0:20033 — 0'12809
1-4 + 0°22694 +0°62778 11:0 — 0:09837 — 0:13006
1°6 +0:14511 + 0°58331 12:0 0:00000 — 0°12500
1:8 + 0:06956 +0°54071 13:0 + 0:09082 —0:11479
2:0 0:00000 + 0°50000 14:0 +0:17106 -—0:10101
eo) — 0:06385 +0:°46111 15:0 + 0°23s02 — 0:08524
2°4 — 0712221 + 0°42406 16.0 + 0°29323 — 0:06753
2°6 —0:17561 | + 0°38864 17.0 + 0°33377 — 0:04971
2°8 — 0°22395 + 0°35492 18-0 + 0°36035 — 0:03222
3:0 — 0'26758 + 0°32282 19:0 + 0:37382 —0'01550
3°2 — 0°30673 + 0°29227 20°0 + 0°37500 0:00000
3°4 —0°34177 + 0:26317 21:0 + 0°36508 + 0:01404
3°6 = OSV ONS + 0:23555 220 + 0°34531 + 0°02640
3°8 — 0°39987 + 0°20933 23°0 + 0°31710 + 0°03698
4:0 — 0:42343 + 0°18442 24:0 + 0°28192 + 0:04572
4°2 -0°44360 + 0°16083 25°0 + 0°24103 + 0:05266
4°4 — 0°46051 + 0°13853 26:0 +0:19611 +0°05779
4°6 — 0°47435 +0°11741 27°0 + 0714830 + 0:06123
4°8 — 0°48542 + 0:09744 28°0 + 0:09889 + 0 06308
5:0 — 0°49366 + 0:07865 29°0 +0:04919 + 0:06345
52 —0°49941 + 0'06088 30°0 0:00000 + 0:06250
5:4 - 0:°50277 + 0°04422
As regards the hyperbolic functions @(c , 1) and G(c, 1), it seems, however, impossible
to calculate their values by means of the corresponding relations, because the
P-functions, which appear in the expressions, have imaginary arguments. But
fortunately, in this case, the series are far more manageable than those of the C- and
S-functions, so that the labour involved in their direct calculation is not nearly so
stupendous as it may appear at first sight, even if an accuracy within the fifth decimal
place is desired. To show this let us first consider the series
jeeee atl i (e+1)(c+9) (c+ 1)(c+9)(c + 25)
2.3 2.3.4.5 2.3.4.5.6.7
which, as we know from the preceding investigations (see (29) ), is rigorously represented
Geeta rs. . Lear
by the transcendent We sin (,/¢ log (1 + ./2))- We want to inquire how many terms
of the series are necessary to obtain the accurate value of this transcendent within, say,
five places after the decimal point. If we call =(x) the sum of the x first terms, and if
672 DR J. HALM
we plot the successive = as ordinates, taking the corresponding as abscissz, we find
that, owing to the continuous change of sign, the = are represented as the corner-points
of a zigzag line; and it can be shown that for sufficiently great values of x this line
oscillates along a straight line parallel to the axis of abscissee, and at a distance from it
equal to the exact value of the series, 2.e. to a sin (,/e log (1+ /2)). Wet ud
NE
demonstrate this for a certain value of c,e.g.c=24. We find
2(2)
1 | +1:00000 | 12 ~ 2°43133
» | —sileee7- [13 |) a ireeont
5) | 253 108e3) aie) o 10566
4 | —4:31251 | 15 | + 1-59235
5 | 38897 | 16s 84708
6 ~3-94285 | 17 | +1:36108
7 | 397938. |) 180 |) = eeso62
g. |. —3:s5e75 ‘|. 19) 1) -Pi-i7409
Q. | o167 1/205 es iearoer
10 ~ 284399 | 21 + 1:02088
11 |) +2-24871 | 92 ~ 133133
the horizontal line are obviously much smaller, and if we repeat this process of forming
arithmetical means, the fourth operation of this kind will lead to the following set of
values for 24(a) :
© 2,(2) | x 3, (2)
13 —0:18840 17 —~ 018841
14 ~0°18842 18 — 018844
15 —~ 0-18840 19 ~ 018842
16 ~0'18844 | 20 ~ 018844
Now we convince ourselves, by computing the higher terms of the series for x > 22,
that however far we may extend the calculations, the values of 2,(x) will always be
found between the last two figures of the preceding table, and will more and more
converge towards their arithmetical mean, viz.,—0°18843. But the exact value of the
series should be
30 may, however, be concluded from the fact that the higher roots of the
equations
cos [Vc + 0°438 x 50°-458]=0 and
sin [/c + 0°438 x 50°-458]=0
agree very closely with those of the corresponding Seiche-equations G(c,1)=0 and
G(c,1)=0. We find for the former 79°099 and 50°465, whereas the corresponding
roots of the latter were previously found to be 79°053 and 50°466. As regards the
lower roots which are included in Table III. we have in the case of the hyperbolic
Seiche Cosine
1:19942 cos [n/c + 0°438 x 50°-458]—0:0004=0; c= 2-742
1:19942 cos [s/c + 0°438 x 50°-458] — 0:0034=0; c= 28-230
and for the hyperbolic Seiche Sine
CC ay
Jex0438 sin [,/¢ + 0°438 x 50°'458]+0:0024=0; c=12°341.
These roots agree almost exactly with those previously found by an entirely
different approximative method (see (35) ).
In conclusion, I wish to express my great indebtedness to Professor Curysrat for the
interest he has taken in this investigation, and especially for having kindly permitted
me to publish this mathematical discourse on the differential equations of his Seiche-
problem along with his own physical and mathematical researches. The general type
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26). 99
?
676 LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER.
of differential equations, of which the Seiche-eq uations are special cases, is well known
to mathematicians through the important rdle it plays in the theory of the associated
LecenpDRE-functions. But, as far as I am aware, its solutions have been investigated only
in the special cases where n represents integers (see WHITTAKER, Modern Analysis,
p. 235). In the theory of the C,“(w) polynomials, which are particular integrals of the
general equations here considered, the two synectic integrals, with which we were
particularly concerned in this investigation, are of less importance than some of the
other hypergeometric series. But their property as synectic solutions renders them
particularly useful in the special physical problem before us. It is not improbable that
in other problems—for instance, in such which are based on the differential equation of
the LrcrnpRE-functions (a =4)—the corresponding synectic integrals, the LEGENDRE
Sine and Cosine, might also be of special importance. Since the latter, as well as their
associated functions, may be derived from the Seiche-functions by differentiation, we
may consider these as the typical representatives of the whole class; and this fact,
doubtless, gives to Professor CHRysTAL’s investigation a considerable importance from
the mathematical point of view,—an importance still more enhanced, on the one hand,
by the introduction of the corresponding hyperbolic functions, to which he has now for
the first time directed the attention of mathematicians, and, on the other, by the
remarkable relations between this general class of functions and another class
represented by simple transcendents.
ms
" 2
“ n 2
= 7. - i) 5 z
\ :
a . | . 7 ; 4
{ , as 7 ’
(677. )
XXVII.—The Tardigrada of the Scottish Lochs. By James Murray. Communicated
by Sir Joun Murray, K.C.B., ete.. (With Four Plates.)
(MS. received April 26, 1965. Read June 5, 1905. Issued separately July 20, 1905.)
INTRODUCTION.
Although they are thoroughly aquatic animals, the Tardigrada are not very abundant
in permanent waters. They are most thoroughly at home in situations where the
supply of moisture is intermittent, and are therefore conspicuous members of that
numerous community of animals known as moss-dwellers. They share with the
Bdelloid Rotifera the power of withstanding dessication.
Although they have their headquarters in land mosses, many species are quite at
home in ponds, rivers, and lakes.
As lacustrine.animals they belong entirely to the littoral region, into which they no
doubt continually migrate from the adjoining mosses. A favourite habitat is that strip
of shore between the highest and lowest levels of the lake, the ‘gréve inondable’ of
Forex. Into this often mossy margin they may migrate in the ordinary way, when the
loch is low. The next step may be involuntary—the loch rises during floods, and the
bears, in common with many other animals, find themselves, willy-nilly, converted into
lake-dwellers. It appears to be certain that of the water-bears introduced into lakes,
by whatever means, some have found the conditions very congenial. Several species
7 hitherto been found nowhere but in lakes.
The condition which renders the margins of lakes favourable to many of the moss-
haunting animals is, I believe, the thorough aeration of the water resulting from the
perpetual lapping of the waves upon the shore; the water of the lake in this respect
resembling running water ; and there are many species of microscopic animals, so sensitive
to impurity that they are never found in bogs or other stagnant waters, which abound
in running streams and in the littoral region of large or pure lakes.
_ No Tardigrade is known to swim—they have no place in the pelagic region of the
Takes—nor are any of them truly abyssal, though, like so many other animals in
Scottish lochs, they may extend to considerable depths, and several species have been
obtained at depths of about 300 feet in Loch Ness.
The observations of the Lake Survey upon Tardigrades have been chiefly made in
Loch Ness and Loch Morar. A few collections were made in Loch Treig and one or
two other lochs, and an examination of these confirms the belief that some of the
water-bears are characteristic of lake margins.
' TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 27). 100
678 MR JAMES MURRAY ON
and to Prof. Ricutrrrs of Frankfort, who kindly consented to examine my drawings, and
assisted me with advice, and with literature to which I had not myself access. Without
this willing help the considerable material at the disposal of the Lake Survey could
not have been utilised.
References to the bibliographical list are throughout the text made by figures
enclosed in parentheses, thus (1), (15).
The animals are all drawn to the same scale, so that their relative sizes may be
seen. The principal measurements are given both in fractions of an inch and in
microns. For convenience of reduction the inch is taken as equal to the round 25,000
microns, which is a near enough approximation for practical purposes.
STRUCTURE.
The Tardigrada are articulated animals, regarded as having their nearest relatives
in the Arachnida.
The structure is only treated here in so far as is necessary for systematic purposes.
Water-bears are segmented animals, having four pairs of jointed legs, the seomenta-
i
In the preparation of this paper I have been greatly indebted to Mr D. G. ScourFimtp,
tion of both body and limbs very obscure and superficial. The blood consists simply —
of a body-fluid, filling the whole of the body cavity between the skin and the alimentary
canal. In the body-fluid are usually numerous large nucleated cells, formerly regarded
as blood-corpuscles, but now called fat-cells (13); small dark granules may also be
present.
Skin.—This may be smooth and hyaline, pigmented, papillose, warted, or spiny,
indistinctly segmented or thickened dorsally and formed into a series of protective
plates, symmetrically arranged (Hchiniscus).
Legs.—There is usually a distinct basal portion of each leg, the skin of which seems
to be an extension of that of the body, forming a kind of sheath for the leg proper; two
joints may sometimes be distinguished in this. There may be one or many claws on
each leg, which may all be free, or united into groups of two or three.
Head.—Two joints, sometimes three, are distinguishable in the head. There may
be many palps and setze on the head, or none; eyes may be present or absent; there
may be a rostral prolongation, or not.
Masticating Apparatus.—This is somewhat elaborate, the food being acted upon by
two sets of organs which function as teeth. The teeth proper are a pair of straight or
curved rods, looking very much like chop-sticks, tapering in front to very fine stiletti-
form points which enter the mouth, a short, funnel-shaped expansion of the anterior end
of the alimentary canal, or the throat, a narrowed portion of the tube, separating the
mouth from the gullet. These stiletto-like points pierce the cells of the plants or
animals which serve as food, which are then sucked. The teeth are much enlarged
posteriorly, and usually forked; they may be connected with the cullet by supports
THE TARDIGRADA OF THE SCOTTISH LOCHS. 679
ealled the bearers. The food passes by the gullet to the pharynx. This is a strong
muscular bulb, through the centre of which the alimentary canal passes. The function
of this organ is supposed to be to force the food into the stomach, which it does by a
‘pumping action. In several genera there are rows of hard rods or nuts round ‘the tube
passing through the pharynx; in these cases the rods seem to have the further function
of pounding the food as it passes, thus acting as a second set of teeth. The pharynx, with
its rows of hard rods, has some analogy with the mastax of rotifers. A short esophagus
leads from the pharynx to the stomach. The large cells forming the walls of the
stomach have contents of a characteristic colour—brown, yellow, red, or blue.
Reproduction.—So far as known, all Tardigrades are oviparous. The eggs are
spherical, oval, or elliptical, smooth, viscous, or spiny. They are either deposited free,
in which case they are spiny or viscous ; or they are laid several together in the skin as
it is moulted, being then always smooth. In some genera, the larvee do not differ in
any important degree from the adults ; in others, they differ considerably, and gradually
acquire the adult form through a series of moults.
There is a marked uniformity of structure throughout the whole group, the main
classification being founded on no more important characters than the texture of the
skin, the number of claws, the form of teeth and pharynx, and the presence or absence
of certain feelers on the head.
EcHINISCUS.
Generic Characters.—Skin of the back thickened and forming a number of plates or
shields, symmetrically arranged singly or in pairs. Claws two or four, separate and
independent. Twoeyes. Teeth and gullet long, straight; no bearers. Four short setze
and two blunt palps near the mouth ; two longer lateral setae between the head and the
next segment.
Plates.—The number of plates varies, ten being most common. When this normal
number is present they have almost invariably the same arrangement :—(1) The head
plate or frontal plate; (2) The shoulder plate, a larger plate, crossing the back and
extending down the sides; (3) First median plate, a small triangular plate in the
middle of the back, the apex pointing backward; (4) First pair of plates, two equal
plates, meeting in the middle of the back, and extending down the sides; (5) Second
median plate, triangular, with apex pointing backward, sometimes quadrangular ;
(6) Second par, similar to the first pair; (7) Third median, triangular, apex directed
forward ; (8) Lumbar plate, a large plate, covering the whole posterior part of the body,
and the fourth pair of legs, usually cut into a trefoil by two deep incisions. The middle
portion of the trefoil I distinguish as the taz-piece. In many species described by
Ricurers it is quite separated from the lumbar plate, and is then called the anal plate.
If the number of plates were constant, or if a greater or less number were due to
subdivision or suppression, the homologous plates could be distinguished through all the
Species by their names or numbers. There are, however, some species—(E. 7slandicus)
680 MR JAMES MURRAY ON
(13)—in which there are extra plates, the homologues of which are difficult to trace.
The third median is often lacking, or it may be united to the lumbar; the second
median also is sometimes absent. '
Owing to these variations, it is judged better to give under each species a formula
setting forth the number and arrangement of the plates, and of the various processes
(setee, spines, knobs) which they bear. When the homologous plates are recognisable,
they will be numbered as above.
Ricuters (9) divides the body into six principal segments :—I. (=head plate);
II. (=shoulder plate); III. (=jfirst pair); IV. (= second pair); V. ( =lumbar plate) ;
VI. (=toil-piece or anal plate).
Processes.—All the species have processes of some sort; many have numerous sete,
spines, or short knobs. Six sete are invariably present, viz., the four near the mouth,
and a pair behind the head. Besides these, there are usually some dorsal and lateral
hairs or spines. The dorsal processes arise (with the single exception of H. gladzator)
from the posterior margins of the plates which bear them. The lateral processes also
spring from the posterior margin, at the ventral limit of the plates (postero-ventral
angle). They are regarded by RicuTers as arising independently of the two plates
between which they are found; but they seem to me to be always more intimately
connected with the anterior of the two, and are often as rigidly joined to it as are the
dorsal processes, remaining attached to it after the skin has been cast, and the softer
integument between the plates decayed away.
Following the practice of PLaTE (5) and subsequent writers, the four short setee of
the face are disregarded (as being invariable) and only the longer head pair reckoned
among the lateral sete. It is understood that all processes are paired, and rise from
the posterior edges of the plates (except the median spine of L. gladiator).
Dorsal processes are rarely found on any but the paired plates ; lateral processes may
be on any or all of the plates which extend over the sides.
RicuteErs (12) distinguishes the lateral processes by the letters a, b, c, d,e; a=the
head seta, b springs from the shoulder plate, c from the first pair, @ from the second
pair, e from the cut separating the tail-piece or anal plate from the lumbar plate; ¢
might as readily be reckoned dorsal as lateral, as when it is a spine it often rises some
distance up the back. The positions of the various processes have been usually
indicated by their relations to the four legs; they can be more accurately located by
reference to the plates. The lateral processes, b, c, d, e, are over the four legs
respectively.
Texture of Skin.—The plates may be quite smooth (#. zslandicus), but are usually
covered with larger or smaller granules, which may be of equal size and uniformly
distributed, or irregular both in size and spacing. Some appear to have perforations in —
place of granules, or show other peculiarities, which will be noticed in the detailed
descriptions. The whole of the skin, as well as the plates, is sometimes finely granular,
the proximal part of the legs in some species coarsely so.
#
THE TARDIGRADA OF THE SCOTTISH LOCHS. 681
There is some doubt as to the precise nature of the apparent perforations of the
dorsal plates of certain species. 1 suspect that they may arise by decay of the granules,
and for this reason have made no use of them as specific characters. They are found
| in living animals, but are commoner in empty skins. That they are of some specific
value is shown by their constant occurrence in association with definite arrangements of
plates and spines. Where they occur, the perforations are very distinct, and marked
by clean sharp edges.
Legs.—The first leg has often a small sharp spine, the last leg a similar spine, or
more commonly a blunt palp, near the base. Both of these have probably been
generally overlooked, and may yet be found to be always present. The last leg has, in
most species, a serrate fold of skin about the middle of its length, which I call the fringe.
The claws are four in number in most species, probably in all, when fully grown and
mature. Generally the inner claws of each four have a decurved spine, called the barb,
near the base, or as high as half-way up the claw. The outer claws are devoid of barbs,
except in a very few species (Z. blumi, etc.). The barbs of the outer claws are straight,
and point outwards or upwards. The barbs of the last legs are larger than the others,
and often these alone have them; there may be as many as three barbs on each outer
claw of the last legs.
Teeth and Pharynx.—tThe teeth are always very long and straight, enlarged and
forked at the ends, which are often closely applied to the pharynx ; the points enter the
mouth. The pharynx is sometimes minute and round, sometimes pretty large and some-
what cordate. As a rule there are no rods, such as are found in Macrobiotus, two
obscure curved lines which diverge from the end of the gullet probably representing
them ; but RicuTers has seen rods in EL. wslandicus. I have never seen symplex forms
in this genus.
Reproduction.—All lay the eggs in the moulted skin. It has been thought that
the number of eggs is characteristic, as it is in many species of Macrobiotus. To a
Rertain extent this is so; but two species have been observed to lay eges when still very
“small (Z. mutabilis and FE. reticulatus), laying then only one egg, while larger
examples laid two, three, and four respectively.
| Development.—Comparatively few of the species have been seen to hatch out, all
which have been so observed having only two claws, which leads RicHrERs to suppose
hat all hatch in this form. Against this must be placed the fact that some individuals,
of species which lay large eges, have been found, so small that they might easily be
_ supposed to be newly-hatched larvee, but with four claws and all the outward characters
of the adult. These species were abundant in the collections where they occurred, and
“increased in them, yet two-clawed larvee were never found (e.g. EL. reticulatus).
The larvee usually lack some of the setee possessed by the adult, and those which
they have are relatively shorter. J] don’t know that any example has ever been kept
under observation from its hatching to maturity ; but where a species is abundant,
examples may be selected at all stages of growth. In examples which I have seen
ao
682 MR JAMES MURRAY ON
moulting, there was a considerable elongation of all the dorsal and lateral processes, as ®
well as development of the fringe and of the barbs of the outer claws. Many observa-
tions of a species, common in Loch Morar, and which I regard as belonging to
E. granulatus, are instructive as bearing on the value of all those points as specific
characters (Plate II. figs. 6a to 67). The larva was not certainly seen, but many
moults of large animals were observed. The youngest individuals seen had four claws,
without barbs on the outer ones; the fringe consisting of short blunt processes standing
far apart; the dorsal processes being a large spine on the first pair of plates, a short spine
on the second pair, and a mere knob on the lumbar plate ; the lateral setae were ¢ and
d (RICHTERS).
In a single moult the large dorsal spine elongated till it might be called a seta, the
short dorsal spine became a long one, the knob became a spine, the fringe acquired lone
teeth standing close together, straight barbs appeared on the outer claws of the last legs,
and the lateral setae elongated. In the last stage seen there were two pairs of ‘dorsal
setee, the first very long; the lateral setee were also very long; the outer claws of all
the legs had straight barbs, and those of the last legs had three such barbs.
Although no new processes appeared during these moults, except the barbs of the
outer claws, the changes are sufficiently great to render imperative extreme caution in
separating species by any of those characters, even if sexually mature individuals are
seen. We may fully expect that the working out of the life histories would lead to the
union of several of the earlier described species, and perhaps of some of the later ones
as well.
Species.—All observers have agreed in basing their species chiefly upon the number
and position of the spines or other processes; but it now begins to be suspected that
this may carry us too far, and give us a multitude of species founded upon larval forms.
RicHTERS advises that no species be described unless the eggs have been seen, or there is
some very marked peculiarity. Now that it is known that some species lay eggs when
not nearly full grown, even this rule may not be a perfect safeguard. It is a safe rule
that no form should be separated from a known species merely because of one pair of
spines more or less, or a difference in size of these appendages, unless there are other
characters, whether of texture, claws, fringe, or what not, to support it. Another rule,
laid down by JennrnGs (7) in regard to Rotifera, might well be applied to Tardigrada,
viz., that no species should be described without an accompanying figure. JENNINGS
remark, that in most instances the description could be better dispensed with than the
figure, applies equally to all microscopic biology.
Echinascus arctomys—Eur. (4), (5), (9).
Specific Characters.—Small; nine minutely punctate dorsal plates. No sete: or
spines except the six invariably present on the head. Legs slender, no fringe on last
pair; all claws without barbs.
THE TARDIGRADA OF THE SCOTTISH LOCHS. 683
In many respects this seems like the larva of some larger species, but the eggs have
been frequently seen. It is distinguished mainly by the lack of characters (fringe,
barbs, setze), which most species have when full grown. No formula of the arrangement
of the plates can be given, as in the examples observed they were obscurely separated,
the median plates being especially uncertain, and the separation of the pairs indistinct.
The number, nine, is that given by Prats. The whole skin is punctate. There is a
blunt palp on the fourth leg.
Loch Ness, frequent, 1904.
Echiniscus gladiator, n. sp. (Plate I. figs. la to Lc.)
Specific Characters.—Small, yellow or pale ‘red, all minutely punctate. Plates
obscure, the median slightly developed, the pairs hardly divided. Large median
recurved spine on anterior edge of second pair of plates. Lumbar plate deeply
trefoliate. Legs slender, no fringe on last; inner claws with decurved barb, very strong
on those of last legs. Eyes clear, not pigmented.
This is related to H. arctomys, which it resembles in narrow form, slender legs, lack
of fringe, and minute punctation, and like that it might be a larva. The eggs have not
been observed in this instance; but it differs markedly from EF. arctomys, the only
species to which it has any resemblance, not only in the great median spine, but in the
strong barbs of the last inner claws.
Length, up to about =), inch ( = 269z).
Among mosses and hepatics from the shores of Burlom Bay, Loch Ness, frequent ;
in Loch Ness, rare, February 1904.
Echimscus mutabilis, n. sp. (Plate I. figs. 2a to 2d.)
Specific Characters.—Fairly large, narrow, yellow, all minutely punctate with
pellucid dots. Plates many, scarcely of firmer texture than the rest of the integument
—partly outlined by folds, partly indicated only by interruption of the dots. Median
line on most plates caused by cessation of the dots. No fringe on last legs. Inner
claws with small decurved barb.
Arrangement of Plates.—(1) Head, entire, with usual six setee and two palps; (2)
Shoulder, divided in pair or four; (8) Median, triangular, divided in three; (4) Pair,
entire; (5) Median, triangular, divided in three; (6) Pair, entire; (7) Median, tri-
‘angular, divided in two; (8) Lumbar, divided in five (an anterior pair, and the usual
trefoil).
The usual ten plates are present, the additional ones arising from division of these.
Two varieties are distinguished :—(a) Plates sharply outlined, the lumbar having its
anterior portion separated as a distinct pair of plates, which partly overlap the posterior
trefoil; dots comparatively large, regularly spaced. (Plate I. fig. 2a.) (b) Plates
684 MR JAMES MURRAY ON >
rather more numerous (from further subdivision), some of them only faintly indicated,
the lumbar with its anterior portion not forming separate plates—general arrangement
the same; dots very minute, as in H. arctomys. (Plate I. fig. 2b.)
These two varieties can be distinguished among the smallest individuals, and appear
to be constant, no intermediate states having been found. The differences are not
sexual, both having been repeatedly found with eggs. A spine on the first leg, and
palp on the fourth, have been frequently seen in both varieties. 7 |
Reproduction.—Kgegs from one to four in number, laid in the moulted skin. An
example measuring z+, inch (about 116) laid a single narrow egg, which measured _
sty inch by 54, inch (43 by 26u). Larger examples laid two, still larger three, and
the largest observed four eggs, which are larger and relatively broader, those in one
skin measuring 34, inch by ;4, inch (66 by 504). They are usually dull yellow, but
sometimes pale red. It appears from the above measurements that the species lays
eggs when far from full grown. The newly-hatched larva has not been seen, but young
measuring no more than 33, inch (110) had four claws, the inner barbed, and all
other outward features of the adult.
Related to EZ. arctomys, which it resembles in narrow form, obscure plates, slender —
legs, lack of fringe, and in the finely punctate skin, it differs in the larger size, more
numerous plates, and in having barbs on all the inner claws. Size, up to ~, inch,
exclusive of legs ( = 269).
In Loch Ness, Loch Morar, and ponds at Fort Augustus, abundant—1903-—4.
Echiniscus wendti—Ricuters. (Plate I. figs. 3a to 3c.) (10), (15).
Specific Characters.—No setee except the usual six on the head, the lateral sete
at the back of the head twice as long as in H. arctomys. A fringe on the last legs.
A strong decurved barb on inner claws of last legs. Granulation small and uniform. —
A spine on the first leg, and a blunt palp at the base of the fourth.
Arrangement of Plates.—(1) Head; (2) Shoulder; (3) Median triangular; (4) —
Pair; (5) Median triangular; (6) Pair; (7) lacking; (8) Lumbar, trefoliate.
Its discoverer distinguishes the species by the long head seta, the fringe, and the
strong barb. Examples from Loch Morar agree in all those characters, but the
granulation is rather coarse, and appears to be variable.
Loch Morar, 1904, frequent.
Echiniscus reticulatus, n. sp. (Plate I. figs. 4a to 4c.)
Specific Characters.—Stout, broad, bright red. Plates ten, arranged on the
normal plan. Lateral setze on head very long. Plates covered with pattern of large
hexagons or circles, a slightly raised rim enclosing a flattish depressed surface. A long —
THE TARDIGRADA OF THE SCOTTISH LOCHS. 685
sharp spine on front legs, a blunter spine on the last legs. Fringe on last legs. All
inner claws with very small decurved barb near base.
Resembling H. wendti in having very long lateral setee on the head and no other
| setze on the body, it differs in the texture of the plates, the small barbs of the inner
claws, and the presence of the third median plate.. This plate is variable, and sometimes
appears to be united to the lumbar plate, though at other times quite distinct. The
hexagonal pattern on this plate is very faint or quite obsolete. The lumbar plate is
rendered trefoliate by two deep cuts, and is besides divided into four facets, the two
lateral and the posterior facets being bent at a sharp angle to the median facet. This
gives the appearance of a separate anal plate; but there is no real separation, the
pattern passing uninterrupted over the angle. The length of the lateral seta is equal
to the diameter of the body at the shoulder, or much greater. The teeth of the fringe
are often bifid.
Reproduction.—One to four eggs laid in the cast skin, the larger number laid by
larger, and presumably older, individuals. A skin measuring +}; inch (214) contained
three bright red egos of 54, inch by g$5 inch (71m by 594). The head seta in this
measured 4, inch (142). The newly-hatched larve have not been seen, but in-
dividuals so small that it might be supposed they had not moulted since hatching had
four claws, with the inner barbed, and the reticulated plates quite distinct.
Loch Morar, very abundant, Loch Ness, rare—1903—4. It has not yet been found
anywhere except in lakes.
Lchiniscus olhonne—Ricuters. (Plate I. figs. 5a—5b.) (10), (@Rs))
Specific Characters.—Small, plates ten, only two median triangular, anal plate
separate. ive lateral setee or spines, and two dorsal spines, on each side. Fringe on
last legs. Barbs on the inner claws, those of the last claws very strong.
Arrangement of Plates.—(1) Head, with longish lateral seta; (2) Shoulder, long
lateral spine and smaller one above it; (8) Median, triangular; (4) Pair, lateral seta and
‘small spine, strong dorsal seta; (5) Median, triangular; (6) Pair, lateral curved spine
and short spine, dorsal short spine ; (7) lacking ; (8) Lumbar, very long whip-like seta ;
(9) Anal. In Scottish examples the anal plate is not separate.
| Only two examples seen; no eggs. Margin of Loch Ness, February 1904. Loch
Earn.
3 Echimiscus granulatus—Doy. (Plate IIL. figs. 6a to 6f) (3), (5).
Specific Characters.—Plates nine, arranged in the normal manner, coarsely granulate.
| Three long lateral setee, and a short spine at the junction of the tail-piece with the
| lumbar plate ; two dorsal sete or spines on each side. Spine on front leg, and blunt
‘palp on last leg. Fringe on last leg. Inner claws with decurved barbs.
Arrangement of Plates.—(1) Head, with moderate lateral sete; (2) Shoulder ;
$ TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 27). 101
686 MR JAMES MURRAY ON
(3) Median, triangular; (4) Pair, long lateral seta, and strong dorsal spine or seta;
(5) Median, triangular; (6) Pair, long lateral seta, and strong dorsal spine or seta;
(7) lacking ; (8) Lumbar, trefoliate, with short spine.
Among forms agreeing with #. granulatus in having three dorsal processes, on the
first and second paired plates and the lumbar plate respectively, diminishing in size
from the first backwards, there is considerable variety in the size of the processes
and in the number of lateral setze. The dorsal processes may all be spines; or the first,
or both first and second, may be setee. There may be only two lateral setae, a and d; or
they may be three, a, c, and d. There is no justification for separating any of these as
distinct species, unless after a full study of the development, as the eggs are unknown.
Three varieties were found in Loch Morar.
First (figs. 6a and 6b). An elongate, large animal, with only two lateral setee, a and
d, one dorsal seta, and two spines. Straight barbs on the outer claws of last legs.
Granules variable in different examples—very coarse or moderately fine; uniform.
Pharynx large, cordate.
Though large, it has not been seen with eggs.
Size, gs inch = 294u
Second. Two large dorsal spines and a small one; three lateral setee, c and d very
long. Barbs of outer claws not seen. Granules moderate. Size, 5 inch = 277.
Third (figs. 6c and 6d), like the second, but first dorsal process a very long seta.
Straight barbs on the outer claws, up to three on those of the last legs. Granules
moderate. Size, up to gy inch = 312n.
The species resembles &. blum: (15) in having barbs on the outer claws. That
species has, however, more numerous lateral and fewer dorsal processes. The elongation
of the last dorsal process in H. granulatus would produce an animal like L. blum. The
absence of the barbs of the outer claws from descriptions of species must not be regarded
as of much importance, as they may have been overlooked, or they may only appear at
a late stage in development. Tor fuller account of appearance of barbs in this species, —
see ante, under development of Hchiniscus.
Habitat.—Loch Morar, abundant ; Loch Ness, frequent.
A larva, probably of this species, is shown in fig. 6e.
The first variety described above differs from this larva in that the second lateral
process is on the second paired plates, instead of the first ; so it may prove to belong to
another species.
Echiniscus spitzbergensis—ScourFiELD. (Plate II. figs. 7a to 7c.) (6).
Specific Characters.—Plates nine, arrangement normal. Four lateral sete (one on
the head, shoulder, and each of the paired plates); long dorsal seta on first pair,
and shorter spine on second pair. Inner claws with small decurved barbs. Granules
very large.
. fa |
a
THE TARDIGRADA OF THE SCOTTISH LOCHS. 687
I identify as this species an animal rare in Loch Morar. Though differing in some
details from Mr ScourFigtp’s species, I do not think we would be justified in separating
it, considering that there were no eggs seen in either case, and in view of the great
change in the size of the processes which takes place during development. Only empty
skins of the Loch Morar animal were seen. In place of the granules the plates were
covered by large quoit-like rings, the centres perforate, which | believe to originate in
the decay of the granules. They further differed in the dorsal spines on the second
pair of plates being long, and the small spines of the same plates lacking. The lateral
sete, a, b, c, d (RicHTERS), increase in size from a to d, which is very long. The
_ lumbar plate is trefoliate ; in ScouRFIELD’s examples, entire.
Length, Loch Morar examples, 735 inch (250).
DouBTFUL SPECIES.
Many examples of Hchiniscus have been found which, while differing more or less
from the descriptions of all known species, could not, in the absence of eggs, be
certainly identified, or regarded as distinct species. They are figured here, with short
descriptions, as an assistance to other observers. All were sufficiently large to be
regarded as probably nearly full grown, though size is not a quite safe criterion of age.
Echvmscus, sp.? (Plate II. figs. 8a—8b.)
Plates ten, normal. Lateral sete five, increasing in length from front to back.
Dorsal processes—a long seta on the first paired plates, a short knob on the second pair.
Fringe on last legs. Mid claws barbed. Granules of moderate size. The section of
the genus having five lateral processes contains about a dozen species. Some of them
(Z. duboisi, E. conifer, E. spinulosus, E. othonne, etc.) have very distinct characters.
If we bear in mind the elongation of the processes during development, many of the
other species will appear less certain, and it is noteworthy that the eggs of most of these
are unknown (14). Some of the forms having fewer lateral processes may be younger
stages of the same species. This and the two following forms belong to this section,
differing mainly in the proportions of the processes.
Loch Ness, at pier, 7th February 1904.
Echiniscus, sp.? (Plate II. figs. 9a—9b.)
Plates normal. Four of the lateral processes are long spines (? setee) with bulbose
bases. Dorsal processes—a long spine on the first paired plates, a very short broad
Spine on the second pair. Granular or perforate. This form, with small perforations,
as shown in fig. 9c, was frequent in Loch Morar, and was regarded as a distinct species
till another form was observed, identical with it in all else, but with fairly large
688 MR JAMES MURRAY ON
uniform granules. It is a curious fact that the perforations have a quite different size
and arrangement from the granules, so that they could not be derived from them, as”
was supposed to be the case with a similar form of E. spitzbergensis. (Plate II. fig. 7a.)
Echiniscus, sp.? (Plate II. fig. 10a.)
Two lateral setae (one after the plates of the first pair). Dorsal seta on plates of
first pair, short broad spine on plates of second pair. Spine on front leg. Fringe.
Inner claws barbed. Nearest /. aculeatus, differs in lateral process not double. (5).
Loch Ness, November 1908.
Two-CLAWED LARVA.
Three larval forms having two claws were seen. ‘Two of these are referred to under
the species to which they are supposed to belong (H. wendti, E. granulatus). The
third could not be identified.
Echiniseus, sp.?, larva. (Plate II. fig. 11.)
Plates ten, arrangement normal. ‘Three lateral processes—a short curved spine on
plate of second pair, a longer seta at junction of tail-piece and lumbar plate. No
dorsal processes. Granules moderate. Fringe of longish blunt spines. Claws two, the
barbs large. Blunt palp on last legs. Mouth palp appears to spring from elongate
curved process which bears the anterior mouth seta. Size ;3, inch.
Shore of Loch Ness at Fort Augustus.
MAacRoBIOTUS.
Generic Characters.—Obscurely segmented, without hardened dorsal plates. Claws
four, united in pairs, or one pair and two free claws. Teeth with bearers; gullet short,
rigid. Pharynx with several rows of hard rods or balls.
The genus Doyeria cannot now be maintained, as it has been shown by RicHTERS
that most (and probably all) species of Macrobiotus may get into a condition in which
the teeth are as in PLatr’s genus Doyeria. The distinction of the genus Diphascon is
also a slender one, there being intermediate forms between it and Macrobviotus.
The species of Macrobiotus are distinguished by the form of the claws, the texture
of the integument, and the number and arrangement of the pharyngeal thickenings.
The last character is most reliable, but in many individuals its value is lessened by
a curious reduction of parts which takes place. The eyes are of little importance, as
THE TARDIGRADA OF THE SCOTTISH LOCHS. 689
they may be present in some individuals of a species and not in others. The fat-cells
in the body-fluid have a characteristic colour; in most species they are clear and
hyaline, but in a few they are golden yellow or dark brown.
The segments of the body are superficial, affecting the skin only. There appear to
be usually two segments to the head, one to each pair of limbs, and intermediate
segments—ten in all; but they are often increased in number by subdivision, and there
are very commonly two between the third and fourth legs.
Simplex Forms (15).—Individuals of species of Macrobiotus are often found which
exhibit a remarkable reduction of the masticating apparatus: the teeth are straight,
without stays—they are not functional; the rods of the pharynx disappear ; in extreme
cases, the mouth and gullet are quite obliterated. This state can only be temporary,
or the animals would die; and they often appear in good health, and may have the
stomach filled with food. I can only suggest that it is temporary, and a preliminary
to moulting ; but if this is so, it is a remarkable parallel, among animals so high in the
scale, to the disappearance of the mouth in ciliata during fission.
In exceptional cases, the pharynx and teeth entirely disappear.
Reproduction.—Two forms of eggs are laid, the one kind round and spiny, the
other smooth and oval or elliptical. The spiny eggs are laid singly and free; the
smooth eggs are laid in the moulted skin, which serves as a protective capsule for them.
So far as known, the same species always lays the same kind of egg. The smooth and
spiny eggs are not, as from analogy we would expect, the summer and winter eggs of
the same species ; but further observation on the point is needed. The laying of smooth
eggs in the cast skin is the prevalent mode of reproduction in the genus as in the order.
It is very difficult to trace which species lay spiny eggs, as, for some unexplained
reason, animals containing such eggs are very rarely seen. When the young contained
in the smooth eggs are ready to hatch, it is seen that the teeth and pharynx are very
large and fully developed. The stiletto-like teeth are continually apphed to one spot
in the shell till they weaken and finally pierce it. At this stage the pharynx is not
very greatly inferior in size to that of the mature animal, and the characteristic
thickenings are all present.
Two groups of species are to be distinguished in the genus. The first, typified by
M. hufelandi, have the two pairs of claws similar, the claws strong, the claws of each
pair rigidly united and one of them slightly larger than the other, the larger claw of
each pair with a strong supplementary point. The second group includes species
having the two pairs of claws dissimilar, slightly united at the base only, the larger
pair having one very long slender claw and a much shorter one, the other pair similar
but smaller, or of two nearly equal claws—supplementary points none, or very
fine.
I believe all species of the first group lay spiny or viscous eggs ; those of the second,
smooth eggs enclosed in the skin. The species having two single claws and a pair form
an extension of the second group.
690 MR JAMES MURRAY ON
Macrobrotus hufelandi—C. Sou. (1), (14).
Specific Characters.—Large, dark-coloured, dark granules, in addition to the fat-
cells, in the body-fluid. Pharynx large, shortly elliptical, with two narrow rods and a
small nut in each row of thickenings. Teeth large, strong, curved, with strong bearers,
entering the throat. Claws, two similar pairs, each pair of a longer and a shorter claw
closely united, the larger claw of each pair with a double point (supplementary claw
near apex).
This is the water-bear par excellence, though no doubt the early observers confused
several species together under this name. It appears to be widely distributed over the
world, though perhaps less so than was formerly supposed.
There is a group of species, all very closely related to M. hufelandi, some so closely
that they can only be distinguished by the different forms of the egg spines. These
occur all over the world, and have no doubt been often mistaken for M. hufelandi, in
the absence of eggs.
One of the largest Tardigrada, attaining to ~) inch (625), and perhaps upwards,
HKyes are normally present—the blind condition having been described as a distinct
species (M. schulzet, GREEFF).
Habitat.—Common in the shallow waters of lakes; in Loch Ness it has been found
at a depth of 300 feet. Loch Morar; Loch Treig.
Macrobiotus echinogenitus—RicutTERS. (10), (14), (15).
Specific Characters.—Hardly distinguishable from M. hufelandi except by the eggs,
which are covered with conical processes, having acute—often curved—tapering points.
Those of M. hufelandi have the processes narrower cones, expanding at the apices into
little discs.
I have seen only the semplex form of this. The eggs are, however, very abundant
in Loch Morar.
Habitat.—Loch Ness, Loch Morar; common.
Macrobiotus islandicus—Ricuters. (Plate IL. figs. 12a to 12¢.) (18).
Specific Characters.—Hyaline, except stomach. Teeth strongly curved, with bearers;
teeth enter the mouth. Pharynx round, two short rods in each row, each about twice
as long as broad, besides a little round nut attached to the end of the gullet. Claws,
two unequal pairs, the longer claw of each pair with a supplementary point. Stomach
cells filled with dark blue granules.
The eggs were not seen, but Ricutrrs found them in Iceland.
Loch Ness, common, 1903-4. Not yet seen elsewhere.
THE TARDIGRADA OF THE SCOTTISH LOCHS. 691
Macrobiotus ornatus—Ricuters. (Plate LIT. figs. 13a to 13¢.) (8).
Specific Characters.—Glabrous and spineless, or finely or coarsely papillose, covered
with large granules on the back, or with many rows of long spines on the back and
sides. With or without eyes. Teeth somewhat weak, slightly curved, with bearers.
Pharynx circular, thickenings three in each row, round or nearly so. Claws, two
similar pairs, one of each pair longer.
I follow RicutTeRs in making the verrucose and spiny forms mere varieties of one
species, although I have seen no intermediate varieties, and would have regarded them
as distinct. As a logical consequence, the glabrous form must also be united with them.
Of the three varieties, the warted one is largest, and is the only one possessing eyes
(in Scottish examples). The spiny form has only been found in ground moss and in
ponds, not yet in lakes. The other two varieties are lacustrine, the glabrous one being
very frequent at lake margins.
Glen Roy, 1902—pond at Fort Augustus (var. spinoszssimus); Loch Ness (var.
| verrucosus) ; Loch Ness, Loch Morar, Loch Treig, smooth variety.
The eggs have not been observed in Scotland, but Ricarers found them in the
cast-off skin.
Macrobiotus annulatus, n. sp. (Plate ILI. figs. 14a to 14c.)
Specific Characters.—Skin pale yellow, stomach brown. All papillose except face
| and distal portion of legs. Papillee large, round, equal; on back and sides arranged in
| regular lines running round the body, but lost on the under surface. The usual apparent
seoments of Macrobiotus here divided into lesser segments, on each of which are two or
| three of the rows ‘of tubercles. ‘Two black eyes. Teeth strong, curved, with bearers.
| Pharynx nearly as broad as long, round or slightly cordate. Two narrow rods in each
| row, and a lesser round nut next the end of the gullet. Claws, two pairs slightly
| united, one claw of each pair longer than the other. Longer claws, with fine
supplementary points.
Reproduction.—Three elliptical eggs are usually laid in the moulted skin; they
| measure about 34, inch (67) long. A curious habit prevails, which I have not
observed or heard of in any other Tardigrade. The skin is not completely moulted, but
remains attached to the front of the head, and is carried about, with its contained eggs,
| for a long time, in some cases till the eggs hatch. As all my observations were made
upon animals kept in captivity, and therefore under conditions different from those
| to which they would be subjected in their natural home, we cannot be sure that this
habit is normal. It is noteworthy, however, that on every occasion when it was
observed the eggs were thus carried, and other species kept in the same way did not do
so. It was under almost continuous observation for more than a year, and many
hundreds of examples were seen carrying the skinful of eggs, and the practice was
repeated by successive generations.
692 MR JAMES MURRAY ON
It is ditticult to imagine how the eggs can be deposited in the skin while it remains
attached to the head, so that one is tempted to suppose that the moult is completed in
the usual way, and the skin picked up again afterwards; but this has not been seen.
The egg measuring 34, inch (67), produced a larva ;1¢ inch (142) long. The
pharynx was 7;/;5 inch (24) long. There was no trace of eyes nor of papille on the
skin or supplementary points to the longer claws, but otherwise the form was as the
adult.
Size, about ;!5 inch (417) or larger. Having some resemblance to M. granulatus
—Ricurers (10), which has, however, claws of quite different structure. The supple-
mentary points of the longer claws of each pair are much more distinct than is usual in
species having smooth eggs.
Habitat.—Bog pool at Fort Augustus, very abundant; margin of Loch Morar,
rare, 1904.
Macrobiotus papillifer, nu. sp. (Plate IIT. figs. 15a to 15c.)
Specific Characters.—Hyaline, two black eyes. Back and sides covered with conical
acuminate processes, arranged in transverse and longitudinal rows. Similar processes
on the head, or lacking. Teeth strong, curved, with bearers. Pharynx nearly as broad
as long, with three equal thickenings in each row, which are about twice as long as
broad. Claws, two nearly equal pairs, one claw of each pair longer.
Length, up to +45 inch (250 microns). Eggs laid in the cast-off skin. Five eggs
were laid in one skin, the animal being seen to leave the old skin by the anterior end.
Halitat.—Loch Ness, common; Loch Morar, rare.
This species is comparable with 1. tuberculatus—PuatE (5). The processes are more
numerous and of different form; but this would not justify its separation, if we had
not a more reliable character in the relatively large pharynx, with three short rods in
each row of thickenings. PLATE says that there are only two rods in each row in J,
tuberculatus, though his figure shows three.
SCOURFIELD, who has seen M. tuberculatus, regards this as distinct.
Macrobiotus oberhduseri—Doy. (8).
Specific Characters.—Dorsum, with nine transverse bands of a brown colour.
Pharynx, small round, with three short oval thickenings in each row. Claws, one pair
and two single claws. Hggs laid in the cast-off skin.
Various diverging if not conflicting diagnoses of this species are given by ditterent
authors, and it is probable that different species have been confused together. An
animal having the transverse bands of colour and small pharynx was observed in Loch
Ness, but it had not the two free independent claws which, according to Prats, this
species should have. This probably indicates only different interpretations of the
structure of the slightly united larger pair of claws.
Habitat.—Loch Ness, among moss growing on pier, February 1904.
fe es SS A a SOE
”
. «
é ad e
£6 ek eee ee ee
LIST OF WORKS REFERRED TO.
(1) Scnuurzz, C. A. S., “ Macrobiotus hufelandi,” Js’s of Oken, 1834, p. 708.
(2) Doyire, Ann, Sc. Nat., Paris. Il. Sér. T. 10. 1838.
(3) Doren, Ann. Sc. Nat., Paris. II. Sér. T. 14, p. 269. 1840.
(4) Enrensere, Mikrogeologie, 1854; Atlas, pl. 35n.
(5) Puatr, L. H., “Naturgeschichte der Tardigraden,” Zool. Jahrb., Bd. iii., Morph. Alt., 1888,
pp. 487-550. a
(6) Scourrienp, D. J., “‘ Non-marine Fauna of Spitzbergen,” Proc. Zool. Soc. Lond., 1897, p. 791.
(7) Jeynives, H. S., “ Rotataria of the United States,” U.S. Fish. Comm. Bull., 1899, p. 67.
(8) Ricutsrs, F., Ber. Senckenbg. Natf. Ges., 1900, p. 40. 4
(9) - » ‘Fauna der Umgebung von Frankfurt-a-M.” Ber. Senckenbg. Natf. Ges., 1902 3.
ein”
Se
(10) 5 » © Nordische Tardigraden,” Zool. Ang., Bd. xxvii., 1903, p. 168.
(11) - , “Der kleine Wasserbar,” Prometheus, 1903, p. 44.
(12) A , ‘“Verbreitung der Tardigraden,” Zool. Ang.. Bd. xxviil., 1904, p. 347. 4
(138) 3 » ‘‘Islandische Tardigraden,” Zool. Ang., Bd. xxviii., 1904, p. 373. 4
(14) ie ,, ‘Hier der Tardigraden,” Ber. Senckenbg. Natf. G'es., 1904, p. 59. 3
(15) FA , “Arktische Tardigraden,” Fauna Arctica, Bd. iii., 1904, p. 495.
EXPLANATION
ails are drawn larger, but to no uniform scale.
siculation of some species is shown.
i mer claw of last legs.
2. Hehiniscus mutabilis, n, sp.
sal view of typical example, three eggs.
sal view of variety.
er claw of last legs,
/, small example of type, with one egg.
3. Echiniscus wendti—RiIcHTERS.
] view.
PLATE
6. Echiniscus granulatus—Doy.
yy, dorsal view.
outer and inner claws of last leg of same.
and more typical example.
» claws of last leg, showing three barbs on
uter claw.
wo-clawed larva, probably of this species.
claws of the larva.
7. Echiniscus spitzbergensis—ScouRFIELD.
parent rings on the plates.
er and inner claws of last leg.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III.
THE TARDIGRADA OF THE SCOTTISH LOCHS.
697
OF PLATES.
The figures of the complete animals are all drawn to the same scale, to enable comparisons to be made ;
Where the granulation of the plates is minute it is
from the drawings, as it could only be indicated in an exaggerated form. The coarser granulation
Puate I.
1. Echiniscus gladiator, n. sp.
6, larva with two claws.
c, claws of larva.
4. Hchiniscus reticulatus, n. sp.
a, dorsal view.
b, reticulation, to larger scale.
c, inner and outer claws of fourth leg.
5. Hehiniscus othonncee—RiIcHTERS.
a, dorsal view.
b, inner claw of last leg.
le
8. Hchiniscus, sp. ?
a, dorsal view.
6, outer and inner claws, last legs.
9. Hchiniscus, sp. !
a, dorsal view.
6, granules seen on some examples.
¢, irregular perforations seen on others.
10. Echiniscus, sp. ?
a, dorsal view.
11. Echinascus, sp. %, larva.
a, dorsal view.
b, teeth and pharynx.
_¢, claws of last leg.
(NO. 27). 103
698 MR JAMES MURRAY ON THE TARDIGRADA OF THE SCOTTISH LOCHS.
12. Macrobiotus islandicus—RIcHTERS.
a, dorsal view.
6, claws.
ce, teeth and pharynx.
13. Macrobiotus vrnatus—RicHTERS.
a, dorsal view, var. spinosissimus, RICHTERS.
b, lateral view, var. verrucosus, RICHTERS.
c, teeth and pharynx.
14. Macrobiotus annulatus, n. sp.
a, mature example, carrying skin with eggs.
b, teeth and pharynx.
c, claws, under pressure.
18. Ege of Macrobiotus hufelandi, C. Scu.
19. Egg of Macrobiotus, sp. ?
20. Egg of Macrobiotus, sp.?
21. Egg of Macrobiotus echinogenitus, RICHTERS.
22. Egg of Macrobiotus, sp. ?
23. Diphascon chilense—Puats.
a, dorsal view.
b, teeth and pharynx.
24, Diphascon spitzbergense—RicHTERS.
a, dorsal view.
5, teeth and pharynx.
Puate III.
15. Macrobiotus papillifer, n. sp.
a, dorsal view.
b, teeth and pharynx.
¢, claws.
16. Macrobiotus macronyx—Doy.
a, lateral view.
b, teeth and pharynx.
c, pair of claws of last leg.
d, pair of claws of first leg.
17. Macrobiotus, sp. ?
a, empty skin with five small eggs.
b, part of reticulation, on larger scale.
c, claws.
Puate LY.
25. Diphascon angustatum, n. sp.
a, dorsal view.
b, teeth and pharynx.
c, claws.
26. Milnesium tardigradum—Doy.
a, dorsal view.
b, teeth and gullet.
¢, claws.
Vol. XLI.
PUAnE. jit
TARDIGRADA OF THE SCOTTISH LOCHS.
.
MURRAY
M‘Parlane & Erskine, Lith Edin®
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IM'Farlane & Erskine, Lith Edin?
MAGROBIOTUS ISLANDICUS, Richters 13, M. ORNATUS, Richters. 14, M. ANNULATUS, n sp.
15,M. PAPILLIFER,n.sp. 16,M.MacRONYX, Doy. 17, Macrostortus. sp.?
7d Soc. Edin? Vol. XUL
Murray: TARDIGRADA OF THE ScottisH Locuys——PuiaTe IV
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| ROBIOTUS HUFELANDI,6,Sch,Ecc. 19,20, 22,Fecs or MACROBIOTUS, sp? 21, M. ECHINOGENITUS. Richters.
49, VIPHASCON CHILENSE, Plate. 24 1), SPITZBERGENSE, Richters. 20, D. ANGUSTATUM, n.sp.
’ 26, MILNESIUM TARDIGRADUM, Doy.
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( 699 )
XXVIII.—The Plant Remains in the Scottish Peat Mosses. By Francis J. Lewis,
F.L.S., Assistant Lecturer in Botany, University of Liverpool. Communicated
by Professor Grixie, LL.D., F.R.S. (With Six Plates.)
PATI
THe Scorrisp .SouTHERN UPLaANps.
(MS. received May 31, 1905. Read July 8, 1905. Issued separately August 7, 1905.)
The following paper deals with an investigation of the successive zones of plant
remains contained in the deeper peat deposits covering areas in the Scottish Southern
Uplands. The field work was carried on during the summer and early autumn of 1904,
and the detailed examination of the peat in the laboratory during part of the winter.
No attempt has been made to work out the detailed flora of the different zones, but atten-
tion has chiefly been directed to the dominant plant remains found at different horizons
in the mosses. Whilst the list of. plants from each zone is small, the general facies of
the flora of any layer can be gauged from the abundant presence of a few characteristic
plants such as Salix reticulata and Empetrum, or Sphagnum and Eriophorum. Thus,
while the investigation is incomplete as regards any addition to the history of the
British Flora, it will, I hope, throw some light upon the succession of vegetation over
the older peat mosses since their origin.
Much work has already been done, chiefly by CLEMENT Rerp (1), on the plant remains
from some of the interglacial and earliest post-glacial deposits in England. The remains
have chiefly been taken from clay and sand beds, and for that reason would generally
be more plentiful and better preserved than the remains contained in the peat; for the
flora of peat mosses is comparatively small, and many square miles are often tenanted by
a few dominant plants, such as Sphagnum or Eriophorum. Although the plant re-
mains from the older peat mosses may not add much to our knowledge of the history of
the British Flora, yet as they date from late glacial times, they will indicate the type of
conditions which have prevailed both in the lowlands and highlands at each successive
period down to the present.
Much has already been written by different observers on the subject of the Scottish
peat mosses, and is summarised in Professor GErkIE'Ss Prehistoric Europe and need not
be referred to in detail here.
The recording of a plant, or set of plants, from a peat moss is of little value without
a description of the beds which lie above and below the plant remains, the character of
the flora of the moss, and other features which would help to determine the age of the
peat. ‘The kind of observations that are needed have been described by CLemuntT Rerp
(2), who lays stress on the point that observations on the succession of plant remains are
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO, 28). 104
700 MR FRANCIS J. LEWIS
far more likely to throw light on the questions at issue, than the collecting of remains
over large areas where no succession can be made out. .
On the Continent the plants preserved at different horizons in peat mosses have been
fully described by SteenstRup, Biyrr, Gunnar ANDERSSON, NarHorst, SCHROETER,
and many others, and I hope that correlation between these zones and those in the
British peat may be possible when more areas have been investigated in this country.
Method of Survey.—The following results have been obtained from sections, made
for the purpose of this survey, in the untouched portion of the mosses. The peat of
many of the lowland and some of the upland districts is still dug for fuel, this being
particularly the case in Wigtonshire, Ayrshire, and Selkirkshire. Even in these districts,
however, the turbaries have trenched very little on the mosses, being confined to the
drier margins. The surface peat, being unsuitable for fuel, is generally taken off the top
of the turbaries and laid down upon the excavated area. This quickly becomes grown
over with vegetation, so that it is frequently difficult to determine the exact boundary
of some of the older turbaries. To avoid any error due to this source, independent
sections have been made in all cases away from the turbaries.
The following results are based upon evidence obtained both by means of sections
-and borings. The borings were made with a 23-inch clay auger with rods to bore to a
depth of 20 feet. Fairly good cores were obtained when dealing with dry peat; but
the evidence from borings alone is not always to be trusted, as a layer of wiry stems
imbedded in soft peat may easily be pushed aside by the boring tool without being re-
presented in the core. Except in the few places where it was impossible to cut sections,
the borings have only been used for verifying facts already ascertained by digging in
other parts of the mosses, or for ascertaining the average depth of a large moss.
The sections were generally in the form of a pit 6 feet wide and 8 feet long where
the depth of peat to be cut through did not exceed 8 or 10 feet; but in many cases the
sections had to be carried down 16 or 17 feet before the basal layers of the moss were
reached, and in such case the section would be enlarged to 12-16 feet in length with a
series of steps or terraces at one end. After the underlying rock had been reached and
cut into as far as possible, the sides of the section were carefully examined for evidence
of stratification. Material would then be cut from each layer, placed in tins, labelled,
and sent to the laboratory for detailed examination. Larger blocks of the peat, to
show the sequence of beds, were also cut from many of the sections and sent to the
laboratory for more detailed examination than was possible in the field. In cases
where the peat rests upon sand, it is frequently traversed towards the base by cracks,
and the inrush of water through these caused much delay. This was particularly the
case in the Merrick mosses, where many sections had to be abandoned when only half
finished owing to the rush of water.
In most of the British peat mosses the plant remains are not so perfectly preserved
as in the Continental peat, and seeds are comparatively few in number. I have found
that the isolation of the plant remains can most easily be effected by examination of
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 701
the peat under a dissecting microscope, though this is at best a tedious process.
Gunnar ANDERSSON (8) has described a special method of loosening the peat by treat-
ment with a strong oxydising agent such as nitric acid. This partly bleaches the peat,
_ which, placed in a metal net, is kept below water. The finer material, consisting of
,
" @
groups of cells and unicellular organisms, floats out in the water ; the coarser remains,
such as seeds, stems, etc., are retained by the net, and can then be spread out on a
slide and examined under the microscope. This method yields good results when
dealing with peat rich in plant remains. Specimens of the peat from different layers
have also been embedded in parattin wax, and serial sections cut with a microtome and
mounted in Canada Balsam for microscopic examination.
The following areas were investigated during last year :—
1. Upland mosses in Kirkcudbrightshire and Ayrshire :
The mosses lying between the Merrick and Kells range.
2. Upland mosses in Selkirkshire :
Mosses in the Tweedsmuir and St Mary’s Loch district.
3. Hill-top mosses in Peeblesshire and Edinburghshire :
Peat of the Moorfoot Hills.
4. Lowland mosses in Wigtonshire :
Flow of Dergoals, Dirskelpin Moss, Knock Moss, Anabaglish Moss.
5. Buried peat and clay beds in the Harn Valley.
6. Mosses resting on the 25-feet raised beach of the south coast :
Moss of Cree in Wigtonshire. Priestside Flow in Dumfriesshire.
A preliminary examination was made of the peat of Lochar Moss in Dumfriesshire,
some of the Scottish Midland Plain mosses, and the hill-top mosses of Cross Fell in
Cumberland ; but, owing to want of time, a complete investigation of these mosses had
to be postponed.
THe Uptanp Mossss or tHe Merrick anp Keuus District.
The mosses investigated in this district lie at elevations of 700-1000 feet above sea-
level, and are situated in the valley running north and south between the Merrick and
Kirriereoch range of hills on the west and the Kells range on the east (one inch Ordnance
Survey—sheet 8). The valley is about 10 miles in length with an average width of 2-3
miles, and is drained to the north by the Gala Lane flowing into Loch Doon, and by
Cooran Lane flowing south. The divide between the two drainage systems is situated
5 miles south of the head of Loch Doon, in the form of a low neck of land with an
elevation of about 1000 feet running between Mullwarchar on the Merrick range to
Corserine on the Kells range. The Merrick range, as a whole, is granitic in structure,
whilst the Kells consists of Silurian rocks.
The marks of glacial action are evident everywhere in the district ; the rocks are fre-
quently ice scratched, perched blocks are numerous, and small moraines in a remarkably
bi
702 MR FRANCIS J. LEWIS
good state of preservation are to be seen at the entrance to many of the small lateral
valleys and along the foot hills of both the Merrick and Kells. These small moraines
are contemporaneous with the numerous moraines in the Loch Skene and Tweedsmuir
district at similar elevations, and belong to the “third” epoch of glaciation, or the
period of local ice-sheets and valley glaciers of the Southern Uplands (4). The mosses
occurring here are evidently younger than the moraines, as in many places they run up
to the foot and actually rest upon these moraines.
The peat forms an irregular border on the sides of the Gala Lane and Cooran Lane,
varying in width from $ a mile to 1} miles. The five miles of peat south of a line
drawn from the foot of Craignaw to Elderholm is covered at present by Sphagnum,
The five miles of peat lying to the north of this line is better drained, and tenanted by
a much drier type of vegetation consisting of Calluna vulgaris, L.;* Eriophorum
vaginatum, L.; Myrica Gale, L.; Carices, and Juncus Squarrosus, L.
Tree vegetation is entirely absent from the district, the first natural woodland on the
east lymg 9 miles away in the Ken Valley on the other side of the Kells range, and
westward, 15 miles away on the other side of the Merrick Hills in the Barrhill district.
For purposes of description the peat can be divided into two districts by a line drawn
across the valley from the foot of Craignaw to Elderholm, for the features presented by
sections in the southern area are somewhat different from those in the northern area.
The northern area will be described first.
The peat is undergoing denudation at the present day, being channelled into peat- —
hags. (Fig. 1.) The amount of denudation, however, is not so great as in other hill
districts situated farther east both in Scotland and England. The first series of sections
were made near the rising place of Cooran Lane, and the following plant-beds were
exposed :—
1. Peat formed chiefly from Scirpus and Eriophorum vaginatum, L., 7 feet.
2. Layer of Pinus sylvestris, L.; trees with stools of large size
and numerous cones, : ; Ber.
3. Peat formed chiefly from Sphagnum, . : 2.
4. Eriophorum vaginatum, L., peat, : : d 6 inches.
5. A layer of the stems of Hmpetrum nigrum, L., sharply divided
from the peat above and below, } : 5a Ses
6. Eriophorum vaginatum, L., peat, : . aa
7. Sphagnum peat, ; : ; ; Ate
8. A layer of Betula.
9. Structureless peat mixed in some places with much coarse granite
sand.
10. Coarse granite sand. Bored through for 2 feet, but further boring
stopped by the rush of water and the difficulty of obtaining
a core.
* The nomenclature of HookgEr’s Student’s British Flora, third edition, is followed throughout.
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 7038
Horizontal exposures were then made of the successive beds, and the same general
features were found to be present. The Empetrum bed can be traced for some distance
without cutting into the peat, as the channels in the peat-hags are worn down to about
a foot below its level. (Fig. 2.) Three sections were made between Elderholm and
the watershed—a distance of about a mile—and the same succession of plant-beds were
exposed in all cases.
Sections were then made on the western margin of the peat at the foot of Craignaw
—one of the out-lying hills of the Merrick range. The ground rises here to a little
over 1000 feet, and the peat is better drained than in the centre of the valley. The
same sequence of beds was found, but the character of the Empetrum bed alters con-
siderably. Empetrum is only occasionally present, and its place is taken by abundant
Salix herbacea and S. reticulata. The Eriophorum and Sphagnum beds are also
thinner above and below the Empetrum bed, and the growth of the peat has been slower
on this sloping, well-drained ground than at the bottom of the valley.
Sections and borings were made north of the divide, towards Loch Doon on each
side of Gala Lane, and the same plant beds were seen to extend here also. A section
near Yellow Tomach, three miles north of the previously described section, exposed the
following beds :—
|. Scirpus and Sphagnum peat, . 8-43 feet.
. Layer of Pinus sylvestris, L.
. Sphagnum peat, with traces of shrubby birch in the lower layers, 1 foot.
. Layer of Empetrum mgrum, L., . 5 : 3 inches.
Oo e c Wb
. Birch remains, with scanty Catan and Santon patches of
Sphagnum.
6. Below the last layer, but not sharply marked from it, stems
and leaves of Salix repens, L.
Racomitrium ellipiticum, B. & 8. Epilobiwm palustre, L.
Comparing this section with the one previously described, it will be seen that layers
1—4 agree, and that the difference lies in the absence of the underlying Eriophorum
and Sphagnum layers in the northern section. In the case of the peat near Yellow
Tomach, the growth of the birch appears to have been nearly continuous up to the
occurrence of the Empetrum bed, although much Sphagnum is mixed with it in places.
This variation at different spots does not, I think, impair the comparison between the
different sections, as we should expect some variation in the contemporaneous vegetation
at different places in the valley ; and the Empetrum bed always stands out as a kind
of landmark— Empetrum dominant in some places, and Salix herbacea, L., and
S. reticulata, L., dominant in others.
The occurrence of a compact layer of Empetrum, mixed with such northern forms as
Salia herbacea and S. reticulata, undoubtedly marks a period in the growth of this
peat when the conditions must have been very different to those under which the under-
lying peat and the overlying Eriophorum, Pine, and Scirpus-Sphagnum zones were
704 MR FRANCIS J. LEWIS
formed. Salix herbacea at the present time is confined to the summits of the highest
English and Scotch mountains. South of the Tweed it occurs on a few of the highest
Welsh mountains, and also on the Lake mountains, seldom occurring much below 2500
feet. In Scotland it is confined to the summits of the Highland mountains, and to a
few of the summits in the Southern Uplands. S. reticulata is still more restricted in
distribution, beg confined to the Highlands between 2000-3200 feet. Northwards,
both plants reach the limits of Arctic vegetation. Extreme northern types are absent
from the present vegetation of the western part of the Scottish Southern Uplands.
The basal peat of Section 1 has not yielded any determinable plant remains,
Microtome sections have been cut and examined under the microscope, when the peat is
seen to be formed of structureless plant remains, except traces of Sphagnum and some
isolated pollen grains agreeing closely with those of A/nus glutinosa. The basal layers
of the peat near Yellow Tomach, however, yield evidence that the conditions about this
time were not greatly different to those prevailing at the present day. These mosses,
then, must have originated some considerable time after the disappearance of the local
glaciers which deposited their moraines between the Merrick and Kells Hills, and at a
period late enough for the climate to have become not less mild than at the present day.
At a later date the whole district became clothed with woodland of a fairly northern
type, mixed with Calluna moor, with a small growth of Sphagnum in the wetter places
and bordering the moorland pools. After this period the vegetation undergoes a com-
plete change. The woodland disappears, and the Calluna is replaced by Sphagnum,
which in turn is again replaced by Eriophorum vaginatum, changes which indicate a
steady increase in precipitation. ‘l’he Eriophorum zone, later, gives place to an Arctic
plant-bed consisting of Salix herbacea, S. reticulata, and Hmpetrum mgrum, and thus
indicating a period when the conditions in the Galloway valleys must have been similar
to those at present obtaining on the summits of our highest mountains. No other con-
clusion can, I think, be drawn from this zone, as it maintains its character so uniformly
over an area many miles in extent, and corresponds closely with the type of vegetation
covering large areas on tundras at the present time.
The presence of moraines on the 45-50 feet raised beaches in the Highlands,
described by Hinxman (5), proves that the smaller moraines found in the Highland
valleys do not merely represent the dying away of the ice-sheet which deposited its
moraines in the valleys of the Southern Uplands, but that they belong to a much later
return to glacial conditions—separated from the former by a period long enough to have
enabled a temperate flora, represented here by the Betula zone, to have overspread the
country. If that is so, the Arctic plant zone found in this peat must be contemporaneous
with this later return to cold conditions—+.e. with the fourth glacial epoch, or the period
of mountain valley glaciers when the snow-line stood at about 2500 feet. The plant-beds
above the Arctic zone show a gradual return from cold conditions to somewhat more
genial conditions, although at first characterised by great precipitation. As the conditions
became drier, the whole of the valley became covered with pine forest. (Fig. 3.)
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 705
According to the geological evidence, after the warm period following the formation
of mountain valley glaciers there was again a partial return to cold conditions, evidenced
by the corrie moraines of the Highlands ; but this moderate degree of refrigeration might
- eause but little change in the vegetation of the valleys in the Southern Uplands. Be
that as it may, the pine forest in this district vanished, and its place was taken by a
much wetter type of moorland vegetation, as the 7 feet of peat above the pine zone to
the present surface is chiefly formed from such plants as Sphagnum, Scirpus cxspitosus,
L., and Carices.
As I have read the evidence, these mosses began to form some time during the inter-
glacial period between the district glaciers and the return of glacial conditions marked
by the mountain valley glaciers ; and if that is so, these mosses reproduce the general
aspect of the vegétation at each succeeding period down to our own.
At the present time the peat is not growing to any appreciable extent, and it is
difficult to say how much peat has actually been denuded away since the cessation of
growth. It is interesting to note that the present vegetation is chiefly made up of the
following plants: Calluna vulgaris, Salisb.; Molinia cerulea, Moench.; Myrica Gale, L.;
Juncus Squarrosus, L.; Erica Tetralix, L.; and a small quantity of Eriophorum
vaginatum, L., and Scirpus cespitosus, L.; but immediately below the surface of the
peat the remains of Sphagnum and Scirpus become dominant—evidence of the prevalence
of an altogether wetter type of vegetation. The question of the denudation of the peat
will be dealt with later.
The Southern Area of the Merrick-Kells Mosses.
A series of borings were made through the peat lying immediately south of the area
just described. The average depth of the peat is about 15 feet. The floor of the moss
is formed of coarse sand, through which borings were carried for 18 inches; but no
change in the character of the sand was observed at this depth. The basal peat
immediately resting upon the sand shows no recognisable plant remains, but consists of
a fairly dry compact mass. Small blocks have been embedded in parattn wax, from
which microtome sections have been made, which on examination with the microscope
showed no structures which could be identified with certainty. Traces of vascular
tissue in the shape of a few spiral vessels were found in one place, and pollen grains
resembling those of the alder, and fragments of birch twigs, but nothing that would
help to determine the conditions under which this layer was formed. Lither this basal
peat is disintegrated drifted material from the higher peat of the north, or the earliest
plant remains have been completely disorganised. A considerable quantity of coarse
grit occurring amongst this basal layer suggests that the peat is really drift.
As far as the borings show, the whole of the upper peat is formed from Sphagnum,
Scirpus sp., and Carices, with here and there traces of Eriophorum. More satisfactory
evidence of the history of this area might be obtained by cutting sections; but the
706 MR FRANCIS J. LEWIS
amount of water present in the upper layers prevented this, as the sections became
filled before they could be carried down farther than 38 or 4 feet. So far as the
evidence collected goes, this peat has had a different history from the 7 or 8 miles of
peat lying immediately to the north, as here all the beds represented in the northern
area from the basal birch to the pine zone are wanting, and the peat appears to have
had an uninterrupted swamp history.
THe Upztanp Mossks oF THE TWEEDSMUIR AND St Mary’s Locu District.
(One inch Ordnance Survey—sheet 16.)—Peat occurs abundantly in the hill district
lying between the head-waters of the Tweed and St Mary’s Loch, both as upland peat
covering the slopes and floor of many of the valleys, and as hill-top peat covering the
summits of the hills up to 2500 feet, and is developed to a greater extent on the Hart-
fell and White Coombe hills than on the Broad Law group. The average depth of the
hill-top peat is about 6-8 feet, and the depth in the valleys about 10-14 feet.
Work in this district was chiefly directed to the Megget Valley, and particularly to
some of its tributary valleys. Megget Water drains the eastern slopes of the Broad
Law group on the north, and the Talla Side and Lochcraig Head on the south, and
some of its tributary valleys run far up into the upland and hill-top peat districts.
The peat about to be described lies in Winterhope, the main southern valley leading into
Megget Water. The burn flowing in this hope rises on the peat-covered ground near
Loch Skene, and flows northward for about 5 miles before joining Megget Water.
Evidences of glacial action are plentiful over the whole of the district, the terminal
and lateral moraines being particularly distinct. They are to be seen in many of the
northern tributary burns of the Megget Water, in the main valley itself, and are
beautifully shown at the junction of Winterhope Burn with Garley Burn. (Fig. 4.) The
moraines are found at altitudes of from 900 feet-1500 feet, and are contemporaneous
with the third period of glaciation or the district ice-sheets and valley glaciers of the
Southern Uplands.
In some places the moraines rise out of the peat-covered districts, as at the head of
Loch Skene (fig. 5), and in other places the moraines are themselves covered thickly
with peat (fig. 9). The peat then in such positions is clearly younger than the
moraines upon which it rests, and cannot be older than the peat described in similar
positions in the Merrick-Kells district, and it contains evidence by which it can be
directly compared with the peat layers in that district.
The sections were made at the junction of Winterhope Burn and Garley Burn, where
a thick covering of peat is developed in the hollows between the moraines. At the
present time it shows the usual “ peat-hag” formation of high mounds and ridges of
peat with deep channels between, the summits of the mounds being covered with
a vegetation consisting of Calluna vulgaris, Salisb.; Erica Tetrahx, L.; Scirpus
cespitosus, L. Farther up Garley Burn and beyond the area covered by peat, clay beds
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 707
alternate with beds of peat. These will be described later. Sections cut through the
deep surface peat showed the following sequence of layers with plant remains. Layers
6, 7, 8, 9, and 10 are shown in fig. 10.
iL.
2. Peat containing much Hmophorum vaginatum and Polytrichum,
3.
Peat containing Calluna stems, with traces of shrubby birch.
Upper forest of Betula alba, L. ;
Menyanthes trifoliata, L. ; Epitbia ee i ve 6.)
. Sphagnum peat, .
. A zone formed mainly of the stems of eiipoetreim ngrum, L.,
with Lowseleuria procumbens, Desv.,
This layer is characterised by a thin ead of Roplioram
above and below.
. Sphagnum peat. Traces of Calluna, :
. Lower forest of Betula alba, L.; Menyanthes tirfoliata, L. ;
Potentilla Comarum, Nestl.,
. Mossy layer,
. Brown sandy peat,
Containing Ranunculus one ike Vola Spas Epobien
palustre, L.—very abundant ; Men ianthes trifoliata, L. ;
Ajuga reptans, L.; Alnus glutinosa, Gaertn. ; Corylus
_Avellana, L.; Salhix purpurea, L.; Fragments of
coniferous wood, water bourne; Potumogeton, sp. ;
Equisetum, sp.; Hypnuim cordifolium, Hedw.; Tor-
tula angustata, Wils.
10. Light gray fine sand,
ie
Moraine material.
Deets
1
ls ”
10 in.
Other sections proved that these layers are continuous through the peat at this place.
Comparison of these beds with those found in the Merrick-Kells mosses will be made later.
Mention has already been made of the clay beds interstratified with peat layers:
The banks of some of the lateral burns draining into Garley Burn were cut back, and
the following strata exposed (fig. 8) :—
. Vegetable soil,
. Sandy clay,
. Peat containing birch,
. Peaty clay.
. Peat containing birch.
. Peaty clay.
. Fibrous peat containing Betula alba, L.; Menyanthes tri-
foliata, L. ; Epilobium angustifolium, L.; Sphagnum, sp. ;
Hypnum, sp.; Alnus glutinosa, Gaertn.; Vaccinium
Myrtillus, L.; Equisetum, sp.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 28).
L=slina,
SEE
5 in.
708 MR FRANCIS J. LEWIS
8. Brown clay, peaty above, and containing scanty remains of
Equisetum; becoming pebbly towards the base, and
resting on moraine material.
The clays of this section contain no stones, and show every evidence of having been
deposited by water; and this alternation of clay beds and peat layers has evidently been
caused by flooding, which has continued uninterruptedly for a period long enough for
about a foot of sandy clay to be deposited. The regular alternation of clay beds with
wood peat is at first very striking when seen in section, but it is difficult to correlate
these beds with those described in the first section unless the clay beds correspond with
the wet-condition peat of layers 8, 6, and 4 of Section 1. There is nothing in the
relative positions of the two sections which would preclude this explanation, for
local flooding affecting Section 1 during a wet period might not have spread to
Section 2.
The peat covering the level ground and slopes on the N.H. side of Loch Skene, and
forming the gathering ground of Winterhope Burn, was next examined. ‘The same
evidence of present denudation is to be seen here, the peat in some cases being wasted
away to within 1 or 2 feet of the underlying glacial deposits. Several sections and
borings were made in this locality, and al] agreed in showing the following changes in
vegetation :—
1. Scirpus and Sphagnum peat, with occasional Calluna, . 3 feet.
2. Empetrum zone, . : ; a
- 8. Traces of Betula.
4. Dry hard peat, with traces of Calluna towards the base, . é Oo ee
5. Pebbles and clay.
On comparing the sequence of beds in the northern area of the Merrick-Kells
mosses and the Winterhope peat, a striking similarity is seen. In both cases two
woodland beds are present, separated by layers showing a considerable increase in
precipitation. Thus, in both districts the basal woodland bed is covered with Sphagnum
peat, which at a later date was replaced by a vegetation in which Hriophorum
vaginatum was the dominant plant. Such plant associations cover the wettest areas
on our moorlands at the present time, having been mapped in 8. Yorks. by Dr Smirx
(6), and on the Northern Pennines by myself (7). The most interesting point, however,
is the fact that thése wet-condition beds are overlaid in both districts by a thin seam
of Arctic plants—Empetrum with Salix herbacea and S. reticulata in the Merrick-
Kells mosses, and Empetrum and Lovselewria procumbens in the Tweedsmuir district ;
and the evidence can, I think, be hardly interpreted in any other way except that a
considerable decrease in temperature took place at the time this bed was forming. The
interest of these two districts is further increased by the fact that a gradual change
takes place above these Arctic plant-beds. Immediately over them lies Hophorum
vayinatum peat, which again is covered with Sphagnum peat. The line of division
between the lower surface of the Arctic plant-bed and the underlying Eriophorum peat
|
|
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 709
is very sharply marked ; there is no gradual transition from Eriophorum conditions to
Hmpetrum and Arctic willow conditions, and this may indicate that some time elapsed
between the close of the Eriophorum formation and the beginning of the Empetrum,
Salix, and Loiseleuria formation, during which time no peat was formed. The Arctic
beds, although only 4-6 inches thick, may have required a length of time for their
formation altogether incommensurate with their thickness. Such plant associations
having Empetrum as the dominant plant, with Arctic willows and trailing plants such
as Loiseleuria, cover large areas in Central and Southern Greenland and have been
described by Warmine (8), and this goes to show that the conditions then obtaining in
the upland valleys of Galloway and Tweedsmuir were essentially similar to present-
day shrub-tundra conditions in Greenland, and very similar to what might have been
expected to prevail during the period of mountain valley glaciers when the snow-line
lay at about 2500 feet, thus giving a permanent snow-cap to the highest hills of the
Southern Uplands. The evidence thus collected from upland peat occupying the same
position with regard to the valley moraines both in Galloway and Tweedsmu1, agrees
in almost every detail. The woodland at the base of the Tweedsmuir peat throws
some light upon the character of the structureless peat met with in some of the sections
of the Merrick-Kells district. During the interglacial period following the district ice-
sheets and valley glaciers, two types of woodland flourished in the Tweedsmuir district :
the first consisted of such trees as Corylus, Alnus, and temperate willows ; the second
of more northern types, such as birch. The sections near Yellow Tomach, in the
Merrick-Kells district, also show the same feature—temperate willows at the base
merging above into birch, and patches of Calluna. In other sections in the Merrick
district the birch rested upon peat in which no plant remains could be recognised ; but
the original vegetation here was probably of the same character as that found farther
north in the same district, and also in Tweedsmuir. The latest forest in the Merrick-
Kells mosses is pine, and in the Tweedsmuir district, birch; but this hardly prevents
comparison between these beds, as it might be expected that diversity of tree vegeta-
tion would occur in different parts of the country during a forest period—even as tree
distribution ditfers at the present day.
THE Hini-rop Peat oF THE MoorFoor HILLs.
(One inch Ordnance Survey—-sheet 24.)—The lower boundary of the peat in the
Moorfoot Hills closely follows the 1750-feet contour line, seldom occurring below, and
generally running somewhat above. From here the peat stretches upwards, and covers
the summits of the highest hills up to 2136 feet. The peat-covered ground is tenanted
by an association dominated by Ericphorum vaginatum, L.; Calluna vulgaris, L.; and
Vacceinvum Myrtillus, L., with Rubus Chamaemorus, L., on the higher ground ; whilst
the lower slopes below the peat covering are dominated by Nardus stricta, L. The dis-
tribution of the different plant associations covering this ground has been described in
detail by Rozerr SmirxH (9). Nowhere in the districts investigated can the present
710 MR FRANCIS J. LEWIS
denudation of the peat be seen in a more striking form, the whole of the peat area being
intersected by deep channels, whilst the larger burns have cut through the peat some
distance into the underlying clay. (Fig. 11.) The boundary of the peat and Nardus
vegetation forms an irregular line along the hill-sides, presenting the general features
found on the hills of the Weardale watersheds (10). Long tongues of dark heath-
covered peat frequently stretch into the surrounding Nardus areas, and outliers of peat
oceur quite low down on the hill-sides. These are islands of peat which have been left
behind by the main peat mass as it retreated up the hill-sides, owing to denudation.
Many of the hill-sides which are still clothed with peat are very steep, and it is difficult
to see how the peat could have accumulated there under present conditions. The peat
attains a depth of 16 feet in some places, but is more usually about 7 or 8 feet in
thickness. Owing to its channelled condition and situation on steep hill-sides it is
generally dry, and the plant remains are better preserved than elsewhere.
The mosses rest upon glacial deposits consisting of stiff gray clay, containing many
stones and occasionally small nests of sand. All the sections agree in showing an
absence of any great development of woodland, but a little shrubby birch appears in
some places in the peat.
The plant-beds exposed at the same horizons in different sections agree with one
another fairly well, but there is rather more variation than was found to be the case in
the flat mosses previously described. This was perhaps to be expected, as the factors of
aspect, degree of inclination of the ground, and altitude would come in on these hill-top
mosses and tend to produce a vegetation which would vary much more at any one
time, and prevent the growth of a uniform plant association such as we find developed
over a flat low level moss. The general sequence of vegetation appears to have been
the same all over the Moorfoot Hills, but some of the beds found to be present in one
place are absent in others.
The lower edge of the mantle of peat in most places contains a basal layer of Betula
alba of shrubby size mixed with Calluna, whilst in other places this growth is replaced
by small Salices. The layers of peat immediately above this are formed chiefly of
Eriophorum vaginatum, which, in the peat situated at higher elevations, rests directly
upon the clay. The peat resting upon the Eriophorum layer is formed of Hmpetrum
mgrum, and this layer has been found to be well developed in all the sections. This
again is overlaid by Hriophorum vaginatum peat, on the higher lying ground. Later,
this is replaced by peat containing much Calluna vulgaris, which above yields place to
Scirpus and Sphagnum mixed with scanty Hriophorum vaginatum.
The four following sections show the variations met with in different positions,
together with the plant remains recognised from each layer :—
ON THE PLANT REMAINS-IN THE SCOTTISH PEAT MOSSES. onl
Half-mile N. of Bowbeat N.W. of Bowbeat Emly Bank at Cleave Burn at
at 1500 feet. at 1900 feet. 1900 feet. 2000 feet.
a 1. Sphagnum, sp. Sphagnum, sp. Sphagnum, sp. Sphagnum, sp.
Scirpus pauciflorus,
Lightf.
S. cespitosus, L. | Scirpus pauciflorus, | Calluna vulgaris, L. | Eriophorum vaginatum, L.
(abundant). Lightf. (scanty). Scirpus pauciflorus.
Eriophorum vaginatum, | Eriophorum vagi- | Scirpus pauciflorus, | Calluna vulgaris, Salisb.
natum, L. Lightf.
2. Calluna vulgaris, Salisb. | Calluna vulgaris, Calluna vulgaris, Salish.
Salisb.
3. Eriophorum angusti- | Hriophorum vagi- | Eriophorum angustifolium,
folium, L. natum, L. L.
E. vaginatum, L. Narthecium assi- | E. vaginatum, L.
Narthecium Ossi- Fragum, Huds. Alisma Plantago, L.
fragum, Huds.
Alisma Plantago, L.
4. Empetrum nigrum, L. Empetrum nigrum, L. | Empetrum nigrum, L. | Empetrum nigrum, L.
Vaccinium, sp. Arctostaphylos- Uva-
urst, Spreng.
5. Hriophorum vagi- | Eriophorum angustifolium,
_ natum, LL. L.
Calluna vulgaris, Salisb.
Molinia ceerulea, Moench.
Polytrichum Commune, L.
Vaccinium Vitis Idea, L.
Scirpus ccespitosus, L,
6. Betula. Calluna, Betula. Calluna.
Carices, sp.
Epilobium palustre, L.
Salia, sp.
Ranunculus repens, L.
Lychnis diurna, Sibth. ?
Ajuga reptans, L.
Viola palustris, L. 4
In the section by Cleave Burn there is no sign of birch at the base of the peat, and
the peat dominated by Eriophorum rests directly upon the clay. There is a sharp
division between the two, the upper surface being smooth and indented by the weight
of the overlying peat, and the dry compressed remains of Eriophorum and Molinia peel
away from this surface, leaving it quite clean. The appearance suggests that some
considerable time elapsed between the deposition of the clay and the growth of the
vegetation which now rests upon it, during which time the clay was consolidated and
denuded to some extent by water, after which it became covered with a growth of
Molinia cxrulea, Moench., Polytrichum, and Eriophorum. At the same time, or possibly
sooner, the lower slopes of these hills became covered with a shrubby growth of birch
712 MR FRANCOIS J. LEWIS
mixed with much Calluna. The zone of Empetrum running through the peat of the
whole district suggests that, at some period, colder conditions prevailed; but the
evidence afforded by Empetrum alone is scarcely conclusive, for, although covering large
areas within the Arctic Circle, it also occurs fairly abundantly at the present day on
many hills of about the same altitude as the Moorfoots, although never forming a pure
association on the North of England or Southern Upland Hills. The presence of
Arctostaphylos Uva-ursi also suggests more northern conditions, as it is not at present
found on the Southern Upland Hills.
If the Empetrum zone represents cold conditions during the formation of these
mosses, it must either be contemporaneous with the same period which produced the
Salix reticulata in the Merrick-Kells peat and the Loiseleuria in Tweedsmuir, or it
must represent the later return to glacial conditions, when the Highland corries were
tenanted by small glaciers whose trace can still be seen in the high level corrie moraines
of the present day. The sequence of the beds above and below the Empetrum agrees
so closely with that in the Merrick-Kells area and in Tweedsmuir, that I think the
evidence is in favour of much the same—or, possibly, somewhat milder—conditions having
caused its growth. If the Empetrum zone here is contemporaneous with the Arctic
zone in the other districts, it might have been expected to contain plants still more
Arctic in character, as the ground lies about 2000 feet instead of 800-1200 feet, and is
not sheltered like the Tweedsmuir and Galloway valleys; and for this reason I suggest
that the Empetrum zone in the Moorfoot peat is contemporaneous with the period of
Highland corrie glaciers. ‘
THe Lowtanp Mossgs oF WIGTONSHIRE.
(One inch Ordnance Survey—sheet 4.)—Between the towns of Glenluce and Newton
Stewart, in Wigtonshire, hes an extensive tract of peat mosses which northward stretch
as far as the Merrick district. The general level of the peat-covered ground lies at about
200-800 feet above Ordnance datum. The whole of the district is flat in character,
broken by a few ridges of Silurian rocks with their longer axes pointing N.N.H. and
S.S.W. in the direction of the great centre of ice dispersal of the glacial period in the
Merrick and Kells range. (Fig. 12.) The mosses here occupy great hollows in the till
between the outcrops of rock. The present vegetation covering the wetter mosses con-
sists of Sphagnum; Hrica Tetralix, L.; Myrica Gale, L.; Eriophorum vaginatum, I,.
—with a little Calluna vulgaris with tufts of Cladonia rangiferina amongst the
scattered Calluna patches. On the drier mosses Calluna is better represented, with
Scirpus sp. and Kriophorum vagimatum as subdominant plants.
The peat covering the district shows no sign of denudation ; the surface is even, and
closely covered with vegetation. Drainage channels have been cut in many places, but
owing to the low-lying level character of the ground they are not very effective. Peat
is chiefly used as a fuel in the district, but owing to the sparsely inhabited nature of
the country the mosses have not been trenched upon by turbaries to any great extent,
ON THE PLANT REMAINS. IN THE SCOTTISH PEAT MOSSES. 713
as the peat has only been dug in a few of the drier places near the edges of the mosses.
The general character of the country is illustrated in fig. 12, where the long whale-
backed hillocks can be seen rising about 30-40 feet above the general level of the moss.
Many of the mosses are of the nature of flow mosses, merely consisting of a crust of
peat firmly bound together by the wiry stems of Myrica Gale, Calluna, and Scirpus,
underlaid by many feet of semi-liquid peat, and I found that it was impossible to cut
sections in such cases, and had to fall back on borings in order to obtain specimens of
the basal peat layers and underlying glacial deposits.
An investigation by means of sections and borings was made of the following mosses
lying in this district: Flow of Dergoals, Dirskelpin Moss, Knock Moss, Anabaglish
Moss.
The Flow of Dergoals represents the wettest type of moss found in the district,
being covered with an association of Sphagnum sp. (dominant), Hrica Tetralix, and
Myrica Gale. Asa result of twelve borings the moss was found to have an average
depth of 18-20 feet, and in one place close to the eastern boundary no bottom was
reached in 30 feet. An endeavour was made to section the central part of the moss,
but the peat proved to be semi-liquid in character at a few feet below the surface. A
section was made close to the eastern margin through 17 feet of peat. Much
Eriophorum vaginatum occurred in the upper 12 feet of peat, with. Polytrichum Com-
mune in places. Below this, woodland began to appear, the peat containing abundance
of Corylus wood and nuts. Lower still the Corylus became more scanty and yielded
‘place to Betula, which continued until the floor of the moss was reached.
The birch zone contained in some places considerable quantities of Polytrichum
Commune and Equisetum, sp. This general succession was fully borne out by the
borings, Betula being everywhere met with at the base of the peat, with much Corylus
mixed with its upper layers. The floor of the moss consists of stiff gray clay packed
full of stones of all sizes. The succession of events over the area covered by this moss
appears to be as follows :—At a period subsequent to the deposition of the till upon
which it rests, the ground became covered with a growth of birch and Calluna. This
woodland was gradually replaced by hazel and alder, which, however, did not stretch
to the centre of the moss, but formed a fringe round the sides of the basin. There is
some evidence that the conditions became wetter as the birch and Calluna died away,
for the peat above this shows a fairly abundant development of Polytrichum and
Equisetum. This may explain the general absence of hazel and alder from the deeper
parts of the moss. Later still the conditions become favourable to the growth of the
wettest types of moorland plants ; all sign of woodland vanished, and a close carpet of
such plants as Eriophorum, Polytrichum, Sphagnum, and Carices covered the ground.
Comparatively recently this vegetation has given place to the present Sphagnum, H7ica
Tetralix, and Myrica Gale association. The general history of the neighbouring mosses
appears to have been the same, but there are, as might be expected, considerable local
variations.
714 MR FRANCIS J. LEWIS
Dirskelpin Moss, Knock Moss, and Anabaglish Moss may be described together,
being all of the same type and continuous with one another. The depth of these
mosses varies from 10 feet to over 20 feet, an average depth in the centre being about
14 feet. In some cases borings were made at short distances from one another from one
side of the moss to the other, and these showed that the peat occupies large hollows in
the till. In several places the surface of the moss is broken by long whale-backed ridges
of Silurian rock. Borings were made round some of these ridges, and the ground was
found to shelve down steeply at the N.N.E. end, as a depth of more than 20 feet of
peat was recorded only 70 feet from the edge of the moss; whilst at the 8.8.W. end of
the ridge the ground shelved much more gradually, as the peat only reached a depth of
3—4 feet 300 feet from the margin. All these whale-backed hills showed the same feature :
a deep excavation on the N.N.E. filled with a growth of peat, and, at the S.S.W. end,
a great accumulation of till covered by very shallow peat.
The features presented by the borings, and confirmed by sections made along the
drier margins of the mosses, were as follows :—The mosses everywhere rest upon a stiff
clay containing in some places numerous nests of sand, the clay being filled with stones
of all sizes. This forms a fairly level floor, rising steeply towards the margins and
round the Silurian outcrops. The upper layers of the till contain many rootlets from
the overlying peat, but otherwise are free from vegetable remains. The peat immediately
overlying the till (for the first 2 or 3 inches) contains no recognisable plant remains, and
is frequently banded with thin layers of coarse sand or grit. Above this occurs an un-
interrupted layer of Betula alba, L., of small size, the largest diameter of wood met with
being only 10 inches. The wood is much decayed, but pieces of bark are well preserved
and mixed with decayed leaves. Corylus Avellana, L., and Alnus glutinosa, Gaertn.,
oceur fairly abundantly in many places towards the top of the birch layer, but are not
found in the very centre of the mosses ; here the only woodland zone present is birch.
At the same time there is no sign of any sharp separation between the birch zone and
the hazel and alder, for they appear to merge gradually into one another; but the
evidence for this must be received with caution, as a zone of wood might easily sink in such
soft peat without leaving any trace of the operation. Above the birch and hazel layers
the peat contains much Hqwisetum, sp., with Phragnutes communis occasionally reaching
a thickness of 4—5 feet. This layer is particularly noticeable in the peat round some of
the lochans which occur here, and shows that after the passing away of the birch, hazel,
and alder vegetation, very wet conditions prevailed when most of these mosses were
covered with swamp, or by a series of shallow lakes. Later still the conditions
evidently became drier again, for a zone of Pinus sylvestris appears immediately above
the Equisetum and Phragmites peat. The trees here, unlike the basal birch, are large in
size, the stools are i situ, and the wood is well preserved and still resinous in smell on
being broken up ‘The peat round the stools contains abundance of pine cones, twigs, and
apparently the remains of leaves. The trees stand at a distance of 9-12 feet apart, but
do not occur in the centre of the mosses but as a fringe round the margins, in much the
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. 715
same way as GUNNAR ANDERSSON found in the Swedish peat. After the pine zone had
flourishk®d for some time, its place was taken by swamp plants showing much wetter
conditions ; for the peat above the pine zone is almost wholly formed from the remains
of Sphagnum, Scirpus sp., and Hriophorum vaginatum.
I found no evidence of Arctic plants.at the base of these mosses, the first recognisable
remains above the till being birch and Calluna. The thin seam of peat generally
underlying this layer contains no recognisable plant remains. It would seem, then, that
these mosses did not originate until genial conditions had replaced the cold under which
the till was deposited, and the frequent presence of sand in the first few inches of peat
suggests that the basal layers are wash peat deposited when the hollows in the till were
partly under running water.
Here, as in the previously described districts, there are two woodland beds present,
separated by peat showing very wet conditions, but, unlike the peat in Galloway and
Tweedsmuir, there is no layer between the woodland beds of a distinctly Arctic type. It
is not unreasonable to suppose, however, that the conditions which would favour the
_ growth of Arctic plants on well-drained mountain valley peat at an altitude of
800-1200 feet might not produce the same results on wet peat lying at only 200 feet
and close to the southern coast. If the basal birch in these mosses is contemporaneous
with the basal birch in Galloway and Tweedsmuir, then the whole of the intervening
beds in those districts are represented by the Equisetum and Phragmites peat here.
If the record contained in these mosses was complete, it should carry the story of
moorland history a stage further back, as the ground has not been glaciated since the
second mer de glace, the district ice-sheets and valley glaciers not having encroached
so far upon the low ground away from the hills.
Lochar Moss (one inch Ordnance Survey—sheets 10 and 6) is the largest tract of
peat in the south of Scotland, and is situated to the 8.E. of Dumfries. The southern
part of the moss lies on the 25-feet raised beach, whilst the northern portion lies at
about 45 feet. A complete investigation of this moss had to be postponed, owing to
want of time; but some borings made near Racks, at 40 feet above Ordnance datum,
showed the peat to be 15 feet in depth. The sections al] filled with water before the
base of the moss was reached, but the borings showed a well-marked basal layer of
birch embedded in dry black peat, overlaid by 12 feet of Scirpus, Sphagnum, and
Calluna peat. The peat immediately overlying the birch zone is almost entirely
formed of Sphagnum, but there is a gradual increase in the amount of Calluna towards
the surface of the peat. ‘The chief point of interest is the presence of the basal birch
layer, thus agreeing with the mosses previously described in Wigtonshire as well as
with the 25-feet raised beach mosses of Cree and Priestside Flow.
THe Buriep Prat oF THE Earn VALLEY.
(One inch Ordnance Survey—sheet 48.)—An apparently continuous bed of
peat underlies the Carse clays of the Earn and Tay valleys. Numerous exposures
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 28). 106
716 MR FRANCIS J, LEWIS
of the peat can be seen from near Forteviot, in the Harn Valley, to as far east
as Stannergate near Dundee. The character of the peat and the plant remains
contained in it has been described, amongst other observers, by JAMIESON (11) and
by G&IKIE (12).
I was enabled to examine the peat at several places between Forteviot and Forgan-
denny through the assistance of Prof. Grrkin, who kindly supplied me with maps showing
the position of some of the best exposures. The peat in these places is about 3 feet
in thickness and forms a brown, dry, hard layer resting upon the valley gravels, silts,
and clays, and overlaid by the Carse clays. The peaty material is crowded with wood
of all sizes, flattened and very brittle, and overlaid by a seam of sand and silt
crowded with leaves often in the most perfect state of preservation. In the peat
which | examined, remains of the following plants occurred: Quercus; Corylus
Avellana, L.—wood and numerous nuts; Betula alba, L.; Alnus glutinosa,
Gaertn.; Salix, sp.; Menyanthes trifoliata, L.—several seeds; Carex, sp.;
Phragmites communis, Trin. ;—a list which adds only one fresh plant to those
already described by the authors mentioned. The overlying sandy clay contains
numerous leaves of Salix, sp., and fragments of oak, birch, and hazel
leaves.
The plants contained in the peat evidently grew where they are now found, as
numerous rootlets penetrate the underlying deposits. The upper leaf-bed, on the other
hand, is clearly drifted material, as the individual leaves are separated by thin layers
of fine sand or silt. The peat, occurring as it does immediately below the Carse clays,
should be contemporaneous with the oldest peat in the Galloway and Tweedsmuir
districts.
THE 25-FEET RAISED Bracu Mosses oF WIGTONSHIRE AND DUMFRIESSHIRE.
(One inch Ordnance Survey—sheets 4 and 6.)
Moss of Cree.—This extensive moss lies on the west side of the River Cree, between
Newton Stewart and Wigtown. Less than a mile to the southward the smaller mosses
of Barrow and Carsegowan are met with, both being similar in character and situation
to the Moss of Cree. On the westward and landward side the moss is bounded by a
series of low hills about 100 feet in elevation, from the bases of which the beach slopes
to the 8.E., the height of the beach at the eastern boundary being about 12-15 feet
above Ordnance datum. Viewed from the margin, the moss presents a fairly smooth
surface with a gradual rise to the centre, which lies about 15 feet higher than the
margins.
The present vegetation over most of the moss consists of Hrica Tetralix, L. ; Calluna
vulgaris, L.—not abundant; Myrica Gale, L.—abundant near the eastward margin;
Salix, sp.; Carex, sp.; Narthecium ossifragrum, Huds. ; Vaceiniwm oxycoccos, L.. ;
Sphagnum ; Drosera rotundifolia, L.; D. intermedia, Hayne. The ground on each
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES, (AWE
side of fie small stream, crossing the moss from east to west, is covered chiefly with
Sphagnum and Molinia.
Hight borings were made across the centre of the moss from north to south, and five
from east to west, and these showed that the floor of the moss was very level with a
general dip to the SE. The total depth of the peat varied from about 6-8 feet near
the edge of the moss to about 20 feet near the centre. Sections made on the eastern
margin of the moss, near Palwbilly, showed the following series of strata :—
1. Sphagnum peat mixed with some Scirpus cespitosus, . . 3-4 feet.
2. Peat formed chiefly from Eriophorum, with traces of Sphagnum
and Calluna, : : f ora
3. Moss peat containing aauitiies of isle sp., and Poly-
trichum Commune, L.
. A layer of Betula alba mixed with leaves of the same tree.
The wood is of all sizes up to 10 or 12 inches in diameter,
and several stools were found with roots penetrating the
i
surrounding peat.
5. Stiff blue stoneless clay, the first few inches containing fairly
numerous pieces of small wood of Quercus, Alnus, and
Pinus. This wood is apparently drifted, the bark in most
cases being worn off and the ends rounded.
Borings were taken down through the clay for 6 feet, but no change in character
was observed at this depth. The wood fragments cease a few inches below the surface
of the clay. This general sequence of beds was repeated in all the sections made from
different places in the moss. Some of the sections laid bare large fragments of pine and
oak wood lying at the base of the moss, but these all bore traces of long drifting.
The clay on the banks of the river at the top of the moss contains many much larger
fragments of these trees, all bearing signs of drifting, the only stools in situ being birch
in the basal layers of the peat.
Priestside Flow.—This moss lies on the Solway coast between Annan and Dumfries,
the inland edge of the moss being 40 feet above Ordnance datum with the coastward
margin 25 feet above O.D. The vegetation is of a much drier type than that covering
the Moss of Cree; Calluna vulgaris being dominant, mixed with some Eriophorum
vaginatum and E. angustifolium. Myrica Gale is absent, and there is but little
Sphagnum. A series of borings showed the peat to have an average depth of about 14
feet, with the same level floor gently sloping seaward as was found in the Moss of Cree.
The first section was made on the inland side about 40 feet above Ordnance datum,
and the following beds exposed :—
1. Sphagnum peat containing Carex, sp., and Scirpus cespitosus, . 7 feet.
2. Eriophorum peat, ; , ; . 4-6 in.
3. Peat containing shrubby neni in aude 1 foot.
4. Peat consisting chiefly of the remains of Phragmites communis, 5 feet.
718 MR FRANCIS J. LEWIS
5. Hard dry peat of a dark red colour, containing remains of
Corylus Avellana, Alnus glutinosa, Quercus—the latter
apparently drifted.
6. Coarse gray sand devoid of plant remains. The Corylus in the
basal layers is particularly abundant.
Two other sections taken on the landward side confirmed these results, and the sides
of a large turbary near by showed the same features. Sections were then made on the
seaward side, and the following beds exposed :—
1. Sphagnum peat containing Calluna and a small quantity of
Myrica Gale, A : . 7-8 feet.
2. Peat consisting chiefly of Biraamites ; ‘ , 34 ,,
3. Stiff gray clay containing remains of Pipa: communis, . 4.
This layer is interstratified with seams of peaty material
containing remains of the same plant. Sandy layers also
run through the clay, and these contain numerous remains
of the rhizomes of Holcus mollis, L. At the bottom of
this layer the clay becomes more sandy and black in colour,
without any determinable plant remains. ‘This seam is
about 5 inches in thickness.
4, Fine sand.
Layer 3 has evidently been formed by constant flooding, which continued for a
period long enough to deposit the clay layers between the peaty material. At the
margin of this raised beach an abundant growth of Phragmites sprang up, only to be
destroyed by flooding, which at the same time deposited a layer of sand and mud over
the plant-bed. This growth of Phragmites may have occurred whilst the beach was
still being raised, and the flooding caused, not by changes in the level of the land, but
rather by shifting of sand-banks close in to the shore. The height of the moss at the place
where these sections were made is about 25 feet above Ordnance datum. It is interest-
ing to note that the basal peat with Corylus, represented in the higher part of the
beach, is absent from the seaward side. It would appear that the higher parts of the
beach actually became clothed with woodland before the seaward side had entirely
emerged from the sea, and that towards the close of the period of upheaval the woodland
died out over the upper ground and the whole beach became covered with a vegetation
indicating wet conditions.
The two mosses first described may fairly be taken as representative of the mosses
lying on the 25-feet raised beach of the south coast. The absence of any remains of
Arctic plants at the base, and still more the presence of such temperate forms as Corylus
and Alnus, with the abundance of nuts of the former, is of interest as showing that these
mosses began to form under climatic conditions which were certainly not less favourable
than those at the present day. Both the birch at the base of the Moss of Cree, and the
Corylus of Priestside Flow, grew in situ, as none of the material shows any sign of water
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. wig
action: the bark on the stems and twigs being quite uninjured, and the nuts in an
excellent state of preservation, and, further, numerous roots of the same trees are to
be found running through the peat. There is, then, every indication that the peat
immediately overlying the clay represents the primitive vegetation covering the surface
of these raised beaches. The drifted pine and oak in the clay underlying the Moss of
Cree also shows that the climate inland was not less favourable to the tree growth than
that at the coast, and much of the drifted timber must be débris from woodland which
existed inland during the period of land elevation,
The Denudation of the Peat.—The sections already described show that considerable
changes have taken place in the distribution of the vegetation during the growth of the
mosses. The youngest peat in each district hitherto examined is formed of plants
indicating extremely wet conditions, such as Sphagnum and Scirpus; but these plants,
although still represented in the vegetation, do not occur in such profusion as they are
found in the peat, but occupy isolated patches in the wettest spots, or occur mixed with
other plants indicating somewhat drier conditions. Of the areas examined, the lowland
mosses of Wigtonshire appear to be the only mosses in which peat is forming at the
present day. These mosses are flat, badly drained, and are still dominated by large
areas of Sphagnum, Scirpus, and Eriophorum. These features are also reproduced on the
peat-covered ground of the flat-topped hills, plateaus, and gently-sloping moorlands
of such districts as the Northern Pennines and Stainmore in Westmorland. The peat in
these latter districts, however, nearly always shows traces of wasting, the greater rainfall
and freedom of drainage favouring denudation. The peat of the hill-sides, although con-
taining thick Sphagnum, Scirpus, and Eriophorum beds, is no longer clothed with these
plants but with a much drier type of vegetation, and denudation has evidently gone on
here for a long period. In the Moorfoot Hills and Tweedsmuir, many of the steepest
nill-sides are thickly covered with peat; but this is only the remnant of what was once a
much greater covering, both thicker and larger in extent. GrrKIE (13) has discussed
the general features of denudation to be met with in Western Europe, and there is little
to add to the account given in his paper.
The phenomena are too universal to be entirely accounted for by drainage operations ;
these may, indeed, accelerate the wasting of the peat in some districts, but cannot
account for it in all. Furthermore, the peat on the eastern side of England and S.
Scotland is denuded to a much greater extent than that in the western districts—ée.,
the wasting began earlier, and is more rapid in those districts having a smaller rainfall,
other factors, such as the slope of the ground and elevation above sea-level, being equal.
Comparing the peat of the Moorfoot Hills with that in the Galloway district, the amount
of denudation is much greater in the former ; for, although the peat is wasting away over
most of the Galloway mosses, the shrinkage is not nearly so marked as it is on the
Moorfoots. The same difference in the amount of denudation can also be seen in England
on comparing the hills of the Lake district with the eastern slopes of the Pennines.
Although the topography of Western Cumberland and Westmorland is not favourable
720 MR FRANCIS J. LEWIS
to any great growth of peat, yet, where it does occur, the amount of denudation to which
it has been subjected is shght compared with the wasting away of the thick mantle of
peat covering all the watersheds of the rivers Tees, Tyne, and Wear.
An examination of the successive beds of vegetation contained in the older mosses
shows that the rate of peat formation has not been uniform, for the length of time
required to form a layer of closely-compressed stems of Empetrum and Arctic willows
only a few inches in thickness, might possibly be sufficient to form several feet of
Sphagnum peat. It would seem, then, that peat formation has been almost arrested
at some stages in the history of the mosses; and I have met with features in the
Merrick-Kells mosses which suggest that the peat has been subjected to denudation
about the time of the formation of the Arctic plant-bed.
SuMMARY AND GENERAL CONCLUSIONS.
The peat in all the districts examined shows a definite stratification of plant remains,
indicating a swing from woodland to heath and moss, and again to woodland. In some
districts, an Arctic plant-bed is interposed between the lower and upper woodland beds.
GuNNAR ANDERSSON has described alternations of woodland beds, with Sphagnum,
and with heather layers, as occurring over large areas in Central and Southern Sweden,
and he attributes such alternation to changes in drainage caused by the throwing up of
a clay or sand bank by natural or artificial causes near a moss territory, thus causing
flooding, and consequently favouring the growth of Sphagnum at the expense of wood-
lands. This may quite possibly have produced like results in similar districts in Britain ;
but in the hill districts described in the course of this paper such causes cannot have
operated, as the mosses are situated on steeply-sloping ground on which no natural or
artificial dam could be created. The regularity of the sequence of the beds, and their
general agreement on similar although widely separated areas, tend to show that these
beds represent successive changes in the vegetation which have been brought about by
climatic changes at the passing away of the glacial period.
None of the Scottish districts investigated by the author show any remains of Arctic
plants at the base of the peat; but, on the contrary, some of them, such as the 25-feet
raised beach mosses, contain remains of hazel in the basal layer. From the discovery by
the late Mr James Bennie, of Arctic plants in the old alluvia of the Edinburgh district
(14), the same features were expected at the base of some of the deeper lowland mosses,
such as those in Wigtonshire. The presence of woodland at the base of these mosses,
however, suggests that they did not originate until a temperate climate had replaced
the Arctic conditions of the mer de glace period. In the Cross Fell peat, at 2500
feet, a bed of Arctic willows and Empetrum has been met with lying on the clay at the
base of the peat (15), and, on recently re-examining this bed, I was struck by its great
similarity to the Arctic bed lying between the two woodland zones in the Merrick-Kells
mosses.
A summary has been given by Prof. Gurkig (16) of many of the more important
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES. hel
_ papers dealing with Arctic zones in the late glacial deposits of the Continent, and I hope
that correlation between these zones and those in the British peat may be possible
when areas have been investigated in the north of Scotland.
The general sequence of vegetation observed in the peat of the several districts may
be summarised as follows :—
The Merrick and Kells mosses, and the mosses in the Tweedsmuir district, occur
above and upon the moraines of the local glaciers of the Southern Uplands, and must,
therefore, be of later date than these.
That these mosses began to grow at some period between the disappearance of the
local glaciers and the reappearance of glacial conditions, is shown by the presence in
both districts of an Arctic plant-bed running between the lower and upper woodland
bed. The conditions which would favour the growth of such a vegetation in the 8.W.
of Scotland at only 800-1200 feet, would be severe enough to cause considerable glacia-
tion in the Highlands. The plant-beds below and above the Arctic bed also tend to
show that this layer indicates one of the smaller and later returns to glacial conditions ;
for the beds below show a gradual increase, and above, a gradual decrease, in precipita-
tion. If this reading is correct, interest would attach to an examination of any deep
peat deposits resting on the 50-feet raised beach, as we might expect to find, in that
ease, the representative of the Arctic zone of the Merrick mosses resting upon the surface
of the beach.
The peat of the Moorfoots contains no widespread forest beds, basal birch only
being found low down on some of the hill-sides. Eriophorum and Molinia have been
found at the base of the peat on the steepest hill-sides, thus showing that these mosses
began to form under extremely wet conditions, the higher ground being covered with
Eriophorum bog whilst the lower slopes supported copses of birch and willows. There
‘is no sign of Arctic vegetation at the base of this peat, but the basal swamp vegetation
gives place above to a formation indicating much drier and probably colder conditions,
represented by a zone of Empetrum with Arctostaphylos Uva-ursi.
The question arises whether this Empetrum bed can be correlated with the Arctic
zone of the Merrick and Kells mosses and the Tweedsmuir peat. If it is contempo-
raneous, then the later return to cold conditions represented by the high level corrie
moraines of the Highlands produced little effect upon the vegetation so far south as the
Moorfoots, for there are no beds above the Empetrum zone in this peat which show
any return to cold conditions.
The lowland mosses of Wigtonshire occupy large hollows. in the till between the
outcrops of Silurian rocks, and reach a depth of about 20 feet. No Arctic plants have
been found at the base, the basal vegetation consisting of shrubby birch, which is con-
tinuous over the area. The beds above this represent lake or swamp conditions; but a
return to forest conditions took place later, when the mosses became fringed with pine
trees of large size. The peat above the pine zone is formed of wet-condition moorland
plants.
722 MR FRANCIS J. LEWIS
The mosses lying on the 25-feet raised beaches contain no Arctic plants, and
the general facies of the vegetation agrees with that in the upper layers of the
older mosses inland. The basal layers consist of birch, hazel, and alder, which
give place above to wet-condition plants such as Sphagnum, Eriophorum, and
Phragmites.
Birch is represented in the basal layers of all the Scottish mosses described in this
paper, and birch has also been found in the lower layers of some of the Highland peat,
as described by Mr Croveu in the East Ross district (17).
In conclusion, I wish to express my thanks to Professor J. Gerkiz, LL.D., F.RB.S.,
for much kindly advice and help during the progress of the work; and to Dr Horns,
K.R.S., for kindly lending me Geological Survey maps and lists of all the Scottish
peat mosses, and for his valuable advice during the progress of the field work.
I am also much indebted to Mr Cremenr Ret, F.R.S., for kindly mee several
of the seeds from the different layers.
The scientific expenses of this investigation have been defrayed by a grant faa
the Government Grant Committee of the Royal Society.
LIST OF REFERENCES.
(1) Rerp, CLEMENT, ‘“‘ Notes on the Geological History of the Recent Flora of Britain,” Ann. of Bot.,
vol. i1., 1888.
“The Origin of the British Flora,” 1899.
(2) “Summary of Progress of the Geological Survey ” for 1898, p. 156.
(3) AnpERsSoN, GuNNaAR, ‘Svenska Vaxvarldens Historia.” Stockholm.
(4) Guixie, J., “ The Great Ice Age,” 1894, p. 614.
(5) Hinxman, L. W., Trans. Geol. Soc. Edin., vol. vi., p. 249.
(6) Smita, W. G., and Moss, C. E., “Distribution of Vegetation in N. Yorks.,” Geographical Journ.,
April 1903.
(7) Lewis, F. J., “Distribution of Vegetation of the Basins of the Rivers Eden, Tees, Tyne, and Wear,”
Part I. Geographical Journ., March 1904.
(8) Warmine, E., “ Ueber Gronland’s Vegetation,” Engler’s Jahrbiicher, Bd. x. 1888.
(9) Surry, Ropert, “ Botanical Survey of Scotland,” Part I. Scottish Geographical Mag., July 1900.
(10) Lewis, F. J., “Distribution of Vegetation of the Basins of the Rivers Eden, Tees, Tyne, and Wear,”
Part I]. Geographical Journ., September 1904.
(11) Jamizson, T. F., “The History of the Last Geological Changes in Scotland,” Quart. Journ. Geol,
Soc., vol, xxi.
(12) Gerkig, J., “ Prehistoric Europe,” 1881, p. 390.
(13) Gurxie, J., “ Buried Forests and Peat Mosses of Scotland,” Trans. Roy. Soc. Edin., vol. xxiv.
(14) Buyniz, James, “Arctic Plant-beds in Scotland,” Ann. Scottish Nat. Hist., January 1894 and
January 1896.
(15) Lewis, F. J., “Interglacial and Postglacial Beds of the Cross Fell District,” Brit. Assoc. Reports,
Sect. K. 1904.
(16) Gurnig, J., “Prehistoric Europe.” 1881.
(17) “Summary of Progress of the Geological Survey” for 1893, p. 87.
ON THE PLANT REMAINS IN THE SCOTTISH PEAT MOSSES, 723
[MERRICK AKELISMosses,| TWEE DSMUIR MOSSES. [WIGTONSHIRE MOSSES. MOORFOOT PEAT. RSF RAISED BEACH PEAT. |
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TRANS. ROY. SOC. EDIN., VOL. XLI. PART IIT. (NO. 28). 107
-
Trans. Roy. Soc. Edvn. Fon. SIL
Lewis: Plant Remains in the Scottish Peat Mosses—PuLatE I.
|
|
|
Fic. 1.—Denudation of the peat at the eastern margin of the Merrick-Kells Mosses.
Kells Range in the background.
Fic. 2.—Pine zone and Empetrum nigrum zone separated by Sphagnum and
Hriophorum, in the Merrick-Kells peat.
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Trans. Roy. Soc. Edin Vou. XU.
Lewis: Plant Remains in the Scottish Peat Mosses.—PuLate LI.
Fc. 3.—Pine zone in the Merrick-Kells peat.
Fic. 4.—Valley moraines in Winterhope.
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Trans. Roy. Soc. Hdin. Wan. SUI
Lewis: Plant Remains in the Scottish Peat Mosses.—Puate ITI.
Fie. 5.—Loch Skene, showing the peat running up to the base of the
moraines at the foot of Lochcraig Head.
Fie. 6.—Upper Birch zone exposed on the banks of Winterhope Burn.
'
i
Trans. Roy. Soc. Edin. VoL. XLI.
Lewis: Plant Remains in the Scottish Peat Mosses.—PuLatTE VY.
Fic. 9.—Peat resting on the moraines at the foot of Loch Skene,
Fic. 10.—Basal layers of peat resting upon fine grey sand in Winterhope.
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Trans. Roy. Soc. Edin. Vou. XLI.
Lewis: Plant Remains in the Scottish Peat Mosses.—Puate VI.
Fic. 11.—Moorfoot Hills. Denudation of the peat on Emly Bank at 1900 ft.
Fic. 12.—Lowland Mosses in Wigtonshire. Dirskelpin Moss.
ow ,
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( 725 )
XXIX.—Semi-regular Networks of the Plane in Absolute Geometry. By Duncan
M. Y. Sommerville, M.A., B.Sc., University of St Andrews. Communicated by
Professor P. R. Scorr Lane. (With Twelve Plates.)
(The cost of the Illustrations of this Paper was defrayed by the CARNEGIE TRUST.)
(Read December 19, 1904. Issued separately August 30, 1905.)
§ 1. The networks considered in the following paper are those networks of the plane
whose meshes are regular polygons with the same length of side.
When the polygons are all of the same kind the network is called regular, other-
wise it is semi-regular.
The regular networks have been investigated for the three geometries from various
standpoints, the chief of which may be noted.
1. The three geometries can be treated separately. For Euclidean geometry we
have then to find what regular polygons will exactly fill up the space round a point.
For elliptic geometry we have to find the regular divisions of the sphere, or, what is the
same thing, the regular polyhedra in ordinary space. The regular networks which do
not belong to either of these classes are then those of the hyperbolic plane.
2. The problem is identical with that of finding the partitions of a polygon into poly-
gons of the same kind, with the same number of polygons at each point.* The boundary
polygon is one of the meshes of the network. For elliptic networks the boundary is
finite, for Euclidean networks it is wholly at infinity, and for hyperbolic networks it is
wholly ideal.
This method gives a convenient mode of representing the networks, viz., by their
stereographic projections upon the Euclidean plane. This representation will be em-
ployed throughout.
3. The problem corresponds to a particular case of the problem of determining all
discontinuous groups of motions in the plane.t
It will be convenient here to collect the results. If 7 is the number of sides of each
polygon, » the number of lines or polygons meeting at each point, N,, N,, N, the
number of meshes, lines, and nodes respectively, the results may be summarised as
follows :—
1. On the Elliptic plane there are five regular networks, corresponding to the five
* See V. ScuiEceL, “Theorie der homogenen zusammengesetzten Raumgebilde,” Nova Acta, Bd. xliv., Nr. 4,
1883.
+ W. Dyck, “ Gruppentheoretische Studien,” Math. Annalen, xx. 1-44 (1882), and W. Burnsipn, “ Theory of
Groups,” ch. xii., xii. Also KuEein and Fricke, “Theorie der elliptischen Modulfunctionen.” (For these references
_ Iam indebted to the referee.)
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 29). 108 ,
726 MR DUNCAN M. Y. SOMMERVILLE ON
regular polyhedra. They are arranged in conjugate pairs, the number of meshes in
one being equal to the number of nodes in the conjugate network. One is self-
conjugate.
n p IS NG Ny
Tetrahedral, 3 3 4 6 4
{ Hexahedral, 4 3 6 12 8
Octahedral, 3 t 8 12 6
J Dodecahedral, . 5 3 12 30 20
| Icosahedral, 3 i) 20 30 12
2. On the Euclidean plane there are three regular networks, all infinite.
n p N, Nee NI,
Square, 4 t 1 2 1
Triangular, 3 6 2 3 1
Hexagonal, 6 3 1 3 2
3. On the Hyperbolic plane there are an infinite number, all infinite.
jo= Bo 25 Dy BO, SO
n> 6,4, 3, 3, any value
ING oN, 2 No= 20: ep om
§ 2. We proceed to investigate the semi-regular networks, and we shall take the
three geometries separately.
I. Tue EvcitipEan PLANE.
We shall consider, first, how the space about a point can be exactly filled with
regular polygons. Hach combination of polygons satisfying this condition determines a
species of node, and all the semi-regular networks must be built up out of the various
possible species of nodes. Two networks will be considered to be of the same type when
they contain only nodes of the same species. It is obvious that there may be varieties of
the same type. The types will be divided into Groups according to the kinds of polygons
involved, and the groups into Classes according to the number of kinds of polygons.
Class A. consists of the regular networks, and contains three groups with one unvaried
type in each. The simplest type in any group is that which contains only one species
of node. I call this the semple type; other types I call composite. A group does not
necessarily contain the simple type.
The Species of Nodes.
§ 3. The angle of a regular n-gon is given by the formula
BING en
ay = (1-5) 180 . avbivekt soled baxiessthonnlywlgn (nn
The following table of values of a, will be immediately useful :
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 727
a ae
On 108 | 120 | 1284 | 135 | 150
co | 99
Taking the four simplest polygons, we find that the sum of the angles is 378", 7.2. >360°,
Hence there cannot be more than three different kinds of polygons at a pot. The
species of nodes therefore fall under three classes.
Cuass A. contains the homogeneous nodes. Denoting the regular polygons by their
initial letters, the nodes of Class A. can be denoted by
1. Ty Tose Cem
§ 4. Ciass B. Let there be at a point p; n,-gons and p, 1.-gons. Then we have
PO + Po%_ = 277,
ala—2)2(1-2)=2.
Integralising, we obtain on the left the function
hence from (1)
MMo(2 — p) + 2(pyNq + Po)
where p=p,+p,. We shall denote this by A. It is easily seen that the sign of A
characterises the network as elliptic, hyperbolic, or Euclidean. For Huclidean networks
A is always zero ; for elliptic and hyperbolic networks A 2 0 respectively.
For the regular networks there is a corresponding function n(2—p)+2p, and for
three kinds of polygons we shall find a similar function. Where there is no risk of
confusion we shall call each of these A. The values of A for the regular networks are as
follows: Tetrahedral 3, Hexahedral and Jee beta 2, Dodecahedral and Icosahedral 1.
Solving now for n,, we have
We have to find the integral solutions of this equation under the following conditions :
Mn, >3,1,P2 >0,p +3 and p+} 5, therefore p,, p. + 4.
The only possible sets of values of p,, p, are then
Dy ally des
Py = 2, 3, 4, 2, 3.
- We shall take these cases in succession.
oa, 5 ae
po=?2 " ae we ey,
whence 2”,— 3,4, 10,
a= 125.8, 1O\.
py = ! < BS 3
Po= Me i, Se a
728 MR DUNCAN M. Y. SOMMERVILLE ON
There are no unequal values of m, and n, satisfying this equation.
ae =x, LO Bs 16
Po=4 4
whence ”,=
No =3.,
p,=2 | — ee 4
pPo=2! "9 7, <2
whence ”,=
Ny = =
oe oe ORT oe
p= 8 1 5 ee oR
whence ,=4
There are thus six species of nodes in this class. They may be denoted by TD,,
SO,, Dec P,, TH, 1,03, 1.8...
§ 5. Crass C. Here we have
2 2 2
p(d a +p x -) f p(1 a ae 2
or A = 1 NN, (2 — p) + 2(p Mots + PoNgN, + PoNN.)=0.
. 2PM No
Solving for n,, Ne = Aen ene
We have to solve this equation in integers under the following conditions : n,+n.+n;>8,
Pi, P2, Pp > 0, P + 38, also p + 4 (for 3a,+0,+a, > 360°), therefore p,, p., Ps $ 2.
Further, if p,=2, n, must be either 3 or 4, for 2a,+4,+a, > 360°. Again, we cannot
have n,=5, m%=6, n;=7 together, for a, +o,+4, > 360°.
The following are therefore the only possible sets of values of p,, 7%, 3, 71:
p,=1, or 2; p,=p,=1; n,=3, or 4.
We shall take these cases in succession.
1 = 12) = 13> — bn. 36
\ Me epee: Otten
Whence 775— is a, sO ek),
y= 42, 24, 18, 15.
PaPe=Ps= 1 ji 4n, Hope 16
hy — 3 ny — 4 N, — 4
whence 7= 5, 6,
n,=20, 12.
py =2, Py=P3= Pa 3, = 9
i — } aimee =e Ny — 3
whence 7,=4,
N,= 12.
Als Sages Qe mt
n= 4 ms feo Es
whence 7,=3,
n,=6.
There are thus eight species of nodes in this class.
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 729
§ 6. Collecting all the species of nodes, we can arrange them in the following
scheme :
Class A, 1. Tg. SSI Bp dele,
Class B. 4. T,S,. 5, TH». Cl Eee De 28. SO) (19) |b Dee.
Class C. 10) TSH Le ESD, 12. SHAD:
(OIG ti 44.) -Sreuesne gis 33
i, Ub. OMS Tee 7,
RDI lin 1S, Se Oe
In future we shall refer to these nodes by their numbers in this scheme.
Of the seventeen species of nodes, only eleven are capable of development to form
networks.
In No. 9 the pentagon must be surrounded alternately with pentagons and decagons,
which is impossible since 5 is odd.
In the same way, when p,=p,=p,=1, n,, nm. and.”; must all be even, for the
m,-gon must be surrounded alternately with n.-gons and i;-gons. Hence 13-17 cannot
be developed by themselves; nor can they be developed in combination, for each
contains a polygon which is not contained in any other node. Similarly, 9 cannot
be developed in combination, hence these six species are excluded from all the
networks.
Again, T,SD cannot be developed by itself, for, taking the square (fig. 1, Plate IV.),
we must have a dodecagon on one side and on the adjacent sides double triangles. At
the free corners of the square we must now have dodecagons, but this brings two
dodecagons at a point and introduces 7; excluding this, we must introduce 4.
§ 7. We can now divide the types of networks into groups and classes. Five kinds
of polygons are at our disposal, but octagons only occur in the combination SO,, hence
there are only four classes.
Class A. Regular networks.
Group I. Triangles (1).
» I. Squares (2),
i LUD Hexacons (3);
Class B. Two kinds of polygons.
Group I. Triangles and Squares (1, 2, 4).
,, I. Triangles and Hexagons (1, 3, 5, 6).
,, IL]. Triangles and Dodecagons (1, 7).
», LV. Squares and Octagons (2, 8).
Class C. Three kinds of polygons.
Group I. Triangles, Squares, and Hexagons (1, 2, 3, 4, 5, 6, 10).
» I. Triangles, Squares, and Dodecagons (1, 2, 4, 7, 11).
,», III. Squares, Hexagons, and Dodecagons (2, 3, 12).
730 MR DUNCAN M. Y. SOMMERVILLE ON
Class D. Four kinds of polygons.
Group. I. Triangles, Squares, Hexagons, and Dodecagons (1, 2, 3, 4, 5, 6, 7,
101112),
The numbers within the brackets denote the species ‘of nodes which the group admits.
‘Lhe Simple Types.
§ 8. Now let us consider the simple types. I observe, in the first place, that when
the species of node admits of no variation, the simple type is 7 general unvaried.
The unique nodes are the following :
1°. Class A,
2°. Those in which p=3,
3°. P=l, po=4,
while the following are varied :
1’. p,=p,=2. Two forms, M,N, and (MN),.
2 =p, —1, p,=2. “Two forms, LIN and ENING
We have then the wnaque simple types.
Class A. - eeS. abl.
py BE Da SOs (tach Sm
i Cy SEND Riios oe
The type T,H is one exception to the rule stated above, for it does admit of a variation.
The network is asymmetrical, its mirror image being different from itself. It exists,
therefore, in two enantiomorphic forms. The one can be obtained from the other by
turning the plane over.
Of the other groups, C. IL. and D. I. do not possess simple types, and there remain
the three simple types T.8,, T,H,, and TS,H, each of which is capable of infinite
variation.
T,H, has a variety in which there are no two triangles and no two hexagons
together. We shall call this the fundamental variety. The opposite sides of any
hexagon, when produced, define a strip which is capable of displacement without
affecting the rest of the network. All the varieties can then be obtained by displacing
any number of such parallel strips through a distance equal to the length of the side
(fig. 6).
TS,H has the fundamental variety in which there are no two squares together. Hach
hexagon is surrounded by squares and triangles, forming a group whose boundary is a
regular dodecagon. All the varieties can then be obtained by turning any number of
such groups through “ This operation, performed upon a single group, brings two
squares together ; performed upon two adjacent but not overlapping groups, it brings
three squares together (fig. 7).
SEMI-REGULAR NETWORKS OF THE. PLANE IN ABSOLUTE GEOMETRY. ‘731
§ 9. The unique types and the fundamental varieties of T,H, and TS.H can be
obtained from the regular networks by fairly obvious dissections. Thus, SHD (fig. 5)
is obtained from either the triangular or the hexagonal network; for the squares,
hexagons, and dodecagons have (1, 1) correspondence with the lines, meshes, and nodes
respectively of the triangular network. In a similar way T,H (fig. 4) is obtained from
the same network ; to each mesh there corresponds a triangle, to each node a hexagon,
and to each line two triangles. And so for the others: it is only necessary to compare
the figures, given below (§ 11), which represent the relative numbers of the various
polygons, with the numbers of nodes, lines, and meshes in the regular networks. In
the diagrams given for the unique types the regular network is indicated by shading.
T,H and all the varieties of T,H, can also be obtained from the regular triangular
network by replacing all the groups of six covertical triangles by hexagons; and TS,H
ean be obtained from SHD by bordering every dodecagon internally with squares and
triangles.
§ 10. The type T;S, forms an exception to what has been said regarding the way in
which the network may be obtained. One of its varieties, that in which no two squares
are together, can be obtained in a simple way from the regular square network ; to each
mesh corresponds a square, to each node a square, and to each line two triangles. But
the other varieties cannot be obtained from this, nor, in general, in any simple way from
the square network. The following forms may be enumerated, though the list is not
exhaustive :—-
(1) 1, 2, 3,.... squares always together. Hach of these is unique, and the series
forms a general type of variety, admitting of an infinite number of mix-
tures (fig. 8).
(2) 2, 3,.... squares or fewer together. Here we can distinguish
(i.) Two similar types, in which there occurs once only (a) a single triangle
surrounded by three squares, (b) a triangular group of four triangles
surrounded by three double squares. The network radiates from this
figure as centre (fig. 10).
(i1.) A general type, obtainable by a dissection of the square network, in which
(a) and (b) are excluded (fig. 9).
(iii.) Further, if an unlimited number of squares may be together, the groups (a)
and (b) may occur more than once, or together.
§ 11. From what has been said it is evident that for any of the simple types, with
the possible exception of T;S,, the relative number of the several kinds of polygons is
definite, and the same for all the varieties. These numbers can be found by inspection
and a knowledge of the number of meshes, lines, and nodes in the regular networks.
General expressions for the ratios may be found as follows. The results show that T.S,
is not an exception in this respect.
732 MR DUNCAN M. Y. SOMMERVILLE ON
m1 ”
Let p’, p”, p’” be the number of n’-, n”-, n’’-gons meeting at each point; N,
the number of nodes, N,’, N.”, N.” the number of n’-, ”’-, n’”-gons in the whole
network.
Then each n’-gon has n’ angles ; but if we count up the whole number of angles con-
tributed by all the n’-gons, each is counted p’ times.
Hence fe en Ne
Similarly g Nope
ne No = p Ns
Therefore N,’: N,”:N,” = ae Ae eee
Hore dso = be — eel Hor S05, 19 30 alm
Wiel, Ibs lets ¢ Il DS SE Easel eo
Td bes pea Tol (hs 11 Sel, Gelels I DW=Be Ds ii
Da a Die
§ 12. Let us investigate the analogous formulee for composite types. Let ,N, be the
number of nodes at which there are p,’ n’-gons, p," n’-gons, p;" n”’-gons, and p;'" n*-gons,
where one at least of the quantities p, is zero, and let
NG sig Ne tastes oe NG ete trates foe
Then Ww No =p, Not Pe aNot <3] Pra NG
=(p; +hypo + .... +h,_-)p-),Ny
, 1
Therefore Ny =—( py + haps + ey Eine
Let N,, N,, No have their usual meanings, then
No =,N + eens N= tht of. +h) NG
NENG +N," +N," +N,".
Also, by the analogue of EuuEr’s polyhedral formula,
N,-N,+N,=1.
N, can also be expressed in terms of ;N,,....,,No thus: at each of the ,N, points there are
p, lines, and each line joins two points, hence
2N,=71;,N p+ .... +9;-No,
whence we get
t=4 A=r A=r
1 i 1
(Daan) Dh, -1P) Sor 1 TANG ‘
vi A A=1
Now, since the number of species of nodes in the whole network is finite, one at least of
the quantities ,N,,....,,N, must be infinite. Hence we may put ,N)=o. The equa-
tion then becomes
A=? , F ” pause iv
> (ee Pr. ee 1 )ina=0.
ee n n n 2
But this is an identity on account of the fundamental relation A=0. Without further
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 733
conditions, then, we cannot find any relation between the k’s, which are therefore inde-
terminate. ‘This shows that in general a composite type admits of infinite variation, the
ratios of the number of polygons being indefinite.
Composite Types.
§ 13. We have defined two networks to be of the same type when they involve
only nodes of the same species, whatever may be their form and structure. The
determination of the composite types in any group thus reduces to finding all the
possible combinations of nodes admitted by the group. In order to eliminate the
impossible combinations, we can find what combinations must occur. We shall take
each group in turn.
Class B. I. Triangles and Squares (1, 2, 4).
(a) 2 must be accompanied by 4 (fig. 11).
Hence the only combinations are 1, 4; 2,4; 1, 2, 4, each of which gives
a composite type. Examples of each are given by joining together infinite
parallel strips of the triangular and square networks.
II. Triangles and Hexagons (1, 3, 5, 6).
(b) 3 must be accompanied by 5 (fig. 12).
Fence the only combinations are 1, 5; 1,65 3,5; 5,6; 1), 3,°5; 1,5,6;
3,5,6; 1,38,5,6. There are thus eight composite types. Hvery variety of
them can be obtained from the triangular network by replacing groups of six
triangles by hexagons.
III. Triangles and Dodecagons (1, 7).
IV. Squares and Octagons (2, 8).
Each of these is unique and admits of no composite types.
§ 14. Class C. I. Triangles, Squares, and Hexagons (1, 2, 3, 4, 5, 6, 10).
The number of combinations of these numbers, two or more together, so
as to include the three polygons, is 105. We proceed to establish rules for the
rejection of impossible combinations.
(a) 2 must be accompanied by 4 or 10 (fig. 11).
(b) 8 - ‘ 5 5; and either 6, or 10 and 4 (fig. 12).
Exclude 6; then we must have 10, since squares and hexagons come
together ; and since there are always two triangles together, we must also
have 4.
Exclude 10; then squares cannot be introduced till the hexagons have
been surrounded by triangles, and we have 6.
(c) 5 must be accompanied by either 10, or 4 and 6 (fig. 12).
Exclude 10; before squares can be added we get 6, and the further
addition of squares gives 4.
TRANS. ROY. SOC, EDIN., VOL, XLI. PART. IIT. (NO. 29). 109
734 MR DUNCAN M. Y. SOMMERVILLE ON
Hence if 10 is excluded, we must have 4 and 6.
For 4 is necessary in order to give squares, and if we exclude 6 we also ©
exclude 5, and therefore 3. We are then left with only 1, 2, 4, which do
not involve hexagons.
(d) 6 must be accompanied by 4 or 5.
Excluding 4 and 5, the hexagon must be surrounded by triangles, and
squares can never be introduced without producing 4.
1 must be accompanied by either 4, or 5 and 6.
Exclude 5 and 6; then T, must be surrounded by either triangles, or tri-
angles and squares. Since hexagons are excluded at this stage, either of
these introduces 4.
—
fa
y
—
Exclude 4 and 6; then T, must be surrounded by hexagons. Now squares —
can only be introduced after the concavities have been filled up. If we fill -
them with hexagons fresh gaps are produced, and if we fill them with tri-
angles there are always two triangles together, and the addition of squares is
impossible without giving 4. Hence we cannot exclude both 4 and 6.
Exclude 4 and 5; then 6 is also excluded by (d), and T, can only be
surrounded by triangles.
Also 1 can only be continued by 4, 5, or 6; hence if we exclude 4, we
must have both 5 and 6.
Rejecting according to these rules, we are left with forty-seven combinations, each of
which gives a composite type. The combinations may be represented by the following
notation. Let C,(a,,....,a,) stand for any one combination of 7 or more of the a’s,
then the forty-seven combinations are
5+C,(4, 6, 10)+C,(1, 2, 3)
4+C,(6, 10)+C,(1, 2)
10+ C,(2, 5).
§ 15. Class C. II. Triangles, Squares, and Dodecagons (1, 2, 4, 7, 11).
(a) 2 must be accompanied by 4 (fig. 11).
(Gi) as Z ; oS (ie):
After rejection there are left eleven combinations, all of which give com-
posite types except 1, 7, 11. There are therefore the following ten composite
types in this group:
Ast eC) On Ter. wl palilnemeaasy, lee
III. Squares, Hexagons, and Dodecagons (2, 3, 12).
Excluding triangles, 12 can only be continued in one way, hence there are
no composite types in this group. |
§ 16. Class D. ‘Triangles, Squares, Hexagons, and Dodecagons (1, 2, 3, 4, 5, 6, 7,
10, 11, 12).
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 735
The number of combinations of two or more together of these numbers which
involve all four polygons is 856, but we have the following rules for the rejection of
impossible combinations :
(a) 2 must be accompanied by 4 or 10.
(b) 3 i a A 5; and either 6, or 10 and 4.
(Os ay - s either 10, or 4 and 6.
(d) 6 x i ‘3 4 or 5.
Or)?
dr) 9 99 1 if <
The previous proofs of these still hold.
(e) 1 must be accompanied by either 4, 5 and 6, or 11.
(9)
(h
ee
—
If we exclude 11, triangles or hexagons must be in combination with
squares, and we have seen that squares can never be introduced if we exclude
4 and either 5 or 6. But 1 may be continued by 11 (fig. 16).
We must have either 11, or 10 and 12.
For, excluding 11, we must have 12 at least, for dodecagons are only given
by 7, 11, and 12, and 7 is excluded by (/).
Starting therefore with 12, we must have fig. 13. The concavities can now
be filled either with dodecagons, or with squares and triangles. The latter
gives 10, the former never introduces triangles.
If 4 and 12 be excluded, the only combination is 7, 10, 11.
Excluding 4 and 12, we must have 11. Let us start therefore with fig. 14
(the heavy lines). a cannot be a square, for that gives a hexagon at b; nor
a hexagon; nor a dodecagon, since 12 is excluded. Hence a must be a
triangle, and we get the figure with dotted lines.
Again, if we start with fig. 15 (the heavy lines), it must be continued as in
the dotted lines.
Lastly, let us start with fig. 16. A dodecagon at @ gives us a variation of
fig. 14 with the hexagon turned through 60°, a square gives fig. 15, and a
triangle fig. 16 with the dotted lines.
The continuation of any of these figures (under the given conditions) will
introduce no angles other than 1, 7, 10, 11; and fig. 16 must be excluded,
since it does not contain hexagons. Hence the only possible combination is
nO, 11.
If 4 and 10 be excluded, the only combination is 1, 11, 12.
We must have 12, by (h); and 11, by (9g).
Starting with 12 we get fig. 17. At awe must put either a hexagon or
six triangles, hence the figure can only be continued as in the dotted lines,
where some of the hexagons, but not all, must be filled up with triangles.
This is the combination 1, 11, 12.
Rejecting according to these rules, there are left 222 combinations. I have tested
736 MR DUNCAN M. Y. SOMMERVILLE ON
these and found composite types corresponding to 176 of them. Of the remainder it is
probable that a considerable proportion do not give types. Thus it seems probable that
the only types which involve 11 without 4 are 1,10, 11, 12; 1, 11, 12; 7, 10,11; and
7 HOt. We
The combinations are all included in the following lists. A. contains the 222 left
after rejection, B. those which I have not verified.
Ae Ab Creo 8 a7 el) O(6.010):
4,5 Oslo aO rt Iboae Sy6))
A 11 PCC, 2, 1)-0,(6, 1012);
A 10) 1 CA, 2) 6):
516) LOM 125 CMI, 887)
10, 1s -W2e eC. 2, Saar):
56,10; 12.2.0, (ln 2a)
10ST C.(2) Oy, le alla 7a 10
Br 3, 25, 6 7 tl, 1 eC).
2k 6, 11 HC.(7, 12)4 6,6):
2, 495, 10; 11,12 €,(7). 4, 11, 12.
3. 45. 6. Wile 1 4, 5, 6, 11.
? ?
BG HlO. dd ISAC. (pearcua):
10, 11, 12+0,(1, 2, 5,7) [except 1, 10, 11,12 and 7, 10, 11, 12]
5, 6, 10, 12.
§ 17. Many of these composite types can be obtained from the simple types by
filling up the hexagons and dodecagons. Thus, as we have seen, the type 1, 11, 12 can
be obtained from the simple type 12 by filling up some of the hexagons with triangles.
From the same simple type can be obtained nine other composite types involving the
nodes 1, 4, 10, 11, 12. In the same way, having obtained one example of one type, it
is generally possible to obtain a number of other types from it by some simple substitu-
tions or displacements. A classification of the composite types might thus be attempted,
based upon their structure. In this way types which are widely separated in the present
classification would be brought together, and vice versa. It is to be noted, however,
that the general variety of a type may fall on the lines of no simple network, so that
a classification such as that suggested would be difficult to apply in the general case.
Il. THe Exurpric PLaNe.
§ 18. We proceed to investigate the semi-regular networks upon the elliptic plane,
or, what is the same thing, upon the sphere, or in general upon a closed surface of con-
stant positive curvature.
We shall first find what species of nodes are possible. Since the angle of a regular
polygon here depends upon the area of the figure, it is obvious that the number of
species of nodes is infinite. Whatever holds on the EHuclidean plane regarding the
number of polygons which can meet at a point will hold @ fortiori for the sphere.
Hence we have only two cases to consider: viz., at a point there may be 1° two, 2° three
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 737
different kinds of polygons, but not more. The species of nodes thus fall under three
classes, Class A. consisting of the homogeneous nodes. We shall take the other two
classes separately, and find those nodes which give simple types.
§ 19. Class B. Let there be p, 7,-gons and p, %-gons at a point; then, if a, a, are
the angles of the 7,- and n,-gon,
Mya, > (n, — 2).
Also Pia, + Pod. = 27.
9
Therefore a,( = =) 4 pi a =) Ze
ny Ny
or, NyN(2 — p) + 2(pyny + pom) =A>0.
Giving A positive integral values we get a series of equations to solve under the
following conditions: 1+, > 3, 3+p45, therefore p,, p.>4. Also, if p,=2, p.=38,
the smallest values of n, and n, which are possible are n;=4, %.=3, but these make
A=0, hence the only possible sets of values of », and p, are
Further, if p,=1, p,=2, in order that the node may give a simple type, m) must
be even, for the n,-gon must be surrounded alternately with n,-gons and 1,-gons.
We have then
2n,p, — A
Nn, => SOIC GIREG
1 n,(p - 2) — 2p»
We shall take each set of values of p,, p, in turn.
net _2m-A_, 8-A
P,=2 woe: Ny — 4 Ta ies 4°
Since 7, is even, A must be even.
A=2. n,=6, 10 A=6. n,=6
n,=5, 3 n,=3
A=4, n,=6, 8 ANS I9) 5 Ny = 4
m=4, 3 m, =any integer.
ope 2, Ay 3—4A
Do=8 pO eo 3
A must be even.
A=2, n=4 A=6. ,=3
nN, =3 nm, = any integer.
A=4 impossible
Pe _ 2n,—A
po=4S 1” 3n, — 8
16-3A
or 3n,=2+ 3, —8
p=) i [A=3. n,=3=n,, excluded. |
n,=5
(=D Dp A> 3
738 MR DUNCAN M. Y. SOMMERVILLE ON
p,=2 4n,—A 4-iA
anare MV On = 4 +o
A=2.. (n= [A=6. n,=3=n,, excluded. ]
n,=5
A=4. m=3 A> 6.
nm, =4
§ 20. Class C. We have here the equation
ni-d)en-Zen(ie
r( ~ ny Po Ny Ps a <2,
or NN.N3(2 — p) + 2(pyNgNz + Pog, + pa) = A >O0.
We have to solve this equation under the following conditions: 7, + nm, + 1; 5 3,
3 > p+ 4, therefore p1, p., ps » 2, and we cannot have m1=5, m,=6, n,=7
together.
Further, if p,=p,=p3=1, %, %,, and n; must all be even, for the 7,-gon must be
surrounded alternately with n,.-gons and 1;-gons. Again, if p=4, n;=3, p,;=2, then
starting with an ,-gon we must have on successive sides an 7,-gon, a double triangle, a
double triangle, an m»-gon, and so on (fig. 18). Hence ”,, and similarly n,, must be a
multiple of 3.
The only possible sets of values of p,, p., 3, 3 are therefore
Pi =P2,=P3=1, n3=4;
p,=2, Pi =P.=1, n,=3 or 4.
We have then
He nn, p,—- A
N(p — 2. m3 — 2s) ~ 2pyns
tata i heh, 16—3A
nm,=4 1 2n, -8 My -4 *
Since n, and n, are both even, A must be a multiple of 8.
NERS Wage (i [A=24. n,=6=n,, excluded.]
n, =10
BeaNe. My 6 [A=32. n,=4, excluded. ]
n= 8
Pie tim | 6n,-A_, 9-4A
i 1 — aT ae
as if 1 Qn, - 6 Ny — 3
Since ”, and n, are both multiples of 3, A must be a multiple of 18, but A=18 gives
n,=3 and any higher multiple is excluded, hence there are no developable nodes of this type.
Dus Pie *) _8m-A . 4-4a
ie V 4mg-8° " * ny —2
= Z
3
A=4, 1, =3 [A=8. ro" | excluded ]
n,=5 nm =4
[A=12. »,=—3=n, , excluded,]
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 739
§ 21. We have found, then, the following developable species of nodes :
Class B. aaa: 2, = SOheSad 3503, 5, 6,
Dy— 2) NNO Gono, G5 4. 4.4. .
Ppa lh m= Sis be Gr,
ea N=4; 3,3,3,.
p= \ m,=5, 4
Po=4) My=3, 3
pPy=2 | m=3, 38
Aa) m,=5, 4
Class C. p,=1) m= 4,4.
=} n= 6, 6.
pj=1! n,=10, 8.
Py) on, 3
nai N=
Pg=2) n=4.
Each of these gives a simple type of network.
§ 22. We shall find the number of polygons, lines, and points in the complete
network.
Let N,’, N.”, N.” be the number of n’-, n’’-, and n”’-gons, N, , N,, Ny the number
of polygons, lines, and points respectively.
Then (§§ 11, 12)
Nea Ne IN NG” ae EMA et eed (1)
HON ep Ni,
nN,” =p'N, (2)
nN ah =p) No
oN, = 2N, (3)
where p=p'+p" +p".
Finally, Evxer’s polyhedral formula is
NMI NENG SO, kee a tok ae C8)
From (2) and (1) we get
p p- ad
Ny= (Stan tam No,
and from (3)
N,=5N,
Substituting in (4),
Pp p pp ky!
(24528, ot 1)N=25
whence
’ An’ nln”
=
A
Hence On! nn” p
N,=——__—*..
AN
N om 4p’ n” ni” N oe 4p” nl” n N ne 4p” n' “wr
: ean Muli hue ee oe dk
740 MR DUNCAN M. Y. SOMMERVILLE ON
For Class B. the corresponding formule are
4n' n” 2n' n"
i ae Sine eae
; 4y)’ n" 3 4y)” n’
eae EAL on ov
where A=n/n'"(2 — p)+.2(p'n" + pn’).
The Simple Types.
§ 23. We proceed now to classify the simple types and investigate their varieties.
The division into classes according to the number of kinds of polygons can still be
made, but the subdivision into groups according to the kinds of polygons involved is
useless, as there are an infinite number of kinds of polygons. We shall therefore, for
the present, classify them according to the types of nodes. I consider two nodes to he
of the same type when the values of p,, p., ps, are the same for both. A network
will not in general admit of variation unless its node does so. But this rule is not
always true; e.g. the type of angle PQ, is unvaried, but, as we shall see, one of the
networks corresponding to this type admits of two distinct varieties. We shall give
for each network the values of N,, N,, N,, etc. Unless otherwise specified, the net-
work is unique.
Class Be Wp 1p — 2
(1) A=2.. @) 7 = 3, N, =20
n”=10, N,”=12
N,=60, N,=90, N,=32 (fig. 19).
(b) n’ =5, N,’ =12
n’=6, N,”=20
N,=60, N,=90, N,=32 (fig. 21).
(2) A=4, (a) n' =3, N, =8
8, NG
N,=24, N,=36, N,=14 (fig. 20).
On =3 Ny =
n'=6, N,’ =8
N,=24, N,=36, N,=14 (fig. 22).
n =n, N, =2.
N,=2n, N,=3n, No=7 +2 (fig. 24),
itll p'= ,p"=3
()A=2. nw =3, Ny ES.
i =4, N= 18.
N,=24, N,=48, N,=26.
This type has two varieties. It contains a group formed by a quadrilateral surrounded
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 741
alternately with quadrilaterals and triangles. The boundary of this group is a regular octagon,
and by turning it round through = we get the other variety (figs. 26, 27).
Cra ce = 85 NG Sie
i =n, No = 2
N,=2n, N,=4n, N,=2(n+1) (fig. 25).
La — 2p =:
(Il) AV i =5 ING = 20)
jh 1, IN ly
N,=30, N,=60, N,=32.
A certain great circle divides this network into two equal groups, By turning one of these
through = a second variety is obtained (figs. 28, 29).
(2) A=4, S65 WES
A i
Nj, =12, N,=24, N,=14.
Like the preceding, this network has two varieties which may be obtained in a similar way,
viz., by turning one of the groups through = (figs. 30, 31).
i = 1, pT SA.
(1) A=1, m =), N, =12
irom NE 80
N,=60, N,=150, N,=92 (fig. 32),
(2) ee N 1G
% = 9), Nj = 32
N,=24, N,=60, N,=38 (fig. 33),
These two networks are asymmetrical, Each exists in two forms which are enantiomorph.
The one could be obtained from the other by turning the sphere inside out, supposing this to be
possible, as it would be in space of four dimensions,
eee Class CC 1 pt, p’=1, p= 1.
(1) A=8. n’ =4, N,' =30
n” =6, N,” =20
n”=10, Nj” =12
N,=120, N,=180, N,=62 (fig. 34).
(2) A=16. n' =4, N,’ =12
n’ =6, Nj” = 8
nu!” =8, Ni” = 6
N,=48, N,=72, N,=26 (fig. 35).
A=4, n =3, N, =20
Ch. NS
dt APN 30)
N,=60, N,=120, N,=62.
Of this type there are five varieties, which may be obtained as follows:—In one of the
varieties (fig. 36) there are no two quadrilaterals adjacent, Each pentagon has a quadrilateral on
each of its sides and forms the centre of a group with a regular decagon as boundary. Let us call
TRANS. ROY, SOC, EDIN., VOL. XLI. PART III. (NO, 29). 110
742 MR DUNCAN M. Y. SOMMERVILLE ON
this the fundamental variety. Then all the other varieties can be obtained from it by turning
some of the groups through 5 Let us denote this operation by R. . In the fundamental variety
the twelve pentagons occupy relatively the same positions as the meshes of the dodecahedral
network, so that with respect to one of the groups the others can be divided into three sets:
5 adjacent, 5 circumjacent, and 1 opposite. Now suppose the operation R to be performed upon
one of the groups. This gives a variety 8, (fig. 37). Next suppose a second group to be operated
upon. The adjacent ones cannot be moved, for the first operation has destroyed their symmetry.
Operating upon the opposite one we get a variety @, (fig. 38), while operating upon one of the
circumjacent groups we get a fourth variety y, (fig. 39). From , we cannot obtain any further
variety, for each of the remaining groups is adjacent to one of those already operated on. From 7,
we can obtain a fifth variety, y. (fig. 40), by turning either of the two groups which are circum-
jacent to both. In f, and , pairs of quadrilaterals occur, 5 in the former, 10 in the latter. In
y, and y, there occur respectively 1 and 3 groups of three quadrilaterals.
§ 25. To every spherical network there corresponds a convex polyhedron whose
vertices are the nodes of the network. The polyhedra which correspond to the semi-
regular networks have for their faces regular plane polygons. These form only a class
of convex polyhedra in general, but they are the only ones whose faces may be regular
polygons, and which, at the same time, may be inscribed in a sphere.
If we examine the numbers of the several polygons in the various natok above
we find that, with the exception of the two infinite series, they can all be’ connected
with the regular networks. ‘The series with two quadrilaterals and an n-gon at each
point corresponds to a series of right prisms on a <8 polygonal base, the altitude
diminishing indefinitely as 1 increases.
The polyhedra corresponding to the other types. can’ be obtained from the regular
polyhedra by cutting off the corners in particular ways: Thus the octahedron (fig. 23)
bounded by triangles and hexagons can be obtained from the regular tetrahedron by
cutting off the corners, either triangles or hexagons corresponding to vertices, according
to the depth of the section. When the numbers of the polygons are the numbers of
faces, lines or vertices of a regular polyhedron; it is evident in what way they corre-
spond. In some, however, the same kind of polygon may correspond to both edges
and vertices, then its number has to be divided into two parts, each a multiple of the
number of edges or vertices of the regular polyhedron.
This holds only for the unique types and the fundamental varieties of the other
types, 7.e. those in which no two polygons of the same kind are adjacent. The other
varieties may or may not be obtainable from the corresponding regular polyhedron.
Those of Class B. are not, while the four derived varieties of Class C. II. may still be
obtained from the regular dodecahedron, since the positions of the pentagons are
unchanged.
§ 26. We may therefore group the simple types in three divisions according to
their morphology.* We shall use the notation 3,'6,' to denote a simple type consisting
* A correspondence between the regular polyhedra and certain general classes of polyhedra was considered by
C. Jordan, “ Recherches sur les polyédres,” Comptes Rendus, 1x. 400-408, lxi. 205-208, Ixii. 1339-1341, 1865-66.
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 743
of triangles and hexagons, where the subscript refers to the number of polygons at a
point, and the index to the number of polygons in the whole network.
I. Tetrahedral. 3,'6,*.
Il. Hexahedral. 3.28.5, eye ee A 83, +202)
4.,°6.", 3,°4.°.
4,°6,°8,".
III. Dodecahedral. 38,7°10,", 5 123 204200 |
5 oe 3.20 5
42°62 0,", 3,95 2A, ®.
With two exceptions, to each hexahedral network there corresponds a dodecahedral
one, each pair being obtained in a similar way from the regular network. Thus
3,°8.° and 3,°°10,” are obtained by shallow sections from the cube and the dodecahedron
respectively ; 3,°4.° and 3,°6," by sections through the middle points of the sides, and
soon. ‘There is no dodecahedral network corresponding to 3,°4;"°, nor is there a hexa-
hedral network corresponding to 3,°5,"4.". It may be noticed that the values of A
for corresponding networks bear the same ratio as the values of A for the regular
networks, viz., 1: 2.
In representing the networks upon the Huclidean plane the method of stereographic
projection has been employed, though in some cases, in order to avoid undue crowding
towards the centre of the figure, strict stereographic projection has been departed from.
For simplicity the nodes are joined by straight lines instead of ares of circles, so that
the figures really represent the conical projections of the semi-regular polyhedra.
Composite Types.
§ 27. At first sight it might appear that a very large number of composite types
could exist, for there are an infinite number of species of nodes, while on the Euclidean
plane where there are a considerable number of composite types there are only a very
few species of nodes. A little consideration will show, however, that it is probable
that the number of composite types is extremely limited.
Let us take any species of node, p,, Po, P33 Ny, M., Mg, and let a,, a,, a, be the
angles of the different polygons, « the length of side, & the radius of the sphere.
Then
T T T
cos cos — os —
& Ny Ny Ng
cos ok = =
“ . a, . Ao a
sin — sin — sin —
2 2 2
and
P12 + Pot + P3043 = 27.
These four equations determine a, , a,, a, and a.
744 MR DUNCAN M. Y. SOMMERVILLE ON
Now if an n,-gon occurs in the same network in a different combination pj’, 5’, p4;
N,, N_, %,, then a,, the angle of the n,-gon, must satisfy the two equations
T
5 cos —
= n , ’ =
Ors = 4, Py 41+ Po O_ + Pyay= 27.
- @&
sin —4
2
If we substitute in the first equation a value of a, corresponding to a possible set of
values of p,', p>, p, obtained from the second, we must get an integral value for n,.
This will not in general happen.
The following negative results may also be obtained at once :
1. No composite types exist with only one kind of polygon, for the angles are all
equal, and there must therefore be the same number of polygons at each point.
2. No composite types exist with p=3 at each point, for the angle and the side
determine n.
§ 28. A certain number of composite types may be obtained by the following
TuHrorEeM.— Whenever a simple type contains a group of polygons bounded by a
regular polygon, the replacement of that group by a single polygon will in general gue
a composite type.
When such a group occurs it may be replaced by a single polygon, for in the
corresponding polyhedron the boundary of the group lies in one plane. Further, the
replacement of the group removes at least one line from the nodes at the boundary, and
the resulting network contains some nodes with p lines and some with at most p—1,
2.€. it contains at least two different species of nodes, and is therefore composite.
It follows that, in order that the simple type may give a composite type in this
way, p must be >3. It may happen that the angle of the boundary polygon is >180°. __
If we exclude this case we get the following composite types:
1. From 3,”° by replacing five covertical triangles by a pentagon.
This may be done in three ways, replacing 1, 2 or 3 sets by pentagons.*
The three networks are of different types. They may be denoted as follows, the
symbol within brackets denoting the species of node and the coefficient the number of
times it occurs in the network.
(a2) 6(8;) + 5(8,5)) (fig. 41)
(6) 2(8;) + 6(8,5,) + 2(8,5,) (fig. 42)
(c) 3(335,) + 6(3,5,) (fig. 43)
2. From 3,°4.'° by replacing one of the octagonal groups (fig. 27 deleting the part
within the heavy lines).
12(3;4,) + 8(4,8,)
3. From 3,°°5,”4,*° (fie. 36) by replacing the decagonal group.
* Tf two opposite groups of five triangles are replaced by pentagons we get the simple type 3,1°5,? (like fig, 25).
+ If both groups are replaced we get the simple type 4,°8,? (like fig, 24),
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 745
There are eight possible varieties. Let X denote the original group, R a group
turned through x O the decagon replacing a group, then, if XY denotes two
Borg g p g group
opposite groups, a three groups mutually circumjacent, the varieties can be ex-
PP groups, y7 group Vf. Ly)
pressed as follows :
(a) 45 (315,49) + 10 (4,5,10,)
(a) O (8) OR
O O
*(y) RX (8) RR
(b) 30 (3,5,4,) + 20 (4,5,10))
O O
(2) OO 8 =(8) OX _~— (y) OR
(¢) 15 (3,5)4_) + 30 (4,5,10))
O
OO
§ 29. Further, if we allow angles >180° we get the following :
1. From 3,°, replacing four covertical triangles by a quadrilateral (fig. 45).
(3,) +4 (8,4,). Angle of quadrilateral 180°,
2. From 3,” (fig. 44).
(3,) +5 (3,5,). Angle of pentagon 216°.
. From 8,°4,"° (fig. 27 bounded by the heavy lines).
4 (3,45) +8 (3,4,8,). iijAngle of octagon 196° 50’.
4, From 3,°4,°, replacing the hexagonal group (fig. 31 bounded by the heavy lines).
3 (8,4.) +6 (3,4,6,). Angle of hexagon 180°.
5. From $,"5,”, replacing the decagonal group (fig.-29 bounded by the heavy lines).
10 (3,5,) + 10 (3,5,10,). Angle of decagon 180°.
6. From 3,%5,"4,” (fig. 37 deleting the part within the heavy lines).
5 (3,5,4,) +10 (3,4,10,). Angle of decagon 204° 6’.
co
These are all the composite types obtainable from the simple types. It seems
probable that there are no others.
Ill. Tot Hyperporic PLANE.
§ 30. This case does not admit of exhaustive treatment. The number of types of
networks is evidently infinite, for there is no limit to the number of lines at a point.
As a rule, the hyperbolic plane contains the types which cannot exist on the
Huelidean or the elliptic plane. For example: one n-gon and two 2m-gons at a point
* Asymmetrical. Two enantiomorphic forms, ux and er -
746 _ MR DUNCAN M. Y. SOMMERVILLE ON
determine a simple hyperbolic network for all values of m and m for which the network
is neither Euclidean nor elliptic. The networks are all infinite.
As regards composite types, we can apply the same remarks as were made in con-
nection with the elliptic networks. The angle of a polygon is determined by the
particular combination in which it occurs, and the multiplicity of composite types is
thus limited. But, at the same time, it is infinite. For, consider the regular network
3, (p>6) (fig. 46). Any group of p covertical triangles can be replaced by a p-gon, so
that from this network alone we obtain an infinite number of composite types.
Note added on July 29, 1905.—Since writing the above, I have come across some
of the previous work on the subject. The semi-regular polyhedra have long been
known. It appears, from the works of Pappus of Alexandria and Keppusr, that they
were described in a lost work of ARcHIMEDES.* Pappus} enumerates the series of
thirteen (7.e. excluding the two infinite groups, figs. 24 and 25), with the numbers
of their faces, edges, and vertices, for which he gives the general formule of § 22.
KeppLeR{ establishes them by taking the different possible combinations, first binary
and then ternary, containing triangles, squares, and pentagons successively. More
recently, accounts of them have been given by Meter Hirscu§ and R. Batrzer.|| An
elaborate article, containing numerous calculations relating to the radius of the cir-
cumscribed sphere, inclinations of the faces, etc., was presented by M. VauarT to the
French Institute in 1854.1 He refers to other writings, in particular to one by
LiponneE (1808), but gives no details of them. He shows also how the semi-regular
polyhedra are obtained by truncating the Platonic solids. The connection between
these polyhedra was also expressed by KEPPLER in an ingenious nomenclature which
he employed to describe them. The following list of names corresponds to the table
on p. 743; the numbers refer to the diagrams :—
I. Tetrahedron truncum (23). his er
II. Cubus truncus (20). Rhombicuboctahedron (26), Cubus simus (33).
Octahedron truncum (22). Cuboctahedron (30). sf
Cuboctahedron truncum (35). =
III. Dodecahedron truncum (19).
Icosihedron truncum (21). Icosidodecahedron (28).
Icosidodecahedron truncum (34). Rhombicosidodecahedron (36).
Dodecahedron simum (32).
In none of these writings is any notice taken of possible varieties, the reason
being probably that these varieties do not exhibit the same symmetry as the funda-
mental varieties. KrppLER gives this as the reason for excluding the two infinite
series.
* See also T, L. Heatu, The Works of Archimedes (Camb, 1897), p. xxxvi.
+ Collectio, lib. v. pars 2.
t Harmonices Mundi (1619), lib. ii. pp. 61-65.
§ Sammlung geometrischer Aufyaben (Berlin, 1805-7), vol. ii. pp. 189-185.
|| Elemente der Mathematik (1862), Bd. ii., Buch v. § 7.
{ Published 1867, under the title “Des Polyédres semi-réguliers, dits solides d’Archiméde,” Mém. de la Soc. des
Sciences phys. et nat. de Bordeaux, v. 319-369.
SEMI-REGULAR NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY. 747
Kerppuer has also gone into some detail regarding the EKuclidean networks. He
gives* all the developable species of nodes and some of the others, with examples of
networks formed with them, and other patterns, containing star-polygons, which may
be derived from them.
It remains to notice a class of. polyhedra connected with the semi-regular
polyhedra.t They are obtained by drawing tangent planes to the circum-sphere at
the vertices. To a regular -gon there corresponds then a regular n-hedral angle.
A regular polyhedron treated in this way gives the conjugate regular polyhedron,
but in a semi-regular polyhedron none of the polyhedral angles are regular, and so
none of the faces of the “conjugate” polyhedron will be regular polygons. The
regular polyhedra have both a circum- and an in-scribed sphere; the semi-regular
polyhedra have only a circumscribed sphere, while the conjugate ones have only an
inscribed sphere. The corresponding networks are constructed simply by taking as
new nodes the centres of the old meshes. The polyhedra conjugate to the fundamental
varieties have their faces all congruent. This does not hold for the other varieties
(with the exception of that corresponding to 3,°4,%, fig. 27). Two of this class are
interesting as being the only ones which have all their edges equal, viz., the rhombo-
hedra formed from the fundamental varieties of 3,°4,° and 3,°5,” (figs. 30 and 28).
There is an analogous Euclidean network conjugate to T,H,, 2.c. 3,6,.
On p. 743 there occurs a misstatement. The hexahedral network 3,°4,°*”
(Rhombicuboctahedron), though it contains only two kinds of polygons, really corre-
sponds to the dodecahedral network 3,°0,"4,* (Rhombicosidodecahedron), being
obtained in a similar way from the corresponding regular network. Thus the corre-
spondence between the hexahedral and the dodecahedral networks is complete.
* Loc. cit., pp. 51-55.
+ Kepruer and BanrzEr, loc, cit.; Mrrer Hirscu, loc. cit., pp. 186-196; J. H. L. MtuuEr, Trigonometrie (1852),
p. 345.
Trans. Roy. Soc. Edin!- Wolk, Xa
SOMMERVILLE—NETWORKS OF THE PLAN
1 ABSOLUTE GEOMETRY.—P.LaTE I.
a
= M‘Farlane & Erskine, Edinburgh.
bus
Trans.
1 ‘ “>
Inoy. oc. Edint-
SOMMERVILLE—NETWORKS OF THE PLANE IN ABSOLUTE
Wiolh, ele ly
Gromeary-— Lente
M'‘Farlane & Erskine, Edinburgh,
Volek
hast Roy. Soc. Edin.
OLD A ITS
DW Sa OO
ERE
ERCEAY
EY , jorsees .
‘
& ‘ woos,
‘ NeZ nos
, 4
Hy. x
'
»
»
.
e
“ewww ce”
MSFarlane & Erskine, Lith. Edin?
ans. Roy. Soc. Edint: Wola ins
SoMMERVILLE—NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY.— PLATE V.
M‘Farlane &Erskine, Inth. Edin?
Trans. Roy. Soc. Edin" ; Vol XEI.
SoMMERVILLE—NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY.—P.uaTE VI.
M‘Farlane & Erskine, Lith Edin™
Vols oobi:
Trans. Roy. Soc. Edin‘.
‘rans. Roy. Soc. Edin!- Vol. XLI.
_ SOMMERVILLE—NETWORKS OF THE PLANE IN ABSOLUTE GEOMETRY.—PLATE IX.
Viol XL
(749 )
XXX.—A Monograph on the general Morphology of the Myxinoid Fishes, based on a
study of Myxine. Part I. The Anatomy of the Skeleton. By Frank J. Cole,
B.Sc. Oxon. Communicated by Dr R. H. Traquarr, F.R.S. (With Three Plates.)
(MS. received June 3, 1905. Read June 19, 1905. Issued separately September 25, 1905.)
CONTENTS.
PAGE PAGE
A. Introduction. : ; : ; ; . 749 | H. Basal Plate ; ; ‘ ‘ ; : 5 agi
B. Notochord . é ; j ; . 750 | I. Dental Apparatus. . 774
C. Cranium and Neural Tube : : : . 754 | J. Skeleton of the Velum or Pharyngeal Valve 5 aut
D. Histology of the Skeleton . : : : . 754 | K, Skeleton of the Club-shaped Muscle 3 . 00g
E. Cranio-pharyngeal Framework . : : . 759 | L. Branchial Skeleton . : : : . 780
F. Nasal Tube and Capsule . : ; . 766 | M. Skeleton of the Tail : F ; : . 783
G. Tentacular Apparatus . 2 : : . 769 | N. Explanation of the Plates . : ; f . 186
A. INTRODUCTION.
The present work was commenced in the summer of 1902, with the object of writing a
complete monograph of the morphology of Myxine. It had previously been undertaken
by the late Professor G. B. Howss, F.R.S., but, owing to the pressure of other work, and
the first indications of the illness which subsequently proved fatal, he handed the work over
tome. During the earlier stages, however, he exhibited a characteristic interest in the
research, and most generously placed his material and the late Dr PotLarp’s sections at
my disposal. His death has removed a kindly and a stimulating figure from our midst ;
a man whose life was devoted to the service of his friends and the advancement of his
favourite study, and whose generous and sympathetic nature was the wonder and the
delight of all who knew him.
The work had not been long i in progress before it became evident that it was much
too extensive for publication as a single monograph. I therefore determined to issue it
in parts, following the example of the illustrious founder of our knowledge of Myxinoid
Anatomy—J. Miiirr. These parts will relate simply to the anatomy of Myzxine, and
will only take cognisance of such literature as contains original observations of Myxinoids.
I have prepared an exhaustive Myxinoid bibliography, which will be published with my
final part, so that in the meantime I need only direct attention to the papers on the
skeleton mentioned below.* The anatomical parts will be followed by a separate con-
* The following works relate to the skeleton generally, those dealing with special points being referred to at the
appropriate places :—A. A. Rerzius, Kgl. Vet. Akad. Stockholm, 1824; J. Munurr, Abh. K. Akad. Wiss. Berlin,
1834; P. Furprinemr, Jena. Zeits., ix., 1875; W. K. Parker, Phil. Trans., 1883; G. B. Howns, Trans. Liv. Biol.
Soc., vi., 1892 ;, Neumayer, Munchen. med. Abhand. (KuprFeR and Rtpineur), Hft. 74, 1898; AymeRs and Jackson,
_ Jour. Morph., xvii., 1901, and Bull. Cincinnati Univ., vol. i., 1900; Autis, Anat. Anz, xxili., 1903.
TRANS. ROY. SOC, EDIN., VOL. XLI. PART III. (NO. 30). 111
750 MR FRANK J. COLE
cluding section of a general character, in which the morphology of the Myxinoids will
be treated in detail and the appropriate general literature discussed. ‘The present part,
therefore, like its successors, is not morphological, but is concerned with descriptive
anatomy only. A very full description of the muscles will constitute Part I., and will
be ready by the end of the year.
As regards the terminology of the skeleton, it is quite clear that the failure of Panes
and Ayers and Jackson to correctly homologise the parts of the Myxinoid skeleton
was due to insufficient data; and another attempt on my part, before the evidence of the
muscles, blood-vessels, and nerves is available, and also the memoir on the development
of the skeleton of Bdellostoma now being prepared by Neumayer, could only end in
failure also. I have therefore adopted the terminology of Ayers and Jackson en bloc,
not because I approve of it—in fact, some of their terms have already been successfully
challenged by Attis—but simply to avoid coining a set of terms which could only last
a few years.* In my concluding section I shall, of course, discuss the morphology of
the skeleton, and revise the terminology, with, let us hope, a reasonable prospect of
arriving at results of some lasting value.
I have great pleasure in acknowledging the kindness of my friend Dr Bzarp in
lending me his sections of Myxine, and especially the series of the 6°5 cm. Hag, which
has been of great use to me. Also the collection of my own material was made
possible by a grant of £50 from the Government Grant Committee, with which I visited
the marine laboratory at Cullercoats, under the charge of Mr ALExanpER MeErx, and
was entirely successful. Living Myaine may be collected at Cullercoats in great
quantities, by methods which I shall describe in my Third Part. The laboratory at
Cullercoats since my visit has unfortunately been entirely destroyed by fire, and it is to
be hoped that the important work which Mr Menrx is doing there will not long be
paralysed for the lack of a new well-equipped laboratory. Finally, I am greatly indebted
to Professor W. F. R. WeEtpon, F.R.S., in whose laboratory at Oxford this work was
done.
B. Norocuorp. (Fig. 18.)
The termination of the chorda at its cephalic and caudal extremities is described
under the parachordal and caudal fin cartilages, and also below. As is well known, the
notochord constitutes the only skeletal support of the back, and there is no appearance
of cartilage, either in the chorda itself or in the neural tube, except in the region of the
head and tail (q.v.). Still less are there any traces of bone or calcified tissue of any
kind whatever, either here or in any other region of the body of Myxine. In this
respect the Cyclostomes share with Amp/zoxus a unique position in the chordate series.
* For example, the structures named ly Aymrs and Jackson “ branchial arches” are, according to BASHFORD DrEan,
developed after the gill pouches have disappeared from this region, and may therefore represent neomorphs developed
in connection with the muscles of the “tongue.” In fact, I am disposed to believe that much of the Myxinoid skeleton
is recent and sesamoidal (as indicated by PonnaRrD), and therefore has no morphology at all!
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. coe
The histology of the notochord of Myxinoids has been described by J. MUuzr,
W. Muuurr,* G. Rerzius,t v. Epner,t and Ayers and Jackson. In transverse section,
the chorda of Myxine is almost circular in the living condition, but is somewhat flattened
dorsally in parts. . The dorsal involution, however, so common in preserved material, and
described by J. MtLrEr, is an artifact produced by the fixing reagent. According to
G. Rerztus, the chorda contains no chondrin, glutin, or mucin, but albumen is always
present. When the chordal tissue or “jelly” is removed the stout sheath does not
collapse, as mentioned by J. MULLER.
Skeletogenous Layer (sk. 1.).—This layer consists of a few coarse fibres surrounding
the elastica externa. As may be seen where the fibres are torn across (as shown in
fig. 18), each fibre is formed of a large number of very fine fibrille. The fibres course
almost straight round the chorda, and are usually closely packed together. External to
these there may or may not be bundles of fibres coursing in various directions, and
which often contain true elastic fibrils. With methyl-blue-eosin the skeletogenous
layer stains a faint purplish blue. Arrived at the dorsal surface of the chorda, the
skeletogenous layer forms the greater part of the pad of tissue filling in the angle
formed by the meeting of the chorda and neural tube. At this place incipient patches
of cartilage may be developed in bdellostoma, according to Ayers and Jackson. The
layer is then continued over the neural tube as the external sheath of the latter. In
_ Bdellostoma, according to AyErs and Jackson, the skeletogenous layer splits at the top
of the chorda so as to roof over the chorda as well as the neural tube. I have seen only
very slight indications of this in Myxine; and, assuming of course that the whole of
the neural tube is not formed by this layer, it is practically not represented between
the chorda and the neural tube, and it thus forms one tube, enclosing both the chorda
and the spinal cord. J. MU ter’s account differs both from mine and Ayers and
J ackson’s, and is clearly inaccurate. The dorsai vertical longitudinal septum separating
the myotomes in the median plane is formed by the skeletogenous layer, and the latter is
also continued into the septa intermuscularia and into the fascia superficialis interna
(which latter is thus analogous to ribs), at these junctions the thickness of the layer
being greatly increased. It thus also forms the connective tissue support of the
myotomes. In the tail it further encloses the large blood-vessels, and is continued
over the caudal cartilages. The skeletogenous layer is non-cellular (:.e. has no nuclei),
but it is well infiltrated with blood-vessels. It is not, strictly speaking, part of the
chorda, and internal to it no nerves or blood-vessels exist. ©
Elastica Eaxterna (el. ext.).—This is a relatively thin cuticular-looking membrane,
staining intensely with eosin, and which closely invests the notochordal sheath as its
outermost covering. According to G. Rerztus, it exhibits the chemical reactions of an
elastic membrane. Its edges are doubtless by an optical effect sharply defined, and it
may give off elastic fibrille into the skeletogenous layer and sparely into the external
layer of the notochordal sheath (the latter according to v. Esner). There are no
' * Jena, Zeits., vi., 1871. t Arch. Anat. Phys., Anat. Abt., 1881. t Z. f. w. Z., 62, 1896 (complete paper).
752 MR FRANK J. COLE
nuclei in the elastica externa, and in Bdellostoma AyERS and Jackson describe parts
of it as exhibiting a “‘ distinctly fibrous structure.” This is also the case in Myxime in
the isolated elastica, as shown by v. Exner, the fibres being circular and spindle-shaped
and closely packed without any spaces. AYERS and Jackson state that no part of the
chorda is a cuticular product—a conclusion previously emphasised by v. EBNER.
There is no elastica interna.
Notochordal Sheath (nt. sh.**).—This consists typically, but not everywhere, of —
three perfectly distinct sheets—the external, middle, and anternal layers of the noto-
chordal sheath. According to G. Rerzius, all three agree in structure and also exhibit
the same micro-chemical reactions, and constitute the true chordal sheath traversed by
perforating tubules (?), representing one sheath only, as first pointed out by KOLLIKER.
As shown by v. Eswnrr, all three layers consist of non-cellular fibrillee coursing
transversely in large undulating curves round the chorda. The curves in the three layers
do not correspond, or rather those of the middle layer do not correspond with the
other two, thus emphasising the boundaries between the layers. The bends of the
curves always corresponding, no matter how they may be directed, linear effects are
produced in the isolated sheath, and in this way we may distinguish a dorsal, a ventral,
and a paired lateral longitudinal line. Of the three layers, the external (nt. sh.) is
usually as wide as the other two together, whilst the internal layer (nt. sh.*) is always
the weakest. v. EpnER has shown that in the tail, where one of the layers is suppressed,
it is the middle one (wt. sh.”). Stained with methyl-blue-eosin the external and
internal layers stain a faint pale-blue, whilst the middle layer is sharply contrasted
in pink.
Chordal Epithelium (ch. ep.).—This is very greatly reduced, and in this respect may
be compared with Bdellostuma (Ayurs and Jackson) and Petromyzon (v. Epnmr).
It consists of a very thin layer of granular protoplasm applied to the internal layer of
the notochordal sheath, and which is raised up at intervals into small heaps, each
lodging a nucleus. There is no observable division into cells, apart from the heaping
arrangement, nor is there more than one layer of the nuclei, in which I[ confirm
G. Rerzrus and v. Hepner. The chordal epithelium is connected with the chordal cells,
or rather the walls of the latter are opposed to the epithelium. In the small 6°5 em.
and 10 cm. Hags the heaping arrangement is wanting, and the nuclei, as one would
expect, are very close together—+.e. a typical epithelium exists. The chordal epithelium
cannot, of course, be morphologically separated from the chordal cells; both form one
coherent tissue. This is more evident in Bdellostoma, according to AyrRs and
JACKSON, where the epithelium may be two or three layers deep, and transitional cells
are found connecting it with the vacuolated chordal cells. .
Chordal Cells (ch. c.).—The entire mass of the so-called chordal “jelly ” consists of
vacuolated nucleated cells. The size of these cells varies in different individuals and
at different regions of the chorda, but generally there is a narrow zone of very small
cells associated with the chordal epithelium, and they then rapidly increase in size
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES, 753
towards the middle of the chorda, where they are largest. The cells are, roughly,
modifications of a spherical type—that is, they present the same appearance in transverse
and longitudinal sections. ach cell is, I believe, quite independent—z.ec. the fibrous-
looking septa forming the network are always double, being formed by the walls of two
adjacent cells, and there is no connection at the angles. This accords with the figures of
G. Rerzius and Ayers and Jackson. Between the walls of adjacent cells there is a
very narrow space, occupied probably by a cement substance, and each wall is marked
by very fine closely applied striations (as shown in the figures and as first pointed out by
G. Rerztvs), indicating that the wall is fibrillar. Lying on the wall of the cell is the
flattened oval nucleus, which is surrounded by a delicate membrane, is very coarsely
granular, and contains one or more nucleolar spots each surrounded by a clear area.
In Bdellostoma, according to AyERs and Jackson, the nucleus may lie in the centre of
the cell, when it is connected with the walls by protoplasmic strands. According to
v. Epner and Ayers and Jackson, the walls of the cell bear a very thin, encrusting
film of granular protoplasm. I find the nuclei in all the cells without exception,
although they have so far only been recognised peripherally. The body of the cell
is occupied by a clear, homogeneous fluid substance to such an extent that the chordal
cells must be regarded as the most intensely vacuolated cells known, or possible. The
fluid contains a granular substance in some forms, according tov. EpnER. Embedded in
the centre of the chordal cells, or generally, perhaps, somewhat nearer the dorsal surface,
is a condensed area known as the fibrous core (=the chordastrang of v. EBNER). Its
extent varies very greatly in different individuals, and in some parts of the chorda
may even be absent. In one specimen the fibrous core was cross-shaped in transverse
section, but it is generally greatly flattened from above downwards and wide from
side to side. As first suggested by KOuuIKEr, and ascertained by v. Esner, the fibrous
core consists simply of chordal cells elongated im a longitudinal direction, and having
relatively thick walls. That this explanation of the fibrous core is the correct one is
obvious from an examination of thin longitudinal sections. Ayers and JacKSoNn state
that in Bdellostoma it is entirely fibrous, but they were evidently unaware that it had
previously been correctly described. |
As the chorda enters the parachordals its sheath may gradually thin down (except
at one place, ventrally, where for a time it is even thicker), until at the extreme tip it is
covered only by the now irregular elastica externa, and even this is wanting for a short
space ventrally. The tapering of the chorda and the condition of its sheath is evidently
very little disturbed by the growth round it of the parachordals. In the tail, as the
caudal cartilages surround the chorda the fibrous sheath gradually disappears, leaving the
elastica externa; but even after the chorda is largely invaded by soft cartilage the
elastica externa and a portion of the fibrous sheath remain. Finally, however, first the
fibrous sheath and then the elastica externa vanish, and there is a fusion, though never
quite complete ventrally, between the now largely cartilaginous chorda and the median
ventral bar of the skeleton of the tail.
754 ‘ MR FRANK J. COLE
C. Tue Cranium anpD NEuRAL TUBE.
The neural tube is a double-walled structure. It consists of an inner cylinder often
selectively staining red with methyl-blue-eosin, and the base of which rests on the
elastica externa of the somewhat flattened roof of the chorda, and an external layer,
present only at its sides and roof, formed by the skeletogenous layer of the chorda.
The former is comprised of fine transverse fibres very closely packed together, and, in
fact, bears some resemblance to an elastic membrane. The cavity of the neural tube is
very much larger than the spinal cord which it contains. There is sometimes seen
wedged in between the fibres of the inner cylinder, in the mid-dorsal region, a wide
conspicuous mass of longitudinal fibres. The neural tube is perforated laterally below
at intervals by the roots of the spinal nerves.
The cranium is entirely membranous, and J. MULLER is of course quite wrong in
describing an infiltrmg cartilaginous substance in the cranium of Bdellostoma. It is
perforated in front by the olfactory nerves, and laterally below by the cranial nerves.
It is simply an expansion of the neural tube, and consists of the same two layers.
Between the cranium and the olfactory capsule the skeletogenous layer is very
extensive, as it also is ventrally and laterally at the termination of the chorda in the
parachordals. The brain almost fills the cavity of the cranium, and in this respect may
be contrasted with the spinal cord. The skeletogenous layer of the cranium is
continued into the median dorsal longitudinal septum between the myotomes of the
head, as in the spinal region. Anteriorly, the floor and roof of the cranium are joined
up by a median vertical septum consisting of a double sheet of the inner wall of the
cranium with the skeletogenous layer between, and which divides the anterior extremity
of the cranial cavity into two chambers, each containing an olfactory lobe.
D. THe HisroLogy oF THE SKELETON. (Figs. 3 and 4.)
I do not propose to consider in any detail the finer structure of the myxinoid
skeleton, which is a somewhat complex and contentious subject, but simply to discuss
such facts as bear directly on the morphology of the skeleton. Consequently I leave
over for the present my observations on the histogenesis of the cartilage.
The first observer to work at the histology of the myxinoid skeleton was J. MULLER,
who distinguished two kinds of cartilage,* which he refers to as “ yellowish” or “ brown”
(hard) and “grey” (soft) cartilage, and which he describes as “cellular cartilage.”
Its peculiar structure, which he roughly worked out, differing apparently from any
other variety of cartilage known, “greatly surprised” him. G. Rerzrus in 1881, m
his work on the auditory organ, figures and briefly describes the cartilage of the
auditory capsule of Myxine; and he states that it consists of a substance containing
closely opposed oval or rounded cell cavities, and a weak intercellular substance which
* 7, in Bdellostoma. In his concluding remark (p. 340) he wrongly excludes Myzxvne.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 755
is arranged in concentric layers round each cell cavity. Here and there two such
cavities are surrounded by the same concentric layers. This concentric structure seems
to me to be due to the nature of Rerzrus’ sections ; but whatever its explanation may
be, no subsequent observer has confirmed Rerzius’ description.
W. K. Parxer describes four varieties of skeletal tissue in myxinoids, which
correspond to my hard and soft cartilage and pseudo-cartilage below, as far as I
understand his description. The hard cartilage, he says, has a “ greenish” colour.
Ayers and Jackson state that the whole of the cartilage (preserved in formol) assumes
a “pink or reddish tinge,” and this, together with their somewhat remarkable neglect
of the literature of the subject, accounts for the failure of these authors to detect
one of the most obvious and striking characteristics of the myxinoid skeleton. Howes
regards the distinction between the two kinds of cartilage as a “subtle” one; but the
difference, as we shall see, is very real. PotLarp* describes the hard cartilage of Myaine
as consisting of ‘only a hard yellow spongework of the intercellular matrix,” the
)
nuclei and protoplasm of the “ procartilage” cells having disappeared. I have,
fortunately, had an opportunity of examining the sections on which this statement
was based, and find that as the material was stained in bulk with picro-carmine, the
stain has reached the cartilage cells in the soft or more penetrable cartilage ; but that
the cells of the hard or denser cartilage are not stained, whilst the intercellular substance
is coloured yellow. With the low power, therefore, PoLtLarn’s description appears
correct ; but examination only with a Zeiss D at once reveals the cells in the hard
cartilage, as shown in fig. 3, so that PoLLarn’s description is inaccurate.
The most reliable description of the cyclostome skeleton we owe to ScHAFFER,t
most of whose points I had made out quite independently before I had an opportunity
of consulting his work. The following abstracts, therefore, may be taken as including
my own results also. All the fresh cartilage is white and uncoloured, but the hard
cartilage is. more opaque. ‘The red colour assumed by the latter arises gradually in
alcohol first on the surface and then penetrates inwards. I have, however, so far not
found the red colour supervene on formol preserved material. The hard cartilage may
be said to consist of a number of units each composed typically of one cartilage cell
(ct. c.), a cell capsule (c. ct. c.), and a ring of secondary ground substance (s. g. s.),
these units being held together by a cement substance (c. sb.), from which, however,
they may be macerated out. I find that the independence of these units is more marked
in some places than in others; for instance, in the palatine bar there is a complete ring
of cement round each unit, as described by Scuarrer, whilst in parts of the middle
segment of the basal plate these rings are by no means complete, as shown in fig. 3.
Hence maceration here has not been successful. In the lamprey, according to SCHAFFER,
the intercellular substance { of the soft cartilage forms a continuous network which
* 1894, p. 349 ; and 1895, p. 415.
+ Z. f. w. Z, 61, 1896, p. 606. A. f m. A., 50, 1897, p. 170.
t ScHarrer’s term for the non-protoplasmic portion of the cartilage.
756 MR FRANK J. COLE
cannot be separated into units, and hence the intercellular substance here corresponds
with the cement of the hard cartilage, so that we have at once a sharp morphological
distinction between the hard and soft cartilages. This distinction, however, only partly
applies to Myxine, for in places we find in the soft cartilage a deposit of secondary
ground substance, and generally cell capsules are differentiated. The soft cartilage of
Myaine, therefore, represents a stage further than that of the lamprey. There seems
to be no question that the hard cartilage of cyclostomes, both as regards its minute
structure and micro-chemical reactions, may be directly compared with the hyaline
eartilage of other animals.
In addition to ScHAFFER’s memoir, the cartilage of cyclostomes has also been
investigated by Srupnicka.* This author finds the cartilage of the tail fin to represent
an intermediate type, which I can confirm ; but there must be added thereto the cartilage
of the branchial skeleton. There is thus no break between the two kinds of cartilage,
and this discontinuity is more in evidence in Myaine than in the lamprey. Stupnicka
doubts the presence (normally) of the cell capsule of Scoarrer in Myaine; and whilst
it is indeed true that there is a conversion of the capsule into ground substance in some
cases, as in higher animals, my fig. 3, which was drawn before I had seen the papers
of either author, amply confirms ScHAFFER in this respect. STUDNICKA was the first
to examine what I have described below as the pseudo-cartilage of Myxine, which he
terms ‘“‘vorknorpel,’ and of which he correctly asserts, on account both of its mor-.
phology and micro-chemical reactions, that it cannot be regarded as true cartilage, but
is a transition tissue. SCHAFFER, in his later paper, compares it with the tissue of
the sesamoid nodule in the Tendo Achillis of the frog, and states that, whilst he does
not regard it as true cartilage, it nevertheless exhibits considerable resemblances to the
simplest form of true cartilage. He considers the posterior segment of the basal plate
as a true sesamoid formation in the tendon of the M. retractor linguze,t and its cells
as peculiarly modified tendon cells. This has been independently stated by Ayzrs
and Jackson, evidently without knowledge of ScuarrrR’s work, and is clearly the
correct view. In this connection [ may mention that, in the cells of the frog's
sesamoid above, Mrves was able to establish the presence of centrosomes, and this
induced ScHarFeR to look for them in the similar tissue of Myaine. He succeeded in
his quest,{ and found that the cells of the posterior segment of the basal plate contained
one or two centrosomes, each surrounded by a clear area. I can confirm this discovery,
and am able to extend it to the cells of the hard cartilage, as shown in fig. 3.
Paraffin sections of the skeletal tissues of Myxine are invariably distorted and
unreliable, and hence the histology of the skeleton is best studied by means of free-
hand sections stained preferably with Mawnwn’s methyl-blue-eosin. Provided care is
taken to avoid being misled by certain deceptive appearances incidental to thick hand
* A. fm, A., 48, 1896, p. 606. Also 51, 1898, p. 452.
+ This is surely a slip of the pen. The muscle should be the M. copulo-copularis, P. FURBRINGER (M. constrictor
musculi mandibuli, Ayers and Jackson).
t Siz, K. Akad. Wren, Abt. iii., 105, 1896, p. 21.
ie
ON THE GENERAL MORPHOLOGY OF 'THE MYXINOID FISHES. On
sections, the micro-anatomy of the connective tissues may be satisfactorily worked out
in this way.
Apart from the notochord, two kinds of skeletal tissue may be distinguished in
Myxine—(a) cartilage and (b) pseudo-cartilage.* Further, there are at least two
varieties of each kind, and all may be said to merge more or less perceptibly into each
other. Of the cartilage, the two varieties are at once obvious. In the living condition,
as already stated, the skeleton is uncoloured, but after it has been a long time in spirit
a marked differentiation arises, the softer cartilage remaining white whilst the harder
cartilage turns a deep reddish brown. This distinction is wonderfully emphasised by
their staining reactions with methy]-blue-eosin, the soft cartilage staining blue and the
hard red. There is also, of course, a considerable difference in consistency, as the
terms soft and hard indicate. The combination of the morphological (already described)
with the micro-chemical distinction makes the difference between typical hard and
soft cartilage a very real one. The distribution of the two kinds of cartilage is
illustrated in the figures by the two colours (representing the staining reactions with
methyl-blue-eosin—soft cartilage, blue; hard cartilage, red), and hence there is no
oceasion to refer to it further here.
Hard Cartilage (fig. 3).—This consists of an intercellular substance or matrix in
which very large cartilage corpuscles or cells are embedded. Each cell (ct. c.) is
surrounded by a deeply staining thick capsule (c. ct. c.); but the matrix immediately
around each capsule only stains slightly, and this, owing to the large size of the cells,
accounts for the reticular appearance of the matrix emphasised by Pottarp, Wedged
in between this secondary ground substance (s. g. s.), as it is called by ScHarrEr, is the
staining portion of the matrix, or the cement substance (c. sb.), which more or less
surrounds each ring of secondary ground substance. The cement is the most massive
in older animals and in the larger cartilages. The cartilage cell itself consists of a very
finely granular slightly staining reticulum, in which is embedded a round or oval
nucleus (n. ct. c.) containing generally a single deeply staining nucleolar body
surrounded by a clear space. In paraffin sections the nucleus appears clear and
vesicular, with scattered globules of chromatin, whilst the sarcode is distinctly reticular
and the centrosomes also visible. I have seen as many as four nuclei in one capsule,
evidently prior to division, and the nucleolus itself may be multiplied. Various stages
in the division of the cell, and the consequent formation of fresh intercellular substance,
may be seen. With methyl-blue-eosin, the matrix stains red, the nucleus light blue,
and the nucleolus a deep blue.
Soft Cartilage.—This is the pro-cartilage of PaRKER and PoLLarp, but not the pro-
cartilage of Srupnicka. It has a very strong affinity for methyl-blue, and in fact
combines with this stain so intensely that it takes time to extract it. That there is,
however, no genetic distinction between the hard and soft cartilage is shown by the fact
* A term applied in 1878 to similar tissue in the frog by StapELMANN. I adopt it in preference to ScHAFFER’S
more cumbrous “ vesicular supporting tissue.”
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 30). 112
758 MR FRANK J. COLE
that the soft cartilage, where it is connected with the hard—as, for example, the lateral
labial cartilage with the external bar of the anterior segment of the basal plate—always
passes imperceptibly into the hard cartilage without any demarcation or trace of suture.
Hence we may regard the hard and soft cartilages as modifications of the same ancestral
tissue. On the other hand the soft cartilage, for example, of the caudal fin and of the
branchial skeleton undoubtedly approaches rather the structure of the hard pseudo-
cartilage, thus connecting up the two kinds.* The essential difference between typical
examples of the two varieties of the cartilage lies in the great reduction of the matrix,
and of its character, in the soft cartilage. This in some places is a continuous, homo-
geneous, almost fibrous looking network; but, generally, cell capsules may be clearly
distinguished, and secondary ground substance may even be added. Apart from this,
the intercellular network is distinctly comparable to the cement substance of the hard
cartilage, and is its characteristic feature. The cells and nuclei of the soft cartilage differ
in no essential respect from those of the hard cartilage.
Pseudo-Cartilage (fig. 4)—The structure of the hard pseudo-cartilage, for we
may distinguish hard and soft varieties here also, is best seen in the posterior segment
of the basal plate and in the superior chondroidal bar. If a thin, free-hand, transverse
section is made of the former it is seen to be U-shaped, and enclosed by a thick
perichondrium of stout. connective tissue fibres among which are interspersed groups
of nuclei. Both the dorsal concave and the ventral convex borders are lined by a
single palisade of vertical chambers, those at the latter border being much the larger.
The central portion of the cartilage is ocenpied by similar chambers (but of much
smaller size and irregular shape), and also by stout fibrous septa which usually pass
more or less directly from one border to the other, branching as they go. All the
peripheral chambers and many of the central ones are further divided by exceedingly
fine partitions into a number of loculi, each loculus containing one cell formed of a
glassy, transparent, unstaining sarcode, and one or more peculiar coarsely granular nuclei.
These nuclei usually have one or more nucleolar bodies, each surrounded by a clear
area. In some of the loculi a number of nuclei, each with an obvious nucleolus, were
massed together, whilst the occurrence of centrosomes in these cells has been already
mentioned. In the central loculi, the nuclei are generally much larger and of a very
irregular shape. .In spite of the fact that the matrix is here almost absent and its
place taken by fibrous septa, and that the character of the cells is different, we may
directly compare the pseudo-cartilage with the true cartilage in terms of the soft
cartilage of the caudal fin and branchial skeleton. AyrERS and Jackson state’ that the
pseudo-cartilage of the posterior seement of the basal plate resembles rather the structure
of the notochord than the cartilage of the remainder of the skeleton ; but this certainly
cannot be accepted.
The soft pseudo-cartilage may be best studied by sections of the thick pad at the
cephalic end of the basal plate (figs. 1 and 10). It has essentially the same structure
* (Op. the description of these two cartilages, and especially of the superior chondroidal bar.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 709
as the hard pseudo-cartilage, except that (1) the intercellular features are generally
much feebler, and hence the softer consistency ; (2) the chambers are all smaller and
of irregular shape—the regular peripheral chambers of the other variety being absent ;
(3) the fibrous septa are not only weaker, but ramify irregularly throughout the tissue ;
and (4) the nuclei are less coarsely granular (but otherwise similar). The soft pseudo-
cartilage, in fact, bears somewhat the same relation to the hard variety as the soft
cartilage does to the hard, whilst cartilage and pseudo-cartilage are connected up into
a series by the hard pseudo-cartilage and the soft cartilage. Compare in this connection
the histology of the superior and inferior chondroidal bars.
EK. Tue Cranto-PHARYNGEAL FRAMEWORK.
Under this generic title we may conveniently deal with that portion of the skeleton
grouped around the mouth, pharynx, and central nervous system, and which exhibits
par excellence that distinguishing feature of the mature myxinoid skeleton—the fusion
of the parts into one continuous coherent whole. To what extent this has been formed
by the fusion of independent elements, or whether it is more or less continuous from
the first, we do not at present know. Our doubts on this point will, I hope, soon be
set at rest by the speedy publication of the elaborate memoir which Dr L. Neumayer
is now preparing on the development of the skull of Bdellostoma, based on material
supplied by Prof. BasHrorp Dran. In the meantime, as far as Myaine is concerned,
there is not a single independent cartilage in the entire skull, except a few of the
nasal rings and the cartilage of the fourth tentacle. The division therefore into the
following regions must, to a certain extent, be artificial in the present state of our
knowledge. :
“ Parachordal” Cartilages (fig. 2, p. c.).—For a considerable distance behind the
skull there is a very gradually diminishing deposit of soft cartilage at the mid-ventral
line between the elastica externa and the skeletogenous layer of the notochord. In
Bdellostoma, according to J. MUuuEr, this is present as a detached ventral plate, and
NEvMAYER also describes a detached ventral half-ring of cartilage behind the parachordals
in Myxime. I have carefully searched for the latter in the sections of the 6°5 cm. and
the 10 cm. Hags, but find no traces of the break. As the skull is approached this
ventral deposit increases in volume, and extends upwards on each side of the chorda.
At the same time similar deposits of cartilage appear in the dorsal region, and all of them
imerease greatly in thickness and join up so as to form a complete ring round the
notochord except for a mid-dorsal break (cp. fig. 2). This tube is thinnest at the mid-
ventral line, and constitutes the soft parachordal cartilages ; but there is no break between
them ventrally. Whilst the parachordals are increasing in volume the notochord is
diminishing in size, and its membranes become gradually reduced. In front, the
parachordals gradually merge into the hard cartilage of the auditory capsule, but the
latter capsules are always separated in the mid-ventral line by a zone of soft parachordal
760 MR FRANK J. COLE
cartilage, and there is always a narrow ring of the same cartilage surrounding the em-
bedded notochord. Opposite the posterior boundary of the auditory foramen the
parachordal tube is completed dorsally for a very narrow space, so as to complete the chordal
roof (cp. fig. 2). This roof is much more extensive in Bdellostoma, so that in this respect
Mywine is the more primitive. In Myxine, Mitiur* did not find the dorsal fusion of
the parachordals at all; but I am inclined to think that it practically invariably occurs, in
spite of the fact that Parxer did not find it also. At the same region independent
nests of soft cartilage appear within the notochordal sheath, and the notochordal
membranes almost entirely disappear. The now cartilaginous notochord is, in places, in
contact with the parachordal tube in which it lies, but there 1s nowhere any fusion
between them.t The cartilaginous tip of the notochord projects freely beyond the
anterior border of the parachordals in the median line, as shown in fig. 2; ~The
parachordals are now supposed to split, and to extend forwards as diverging arms of
hard cartilage on each side, forming the inner boundary of the auditory foramen (au. f.),
and meeting the trabeculze opposite the anterior border of the auditory capsule. This
is certainly the appearance suggested by dissections (fig. 2), but an examination of serial
sections seems to me to indicate that the so-called parachordal cartilages terminate with
the soft cartilage—.e. they are composed entirely and only of soft cartilage. For it must
not be forgotten that the diverging arms are, as far as we can see, nothing more or less
than the inner wall of the auditory capsule completing the auditory foramen, which is
presumably a perforation in the wall of the capsule and not an enclosure by the capsule
with a fused parachordal. Ayers’ and Jackson’s fig. 4 is misleading on this point, as it
does not show the distribution of the hard and soft cartilage, which seems to me may
have some significance in this connection. The shading of this region in their fig. 7,
and also the figure of Rerzius,{ support the view suggested above; but it must not be
forgotten that the (assumed) complete fusion of the auditory capsule with the trabecula
in front admits the possibility of a similar fusion of the capsule and parachordal behind,
although there is absolutely no evidence for it in either case.
Auditory Capsule (figs. 1 and 2, aw. c.).—This is fused behind and internally with the
parachordal, as above stated. It is an oval-shaped hollow capsule of hard cartilage,
sloping upwards and outwards, with its dorsal or inner wall perforated by the large
ego-shaped auditory foramen (fig. 2, au. f), which is, however, closed by a tough, fibrous
membrane, about half of which consists of the fibrous cranial wall. This membrane is
perforated to admit the exit of the auditory nerves. Just opposite the second fenestra
of the skull (f-*), the dorso-external border of the auditory foramen is connected by
means of an internal column of hard cartilage with the ventro-external wall of the
* See his concluding remark, p. 340.
+ Since writing the above, examination of further series of sections, especially of a vertical longitudinal series,
indicates that fusion does take place ventrally between the cartilage of the notochord and that of the parachordals.
In fact, I now question whether the so-called anteriorly projecting tip of the chorda is not after all a part of the
parachordals. But these questions are difficult to settle with adult material.
{ Das Gehdrorgan d. Wirbelthiere, i., 1881.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 761
capsule. This column passes from above downwards and outwards, and for a few
sections divides the auditory chamber into a larger ventro-internal cavity, open widely
_ by the auditory foramen, and a smaller closed dorso-external cavity. As, of course, the
connection is only a rod, the division of the auditory chamber into two, seen in a few
sections, is apparent but not real. This column has been overlooked by all writers on
the myxinoid skeleton except Parker, who figured it in his sections but failed to under-
stand its real nature. Rerzivus (op. cit.) also found it, and states that it corresponds in
direction to a continuation of the bridge of soft cartilage described below as connect-
ing the auditory capsule with the hyoid arch. This is quite true, but whether the fact
has any significance cannot be determined by adult anatomy. It must, however, be
emphasised that the two structures represent two different kinds of cartilage. The
dorso-external wall of the auditory capsule behind fuses by means of a very short but
wide bridge of soft cartilage (forming the posterior boundary of the second fenestra)
with the dorsal extremity of the hyoid arch. Where this fusion occurs the entire
thickness of the capsule consists of soft cartilage. There is, in fact, here a ragged oasis
or plug of soft cartilage in the wall of the capsule. In front, the dorso-external surface
of the capsule forms the dorsal boundary of the second fenestra of the skull (f-”).* The
anterior margin of the capsule fuses with the posterior extremity of the trabecula.
‘ Trabecula” (figs. 1 and 2, tr.).—The trabecular bar fuses behind with the auditory
capsule, as just described. It then passes almost straight forwards as a stout rod of
_ hard cartilage, its lateral border behind being fused by a very short but wide bridge
of soft cartilage with the dorsal border of the superior process of the pterygo-quadrate.
At this region the trabecula itself is invaded by numerous nests of soft cartilage. The
above bridge forms the ventro-anterior boundary of the second fenestra of the skull,
and the posterior boundary of the first (f."). In front, the outer edge of the trabecula
forms the entire dorsal or internal boundary of the first fenestra. At its anterior extremity
the trabecula becomes gradually converted into soft cartilage, PaRKER’s figures of the
distribution of the hard and soft cartilage at this region being inaccurate according to
my dissections and sections. From its inner border in front the trabecula despatches
downwards and forwards a rod of soft cartilage (the sustentaculum of NrEuMaYER), which
fuses with the central expanded portion of the hypophysial plate. This cannot be fully
shown in such a view as illustrated in fig. 2, owing to the perspective. The trabecula
finally bends outwards to fuse with the posterior extremity of the palatine bar, which
here consists entirely of soft cartilage also.
An interesting observation recorded by ALuis is that in a “12 mm.” ¢ Bdellostoma
the “pharyngeal basket is nowhere connected with the trabecula,” the bridges of soft
cartilage described above being absent. From the fact that these bridges are of soft
cartilage (PARKER, however, figures the anterior one as hard cartilage in Bdellostoma),
ALLIs concludes that they must represent later additions. On the other hand, the fact
* All the fenestrz are closed by fibrous membranes or tissue.
+ This measurement is obviously erroneous.
762 MR FRANK J. COLE
that the hard cartilage in the region of the bridges is either wholely or largely invaded
by soft cartilage suggests precisely the opposite view that the hard cartilage replaces
the soft. A careful examination of the sections of the 6°5 cm. and the 10 em. Hags
undoubtedly reveals the presence of the bridges exactly as in the adult, and as they
are also figured so by Neumayer, I cannot confirm ALLIs’s observation as far as Myxine
is concerned. However, in the absence of information as to the size of his embryo, this
is not conclusive.
Hypophysial Plate (figs. 1 and 2, h. ».).—This occupies the median hypophysial
fontanelle at the base of the skull, bounded by the palatine bars and their commissure,
the trabeculee, auditory capsules, and parachordals. Its function is to provide a basal
support for the hypophysial canal or naso-palatine duct. It consists of a central plate,
fused with processes from the trabeculee and the nasal capsule, which sends out a rod in
front and a wider process behind. The anterior half of the rod is sometimes formed of
hard cartilage (as shown in fig. 2), thus differmg from the remainder of the plate, which
is of soft cartilage. J. MULLER states that it is composed of hard cartilage in
Bdellostoma, but Parker found no hard cartilage in it either in Bdellostoma or in
Myxine. It commences under the nasal chamber, just behind the palatine commissure,
as a circular deposit of cartilage in the stout membrane connecting the palatine bars.
Where the hypophysial canal separates from the nasal chamber, and during its associa-
tion with the hypophysial plate, it forms a tri-radiate tube, T-shaped in transverse
section, and situated immediately below the floor of the membranous cranium, ventrally
partly fitting for a time into a median groove in the roof of the pharynx. The
hypophysial plate is situated at the base of the upright piece of the T. Itis at first
slightly saucer-shaped, but further, posteriorly, it becomes bent up sharply at the sides
of the hypophysial canal in the form of a V. At the external margin of its widest part
it fuses first with the backwardly coursing rod of soft cartilage from the posterior
transverse bar of the nasal capsule, and immediately afterwards with a forwardly
coursing similar rod from the trabecula, as elsewhere described. PARKER does not
describe either of these fusions in Myxime; but his fig. 3, pl. 10, seems to indicate
that he saw something of the trabecular fusion, and this one is described and figured in
dellostoma. Behind this region the hypophysial plate narrows down into the posterior
process, which is bent upwards from below on each side of the vertical limb of the
hypophysial canal in the shape of a U. This process expands at its posterior extremity,
and is fenestrated to a greater extent than is shown in fig. 2.
NEuMAYER’S figures of the preceding region agree with mine except that the
parachordals are figured and described as completely fusing dorsally, and a fusion is
described between the hypophysial plate and the subnasal bar. The latter statement
is dealt with elsewhere ; and, as regards the former, | am quite unable to confirm it.
The dorsal parachordal fissure is quite characteristic of Myaie.
Superior Lateral Cartilage (figs. 1 and 2, s. l. c.).—Consists of soft cartilage, and in
front fuses with the dorso-posterior border of the hyoid arch (hy.), there containing a
.*
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 763
few nests of hard cartilage. It soon fuses below with the dorsal extremity of the first
branchial arch, and then passes downwards and backwards over the roof and on to the
lateral wall of the pharynx under the constrictor muscle to subsequently fuse below with
the upper end of the second branchial arch. It is continued beyond the latter arch as
a small rod, rising slightly until it again reaches the roof of the pharynx, where it
terminates sometimes in a bifid extremity. This, however, may vary in the two sides of
_ the same animal, as shown in fig. 2.
Inferior Lateral Cartilage (figs. 1 and 2, 7. J. c.).—Also consists of soft cartilage, and
widens considerably in front to fuse with the ventro-posterior border of the hyoid arch,
the latter at this region being likewise formed of soft cartilage. The inferior lateral
courses almost straight backwards on the ventral wall of the pharynx, and between it
and the posterior segment of the basal plate, but slightly external to the latter. It
passes internal to the first branchial arch without however being in any way connected
with it, and by its dorsal border fuses behind with the ventral extremity of the upper
division of the second branchial arch. The inferior lateral cartilage may terminate in
this way, as shown in fig. 2, or, as perhaps is more generally the case, and as in
Bdellostoma, it may be extended beyond the second branchial arch as a tapering rod
coursing upwards on the /ateral surface of the pharynx, where it terminates after a
shorter course than the superior bar. Neumayer figures its absence behind the second
branchial arch, but its presence here is shown by P. Ftrprincer and Parker. I have
added it in fig. 1 (although it was not present in the specimen from which the drawing
was made) in order that both conditions may be represented.
“ Branchial” Arch 1 (figs. 1 and 2, br. a.').—This is of soft cartilage in Myaine but
of hard in Bdellostoma, according to J. Mttuer. It arises dorsally, as above described,
from the superior lateral cartilage, and courses in a half-ring round the lateral wall of the
pharynx, bending first backwards and then forwards over the inferior lateral cartilage.
It finally fuses with the lower division of the second branchial arch, when this is present
(fig. 1), and at once becomes gradually merged into the hard cartilage of the middle
seoment of the basal plate, as elsewhere described.
“ Branchial” Arch 2 (figs. 1 and 2, br. a.*).—Formed of soft cartilage. There is a
somewhat surprising variation in this arch, since the lower division is not always
present. It was, for example, undoubtedly absent in the specimen on which figs. 1 and
2 were based ; but I have found it in others. It was not found by Parksr in Myzine,
but is figured by P. FUrRBRincER and Neumayer, and it is present in all my series of
sections without exception.* | have therefore added it in fig. 1, which may in this respect
be compared with fig. 2. This lower division of the arch, after fusing in front with the
first branchial, passes backwards at the side of and external to the dorsal boundary of
the posterior segment of the basal plate, finally rising slightly above the latter to
terminate freely at about the level of the extremity of the superior lateral cartilage.
Ayers and Jackson describe in Bdellostoma a fusion of the posterior extremity of the
* In two museum preparations made by Fric of Prag, it was present in one and not in the other.
P My 8, p
764 MR FRANK J. COLE
lower division with the inferior lateral cartilage, which eliminates the break in the course
of the arch. As this fusion was not found by J. MULLER or PaRKER in Bdellostoma, and
has never been seen in Myaxzne, it must represent another and an important variation in
the structure of the arch. The wpper division of the second branchial arch is very
short; it fuses above and below with the superior and inferior lateral cartilages, as
above described, and in one series of sections despatched forwards in front a blunt
process similar to that figured and: described in Bdellostoma by AyERs and JACKSON.
As, however, this seems to be not of general occurrence, I have not introduced it into
the figures.
“ Hyoid” Arch (figs. 1 and 2, hy.).—The connections of this arch above and below
with the auditory capsule and superior and inferior lateral cartilages, have been already
described. Dorsally in front, it fuses also with the hard cartilage of the posterior
extremity of the superior process of the pterygo-quadrate, and similarly below
and in front with the inferior process of the pterygo-quadrate. The hyoid arch is short
but wide, and is bent round the lateral wall of the pharynx, lying just external to it.
It is composed of hard and soft cartilage, distributed as shown in figs. 1 and 2.
According to PARKER, it consists almost entirely of soft cartilage in Myaine and of
hard in Bdellostoma ; but I have succeeded in confirming the distribution of the two
kinds of cartilage shown in my figures in serial sections, and, further, PaRKER’s own
sections do not bear out his dissections. Posteriorly, the hyoid arch sends backwards a
broad, blunt process of soft cartilage, which projects into the fourth fenestra of the skull,
as in Bdellostoma. Anteriorly, a corresponding process, although a very slight one, is
despatched forwards into the third fenestra, which represents the much more extensive
process in Bdellostoma described by Parker and Ayers and Jackson, but not found
by J. Mtxuer. In one series of sections, the ventral margin of soft cartilage at the
region of the junction of the hyoid with the inferior process of the pterygo-quadrate
sent downwards and forwards a blind rod of cartilage ; but this seems to be a variation
of little importance, beyond that it is one of the numerous examples of the sporadic
appearance of soft cartilage in the connective tissues of Myxine generally. It is,
however, also figured by NEUMAYER. 3
The posterior boundary of the hyoid assists the superior and inferior lateral
cartilages, and the upper division of the second branchial arch, in forming the large
and somewhat irregular fourth fenestra of the skull (f*), whilst its anterior border
forms the posterior boundary of the third fenestra (f°).
‘« Pterygo-quadrate” (figs. 1 and 2, p. g.).—This is a tri-radiate structure formed
mostly of hard cartilage. It sends upwards and forwards a thick bar or anterior
process which forms the ventral or external boundary of the first fenestra (f''), and
fuses in front with the zone of soft cartilage (absent in dellostoma, according to
PaRKER) forming the posterior extremity of the palatine bar. The second one is the
superior process, which, with the anterior process, forms the subocular arch of AYERS
and Jackson. ‘The superior process passes backwards and slightly upwards to complete
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ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 765
the ventral or external boundary of the second fenestra, to constitute the dorsal
boundary of the third fenestra, and to fuse behind with the hyoid arch as above
described. Both the above processes consist entirely of hard cartilage. The third or
mferior process forms the ventral boundary of the third fenestra, and fuses behind
with the hyoid arch. It exhibits at about the middle of its course a conspicuous zone
of soft cartilage absent in Bdellostoma, according to Parkkr, and is in fact more or
less generally invaded by nests of soft cartilage. Its posterior upper inner surface
receives the rod of soft cartilage from the external lateral velar bar, as elsewhere
described. The pterygo-quadrate, lying nearer the surface, takes no part in the
skeletal support of the pharynx, except to a slight extent the inferior process.
“ Palatine” Bar (figs. 1 and 2, pl.).—Forms with the above the palato-pterygo-
quadrate of Ayers and Jackson, and commences behind by a wide stout base of soft
eartilage fused with the trabecula and anterior process of the pterygo-quadrate, as
above described. It then passes forwards and somewhat inwards, lying at the lateral
margin of the ventral wall of the cranium and nasal capsule, to expand in front and
to fuse, as the palatine commissure, with its fellow of the opposite side at the level
of the anterior border of the nasal capsule. The commissure is a wide thickish bar
of hard cartilage, and somewhat arched, with the convexity dorsal. Into the ventral
concavity fits the base of the median dorsal tooth. Parker figures an anterior
“ethmoid” tract of soft cartilage in the commissure, and I also find some evidence
of this in my sections. The cornual cartilage fuses irregularly with the external angle
of the commissure, and where this occurs there is an invasion of the hard cartilage by
nests of soft cartilage. Ayers and Jackson state that in Bdellostoma the cornual
cartilage is ‘‘attached” to the palatine, and I take it this does not mean fusion.
Immediately in front of the palatine commissure and the median dorsal tooth a
median pad, consisting of soft pseudo-cartilage, is seen, which passes forwards over the
roof of the pharynx for a short distance. It is invaded, especially in front, by several
nests of true soft cartilage. Anteriorly, it lies between the diverging palato-ethmoidalis
profundus muscles, with which it is very closely connected. Its true relations are
shown in vertical longitudinal sections, when it is seen to arise from the anterior
border of the base of the median dorsal tooth, pass forwards for a short distance, and
then curve backwards round the anterior margin of the palatine commissure to be
inserted into the posterior extremity of the subnasal bar. Only the former part
consists of pscudo-cartilage. I shall refer to it again in my next part on the muscles.
In the meantime I need only point out that it corresponds to the occurrence of soft
pseudo-cartilage in the tendons of other muscles, such as those of the “lingual”
apparatus, as described elsewhere.
Cornual Cartilage (figs. 1 and 2, c. c.).—Fuses behind, as above described, with the
palatine commissure, and consists of soft cartilage. It passes forwards and outwards in a
curve immediately internal to the M. tentacularis posterior, its anterior free extremity
coursing parallel and just external to the lateral labial cartilage. In the sections the
TRANS, ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 30). 113
766 MR FRANK J. COLE
dorsal surface, near the tip, gave off on both sides a short backwardly projecting hook,
which then curved upwards and inwards and finally downwards, to be connected by a
short stout ligament with the lateral labial cartilage just behind where the latter fuses
with the cartilage of the third tentacle. It certainly appeared to express a tendency
to, or to be a relic of, a cartilaginous connection between these two elements. The
cornual cartilage terminates in front opposite the fourth nasal ring.
F. Nasat Tuse anp CapsuLe. (Figs. 1, 5, and 6.)
The nasal aperture is a large opening situated terminally on the dorsal surface of
the head. ‘It is guarded laterally by two short, poimted tentacles on each side—the
nasal ‘‘ barbels”—and dorsally by a truncated lip. I am not able to follow W. K.
PaRKER in distinguishing “three nasal barbels on one side, and four on the other.” *
This external opening leads into a long dorsal tube (n. ¢b.), which in a 454 cm. Hag
measured 14mm. ‘The latter, in its turn, passes first into the olfactory chamber and
then into the hypophysial duct or naso-palatine canal. As in Bdellostoma, according
to J. MULuer and Ayers and Jackson, the nasal tube is widest in front, and gradually
tapers as it approaches the olfactory capsule (n. c.). ParKER, however, figures it as
being much narrower anteriorly. It is remarkable in the myxinoids on account of
its strong superficial resemblance to a trachea, and it is supported at intervals by
cartilaginous rings, which are, however, imperfect ventrally. In some sections of a 6°5
cm. Hag, lent me by Dr Brarp, the nasal rings so closely approximated in the
mid-ventral line as to be almost in contact, whilst in another series of a 25 cm. Hag
the posterior rings overlapped. The number and form of these rings are subject to
variation (cp. figs. 1 and 6). In the specimen and in the series above, there were
eleven in both cases. PARKER also describes and figures the same number, but, as he
failed to find the first one, his total should be twelve. Ayers and JAcKSON state that
there are normally nine in Bdellostoma, with occasional variations of cight and ten.
J. MGLLER gives ten for Bdellostoma, and ParKER distinguishes twelve. The latter
author figures all these arches in Myaine as independent ; but, as shown in figs. 1 and 6,
about the first and last three are usually connected up, the last being further fused at
intervals with the anterior transverse bar of the olfactory capsule. These connections
I have found both in dissections and in serial sections. As, however, stated by AyERs
and Jackson for Bdellostoma, “the nasal arches are found to vary to a considerable
extent in number, form, and size, both relative and absolute.” t
The first nasal ving (1) is situated at the anterior edge of the dorsal lip of the
external aperture. It is connected dorsally with the second ring by a backward median
process (fig. 5). These parts, as well as the dorsal portions of the other nasal rings, can
be seen in the living fish showing through the skin. In the neighbourhood of the
median process there projects, downwards and forwards into the cavity of the tube, a
* Op. cit., p. 386. t+ Op. cit., p. 199.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 767
dorso-median fold of its lining. This lies near the external nasal opening, and is
supported by a delicate strip of free cartilage (cp. fig. 1). It is probably not the
structure referred to by Parxer as the nasal valve, which is merely an adventitious
fold of the lining mucous membrane of no importance, and occurring capriciously at all
parts of the tube. It is, doubtless, a very small tentacle. Latero-ventrally, on each
side, the first four rings were all connected up by a longitudinal bar (fig. 1).* In some
serial sections prepared by the late Dr Poxtarp and lent me by the late Prof.
G. B. Howes, the third arch sent back and the fourth arch despatched forwards processes
which overlapped but did not fuse. Further, the fifth and the sixth arches sent
forwards prominent projections which did not, however, quite reach the arches in front.
As also described by J. MULLER and Ayers and Jackson for Bdellostoma, the lateral
connecting bar in front sends forwards a strip of cartilage (fig. 1), which the latter
authors found in one case to fuse with its fellow of the opposite side in the mid-ventral
line. These cartilages therefore express a tendency to form a complete ring round the
external nasal opening, but may represent a pair of vestigial tentacles. Arches five to
eight are quite independent; but the last three are connected ventro-laterally by a
longitudinal bar with each other, and the last with the nasal capsule (fig. 1). Dorsally
the tenth arch is Y-shaped, and also connected in the middle line with the eleventh
(fig. 5). The last or eleventh arch is fused with the anterior transverse bar (a. t. b.)
of the olfactory capsule at five places—by one median and two lateral pairs of rods
(figs. 1, 5, and 6). Asa result, four fenestrae are formed—a small dorsal and a large
lateral one on each side. This corresponds exactly with the condition in Bdellostoma
described by J. MULuER,{ and also practically with the figures of Ayers and Jackson.
In a series of sections of a 25 cm. Hag the following variations from the above
description may be noted (cp. fig. 6). Arches 7 and 8 were fused ventrally, but 9, on
the other hand, was independent, although underlapping 10 below. Ring 10 joined
not directly with 11 to complete the large anterior fenestra (but it ded on the other
side), but with the process connecting the latter ring with the anterior transverse bar
of the nasal capsule (a. ¢. b.). At this region an additional independent cartilage was
_ present on the left side only, and there was also an additional fenestra dorsally
separating rings 10 and 11. Anteriorly, this specimen agreed even in the smaller
details with the above description, and hence these posterior variations become the more
interesting. é
The olfactory capsule itself (n. c.), like the nasal rings, protects only the roof and
sides of its cavity. In front the latter is connected with the lumen of the nasal tube,
and below with the hypophysial canal. It is shut off posteriorly from the cavity of the
brain-case by the double wall of the cranium, as described by J. Mtiier. The capsule
consists essentially of a series of longitudinal rods fused in front and behind respectively
with an anterior (a. t. b.) and a posterior (p. t. b.) transverse bar. There are nine of these
* Tn one series of sections the fourth ring was not included on one side.
+ Op. cit., p. 109.
768 MR FRANK J. COLE
longitudinal rods, of which the two lateral are larger and more irregular in shape than
the rest, and are called by AyERs and Jackson the lateral plates (fig. 6, J. p.). The seven
dorsal ones are all very narrow and straight, the middle one occupying the mid-dorsal line.
The spaces between these rods are of regular shape except the two lateral, and they are
perceptibly wider than the rods themselves. There are seven olfactory lamime in
Myzxine, produced by a corresponding number of longitudinal invaginations from the roof
of the olfactory chamber. The lateral plates lie at the side of the bases of the
most lateral laminze, whilst the other seven bars are situated immediately above the
dorsal bases of the laminz. Thus the form of the capsule is clearly identified with
the conformation of the olfactory organ, and is essentially the same both in Myaxine and
Bdellostoma. |
Whilst examining a series of transverse sections I discovered a cartilaginous connection
between the posterior transverse bar of the olfactory capsule and the hypophysial plate,
which I afterwards found by careful dissection of the adult animal (figs. 1 and 2, h. p.’).
It was not seen by J. MULier, Parker, or Ayers and Jackson, but I| learned afterwards
that it was described for Myaine by Neumayer,* and it has lately been independently
mentioned by ALLIs in Bdellostoma.t It consists of a small cylindrical rod passing from
the ventral extremity of the posterior transverse bar downwards and backwards to fuse
with the hypophysial plate just where the latter fuses with the trabecula. There is
thus at this point a complete ring round the nasal organ and the hypophysial tube—
formed above by the olfactory capsule, at the sides by the connections now in question,
and below by the hypophysial plate.
The nasal rings consist of the white soft cartilage, but the olfactory capsule, with
the exception of the anterior transverse bar, is formed of the brown hard cartilage. The
anterior bar seems to represent a transition condition, whilst the larger lateral bars of
the capsule are the toughest of all.
NEUMAYER’S results on the nasal tube and capsule are sufficiently remarkable to call
for special notice. The material he used was that collected by O. Maas for his well-
known work on the renal organ of Myxine, but he does not state the size of the
specimen on which his wax model was based. It was, however, probably Maas’ 8°5 or
9°8 cm. Hag. The nasal tube is described and figured as a continuous cylinder with a
few irregular perforations, and no indications of its tracheal nature, except perhaps as
regards the first three rings. If this description is confirmed, then we must regard the
nasal tube of Myaine as primitively a more or less continuous structure which has
secondarily become differentiated into rings. Similarly, the anterior transverse bar of
the capsule would seem to belong rather to the tube, as indeed is otherwise probable,
since two of the nine longitudinal rods fail to reach it. NeruMaAYER also figures, but
does not describe, a fusion of the anterior transverse bar of the capsule with the palatine
bar and of the postero-ventral region of the tube with the subnasal cartilage (“ inter-
* Op. cit., p. 3 and fig, 4. Apparently also by PotLaRD (p. 396).
+ Anat. Anz, Xxiii., pp. 269-270,
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 769
trabeculare anterius”). With special reference to these unexpected results I worked
over very carefully Dr Brarp’s sections of a 6°5 Hag—a younger form than any at
NeuMAYER’S disposal. I must point out that this specimen had been somewhat
damaged before coming into Dr Brarp’s hands, that it was not, in fact, properly
preserved, and that the sections are very irregular. Nevertheless I think I can
positively state that, excepting to a certain extent the nasal tube, NeumMayer’s results
are either hopelessly inaccurate or that there must be some explanation of them that
does not occur to me. It is difficult to believe that a careful and laborious worker as
Dr NEuUMAYER is well known to be could be so far in error, and we must therefore await
a re-investigation of the embryonic skeleton of Myxine. As we should expect, and as
pointed out by BEarp* and Neumayer, the nasal skeleton is relatively very large in the
young forms. The reconstruction of the nasal skeleton given by Pottarpt is in exact
acreement with my fig. 1, based on dissections.
G. THe TenracuLar Apparatus. (Figs. 1 and 2.)
Omitting the problematical tentacles mentioned in connection with the nasal
skeleton, there are four tentacles on each side both in Myzine and Bdellostoma. These
are the nasal and oral barbels of W. K. Parker. Of them only one, the fourth, has an
independent skeleton, that of the other three being fused with portions of the internal
framework. I therefore describe under the above head the subnasal cartilage or bar
and the lateral labial cartilage, but this is done simply as a matter of convenience. The
whole of the apparatus consists of soft cartilage, except the central portion of the
subnasal bar and the free internal extremity of the cartilage of the fourth tentacle.
All the cartilages extend to the tips of the tentacles.
The cartilage of the first tentacle (1), morphologically the second, passes downwards
and backwards at the side of the nasal opening, crosses externally the base of the second
tentacle, and terminates blindly on the surface of the muscles at about the level of the
subnasal bar. A short distance before it terminates, it fuses by its posterior surface
with the lateral “labial” cartilage (l. 1. ¢.). The latter passes at first upwards and
backwards to give off a projection, the wternal process, into which the M. nasalis is
partly inserted. Ayers and Jackson state that this process in Bdellostoma is attached
to the nasal tube by a membranous ligament, but in Myxine it is only imdvrrectly con-
nected with the nasal tube and skeleton by means of the insertion of the M. nasalis.
Also in Bdellostoma, according to J. MOLLER and Ayers and Jaoxson, the anterior
extremity of the lateral labial is connected by ligament with the tip of the cornual
eartilage.{ Behind the internal process, the lateral labial bends downwards and back-
wards in a slight curve, and receives ventrally the cartilage of the third tentacle (38),
which fuses with it. The latter cartilage is a stout rod, thicker at its base than the
* Anat. Anz., vili., 1893, p. 59.
+ Zool. Jahrb., Abt. Morph., viii. ; Taf. xxv., fig. 11, 1895.
{ Cp. the description of the latter cartilage.
770 MR FRANK J. COLE
lateral labial itself, and shows in the sections as it approaches the labial some nests of
hard cartilage. The stout base passes downwards and forwards, and lies within the
contour of the body, forming more than half the length of the cartilage. The tentacle
itself in the living animal is either almost perpendicular, or it can be rotated forwards ;
hence the inclination of the external portion of the cartilage is subject to muscular
control, and consequently varies in preserved material. The cartilage of the third
tentacle is the longest ofall. After receiving it the lateral labial, connected by ligament
in Bdellostoma with the tip of the cornual cartilage, according to J. MULLER, passes at
first backwards, downwards, and inwards in a gentle curve, until it almost reaches the
median plane, and thus arrives at the level of the pad of soft pseudo-cartilage at the anterior
end of the basal plate. Here it makes a sudden downward and external sigmoid twist
over the outer surface of the above pad, to fuse with the external bar of the anterior
segment of the basal plate, as described elsewhere. Hence the lateral labials and basal
plate form a cartilaginous circle round the mouth that is only broken for a short distance
in the mid-dorsal line.
The cartilage of the second tentacle (2), morphologically the first, is connected with
the first by ligament in Bdellostoma, according to J. MULLER. On entering the body
it passes at first straight backwards but soon takes a sharp bend inwards and downwards,
underneath the nasal tube, to fuse with its fellow of the opposite side, and in that way
to form the median suwbnasal cartilage or bar (sn. b.) passing backwards in the middle
line underneath the nasal tube (fig. 2). In Bdellostoma the conditions are apparently
somewhat different, the cartilage passing gradually into a transverse bar placed at right
angles to the anterior extremity of the subnasal bar, and which AveErs and Jackson call
the transverse “labial” cartilage. J. MULLER figures the transverse labial in Bdellostoma
as suturally distinct from the subnasal bar, and in his description he says it is ‘‘ strongly
connected” with the latter bar. AYERS and Jackson confirm this, and state that the
‘transverse labial cartilage is attached to the anterior end of the subnasal cartilage.”
PaRKER also figures it as distinct from the subnasal. Nrumayer’s figure of Myaine
certainly allows a transverse labial to be delimited, and I find his figure to a certain
extent confirmed by the sections of the 6°5 cm. Hag, and also by the sections of a very
small My«ine kindly presented to me many years ago by Mr J. T. CunnineHam.*
According to NruMayeEr’s figure, and the figure and description of PoLLarp,* there is,
as I find also, no break between the skeleton of the tentacles and the subnasal bar, and
it is difficult to escape the conclusion that this must likewise apply to Bdellostoma, in
spite of the concensus of opinion above. The subnasal bar being thus formed by the
fusion of the cartilages of the second pair of tentacles, is composed at first of soft
cartilage. It soon flattens out so as to become narrow from side to side and deep from
above downwards (cp. figs. 1 and 2). It lies a short distance below the nasal tube,
* J have no actual record of the size of this specimen, but it would be about 10cm. I have already referred to it
as the 10 cm. Hag.
+ Anat. Anz., ix., p. 351; and Zool, Jahrb., Anat. Abt., viii.
EAP.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. Th
which it supports, and is soon gradually converted into typical hard cartilage.
Posteriorly it becomes first of all more rounded, and then opposite the ninth nasal ring
it consists again of soft cartilage, of which the remainder is formed. It now flattens out
from side to side and becomes narrow from above downwards, and its expanded posterior
free extremity lies underneath the junction of the nasal tube with the nasal capsule—
that is, between the latter and the palatine commissure, with which commissure it is
connected by stout ligaments. It may even project slightly behind the commissure, as
figured by PaRKER.
The cartilage of the fourth tentacle (4) is quite independent; but, according to
J. Mtuter in Bdellostoma, it is connected by ligament with the basal plate, and
according to AYERS and Jackson with the base of the third tentacle also. It consists
of a slightly curved and somewhat vertical rod of soft cartilage, situated entirely in
the curiously shaped tentacle, and rather tilted towards the middle line. To this
part is fused, at somewhere about the middle of its length, a stout rod which passes
within the contour of the body outwards, upwards, and backwards on the surface of the
muscles, where it terminates. The latter internal rod consists largely of hard cartilage.
According to all published accounts, the shape of this tentacular cartilage of Myaxine
is different from the corresponding one in Bdellostoma, where it forms an irregular
plate. I have, however, seen indications of a similar shape in some specimens of
Myzxine.
PARKER went seriously wrong on the tentacular skeleton of Myaine. He figures all
the tentacular cartilages as independent, and altogether missed the lateral labials. It is
difficult to understand how so wonderfully skilled a dissector as ParRKER could have
made these mistakes, especially as the cartilages are actually shown in his sections
(which, however, he entirely misinterprets), and as they are by no means difficult to
dissect. His description of Bdellustoma is much happier, although not quite correct,
and he is also inaccurate in figuring and describing the subnasal bar of Myxine as
consisting entirely of hard cartilage. NEUMAYER figures and describes a fusion between
the posterior end of the subnasal bar and the anterior end of the hypophysial plate, but
I find no traces whatever of this either in the 6°5 cm. or in the 10 cm. Hag. Apart
from this, his description of the tentacular apparatus, as far as it goes, agrees exactly with
mine. P. FURBRINGER inaccurately describes the lateral labial of Myxine as a connective
tissue connection, but his figure and description of the tentacular apparatus (the skeleton
not directly concerning him) is clearly inspired by J. MUxuer’s. Howes’ account of
Bdellostoma is also wrong on practically all points, as pointed out by Potuarp, whose
description of Myxine (op cit.) was the first to exhibit any degree of accuracy.
H. Tae Basa Puatr. (Fig. 10. Also figs. 1 and 2.)
?
The base of the cranial skeleton is formed by the stout ‘‘ beam” underneath the
gut, called by J. MUtier the “tongue bone” and referred to by Howes as the
772 MR FRANK J. COLE
‘‘dominant monster of the Hag.” It may be regarded as consisting of a linear series
of three pieces—the anterior, middle, and posterior segments of the basal plate (b. p.*~*),
Looked at from the side (fig. 1) the posterior segment is horizontal, whilst the two
anterior segments constitute a dorsally inclined plane.
The anterior segment is the most complex. It consists of three pieces—a median,
the internal bar of the anterior segment (7. b. p.’), and two lateral, the external bars of
the segment (e. b. p.’). The two latter, and to a slight extent the former, bear in front
pads of soft pseudo-cartilage (uncoloured and obliquely striated in the figures) which
contain nodules of true soft cartilage, especially near the dorsal border. The lateral
labial cartilage (/. /. c.), composed of soft cartilage, courses downwards in a sigmoid
twist over the dorso-external face of the large outer pad to merge gradually and
without any break into the hard cartilage of the external bar, which extends a short
distance in front of the internal bar. The anterior border of the latter, covered with
a layer of smooth soft pseudo-cartilage, forms a concave pulley surface for the tendon
of the M. copulo-glossus profundus (=the protractor of the dental plate—Avyers and
Jackson), which tendon is shown cut across in fig. 10 (c.g. p.). This tendon passes
forwards from its muscle wnder the internal bar, doubles round the pulley border on
to its dorsal surface, and then courses backwards over the bar, to be inserted into the
anterior arch of the dental plate. The dorsal surface of the imternal bar also bears a
thick pad of soft pseudo-cartilage anteriorly, against which the dental apparatus glides
backwards and forwards. Just in front of the posterior fenestra this pad thins down
and splits into a paired structure, which assists in forming the angular depression in
which the V-shaped dental skeleton works. The internal bar is composed entirely
of hard cartilage except where it passes into the middle segment behind, and consists
of one piece only; for whilst it thins down somewhat in the middle line, there is no
break or even a change in the character of the cartilage. Posteriorly, there is a large
elongated fenestra closed by fibrous tissue, and we find a zone of soft cartilage inter-
posed between the internal bar and the hard cartilage of the middle segment. But here,
again, itis a gradual transformation, and there is no break or suture between the two seg-
ments. On the other hand, the external baris quite independent of the internal bar and
of the middle segment, being separated from the latter by a pad of soft pseudo-cartilage
(uncoloured and obliquely striated in figs. 10 and 1). A transverse section through the
anterior segment of the basal plate shows that the three pieces form a deep crescentic
trough which lodges the dental apparatus. The internal bar is slightly curved, with the
concavity dorsal; and the external bar, separated from the internal by a fibrous packing,
projects upwards and outwards (cp. fig. 1).
The middle segment (b. p.”) is comprised of one piece of hard cartilage, but in the
middle line it is very thin and there consists of soft cartilage (fig. 10). There is, how-
ever, certainly no break or suture. In transverse section the cartilage is seen to be
very thick laterally and to form a shallow cup, with the concavity dorsal. In order to
provide a groove for the keel of the dental skeleton, and behind for the retractor tendon,
=.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 773
it is seen that the narrow trench in which these parts play is formed by the posterior
continuation of the paired rails described above, which are here much deeper vertically
and are raised up more perpendicularly from the basal plate. In this way a deep
narrow trough arises—the sides represented by the paired rails and the floor by the basal
plate. Posteriorly, as above mentioned, this trough transmits the tendon of the M.
longitudinalis lingue, which is thus kept in the middle line. Here the rails become
almost entirely fibrous, and finally pass over into the fibrous roof of the canal formed by
the posterior segment of the basal plate, as described and figured for Bdellostoma by
J. MtuiEr. The rails therefore represent the bifurcated fibrous roof of the posterior
seoment of the basal plate continued forwards over the dorsal surface of the middle
and anterior segments, as is evident from their relations and histology. The appearance
of soft pseudo-cartilage in them thus corresponds to the existence of the same tissue in
the tendons of some of the muscles. The postero-external angles of the middle segment
receive the ventral extremity of the first branchial arch, consisting of soft cartilage, which,
however, gradually mixes with the hard cartilage of the basal plate without a break.
When the detached lower division of the second branchial arch is present (fig. 1), it fuses
with the first arch shortly before the latter reaches the basal plate, as described for
Bdellostoma by AYERS and Jackson.
The posterior segment (b. p.’) is about half again as long as the other two segments
together, and is immovably attached to the middle segment. Even here, at the
junction-place of two skeletal tissues of different character, it is not possible to establish
a joint. The posterior border of the middle segment is ragged, and bears small out-
growths of soft cartilage. The matrix of the posterior segment is very closely connected
with this border, also contains nests of soft cartilage, and even in parts seems to be in
direct organic connection with the middle segment. The posterior segment is formed
of a thick sheet of hard pseudo-cartilage bent up longitudinally at the edges so as to
form in transverse section the figure of a U, and roofed over dorsally in front by fibrous
tissue, as above described, and behind by the anterior extremity of the M. copulo-copularis.
Its cavity transmits the tendon of the M. longitudinalis lmgue. Posteriorly, the segment
narrows down in the vertical plane; the sides of the U first of all diverge and then
disappear, and in this way leave only the solid keel, which tapers down to a point and
vanishes.
In Bdellostoma, according to J. Mt.umr, the anterior segment of the basal plate
consists of fowr pieces, the internal bar being divided in the middle line, and the two
halves connected by ligament. Further, it is separated by a movable joint from the
middle segment, the latter segment in its turn consisting of two pieces meeting at a
median suture. This description is confirmed by AyrERs and Jackson, except that
the inner bars of the anterior segment are stated to be fused in the middle line
anteriorly, where, further, they are divided by a transverse suture. Again, according to
Ayers’ and JacKson’s figure and apparently their description, the lateral labial cartilages
are not fused to the external bars of the anterior segment but are only “attached ”
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 30). 114
774 MR FRANK J. COLE
to them.* Finally, there are indications of a division of the middle segment into four
pieces. PARKER also describes the two anterior segments of bdellostoma as consisting
of six pieces “all connected together by tracts of soft cartilage,’ but he also quite
erroneously makes the same statement with regard to Myaime, although it is contra-
dicted by his own sections, which he misinterprets. PARKER entirely missed the
lateral labials in Myaine, and failed to observe their correct relation to the anterior
seoment of the basal plate in Bdellostoma. P. FUrRBRINGER also describes six pieces
in the first two segments of Myxime; but his paper is not directly concerned with the
skeleton, and his mind was evidently prejudiced by J. MULuER’s work. NerumMayer’s
description and text-figure of Myaine, as far as they go, agree exactly with mine.
In this connection I felt it important to examine very carefully the condition of the
basal plate in Dr Brarp’s sections of a 6°5 cm. Hag, and found that it agreed absolutely
with the condition described above for the adult—z.c. the anterior segment consisted
of three pieces and the middle segment of one, nor was there any difference in the
connections between these parts and in the distribution of the hard and soft cartilage.
We can therefore only conclude either that the basal plate of MWyaxine differs in some
important respects from that of Bdellostoma, or that the latter has still to be accurately
described. I am convinced from my dissections, and from the examination of three
series of sections (apart from those of Dr BEarp’s small Myaine), that the basal plate
of Myzxine is here correctly described for the first time.
I. SKELETON oF THE DentTaL Apparatus. (Figs. 7, 8, 9, and 1.)
This portion of the skeleton has been picturesquely described by Parker as a
“curious apron with slits in it and short strings projecting from it.” The teeth are
laid on a somewhat complex skeletal framework, bent up from the middle line at an
angle so as to form a V-shaped figure in transverse section. Its natural position—or,
rather, one of them—in longitudinal space is seen in fig. 1 (a. d. p., p. d. p.). The whole
apparatus, however, slides backwards and forwards in the trough formed by the basal
plate, as already described, being drawn forwards by a protractor muscle, the copulo-
glossus profundus (c. g. p.), and withdrawn by a retractor muscle, the longitudinalis
linguee (/. /.), the tendons of which muscles only are shown in the figures. The teeth as
a body thus move backwards and forwards, so that the Hag rasps its way into the body
of its victim ; and not only this, but the whole apparatus with the teeth can be actually
protruded entirely out of the mouth. This was first observed by Gunner, who
described and figured the everted teeth in 1766. His statements were stoutly con-
troverted by J. Mtiuer, who, on purely anatomical grounds, asserted that Gunwnur’s
“entirely inaccurate.” I can, however, with other observers, fully confirm
this old writer, for I have repeatedly observed the living Hag protrude its teeth in the
way described, and have succeeded in preserving several with the teeth out. By this
work was
* This agrees with J. MULumr’s figure and description. Nevertheless I doubt it.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 779
very curious device the rasping action is, of course, made immensely effective, and a few
Hags will completely clear out a full-sized cod in an hour and a half. I shall give a
full description of the process in my second part on the muscles, but in the meantime
one may point the moral that to make physiological deductions from anatomical data is
attended with some risk.
The dental skeleton is composed entirely of soft cartilage, except the greater portion
of the posterior arch, which consists of hard cartilage. It commences in front as an
irregular deposit of soft cartilage in the tendon of the M. copulo-glossus profundus,* and
is at first almost flat, but slightly arched (with the concavity dorsal), taking no part in
supporting the first tooth of the outer row, which is raised up almost at right angles to
it. The cartilage soon widens out, and despatches a process forwards on each side to
support the anterior teeth of the outer row (0. 7, t.). This is the anterior arch of the
dental plate (a. d. p.), and it at once assumes the characteristic shape of an obtuse V,
the teeth resting on the inner surfaces of the two arms. The tendon of the M. copulo-
glossus profundus (c. g. p.) widens out very considerably behind, to be inserted into
practically the whole of the anterior border of the anterior arch of the dental plate
(fig. 7), the posterior wide portion of the tendon consisting of a tissue very similar to
soft pseudo-cartilage. The anterior “ fine comb of horny spikes” described and figured
by Parker in Mysxine, but not in bdellostoma, is nothing more than this tendon cut
across (cp. figs. 7 and 10). The arch never extends laterally beyond the bases of the outer
row of teeth, and hence its lateral surface has a curve similar to that of the fused bases
of this row of teeth. Both rows of teeth with their papillae may be said to rather rest
on the arch, since they are only loosely attached to it. The dental skeleton is, in fact,
always more or less completely separated from the teeth, as emphasised by J. MU.uER,
by a series of spaces sometimes containing blood. I have not yet investigated the
vascular system of the head, and therefore cannot say whether these spaces are blood
sinuses or not. The anterior arch bears two fenestre, and as I find these both in
dissection and in serial sections, they must be of constant occurrence. The larger one
is elongated from before backwards so as to almost divide the anterior arch into two,
and is covered over by fibrous tissue, while the smaller one transmits the nervus
dentalis of J. Mttuer. The postero-external angle of the arch gives off two rods—
the posterior external (a. d. p.’) and the posterior imternal (a. d. p.") processes of the
anterior arch. The former is plate-like and much the larger of the two, crossing over
the latter dorsally to it, and courses inwards and upwards in the fold of mucous
membrane situated over and almost obscuring the posterior teeth of the mner row
(z. r. t.), to terminate blindly in this fold immediately dorsal to the last tooth of the
inner row. ‘The internal process is a small rod which passes almost straight backwards
below the external border of the inner row of teeth, and finally turns inwards to fuse
with the posterior arch of the dental plate. The product of this fusion then continues
backwards as a stout rod (turning slightly upwards) along the ventro-lateral border of
* This is the ‘median dorsal bar’ of AyERs and Jackson. It is, of course, ventral.
776 MR FRANK J. COLE
the pharynx, where it soon terminates. As shown in fig. 8, the external boundary of
the fusion rod may be somewhat irregular and perforated.
The posterior arch of the dental plate (p. d. p.) is not concerned with the support.
of the teeth, but serves for the attachment of the tendon of the M. longitudinalis
linguee, which fans out as it approaches the arch so as to be inserted into practically the
whole of its posterior border. The actual appearance of the posterior arch is not shown
in any of the figures, for it must be remembered that all the figures represent the dental
skeleton flattened out. The floor of the mouth sends down a longitudinal gully-like
evagination or keel, into which, doubtless, the food drops after being liberated from the
teeth in order to be passed backwards into the cesophagus. This evagination is very
compressed from side to side, in the empty mouth, and lies entirely below the level of
the teeth. In front, its base rests on the anterior arch, which, however, does not support
its sides (except for a very abbreviated space posteriorly), since the arch, which is not
bent, has to make too wide a deflection in order to take up a position external to the
bases of the teeth. Hence the obtuse V. The posterior arch, having no connection
with the teeth, is not deflected away from the diverticulum, but is sharply bent up on
each side of it from the middle line so as to form in transverse section an acute V-shaped
figure. The dorsal extremities of the arms of the V are continued backwards and
outwards as spherical rods just internal to the inner row of teeth, to fuse with the
internal process of the anterior arch as above described. In the sections, the posterior
arch was cleft by a deep fissure behind, but there were no further indications of a
separation of the arch in the middle line into two halves. The arch consists mostly of
hard cartilage, but there is a median block of soft cartilage, and more soft cartilage
where it fuses with the anterior arch. The tendon of the M. longitudinalis lingue, as
it fans out to be inserted into the arch, exhibits the same soft pseudo-cartilage-like
appearance in its median portion as in the tendon of the protractor muscle.
The large space between the anterior and posterior arches is entirely filled in by
ligamentous tissue containing the same soft pseudo-cartilage-like tissue. It is, in fact,
the direct continuation of the tendon of the M. longitudinalis lingue, as described by
J. MtLurR ; and its presence is obviously necessary, or the pull of the tendon would
break the slender cartilaginous connections between the two arches.
I am not describing the teeth here, since, as J. MULuer first pointed out, they do
not belong to the skeleton, but only rest on the skeletal parts of the “tongue.” They
will be described with the skin in my third part. In the meantime I may point out
that according to my dissections, and also a reconstruction of the teeth from serial
sections, there are nine apparent teeth in the outer row (0. 7. ¢.) and ten* in the inner
row (7. 7. t.). Cp. fig. 9. In both rows, however, the first two teeth are fused at the
base, and for this and other more important reasons each pair corresponds morpho-
logically to one tooth only. ence the above numbers should be reduced by one in
each row. The last tooth in each row is liable in some specimens to be overlooked,
* PARKER gives for Myaine 7 and 9, and J. Mtxumr 8 and 8-9, which illustrates my point below.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 06
owing to a covering fold of mucous membrane, and this explains some of the so-called
variations in the number of teeth referred to by systematists. As pointed out by AYERs
and JACKSON, it is quite a simple matter to obtain excellent microtome sections of the
teeth, provided they are embedded in celloidin. And even with paraffin embedding I
have serial sectioned three heads of moderately sized Hags (about 25 cm.) without in
any way damaging the teeth or losing a section.
J. MULEr’s description of the dental skeleton of Bdellostoma calls for no comment,
except that he does not figure or mention the small perforation transmitting the
dental nerve, but refers to it in his later work on the nerves. It is not described by
Ayers and Jackson or by Parker in bdellostoma, although the latter author figures it
in Myxine. Parker also describes and figures in Myaine a long median rod of soft
cartilage projecting backwards from the posterior arch, but not found in Bdellostoma, and
in the latter type he describes the anterior arch as formed largely of hard cartilage.
Neumayer figures and describes the two arches in Myxine as unfused and only joined
up by connective tissue. The slender cartilaginous connections of the adult may well
be secondary.
J. SKELETON OF THE VELUM OR PHARYNGEAL VALVE.
(Fig. 16. Also figs. 2 and 1.)
The skeleton of the velum, of which J. MULLER says nothing similar is known in the
animal kingdom, commences, as the external lateral velar bar (e. 1. b.), by a club-shaped
ventrally scooped out head (fig. 16) of hard cartilage at the posterior end of the third
fenestra of the skull. This is connected near its extremity by a short bridge of soft
cartilage (e. /. b.’) arising from the inner or ventral edge of the bar, which fuses near the
ventral border of the fenestra with the junction of the inferior process of the pterygo-
quadrate with the hyoid arch. This bridge is not present in Bdellostoma, according
to Ayers and Jackson, but the head of the external bar is connected by ligament only
with the pharyngeal wall. J. Mi.uer’s description of Sdellostoma more nearly
approaches the Myxine condition, there being precisely the same connection, but
formed, however, partly by a cartilaginous articular tubercle and partly by ligament. In
Myzxine, Parker says that the bar is ‘‘ joined to the general thickness of cartilage in the
hind part of the oval fenestra,” but does not state the nature of the junction ; whilst in
dellostoma he says that it is “confluent with the hyomandibular.” His figures give
no assistance on this point.
At first the external bar lies above and external to the pharynx and anterior to the
base of the velum, but it soon assumes a position internal to an anteriorly directed
blind diverticulum of the gut which surrounds it on all sides except internally. This
diverticulum then fuses below the bar with the naso-palatine duct or hypophysial
canal, and above the bar it approximates very closely to the same canal but does not
fuse with it. Asa result the bar is surrounded on all sides, except for a very narrow
778 MR FRANK J. COLE
breach, by a double mucous enclosure. At about section 700 in the chart (fig. 16)
the hard cartilage becomes gradually replaced by soft cartilage, of which the whole
of the remainder of the velar skeleton is formed. Subsequently the fused diverticulum
and hypophysial canal join up with the wall of the pharynx in such a way that
the ventral wall of the canal portion and the inner wall of the diverticular portion
first fuse with the dorso-lateral wall of the pharynx, and then the product of this
fusion disappears. In this way the connection between the cavities of the three
structures is established. It follows, therefore, that the velum is a double structure,
each half supported by the external lateral velar bar and each formed as an evagination
of the dorso-lateral wall of the pharynx. These two halves are connected by a dorsal
median double partition, called by J. MULLER the “ suspensory ligament” of the velum ;
and a transverse section of this region would suggest (of course, wrongly) that the
velum had been formed by a median dorsal invagination of the roof of the pharynx,
and that this invagination had then sent out on each side into the cavity of the pharynx
a lateral extension.
The external bar now gives off the internal lateral velar bar (7. 1. b.), which courses
laterally in the velum internal and ventral to the external bar. Parker figures and
describes the internal bar as independent of the external in Myaxvine ; and although this
condition is sometimes suggested, as on the right side of fig. 2, I have always found
it fused with the external bar, and as such Parker figures and describes it in Bdellostoma.
The two internal bars subsequently become connected by a transverse bridge, the
anterior transverse velar bar (a. t. v. b.), which traverses the now enlarged isthmus
connecting the lateral wings of the velum. From this transverse bar three processes
arise, as follows: (1) a pair of narrow rods which pass forwards and gradually ascend
dorsally im the median partition until they reach the roof of the pharynx, where they
form a portion of the swprapharyngeal skeleton (sp. sk.’, fig. 16) suspending the velum
from the dorsal pharyngeal wall. Here each rod gives off externally a long blind
process, which passes outwards and backwards over the roof of the pharynx, the main
stem being then continued almost straight forwards, but slightly outwards, below the
notochord and over the pharynx; (2) a narrow rod which arises from the dorso-
posterior surface of the bridge, and passes forwards and upwards in the median
partition until it reaches the roof of the pharynx, where it constitutes the remainder
of the suprapharyngeal skeleton (sp. sk.”). It at once bends sharply backwards on
itself, and extends posteriorly as a wide plate in the middle line under the chorda
and over the pharynx. Behind the suprapharyngeal skeleton the position of the
longitudinal bars is reversed, the external bar having now crossed over above the
internal so as to occupy the more median position. In Bdellostoma, according to the
figures of J. MUnier, Parker, and AvERS and Jackson, there is no such crossing; but
I suspect the drawings of these authors must be diagrammatic in this respect, or the
velum must be widely different in Bdellostoma. The two internal bars are finally
connected up a second time by the posterior transverse velar bar (p. t. v. b.), which
ae
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 709
lies near the ventral surface of the now much folded velum, and which has a very
ragged or “mossy” posterior border. Behind this border there may be several detached
nodules of cartilage. The posterior portions of the external bars are placed asymmetrically
somewhat near the middle line, under the dorsal surface of the velum, and continue
so for the remainder of their course. The internal bars are prolonged beyond the
posterior transverse bar, and curve first outwards and then upwards and inwards
under the surface of the velum, until they reach the dorsal surface, where they
terminate over the extremity of the external bars.
The skeleton of the velum is subject to some variation, especially as regards the
suprapharyngeal skeleton and the irregular processes from the posterior border of the
posterior transverse bar. In one specimen there were three distinct rods arising from
the latter bar—a median shorter one and two longer symmetrical ones. In this connec-
tion, compare figs. 2 and 16. In Bdellostoma, according to J. MULuER, Parker, and
AvERS and Jackson, there is only one process from this bar—a median one bifid behind.
Myxme agrees with Ayrrs’ and Jacxson’s account of Bdellostoma except in one
striking respect. The suprapharyngeal plate or cartilage of these authors is clearly the
expanded posterior plate of the rod sp. sk.”, but the anterior rods sp. sk.’ do not end
blindly but are fused to the antero-external angles of the above plate. Without
wishing to cast doubt on this description, which may be based on a variation or on a
different species, it must be mentioned that the descriptions of the suprapharyngeal
skeleton of Bdellostoma given by J. MiLumr and W. K. ParKer agree essentially with
mine of Myxine—except that Parxer missed the plate sp. sk.” in Myaine, and describes
it in Bdellostoma as a thin rod bifid behind.
K. SKELETON OF THE CLUB-SHAPED MUSCLE.
This consists of two bars, placed one above the other, at the posterior extremity of
the muscular complex known as the club-shaped muscle. I describe them now as found
in a 35 cm. Hag.
Inferior Chondroidal Bar.—This is composed of perfectly typical hard cartilage
throughout, with the matrix very strong superficially in older specimens. The posterior
portion of its length (8 mm.) comes to the surface of the M. perpendicularis (P.
FURBRINGER) at the mid-ventral line. This portion lies behind the posterior extremity of
the M. copulo-copularis (P. F.; M. constrictor musculi mandibuli, AvYERs and Jackson),
and gives origin to the fibres of the perpendicularis. In front of this region the bar
disappears into the copulo-copularis for about 3 mm., the posterior fibres of the latter
muscle being inserted into it. It was a slightly asymmetrical laterally compressed rod
pointed behind and blunt in front, 11 mm. long and 1 mm. deep. It has no connection
with the fibres of the M. longitudinalis lineuz (P. F.; M. retractor mandibuli, A. and J.).
Superior Chondroidal Bar.—Consists of hard pseudo-cartilage exactly as in the
posterior segment of the basal plate, but may contain here and there small nodules of
780 MR FRANK J. COLE
true (soft) cartilage. The bar comes to the surface of the M. longitudinalis lingue in
the mid-dorsal line, and extends in front between the posteriorly diverging halves of the
M. copulo-copularis, with which, however, it is not connected. The whole edge of the
bar and the lateral portions of its ventral surface provide an origin for some of the
dorsal fibres of the longitudinalis linguee, whereas the median portion of the ventral
surface gives attachment to the M. perpendicularis. Behind the latter muscle the bar
sends downwards and backwards in the mid-longitudinal vertical plane a thin tough
sheet, the two sides of which give origin to a considerable bulk of the fibres of the
longitudinalis lingue, and which separates the two halves of this muscle in the middle
line posteriorly. In front of this they are separated by the perpendicularis. This
tough sheet in the specimen dissected consisted of hard pseudo-cartilage like the
remainder of the bar, but in a series of sections of a 25 cm. Hag it was composed of
connective tissue. It thus seems to chondrify as the animal grows. The superior
chondroidal bar is a broad dorso-ventrally compressed plate rounded behind and pointed
in front, 11 mm. long and 5 mm. at its widest part.
In Bdellostoma, according to AyERS and Jackson, there is a difference of some
importance. oth bars consist of the hard pseudo-cartilage, similar to that of the
posterior segment of the basal plate, and, to quote AYERS and Jackson, “are not,
therefore, to be regarded as skeletal derivatives of the visceral or branchial arches, but
simply as chondroidal modifications (7.e. condensations of connective tissue) in the
muscular fascia” (op. cit., p. 212). Now we have seen that the inferior chondroidal bar
of Myxine is composed entirely of typical hard cartilage, and further, that the superior
bar may contain nodules of true soft cartilage, as in the so-called branchial arches. We
must therefore conclude either that these bars in Myxie and Bdellostoma are not
homologous, which is surely incredible ; or that the histology of the skeleton, as we have
the best reason for supposing, is but an equivocal morphological guide. There are,
however, strong grounds for believing that Ayers’ and Jackson's description of the
inferior bar is inaccurate ; for J. MUuier’s description of the two bars in Bdellostoma
agrees exactly with mine in Myaine, and W. K. Parxsr, who seems to have missed the
superior bar altogether, describes the inferior bar both of Myaine and Bdellostoma as —
formed of ‘hard cartilage” and colours it green in his figures.
L. THe Brancwiat SKELeTon. (Figs. 11-15.)
This was first described for Myxine by Burne,* having previously been missed by
J. Muxyer (who first found it in Sdellostoma, but whose language is ambiguous as
regards Myxie) and W. K. Parker. SCHREINER? notes its presence in Myaine; and
it 1s, in fact, quite easily seen by any one accustomed to careful dissection. On the other
hand, Burne failed to find the so-called “ gill bars” of AyERs and Jackson in Bdellostoma,
and I am able to supplement his description of Myavine in several important respects.
* P. Z.S., 1892, p. 706. + Bergens Museum Aarbog, 1898, No. 1, p. 6.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 781
The branchial skeleton is situated entirely posteriorly in relation to the fused gill
ducts, and on the left side to the ductus cesophago-cutaneus also. To take the latter
side first (fig. 11), we find in dissections that about half the skeletal apparatus in its fully
developed form is connected with the fused gill ducts, and the other half with the ductus
cesophago-cutaneus and the cesophagus itself. The latter portion lies on the external
lateral wall of the cesophagus and the ductus, and passes generally downwards and
backwards. Above, it has two processes—a dorsal posterior one (x’), which passes under
the constrictor muscle on to the roof of the cesophagus ; and a ventral anterior one (x),
which passes straight on to the ventral surface of the cesophagus. Below, it has one
process (a*)—a posterior one which passes backwards towards the caudal wall of the
ductus—and a vertical rod (x*), which connects it with the second portion of the apparatus.
The latter commences with a horizontal rod (y’), which passes forwards in a curve over
the branchial cloaca, bears a blunt process in front (y’), and then suddenly dips down,
bends round under the ventral border of the first gill duct, to terminate in a lanceolate
plate (y*), which turns upwards and forwards and lies on the inner surface of the
first two efferent gill ducts. The plate in the specimen figured was pierced by two
fenestree.
We may now turn to fig. 13, which represents this apparatus as reconstructed from
serial sections, and we note at once that it consists of two perfectly distinct parts. The
dorsal one commences ventrally on the anterior external wall of the ductus, and below,
it sends inwards a hook-shaped process underneath the ductus (x*), At about section
3070 (cp. the chart) the process x has reached the cesophagus, on the outer wall
of which it lies for the rest of its course. The process x* passes backwards and down-
wards over the external surface of the ductus, and terminates a short distance beyond it.
The ventral part begins anteriorly by a perforated plate (y’), which lies immediately
internal, and is related, to the first four efferent gill ducts (including the fifth posteriorly),
instead of the first two, as in fig. 11. The knob y’ is represented in the sections by a
long blind process extending forwards for some distance external to the first four efferent
gill ducts. The bar y’ bends round under the ventral wall of the branchial cloaca to
fuse with y*; whilst above, it passes backwards external to the branchial cloaca, exhibit-
ing a longitudinal fenestra, and behind ends blindly before the branchial cloaca fuses
with the ductus.
A comparison of these two figures renders it abundantly clear that the branchial
skeleton of the left side is a complex of at least two parts (see below), the point of
junction in fig. 11 being where x* meets y’. In fig. 13, therefore, the greater portion of
x* has been lost, in this way separating the two sections—one of which clearly belongs
to the efferent gill ducts, and the other to the ductus cesophago-cutaneus. This view of
the branchial skeleton is borne out by its wide range of variation, and I have dissected
two specimens in which each half of the apparatus was respectively missing. One of
these variations is represented in fig. 12, which obviously represents the ductus portion
of the skeleton, and corresponds exactly with the dorsal portion of fig. 13, except that
TRANS. ROY. SOC, EDIN., VOL. XLI. PART III, (NO. 30). 115
782 MR FRANK J. COLE
in the latter the extension x* is wanting. Burne and AyrErs and Jackson also mention
that it varies in Bdellostoma.
On the right side (fig. 14) the branchial skeleton also varies considerably, but I
figure and now describe its most highly differentiated condition as I have found it. The
apparatus is at once simpler and more complex on this side—simpler in so far as the
portion related to the ductus cesophago-cutaneus is necessarily wanting, as there is no
ductus on this side; and more complex in as much as a complete ring is formed round ~
the branchial cloaca. That this ring is a secondary formation is indicated by the fact
that in one specimen dissected it was incomplete; but there were present an anterior
and a posterior process from the perforated plate which did not quite meet external to
the branchial cloaca to form a perfect ring (cp. below and fig. 15). The posterior
process of fig. 14, which passes upwards separate from and posterior to the last efferent
gill duct, represents y* of fig. 11, whilst the bar lying external to the branchial
cloaca is clearly y” of figs. 11 and 13. The fenestrated plate y® on the inner surface
of the first two efferent gill ducts will naturally correspond with the same structure on
the other side, but instead of having two large perforations it had four small ones.
If we now turn to the reconstruction from the serial sections (fig. 15), we observe
that the branchial skeleton here consists of two separate pieces—one external and the
other internal to the branchial cloaca, as well as two small detached cartilages (z*, 2’).
This condition must not be confused with the imperfect ring just described, where two
processes from the perforated plate embraced the branchial cloaca externally. These
two processes are doubtless similar to the two in fig. 15 seen underneath y”, and which
seem to represent an attempt to complete the circle--not by extending round on to the
external surface of the branchial cloaca, as above described, but by fusing with y*. It
therefore seems as if the circle may be formed in more ways than one. In fig. 15, y”
and y* are related rather to the branchial cloaca than to individual gill ducts,* except
that the last efferent gill duct passes between y* and the posterior extension of y’.
The two latter processes serve to support the ventrally directed portion of the branchial
cloaca just above its external opening. The separate cartilage z* curls round under the
ventral edge of the branchial cloaca as if to fuse with y”, but it does not do so. It is
evidently a detached portion of the backward blunt process given off from the perforated
plate in front. The posterior downward process from the same plate is separated from
y* by the ventral extension of the branchial cloaca. The detached cartilage 2” is
situated behind and above the external branchial opening, and, perhaps, represents the
extremity of the line of chondral deposit forming y’.
A comparison of figs. 13 and 15 shows at once that the corresponding parts of the —
two sides are essentially similar, and further, that the efferent gill duct portion of the
branchial skeleton may itself be a complex formed of at least two pieces; and hence on
* It is, perhaps, rather a refinement of description to associate any part of the branchial skeleton with individual
gill ducts, since, apart from the ductus cesophago-cutaneus portion, its function on both sides and in all cases is to
strengthen the wall of the branchial cloaca, and it is possible that all the gill ducts have contributed to it.
-a
~~
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 783
the left side there are perhaps no less than three parts in the apparatus. The only
important difference between the two sides in the reconstructed figures is that the
connection between y* and y* is wanting on the right side; but we have seen that the
ring condition is subject to variation. The two posterior rod-like extensions of the
perforated plate on the left side are represented by only one on the right—but this is
quite a minor point ; whilst we have already seen that the condition illustrated in fig. 14
may be easily deduced from that shown in fig. 15.
It now becomes a matter of interest to enquire how this skeleton may have been
built up. AyeERs and Jackson suggest that on the left side it is a complex of the
skeleton of the /ast efferent gill duct, together with that of the ductus cesophago-cutaneus.
This may, indeed, be true for Bdellostoma ; but in Myxine it would seem as if all the gill
ducts had a share in it, and this may explain why the apparatus is the more complex in
Myxine. In any case, we may question whether the perforated plates of Myaine are
represented in Bdellostoma at all, and, as Myaine is obviously the more specialised form
as regards its gills, it would follow that this portion of the branchial skeleton is
a neomorph of no special significance as regards the gill cartilages discovered in
Bdellostoma by AyvERS and Jackson. It is, however, conceivable that, by a concentra-
tion of the latter cartilages due to the confluence of the gill ducts, the branchial skeleton
of Myxine may owe its existence. The bearing which these conclusions have on the
branchial skeleton of cyclostomes generally is not without interest, for it would seem
that every cyclostome must be considered on its merits; and we cannot, for example,
say that Myxvne is intermediate between the lamprey and Bdellostoma.
The cartilage of the branchial skeleton is histologically the feeblest of the true
cartilages, even if it can be called such, in the whole body, being distinctly weaker than
that of the tentacles and somewhat weaker than that of the caudal fin. The cartilage cells
are relatively large, and are embedded in a rather delicate network which seems in places
to be continuous and in others to consist of capsules around the cells, each of them
independent. ‘There is only a slight deposit of cement—provided the above network
does not, as I think, represent that substance. In this connection, compare the cartilage
of the caudal fin. The branchial cartilage is, in fact, one of the numerous transition
connective tissues of Myxine, and this is indicated by its staining reactions, since it
colours neither a distinct blue nor red, but an indefinite colour suggesting both these dyes.
It may, however, be regarded as an extreme variety of the soft cartilage.
M. SxeLeton or THE CaupaL Fin. (Fig. 17.)
Of the so-called “fins” of Myaine the adipose dorsal fin has no skeletal support, or,
at the best, but a very few short detached rods extending only a very short distance
beyond the contour of the back muscles (“‘fin” 1). This passes without a break into
the caudal fin (‘‘fin” 2), which possesses an elaborate skeletal framework and which passes
round the extremity of the tail and then forwards as far as the cloaca. In living
784 MR FRANK J. COLE
material the fin rays and the pulsating caudal heart are plainly visible. In front of
the cloaca there is an adipose median pre-anal fin, with no skeleton (‘‘ fin” 8).
It is very surprising that although J. Mtuier dissected the tail of Bdellostoma, he
should have failed to recognise its skeletal features. In a brief reference * he describes
the median cartilages as fibrous vertical sheets—that is, merely local thickenings of the
fibrous septum separating the two halves of the body musculature. ScHNEIDER, in 1879,
for the first time briefly describes the caudal skeleton of Myxine and Bdellostoma ; and
CLELAND,t unaware of SCHNEIDER'S work, subsequently published two descriptions of
Myxine. These are, however, very inaccurate. The first detailed account of the tail of
a myxinoid was published by G. Rerzius,t whose work I can confirm except in some
minor points.
Myxime possesses, as far as external features go, a diphycercal caudal fin.
When, however, a dissection of the tail is made it is seen that the notochord (nt.) near
its extremity takes a slight downward turn, and that its tip is buried in a median vertical
sheet of cartilage (m. d. b., m. v. b.) which in front splits up dorso-ventrally so as to
extend forwards under the notochord, over the neural tube, and also slightly between
these two structures. This cartilage is unevenly distributed above and below the
notochord, passing further forwards above and being deeper below. To it are fused,
above and below, the posterior fin rays (f. r.), which are, of course, not comparable to the
true fin rays of the higher fishes, the whole apparatus being characteristic of the
myxinoids. J. MU Lier and Ayers and Jackson describe an imperfect segmentation of
the fin rays of Bdellostoma as in the bony fishes, but I have seen no traces of this in
Myzxine. Further, there is no indication of a segmental arrangement of the fin rays,
except anteriorly. The cartilage partly encloses the bulbous extremity of the neural
canal (containing the enlarged termination of the spinal cord), since the latter extends
further backwards than the notochord. It may be conveniently divided into the
following two portions :—
Median Dorsal Bar (m. d. b.).—This is narrower than the median ventral bar, but
extends further forwards. The posterior portion of it is attached in the middle line by
an expanded base to the roof of the neural tube ; but the anterior half is lifted up above
the neural tube, and is there merely a thin bridge of cartilage connecting up the bases
of the fin rays. There were forty eight fin rays connected with this cartilage in the
specimen figured. Rerzrus gives about thirty for Myaime, and Ayers and JACKSON
twenty-five to forty for Bdellostoma.
In front of the median dorsal bar there are about forty-five free fin rays not con-
nected with any longitudinal cartilage, but inserted by their bases into the septum
between the two halves of the body musculature and connected by fibrous tissue. In
Bdellostoma, according to AyERS and Jackson, the anterior dorsal fin rays have such
expanded bases as to almost complete the dorsal bar in front. There are apparently
* Op. cit., p. 91. + Fourth Ann. Rep. Fish. Bd., Scotland, 1885. Also Rep. Brit. Assoc., 1885.
t{ For the comple‘e paper, see Biol. Unters., vil., 1895, p. 26.
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 785
many more fin rays in Myxine than in Bdellostoma—as, for example, in the specimen
figured there were altogether 147 fin rays in the caudal fin as against a maximum of
ninety-four in Bdellostoma, according to AyERS and JAcKsoN.
Median Ventral Bar ( m. v. b.).—Commences as a short thin rod closely attached
to the mid-ventral region of the notochord. In front, one or two nests of cartilage cells
may occur in the same position (fig. 17). This rod soon widens out, by a concave
forward sweep, into a wide plate (with an expanded chordal base) to which the ventral
fin rays are fused. In Bdellostoma, according to AvERs and Jackson, the bar arises far
forwards as a pair of long slender rods which fuse behind in the mid-ventral line.
This is, therefore, very different from Myxine. The bar sends forwards a prominent
projection with a rounded extremity which gives origin to the pair of wide, somewhat
diffuse, muscle sheets of small fibres which pass one on each side of the caudal hearts
externally, as described by G. Retzius, and which are responsible for the pulsation
of these organs. In one specimen there was a perforation in this bar near the anterior
end which [| have since failed to find either by dissection or in serial sections, and which
transmitted an anastomosis between the caudal hearts. As the median ventral bar
passes backwards, and the.notochord is tapering down, its base becomes more expanded
and begins to creep up at the sides of the chorda. At the same time, a small rod of
cartilage is deposited dorsally on each side in the angle formed by the base of the fibrous
neural tube (sp. c.) and the roof of the notochord, one or more nests of cartilage cells
being found at short intervals in front of these rods (two are shown in fig. 17). The
rods and the median ventral bar then suddenly fuse, so that the chorda is now completely
invested with cartilage, except dorsally. Shortly afterwards this compound rises up and
fuses with the median dorsal bar, thus forming a complete cartilaginous neural tube
except that its floor is formed by the roof of the chorda. The latter itself becomes here
eradually invaded by cartilage cells and is soon almost entirely merged into the median
ventral bar, with the result that the cartilaginous neural tube is finally completed at its
only lacuna—-the base. However, nests of notochordal tissue occur at intervals
embedded in the cartilage behind this region, thus indicating that the chorda extended
further back than appears in the adult. Immediately behind the termination of the
chorda a large fenestra arises on each side of the tube formed by the fused median
dorsal and ventral bars, and the spinal canal is thus exposed laterally. The latter,
however, does not entirely fill this fenestra, even at its expanded termination lodging
the curious dilated filum terminale,* as shown in the figure. The ventral edge of the
bar bears thirty-three fused fin rays, of which only one was bifurcated in the specimen
figured, as against the five bifurcating rays attached to the dorsal bar. G. Rerztus gives
about thirty, but does not figure any bifurcating rays although such are mentioned in
the text. In bdellostoma, according to AvERs and Jackson, there are only about twenty
fused ventral rays, of which nearly all are bifurcated, and the median ventral bar
extends forwards under the notochord as far as the cloaca without fusing with the
* In Bdellostoma, according to Ayers and Jackson, the spinal cord is not dilated.
786 MR FRANK J. COLE
anterior ventral fin rays. According to BasHrorD Deay, the fin rays arise as unbranched
structures in Bdellostoma.
In front of the ventral bar there were in the specimen figured twenty-one free fin.
rays, all situated behind the cloaca, which extend a short distance within the contour
of the body between the slime sacks, and none of which were bifurcated. AvyErs and
JACKSON figure fourteen, with all but one bifurcated.
I may mention here that in Bdellostoma AyeERs and Jackson describe “a very thin
irregular sheet of cartilage in the wall of the cloaca, especially in the anal region,” which
they believe possibly “serves to expand the anal opening in anal respiration” (p. 217).
I have failed to find this cartilage in Myzxine either by dissection or in serial sections.
The minute structure of the cartilage of the fin rays and dorsal and ventral bars
indicates that it is an extreme variety of soft cartilage, but not so primitive as that of
the branchial skeleton. Its staining reactions resemble those of the latter cartilage, but
there is a tendency in the direction of differentiation. It consists of large cells, each
surrounded by a distinct deeply staining zone that I take to represent the cell capsule,
embedded in a practically continuous reticulum of what is clearly cement. The inter-
cellular substance or cement is, however, distinctly weaker than in typical soft car-
tilage, but it is, on the other hand, more continuous or reticular than in the hard
cartilage, thus accentuating the difference between typical hard and soft cartilage
already referred to.
April 26, 1905.
N. EXPLANATION OF THE PLATES.
REFERENCE LETTERS.
a. d. p. Anterior arch of the dental plate. ch. c. Chordal cells forming the notochordal
a. d. p.’ Posterior ort Ba “Jelly.”
a. d. p.” Posterior internal es aes ch. ep. Chordal epithelium,
a. t. b. Anterior transverse bar of the nasal capsule. cl. Cloaca.
a. t. v. b, Anterior transverse velar bar. cr. Membranous cranium.
au. c, Auditory capsule. cs. Centosomes of the cartilage cell.
au. f. Auditory foramen. c. sb. Cement substance of the hard cartilage.
b. p.* Anterior, middle, and posterior segments ct, c. Cartilage cell.
of the basal plate. d. ces. ct. Ductus cesophago-cutaneus.
br. a. First ‘‘ branchial” arch. d, t. Median dorsal tooth.
br. a.” Second “branchial” arch. In fig. 1, con- | e. 0. p.’ External bar of the anterior segment of
sisting of separated upper and lower the basal plate.
divisions. e. l. b, External lateral velar bar.
br. ap.’ Left | branchial epee e. . b.’ Short rod of soft cartilage connecting
br. ap.” Right above with the posterior extremity of
c. ¢. Cornual cartilage, the inferior process of the “ pterygo-
c. ct. c. Capsule of the cartilage cell. quadrate” (cp. figs. 1 and 2),
c. g. p. Tendon of the M. copulo-glossus profundus el. ext. Elastica externa of the notochordal sheath,
(P. Ftrerineer) cut across (=the f.* The four fenestre of the skull,
tendon of the protractor muscle of the | “jin” Dorsal, caudal, and the adipose pre-anal
dental plate, Ayers and Jackson). “fins,”
ON THE GENERAL MORPHOLOGY OF THE MYXINOID FISHES. 787
f.r. The so-called “ fin rays” composed of soft pen Parachordal” cartilage.
cartilage (although not coloured). p. d. p. Posterior arch of the dental plate.
h. p. Hypophysial plate. pl. | REECE bar.
h. p.. Rod connecting above with the posterior p. q. “ Pterygo-quadrate.
transverse bar of the nasal capsule (figs. p. t. b. Posterior transverse bar of the nasal cap-
1 and 2). sule.
hy. “Hyoid” arch. p.t.v. b, Posterior transverse velar bar.
7. b. p.’ Internal bar of the anterior segment of 8. g. 8. Secondary ground substance of the hard
the basal plate. cartilage. ;
7. l. 6. Internal lateral velar bar. sk. 1, Skeletogenous layer of the notochorda
i. 1. c. Inferior lateral cartilage. sheath containing elastic fibrils exter-
7. r. t. Inner row of ventral teeth. nally.
1.1. Tendon of the M. longitudinalis lingue s. 1. c. Superior lateral cartilage.
(P. FUrBRInGeR) cut across (= the sn. b. Subnasal bar.
tendon of the M, retractor mandibuli, sp. c. Membranous neural tube.
Ayers and Jackson). sp. cd. Spinal cord. Note the expanded termina-
1. 1. c. Lateral labial cartilage. tion.
1. p. Lateral plate of the nasal capsule. sp. He Suprapharyngeal skeleton (fig. 1).
m. d.b. Median dorsal bar of the caudal fin sp. sles Anterior | connecting processes of the
skeleton. sp. sk.” Median j
m., v. b, Median ventral bar of the caudal fin suprapharyngeal skeleton. In Bdello-
skeleton. stoma, according to AYERS and JACKSON,
n. c. Nasal capsule. all three fuse with a median dorsal
n. ct. c. Nucleus of the cartilage cell. suprapharyngeal plate represented in
nt. Notochord. Mywine by the expanded extremity of
nt. sh.—* External, middle, and internal layers of ; sp. sk. A
the fibrous notochordal sheath. | ir. “ Trabecula.
1—4 7
ances! tube. hes The various portions of the branchial
ad es oh. skeleton. Cp. text.
o. r. t. Outer row of ventral teeth. ge
Puate I,
Fig. 1. Dissection from the left side of the skull of a 454 cm. Hag. x4. Tentacular cartilages and the
rings of the nasal tube numbered from before backwards. ‘Lhe colours and shading indicate the different
kinds of cartilage, and also the staining reactions of the same with Mann’s methyl-blue-eosin: hard cartilage,
red ; soft cartilage, blue ; hard pseudo-cartilage, blue (dotted) ; soft pseudo-cartilage, uncoloured and obliquely
striated.
Fig. 2. Dissection from the dorsal surface of the skull of a 454 cm. Hag. x4. Tentacular cartilages
numbered from before backwards. The third tentacle, branchial arches, and suprapharyngeal + velar
skeleton have been displayed for the sake of clearness. Nasal tube and capsule removed, and dental
skeleton not shown. The correct relations of the parts have been maintained (cp. in this respect AYERS’ and
JacKson’s fig. 7). Colours, etc. as in fig. 1.
Puate II.
Fig. 3. Transverse hand section of the “hard (brown) cartilage” taken from the middle segment of the
basal plate of a 35 cm. Hag, and stained with Mawnn’s methyl-blue-eosin. Zeiss apochr. 1°5 mm., compens.
oc. 4.
Fig. 4. Portion of transverse hand section through the posterior segment of the basal plate of the same
fish, to illustrate the structure of the “hard pseudo-cartilage.” Methyl-blue-eosin. The upper border is the
dorsal concave and the lower the ventral convex border of the cartilage. Same lens and eye-piece as fig. 3,
but much less magnification.
788 MR FRANK J. COLE ON THE MORPHOLOGY OF THE MYXINOID FISHES.
Fig. 5. Dissection from the dorsal surface of the nasal skeleton of a 454 cm. Hag. x4. Nasal rings
numbered from before backwards. As only those portions of the skeleton visible in a mid-dorsal view are
shown, the figure should be compared with fig. 1.
Fig. 6. Reconstruction from serial sections of the skeleton of the posterior portion of the nasal tube, and’
of the anterior portion of the nasal capsule of a 25 cm. Hag as seen from the left side. The scale in this
and subsequent figures refers to the enumeration of the sections—numbered consecutively from the anterior
extremity backwards. Nasal rings numbered from before backwards. Cp. with figs. 1 and 5. x 22.
Fig. 7. Dissection from the ventral surface of the dental skeleton of a 454 cm. Hag. x44. The parts
have been displayed for the sake of clearness—cp. fig. 8 for the natural relations. Colours as in fig. 1.
Fig. 8. Reconstruction from serial sections of the dental skeleton (without the teeth) of a 25 cm. Hag as
seen from the dorsal surface. The two halves of the dental plate in transverse section form a distinct V,
but in the figure they are represented flattened out. Otherwise the fig. is not diagrammatic. x 7.
Fig. 9. Dissection from the dorsal surface of the teeth and dental skeleton of a 454cm. Hag. x44. The
parts have not been displayed to such an extent as in fig. 7. Teeth numbered from before backwards.
Colours as in fig. 1.
Fig. 10. Dissection from the ventral surface of the basal plate of a 454 cm. Hag. x3. Colours, ete.
as in fig. 1.
Fig. 11. Dissection from the left side of the branchial +cesophageal duct skeleton of a 354 cm. Hag.
x 6. Efferent gill ducts numbered from before backwards. Cartilage blue.
Fig. 12. The corresponding cartilage, with a similar orientation, of a 35 cm, Hag, to show the absence of
the ventro-anterior (efferent gill duct) portion of the preceding figure. x 6.
Puate III.
Fig. 13. Reconstruction from serial sections of a 25 cm. Hag of the branchial + cesophageal duct skeleton
of the left side seen from the external surface. The orientation is exactly the same as in figs. 11 and 12.
x 22.
Fig. 14, Dissection of the same 355 cm. Hag of fig. 11 from the right side to show the branchial
skeleton, x6. Efferent gill ducts numbered from before backwards. Cartilage blue.
Fig. 15. Reconstruction from serial sections of a 25 cm. Hag of the branchial skeleton of the right side
seen from the external surface. The orientation is exactly the same as in the preceding figure. x 22.
Fig. 16. Reconstruction from serial sections of the skeleton of the pharyngeal velum of a 25 cm. Hag as
seen from the ventral surface. The natural relations of the parts have not been disturbed, and this figure
should therefore be compared with fig. 2, where the velar skeleton is represented displayed. There was a
series of detached nodules of cartilage in the region of the posterior transverse velar bar (p. ¢. v. 6.) which
have been omitted from the figure. x 15.
Fig. 17. Dissection from the left side of the skeleton of the ‘‘ caudal fin” of a 3l em. Hag. x2. Where
the “fin rays” are not fused with a longitudinal cartilage, z.e. as they are posteriorly, they are connected up
by fibrous tissue (not shown in the figure). Spinal cord black. Slime sacks omitted,
Fig. 18. Thin transverse section of the notochord and its sheath of a 34 cm. Hag taken at about the
middle of the body. Two of the chordal cells are shown as they appear in thick sections, in which the whole
of one wall of a cell with the opposed nucleus may be seen. In two others, the nucleus is shown in section
embedded in a thin layer of protoplasm. Zeiss apochr. 1°5 mm., compens. oc. 4.
Boy, OOc, Ldint® VoL Xi
MSF. J. COLE ON THE MoRPHOLOGY OF MyxINE.—— Part lL Puare I,
f
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2 |
: 4
3 Fuge eS
J 6, del. .
M‘Farlane & Erskine, Lith. Edin”
pans. Roy. Soc. Edin’. Vol nh
Mer. J. Cote oN THE MorpHotocy or Myxine — Paarl, Prats IL
does. cb.
ees
Fig.ll x 6
3380
lj fad p. 560
JBIyeR tS) BS 7/
620
CONCAVE BORDER
CONVEX BORDER
Fig. 7 x 43
M‘Farlane & Erskine, Lith. Ediné
ams. Roy. Soc. Edin®
Voli
M? F J. COLE ON THE MoRPHOLOGY
OF Moca === seu I, Puare III.
50 70 90 110
Figly x 2
saa
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980
Fig. 18.
€, del.
M‘Farlane & Erskine, Lith™’ Edin™
(789 )
XXXI.—The Life-History of Xenopus levis, Daud. By Edward J. Bles, B.A., B.Sc.,
Assistant in Zoology at the University of Glasgow. (With Four Plates.)*
(Read January 18, 1904. MS. received January 11, 1905. Issued separately November 8, 1905.)
INTRODUCTION.
The present communication is intended to be the first of a series dealing with
observations on the life-history of the Anura Aglossa and their anatomy at different
stages of development. Xenopus levis, with its small ova and protracted larval
free-swimming stages, must necessarily form a basis for the study of the develop-
ment of that other remarkable Aglossan, Pipa americana. Although the adult
Aglossan is an aberrant and specialised Anuran, there are Urodele features in the
development of Xenopus which make its embryology of great general interest.
These primitive features, combined with others peculiar to the genus, impress a
character upon the early life-history of this frog which is widely divergent from
that of the Phaneroglossa with small ova.
The fullest account of the development of Xenopus is contained in a short paper
by Bepparp, published in 1894. He has cited and reviewed the scanty earlier
literature. Nothing has since been contributed to the subject but a note on the
breeding habits by myself (1901). Brpparp’s observations were made on material
obtained at the gardens of the Zoological Society of London. Specimens of Xenopus
levis from Zanzibar spawned there a few months after their arrival. The earliest
stage observed was the larva shortly after hatching; some frogs were reared from
the tadpoles. The most important new fact made known in the paper was the
presence of a cement organ (‘“‘sucker”). Its structure was described. W. K. Parker’s
observations on the presence of external gills and the absence of so-called internal
gills were confirmed. Some details of the internal structure were described. Figures
drawn from fresh specimens are given of three tadpole stages, early and late.
BEppaRp confirms the absence of horny teeth already noted by Parker (’76)
and Lustre (90). But he did not connect this deficiency with the absolutely
different method of feeding which must necessarily follow. The food of all our
European tadpoles is obtained by the scraping action of the lips with their rows
of horny teeth, sometimes, but rarely, aided by the biting horny jaws. The teeth
act exactly like the radula of a gasteropod and are used to rasp away animal or
vegetable matter from any substratum. Brepparp found numbers of Cyprids and
nothing else in the alimentary canal of the Xenopus tadpoles, and concluded
* Grateful acknowledgment is due to the Carnegie Trust for generously defraying the cost of reproducing the
plates illustrating this paper.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 31). 116
790 MR EDWARD J. BLES ON THE
that they were purely carnivorous and adopted this diet from choice, and states
that “there was plenty of water-weed on which they could have fed.” These
statements it is impossible to bring into harmony with the observations recorded
in this paper, and it is difficult to conceive, taking the facts as known to Brpparp,
how a tadpole without any buccal hard parts could feed on water-weed. The
other observations which Brpparp records I can confirm, with the exception of
only one or two minor points regarding the cement organ.
It may be convenient to give here a brief summary of the main observations
described and conclusions reached in this paper.
(1) The conditions are enumerated and discussed under which Xenopus and other
Amphibia can be induced to breed freely in captivity (pp. 795 and 796).
(2) A detailed account is given of the breeding habits of Xenopus (pp. 797-798).
(3) The remarkable method of oviposition is described in some detail (p. 798).
(4) It is concluded that fertilisation is external in Xenopus (p. 799).
(5) The ege-envelopes are described and the occurrence of a rudimentary egg-shell
noted (p. 800).
(6) The segmentation of the ovum and the development of the embryo within
the ego are described and figured for the first time (pp. 801-806).
(7) The late embryo is shown markedly to resemble he ene stages in
Urodele development.
(8) The posterior ends of the medullary folds are found not to enclose the blasto-
pore nor meet behind the anus (p. 803).
(9) The early development of the face is described and frontal views figured
(pp. 806 and 811).
(10) The “frontal gland ” and its secretion are shown to be functionally concerned
in the hatching process (pp. 807-809), and the development of the gland is described
(pp. 804, 805, and 806).
(11) It is shown not to be connected with the formation of the neuropore and, as it
is not a sense-placode, lends no such support as v. Kuprrer claimed it did to his theory
of monorhiny and amphirhiny (p. 809).
(12) The process of hatching in an Anuran is described for the first time (p. 807).
(13) An account is given of the habits of the tadpole after hatching and before it
begins feeding (p. 810).
(14) The development of the pectoral lymph-hearts at this early stage is noted
for the first time in an Amphibian (p. 812).
(15) The Xenopus tadpole is shown to breathe by its lungs as soon as it beguil to
feed (p. 812).
(16) The development of the cement organ is traced from the first appearance to
its disappearance (pp. 803, 804, 805, 806, 811, and 813).
(17) A brief account is given of the feeding habits. The manner of taking food
is seen to be remarkably similar to that of Ammocctes (pp. 813--814).
d
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. oul
(18) A few cases of branching tentacles in old tadpoles are figured, and it is argued
from the frequent symmetry of the branching that there is a congenital tendency to
branch and that the branching is not due to regeneration after injury. The branching,
if the above view is correct, is evidence in support of the theory that the tentacles
are external gills of the mandibular arch (pp. 814-816).
(19) A very curious difference between the behaviour of the dark chromatophores
of the head and abdomen and those in the distal part of the fin-fold is described.
The latter expand at night, while the former contract (p. 816).
(20) The arm is developed in a sac shut off from the gill-chamber. When it is
protruded it is found that the action of the branchial current is not interfered with as in
terrestrial Anura and feeding by the branchial current goes on as before (p. 817).
(21) The external features of the process of metamorphosis are described (p. 817).
(22) The young frog is found to feed on small Crustacea, chiefly Daphnia, like a
young Urodele.
(23) One specimen, a male, was seen to become sexually mature when two years old.
In this paper very little is said about the internal anatomy of embryos and tadpoles.
It is hoped that this omission will be made good later.
Metuops oF PRESERVATION, EXAMINATION, ETC.
It is not proposed to give full particulars here of all the methods used in this
investigation. There are, however, one or two new devices which may be useful to
others and are therefore worth recording.
The early stages of Xenopus (segmentation, gastrulation) are best preserved in a
4 per cent. formaldehyde solution, after stripping all the jelly from the vitelline
membrane. The latter is so close-fitting that it cannot be removed from the living
egg in these early stages. When the embryo elongates, the vitellime membrane swells
up and can easily be removed. From this stage onwards the best preservative for
general purposes is the one formulated below. Of course, for some special stains,
special preserving fluids are indicated, such as corrosive sublimate for HEIDENHAIN’s
iron-hematoxylin, and so on.
The following mixture was made as the result of experiments to discover a killing
and fixing fluid with the advantages and without the faults of Perenyi’s fluid. As in
PERENYIS fluid, the basis is strong alcohol, but glacial acetic acid replaces the nitric acid,
and formalin the chromic acid. The fluid has greater penetrating, fixing, and hardening
power than PErEnyrs, and it has the same great advantage of not making the yolk hard
and brittle. The nuclear structures are far better preserved than they are by PERENyI’s
fluid, mitotic figures are often perfectly fixed, and the embryos and tadpoles of all ages
are killed almost instantaneously if they are transferred to the preservative with a
minimum quantity of water.
Mix 90 c.c. of 70 per cent. alcohol with 3 c.c. of glacial acetic acid. Any
792 MR EDWARD J. BLES ON THE
quantity of this mixture can be made as a stock solution, as it keeps indefinitely. Just
before use add 7 c.c. of formalin (40 per cent. formaldehyde solution) to each 93 c.c. of:
the above stock solution. This killing and preserving fluid contains :—
90 vols. 70 per cent. alcohol,
3 ,, glacial acetic acid, and
7 ,, formalin, in every
100 vols.
The fluid cannot be used with confidence when more than a fortnight old for killing,
but embryos and larvee of Anura, if killed in a large quantity of the fresh fluid, may be
left in it indefinitely for preservation. The same reason can be given for both these
statements, viz. that the fluid after a fortnight has begun to decompose, which impairs
its killmg and hardening powers but not its preserving property. The formalin and
acetic acid both disappear from the fluid sooner or later, as can easily be proved by the
disappearance of their characteristic odours; these are replaced by an aromatic odour
mixed with that of the spirit, and this mixture is as good a preservative as pure 70 per
cent. alcohol. This property of purifying itself, as it were, makes the fluid particularly
useful for recommending to collectors at a distance. Specimens can be killed in it and
then either sent off in the same fluid or forwarded in a change of the fluid after twenty-
four hours, according to the bulk of the specimen and the relative size of the bottle or
jar. It will then travel any distance without further preparation.
From the reports of friends and colleagues who have used this mixture and from
my own experiments, I gather that it is useful for the most diversified objects, from the
egos and yolky larvee of Echinoderms to the larvee and adults of Anopheles, the newly
hatched fry of Salmo fario, and a full-grown Ammocete. It is, judging from these
examples, worth a trial on almost any object, especially yolky embryos. Of course it
decalcifies and is useful for preserving and decalcifying small Craniates or their heads
when required for sections. The specimens should be transferred from this fluid to
50 per cent. alcohol, washed and passed into 70 per cent., and can then be treated as
required.
A Simple Prism Reflector.—All students of Anuran tadpoles have sooner or later
felt the want of a convenient method of examining these objects from all points of view
without the risk of damaging the specimen. A simple and cheap means of carrying
this out is to build a trough as shown in Text fig. 1. The base is an ordinary
3 inches by 1 inch or 3 inches by 13 inch glass slide. The sides of the trough are of
plate glass ; the right-hand end is a piece of ordinary thin glass ; the end over the middle
of the slide is a piece of No. 2 or No. 3 cover-glass.
The cementing can be done in a few minutes if marine glue is used; the objects
can then only be examined in water or formalin, but if the trough is to contain spirit
the cement used must be carefully applied and allowed to thoroughly harden before use.
Bichromated gelatine, Lovett’s cement, or some such spirit-proof cement can be used.
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. 793
When an object is to be examined under the microscope, a thick piece of glass or
several thin pieces are laid in the bottom of the trough, the appropriate fluid poured in,
and the object then placed as close as possible to the cover-glass end of the trough, with
the surface of the object so placed that by looking through the end of the trough
horizontally the required view of the object can be obtained. But the same view can
be seen by fixing a right-angled prism against the cover-glass and examining the
reflection of the object thrown up vertically from the internal surface of the hypothenuse
side, and the whole arrangement can be put on the stage of a vertical binocular
microscope with the objective over the horizontal face of the prism and the reflected
image enlarged by the use of low powers. With the arrangement shown in Text fig. 1
it is possible to use a Zeiss A objective. ‘The prism is fixed to the cover-glass with a
drop of cedarwood oil or castor oil or glycerine. The object is easily moved about into
any required position while the eyes are at the microscope, as the lower end of the tube
does not come in the way of the right hand.
The side views of eggs and the frontal views of larvee figured on the plates were
drawn with the help of this little appliance.
Text Fie. 1.—Glass Trough with prism for internal reflection. (Natural size.)
Before concluding these introductory remarks, I wish to acknowledge very grate-
fully the help of the artists who have so patiently and carefully carried out my wishes
in making the illustrations for this paper. A member of the zoology class of 1903,
Mr Horatio Marruews, kindly provided the drawings of figs. 12, 13, and 14 from the
living embryos. The rest of the drawings (excepting four) are from the skilful brush
of Mr A. K. Maxwe tt, whose work I[ have controlled and confirmed throughout. Figs.
16, 17, 18 and 19 were sketched by myself from the larva as it hatched, and these
_ sketches have been carefully elaborated, with the help of the identical specimen (killed
five minutes after hatching), by Mr E. Witson of Cambridge.
OBSERVATIONS ON BREEDING AND DEVELOPMENT.
Breeding Halits—My embryological material has all been obtained from speci-
mens of Xenopus which I have now kept in captivity for seven years, since December
1896. Spawn was first obtained in February 1899, when the frogs were in the
Tropical Lily Tank of the Cambridge University Botanic Garden, and a note on the
794 MR EDWARD J. BLES ON THE
observations then made has already been published (Buzs, 01). Since then the same
female has spawned during the spring and summer of 1901, 1902, and 1903, under
conditions easily established anywhere. The methods adopted are possibly more or
less applicable to the breeding of other Amphibia in confinement, and I will therefore
enter into details.
In the first place, the most necessary condition of success in this and similar cases
is that the frogs should be allowed to hibernate. But, in order to accomplish this suc-
cessfully, a frog must be in the best health and condition when the winter sets in, and
must have passed the summer in the best circumstances as regards heat, light, and
food supply.
—=
C | 2 4
Text Fic. 2.—Tropical Aquarium described in
text. The diameter of the bell-jar is 20
inches ; other parts are in proportion.
Xenopus is practically a purely aquatic animal, probably more so than any caduci-
branchiate Urodele, and should be kept in an aquarium at a tropical heat during the
summer in a place which is reached by the early morning or the evening sunshine. The
direct rays from the sun will thus not strike the aquarium for more than an hour or so.
The form of tropical aquarium I have found perfectly successful is one devised by my
friend the late Mr J. 8. Bupcerr, who kindly gave me permission to describe it here.
Text fig. 2 shows a bell-jar 20 inches in diameter standing on an iron tripod.
The circular ring at the top of the tripod is slightly dished inwards to adapt it to the
bottom of the bell-jar. Upon the upper surface of this ring rests the flange of a
galvanised iron tank containing water, and heated below by a Zeiss micro-burner
(Bunsen), This tank acts as a water-bath, and is kept 10°-15° C. hotter than the
aquarium, according to the quantity of water in the latter. I find that this particular
LIFE-HISTORY OF XEHNOPUS LAVIS, DAUD. 795
burner is very convenient, as the temperature of the aquarium remains constant some-
times for weeks together, and a variation of a degree can be put right by slightly
lowering or increasing the flame. Between the bottom of the aquarium and the flange
of the water-bath I have a coil of three turns of asbestos cord, which keeps the glass
away from the hot metal, and prevents evaporation from the water-bath.
In such aquaria my Xenopus have now lived for years, and in them they have
spawned, and the tadpoles been reared, in one case to maturity.
The bottom of the aquarium is covered with earth and stones, and Vallisnerva
thrives in it. During the summer the Xenopus are kept at about 25° C., and the
temperature may rise occasionally to 28°-30° C. They are fed daily with small earth-
worms or thin strips of raw calves’ liver, and are fed until they refuse to eat more,
which they do in a comical manner, by pushing aside the food with the palm of the
hand when it is held near them. ‘The water in the aquarium is never changed.
In December the temperature is allowed to sink to 15°-16° C. during the day,
and it may sink to 5°-8° during the night. The frogs then become lethargic and torpid,
take no food for days, eat very little at a time and move about rarely, spending very
little time, at any rate during the day, at the surface of the water. I have on a few
occasions approached the aquarium very quietly and found one or the other of the
frogs lying flat on the stones with what appeared to be a translucent film dimming
the brightness of its eye.
A sudden noise, however slight, makes the frog start up, and the film moves slowly
outwards and forwards, uncovering the eye, and is recognised as the lower eyelid. The
frog then moves away. Judging from analogy, one might conclude that the frog had
been aroused out of its sleep. Whether this conclusion is justified or not, the facts
seem worth recording, as the evidence of the occurrence of sleep in the lower vertebrates
is somewhat slender.
When the temperature of the aquarium rises in the spring and the days become
brighter, a change in the behaviour of the frogs becomes evident. The female and males
spend a great part of the day at the surface of the water with eyes and nostrils above the
surface. The males become exceedingly restless, swimming about with an air of wishing
to escape from the aquarium. Both sexes are now very shy, and difficult to feed.
There may or may not already be attempts at pairing, but by taking the
following measures pairing will take place immediately (with or without spawning), or
at least the male, after being silent the whole winter, will commence to croak at once.
First, the temperature of the aquarium is raised to 22° C. and, secondly, when it has
become constant, a certain amount of the water, say 2 gallons, is drawn off morning
and evening, allowed to cool for twelve hours, and then run in slowly in the following
manner, in order to simulate the fall of rain. The cooling vessel is raised above the
level of the aquarium, and a syphon is used to run off the water. The lower end of
the syphon is drawn out to a fine point, and turned up in such a way that the water
rises up like from a fountain, and falls as spray into the aquarium. The third condition
796 MR EDWARD J. BLES ON THE
to be established is to bring the water into such a state that the larvee will find their
food when it is required. This condition will be explained later (pp. 813-14).
By carrying out such measures I obtained from one female between April and July
1903 more than fifteen thousand eggs. Of these, twelve thousand were taken out of
the aquarium and counted, and the remainder were estimated at three to five thousand.
Some general significance may, I believe, be attached to the results in breeding this
frog, the more so as they are in accordance with other similar results obtained by
SEMPER (1878) with Axolotls and by myself with Axolotls, Triton waltliu, and Dis-
coglossus.* SEMPER showed that by feeding them copiously, and by keeping Axolotls
crowded together in small vessels, he could obtain spawn from the same individual three
or even four times a year after a sudden transference to an aquarium stocked with
growing plants, with stones on the bottom and supplied with running water. I have
repeated his experiments and can fully confirm his statements. With Dviscoglossus
pictus | have had a similar experience. Specimens kept ina small vivarium for four
and six years have been given a superabundance of food during the summer, allowed
to hibernate, and, when they showed signs of readiness to breed, a little tank in a
corner of the vivarium has been filled with suitable pond water, and invariably within
forty-eight hours the frogs have spawned. On two occasions the males have taken to
the water in the spring and assumed their nuptial characters, but for several weeks the
water which had stood in the tank during the winter has been allowed to stand. No
pairing took place, but as soon as the water was changed spawn was deposited in
twenty-four hours. Two female Discoglossus have each spawned twice every summer
for the last three years, just as they do when free. Two pairs of Triton waltliz, which I
have reared from larvee, have spawned when two years old. In their case the same treat-
ment was carried out. They were well fed in the summer, kept cold in the winter, and
fresh water added to the aquarium when they showed readiness to pair.
These various experiences appear to indicate that the difficulty met with in
breeding Amphibia kept in confinement is not due to any toxic influence on the
gonads due to the results of close confinement. Darwin was inclined to believe
that the functions of the generative organs were sometimes impaired by captivity,
but unless and until concrete evidence is given to show what specific influence
is at work, it would very often be simpler to assume that the external conditions are
unfavourable for breeding, or deficient.
In the case of Xenopus all the other conditions may be present, but if there is
no daily change of the water there is no oviposition, and although the male may
embrace the female, the behaviour of the latter clearly shows that she is not
ready to spawn.
If the view is correct that breeding is brought about in animals, especially in
those with a fixed breeding season, as the response to a certain set of definite
external stimuli on the sexually mature of the species, it may help to explain
* And also by P. Kammerer (’04) with Salamandra maeulosa and S. atra.
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. TOY
why some animals appear in great numbers in one year and are much less numerous
in another. Entomologists are familiar with this phenomenon, and it may be worth
considering whether such fluctuations in numbers are not due to causes of the
nature indicated.
It is obvious that changes in the environment affecting the breeding habits might
lead to rapid divergence through the action of Natural Selection, and the diversity
in the breeding habits of allied tailless Batrachians has perhaps been established
through the agency of such induced sterility.
The male Xenopus begins to assume nuptial characters a couple of days after
the temperature is raised to 22° C. The dorsal surface of the hand darkens and
the area covered with nuptial asperities extends along the arm towards the axilla;
the whole patch blackens from the hand inwards in the course of about two days.
The shape of the patch has already been figured (Buus, ’01).
The abdomen of the female becomes very much distended during the winter by
the enormously enlarged ovaries, so much that the lungs are displaced upwards
and raise the dorsal body-wall on either side of the vertebral column into two
great projecting longitudinal humps. The three flaps of skin surrounding the cloacal
aperture are flaccid until the spring, when they become swollen and turgid and
more highly vascularised. I was unable to detect any change in the epidermis
of the breeding female until last year (1903), when the back of the hands
became darker at the same time as the nuptial asperities appeared in the male.
Special attention was paid to this pomt in the seasons before, and it is certain
that nothing of the kind occurred then, so that it appears that a secondary sexual
character of the male is making its appearance with age in the female (see BouLENGER,
97, p. 72, for similar cases).
During the first week of the newly established spring conditions the males become
vocal. They have been silent throughout the winter, and their first attempts are
intermittent and low in tone. Their voice strengthens from day to day, and at
night-fall, especially if fresh water has been added, becomes a loud and continuous
metallic rattle, kept up for hours with hardly a break. The noise made by a
single frog is loud enough to be heard at a distance of 100 yards or more in
the open.* It resembles the voice of Hyla arborea more than that of any European
frog, but has two alternating notes extremely like those made in winding up an
old grandfather’s clock with a crank handle. By rubbing the corrugated handle
of a pair of large forceps backwards and forwards against the rounded edge of
an empty tin tobacco box, I have imitated the sound so exactly that the frogs
have responded. The croak is produced under water, and although air is no doubt
passed to and fro between the lungs and the buccal cavity, there is no movement
of the pectoral or gular region visible externally.
Normally, pairing only occurs at night. The male croaks loudly and incessantly
* J had not heard its full strength when I made the statement in my former account (BuEs, ‘01, p. 211).
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 31). 117
798 MR EDWARD J. BLES ON THE
during the twilight until he seizes the female. There is nothing resembling the
courtship of Urodeles. The male makes a sudden dash and clasps his mate round
the lumbar region; his arms are too short to meet on the ventral surface. In the —
amplexus being inguinal, Xenopus resembles the Discoglosside and Pelobatidee
(BouLencrr, '97, p. 69). The note of the male changes at the commencement of
pairing. In a low tone he utters ‘cd, cé6, cd, c6, ....” and at each syllable
strikes the under side of his head against the back of the female. Between each
stroke the floor of the mouth of the male is seen to bulge considerably so as to
carry his head away from the back of the female. When spawning begins he is
silent, but every now and again while the amplexus lasts he croaks loudly during
the short intervals when oviposition stops.
The account given by Lestiz (’90) of the breeding of Xenopus speaks only of
spawning taking place in August, z.e. the South African spring.
According to my observations, I should conclude that, like Discoglossids, the
same female may spawn in the wild state several times during the sprmg and summer,
and that the males are ready to pair at any time in those seasons. My female Xenopus
had spawned for the first time in the year in February (Cambridge), April (Cambridge),
and May (Glasgow), in successive years, for a second time in June, and a third time at
the end of August in the same summer (Glasgow, 1902); in the following year three
batches of eggs were laid at corresponding times. Thus the animals became acclima-
tised to a difference of six months in the seasonal changes.
Hach batch of mature eggs was usually deposited in the course of five days, one
night in which pairing did not take place intervening between the nights when eggs
were laid. On one occasion spawning took place on five nights; between the third and
fourth night of spawning there was an interval of three nights; the others were on
alternate nights as usual.
It has so often happened that male and female have been seen to cast their skin
the morning after pairing, that it is probable that ecdysis is usual at this time. The
skin is loosened all over the body, the legs are then freed, and the skin which is
attached to the snout is drawn forward, crammed into the mouth, and eaten in exactly
the same way as it is by many terrestrial frogs.
Oviposition.—The amplexus is continued from the evening until the next morning,
and may last until 9 a.m. Spawning does not commence immediately, but may begin
an hour after pairing. From this time onwards eggs are laid at frequent intervals all
through the night. As a rule the eggs are laid singly, and the pair swim about or
come to the surface to breathe between each act of spawning, But occasionally three
or four eggs are laid in quick succession in the same spot, and somewhat rarely eight
to ten eggs will be emitted in a group.
The egg is held between the three protruding flap-like lips of the cloacal spout,
while the pair swim about restlessly for half a minute to two minutes; the female then
grasps a long leaf or a twig of water-plant between her outstretched feet, and the pair
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. (oS)
come to rest in such a position that the cloacal spout of the female becomes applied to
the anterior end of a shallow median groove on the ventral surface of the male, which
runs back to the cloacal opening of the male for about three-quarters of an inch. This
groove is formed by two skin folds over the ventral edge of the pelvic symphysis. The
ego is passed out, travels rapidly along this groove, over the cloacal aperture of the male
and directly backwards about 4 inches to the weed held by the outstretched legs of the
female, where it adheres. The egg has to travel about 5 inches from the female to the
weed, and is carried this distance in a straight course. This is partly due to the fillip
it receives from the tumid lips of the cloaca as it passes out, and partly to a backwardly
directed current in the water, created by gentle swimming movements of the feet of the
male. The pair immediately swim away, another ege appears in the cloacal spout of
the female, and the process is repeated. As each egg or group of eggs is laid, a spas-
modic quiver can be seen momentarily passing over the body of the male, and at this
time, I have reason to believe, a very small number of spermatozoa are emitted.
Fertilisation.—The curious method of oviposition resembles in the action of the
female the spawning of Urodeles and is so unlike that observed in the Phaneroglossa,
that the question of fertilisation is raised. Quite a number of considerations point to
the conclusion that each egg is fertilised as it is laid and after it has passed into the
water, but all attempts to secure spermatozoa in the water as the eggs were laid proved
unsuccessful, as were also attempts made to observe fertilisation in the living ege.
One set of observations repeated at different times proves, I believe, that fertilisa-
tion does occur after or during deposition of the egg, as in other Anura. The eggs
when attached always have the dark pole below, and within half an hour rotate within
the egg-membranes, so that the dark pole is above and the light pole below. In
Xenopus eges which are unfertilised this rotation does not take place at all as a rule,
or may be incomplete or take an hour or more to complete. ‘This agrees exactly with
the rotation described in eggs of other Anura with external fertilisation (R. Herrwic,
03, p. 534).
Further, there are at each spawning a number of eggs (100-200) which do not
become attached, presumably by accident, but fall to the bottom of the aquarium.
It is exceedingly rare to find a fertilised egg among these. This seems to point to the
conclusion that a very limited number of spermatozoa are emitted, otherwise it is
difficult to understand why these eggs should not have spermatozoa carried to them in
a small aquarium with water kept in constant motion by the active pair of frogs.
Every now and then during spawning an egg is passed which does not pass along the
ventral groove of the male in the normal manner, and these drop to the bottom. This
would account for these eggs not being fertilised. It is hardly probable that they are
all immature eggs; that would not account for them not having been attached, as they
are in other respects quite normal. One of these ova has been figured in fig. 1, Plate I.
The Egg-envelopes.—The diameter of the whole egg when laid varies between 2°75
and 3°0 millimetres. It is surrounded by a layer of transparent jelly-like substance,
800 MR EDWARD J. BLES ON THE
the outer coat being extremely adhesive. One result of this is that the eggs stick to
the first foreign body they touch in the water. Another consequence is that the eggs
become coated with a thin layer of mud when laid in turbid water; the suspended _
particles stick to the surface. The appearance of an egg laid in fairly clear water is
shown in fig. 11, Plate II. Within a few hours the outer layer changes in consistency ;
it becomes hard and horny, and floating particles no longer stick to it. The horny coat
is exceedingly tough, and might be regarded as a rudimentary egg-shell. In this
capacity its function would only be transitory, as on the second day after spawning
this outer envelope splits and its contents ooze out. The substance of the outer coat is
so tough and unyielding that the contents are tightly pinched as they issue; the jelly
and the soft embryo itself are both constricted between the lips of the chink. The ege
thus freed is composed of a thick outer layer of jelly, the vitellme membrane and the
elongated embryo lying in the fluid within the vitelline membrane (see fig. 12, Plate II).
The whole remains adherent to the original place of attachment; the outer coat shrinks
and forms a shrivelled ring round the place of attachment of the egg to the substratum.
The escape of the egg-contents only occupies a few minutes.
A very similar shell-like structure, which seems to be undescribed, is found in the
egg of Hyla arborea var. meridionalis. Here it is not superficial, but enclosed in a
thin, soft, adhesive layer which holds together a number of eggs in a clump. Inside this
layer is a tough, thin, whitish translucent membrane ; then follows a layer of jelly and
then the vitelline membrane. This “‘egg-shell” is also burst at an early stage. On
the third or fourth day after the spawn is laid, the spherical shell is found in two hemi-
spherical pieces lying embedded next to each egg in the jelly of the clump. In this
ease the split extends meridionally completely round the “shell.” The splitting of this
membrane in the case of both Xenopus and Hyla is most likely due to the absorption
of water by the inside jelly and its consequently swelling until the internal pressure
bursts the non-extensible membrane. This membrane is comparable with the true
membranous ege-shell discovered by Guppy in the large eggs of Rana opisthodon,
which are laid in the crevices of rock and enclose the young frog until perfectly formed.
The Ovum.—The history of the ovum is here taken up at the period of oviposition.
It then measures 1°5 millimetres in diameter, so that it ranks among the smaller
Anuran eggs.
While rotating within the ego-membranes after fertilisation, it can easily be seen
that the pigmented and unpigmented areas of the surface are approximately equal (see
fio. 1, Plate I). The pigmented area usually covers rather less than a complete hemi-
sphere. The dark half is of a rich brown colour, while the yolk is of a very pale
greenish-blue colour.
Fig. 1 represents an unfertilised egg about twenty-four hours after oviposition. It
is easily recognised by the patch of unpigmented protoplasm which has risen with the
ege-nucleus inside it to the surface, and has displaved the superficial layer of dark
pigment from the upper pole. This appearance is very characteristic of unfertilised
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. 801
eggs on the second day after spawning. In other respects the egg shows the normal
appearance before segmentation commences.
Segmentation.—The details of segmentation do not appear to differ much from
those seen in small eggs of other Anura, and are, therefore, not described in detail.
I have had figures of a few stages made as accurately as possible to show the
general course of the processes.
The first furrow is, as usual in Anura, meridional and divides the eggs into two
equal blastomeres. It is completed one hour to one and a half hours after fertilisa-
tion. ‘The next vertical furrow appears within two and a half hours after fertilisation,
and the third (horizontal) one within the next hour. The third furrow does not form
exactly parallel to the equator, but is bent in the manner shown in fig. 2, Plate LI.
The egg is viewed here from the right side, according to the statement made by O.
ScHuttze and Kopscx to the effect that the unpigmented portion of the egg reaches
much nearer the upper pole on that side of the egg which is to become the posterior
end of the embryo. In this egg there is at the upper pole a marked departure from the
radial symmetry which, as shown in fig. 24, is still present at the lower pole. The egg
has become bilaterally symmetrical with an elongated and a more rounded cell on each
side at the upper pole. The pigment is not altogether confined to the cells of the upper
hemisphere ; there is a patch posterior to them (fig. 2, Plate 1). The egg represented
in figs. 3 and 3a, Plate I, is at a stage reached about four hours after fertilisation.
The segmentation has become irregular, especially of the yolk cells. There is still
a marked difference in the bulk of the cells of the upper and lower hemispheres,
but the latter are now rapidly dividing. Furrows start from the edge of the
pigmented areas and extend downwards over the yolk cells until they meet an
existing furrow near to, but not accurately at, the lower pole of the egg. At the
stage shown in fig. 4, the cells of the upper and lower hemispheres are almost equal
in size and are again arranged fairly regularly. This return to a regular arrangement
must be a result of the mobility of the superficial cells, together with the need for a
geometrical arrangement in order to accommodate a given number of cells of a certain
size in a limited space. That the cells of both the upper and lower poles are movable
to a certain extent can easily be observed in the living egg. Newly divided cells
may push apart two cells which were in contact with each other until the edges
which were touching are separated by the whole diameter of the intruding cells.
If there are intercellular strands of protoplasm at this stage they must certainly
become broken in the shifting about of the cells.
At the stage shown in fig. 5, the cells have become smaller and have lost both
the regular arrangement and the roughly hexagonal outlines seen in the earlier
stage. The yolk cells near the equator are dividing more rapidly than those
at the yolk pole and are appreciably smaller. The living segmenting egg at this
stage has a feature which is shown here in the figure (fig. 5) of a preserved specimen.
A number of cells at the margin of the spreading epiblast are of much paler brown
802 MR EDWARD J. BLES ON THE
than the neighbouring epiblast cells. This difference in tint is found, by watching
the cells in a living egg, to be the sign of an approaching division of the pale cell.
The pigment reappears apparently undiminished in quantity after division. The cause —
of such cells turning pale at this particular time I hope to discuss later, as there
appears to be some parallel between this process and that of contraction in the
chromatophores.
Gastrulation.—A stage of the development of the blastopore is shown in figs. 6
and 6a. In the side view (fig. 6), the egg is shown in the vitellme membrane and
lying with its orientation as in life, the lowest point on the egg sphere being 30°
behind the middle of the dorsal lip of the blastopore. This view shows very clearly
features not easily shown in the ventral] view, namely, the extent of the depression of
the posterior lip of the blastopore and the sharp, slightly puckered edge of the dorsal
lip, which is not depressed, but remains up to the edge coincident with the surface
of the sphere of the egg. At this stage indications are already noticed of the
arrangement of ectoderm cells in rows, forming alternating light and dark streaks lying
in the position of great circles roughly coaxial with the great circle passing through
the longitudinal axis of the embryonic area. These streaks are indicated in fig. 6,
passing from the posterior edge of the upper pigmented area towards the blastopore.
In fig. 6a, the lower ends of these streaks are seen near the right-hand angle
of the blastopore. In this figure (6a) the blastopore has reached the greatest lateral
extension it attains as a crescentic opening.
In fig. 7 the ege is seen from behind, and a stage is represented where the blastopore
has just become circular. The yolk plug does not protude; at no time does it become
prominent in Xenopus. The pigmented cell-area now extends back to the edge of the
upper lip of the blastopore. A peculiar feature of this stage is the constant occurrence
of alternating bands of darker and lighter cells arranged as described above in the previous
stage figured (fig. 6). The observation that epiblast cells undergoing mitotic changes
become pale at certain stages of the process leads to the interesting conclusion that the
lighter patches are areas in which the epiblast cells are proliferating simultaneously.
The Embryo.—AIn figs. 8 and 8a, representing views of the same egg seen from behind
and from before, an early stage of the development of the medullary folds is shown. The
view from behind (fig. 8) shows that the medullary folds are externally much less obvious
at the hinder end than they are in the head region seen in fig. 8a. On the dorsal contour
of the latter figure, the gentle elevations are due to the swollen medullary folds, and the
slight notch between them indicates the neural groove (Liickenrimne). The neural groove
extends far forwards, as far as the anterior wall of the brain, and can be seen between
the paired dark patches on the exposed floor of the thalamencephalon. These areas
are occupied by the pigmented cells of the optic vesicles, and closely resemble those
described by EycLesHEIMER in Rana pabustris (93). Returning to the medullary folds, it
will be seen from fig. 8a that at about the middle of their length the medullary folds
have converged from the anterior end to lie side by side. It is thus possible to identify
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. 803
the elevations on the upper contour of fig. 8, Plate 1, near the middle line as the medul-
lary folds, otherwise it would be ditticult to make out their position in the posterior view
of this stage. They flatten out and disappear towards the blastopore. On the outer side
of each medullary fold is a band of pale ectoderm cells which can be seen at the pomts
a and b to be slight ridges. These bands of proliferating ectoderm cells meet at a point
just anterior to the future anal perforation, marked at this stage by a small pigmented
area at the hinder end of the closed and elongated blastopore. As these bands lie ex-
ternal to the medullary folds, it is certain that at this stage the medullary folds do not
enclose the blastopore or meet behind the anal opening. The archenteron is now com-
pletely closed to the exterior, as for a short time the blastopore is quite closed ; there is
noanus. ‘The anal opening is formed in a few hours after this stage has been passed
through. The neurenteric canal and postanal gut persist for a long time; they are
present at the stage shown in fig. 14. The dark area (fig. 84) anterior to the medullary
folds, and extending a short distance back along the sides of the fore-brain region, is a
region covered with modified, deeply pigmented ectoderm cells, the greater number of
which are destined to become secretory epithelium cells. ‘The median ventral portion
of this area is the precocious rudiment of the cement organ (‘‘ Sucker”) ; the lateral dorsal
portions contribute to the formation of the frontal gland (‘‘ Stirnknospe,” v. Kupprmr,
“Stirnstreifen,” Hinsperc). This area corresponds in its position and relations to
other parts exactly to O. ScHuurzr’s “ Sinnes-platte,” Morean’s “Sense-plate.” It
is not to be regarded as a lateral extension of the medullary plate (Moreay, ’97,
p. 57). It is a part of the general ectodermal covering without any obvious
connection with the central nervous system and formed by differentiation in the
cells of the superficial epidermic layer of the ectoderm only. The deeper nervous
layer of the ectoderm is not modified and there would seem to be no justification for
the term “ Sinnes-platte.”
The portions of the ectoderm from which: the epithelium of the nasal pits is derived
are enclosed by or are possibly included in this dark area; it is not possible to identify
them at this stage.
The medullary folds have arched over and their edges have met along their whole
length in the next stage figured (fig. 9). The ectoderm is raised as a gentle ridge over
the closed neural tube, and there is a line of deeply pigmented ectoderm cells along the
median external line of junction of the folds, and at the bottom of the shallow groove
formed by the rounded edges of the folds. The anterior end of this pigmented groove
marks the position of the neuropore. A short distance posterior to the neuropore, the
pigmented groove is intersected by a crescentic band of pigmented ectoderm, the early
rudiment of the frontal gland. Below the position of the neuropore is a large pigmented
patch of ectoderm, the rudiment of the cement organ. It shows some indication of a
paired nature in the presence of a more deeply pigmented patch at each end of the
transversely elongated area. This figure (9), compared with fig. 8a, shows that the greater
part of the pigmented area in front of the medullary folds at the earlier stage becomes
804 MR EDWARD J. BLES ON THE
cement organ at the later stage. And the postero-lateral horns of this crescentic area
(fig. 8A) are carried inwards towards the median dorsal line as the roof of the fore-brain
closes in and give rise to the transverse band of cells I have called the frontal gland.
This will be dealt with in detail later. We shall see that the area shown in fig. 9.
enclosed by the line of the frontal gland and the upper edge of the cement organ is
the part from which the anterior organs of the face develop, viz.—the stomodceum
and the nasal pits. At this stage the egg has just begun to elongate in the direction
of the future axis of the body.
In fig. 10 an early stage in the elongation of the larva is represented, and it will be at
once observed that the dorsal concavity which is so marked a feature of corresponding
stages in all such forms as Rana, Bufo, Hyla, Bombinator, and Discoglossus is not only
absent here, but there is a distinct convexity of the dorsal contour in side view—the
two ends of the embryo are slightly bent ventralwards, so that there is a shallow ventral
concavity. It is this feature in its general appearance which in early embryonic stages
of Xenopus recalls rather a Urodelan embryo than one of the familiar Anuran embryos.
The difference is due mainly to the fact that while the embryo of the typical Phanero-
glossa owe their increase in length from the beginning to the elongation of the tail and
sometimes of the head also, the abdominal region remaining short, the embryo of
Xenopus for sometime grows in length in the trunk region, the tail remaining short
and stunted. Connected with the checked growth of the trunk in the forms mentioned |
above is the persistence of the anus in its position high up on the posterior surface of
the ege, which involves the outgrowth of the tail, so as to make it sprout not directly
backwards but obliquely upwards at an obtuse angle with the long axis of the body. In
Xenopus, on the other hand, the growth takes place in such a way that the anus is
swung round from its equatorial position on the spherical egg to a ventral position in
the elongating embryo, as indicated in fig. 10. As indicated in figs. 10 and 12-14, the
tail remains a mere stump, while the trunk elongates considerably. A form of embryo
results, bearing considerable resemblance in the proportions of its main regions to
Urodele jarvee and also to young Dipnoan larvee, where the anus is placed close to the
posterior end of the body at the root of a very short tail. This short-tailed, long-
bodied phase of the development of Xenopus may, with some confidence, be looked
upon as primitive.
Returning to stage 10, it will be seen that the region of the spinal cord is pinched
up, as it were, from the ventral part of the trunk, and the fore- brain swells out the tip of
the head. Behind the fore-brain is an elevation of the whole branchial region. ‘There
is an accumulation of yolk at the posterior end producing a swelling out of that part.
The fin-fold has not made its appearance. The cement organ is beginning to assume its
characters, showing a compact group of cells with densely pigmented inner ends and
outer ends filled with a clear mass of secretion. At the extreme anterior end is placed
the frontal gland, seen better in the frontal view (fig. 10a). This shows how the frontal
gland has become continuous with the pigmented band of cells along the sagittal line.
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. 805
The position of the neuropore is indicated by a few pigmented cells forming a short
longitudinal streak exactly at the extreme anterior end of the animal. Between the
neuropore and the cement organ is the region of the stomodceum.
The next change in the external appearance of the embryo is due to the outgrowth
of the median fin-fold of the tail. An early condition is shown in fig. 12. The trunk
is slightly longer than before (stage of fig. 10), and the back of the embryo has become
straighter.
The growth in length of the embryo has stretched out the vitelline membrane into
an ellipsoidal form. In the particular embryo drawn the cement organ happened to be
larger than it is usual to find it at this stage. The line of the frontal gland is well
defined ; it extends ventrally as far as the edge of the cement organ, and between it and
that edge is enclosed a patch of deeply pigmented ectoderm. The portion of the
median fin-fold to develop first is that bordering the tail region ; in fact, the extent of
the tail region is fairly well defined by the limits of the fin-fold at this stage. The
fold is deepest in the post-anal ventral part, extends round the posterior end of the
embryo, and fades away just before reaching the dorsal surface.
When the embryo has reached a length of 3°8 millimetres (fig. 13) the fin-fold has
grown up along the dorsal surface and extends forwards as far as the part over the
hind-brain, practically marking out the whole length of the organ. The fin is still
deepest in the post-anal ventral portion. It is necessary at this stage to distinguish
between a ventral post-anal abdominal part of the tail into which the posterior end of
the yolk mass is drawn out, and a dorsal part which, it will be seen, grows out more
vigorously and gives rise to the segmented, muscular part of the tail. In the head
there is remarkably little indication externally of the developing eye, brain, and
visceral arches. The position of the eye can just be discerned by the dark patch drawn
in the figure; the mandibular arch is slightly raised above the general surface, and the
posterior group of visceral arches is just discernible as another broad and gentle
elevation on each side of the head. The line of the frontal gland is very distinct and
obviously continuous with the cement organ at its lower ends. The cells of the cement
organ are filled with clear secretion at their outer ends, and thus produce an appearance
of a low translucent ridge running across the dark cement organ from side to side. No
indications of nasal pits or of the stomodceum are to be seen. The myotomes are just
beginning to be visible externally in the hinder trunk region.
Further growth is shown in the embryo of fig. 14, drawn after removal from the
egg. The tail has grown out more especially in its dorsal muscular part, and the fin-
fold of the tail has now become widest along this muscular part. The post-anal
abdomen has also been slightly drawn out in length by the growth of the tail. The
dorsal fin has become higher, and now reaches forwards on the head as far as the hind
level of the fore-brain. Numerous myotomes can now be seen in the living embryo.
The eye is plainly seen and also indications of the lens thickening. A bulging behind
the branchial region indicates the position of the heart; more dorsally the ear vesicle
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 31). 118
806 MR EDWARD J. BLES ON THE
may be seen faintly through the skin, and a swelling shows the position of the
pronephros.
All the preceding stages are still enclosed within the ege. We now pass on to.
the larvee at the time of hatching. Fig. 16, Plate III, shows the larva at the normal
stage of hatching with the vitellme membrane now enormously swollen out. The
more or less thin layer of jelly which surrounds the membrane has not been drawn.
Compared with the last stage illustrated (fig. 14), the muscular portion of the
tail has grown, while the abdominal portion of it has become insignificant. The length
of the tail (fig. 15a) is still only about half the length of head and trunk together ;
the fin-fold has not yet become a powerful swimming organ. The head is now fora
time divided from the trunk by a constriction, a neck, which is the more marked
since the trunk is swollen just behind the constriction by the bulging of the skin
over the pronephros (see fig. 16, Plate III). On the somewhat flattened anterior surface
of the head the following can be made out (fig. 15, Plate III). On the ventral surface
of the head is a conspicuous cement organ projecting downwards and forwards,
exceedingly deeply pigmented at its base, so as to appear almost black. Running
round the anterior edge of the protuberance is a clear-looking ridge with its outer
end curved backwards; this is composed of the outer ends of the tall columnar
cells of the cement organ filled with the cell-secretion. The oval patch behind the
crescentic ridge is formed by the inner ends of the pigmented gland cells shining
through the epidermis. The outline of the cement organ is thus crescentic and not
circular, as Brpparp described it in his Xenopus tadpoles. Running up from the
anterior border of the cement organ, and passing obliquely outwards, is the pair
of bands of pigmented cells connecting the frontal gland with the cement organ.
The cells of all three structures are found to be essentially similar when examined
in sections, so that there is a continuous line of mucus-secreting cells enclosing an
area shaped roughly like an inverted trefoil on the anterior surface of the head.
The base of the trefoil above contains the paired rudiments of the nasal pits, and
the apex contains the stomodceeum. The lateral bands of mucus cells are narrow
and meet the ends of the broad transverse band which forms the frontal gland just
internal to the level of the outer edge of the nasal pits, so that the nasal pits are
bordered dorsally by the frontal gland. By comparing fig. 15 with fig. 10a
(Plate I), it will be seen that the frontal gland is dorsal to the neuropore, and
that the neuropore, if it persisted or if traces of it remained until this stage,
would lie between the centres of the nasal pits. Another point worth notice is
brought out by a comparison of the frontal view of these two stages, and that
is the very close proximity of the neuropore to the small area from which the
stomodceeum will be formed later in development. Taking into account the
thickness of the ventral wall of the fore-brain, it will be seen how little space is
available between the cement organ and the brain for the potential mouth at the
earlier stage (fig. 10a).
LIFE-HISTORY OF XHNOPUS LA&VIS, DAUD. 807
Hatching.-—The larva of Xenopus hatches forty-eight hours after the egg is laid,
when the eggs are kept undisturbed in a constant temperature of 22°C. I found, for in-
stance, that a batch of some hundreds of eggs, laid on the night 24th-25th August 1903,
had all hatched on the morning of 27th August, with the exception of twenty or thirty.
As the larvee might be expected to emerge from these during the course of the day, they
were placed for observation in a little tank kept at a temperature of 22° and were
watched from the side through a horizontal binocular microscope (Zeiss’ Braus-Driiner
model) under a low power. The view of the ege obtained in this way is represented in
fic. 16, Plate III. ‘The jelly on the surface is not shown ; a very thin layer of it covers
the vitellime membrane, the thinness being partly due to the way in which the vitelline
membrane has swollen up, the jelly having now to cover a much larger surface. At an
early stage the membrane loses its spherical form and becomes ellipsoidal (see fig. 12) ; it
is elastic and becomes swollen up by the pressure of its fluid contents. It is easy to test
this by tearing a hole in the membrane; a jet of the fluid is forced out through the
hole and the membrane collapses and shrinks. The egg is, then, in a condition of tur-
gidity, and this forms a factor in the hatching process. The larva lies on the lowest part
of the vitelline membrane, the side of its body in contact with it and roughly parallel to
the long axis of the egg, which is always horizontal. In this position the larva is attached
by the secretion of its cement organ to the vitelline membrane about two hours before
the hatching occurs. Before attaching itself it seems to have sunk down to a position
of equilibrium with its centre of gravity over the lowest point in the curve of the egg
membrane. ‘This is indicated by the position of the tip of the tail, which is always at a
higher level than the head. The surface of the larva is richly ciliated and the fluid in
the egg membrane is kept in rapid rotation, the current over the body of the larva
passing from head to tail. The larva lies perfectly still, except that every ten to fifteen
minutes it turns over from one side to the other. It will be seen from fig. 16 that the
head of the larva only touches the vitelline membrane where the surface of the eye
rests upon it; the cement organ is not itself in contact, as a short string of secretion
passes from the gland to the membrane. The first sion that hatching is about to take
place is a slight bulging outwards of the vitelline membrane opposite the head of the
larva. In the course of the next five minutes the membrane under the anterior part of
the head softens and the head sinks into the soft place, the membrane partly moulding
itself to the contours of the head and partly bulging beyond the head, as drawn in fig.
174, Plate III. It will be observed that in this position the extreme anterior end of the
head where the frontal gland is situated is not actually touching the vitelline membrane,
although very close to it. In another five minutes the membrane has moulded itself by
a further softening to the anterior contour of the head (see fig. 178), and now the
frontal gland touches the vitelline membrane. When this stage is reached the hatching
is rapidly completed. During the next three minutes the pouch of vitelline membrane
in which the head lies distends more and more, until an imaginary line drawn in the
original smooth curve of the membrane would pass through the middle of the cement
808 MR EDWARD J. BLES ON THE
organ (fig. 17c). In this position the tadpole remains for not more than thirty
seconds ; the stretched part of the membrane then bursts, and the larva is shot out head
foremost, as shown in fig. 18. In the same instant the vitellme membrane shrivels up |
like a burst indiarubber toy balloon. The larva may remain motionless with its tail
between the torn edges of the eeg membranes for one minute ; it then wrigeles and frees
the tip of its tail, the tail swings round through an are of 180° and the larva is then
seen hanging, as in fig. 19, by a thread of mucus to the still further shrunken ego mem-
branes. This thread of mucus is the short thread which attached the larva to the inside
of the vitelline membrane and now drawn out to the length of the larva. It is
apparently pulled out when the tadpole bursts out of the membranes, but it is not
shown in fig. 18, as it is hidden by the body.
The following suggestions are offered as to the method of this hatching process.
The larva attaches itself and fixes its position in relation to the vitelline membrane.
Hach time the animal turns over it must necessarily straighten itself, and in so
doing the frontal gland touches the vitellme membrane, and smears it with a
little of the secretion of the frontal gland. The secretion is of a different nature
to the secretion of the cement organ; it acts upon the vitellme membrane and
softens it. The softened patch is distended by the pressure of the fluid in the
turgid ego, and the head of the larva sinks into the pouch which is formed. When
the frontal gland comes into contact with the vitelline membrane in the last
stages of hatching, the softening process is hastened, and when the larva’s head
is pressed against the pouched-out membrane, the fluid pressure in the ege must
act, not on the membrane, but on the body of the larva. The fact that the
softening process only goes on opposite the anterior surface of the head is shown
by the vitellme membrane retaining its normal curvature at all other points, even
so close to the head as opposite the neck (see figs. 174 and B).
To test the hypothesis that the secretion of the frontal gland acts on the egg
membrane, the following experiment was made. Four eggs out of six left
unhatched at 12 p.M. on 27th August were hung up, so that the long axis ay
(fic. 16) was vertical instead of horizontal, and the head of the larva uppermost.
By grasping with fine forceps a little of the jelly at the pole 2, and drawing it
out of the water against the glass of the tank, the eggs could be fixed in this
position. Of the four eggs slung up in this way, none were hatched at 6.30 P.M. ;
the two eggs left in the normal position hatched out the larve between 1 P.M.
and 2 p.m. At 6.30 p.m. the four eggs were returned to the normal position, and
within half an hour all were hatched. The larvae were thus prevented from
hatching for about five hours.
The reason appears to be this. When the egg is carefully revolved into the
new position, the larva remains attached, but slides down towards the pole y;
the head is consequently carried away from the egg membrane near the pole 2,
and when the larva moves, it is easy to see that the head apex, where the frontal
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. 809
gland lies, swings out away from the membrane and never touches it. There
was not the slightest bulging of the membrane opposite the head in the reversed
eggs.™
Regarding the action of the secretion of the frontal gland, there seems to be
reason to believe that it is digestive, and probably is due to a peptic ferment.
Miss R. Atcock (’91 and ’99) discovered that the external epithelium of the skin
in the Ammocetes of Petromyzon planert and in P. fluviatilis produces a peptic
ferment capable of digesting fibrin in a 02 per cent HCl solution. In the
frontal gland, then, a similar secretion is probably localised in an appropriately-
placed patch of epithelium, and the acid medium requisite for the action of the
peptic ferment is, no doubt, supplied by the excretion from the pronephros. But
it is not necessary to dwell on this poimt, as the specific action of the frontal gland
ean no doubt be tested by experiment.
It is obvious that the frontal gland is actively secreting at hatching time
from the coating of secretion which hardens on the surface of the gland in larve
preserved at this stage. The light band seen (fig. 15) running along the middle
of the gland is produced by coagulated secretion. After hatching, the frontal
gland begins to atrophy, and has disappeared three or four days later, before the
tadpole begins to feed.
Considerable morphological importance has been attached to the frontal gland by
von Kuprrer (’93, p. 78, 94 and ’03, pp. 188 and 190). He regarded it as the
“anpaarige Riechplakode” of the frog and uses it as evidence of a monorhine stage in
the development of an amphirhine form of Vertebrate, believing that it arises as a
sensory thickening of the ectoderm at the spot (the neuropore) where the brain retains
its connection with the ectoderm longest; the connection he considered to be the
primitive unpaired olfactory nerve. It would not be necessary to refer to this view
here if von Kuprrer had not repeated his interpretation of the ‘‘ Stirnknospe” in his
chapter on ‘‘ Die Morphogenie des Centralnerven-systems” in O. Hertwie’s “ Hand-
buch der Entwicklungslehre der Wirbeltiere.” In the same work Karu Prrer (’02), in
the chapter on ‘“‘Die Entwicklung des Geruchsorgans in der Reihe der Wirbeltiere,”
gives weighty reasons for rejecting von Kuprrer’s fascinating theory of Mono- and
Amphirhiny (Prerer, ’02, pp. 12-13, p. 26). Prrsr, in this chapter, refers to his own
paper on voN Kuprrer’s theory (01, p. 654), where he includes observations on Bufo
“emerea” (syn. B. vulgaris), showing that the ‘‘Stirnknospe” has in the toad no
connection with the neuropore and that it must be placed in a different category to the
sense-organs Of the Anura, since it develops from the external layer of the ectoderm,
while the sense-organs are all derived from the inner nervous layer (see also PeTErR, 01a).
CoRNING (’99) and Hinspere (01) have described the frontal gland in Rana temporaria
and f. esculenta, and it can be gathered from their descriptions and Prrer’s of the
3
* It has been possible to show by experiment on Hyla larve that the surface of the frontal gland only, and no ~
other part of the ectoderm, has the power when touching it to soften the vitelline membrane.—9th April 1904.
810 MR EDWARD J. BLES ON THE
toad that the gland is at the height of its development in each of the three species when
the larva reaches the size at which hatching occurs, and that it rapidly atrophies after
hatching. Its structure in these forms and in Xenopus is essentially similar.
The results arrived at on this subject may be summed up by stating that the main
function of the frontal gland in the Anura is to soften by means of its secretion the
tough and turgid egg membrane in order to allow the larva to escape at an early stage
of development before any external hard parts have been formed which might be used
for breaking out. The frontal gland is a transitory structure, like the ege-tooth of
lizards, and like it again only actively functional for a few minutes in the life of each
individual. Its interest is chiefly physiological, but it may serve as a warning to
morphologists of the danger run in assuming that an inconspicuous organ, the function
of which is not known, is vestigial.
The Larve after Hatching.—The first few days after hatching are spent by the
tadpole attached to weeds, etc. Its abdomen contains a considerable amount of
yolk which must be absorbed and the alimentary canal opened up before it can begin
to swim about and feed. This does not come about for a period varying between »
three days and a week in an aquarium kept at 22° C. The cement organ is
functional during the whole of this time. The tadpoles at this stage never lie on
the bottom of the aquarium, where, owing to their pale colour, they would stand out
conspicuously against the sediment. Those found on the bottom are prematurely
hatched younger larve. The secretion of the cement gland is extremely tenacious.
If a tadpole is induced to move, the mucus thread breaks away from the surface
of the sucker and the animal swims with a curiously stiff flickering wriggle, remarkably
like that of a young Ampioxus. For the first day or two after hatching a free-
swimming larva always tends to assume the vertical position with its head up, and
consequently the swimming movements carry it towards the surface. Another
physiological character tends in the same direction. Although not clearly discernible
at any given time in any particular individual, the larvee respond to light stimuli
in such a way that it could be put down to feeble positive heliotropism. If an
aquarium containing some hundreds is disturbed and the larvee scattered, the
great majority of them will, in twenty-four hours, be near the surface or on the
light side of the vessel; a few dozen, however, will be distributed at random. The
mucus from the cement organ is both very adhesive and very tough. Whatever
the cement organ touches it immediately becomes fixed to and the tadpole comes to
rest. This applies to so unsubstantial an object as the surface film. A 20-inch
bell-jar, four or five days after spawning has taken place in it, will have one hundred
to two hundred larvee hanging from the surface film in the position of the larva in fig. 19,
Plate III. The thread of mucus is of varying length, and may either be as long as or
rather longer than the larva. The surface film is, of course, drawn down into a slight
dimple by the weight of the animal. I have never seen any movement in an attached
larva, except when in the act of swimming away; it usually hangs down perfectly
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. 811
quiescent. A strong continuous current suiicient to sway them 45° from the normal
will not induce more than one in twenty or thereabouts to detach itself.
The most obvious changes during the first days of this phase are the darkening
of the pigmentation both of the eye and of the nasal pit, which both become more
conspicuous, the fin becoming wider, but only very gradually (cf. fig. 22a), and
three short unbranched external gills appearing on the three branchial arches. The
gill slits are closed. As the yolk is absorbed the larva becomes more and more
transparent, and at the same time the ciliation disappears part passu with the
yolk, except the ciliation in the nasal pits, which persists. As it becomes more
transparent the larva becomes more and more restless, and about four to six days
after hatching spends more time swimming about than hanging on by its cement
organ. At this time the mouth opens and the branchial current of water is set
up with its rhythmic action. By this time the operculum has grown back from
the hyoidean arch and fused in the mid-ventral region with the body-wall under
the pericardium to form the gill-chamber. The upper, lateral ends of the folds
remain free and form the ventral or outer lip of the spiracle on each side of the
neck. The spiracle at all stages opens upwards and backwards and is not produced
into a spout; the inner wall of the spiracle is the body-wall of the animal.
The mouth opens and the branchial respiratory current begins some hours,
probably about twelve hours, before the animal takes in food. It is easy to see that
the gut still contains a mass of yolk, and in sections the cesophagus is found to be
solid. Hxactly the same condition of things has been described in the common frog
(MarsHaLt and Buss, 90, pp. 223-4), with the difference that in Rana the branchial
chamber is not completely formed and that feeding begins after a much longer interval.
Drawings of the animal at this stage are given in figs. 22 and 22a. In the
front view of the head an attempt has been made to show the commencing transparency
of the tissues. It brings out clearly the fact’that the chromatophores of the skin
are confined to the dorsal surface; the ventral is free from them except in one
place to be referred to later. Covering the whole underside of the head there is
a large continuous lymph space, well marked off from the other lymph spaces, which
I propose to call the suwbmental lymph sac. Through its translucent walls can be
seen the ventral wall of the buccal cavity. The cement organ is at the extreme
tip of the head (see fig. 22a), and immediately above it is the mouth or rather
the lower jaw, still showing at the symphysis the junction of the mandibular arches.
At this stage the lower lip protrudes in front of the upper; this condition becomes
still more pronounced in older tadpoles, where the mouth opening comes to lie on
the upper surface. The ventral chromatophores on the skin of the mandible then
face upwards and become practically dorsal. This disposition of the mouth vanishes
at the metamorphosis and is apparently adapted to the peculiar feeding habits of
the tadpole. The oral tentacles have not yet made their appearance. Above the
mouth are the large shallow depressions of the nasal pits, with their well-marked
812 MR EDWARD J. BLES ON THE
raised rim incomplete behind. The median swelling behind the olfactory pits is
caused by the brain. The eyes stand out prominently from the side of the head.
In the side view there are very obvious alterations to be observed in the proportions .
of the parts of the animal. At hatching the tail was only one-third of the total length ;
it is now two-thirds, while the abdomen, which was very elongated, now appears very
short in proportion. The fin-fold has grown considerably, and has grown out from
below the abdomen, drawing out the cloaca, so that the cloacal opening comes to lie at
the edge of the fold. The pronephros tubules can be seen quite distinctly through the
transparent skin.
The Lymph Hearts.—Just behind the pronephros on each side is the newly de-
veloped lymph heart. It lies in a small lymph space immediately below the skin on a
level with the inner ccelomic outline of the pronephros. It can be best located in the
living animal by the movements of the nearest chromatophore of the skin, which, under
the microscope, are more conspicuous than the pulsations of the lymph heart itself.
Delicate trabeculze run across the enveloping lymph space from the heart to the integu-
ment, and these pull down the skin at each contraction of the heart. At this stage the
pulsations are very irregular; they sometimes cease for one or two minutes, and seldom
continue uninterruptedly for even twenty beats, hence it is dithcult to time them.
When most regular they average forty beats a minute.
This early appearance of the pectoral lymph hearts is after all not very remarkable
when the extent and physiological importance of the lymph spaces in the tadpole is
considered. However, the find was an unexpected one, as I had already paid a little
attention to the subject and found that the pelvic lymph hearts do not appear in &.
temporaria and Bufo calamita before the metamorphosis.
The Tadpole.—tIt is not ditticult to notice the commencement of feeding in a batch of
young tadpoles. Those which have not begun, only swim about fitfully and then hang
by the cement organ, the breathing movements continuing while they hang. Those which
have begun to feed are suspended in mid-water, making little or no progress, and are
steadily gulping away ; the feeces appear in the cloaca within twenty minutes or half an
hour afterwards ; thus the time at which the alimentary canal is open to the passage of
food can be easily and definitely fixed. This is important, because it makes the follow-
ing interesting fact easy to determine by watching at the correct time, namely, that
within two hours after beginning to feed the tadpoles rise to the surface for air and
begin to use their lungs as breathing organs. Brpparp observed that Xenopus does not
develop “internal” gills (94, p. 106) and concluded that respiration was carried on
through the blood-vessels of the “filters” placed on the internal side of the branchial
arches. His observations are correct, but as he paid no attention to the use of the lungs,
he was led to a conclusion which turns out to be of subsidiary importance. It is
possible that a certain small amount of oxygenation of the blood does go on in the pro-
cesses of the filtering apparatus. And until feeding commences respiration is carried on
by the external gills. But as the tadpoles are constantly rising to the surface for air
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. 8138
and do so more frequently the warmer the water is, it follows that the lungs are not
only hydrostatic in function but also respiratory. Reducing the quantity of water has
the same effect as raising the temperature. It is difficult to follow an individual
tadpole under normal conditions in a large aquarium, but isolated ones in small
aquaria will rise every five to ten minutes.
The tadpole shown in fig. 23 should be glanced at as an intermediate stage
before proceeding to the typical and final form. This specimen is in the condition
reached after about two days spent in feeding. During the first few hours feeding
may be interrupted now and then for a few minutes while the animal suspends
itself by its cement organ, then this organ begins to atrophy and by this stage
has completely disappeared. The snout has not yet assumed the characteristic shape,
which is seen one or two days later. Here it is rounded; but it is important to
note that there is no trace in this transitional stage of lips like those bearing the
horny teeth in ordinary tadpoles. W. K. Parker and Brpparp have already drawn
attention to the total absence of horny teeth. The pronephros and the lymph heart
are very clearly seen at this stage; the transparency of the tissues is still increasing.
The contents of the ccelom are, however, beginning to disappear from view, as the
chromatophores are rapidly increasing in the abdominal wall. The hind limb is. just
forming as a rudimentary bud. The tail has lengthened and its shape is quite typical.
A day or two later the appearance of the tadpole has undergone a very obvious
change. The shape of the snout becomes like that of the advanced tadpole shown
in fie. 24, Plate IV. It may be described as wedge-shaped, with the lower lip form-
ine the slightly curved edge of the wedge. The tentacles sprout exactly at the
angles of the mouth and soon become long slender processes. This stage is one
which persists for about two and a half months without any marked changes, apart
from the great increase in size and the growth of the hind limb. It is, therefore,
the typical larva of Xenopus, but for various reasons I must omit its full description
here and reserve it for a future communication. The chief reason for so doing is
inherent in the tadpole itself. It is so transparent in the head region that almost
all the complicated structure of the vertebrate head can be studied in the living
animal, and it would be necessary to give accurate figures to make all this clear
in a description. The difficulty lies in my inability to produce such figures, and,
as fig. 24 shows, the dead specimen allows very little internal structure to be seen. I
will confine myself to giving a brief account of the extraordinary feeding habits. The
tadpoles [ have reared (one male was brought to maturity) were fed exclusively until
the metamorphosis on pure culture of the green Flagellate Chlamydomonas. They
thrive best in water which is thick with the Flagellates. In this they float almost
vertically in mid-water, rapidly undulating the posterior third of the tail and at the
rate of forty to fifty a minute take in gulps of the water. The water passes out through
the spiracle ; the Chlamydomonas are retained by the filters in the buccal cavity and
drawn into a ciliated groove on either side of the pharynx. In this groove the green mass
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 31). 119
814 MR EDWARD J. BLES ON THE
can be seen passing back in a kind of helicoid vortex towards the cesophagus, where
the two green currents converge and disappear. very day for ten weeks fresh
culture must be added to the aquarium water; even so few as ten large tadpoles
will clear twenty gallons of water in a single day of one added gallon of thick
culture. When the water is clear they swim restlessly about like fish, as though
searching for food, taking a gulp every now and then, as if to test the water, and
then swimming on. As soon as fresh culture is poured in they immediately suspend
themselves in mid-water and commence egulping regularly. That the current of
water through the gill-slits is not kept up except when feeding confirms the state-
ment made above that it is not a respiratory current. This method of feeding is
so remarkable that it is desirable to find out whether it is normal in the natural
habitat. It is interesting that the only Craniate known to feed in a similar way
is Ammocetes ; according to A. SCHNEIDER its chief food is Huglena. In both cases
the food is filtered out and then collected in a ciliary current. Xenopus tadpoles
kept in Huglena culture were starved to death, however. Mr Brpparp’s tadpoles
fed on Cyprids and nothing else; mine invariably rejected any small Crustacean
which entered their mouths and starved amid an abundance of Ostracods and Cladocera.
The movements of the tadpoles, their way of taking in water, the ciliated bands,
the dorsal position of the mouth and the shape of the lips, all point to micro-plankton
being a staple item of their diet, quite apart from the fact that they thrived on
it. I would like to suggest that the swarms of Cyprids in the Zoological Gardens
Tank were feeding on micro-organisms which also formed the staple food of the
Xenopus tadpoles, the Cyprids being swallowed incidentally.
The Mature Tadpole.—Fig. 24 is introduced to supply a more detailed figure than
that published by W. K. Parker and copied in so many text-books. At the same
time it should be observed that this tadpole in one important respect, which is probably
diagnostic, differs from Parxesr’s. It will be seen that the long tentacles in fig. 24 are
given off from the angles of the mouth; in fact a groove from the Junction of upper and
lower lip is often continued up the base of the tentacle. Now, in all ParKer’s figures
the tentacles are given off above the mouth, from behind the upper lip. The species to
which Parker's specimens belong is, most probably, Xenopus calcaratus from Lagos.
The attitude of the tadpole in fig. 24 is that taken when swimming rapidly in a
vertical position to the surface of the water for air. The hind leg is stretched back, as
in a swimming Urodele, and the resistance of the water as it shoots up seems to sway
back the slender tentacles, usually directed straight forwards, into the position figured.
There are three points in connection with this stage still to be mentioned, regarding
the tentacles, the coloration, and the fore limb.
Brpparp mentions that he “ more than once observed the tentacle of one side to be
bifid.” This I found to be quite frequent among a limited number which reached this
stage (length of 60 mm.); out of eight specimens, six had both tentacles branched. —
Four of these, picked at random, are reproduced here. It will be seen that in A, B, and
LIFE-HISTORY OF XHNOPUS LAVIS, DAUD. 815
RIGHT SIDES LEFT SIDES
TExT Fie. 3.—A, B, C, and D. Tentacles of the right and left sides of four Tadpoles
(Xenopus levis) about 60 mm. long.
816 MR EDWARD J. BLES ON THE
D the right and left tentacles are symmetrical as far as the general arrangement of the
branches is concerned, but the position and sizes of the branches differ on the two
sides, so that the symmetry is very imperfect. In C the right tentacle has a secondary
branch on its backwardly directed fork which is not represented on the left side.
Branched tentacles have only been found in the late tadpole stages over 50 mm. long,
As BouLrencEr pointed out (footnote to LEsiiz, 90), the tentacle of Xenopus may
be homologised with the balancers of Urodele larvee. These must be the representa-
tives on the mandibular arch of the external gills on the branchial arches. If these
homologies are correct, the tentacle in Xenopus is an external gill, and this conclusion
is supported by the fact that from its very earliest appearance it has a capillary loop
doubling into it, supplied from the dorsal end of the first branchial aortic arch. The
branches figured above are, on this hypothesis, the result of a tendency to branch ma
persisting gill similar to that found in all external gills which persist for some time
during the life or, as in Proteus and Siren, for the whole of the life of the individual.
In the last two animals the tendency to form branches and secondary branches is
especially well marked. If the branching is put down to regeneration after injury, how
is the bilateral symmetry to be accounted for ?
Coloration.—A most remarkable feature in the behaviour of the chromatophores is
found in tadpoles of 15-18 mm. and onwards. As is not uncommon among tadpoles, the
dark chromatophores on the head and trunk contract at night into spherical masses, but
what is most unusual, if not at present unparalleled in any vertebrate, is the fact that
other chromatophores, apparently of the same nature, namely, those in the distal half of
the tail, expand at dusk as the others are contracting.
The end of the tail, which in the day-time is so transparent that the presence of
chromatophores would never be suspected, becomes, to the naked eye, jet black after
nightfall. The expansion takes place in the chromatophores in the fin-fold, but not in
those on the myotomes of the same (distal) part of the tail; the latter contract at night
in harmony with those in the trunk region and anterior myotomes of the tail. The
general effect is well shown in fig. 24, although the contrast is much stronger in the
living animal, where the pale regions become of glassy transparency. The explanation
is, I believe, due to a need for protective colouring in the transparent part of the tail
tip. Itis kept undulating constantly ; in the daylight it needs no pigmentation —it is
protected by its transparency ; but the refractive stellate cells of the mesenchyme in the
fin-fold would at night be lable to catch and reflect any stray light rays, and the ex-
panded chromatophores effectively prevent this. Moreover, they are absent in the part
of the fin-fold which does not move actively. But when the physiology of the case is
considered it seems to make the solution of the problem of control over the pigment cells
more dificult than ever. Taking tadpoles from daylight into a darkened room has the
same effect as the changes from day to night.
In figs. 20 and 21, Plate III, the appearance of the skin is shown under the microscope
of the part of the tail marked with a cross in fig. 24, in a specimen killed in the daytime
LIFE-HISTORY OF XENOPUS LAVIS, DAUD. 817
(fig. 20) and one killed during the night (fig. 21). The pale brown network in fig. 20
suggests, by the sharp double outlines occurring in many places, the presence of inter-
cellular passages into which the chromatophores expand radially and leave pigment
granules behind adhering to the walls of the passages.
The Fove-limb.—In fig. 24 the fore-limb is seen lying under a transparent patch of
integument, and in fig. 25 this region is shown magnified in a slightly older larva.
Here the arm has burst through the thin wall of the sac, the edges of which are still
present, and it can be seen that the wall of the branchial chamber immediately in front
of the arm-sac is intact, nor is the spiracle affected in any way. This is probably what
PARKER was referring to when he stated, ‘“‘ The fore-limbs are not hidden beneath the
opercular fold” (ParKeER, ’76, p. 626). The explanation of the difference between
Xenopus and the more familiar tadpoles is that in the latter the fore-limb develops
a diverticulum of the gill-chamber which remains in communication with it, so that the
developing arm protrudes into the branchial space ; i Xenopus a similar diverticulum
is formed, which becomes completely shut off from the gill-chamber, and the arm cannot
encroach on that space. The arm emerges in the common frog by breaking through the
wall of the branchial chamber on the right side and by passing through the spiracle on
the left side, blocking up this passage completely. The appearance of the arms there-
fore in typical tadpoles sharply marks the abrupt cessation of branchial respiration. In
Xenopus the arm appears by the rupture of what may be called the “ brachial sac.”
This event in no way interferes with the habits of the tadpole. It remains floating in
mid-water in the same position as before, taking in water at the mouth and passing it.
out by the spiracles, these being, as shown in fig. 25, Plate IV, quite unaffected by the
protrusion of the arms. In fact the branchial current is used here not for respiration,
but for nutrition, and is not interfered with during the metamorphosis. The main
part of the change into the adult condition is very gradual, and feeding can be
continued almost without a break while it is goimg on.
Metamorphosis.—The metamorphosis is completed ten to twelve weeks after
fertilisation, in a constant temperature of 20° to 22° C. At this temperature the
whole change from the mature tadpole into the tailless frog is passed through
in about 15-20 days, but I have no doubt that in its native African pools the
temperature in the late spring will be much higher’ and the metamorphosis
correspondingly much more rapid. The commencement of the metamorphosis is
well marked by the protrusion of the arms, the beginning of co-ordinated swimming
movements of the legs, and the first appearance of blood-vessels across the width
of the fin-fold of the tail. It is a remarkable fact that until this time the whole
of the fin-fold is completely non-vascular. The usual sub-vertebral vessels are of
course present and supply the tail-myotomes, but they give off, until this period
of development, no vessels into the fin. The space between the two bounding
layers of integument is filled with a loose trabecular tissue composed of stellate
mesenchyme cells, the interstices of which seem to be filled either with fluid or
818 MR EDWARD J. BLES ON THE
with a gelatinous matrix. It was not possible to make out any circulation of
lymph or movement of lymph-corpuscles in the tail fin. The first capillaries appear
near the tip of the tail, and they spread towards the proximal parts, becoming —
more and more numerous as the time for the resorption of the tail approaches ;
thus obviously raising the suggestion that the process of resorption is carried on
by methods connected with this vascularisation. The tail is not used for the respira-
tory function.
The limbs now grow rapidly. The arm rotates from the shoulder-joimt through
90°, and about forty-eight hours after protrusion has left the position shown in fig. 25,
Plate IV. (where the arm hangs down in a plane at right angles to the long axis of the
animal) for the adult position: namely, directed forwards towards the mouth and
lying in a horizontal plane parallel to the long axis. At first the arms are ridiculously
out of proportion to the size of the head; they have lagged behind in development
very considerably. The deficiency is made up in three weeks, and by the end of
the metamorphosis the length of the arms is such as to allow of the fingers just
meeting in front of the head. The legs are developed in the primitive fin position,
and, apart from the bending of the limb, are kept in this position throughout life.
Soon after the stage of fig. 23, Plate IV, where the leg is still in the primitive position,
the thigh is swung round at the hip-joint until it stands out at right angles to
the body ; the knee-joint is bent so that the tibia remains parallel to its original position,
and the ankle is bent so as to turn the foot out through 90°, the sole facing backwards
instead of inwards. These changes go on during the three days after the arms
emerge; at the same time the black claws appear on the three preaxial digits, some
weeks before they come into use. The legs now assist the tail quite efficiently in
swimming, and grow rapidly, especially the feet.
The colour of the skin changes gradually in character. Fig. 24 still shows
the tadpole coloration; two to three weeks later the adult coloration had been
assumed, and then the whole creature becomes a strange mixture of larva and
adult. The whole habit is larval; the creature still swims in mid-water in an
upright position; there is a long tail, mouth and tentacles are unchanged, spiracles
are present, but the body itself, in shape and colour, and also the appendages,
are adult in character. In two days after this condition is reached (about fourteen
days after the arms emerge) the tentacles have almost disappeared, and then the
mouth very quickly transforms from the larval to the adult state. The whole
process is finished in four to six hours. When the tentacles are very much
shrunken, the angle of the mouth, where they were attached until now, seems to grow
back under them; the gape of the mouth is consequently widened, and at the
same time the stumps of the tentacles become dorsal to the mouth. A minute
basal part of the tentacle persists throughout life in Xenopus levis, As the
mouth metamorphoses the spiracles close up.
Immediately after the mouth has transformed, the tailed frog ceases to keep
LIFE-HISTORY OF XENOPUS LA:VIS, DAUD. 819
constantly to its larval free-swimming habits, and spends more and more time
lying on the bottom. At this time the tail has begun to atrophy, the blood-
vessels in the fin spread, the notochord at the tip becomes wavy, and the pigmenta-
tion darkens. At the end of a week the greater part of the tail is absorbed;
about one-third of it is left, very deeply pigmented, and the young frog has thus
reached the stage at which the typical Phaneroglossan lands and becomes terrestrial.
There is not the slightest tendency to land in the case of Xenopus. It swims
about actively in search of food, and for some weeks lives on small, free-swimming
Crustacea. Seven specimens reared to this stage consumed enormous quantities
of Daphma pulex; a great swarm of these vanished every twenty-four hours, and
the frogs throve.
Their hands are at once used in the grown-up manner to cram the food into
their mouths; the arms are not used for progression at all, except to push aside
water-weeds—hence one of their functions as limbs has almost disappeared. The
size of the arm is altogether out of proportion to the size of the leg, which is an
extremely powerful swimming organ. The limbs of Xenopus as a frog are paralleled
by the limbs of Macropus as a marsupial.
When W. K. Parker (76) described the skull in larval Xenopus, he laid
stress upon what he considered Chimeroid features in the chondrocranium, and
was naturally led to attach morphological importance to the lash-like tail end of
the Xenopus tadpole. Now, although this close resemblance does not exist, there
is a certain degree of resemblance which suggests similarity of function. The end
of the tail of the Xenopus tadpole has a very narrow dorsal and ventral fin-fold
(see figs. 23 and 24, Plate IV), and it is easy to see in the living animal that
the constant undulatory movement of this narrow membrane has very little
propelling power. The suggestion is, then, that the Xenopus tadpole, Chimera,
and such fishes with a narrow lash-lke tail end as the Mormyride, use that part
for suspending themselves either in mid-water or, in the case of bottom - feeders
or mud-feeders, just over the bottom, by means of a rapid undulatory movement.
Sexual maturity appears to be reached at an early age. One male was kept
until two years old, when it began to pair.
820 MR EDWARD J. BLES ON THE
TITLES OF THE PAPERS, ETC., REFERRED TO IN THE TEXT.
Atcock, R., “On Proteid Digestion in Ammocetes,” Proc. Camb. Phil. Soc. 1891.
Aucock, R., “On Proteid Digestion in Ammocetes,” Journ. Anat. and Phys., vol. xxxiii. pp. 612-637.
1899.
Bepparp, F. E., “‘ Notes upon the Tadpole of Xenopus levis (Dactylethra capensis),” P.Z.S., 1894, pp. 101-
107. Plate XIII. 1894.
Buss, E. J., ‘‘ On the Breeding Habits of Xenopus levis, Daud,” Proce. Camb. Phil. Soc., vol. xi. pp. 220-222.
Two figures in text. 1901.
Cornine, H. K., “ Ueber einige Entwicklungsvorgiinge am Kopfe der Anuren,” Morph. Jahrb., Bd. xxvii.
p. Loz) 1899:
Eycursuymer, A. C., “The Development of the Optic Vesicles in Amphibia,” Journ. Morph., vol. viii.
1893.
Hertwie, R., “ Hireife und Befruchtung.” IItes Kapitel. Handb. d. vergl. und exp. Entwick. lehre der
Wirbeltiere, p. 534, 1903.
Hiyspere, V., ‘“‘Die Entwicklung der Nasenhohle bei Amphibien,” Arch. f. mikr. Anat., Bd. lviii.
pp. 414-419, pp. 425 and 436. 1901.
Kammerer, P., “Beitrag zur Erkenntniss der Verwandtschaftsverhiltnisse von Salamandra atra und
maculosa,” Arch. f. Entw. mech. d. Organismen, Bd. xvii. pp. 165-264. 1904.
Kuprrer, K. von, ‘Studien zur vergleichenden Entwicklungsgeschichte des Kopfes der Kranioten.”
1 Heft: “Die Entwicklung des Kopfes von Acipenser sturio,” p. 78. 1893.
—— “Ueber Monorhinie und Amphirhinie,” S. B. d. math. phys. Kl. Akad. Wiss. Miinchen. 1894.
—— ‘Die Morphogenie des Centralnervensystems,” Handbuch d. vergl. und exp. Entwick. lehre d.
Wirbeltiere, Bd. i. Abth. 3, pp. 188-190. 1903.
Lusuiz, J. M., ‘‘ Notes on the Habits and Oviposition of Xenopus lewis,” P.Z.S., p. 69. 1890.
Marsuatt, A. M., and Buns, E. J., “The Development of the Blood-Vessels in the Frog,” Stud. Biol, Lab.,
Owens College, Manchester, vol. 1. 1890.
Morean, T. H., “‘ The Development of the Frog’s Egg.” New York and London. 1897.
Parker, W. K., ‘‘ On the Structure anil Development of the Skull in the Batrachia,” Part I1., Phil. Trans.,
vol. elxvi. p. 601. 1876.
Purmr, K., ‘‘ Mittheilungen zur Entwicklungsgeschichte der Eidechse. III. Die Neuroporusverdickung und
die Hypothese von der primiiren Monorhinie der amphirhinen Wirbeltiere,” Arch. f. mikr. Anat.,
Bad. lviii. p. 643. 1901.
— ‘Der Einfluss der Entwicklunesbedingungen auf die Bildung des Centralnervensystems und der
Sinnesorgane bei den verschiedenen Wirbeltierklassen,” Anat. Anz., Bd. xix. 1901a.
—— “Die Entwicklung der Geruchsorgans und Jakobson’schen Organs in der Reihe der Wirbeltiere,”
Handb. d. vergl. uni exp. Entwick. lehre d. Wirbeltiere, Bd. ii., Abth. 2, p. 12 and p. 26. 1902.
ScHaurnstanp, H., “ Die Entwicklung von Xenopus capensis,” Verh. d. Ges. deutsch. Naturf. und Aerzte.
63 Vers. zu Bremen. 1890.
(This paper is omitted by Brpparp, and I have not seen it.)
Semper, C., “ Ueber eine Methode Axolotl-Eier jederzeit zu erzeugen,” Zool. Anz. I. Jahry., p. 176. 1878.
EXPLANATION OF PLATES.
Puate I.
Xenopus levis, Daud. Segmentation stages, blastopore formation, medullary plate, and early embryo,
All figures on this plate numbered alike are drawn from the same egg, and figs. 1-9 are magnified x 28°5.
Fig. 1. Unfertilised egg.
Fig. 2. Egg with eight blastomeres, seen from the right side,
Fig. 24. Seen from below.
Fig. 3. Egg with about thirty-two blastomeres, seen from anterior side.
LIFE-HISTORY OF XENOPUS LAEVIS, DAUD. 821
Fig. 3a. Seen from below.
Fig. 4. Early blastula stage.
Fig. 5. Late blastula stage.
Fig. 6. Egg with early stage in the formation of the blastopore. The egg is in its natural position, and
is seen from the right side.
Fig. 64. The same stage seen from below.
Fig. 7, Stage showing circular blastopore with large yolk plug.
Fig. 8. Stage with open medullary groove, seen from behind,
Fig, 8a. The same stage seen from before.
Fig, 9, Stage after closure of medullary groove.
Fig. 10. Embryo, 3 mm. long, taken out of egg. (x 25.)
Fig. 104. Anterior end of the same embryo viewed in the direction of the arrow in fig. 10. (x 48.)
Puate II.
Fig. 11. Ege deposited on a leaf of Myriophyllum proserpinnacoides. ( x 6.)
Fig. 12. Embryo, 3°2 mm. long, in vitelline membrane ; the jelly surrounding this has been stripped off.
Drawn from life. (x 25.)
Fig. 13. Embryo, 3°8 mm. long, taken from egg. Drawn from life. (x 25.)
Fig. 14. Embryo, 5 mm. long, taken from egg. Drawn from life. (x 25.)
Puate III.
Vig. 15. Head of larva just hatched, seen from before, in the direction of the arrow in fig. 15a. (x 60.)
Fig. 15a. Outline of larva, 5 mm, long, just hatched, seen from side, ( x 15.)
Fig. 16. Larva, 4°5 mm. long, lying in the egg attached to the vitelline membrane by the cement organ
before hatching commences ; the larva is seen from the ventral side. The layer of jelly outside the vitelline
membrane is omitted. (x 11.)
Fig. 17. A, B and C, Head of larva during process of hatching, to show the yielding vitelline
membrane. A., 8’ 15” before hatching. B., 3’ 15” before hatching. C., 15” before hatching. (x 12.)
Fig. 18. The position of the same larva when it emerged from the egg. The vitelline membrane has
shrunk and caught the tip of the tail. (x 10.)
Fig. 19. The same larva as in figs. 17 and 18, as seen a few seconds later, hanging by a thread of
mucus to the further shrunken vitelline membrane. ( x 10.)
Fig. 20. Portion of the skin of the tail-fin of a tadpole, 62 mm. in length, killed during the daytime:
from the middle of the length of the tail. (x 170.)
Fig. 21. A corresponding portion of the tail-fin of the tadpole drawn in fig. 24, which was killed at
night. (x 170.)
Puate LV.
Fig. 22. Anterior view of the head of a larva 10 mm. long. The stage reached is a few hours earlier
than that at which the animal begins to feed. (x 33.)
Fig. 22a, Outline sketch of the same larva as fig. 22 in side view. (x12.) (From a formalin
specimen. )
Fig. 23. Side view of a tadpole 12°4 mm. long, which has fed for two days. (*11.) (From a
formalin specimen.)
Fig. 24. Side view of a tadpole, 60 mm. long, with the arm not yet extruded. Drawn in the position
in which the rapid ascent to the surface is made to obtain air, (x 3.) (From a specimen killed at night
and preserved in alcohol-formalin-acetic acid mixture.)
Fig. 25. The left pectoral region of a tadpole, 62 mm. long, slightly older than that shown in fig, 24,
to show the extruded arm and the spiracle into which a style has been passed. (x 13.) (Preservation as
described above, fig. 24; killed at nightfall.)
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 31). 120
\"
| Bles: Life History of Xenopus laevis. Plate I
SErCUES thy
ectoderm.
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neural groove.
cement organ.
al
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. Bles; Life History of Xenopus laevis. Plate II.
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Trah@!Roy. Soe Edin? Vol XLI:
15 16
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AIX SoV
ee a
Eijs. Mic fistery of Xenopus laevis. Plate Il
rans. Roy. Soc, Edin™ Mol. XU.
Werner &Winter lith. Frankfort °M
Life History of Xenopus laevis. Plate IV
Bles.
‘SUDLLO BSUBS UIYS
‘qqop.nds our passad ajARs
/ ;
UPUOPQM Jo]
Vol .XLI.
peas P)0f UL. \-Ppeunds —_—
2n+3 1—w"
That is,
| Ron +1 |< | Tones | /Q = w?) . . U : O o (15).
In like manner,
Ee eaneee (iia seen tte Ey TU wl P trode Sate),
Similarly, if we write
Wigan = 4 Re
where ihe = B,2"/n ’ (17)
Beco)... 2. (1-1/(n—1)n), : edi 3
B,=¢,
then we can show that
etea aul (ea cy Ae eo MUGS):
The formulee (15), (16), and (18) enable us to estimate the accuracy of the approximation
obtained by taking any given number of terms of the respective series. It is obvious
that the formule (9), (10) are most convenient for nodes near the deepest part of the
lake ; and (11), (12) most convenient for nodes near the ends. In most of the calcula-
tions tabulated below the equation L/(c, z)=0 is used; but in many cases we verified
our results by working with the other formule as well. Other things being equal, the
formule (11), (12) have an advantage, in respect that tabulation of the steps for the
calculation of B is one continuous operation, and there is less chance of error by in-
advertence in the entries.
§ 12. As for the periods, so also for the nodes we get first approximations by taking
the mean between the extreme cases of a complete symmetric parabolic lake and a
semiparabolic lake. As might be expected, these first approximations are not so close
for the nodes as they are for the periods. Fortunately the series are very manageable.
If we denote the vertical seiche displacements at the Western end, deepest
TRANS. ROY. SOC, EDIN., VOL, XLI. PART III. (NO. 32). 122
832 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
normal point, and Eastern end of the lake by (, G@, , respectively, we see from
H.T.S. § 39 that
AC(¢, 1) _: oes ;
“Se, 1) sinnt, Ly ase, 1) sin mt . : ; (19).
A :
Hence, if we bear in mind the values of ¢ and c’ corresponding to the first three pure
seiches, we get the following table of relative signs :—
by ai im
Uninodal : : : - = ae
Binodal . ‘ : ; St ae
Trinodal : 4 : = ab a
We infer that the uninode is east of O; that the binodes are on opposite sides of O;
and that there is one trinode west of O, and two east of O.
§ 13. Uninope or Earn. (Hast of Deepest Normal Point.)
We have taken T, = 14°50’, c= 3°5785.
Coetticients of L’(3°5785, z).
c Cc . B,
= [ey — et o (os
2 log( 1 5) logB, | log =
1 log ¢ |= *D5370
2| 7893 T-39724 55370 | °55370
3| 4036 160595 45094 | -14991
4| -7018 T-84621 | 05689 | 157977
5| “8211 191440 | T-90310 | 1-30104
6 | -8807 194483 | 181750 | T-11853
7| -9148 196133 | 176233 | 3-98418
8 | 9361 197132 | 1-72366 | 3-87856
9} +9503 97786 | 1-69498 | 5-79189
10) -9603 198241 | 1-67284 | 3-71860
11] -9675 98565 | 1-65525 | 365595
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG. 833
Value of L/(3°5785 , °32).
n log = log 2” log T,, 2 qT,
0 1:00000
i “55370 1°50515 ‘05885 1°14513
2 "14991 1:01030 1:16021 14461
3 L:57977 2°51545 2:09522 01245
4 1°30104 2-02060 3:32164 | -00210
5 1:11853 352575 4:64428 00044
6 2°98418 303090 401508 ‘00010
if 2°87856 4:53605 5°41461 ‘00002(6)
8 | 2:79189 4:04120 6-83309 ‘00000(68)
9 | 3:71860 554635 6° 26495 00000(18)
10 | 9:65525 5:05150 7°70675 | 00000(05) |
Series error < ‘000008 1:15974 114513
Hence L(3-5785 , °32) = +-01461.
Calculating in like manner for z= °325 and z= °33, we get the following values :—
z I'(é <2) Diff.
320 | +:01461 | ‘01254
325 | +:°00207 | -01248
*330-| —-01041
Interpolating, we find ,z, = "3258; and therefore ,w,=°3484. It follows that
10 = 3484 x 145°5 x 480,100 sq. ft.
= 50°7 x 480,100 sq. ft.
and 1, = 25°24 x 692-9 ft.
§ 14. HastERN BINoDE OF Harn.
T=814’, C=11°3541.
Coefficients of L/(11°3541, 2).
Cc Cc B,,
hat “na — 1) ie ( : n(n — a) log, log n
1 log c= 1:05515 1:05515 1:05515
2 46771 66998 1:72513 1:42410
3 | 8924 1:95056 167569 119857
4 0538 3-73078 ‘40647 180441
5 4323 163579 04226 1°34329
6 6215 1:79344 1:83570 1:05755
a °T297 1:86314 169884 2°85374
834
Value of Li(11°3541 , “117).
PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
13}.
7 log 3 log 2” log T,, mn! Th
(0) 1:00000
1 1:05515 T:06819 12334 1°32843
2 1:42410 2'13637 156047 36347
3 1:19857 3°20456 2-40313 02530
4 1°80441 427274 407715 °00019(4)
5 134329 5°34093 668422 ‘00000(5 )
6 1:05755 640912 7°46667
Series error <:000006 1:36347 1°35393
Hence L’(11°3541 , 117) + =°00383.
Calculating in like manner, we get the rest of the following table :—
a Le, 2) Din. tor 00
“117 | +°00951 00568
‘118 | 4+ -00383 -00570
120 | —:00757
Hence pe le.
3, = 7627.
9¥_ = 111°0 x 480,100 sq. ft.
oly = 39°05 x 692°9 ft.
S15. Western Binopr or Earn. (West of Deepest Normal Point.)
re eG == Osi ie
Coefficients of 8’(2°3011, w).
» Gee, hf ap ie oO => c ) o o Avy,
2n I~ Ge 9) (Gn = 1))!°8\1 (an —2)(2n—1)) | 198 Am | 18 9,
2 log ¢|= 36194 36194 | “06091
4 3835 178993 "15187 | 154981
6 ‘1151 194689 09876 | 1°32061
ON THE PERIODS AND NODES OF LOCHS EARN AND
Value of S’(2°3011, -09).
2n | log = log w*” log Ti, i To
0 litte cS 1:00000
2} 06091 | 3:90849 | 3:96940 00932
4} 154981 | 581697 | 5°36678 “00002
6 | 1:32061 | 772546 | 7-04607 °00000(01)
Series error < ‘009001 1:00000 | °:00934
S/(2°3011 , 09) = + 99066.
Coefficients of C’(2°3011, w).
,
(S)
In+1 | In
Batis ceg| | (aa) log Ay. 41 | log 22
Q@n—1)9n | °8\" ~@n—1y2n)| C8 | 8 an I
1 log c|/= -36194 36194 | _°36194
3 *1506 117782 153976 | 1:06264
5 8082 1:90752 144728 | 2:74831
|
Value or C/(2"3011, 09):
(9) o Aan o 2n+1 o Tae es
2n +1 | log TTI log w log Ty,44 i i
1 _°36194 3:95494 Ik 31618 ‘20710
2 1:06264 | 4:86273 5°92537 | °00008
5 2°74831 | 6:77121 | 751952 | -00000(03)
Series error <‘000001 ‘00008 20710
C’(2'3011, -09) = — 20702
(09) = — 99066 x -21271 + 20702 = — -00370.
In this way we get
w g(w) | Diff. for 001
09000 | —-00370 | 00235
09192 | +-00080 | 00235
"10000 | + -01970
9, = 0916.
¥; = 600 x 480,100 sq. ft.
g@ = 13°98 x 692°9 ft.
835
836 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
my
16. Mippie TRInoDE oF Harn. (Kast of Deepest Normal Point.)
T, = 5°743', c= 22'8123.
Coefficients of L'(22°8128 , z).
| Cc ¢ b,
vie i ~n(n— 1) log( 1g = 5) log B, log n
1 loge|= 1°35817 1-35817 1°35817
2| 10°4062 101729 2°37546 2°07443
3 2°8021 “44748 2°82294 2°34582
4 "9010 195472 2°77766 2°17560
5 1406 114799 1°92565 1°22668
6 2396 137949 130514 52699
7 4569 1-65982 96496 11986
8 5926! 177276 73772 183463
9 6832 183455 57227 161803
10 7465 187303 44530 1-44530
oh 7926 | T-89905 34435 130296
12 "8272 191761 26196 118278
13 8538 193136 19332 107938
Value of Ii(2)78i123,, 25),
n i be Ty
n log aa log 2” log T,, be bag
0 1:00000 570310
1 1°35817 1°39794 ‘T5611
2 2:07443 279588 ‘87031 7°41840
3 2°34582 219382 53964 346450
4 217560 359176 1:76736 *H8528
5 1:22668 4:98970 2:21638 01646
6 52699 4:38764 491463 "00082
ih "11986 578558 590544 00008
8 1:83463 5:18352 5:01815 ‘00001
9 161803 658146 619949 -00000(16)
10 1-44530 7-97940 742470 00000(026)
Series error< ‘0000004 9:00368 9:18497
Therefore L'(22°8123, °25) = — *18129.
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG.
Continuing the calculation in like manner, we get—
ae | Iui(e, 2 | Diff. for :01
4 |
lll tex ‘18129 | -04077
29 | ~-01822 | -04023
30. | 02200 |
Hence gto = “2945.
a= ‘4110.
3%) = 99°81 x 480,100 sq. ft.
gto = 27°14 x 692°9 ft.
Nel7. HASTERN TRINODE OF Harn.
T=5°743', c=22°8123.
The Coefficients of L’(c, z) are the same as for the Middle Trinode.
Value of L/(22°8128 , -06).
loo B, log 2” aa T, qT,
n oS 0g z log T,, i Zs
0 100000
1 1°35817 2-77815 *13632 1°36874
2D 2°07443 3°55630 1:63073 | 42730
3 | 234582 | 4:33445 | 9-68097 | 04789
4 2:17560 5'11261 3:28821 00194
5 1°22668 789076 511744 00001(3)
6 ‘52699 8°66891 719590 00000(016)
7 11986 9:44706 9-56692
Series error < ‘0000002 1:42924 1:41664
L'(22°8123, -U6)= + 01260.
We find the following values in like manner :—
z Iai(es 2) Diff. |
060 + 01260 01075
061 + 00185 01062
062 — 00877
Therefore a@, = 06117.
3, = 8777.
323 = 127°7 x 480,100 sq. ft.
gig = 43°1 x 692°9 ft.
837
838 PROFESSOR CHRYSTAL AND MR E, MACLAGAN-WEDDERBURN
§ 18. Western Trrnope or Earn. (West of Deepest Normal Point.)
T,=5°743', c= 4°6280.
Coefticients of L’(4°6230, z).
Cc os ‘ =. Ba
m |INaop | el~agen) | 88. Bie
1 log ¢'|= 66492 66492 66492
2 13115 ON a ee ‘78269 _°48166
3 "2295 1:36078 14347 166635
4 6147 1°78866 1:93213 1:33007
5 ‘7688 T:88581 T:81794 1:11897
6 8459 T:92732 1:74526 2°96711
7 8899 T-94934 169460 384950
§ | “9174 1:96256 1°65716 2°75407
Value of L’'(4°6230, °25).
B ry.
n log a log 2” loge, He t
0 | 1-00000
1 66492 139794 | _'06286 1:15574
2 48166 2-79588 | 1:27754 18947
3 1°66635 3:19382 3°86017 ‘00725
4| 433007 3:59176 792183 | -00084
5 | 111897 798970 4-10867 00012(8)
6 296711 438764 535475 00002(3)
7} 3-84950 578558 | 6 -63508 -00000(4)
8 275407 HalSso2° 1" i 9ato9 00000(09)
Series error < 000002 119771 1:15574
Hence L'(4:6230, -25) = + :04197.
Calculating in the same way for z= ‘275 and z= 300, we get the following table :—
z L'(c’, 2) Diff.
"250 + 04197 ‘07289
"275 — 03092 06847
“300 — ‘09939
Therefore 3% = 2644.
3W, = °4712.
3U, = 30°87 x 480,100 sq. ft.
gt = lib x G92 Ott,
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG. 839
§ 19. Data For Locu Treic.
| |
r v o oa
oe Bid Unit Unit Unit a a2 Unit
ite 2 3465 | 7744 x 102 106 OS
‘ Feet. | Sq. Feet. | Cub. Feet. Cub. Feet.
0 0:0 24:47 0 0000 | -0000 0
1 2:2 22°73 239 1370 70188 | 33
2 6:0 18°34 972 4382 1920 426 a=4814 x 104
3 9°8 13°26 1804 “7064 4990 1274 Gi) = WSS) sx IO
S. Trinode | [12:2] [9°37] | p=a/a =2°5403
4 | 13°8 6:79 2227 | -9230 | 8519 | 2056 | p2=6-4529
5 | 181 0:00 2704 1:0000 | 1:0000 2704 log p= "40488
S. Binode | [187] | [0-89] | h= 2507 x 108
Galei22:3e i) eG Lh 2568 | “9903 | -9807 2543
W262 11°47 2307 9660 9332 222
5 29:5 S10 - 15:96 2201 ‘9340 8724 2056
9 | 34°6 22°36 2357 8706 SAY) 2052
Uninode | [35-6] [23°61] |
INO) || aksir/ 27°64 1831 8023 6437 1469
Mid. Trinode | [39:2] [28:03]
ll | 42:0 31:24 1772 “TATA 5586 1325
12 | 43-9 33°75 1816 “7051 “4972 1281
13 | 46:9 37°84 2067 6293 3960 | 1301
14) 51:1 42°72 1394 D266 Ohne |) 734
15 | 56-4 48°20 773 3989 "1591 308
N. Binode | [56-7] [48-40]
16 | 60:0 50°98 440 *B274 1072 144
17 | 64:3 54:40 626 2340 0548 147
N. Trinode | [65-2] [55°12]
18 | 68:3 5T D7 297 1420 "0202 | 42
WE) (eh 59°43 138 0858 ‘0074 | 12
AO) 12 60°28 107 0594 0035 6
21 | 75°8 61°40 43 0240 0006 1
22 | 776 61°83 24 0105 ‘0001 0
23 | 78:0 62°16 0 0000 0000 0
. h=Zoa/Za? = 25072 x 105 88316 22143
Periops oF Locu
TREIG.
§ 20. A few rough trials shew very readily that the uninodal period of the lake is
nearly 9’. Using the method already explained for Harn, we derive the following table
of first approximations :—
| !
| a a6 | Te
| Parabolic . ; : . | 9:00 5:19 | 3°67
| Semiparabolic . : = || S0X0) 4-93 3°40
eq ei O00" | 95.064.) 3°54
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO.
32).
123
840 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
Taking T, = 9°00, T, = 5:06, T, = 3°54 as a basis, we proceed exactly as in the case
of Earn, and the results are given below.
§ 21. After the calculations had been made, it was found that the shrinkage error of
the 6-inch ordinance map of the lake, on which the soundings were plotted, was not
negligible. It amounted, in fact, to about °5 per cent. As the areas v were measured
with a planimeter, and the breadths b(#) with an absolute scale, the linear error 6A/A
enters twice into v, once into b(«), and once into A(x).* The values of a in the table
on p. 839 are unaffected, and p=«a/a’ is also unaffected by this error. But da/a=200/,
dh =20/A. Since the values of ¢ and c’ depend merely on p, we have (H.T.S.(45) )
@T/T =ea/a— 4eh/h =0r/r. (20).
Hence, to correct for the map error, we have to multiply each of the periods obtained
from the data of the table on p. 839 by the number i:005.
§ 22. Uninopau Perriop or TREIG.
|
r ¢ a | RG+a)) HG-a) |43+a)| 43-0) | Kiel)
eee
9:05 | 38433] 4-0464 | 2:2616| -2384 17616 | —-2616 | —1-98857
9:10 | 3°8012| 4:0255 | 22564} -2436 17564 | —-2564 | -1-91295
9-15 | 3°7598 | 40049 | 22512 | -2488 T7512.) = 2519 deed oles
a H EPs
oie a, BR alehi He a5) | 1840) eG Sa) 02 eon
|
| a
| 9-05 | -5956 | 1:8391 | 1-7098 | -7902 1:2098 -2902 75462
910 | -5891 | 1:8320 | 1:7080| -7920 | 1-2080| -2920 ‘T5753
9-15 -5827 | 1°8251 | 1:7063| -7937 1:2063 | -2937 "76024
| | |
| )
Det) S5e(c) Diff.
| 9-05 —-06162 | -07299
| 910 | +:01137 | -07962
| 915 | +:09109
| |
T, = 9°093' = 9:09’, say.
c, =3°8078 ; Cp DoOU:
Corrected for map error, T, = 9°14’.
* The depths were, of course, read from the map.
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG.
§ 23. BrnopaL Periop or TREIG.
— | Y
at c a 4(5 + a) 4(5 — a) | 4£(3 +a) 4(3 — a) Kier 1)
| | |
6:06 | 12°2943 | 7:0836 30209 | —-5209 2°5209 | —1:0209 — 22608
507 |12°2456 | 70698 | 30175 | -—-5175 | 2°5175 | -—1-0175 | —-18883
DOS) | 121980.| 70564 |. 3-014 |) Sonal | 25141 | —1-0241 | —-15178
T c a |#5+a0)) 40-a) | 48+a)) 43-2) Ke, 1)
|
5-06 | 1:9052] 2-9361 1:9840| -5160 14840 | -0160 — 06223
5:07 | 1:8977 | 2°9310 |/1:9828 | -5173 14828 | -0173 —-06714
508 | 1:8903 | 2:9260 | 19815 | -5185 14815 | -0185 — 07165
|
T | xc) | CDi.
5-06 | --06799 | -04972
5:07 — "01827 | -04850
5:08 +°03023 |
| |
T= 5:0738' = 5-074’, say.
C= 12°2275 ; Cp — 8950;
Corrected for map error, T, = 5099.
§ 24. TRINODAL PERIop oF TREIG.
ae c a 4(5 +a) 4(5-a) | $(3+a) 4(3 -—a) K(e, 1)
3550 | 24°977 | 10°0453 | 3:7613 | —1:2613 32613 | —1:7613 4°60935
3°565 | 24°767 | 10°0035 | 3°7509 | —1-2509 3°2509 | — 1°7509 4°89966
3°575 | 24-629 | 9:9758 | 3°7440 | —1:2440 | 3-2440 | -1:7440 | 5:10266
rT c a. 45+a')| 4(5-a) | 4(3+e)| 2(3-ca) | Ke, 1)
3-550 | 3:8707 | 4:0599 | 2°2650 ‘2350 1:7650 | —‘2650 | —2-03981
3°565 | 378382 40438 | 2:2609 2391 17609 | —°2609 — 1:97823
3°575 | 3°8168 4:0333 2°2583 ‘2417 17583 | —°2583 — 1:94017
841
842 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
iD | x(¢)_| Diff. for -01,
3550 | — 57233 30446
3°565 | — 12564 29974
3°575 | + 17410
T, = 3°5692' = 3°569’, say.
Cg = 24°711 ; c', = 3'8294.
Corrected for map error, T, = 3°587.
§ 25. Preriops sy Du Boys’ Rutz.
The distances from the southern end of the lake are denoted by 2, the unit being
2x 1760/2°54 feet. The depth, h, is entered in feet.
| /1/mean /h 1/ mean /h
2 h Jh | Mean /h da x h wie | Mean ful da
ie JSh
0 dx=1 throughout / 20 | 4388 |) 20°93 20°89 “0479
1 8 9°22 4°61 2169 21) 433] 20°61 20°87 0479
2}. 165} 12°85 11-03 0907 22} 408! 20:20 20°50 0488
34 240 | 15°49 Le 0006 23; 406 | 20°15 20°17 0496
£ | 208 |" 116706 15°77 0634 24) 404] 20°10 20°13 0497
5 | 272) 16°49 16:27 0615 25 | 402 | 20:05 20°17 0496
Cf e202 alte L709 1679 “0596 26) |) S329 S987 20°01 ‘0500
Ci S05 W7-6il 17°35 ‘0576 2) 8500) LSet 18°80 ‘0532
8 | 322/ 17°94 | 17-77 0563 28:4) “ol Lee li-64 18°17 0550
9} 333°) 8-25 18:09 | -0553 299\ 7 20s n0G 17°35 0576
10 | 362 | 19-03 18°64 0536 30 | 280] 16°73 16°89 0592
ET erolo sa O82, ions 0515 St) 2865 e slG ou 16°82 0595
Pah 43: | 520-32 20:07 ‘0498 Be 202m alg Og 17°00 0588
13| 429 | 20-71 20°52 ‘0487 33 | 260] 1612 16°56 0604
14 434 | 20°83 20°77 0481 34 213) 14°59 15°35 0651
15 | 436 | 20-88 20°85 0480 35 | 228 | 15°10 14°85 0673
16) 431 20°76 20°82 0480 36; 210) 1449 14°79 0676
17 | 426 | 20°64 20°70 0483 37 153 12°37 13°43 ‘0745
18 | 428 | 20°69 20°66 0484 38 129 11°36 11°86 0843
19 | 435 | 20°86 20°77 0481 39 0 0 | 5°68 ‘1761
— =
_ 2x 1760 x 2°5065
Hence aqua ———,
2-54 x /39°2
=6120"= 10207
Therefore ri DLO"
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG. 843
Correcting for the map error, we have :—
aT, = 10-25",
Pies eai tee
l= 3°49",
In this case Du Boys’ value is about 12 per cent. in excess for the uninodal period ; only about ‘6 per
cent. in excess for the binodal; while it is about 5 per cent. in defect for the trinodal. The difference
between Earn and Treig in this last respect may be due to the fact that at the shallow end of Treig the
normal points lie above the representative parabola; whereas the opposite is the case with Earn.
Nopves or Locu TREtc.
§ 26. The table of the signs of (,, Go, C,, corresponding to that given for Earn on
p. 832, is as follows :—
|
| by & bs
=
Uninodal . ; ; : | - - +
isbimodalNe a4 ie. ou | 5S Pe eiih ad
Trinodal . : : F = 4 i
The uninode therefore lies north of the deepest normal point. The two binodes
are on the same side of the deepest normal point—of course, on the northern side. One
trinode lies south of the deepest normal point; and a rough trial easily shews that
there is one, and therefore two, trinodes north of the deepest normal point.
UninovE or Treia (North of Deepest Normal Point).
§ 27. We have taken T, = 9°14’, c=3°8073.
Coefticients of L’(3°8073, z).
¢ ¢ B,
0 | Uo | een) | eB. | es
7. o cr |
0 logie= 58062 |
1 9037 T-95602 | 58062 58062
2 ‘3654 156282 ' 53664 23561
3 6827 183424 09946 | 1:62234
4 “8096 1:90829 T-93370 | 1:33164
5 8731 T-94106 | 184199 T-14302
6 9093 T-95873 | 1°78305 T-00490
"i 9320 | 196942 174178 | 289668
8 “On — | T-97641 | T-71120 | 2:80811
9 ‘9577 T:98123 _ * 168761 | 373337
844
Value of L/(3°8073, °305).
PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
l By
n 08 log 2”
nr
0
] “58062 1°48429
2 23561 2:96859
3| 1:62234 245289
4 | 133164 3°93719
5 114302 3°42149
6 | 1:00490 4:90579
7 | 2°89668 4:39009
8 | 2-80811 587439
9 | 3°73387 535869
Series error < ‘000002
ap Ty
loe T,, ia be
1:00000
06491 AGP
1:20420 16003
2:07523 01189
3°26883 00186
456451 ‘00037
5°91069 ‘00008
528677 00001(9)
668250 ‘00000(48)
6:09206 -00000(12)
1°17425 1:16121
Hence L'(3°8073, °305) = +°01304.
Calculating in like manner for z= ‘310, and z=°315, we get the following values :—
z (espe) Diff.
305 + 01304 ‘01301
310 + 00003 01287
Ge lt5) — 01284 |
Interpolating, we find ,z,="310; and therefore ,w,=°380. It follows that
1”, =°380 x 62°16 x 774,400 sq. ft.
= 23°61 x 774,400 sq. ft. ;
and =a, = 35°6 x 346°5 ft.
§ 28. Sours BinopE or Tree (North of Deepest Normal Point).
‘at =>
Coefficients of 8’(12°2275, w).
DH099) se — 12227,
9 La sete ec ae log ( ah = ) loo
” |'~@n=a)@na1) | °8\'~@acayenci)| 8 Am °8 On
2 log | = 108734 108734 | -78631
4 1:0380 01620 110354 | 50148
ON
Value of 8’(12°2275, -0142).
THE PERIODS AND NODES OF LOCHS EARN AND TREITG.
| |
| | ee as At
| 2n | log los | log Ty, aie Dy
| |
| o| | | 1-00000
2 T8631 | 130458 _ 3-09089 00123
4 -50148 | 860915 | 711053 -00000(01)
|
Series error<-000001 100000 | 00123
S'(12:2275, 0142) = + 99877.
Coefticients of C’(12'2275, w).
Vo eel (ee eee
i @a—tyan| 8’ ~@aa dan) | es Ann | les
1 log c= 1:08734 108734 | 1:08734
3 51138 70874 179608 1-31896
5 0190 2:27875 07483 | 1:37586
Value of C’(12°2275, 0142).
IN. : | | n tS T
2n+1 log 751 lose = logit ss, a of a
1 | 1:08734 3-15229 123963 17363
3 | 131896 | 645686 577582 00006
5 | 1:37586 | 10-75144 10:12730 |
Series error< ‘000001 00006 17363 |
In this way we get
('(12-2275, 0142) = —-17357..
(0142) = — -17464 x -99877 + 17357 = — -00086.
» | wm | Be
|
01420 | —-00086 00012
01425 | —-00U25 | 00012
01429 | +-00024 |
Hence
9, = "01427.
o¥, = 89 x 774,400 sq. ft.
ot, = 18°7 x 346°5 ft.
845
846 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
Norta Binope or Treie (North of Deepest Normal Point).
\ 29. 5099" eet yo:
Coefficients of L’(12°2275, z).
é B
jee Cn ay | af Pes; g loo B. loot =
n(n + 1) al ae! Hone Pes,
0 log c= 108734
Ts sapieRS ‘70874 ~~ | 1-°08734 | 108734
2| 1-0380 01620 =| -:1°79608 | 1-49505
3 0190 || 227875 181228 | 1-33516
4 3886 | 1:58950 09103 | _-48897
5| 5924 | 177262 168053 | 2-98156
6 ‘7089 | 185058 | 145315 | 2-675v0 |
Value of L/(12°2275, 1150).
| |
B | T a
loo = log ao] eZ a
n ) a 0g Zz log T, | fl ms
0 ee | 1-00000
1 | 1-08734 | 1-06070 | 14804 1-40618
2 | 1:49505 | 212140 | 161645 - -41348
3 | 133516 | 3-18209 | 251725 03290
4| 48897 | 424279 | 473176 | -00054_ |
5 | 2-98156 | 5:30349 | 6:28505 = -00000(19)
6 | 267500 6-36419 | 7:03919 — -00000(01)
a Saree | =
Series error <-000001 | 141402 1:43908
Hence L'(12°2275, -1150) = — -02506.
Calculating in like manner, we get the following table :—
"1100 | +:00492 -01525
1125 | —-01033 | :01473
"1150 | —:02506
Hence f= LLOS:
9W,= “1785.
oly = 48°40 x 774,400 sq. ft.
ot) = 56'7 x 346°5 ft.
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG.
§ 30. Sourn TrinovE or Treic (South of Deepest Normal Point).
T,=3°587; c’=3°8294.
Coetticients of L/(3°8294, z).
Bt / c B
Ne ee rene ) loe B, | log 2
és n(n + 1) sae n(n +1) ve 7
1 log |c’ = 58313 58313 58313
2 9147 196128 04441 | °24338
3| 3618 T'55847 ‘10288 | 1-62576
4 6809 1-83308 193596 1°33390
5 "8085 1:90768 1°84364 114467
6 $724 194072 1:78436 100621
7 9088 1:95847 1:74283 | 2°89773
8 9316 96923 171206 | 2:80897
Value of L/(3°8294, °3085).
B, wit o M, Ie
n log = log z log T,, st =
0 1:00000
1 58313 | 1:48926 07239 118138 |
2| 24338 297852 1:22190 *16669 |
3 | 1:62576 | 246778 | 2-09354 01240
4 | 1°33390 3°95704 3°29094 "00195
5 | 1:14467 3°44630 4:59097 00039
6 | 1:00621 | 4:93556 | 5:94177 00009
1 | 2897738 4-42482 532255 00002
8 | 2°80897 591408 | 6:72305 00000(5)
Series error <‘000008 1:18154 1:18138
Hence L'(3°8294, -3085) = + 00016.
Calculating in like manner, we get the following table :—
Hence
2 Se lus(cz) Diff.
*3085 | + 00016 | -00130
°3090 | — 00114 | :00125
3095 | — 00239
3%, = 3086.
+3828.
Boia
3¥,= 9°367 x 774,400 sq.
gi, = 12°2 x 346°5 ft.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 32).
124
847
848 PROFESSOR CHRYSTAL AND MR E. MACLAGAN-WEDDERBURN
§ 31. Mippie Trinope or Tretia (North of Deepest Normal Point}.
Deer O87 S) Kee Aaa
Coefficients of L/(24°711, z).
| B
ee eI ge ) be (hee
a n(n + 1) °8 n(n — 1) log B,, oo
Wh log} c= 1°39289 1°39289 1:39289
WAN Wa lesiaysys) 1:05521 2°44810 2714707
3 3°1185 49395 | 2°94205 2°46493
4 1:0592 02498 2°96703 2°36497
5 Zao 1°37199 2°33902 1°64005
6 1763 1:24625 1°58527 80712
if ‘4116 161448 1:19975 35465
8 D587 1:74718 94693 704384
9 "6568 181743 ‘76436 181012
10 ‘7254 1:86058 "62494 162494
11 aoa: T:88953 51447 1:47308
Value of L/(24°711, °274).
B wt T
] psy o n n
n Oe log # log T,, i az
0 1:00000
1°39289 143775 83064 6:77080
2 | 214707 2°87550 1:02257 10°53341
3 | 2°46493 2°31325 ‘77818 6°00040
4 | 2:36497 3°75 100 11597 1:30609
5 | 164005 318875 282880 "06742
6 80712 4:62650 343362 00271
7 35465 4:06425 441890 4 ‘00026
8 04384 550200 5°54584 00003
9 1°81012 6°93975 6°74987 “00000
10 | 162494 | 637750 | 6-00244 00000
1] 1°47308 7°81525 7°28833 “00000
Series error< ‘000001 12°83950 | 12°84163
Hence L'(24°711, :274)= — :00213.
And we get the following table :—
Z L'(ec, z) Diff.
273 | —:00637 00424
274 | —-00213 00447
275 | +:00234
ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG. 849
"2745,
aes AOE
U2 = 28°03 x 774,400 sq. ft.
glo = 392 x 346°5 ft.
Hence a%q =
NortH Trrnope or Treie (North of Deepest Normal Point).
oo ae eel,
The coetticients of L’(24°711, z) are the same as for the Middle Trinode.
§ 32.
Value of L/(24°711, °0560).
B, nm Db 1.
n log = log z log T, i ms
0) | 1:00000
1 | 1:39289 | 2°74819 | -14108 1:38384
2' 214707 | 3:49638 | 1°64345 ‘44000
3 | 2°46493 | 4:24457 | 2°70950 "05123
4 | 2:36497 | 6:99276 | 3°35773 00228
5 | 164005 | 7°74095 | 5°38100 00002(40)
6 | ‘80712 | 848914 | 7:29626 | 00000(02)
Series error < ‘000001 144229 | 1°43509
|
Hence L'(24'711, 0560) = + :00719.
In this manner we get the following table :—
Bey) Dit
al
0560 | +:00719 | -00575
0565 +:00144 | -00571
0570 | —-00427
Therefore gg= ‘0566.
g,= 8868,
33 = 99°12 x 774,400 sq. ft.
3, = 65°2 x 346°5 ft.
AGREEMENT BETWEEN THEORY AND OBSERVATION.
§ 33. Sufficient observations are not yet available to enable us to test the above
theoretical results with the degree of accuracy which we believe to be attainable. We
may, however, conclude this memoir by stating what is already known to us—with the
reservation that the results alluded to are merely preliminary, and subject to future
correction and refinement.
850 ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG.
§ 34. In October and November 1904, a series of observations on Treig were made
under the superintendence of Mr E. Mactagan-WEDDERBURN. Only one limnograph
was used, and it was placed at the northern end of the lake. The observations were
brought to an untimely conclusion by the partial destruction of the instrument during
a storm. The seiches observed were rarely pure for any considerable time; and the
depth of the lake varied considerably during the observations, so that the periods do
not all belong to the same surface-level. T, varied from 9°09’ to 9°45’, the mean of
all the determinations attempted being 9°18’. T, varied from 5°11’ to 5°22’; mean, 5°15’,
Nothing is known as yet regarding the actual position of the nodes of Treig.
§ 35. In June 1905, observations were begun on Loch Harn by Mr James Murray
under the superintendence of Professor CurystaL. ‘Two Sarasin limnographs were
established—one at the uninode, the other at the binode, as determined by the above
calculations. Unfortunately, these instruments proved insufficiently sensitive for the
great majority of the delicate seiches which have occurred in the lake during June and
July. Mr Murray has, however, acquired great skill in using the index limnograph
of ENpR6s ; and a considerable number of his charts are already at our disposal. The
results here given are merely preliminary, and must not be understood as anticipating
the more accurate determinations which Mr Murray will doubtless make later on.
Allowance being made for wind denivellations due to the shallow edges of the lake,
the traces at the two supposed nodes are nearly pure sinusoids. The calculated positions
of the uninode and binode cannot therefore be far out. The values obtained for T, vary
from 14°35’ to 14°77’, the mean being 14°55’; for T,, 7°97’ to 8°36’, mean 8°10’. No
good determination of T, has yet been made.
§ 36. The close agreement between the observed and calculated periods may be
partly fortuitous. We cannot regard this as finally established until we have additional
observations, in which the essential data are more certainly determined.
As regards the agreement between theory and observation to be expected in general,
we may point out that more accurate calculation of the periods is to be expected than
of the nodes ; and that least accuracy of all can be hoped for in the calculation of the
amplitudes of the seiches at different parts of the lake. The periods obviously depend
more on the whole configuration of the lake, and less upon local irregularities, than do
the nodes or the amplitudes. The nodal line would be very seriously displaced by a
sudden alteration in the depth or breadth of the lake which might affect the periods
very little. Thus, for example, it is easy to see from the position of the dots in fig. 1,
with reference to the parabola, that the Western Binode of Earn probably lies some
distance west of the position calculated above. The amount of the displacement might
be calculated by RayeicH’s method if the data from soundings were sutfticiently
accurate. Also, a gently shelving shallow shore would cause flow across the lake,
contrary to the hypothesis of the theory ; and the effect of this might be to deform the
nodal line, and to alter very considerably the amplitude of the seiche near the shore.
These points we propose to discuss in detail in a subsequent communication.
CALCTLATIONS
OP THE PERIODS AND NODES OF LOCHS EARN AND TREIG. PLATE I.
BATHYMETRICAL SURVEY OF THE FRESH-WATER LOCHS OF SCOTLAND
UNDER THE DIRECTION oF SIR JOHN MURRAY, K.C.B., F.R.S., D.Sc, anD LAURENCE PULLAR, F.R.S.E.
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Trans. Roy Soc, Edin® Vol SLI
POSITIONS OF NODES AS CALCULATED BY PROFESSOR GHRYSTAL AND E. MACLAGAN-WEDDERBURN, M.A. 1905
3
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ALCULATIONS OF THE PERIODS AND NODES OF LOCHS EARN AND TREIG. PLATE I]. WRC Bay 1S) EE Ve 2a
BATHYMETRICAL SURVEY OF THE FRESH-WATER LOCHS OF SCOTLAND
UNDER THE DIRECTION OF SIR JOHN MURRAY, K.C.B., F.R.S., D.Sc., ann LAURENCE PULLAR, F.R.S.E.
POSITIONS OF NODES AS CALCULATED BY PROFESSOR GHRYSTAL AND E. MACLAGAN-WEDDERBURN, M.A. 1905 =
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soo|__{ 114
XXXIII—The Alcyonarians of the Scottish National Antarctic Expedition. By
Prof. J. Arthur Thomson, M.A., and Mr James Ritchie, M.A. (With Two
Plates.)
(MS. received May 30, 1905. Read July 3, 1905. Issued separately January 18, 1906.)
The Alcyonarians collected by Mr W. 8. Bruce on the Scotia voyage represent
nine species—six of which are new, namely :—
Primnoisis ramosa, ni. sp.
Thouarella brucei, n. sp.
Amphilaphis regularis, Wright and Studer.
Primnoella scotix, n. sp.
Primnoella magellanica, Studer.
Paramuricea robusta, n. sp.
Gorgona wiighti, n. sp.
Gorgonia studeri, n. sp.
Umbellula durissima, Kolliker.
Apart from the six new species, the collection is of interest in extending our know-
ledge of the geographical distribution of previously recorded forms. Thus Amphilaphis
regularis, Wright and Studer, previously collected off Inaccessible Island, Tristan da
Cunha, and off Nightingale Island, was got in abundance off St Helena; Primnoella
magellanica, Studer, previously collected off Monte Video and in the Magellan
Straits, was obtained at Burdwood Bank 54° 25’ S., 57° 32’ W.; while Umbellula
durissima, Wright and Studer, previously obtained by the Challenger from the North
Pacific Ocean, south of Yeddo, was found by the Scotia at 48° 06’ 8., 10° 5’ W.
It may also be noted that the fine specimens of Umbellula durissima, Kolliker,
give us a better idea of this beautiful species than the single young specimen collected
-by the Challenger. Several of the specimens obtained by Mr Bruce are much
larger, older, and of more vigorous growth than that which KoOuurker described and
named.
With the exception of the much-weathered Primnoisis ramosa, un. sp., all the
specimens are admirably preserved.
Family ISID.
Sub-family Mopszinz.
Primnoisis ramosa, n. sp., Pl. I. fig. 2.
The specimen is much weathered, quite devoid of polyps, and without the basal
portion. Although far from complete it attains a height of 230 mm., and a maximum
lateral expansion of 45 mm. The bare stem bends frequently, at irregular intervals,
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 38). 125
852 THOMSON AND RITCHIE ON THE ALCYONARIANS
throughout its course, and gives off many branches which are also naked. The
branches arise at various acute angles, and some of them, especially towards the
lower end, are almost as thick (1°5 mm.) as the main stem (1°75 mm. at the lowest
part). Like the latter, they give origin to smaller branches, which may bear minute
twigs with a single jomt or with two joints. Small branches with only a few joints
are much more frequent on the stem than the large branches already mentioned,
and they stand off from the stem at greater angles than the large branches—some,
indeed, arising perpendicularly.
All the branches spring from the calcareous internodes, and are equally developed
on all sides. They vary in number from 3 to 7, or even 8, per joint, 7 perhaps being
the most common number. They seem to arise quite irregularly, a frequent interval
between two on the same side being 4 mm.; but very occasionally 3 or 4 arise in
a whorl.
The axis consists of alternate horny nodes and calcareous internodes, the latter
being covered with very fine longitudinal grooves. The internodes are much longer
than the nodes, and are themselves longer towards the apex of the colony. The
following measurements of successive internodes were taken :—(a) from the lowest
joint upwards, 5, 6°5, 7, 9 mm.; (>) from the topmost jomt downwards, 9, 9°5, 10, 9,
10 mm. Near the base the horny nodes are only about 0°5 mm. in length, and
gradually decrease towards the apex. The branches never begin with a horny node;
in every case a process arises from the originative calcareous node, and on this the
first horny node of the branch is based.
This species most closely approaches P. antarctica ; but the branches arise from all
surfaces of the stem and secondary branches, and are equally developed on all sides,
whereas in P. antarctica the branches arise from only four sides and are unequally
developed. Moreover, in the new species the calcareous internodes are much longer
than in P. antarctica, and may bear 7 or 8 branches, whereas in P. antarctica there
are only about 4 per joint.
The specimen bears several siliceous sponges, several Polyzoa, a small brown
Actinian, and several worm-tubes.
Locality.—Station 411, lat. 74° 1’ 8., long. 22° W.; 161 fathoms. Surface tempera-
ture 28°9°, March 12, 1904.
Family PRIMNOID AL.
Sub-family PRimnoin a.
Thouarella brucei, n. sp., Pl. I fig. 1; Pl. EH. fig. 1.
Several specimens of strong upright branched colonies of a creamy-white colour
were found at various stations. The largest specimen is a bushy colony 14 cm. in
height by 10°5 cm. in maximum breadth, with an axis 5 mm. in breadth at the base;
———
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 853
but like the others, with one exception, it lacks the basal attachment. The single
complete specimen is a graceful bush, 9 cm. in height by 4 cm. in maximum breadth,
with an axis 1 mm. in breadth at the base, and an expanded disc of attachment almost
1 cm. across. Of the other specimens the following measurements were taken :—
(a) 14 cm. in height by 3 in breadth, a single branch, with an axis 4 mm. in breadth ;
(b) 11 cm. in height by 9°5 cm. in maximum breadth, a bushy colony with an axis
3 mm. in breadth at the base; (c) 8 cm. in height by 9 cm. in maximum breadth, a
bushy colony with an axis 2 mm. in breadth. The colonies bear Comatulids attached
by their cirri, encrusting Polyzoa, hydroids, and several sponges.
The branching of the specimens differs from that of the previously described species
of Thouarella. A main stem, 1 to 5 mm. in diameter, gives off strong branches almost
as thick as itself, and sometimes attaining a length of 12 cm. They arise in at least
three directions and at irregular intervals. From these branches, as also from the
intervals between them on the main stem, slender twigs arise on all sides, and at
varying angles. But the strong branches of the first degree may also bear strong
branches of the second degree, likewise carrying slender twigs. The larger branches
show a tendency to curve inwards towards the main stem.
In all cases the slender, graceful twigs spring from all sides at very irregular
intervals, and are equally developed all round. Asa result of the repeated branching,
of the incurving of the larger branches, and of the very numerous close-set twigs, the
colony bears a characteristic resemblance to a thickly-growing sturdy bush.
Where the ccenenchyma has been rubbed off in the lower parts of the colonies, the
stout, almost inflexible axis is exposed. It is tawny-brown in colour, with in some
places a yellowish sheen ; but it becomes lighter in colour (honey-yellow), as well as
very flexible, towards the tips of the branches and in the twigs. It is composed of
horny and calcareous materials, and is circular in cross section.
The calices, which are about 1 mm. in height, are borne chiefly on the twigs, but
they are occasionally borne by the twig-supporting branches and by the main stem.
On the twigs they are closely approximated, arising in all directions and without any
definite arrangement. ‘They are pear-shaped, and generally bent inwards to the axis.
The number of transverse rows of scales varies slightly, but five is a very common
number. The number of longitudinal rows is about seven. The scales appear to be
similar in size and structure on all sides of the polyp, there being none distinctively
dorsal or ventral. ‘They have a convex upper edge, frequently assume an almost
quadrangular form, and are thickly tuberculated. Fusion of the tubercles occasionally
gives rise to very slight ridges running outwards from the nucleus. The embedded
edges of all the scales are more ragged than the free edges.
The rows of scales are surmounted by about seven opercular scales, all of which have
a ridge projecting for a considerable distance, usually bordered by a narrow leaf-like
wing.
This species is marked off from others previously described by the origin of strong
854 THOMSON AND RITCHIE ON THE ALCYONARIANS
branches in at least three directions, by the origin of twigs on all sides of the axis, by
the cylindrical shape of the axis, and by the detailed speculation of the polyps.
Localities.—Burdwood Bank, 56 fathoms, December 1, 1903; Gough Island, 100
fathoms, April 22, 1904; St Helena.
Amphilaphis regulams, Wright and Studer, Pl. II. fig. 5.
Numerous fine specimens of this graceful form were obtained from St Helena. The
following measurements of height and lateral expansion were taken in cm. :—40 by 25,
33 by 15, 26 by.15, 20 by 30, 17 by 9, 20 by 19, 20 by 10,16 by 11; but none of
these represent complete specimens. As is the case with Thouarella brucei, there are
very noticeable differences in the vigour of the various specimens, for some have the
polyps much more crowded than others.
The specimens agree closely with the description by Wricur and Sruper, but it
may be noted that the figures of the spicules given in the Challenger Report do not
show the prominent spines described in the text. We have therefore given a
supplementary figure.
We add a few details in reference to the spicules. The scales of the operculum
are roughly triangular, usually with an indentation in the base directly opposite the
nucleus. A strong ridge, sometimes double, extends from the apex of the triangle
towards the nucleus, which, however, it seldom reaches. The calyx scales resemble a
rude ellipse, toward the upper edge of which the tubercles have become fused to form
prominent ridges, frequently 0°08 to 0°1 mm. in length, radiating from the nucleus and
projecting as spines beyond the edge. The arrangement of the ridges resembles that of
the teeth in a comb.
The specimens bear numerous small Actinians, clusters of Polyzoa, clambering
Ophiuroids, serpuloid worm-tubes, small barnacles, ete.
J ocality.—St Helena. }
Primnoella scotiz, n. sp., Pl. I. figs. 3 and 8.
A simple upright colony, 105 mm. in height, of a dirty yellowish-white colour.
The basal portion is absent and the axis has disappeared. It looks as if the dredge had
dragged the colony from off the axis, for there is a slightly oval central canal, a little
over 1 mm. in diameter at the base and narrowing to 0°5 mm. towards the apex.
The stem is closely covered with polyps arranged in whorls of 9 to 11, the most
frequent number being ten. The calices are closely apposed to the stem and are
pressed against one another laterally, and the whorls themselves overlap, so that the
general effect is that of a uniformly thick rod with a diameter of 4 mm.
The calices are from 2°5 to 3 mm. long and 1 mm. broad, but owing to the over-
lapping at the base less than 2 mm. of the calyx is visible. Under the lens the
—_~ =
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 855
verrucee appear as slightly flattened cylinders covered with fine horizontal striz, which
higher magnification shows to be the smooth edges of regularly arranged broad
imbricating scales. These are arranged in two longitudinal parallel rows along the
dorsal surface, those in one row interlocking with the alternate scales of the other row.
The upper edges of all the dorsal scales are parallel, and the two rows meet in the
middle without any distinct angle or keel. Hach row has from 21 to 28 scales.
On the ventral side of the calyx there are two small longitudinal rows along the
edges, but the rest of the surface is covered with indistinct roundish scales irregularly
disposed.
There does not seem to be any special operculum, but several of the uppermost
scales bend over so as partly to cover the mouth of the calyx, within which the
retracted tentacles of the polyp can usually be seen.
The dorsal calyx-scales are roughly rectangular, very broad and slightly curved to
fit the cylindrical polyp body. ‘The upper or projecting margin of each scale is smooth,
while the lower or overlapped margin is toothed. The whole of the inside of the scale,
except a narrow strip along the upper edge, is covered with numerous small tubercles.
On the external surface there are numerous very fine wavy lines running from edge to
edge of the scale. |
The other scales are irregular in outline, sometimes with toothed margins, sometimes
smooth-edged ; they may be almost free from tubercles or covered with them.
All the scales are colourless, and show an eccentric darker nucleus from which any
slight ridges on the surface run. From these nuclei, as is shown by polarised light, the
rest of the scale has been deposited in concentric zones.
Locality.—Burdwood Bank, lat. 54° 25’ S., long. 57° 32’ W.; 52 fathoms. Surface
temperature 41°8°, December 1, 1903.
Primnoella magellanica, Studer, Pl. I. fig. 3.
An almost complete specimen of this species, lacking only a small part of the basal
region. The stem reaches a height of 148 mm., but towards the lower end the
coenenchyma has disappeared, exposing the brown axis for about 15 mm., while for the
next 30 mm. the whorls of polyps are broken and incomplete.
The specimen agrees with the description of P. magellanica given in the Challenger
Report except in the following particulars. In the Challenger specimen the number
of polyps in a whorl was 8; in the Scotia specimen there are 9, 11, 12, 18, 10, 12,
12, 13, in the various whorls counted. In the Challenger specimen the opercular
scales were in length and breadth 0°48 x 0°2 mm., while the corresponding measurements
for the Scotia specimen are 0°65 x 0°35, 0°625 x 0°375 mm. Similarly for the calyx
scales, the measurements for the Challenger specimen were 0°31 x 0°3, 0°36 x 0°37;
and for the Scotia specimen 0°3x0°3, 0°425x 0°35, 0°3x0'25. Thus there are
decidedly larger dimensions in the scales of the Scotia specimen. The larger and
856 THOMSON AND RITCHIE ON THE ALCYONARIANS
variable number of polyps in a whorl is of greater importance, but it probably means
nothing more than a greater vigour of growth.
The figure in the Challenger Report shows the whorls too far apart, as the text
points out; we have therefore given a supplementary figure.
Locality.—Burdwood Bank, lat. 54° 25’ S., long. 57° 32’ W.; 52 fathoms. Surface
temperature 40°8°, December 1, 1903.
Family MURICEID/AL.
Paramuricea robusta, n. sp., Pl. I. fig. 6; Pl. IL figs. 2 and 7.
A strong upright colony of a light brown colour, expanded for the most part in
one plane, 27°5 cm. in maximum height by 14 cm. in maximum breadth. Not far
from the base, which is expanded to 2 cm. and soon narrows to 1 cm., a strong
side-branch is given off with a diameter of 6 mm., and this, like the main stem, bears
strong offshoots from which smaller, usually simple, branches arise. The branching
is very irregular, but anastomosis is rare, being represented in one of the specimens by
only two instances, one of which shows the junction of an apparently broken branch of
the first degree with the main stem. In another specimen, 18 em. by 12 cm., there is no
anastomosis. Towards the base of the colony the main stem is distinctly flattened, 9°5
by 8 mm., immediately above the basal thickening.
The axis is horny, non-calcareous, fibrous, and of a brownish colour. It narrows
from about 6 mm. near the base to 1 mm. near the tips of the branches.
The ccenenchyma is relatively thin (0°5 mm.) and somewhat translucent, allowing
the brownish axis to shine faintly through. Its surface is rough, owing to the abundance
of large colourless spicules which cover it. Some of these spicules project from the
tops of the verrucze as crowns of spines.
The yellowish verruce are cylindrical with a slightly conical summit, 1°5 mm. in
height by 1 mm. in diameter, and arise perpendicularly from all sides of the main stem
and its branches. They are closely set, without any regular interval between them.
Four or five are always grouped at the tip of a branch, giving it a knobbed
appearance.
The polyps are wholly retracted, and an operculum of 8 parts, each composed of
about 5 spicules resting on the bases of the tentacles, closes over the aperture. Round
the top of the verruca a few rows of spicules are arranged horizontally, and on this
support the bases of the opercular covering rest.
Various types of spicules characterise the species. Most characteristic are the large
tuberculate clubs whose ‘ handles’ form the spiny crowns of the verrucze, while the much
divided root-like ‘ heads’ are embedded in the coenenchyma. ‘There are also simpler clubs
with heads covered with tubercles and spiny processes. Curved spindles are common,
some knobbed and thickened, with comparatively large projecting processes and smaller
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 857
spines; others are more regular, boomerang-like, with spines and tubercles only ;
others again are almost smooth with only a few small warts.
The following measurements were taken :—complex clubs, 0°8 to 0°9 mm. in length
by 0°45 between the extremes of the spreading heads; broad almost straight spindles,
06502 mm.; narrow curved spindles, 0°7 x 0°04, 0°5x 0°05, 0°425 x 0:06 mm. ;
simple forks with few spines, 0°5 mm. in length by 0°1 at the forked end.
In general the colony presents a remarkably sturdy, rigid appearance, due to the
thickening effect of the numerous polyps which arise from the flexible twigs and branches.
The various specimens bear numerous epizoic animals, e.g. small Actinians, Polyzoa,
worm-tubes.
This new species may be distinguished from most of the other representatives of the
genus by the absence of any arrangement of the verruca spicules in longitudinal rows. It
is separated from all by the characters of its spicules, and in particular by the large
tuberculate clubs with expanded divaricate heads. From P. ramosa, which it most
nearly approaches in appearance, and from P.laxa, it may be distinguished, apart
from the spicules, by the absence of any intermediate part of the stem or branches
free from polyps. The verrucee are distributed equally on all sides of the stem and
_ branches instead of being disposed, for the most part, on opposite sides. From P. ramosa
itis also distinguished by the excezdingly rare occurrence of anastomosis. Some of the
spicules of KOLLIKER’s P. spinosa closely resemble some of those in our species, but in
P. spinosa the coenenchyma is very thin, the polyps are rather sparse, and there are
many other points of difference.
Localities.—Gough Island, lat. 40° 20’ S., lone. 9° 56’ W.; 100 fathoms; surface
temperature 55°2°, April 22, 1904. St Helena.
Family GORGONIDA.
Gorgoma wrighti, n. sp., Pl. I. figs. 7 and 8; Pi. IL figs. 6 and 9.
A much-branched, flexible, upright white colony with a general height of 22
em. by about 10 cm. in breadth. The main stem gives off, about 25 mm.
above the base, a strong branch which bears long flexible offshoots, and these
again bear numerous usually simple branches. There are even some branches of
the fourth degree, and with the base of one of these another branch unites—the
only instance of anastomosis in the colony. The branches have a fairly uniform
thickness of 2 mm., and can hardly be said to taper toward the blunt, rounded, or
swollen tip. The larger branches are very slightly flattened towards their base. They
all arise at angles rather less than 90°, and the whole system shows a tendency to
spread in one plane, though here and there a branch arises at right angles to the
rest. The branches of the same degree are markedly parallel when not twisted out
of their original direction. There is a tendency in the secondary branching to
858 THOMSON AND RITCHIE ON THE ALCYONARIANS
preponderate towards the side more remote from the main axis. The first main
branch is 150 mm. in length and 2°5 mm. in breadth.
Towards the base of the colony a portion of the axis is exposed. It is slightly
flattened, 3 mm. in breadth, horny, non-caleareous, and very flexible. The colour
is a rich dark brown, fading into pale brownish yellow towards the tips of the
branches. There are very marked ‘chambers’ or curved transverse septa. A
cross section shows a central canal filled with whitish material.
The ecenenchyma is thick (0°375 mm.) and has a granular appearance, due to the com-
plete covering of spicules. On one of the branches there is a calcareous cirripede gall.
The polyps occur on all surfaces of the stem and branches, but are more frequent
along the opposite sides than along the middle. They are completely retractile, and
when withdrawn leave small almost circular openings, which are on a level with the
surface on the older portions, while in the younger parts their margins are slightly
raised to form lips, giving a warty appearance to the terminal regions.
The spicules are translucent spindles and scaphoids, almost always curved, and bear-
ing numerous spines which often equal or exceed the diameter of the spicule proper.
The spines are generally developed to a much greater extent on the convex side of
the spicule. They are frequently tubercled or almost branched. Some of the spindles
are fairly smooth with only a few tubercles. The following measurements were taken
of the length and maximum breadth including the spines :—0°85 x 0°1, 0°8 x 0:1, 0°75 x
0°06, 0'7 x 0°04, 06 x 0°06, 0°5 x 0°03, 0°4 x01, 0°3x0:075 mm. As almost every
possible adjective is already preoccupied as the specific name of some Gorgonia or so-
called Gorgonia, we have named this new form G. wiightc after Prof. E. PERcEvaL
WRIGHT, joint-author of the Challenger Report on Aleyonarians.
Locality.— Station 81; lat. 18° 26’ S., long. 37° 58’ W.; 40 to 50 fathoms.
Gorgoma studert, n. sp., PIV. fig. 4; Pl. IL. fig. 4.
A portion of an upright branched white colony, consisting of what may be part of
the main stem (30 by 2 mm.), bearing on one side two parallel branches from one of
which a smaller branch arises. The distance between the two parallel branches is 13
mm. ; the leneth of the longer simple branch is 95 mm., of the shorter 70 mm., and of
its branch 35 mm. There is an indication that still another branch arose from the last,
so that branching of at least the third degree is present. The branches, which taper
almost imperceptibly towards their tips, have a diameter of 2mm. They le in one plane,
leave the axis at an angle of about 70°, and are slightly compressed in their older
portions.
The axis is horny, non-calcareous, and flexible, of a brown colour passing into a horny
yellow in the younger portions. It shows transverse ‘chambers’ or curved septa. Its
diameter at the oldest part is 0°8 mm.
The polyps show a tendency to bilateral arrangement, being more frequent along the
OF THE SCOTTISH NATIONAL ANTARCTIC EXPEDITION. 859
two opposite sides of the branches, although by no means confined to these. They are
not wholly retracted, but protrude from the surface of the coenenchyma as small
roundish warts surrounded by a gently sloping spicular dome, which rises gradually to
form a very slight lip around the polyp aperture. .
The spicules, which are whitish and translucent, are of three main types. (a) Most
abundant are long narrow spindles, e.g. 0°75 x 0:06, 0°7 x 0°05 mm., covered with warty
tubercles, which are frequently produced into blunt spines. The spines show a marked
tendency to unilateral development, being often more prominent and more numerous on
one side of the spindle. () Less abundant are scaphoid forms, ¢.g. 0'7 x 0°12, 0°4 x 0°06
mm. (c) There are also some forms which approach the ‘club’ type and differ greatly in
size, e.g. 0°45 x 0°12, 0°25x 0:06 mm. Their heads are covered with long blunt pro-
cesses, similar to the blunt spines of the spindles, and these are sometimes continued
down the ‘handle’ of the club. Both the ‘scaphoids’ and the ‘clubs’ are readily
derivable from the spindle type. .
We have named this new species G’. studer after Prof. TH. SrupER, joint-author of
the Challenger Report on Aleyonarians.
Locality.—Station 81 ; lat. 18° 26’ S., long. 37° 58’ W. ; 40 to 50 fathoms.
Famiuy UMBELLULIDA.
Umbellula durissema, Kolliker, Pl. I. fig. 5.
About twenty specimens of this beautiful form were obtained from one locality,
from a depth of 1742 fathoms (April 13, 1904). Only one specimen was obtained by
the Challenger expedition, and that much younger and smaller than the best of the
Scotia specimens.
The following total length measurements were taken :—50, 45, 42, 37, 34, 32, 22,
20,18, 17cm. The heads vary from 2°8 cm. in height and breadth to 1°7 in height
by 0°5 in breadth. ‘he stalk is very slender in proportion to the head, and the follow-
ing breadth measurements were taken :—3°5 mm. almost at the base and 1 mm. near
the top of the largest specimen ; 1°5 mm. at the base and 0°5 mm. near the top of the
smallest specimen.
There is considerable diversity in the number of polyps—thus one head had 9, one
had 7, five had 6, one had 5, and four had 3 polyps. The colouring of the polyps is
exceptionally beautiful—a milky blue fading basally into white; the tentacles are
chocolate brown. Hight vertical rows of rod-like spicules extend up the surface of the
polyps and are continued into the tentacles. The largest polyps measure 15 mm. by
8 mm., not including the tentacles, which are 15 mm. in length. The minute siphono-
zooids are exceedingly numerous, covering the whole ventral surface of the head except
a narrow median ridge, and also extending in bands between the bases of the polyps or
autozooids. ‘The bluish colour was not noticed in the Challenger specimen, and
seems to be gradually fading in those under our observation.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 33). 126
860 ON THE ALCYONARIANS OF THE SCOTTISH ANTARCTIC EXPEDITION.
The larger spicules are rods with rounded or swollen ends, and have the following
dimensions in mm. :—2'5 x 0°25, 2x 0°2, 2x 0°15, 1°8x 0°18, 1°45 x 0°125, 1 2X0
12x01. Besides these there are minute rods, 0°14 x 0°023, 0°1 x 0°02.
Locality.—48° 06’ 8., 10° 5’ W. Bottom at 1742 fathoms, pebbles and diatom ooze.
Surface temperature 40°8° F.
EXPLANATION OF PLATES.
Prats I.
Fig. 1. Thouarella brucei, n. sp. A branch with twigs. Nat. size.
Fig. 2. Primnoisis ramosa, n. sp. A portion of the axis with branches, Nat. size.
Fig. 3. Primnoella magellanica, Studer. Three whorls of polyps. x9
Fig. 4. Gorgonia studeri, n, sp. The whole fragment, natural size; and a portion of the axis with
verruce, magnified about 10 times.
Fig. 5. Umbellula durissima, Kolliker. The largest head, magnified about 24 times.
Fig. 6. Paramuricea robusta, n. sp. A small piece of a branch with verruce, magnified about 2 times.
Fig 7. Gorgonia wrighti, n. sp. Showing the mode of branching. Nat. size, —
Fig. 8. Gorgonia wrighti, u. sp. A portion of the axis, showing the chambers, magnified about 10 times,
Pirate II,
Fig. 1. Thouarella brucei, n. sp.
Fig. 2. Paramuricea robusta, n. sp.
Fig. 3. Primnoella scotiz, n. sp.
Fig. 4. Gorgonia studert, n. sp.
Fig. 5. Amphilaphis regularis, Wright and Studer.
Fig. 6. Gorgonia wrighti, n. sp.
Fig. 7. Paramuricea robusta, n. sp. A small portion with two verruce. x 10.
Fig. 8. Primnoella scotiz, n. sp. The apex with four whorls of polyps. x 8,
Fig. 9. Gorgonia wrighti, n. sp. A small portion of the stem. x 10.
Trans. Roy. Soc. Edin? Vol in
MAIOMSON AND. RITCHIE: ALCYVONARIANS.
G. Davidson, del. 2-6, M‘Farlane & Erskine,Lith Edin®
J. Ritchie, del. 17, 8.
“SCOTIA” ALCYONARIANS. Plate I.
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APPENDIX.
TRANSACTIONS
OF THE
ROYAL SOCIETY OF EDINBURGH.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 127
Pp
Pete COOWN C hd,
OF
Hi wove SsOCtTETY OF EDINBURGH.
OCTOBER 1905.
PAREsSHtOvEeNils.
THE Rigut Hon. Lorp KELVIN, G.C.V.O., P.C., LL.D., D.C.L., F.R.S., Grand
Officer of the Legion of Honour of France, Member of the Prussian Order
Pour le Mérite, Foreion Associate of the Institute of France, Emeritus
Professor of Natural Philosophy in the University of Glasgow.
VICE-PRESIDENTS.
Tue Hon. Lorv M‘LAREN, LL.D. Edin, and Glas., F.R.A.S., one of the Senators of the
College of Justice.
Tue Rey. Proressor FLINT, D.D., Corresponding Member of the Institute of France.
ROBERT MUNRO, M.A., M.D., LL.D., Hon. Memb. R.1.A.
Sir JOHN MURRAY, K.C.B., D.Sc., L.D., D.C.L., Ph.D., F.R.S., Director of the
‘Challenger’ Expedition Publications.
RAMSAY H. TRAQUAIR, M.D., LL.D., B.R.S., F.G.S., Keeper of the Natural History
Collections in the Royal Scottish Museum, Edinburgh.
ALEXANDER CRUM BROWN, M.D., D.Sc., F.R.C.P.E., LL.D., F.R.S., Professor of
Chemistry in the University of Edinburgh.
GENERAL SECRETARY.
GEORGE CHRYSTAL, M.A., LL.D., Professor of Mathematics in the University of
Edinburgh.
SECRETARIES TO ORDINARY MEETINGS.
DANIEL JOHN CUNNINGHAM, M.D., LL.D., D.C.L., F.R.S., F.Z.S., Professor of
Anatomy in the University of Edinburgh.
CARGILL G. KNOTT, D.Sc., Lecturer on Applied Mathematics in the University of
Edinburgh.
TREASURER.
PHILIP R. D. MACLAGAN, F.F.A.
CURATOR OF LIBRARY AND MUSEUM.
ALEXANDER BUCHAN, M.A., LL.D., F.R.S., Secretary to the Scottish Meteorological
Society.
COUNCILLORS.
ANDREW GRAY, MA, LED. -F.BS., JAMES COSSAR EWART, M.D., F.R.C.S.E.,
Professor of Natural Philosophy in the F.R.S., F.L.S., Professor of Natural History
University of Glasgow. in the University of Edinburgh.
ROBERT KIDSTON, F.R.S., F.G.S. BENJAMIN NEEVE PEACH, LL.D., F.R.S.,
DIARMID NOEL PATON, M.D., B.Sc., F.G.S., late District Superintendent and
F.R.C.P.E., Superintendent of Research Acting Palontologist of the Geological
Laboratory of Royal College of Physicians, | Survey of Scotland.
Edinburgh. | JAMES JOHNSTON DOBBIE, M.A., D.Sc.,
JOHN CHIENE, C.B.. M.D, UL. D., F.R.S., Director of the Royal Scottish
F.R.C.S.E., Professor of Surgery in the | Museum, Edinburgh.
University of Edinburgh. | GEORGE A. GIBSON, M.A., LL.D., Professor
JOHN GRAHAM KERR, M.A., Professor of of Mathematics in the Glasgow and West ot
Zovlogy in the University of Glasgow. Scotland Technical College, Glasgow.
WILLIAM PEDDIE, D.Sc., Lecturer on Natural JOHANNES P. KUENEN, Ph.D., Professor
Philosophy in the University of Edinburgh. of Natural Philosophy in University College,
LEONARD DOBBIN, Ph.D., Lecturer on Dundee.
Chemistry in tue University of Edinburgh.
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Date of
Election,
1898
1898
1896 |
1871
1875
1895
1889
1894
1888 |
1878
1893
1883
1905
1905
1903
1905
1883
1881
( 867 )
ALPHABETICAL LIST
OF
THE ORDINARY FELLOWS OF THE SOCIETY,
B.
K.
N.
Nordic
C.
C.K.
V.J,
CORRECTED TO OCTOBER 1905.
N.B.—Those marked * are Annual Contributors.
prefixed to a name indicates that the Fellow has received a Makdougall-Brisbane Medal.’
» » 6 Keith Medal,
” ” AA Neill Medal.
53 55 Nar cal the Gunning Victoria Jubilee Prize.
as ie 0 ‘eontributed one or more Communications to the Society’s
TRANSACTIONS or PROCEEDINGS.
* Abercromby, The Hon. John, 62 Palmerston Place
Adami, Prof. J. G., M.A., M.D. Cantab., F.R.S., Professor of Pathology in M‘Gill
University, Montreal
* Affleck, Jas. Ormiston, M.D., F.R.C.P.E., 38 Heriot Row
Agnew, Sir Stair, K.C.B., M.A., Registrar-General for Scotland, 22 Buckingham Terrace
Aitken, John, LL.D., F.R.S., Ardenlea, Falkirk 5
* Alford, Robert Gervase, Memb, Inst. .C.E., Prison Commission, Home Office, Whitehall, London
* Alison, John, M.A., Headmaster, George Watson’s College, Edinburgh
Allan, Francis John, M.D., C.M. Edin., M.O.H., City of Westminster, Westminster
City Hall, Charing Cross Road, London
* Allardice, R. E., M.A., Professor of Mathematics in Stanford University, Palo Alto, Santa
Clara Co., California
Allchin, W. H., M.D., F.R.C.P.L., Senior Physician to the Westminster Hospital,
5 Chandos Street, Cavendish Square, London 10
Anderson, J. Macvicar, Architect, 6 Stratton Street, London
* Anderson, Sir Robert Rowand, LL.D., 16 Rutland Square
Anderson, William, F.G.S., Government Geologist, Pietermaritzburg, Natal
* Anderson, William, M.A., Head Scieuce Master, George Watson’s College, Edinburgh,
29 Lutton Place
Anderson-Berry, David, M.D., C.M. Edin., F.S.A. Scot., 23 Grosvenor Crescent,
St Leonards-on-Sea 15
* Andrew, George, M.A., B.A., H.M.1LS., 3 Mayfield Gardens
Andrews, Thos., Memb. Inst. C.E., F.R.S., F.C.S., Telford Medallist and Prizeman,
Inst.C.E., Gold Medallist aud Bessemer Prizeman, Soc. Engineers, Metallurgical
Testing Laboratory, Wortley, near Shettield
Anglin, A. H., M.A., LL.D., M.R.L.A., Professor of Mathematics, Queen’s College, Cork
868 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Date of
Election.
1867
1899
1893
1883
1885
1894
1896
1877
C.
B.C.
Annandale, Thomas, M.D., F.R.C.S.E., Professor of Clinical Surgery in the University of
Edinburgh, 34 Charlotte Square
Appleyard, James R., Royal Technical Institute, Salford, Manchester 20
* Archer, Walter E., 17 Sloan Court, London
Archibald, John, M.D., C.M., F.R.C.8.E., Hazleden, Wimborne Road, Bournemouth
* Baildon, H. Bellyse, M.A., Ph.D., F.R.S.L., Lecturer on the English Language and
Literature, University College, Dundee
* Bailey, Frederick, Lieut.-Col. (/ate) R.E., 7 Drummond Place
* Baily, Francis Gibson, M.A., Professor of Applied Physics, Heriot-Watt College 25
Balfour, I. Bayley, M.A., Se.D., M.D., LL.D., F.R.S., F.L.S., King’s Botanist in Scotland,
Professor of Botany in the University of Edinburgh and Keeper of the Royal Botanic
Garden, Inverleith House =
Balfour-Browne, William Alexander Francis, M.A., Barrister-at-Law, Director of the
Sutton Broad Biological Laboratory, Catfield, Great Yarmouth
* Ballantyne, J. W., M.D., F.R.C.P.E., 24 Melville Street
Bannerman, W. B., M.D., B.Sc., Lt.-Colonel, Indian Medical Service, Director, Plague
Research Laboratory, Bombay, India
* Barbour, A. H. F., M.A., M.D., F.R.C.P.E., 4 Charlotte Square 30
* Barclay, A. J. Gunion, M.A., 729 Great Western Road, Glasgow
Barclay, George, M.A., 17 Coates Crescent
* Barclay, G. W. W., M.A., 91 Union Street, Aberdeen
Bardswell, Noél Dean, M.D., M.R.C.P. Ed. and Lond., Mundesley, Norfolk
Barnes, Henry, M.D., LL.D., 6 Portland Square, Carlisle 35
Barnes, R. S. Fancourt, M.D., M.R.C.P.L., Consulting Physician to the Royal Maternity
Charity of London, 15 Chester Terrace, Regent’s Park, London
Barr, Sir James, M.D., F.R.C.P. Lond., 72 Rodney Street, Liverpool
Barrett, William F., F.R.S., M.R.I.A., Prof. of Physics, Royal College of Science, Dublin
Barry, T. D. Collis, Staff Surgeon, M.R.C.S., F.L.S., Chemical Analyser to the Government
of Bombay, and Prof. of Chemistry and Medical Jurisprudence to the Grant Medical
College, and of Chemistry, Elphinstone College, Malabar Hill, Bombay
* Bartholomew, J. G., F.R.G.S., The Geographical Institute, Dalkeith Road 40
Barton, Edwin H., D.Sc., A.M.LE.E., Memb. Phys. Soc. of London, Senior Lecturer
in Physics, University College, Nottingham )
* Baxter, William Muirhead, 14 Grange Road
* Beare, Thomas Hudson, B.Se., Memb. Inst. C.E., Professor of Engineering in the University
of Edinburgh
* Beattie, John Carruthers, D.Sc., Professor of Physics, South African College, Cape Town
Beck, J. H. Meining, M.D., M.R.C.P.E., Rondebosch, Cape Town 45
* Becker, Ludwig, Ph.D., Regius Professor of Astronomy in the University of Glasgow, The
Observatory, Glasgow
Beddard, Frank E., M.A. Oxon., F.R.S., Prosector to the Zoological Society of London,
Zoological Society’s Gardens, Regent’s Park, London
* Bega, Ferdinand Faithful, Bartholomew House, London
* Bell, A. Beatson, 17 Lansdowne Crescent
Bell, Joseph, M.D., F.R.C.S.E., 2 Melville Crescent 50
* Bennett, James Bower, Memb. Inst. C.E., 2 Thorburn Road, Colinton
| * Bernard, J. Mackay, of Dunsinnan, B.Sc., Dunsinnan, Perth
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 869
Date of
Election.
1875 Bernstein, Ludwik, M.D., Lismore, New South Wales
1893 | C. |* Berry, George A., M.D., C.M., F.R.C.S., 31 Drumsheugh Gardens
1897 | C. | * Berry, Richard J., M.D., F.R.C.S.E., Professor of Anatomy in the University of Mel-
bourne, Victoria 55
1904 * Beveridge, Erskine, LL.D., St Leonard’s Hill, Dunfermline
1880 | ©. Birch, De Burgh, M.D., Professor of Physiology in the University of Leeds, 16 De Grey
Terrace, Leeds
1900 * Bisset, James, M.A., F.L.S., F.G.S., 9 Greenhill Park
1384 * Black, John S., M.A., LL.D., 6 Oxford Terrace
1850 Blackburn, Hueh, M.A., LL.D., Emeritus Professor of Mathematics in the University of
Glasgow, Roshven, Lochailort 60
1897 * Blaikie, Walter Biggar, 6 Belgrave Crescent
1904 | C. |* Bles, Edward J., B.A., B.Sc., Assistant to the Prof. of Natural History, Univ. of Glasgow
1898 | C. |* Blyth, Benjamin Hall, M.A., Memb. Inst. C.E., 17 Palmerston Place
1878 | C. Blyth, James, M.A., LL.D., Prof. of Natural Philosophy in Anderson’s College, Glasgow
1894 * Bolton, Herbert, Curator of the Bristol Museum, Queen’s Road, Bristol 65
1884 Bond, Francis T., B.A., M.D., M.R.G.S., Gloucester
1872 | C. Bottomley, J. Thomson, M.A., DSe., LL.D., F.R.S., F.C.S., Lecturer on Natural Philo-
sophy in the University of Glasgow, 13 University Gardens, Glasgow
18G9) |) C: Bow, Robert Henry, C.E., 7 South Gray Street
1886 * Bower, Frederick O., M.A., D.Sc., F.R.S., F.L.8., Regius Professor of Botany in the
University of Glasgow, 1 St John’s Terrace, Hillhead, Glasgow
1884 | GC, Bowman, Frederick Hungerford, D.Sc., F.C.S. (Lond. and Berl.), F.LC., Assoc. Inst. C.E.,
Assoc. Inst. M.E., M.LE.E., &c., 4 Albert Square, Manchester 70
1901 Bradbury, J. B., M.D., Downing Professor of Medicine, University of Cambridge
1903 | C. |* Bradley, O. Charnock, M.B., Ch.B., D.Se., Royal Veterinary College, Edinburgh
1886 * Bramwell, Byrom, M.D., F.R.C.P.E., 23 Drumsheugh Gardens
1895 * Bright, Charles, Assoc. Memb. Inst. C.E., Memb. Inst. E.K., F.R.A.S., F.G.S., 21 Old
Queen Street, Westminster, London
1886 Brittle, John Richard, Memb. Inst. C.E., Farad Villa, Vanbrugh Hill, Blackheath, Kent 75
1877 Broadrick, George, Memb. Inst. C.E., Broughton House, Broughton Road, Ipswich
* 1893 Brock, G. Sandison, M.D., 2 Via Veneto, Rome, Italy
1892 * Brock, W. J., M.B., D.Sc., 5 Manor Place
1901 | C. |* Brodie, W. Brodie, M.B., 28 Hamilton Park ‘lerrace, Hillhead, Glascow
1887 * Brown, A. B., C.E., Memb. Inst. Mech. E., 19 Douglas Crescent 80
1864 | C. Brown, Alex. Crum, M.D., D.Sc., F.R.C.P.E., LL.D., F.R.S. (Vicz-Prestpent), Professor
ee: of Chemistry in the University of Edinburgh, 8 Belgrave Crescent
1898 * Brown, David, F.C.S., F.1.C., Willowbrae House, Midlothian
1883 * Brown, J. J. Graham, M.D., F.R.C.P.E., 3 Chester Street
1883 * Bruce, Alexander, M.A., M.D., F.R.C.P.E., 8 Ainslie Place 85
1898 . |* Bryce, T. H., M.A., M.D. (Edin.), 2 Granby Terrace, Glasgow
1888 * Bryson, William A., Electrical Engineer, 16 Charlotte Street, Leith
1869 |C.B.| Buchan, Alexander, M.A., LL.D., F.R.S., Secretary to the Scottish Meteorological Society
C.
1885 | GC. Brown, J. Macdonald, M.D., F.R.C.S., 2 Frognal, London, N.W.
Cc
C
V. J. (Curator oF Lisrary anpD Museum), 2 Dean Terrace
1870 |C.K.} Buchanan, John Young, M.A., F.R.S., Christ’s College, Cambridge
1902 | * Buchanan, Robert M., M.B., F.F.P.S.G., 2 Northbank Terrace, Glasgow 90
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 128
870 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Beet) |
1882 _* Buchanan, T. R., M.A., 12 South Street, Park Lane, London. W.
1887 | C. |* Buist, J. B., M.D., F.R.C.P.E., 1 Clifton Terrace
1905 | _ Bunting, Thomas Lowe, M.D., Scotswood, Newcastle-on-Tyne
1902 | * Burgess, A. G., M.A., Mathematical Master, Edinburgh Ladies’ College, 2 Craigcrook Terrace,
/ | Blackhall
1894 LC. K.| * Burgess, James, C.I.E., LL.D., M.R.A.S., M. Soc. Asiatique de Paris, H.A.R.1.B.A.,
22 Seton Place : 95
1902 * Burn, The Rev. John Henry, B.D., The Parsonage, Ballater {
1887 | * Burnet, John James, Architect, 18 University Avenue, Hillhead, Glasgow 7
1888 | '* Burns, Rev. T., F.S.A. Scot., Minister of Lady Glenorchy’s Parish Church, Croston Lodge,
| Chalmers Crescent
1903 * Butler, Rev. Dugald, M.A., Minister of the Tron Parish, 54 Blacket Place
1896 | * Butters, J. W., M.A., B.Sc., Rector of Ardrossan Academy 100
1887 | C. |* Cadell, Henry Moubray, of Grange, B.Sc., Bo'ness
1897 * Caird, Robert, LL.D., Shipbuilder, Greenock
1893 | ©. Calderwood, W. L., Inspector of Salmon Fisheries of Scotland, 7 Kast Castle Road, Merchiston
1894 * Cameron, James Angus, M.D., Medical Officer of Health, Firhall, Nairn
1905 | C. |* Cameron, John, M.D., D.Se., M.R.C.S. Eng., Demonstrator of Anatomy, University of
Manchester, Anatomy Department, Owens College, Manchester 105
1904 * Campbell, Charles Duff, 21 Montague Terrace, Inverleith Row
1878 Campbell, John Archibald, M.D., Gothic Villa, St Aubyn’s Road, Jersey ;
1899 | ©. | * Carlier, Edmund W, W., M.D., B.Sc., Prof. of Physiology in Mason College, Birmingham ‘
1902 * Carmichael, Sir Thomas D. Gibson, Bart., M.A., Malleny House, Balerno a
1905 | C. |* Carse, George Alexander, M.A., B.Sc., 120 Lauriston Place 110
1901 Carslaw, H. S., M.A., D.Sc., Professor of Mathematics in the University of Sydney,
New South Wales .¥
1905 Carter, Joseph Henry, F.R.C.V.S., Stone House, Church Street, Burnley, Lancashire
1898 + Carter, Wm. Allan, Memb. Inst. O, i., 32 Great King Street
1898 Carus-Wilson, Cecil, F.R.G.S., F.G.S., Royal Societies Club, St James Street, London .
1882 * Cay, W. Dyce, Memb. Inst. C.1., 1 Albyn Place 115 ;
1890 Charles, John J., M.A., M.D., C.M., Prof. of Anatomy and Physiology, Queen’s College, Cork é
1899 * Chatham, James, ee oon 98 Inverleith Place ;
1874 Chiene, John, C.B., M.D., LL.D., F.R.C.S.E., Professor of Surgery in the University of
Edinburgh, 26 Charlotte Square
1880 |C. K.| Chrystal, George, M.A., LL.D., Professor of Mathematics in the University of Edinburgh
(GENERAL SECRETARY), 5 Belgrave Crescent }
1891 *Clark, John B., M.A., Mathematical and Physical Master in Heriot’s Hospital School, .
Garleffin, Craiglea Drive 120 F
1903 * Clarke, William Eagle, F.L.S., Natural History Department, Royal Scottish Museum,
| Edinburgh, 35 Braid Road
1875 Clouston, T. 8., M.D., Vice-President of the Royal College of Physicians, Tipperlinn ‘
House, Morningside
1892 * Coates, Henry, Pitcullen House, Perth
1887 | * Cockburn, John, F.R.A.S., The Abbey, North Berwick
1904 | C. | Coker, Ernest George, M.A., 1D.Sc., Professor of Mechanical Engineering and Applied
| | Mechanies, City and Guilds Technical College, Finsbury, Leonard Street, City Road,
| London, E.C. 125
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 871
Date of
Election.
1904 Coles, Alfred Charles, M.D., D.Se., York House, Poole Road, Bournemouth, W.
1888 | C. Collie, John Norman, Ph.D., F.R.S., F.C.S., Professor of Organic Chemistry in the
University College, Gower Street, London
1904 | C. |* Colquhoun, Walter, M.A., M.B., Muirhead Demonstrator of Physiology, University of
Glasgow, 7 Stanley Street, Glasgow, W.
1886 Connan, Daniel M., M.A.
1872 Constable, Archibald, LL.D., 11 Thistle Street 130
1894 Cook, John, M.A., Principal of the Government Central College, Bangalore, India
1891 * Cooper, Charles A., LL.D., 41 Drumsheugh Gardens
1905 * Corrie, David, F.C.S., Nobel’s Explosives Company, Polmont Station
1375 Craig, William, M.D., F.R.C.S.E., Lecturer on Materia Medica to the College of Surgeons,
71 Bruntsfield Place
1898 * Crawford, Francis Chalmers, 19 Royal Terrace 135
1903 Crawford, Lawrence, M.A., D.Sc., Professor of Mathematics in the South African College,
Cape Town
1887 * Crawford, William Caldwell, 1 Logkharton Gardens, Colinton Road
1870 Crichton-Browne, Sir Jas., M.D., UL. D., F.R.S., Lord Chancellor’s Visitor and Vice-President
of the Royal] Institution of Great Britain, 61 Carlisle Place Mansions, Victoria Street,
and Royal Courts of Justice, Strand, London
1886 * Croom, Sir John Halliday, M.D., F.R.C.P.E., Professor of Midwifery in the University of
Edinburgh, Vice-President, Royal College of Surgeons, Edinburgh, 25 Charlotte
Square
1898 * Cullen, Alexander, F.S.A. Scot., Millburn House, by Hamilton 140
RSTSe) (C: Cunningham, Daniel John, M.D., LL.D., D.C.L., F.R.S., F.Z.S., Professor of Anatomy in
the University of Edinburgh (Secretary), 18 Grosvenor Crescent
1898 * Currie, James, M.A. Cantab., Larkfield, Golden Acre
1904 * Cuthbertson, John, Secretary, West of Scotland Agricultural College, 4 Charles Street,
Kalmarnock
1889 * Dalrymple, James D. G., F.S.A. Lond. and Scot., Meiklewood, Stirling
1885 * Daniell, Alfred, M.A., LL.B., D.Se., Advocate, c/o Messrs Buchan & Buchan, S.S.C.,
37 Great King Street 145
1897 * Davidson, Huch, of Braedale, Lanark
1884 Davy, R., F.R.C.S. Eng., Surgeon to Westminster Hospital, Burstone House, Bow, North
Devon
1894 * Denny, Archibald, Braehead, Dumbarton
1069 | C. Dewar, Sir James, M.A., LL.D., D.C.L., D.Sc. Dub., F.R.S., F.C.S., Jacksonian Professor of
V. J. Natural and Experimental Philosophy in the University of Cambridge, and
Fullerian Professor of Chemistry at the Royal Institution of Great Britain,
London
1905 * Dewar, James Campbell, C.A., 27 Douglas Crescent 150
1904 Dickinson, Walter George Burnett, F.R.C.V.S., Boston, Lincolnshire
1884 * Dickson, The Right Hon. Charles Scott, K.C., Lord-Advocate of Scotland, M.P. for the
Bridgeton Division of Glasgow, 22 Moray Place
1888 | C. |* Dickson, Henry Newton, M.A., D.Sc., 2 St Margaret’s Road, Oxford
1876 | C. Dickson, J. D. Hamilton, M.A., Fellow and Tutor, St Peter’s College, Cambridge
iWeksiay || (Op Dixon, James Main, M.A., President, Columbia College, Milton, Oregon, United
States ils
872 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Date of
Election.
1897
1904
1881
1902
1867
1896
1905
1882
1892
1901
1866
1901
1878
1904
1859
1903
1892
1899
1893
1904
1904
i885
ouING
|* Dobbie, James Bell, F.Z.S., 2 Hailes Street
/* Dobbie, James Johnston, M.A., D.Sc., F.R.S., Director of the Royal Scottish Museum,
Edinburgh, 27 Polwarth Terrace
Dobbin, Leonard, Ph.D., Lecturer on Chemistry in the University of Edinburgh, 7 Cobden
Road
Dollar, John A, W., M.R.C.V.S., 56 New Bond Street, London
Donaldson, J., M.A., LL.D., Principal of the University of St Andrews, St Andrews —_ 160
* Donaldson, William, M.A., Viewpark House, Spylaw Road
* Donaldson, Rev. William Galloway, Minister of St Paul’s Parish, 11 Claremont Creseent
* Dott, D. B., Memb. Pharm. Soc., 29 Spring Gardens
Doreee miele C.E., M.R.1.A., F.G.S., Editor of Indian Engineering, Caleutia
* Douglas, Carstairs Cumming, M.D., -B.Sc., Professor of Medical Jurisprudence and Hygiene,
Anderson’s College, Glasgow, 2 Royal Crescent, Glasgow 165
Douglas, David, 22 Drummond Place
* Drinkwater, Thomas W., L.R.C.P.E., L.R.C.S.E., 25 Blacket Place
Duneanson, J. J. Kirk, M.D., F.R.C.P.E., 22 Drumsheugh Gardens
* Dunlop, William Brown, M.A., 7 Carlton Street
Duns, Rey. Professor, D.D., 5 Greenhill Place 170
* Dunstan, John, M.R.C.V.S., 1 Dean Terrace, Liskeard, Cornwali
Dunstan, M. J. R., M.A., F.LC., F.C.S., Principal, South-eastern Agricultural College,
Wye, Kent
* Duthie, George, M.A., Inspector-General of Education, Salisbury, Rhodesia
Edington, Alexander, M.D., Colonial Bacteriologist, Graham’s Town, South Africa
* Edwards, John, 4 Great Western Terrace, Kelvinside, Glasgow i)
* Elder, William, M.D., F.R.C.P.E., 4 John’s Place, Leith
Elgar, Francis, Memb. Inst. C.E., LL.D., F.R.S., 18 Cornwall Terrace, Regent’s Park,
London
Elliot, Daniel G., Curator of Department of Zoology, Field Columbian Museum, Chicago,
U.S.
* Erskine-Murray, James Robert, D.Sc., 39 Watcombe Circus, Nottingham
* Evans, William, F.F.A., 38 Morningside Park 180
Ewart, James Ceossar, M.D., F.R.C.S.E., F.R.S., F.L.S., Professor of Natural History, Uni-
versity of Edinburgh
* Ewen, J. T., B.Sc., Memb. Inst. Mech. E., H.M.LS., 104 King’s Gate, Aberdeen
Ewing, James Alfred, M.A., B.Sc., LL.D., Memb. Inst. C.E., F.R.S., Director of Naval
Education, Royal Naval College, Greenwich
Kyre, John W. H., M.D., M.S. (Dunelm), D.P.H. (Camb.), Guy’s Hospital (Bacterio-
logical Department), London, 19 Villiers Street, London :
Fairley, Thomas, Lecturer on Chemistry, 8 Newton Grove, Leeds 185
* Fawsitt, Charles A., 9 Foremount Terrace, Dowanhill, Glasgow
Fayrer, Sir Joseph,, Bart., K.C.S.L, M.D., F’R.C.P.L., F.R.C.S. L. and E., LL.D., FRSs
Honorary Physician to the Queen, Lamorna, Falmouth
* Felkin, Robert W., M.D., F.R.G.S., Fellow of the Anthropological Society of Berlin,
12 Oxford Gardeus, North Kensington, London, W.
* Fergus, Andrew Freeland, M.D., 22 Blythswood Square, Glasgow
| Ferguson, James Haig, M.D., F.R.C.P.E., F.R.C.S.E., 7 Coates Crescent 190
* Ferguson, John, M.A., LL.D., Professor of Chemistry in the University of Glasgow
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 873
Date of
Election.
1868 | C. Ferguson, Robert M., Ph.D., LL.D. (Socrery’s Representative on GrorcE Herrot’s
Trust), 5 Douglas Gardens
1898 * Findlay, John R., M.A. Oxon., 27 Drumsheugh Gardens
1899 * Finlay, David W., B.A., M.D., LL.D., F/R.C.P., D.P.H., Professor of Medicine in the
University of Aberdeen, 2 Queen’s Terrace, Aberdeen
1900 | C.N. | * Flett, John S., M.A., D.Sc., Geological Survey Office, 28 Jermyn Street, London 195
1880 Flint, Robert, D.D., Corresponding Member of the Institute of France, Corresponding
Member of the Royal Academy of Sciences of Palermo, Emeritus Professor of
Divinity in the University of Edinburgh (Vicu-Presipent), 1 Mountjoy Terrace,
Musselbureh
1872 | ©. Forbes, Professor George, M.A., Memb. Inst. C.E., Memb. Inst. E.E., F.R.S., F.R.A.S.,
34 Great George Street, Westminster
1904 Forbes, Norman Hay, F.R.C.S.E., Drumminor, Tunbridge Wells, Kent
1892 * Ford, John Simpson, F.C.S., 4 Nile Grove
1858 Fraser, A. Campbell, Fellow of the British Academy, Hon. D.C.L. Oxford, LL.D., Litt.D.,
Emeritus Professor of Logic and Metaphysics in the University of Edinburgh, Gorton
House, Hawthornden’ 200
1896 * Fraser, John, M.B., F.R.C.P.E., one of H.M. Commissioners in Lunacy for Scotland,
13 Heriot Row
1867 | C Vraser, Sir Thomas R., M.D., LL.D., F.R.C.P.E., F.R.S., Professor of Materia Medica in
K. B. the University of Edinburgh, Honorary Physician to the King in Scotland, 13 Drum.
sheugh Gardens
1891 * Fullarton, J. H., M.A., D.Se., Brodick, Arran ,
1891 * Fulton, T. Wemyss, M.D., Scientific Superintendent, Scottish Fishery Board, 417 Great
Western Road, Aberdeen
1888 | ©, | * Galt, Alexander, D.Sc., Keeper of the Technological Department, Royal Scottish Museum,
Edinburgh 205
1901 Ganguli, Sanjiban, M.A., Principal, Maharaja’s College, and Director of Public Instruction,
Jaipur States, Jaipur, India
1899 Gatehouse, T. I., Assoc. Memb. Inst. C.E., Memb. Inst. M.E., Memb. Inst. E.E.,
Tulse Hill Lodge, 100 Tulse Hill, London
1867 Gayner, Charles, M.D., F.L.S.
i900 Gayton, William, M.D., M.R.C.P.E., 11 Redbourne Avenue, North Finchley, London,
NSW.
1889 * Geddes, George H., Mining Engineer, 8 Douglas Crescent 210
1880 | C. Geddes, Patrick, Professor of Botany in, University College, Dundee, and Lecturer on
Zoology, Ramsay Garden, University Hall, Edinburgh
1861 |C. B.| Geikie, Sir Archibald, LL.D. Oxf., D.Sc. Camb. Dub., F.R.S., F.G.S., Foreign Member
of the Reale Accad. Lincei, Rome, of the National Acad. of the United States,
Corresponding Member of the Institute of France and of the Academies of Berlin,
Vienna, Munich, Gottingen, Turin, Belgium, Stockholm, Christiania, Philadelphia,
New York, &c., 3 Sloane Court, London
Geikie, James, LL.D., D.C.L., F.R.S., F.G.S., Professor of Geology in the University of
Kdinburgh, Kilmorie, Colinton Road
TSS C: Gibson, George Alexander, D.Sc., M.D., LL.D., F.R.C.P.E., 3 Drumsheugh Gardens
1890 * Gibson, George A., M.A., LL.D., Professor of Mathematics in the Glasgow and West of
Scotland Technical College, 8 Sandyford Place, Glasgow 915
1871 |C. B.
Ww
874 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Date of
Election.
1877
1892 |
1900
1887
1880
1898
1901
1899
1897
1891
1898
1883
1880
1886
1897
1905
1905
1899
1888
1905
1899
1881
1876
1902
1896
1896
1888
1869
1877
188]
1880
1892
C.
Q
Gibson, John, Ph.D., Professor of Chemistry in the Heriot-Watt College, Ringlewood,
Colinton, Midlothian
Gifford, Herbert James, Assoc. M. Inst. C.E.
Gilchrist, Douglas A., B.Se., Professor of Agriculture and Rural Economy, Armstrong
College, Newcastle-upon-Tyne
* Gilmour, William, 9 Inverleith Row
Gilruth, George Ritchie, Surgeon, 53 Northumberland Street 220
* Glaister, John, M.D., F.F.P.S. Glasgow, D.P.H. Camb., Professor of Forensic Medicine in
the University of Glasgow, 3 Newton Place, Glasgow /
Goodwillie, James, M.A., B.Sc., Liberton, Edinburgh
* Goodwin, Thomas §., F.C.S., Professor of Chemistry, Veterinary College, Glasgow
Gordon-Munn, John Gordon, M.D., 34 Dover Street. London, W.
* Graham, Richard D., 11 Strathearn Road 225
* Gray, Albert A., M.D., 14 Newton Terrace, Glasgow
* Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the University
of Glasgow ,
Gray, Thomas, B.Sec., Professor of Physics, Rose Polytechnic Institute, Terre Haute,
Indiana, U.S.
* Greenfield, W. S., M.D., F.R.C.P.E., Professor of General Pathology in the University of
Edinburgh, 7 Heriot Row
Greenlees, Thomas Duncan, M.D. Edin., The Residency, Grahamstown, South Africa 230
* Gregory, John Walter, D.Sc., F.R.S., Professor of Geology in the University of Glasgow,
4 Park Quadrant, Glasgow
* Greig, Robert Blyth, F.Z.S., Fordyce Lecturer in Agriculture, University of Aberdeen,
Torloisk, Cults, Aberdeenshire
* Guest, Edward Graham, M.A., B.Sc., 5 Church Hill
Guppy, Henry Brougham, M.B., Rosario, Salcombe, Devon
* Halm, Jacob E., Ph.D., Assistant Astronomer, Royal Observatory, and Lecturer on
Astronomy in the University of Edinburgh, Royal Observatory, Blackford Hill,
Edinburgh ‘ 235
Hamilton, Allan M‘Lane, M.D., 44 East Twenty-ninth Street, New York
Hamilton, D. J., M.B., F.R.C.S.E., Professor of Pathological Anatomy in the University
of Aberdeen, 35 Queen’s Road, Aberdeen
Hannay, J. Ballantyne, Cove Castle, Loch Long
* Harereaves, Andrew Fuller, F.C.S., Eskhill House, Roslin
* Harris, David, Fellow of the Statistical Society, Lyncombe Rise, Prior Park Road,
Bath 240
* Harris, David Fraser, B.Sc. (Lond.), M.D., F.S.A. Scot., Lecturer on Physiology in the
University of St Andrews
* Hart, D. Berry, M.D., F.R.C.P.E., 29 Charlotte Square
Hartley, Sir Charles A., K.C.M.G., Memb. Inst. C.E., 26 Pall Mall, London
Hartley, W. N., D.Se., F.R.S., F.LC., Prof. of Chemistry, Royal College of Science for
Ireland, Dublin
Harvie-Brown, J. A., of Quarter, F.Z.S., Dunipace House, Larbert, Stirlingshire 245
Hayeraft, J. Berry, M.D., D.Se., Professor of Physiology in the University College of
South Wales and Monmouthshire, Carditf
* Heath, Thomas, B.A., Assistant Astronomer, Royal Observatory, Edinburgh
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 875
Date of
Election.
1862
1893
1890
1900
1890°
1896
1881
1894
1902
1904
1885
1881
1896
1904
1897
1893
1899
1883
1872
1886
1887
1887
1882
1904
1904
1875
1894
1889
1882
1901
1900
Hector, Sir J., K.C.M.G., M.D., F.R.S., Director of the Geological Survey, Colonial
Laboratory, Meteorological and Weather Departments, and of the New Zealand
Institute, Wellington, New Zealand
Hehir, Patrick, M.D., F.R.C.S.E., M.R.C.S.L., L.R.C.P.E., Surgeon-Captain, Indian Medical
Service, Principal Medical Officer, H.H. the Nizam’s Army, Hyderabad, Deccan, India
Hele, T. Arthur, M.D., M.R.C.P.L., M.R.C.S., 3 St Peter’s Square, Manchester 250
Henderson, John, D.Se., Assoc. Inst. H.E., Kinnoul, Warwick’s Bench Rd., Guildford,
Surrey
* Hepburn, David, M.D., Professor of Anatomy in the University College of South Wales
aud Monmouthshire, Cardiff
* Herbertson, Andrew J., M.A., Ph.D., Reader in Geography, and Curator, School of
Geography, University of Oxford, 4 Broad Street, Oxford
Herdman, W.A., D.Se., F.R.S., F.L.S., Prof. of Natural History in University College,
Liverpool, Croxteth Lodge, Ullet Road, Liverpool
Hill, Alfred, M.D., M.R.C.8., FJ-C., Valentine Mount, Freshwater Bay, Isle of Wight 255
* Hinxman, Lionel W., B.A., Geological Survey Office, George IV. Bridge
Hobday, Frederick T. G., F.R.C.V.S., 6 Berkeley Gardens, Kensington, London
Hodgkinson, W. R., Ph.D., F.1.C., F.C.S., Prof. of Chem. and Physics at the Royal Military
Acad. and Royal Artillery Coll., Woolwich, 18 Glenluce Road, Blackheath, Kent
Horne, John, LL.D., F.R.S., F.G.S., Director of the Geological Survey of Scotland, Sheriff-
Court Buildings, Edinburgh
Home, J. Fletcher, M.D., F.R.C.S.E., The Poplars, Barnsley 260
* Horsburgh, Ellice Martin, M.A., B.Sc., Lecturer in Technical Mathematics, University of
Edinburgh, 11 Granville Terrace
Houston, Alex, Cruikshanks, M.B., C.M., D.Sc., 14 Upper Addison Gardens, Kensington,
London
Howden, Robert, M.A., M.B., C.M., Professor of Anatomy in the University of Durham,
14 Burdon Terrace, Newcastle-on-Tyne
Howie, W. Lamond, F.C.S., Hanover Lodge, West Hill, Harrow
* Hoyle, William Evans, M.A., D.Sc, M.R.C.S., 25 Brunswick Road, Withington,
Manchester 265
Hughes-Hunter, Colonel Charles, of Plas Coch, Llanfairpwll, Anglesea, and Junior United
Service Club, London
Hunt, Rev. H. G. Bonavia, Mus.D. Dub., Mus.B. Oxon., The Vicarage, Burgess Hill,
Sussex
* Hunter, James, F.R.C.8.E., F.R.A.S., Rosetta, Liberton, Midlothian
* Hunter, William, M.D., M.R.C.P. L. and E., M.R.C.S., 54 Harley Street, London
* Inglis, J. W., Memb. Inst. C.E., Kenwood, Barnton, Midlothian 270
Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal
* Ireland, Alexander Scott, §.8.C., 2 Buckingham Terrace
Jack, William, M.A., LL.D., Professor of Mathematics in the University of Glasgow
Jackson, Sir John, LL.D., 10 Holland Park, London
* James, Alexander, M.D., F.R.C.P.E., 10 Melville Crescent 27
* Jamieson, Prof. A., Memb. Inst. C.E., 16 Rosslyn Terrace, Kelvinside, Glasgow
* Jardine, Robert, M.D., M.R.C.S. Eng., F.F.P. and S. Glas., 20 Royal Crescent, Glasgow
Jee, Sir Bhagvat Sinh, G.C.I.E., M.D., LL.D. Edin., H.H. The Thakore Sahib of Gondal,
Gondal, Kathiawar, Bombay
cr
876 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Date of
Election.
1900 | * Jerdan, David Smiles, M.A., D.Se., Ph.D., Temora, Colinton, Midlothian
1895 Johnston, Lieutenant-Colonel Henry Halcro, C.B., R.A.M.S., D.Se., M.D., F.L.S., Orphir
House, Kirkwall, Orkney 280
1903 | * Johnston, Thomas Nicol, M.B., C.M., Corstorphine House, Corstorphine
1902 Johnstone, George, Lieut. R.N.R., Marine Sa ala ae British India Steam Navigation
Co., 16 Strand Road, Calcutta, India
1874 Jones, ir rancis, M.Se., Lecturer on Chemistry, Beaufort House, Alexandra Park,
Manchester
1888 Jones, John Alfred, Memb. Inst. C.E., Fellow of the Univ. of Madras, Sanitary Engineer to
the Government of Madras, c/o Messrs Parry & Co., 70 Gracechurch St., London
1905 Jones, George William, M.A., B.Sc., 28 Roseneath Place 285
1847 |C.K.| Kelvin, The Right Hon. Lord, G.C.V.O., P.C., LL.D., D.C.L., F.R.S. (Prusmpent), Grand
Vv. J Officer of the Legion of Honour of France, Member of the Prussian Order Powr le
Mérite, Foreign Associate of the Institute of France, and Emeritus Professor of
Natural Philosophy in the University of Glasgow, Netherhall, Largs, Ayrshire, and
15 Eaton Place, London, S.W.
1892 * Kerr, Rev. John, M.A., Manse, Dirleton
1903 |C.N.| * Kerr, John Graham, M.A., Professor of Zoology in the University of Glasgow
1891 Kerr, Joshua Law, M.D., Biddenden Hall, Cranbrook, Kent
1886 | C. N.| * Kidston, Robert, F.R.S., F.G.S., 12 Clarendon Place, Stirling 290
1877 King, Sir James, of Campsie, Bart., LL.D., 115 Wellington Street, Glasgow
1880 King, W. F., Lonend, Russell Place, ‘Trinity
1883 * Kinnear, The Rt. Hon. Lord, one of the Senators of the College of Justice, 2 Moray Place
1878 Kintore, The Right Hon. the Karl ‘of, M.A. Cantab., LL.D. Cambridge, Aberdeen and
Adelaide, Keith Hall, Inverurie, Aberdeenshire
1901 * Knight, The Rey. G. A. Frank, M.A., St Leonard’s United Free Church, Perth 295
1880 |C. K.| Knott, C. G., D.Se., Lecturer on Applied Mathematics in the University of Edinburgh (late
Prof. of Physics, Imperial University, Japan), (Srcrmrary), 42 Upper Gray Street,
Edinburgh
1896 | ©, | * Kuenen, J. P., Ph.D. (Leiden), Prof. of Natural Philosophy in University College, Dundee
1886 * Laing, Rev. George P., 17 Buckingham Terrace
1878 | C. Lang, P. R. Scott, M.A., B.Sc., Professor of Mathematics, University of St Andrews
1885 | C. |* Laurie, A. P., M.A., D.Sc., Principal of the Heriot-Watt College, Edinburgh 300
1894 | ©. |* Laurie, Malcolm, B.A., D.Sc., F.L.S., Royal College of Surgeons, Edinburgh
1870 Laurie, Simon S8., M.A., LL.D., Emeritus Professor of Education in the University of
| Edinburgh, 22 George Square
1905 * Lawson, David, M.A., M.D., L.R.C.P., and S.E., Druimdarroch, Banchory, Kincardineshire
1903 * Leighton, Gerald Rowley, M.D., 51 E. Trinity Road
1874 |C. K.| Letts, E. A., Ph.D., F.LC., F.C.8., Professor of Chemistry, Queen’s College, Belfast 305
1905 * Lightbody, Forrest Hay, 56 Queen Street
1889 * Lindsay, Rev. James, D.D., B.Sc., F.G.8., M.R.A.S., Corresponding Member of the Royal
Academy of Sciences, Letters and Arts, of Padua, Associate of the Philosophical
Society of Louvain, Minister of St Andrew’s Parish, Springhill Terrace,
Kalmarnock
1870 |C.B.| Lister, The Right Hon. Lord, P.C., M.D., F.RIC.S.L., F.R.C.S.E., LL.D., DiC.L., FaRSe
Foreign Associate of the Institute of France, Emeritus-Prof. of Clinical Surgery, King’s
College, Surgeon Extraordinary to the King, 12 Park Crescent, Portland P]., London
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 877
Date of
Election.
1903 Liston, William Glen, M.D., Captain, Indian Medical Service, c/o Grindlay Groom & Co.,
Bombay, India
1903 * Littlejohn, Henry Harvey, M.A., M.B., B.Se., F.R.C.S.E., 1 Atholl Crescent 310
IS97- |) C. Lloyd, Richard John, M.A., D.Lit., 494 Grove Street, Liverpool
1898 * Lothian, Alexander Veitch, M.A., B.Sc., 16 Clarence Drive, Hyndland, Glaszow
1884 * Low, George M., Actuary, 11 Moray Place
1888 * Lowe, D. F., M.A., LL.D., Head Master of Heriot’s Hospital School, Lauriston
1904 * Lowson, Charles Stewart, M.B., C.M., Captain, Indian Medical Service, c/o Messrs Thomas
Cook & Son, Bombay, India 315
1900 Lusk, Graham, Ph.D., M.A., Pref. of Physiology, Univ. and Bellevue Medical College, N.Y.
1894 * Mabbott, Walter John, M.A., Rector of County High School, Duns, Berwickshire
1887 M‘Aldowie, Alexander M., M.D., 6 Brook Street, Stoke-on-Trent
1891 Macallan, John, F.I.C., 3 Rutland Terrace, Clontarf, Dublin
1888 | C. M‘Arthur, John, F.C.S., 196 Trinity Road, Wandsworth Common, London 320
1883 *M‘Bride, P., M.D., F.R.C.P.E., 16 Chester Street
1903 * M‘Cormick, W. S., M.A., LL.D., 13 Douglas Crescent
1899 * M‘Cubbin, James, B.A., Rector of the Burgh Academy, Kilsyth
1905 * Macdonald, Hector Munro, M.A., F.R.S., Professor of Mathematics, University of Aber-
deen, 33 College Bounds, Aberdeen
1894 * Macdonald, James, Secretary of the Highland and Agricultural Society of Scotland,
2 Garscube Terrace 325
1897 | C. |* Macdonald, James A., M.A., B.Se., H.M. Inspector of Schools, Glengarry, Dingwall
1904 * Macdonald, J. A., M.A., B.Sc., Olive Lodge, Polwarth Terrace
1886 * Macdonald, The Rt. Hon. Sir J. H. A., K.C.B., K.C., LL.D., F.R.S., M.LE.E., Lord Justice-
Clerk, and Lord President of the Second Division of the Court of Session, 15 Abercromby
Place
1904 Macdonald, William, B.Sc., M.Sc., Chief of the Division of Publications under the Depait-
ment of Agriculture, Pretoria Club, Pretoria, Trausvaal
1886 * Macdonald, William J., M.A., Comiston Drive 330
1901 | C. |* MacDougal, R. Stewart, M.A., D.Sc., 13 Archibald Place
1888 | C. | * M‘Fadyean, Sir John, M.B., B.Sc., Principal, and Professor of Comparative Pathology in
the Royal Veterinary College, Camden Town, London
1878 | C. Macfarlane, Alexander, M.A., D.Sc., LL.D., Lecturer in Physics in Lehigh University,
Pennsylvania, Gowrie Grove, Chatham, Ontario, Canada
1885 | C. |* Macfarlane, J. M., D.Sc., Professor of Botany and Director of the Botanic Garden,
University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A.
1897 * M‘Gillivray, Angus, C.M., M.D., South Tay Street, Dundee 335
1878 M‘Gowan, George, F.1.C., Ph.D., 21 Montpelier Road, Ealing, Middlesex
1886 * MacGregor, Rev. James, D.D., 3 Eton Terrace
1880 | C. MacGregor, James Gordon, M.A., D.Se., LL.D.. F.R.S., Prof. of Natural Philosophy in the
University of Edinburgh, 24 Dalrymple Crescent
1903 *M‘Intosh, D. C., M.A., 37 Warrender Park Terrace
1869 |C. N.| M‘Intosh, William Carmichael, M.D., LL.D., F.R.S., F.L.S., Professor of Natural History
in the University of St Andrews, 2 Abbotsford Crescent, St Andrews 340
1895 | C. |* Macintyre, John, M.D., 179 Bath Street, Glasgow
1882 * Mackay, John Sturgeon, M.A., LL.D., late Mathematical Master in the Edinburgh
Academy, 69 Northumberland Street
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 129
878
Date of
Election.
1873
1900
1894
1898
1904
1905
1904
1894
1869
1869
1899
1888
1876
1876
1893
1884
1890
1898
1880
1882
1901
1888
1892
1903
1864
1866
1885
1898
1890
1902
1901
1888
1902
1885
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
C. B,
C.
CK:
C. B.
C.B:
M‘Kendrick, John G., M.D., F.R.C.P.E., LL.D., F.R.S., Professor of Physiology in the
University of Glasgow, 2 Buckingham Terrace, Glasgow
* M‘Kendrick, John Souttar, M.D., 2 Florentine Gardens, Hillhead, Glasgow
* Mackenzie, Robert, M.D., Napier, Nairn 345
Mackenzie, W. Cossar, D.Sc., Principal of the College of Agriculture, Gheezeh, Egypt
* Mackenzie, W. Leslie, M.A., M.D., D.P.H., Medical Member of the Local Government
Board for Scotland, 1 Stirling Road, Trinity
Mackenzie, William Colin, M.D., F.R.C.S., Demonstrator of Anatomy in the University
of Melbourne, Elizabeth Street North, Melbourne, Victoria
* Mackintosh, Donald James, M.V.O., M.B., Supt. of the Western Infirmary, Glasgow
Maclagan, Philip R. D., F.F.A. (TRasurer), St Catherine’s, Liberton 350
Maclagan, R. C., M.D., F.R.C.P.K., 5 Coates Crescent
M‘Laren, The Hon. Lord, LL.D. Edin. & Glasg., F.R.A.S., one of the Senators of the
College of Justice (Vicu-Presipent), 46 Moray Place
Maclean, Ewan John, M.D., M.R.C.P. London, 12 Park Place, Cardiff
Maclean, Magnus, M.A., D.Sc., Memb. Inst. E. E., Prof. of Electrical Engineering in
the Glasgow and West of Scotland Technical College, 51 Kerrsland Terrace, Hillhead,
Glasgow
Macleod, Very Rev. Norman, D.D., Westwood, Inverness 355
Macmillan, John, M.A., D.Sec., M.B., \C.M., F.R.C.P.E., 48 George Square
M‘Murtrie, The Rev. John, M.A., D.D., 13 Inverleith Place
Maepherson, Rey. J. Gordon, M.A., D.Sc., Ruthven Manse, Meigle
M‘Vail, John C., M.D., 20 Eton Place, Hillhead, Glasgow
Mahalanobis, S. C., B.Se., Professor of Physiology, Presidency College, Calcutta, India 360
Marsden, R. Sydney, M.B., C.M., D.Sc., F.LC., F.C.S., Rowallan House, Cearns Road,
and Town Hal], Birkenhead
Marshall, D. H., M.A., Professor of Physics in Queen’s University and College, Kingston,
Ontario, Canada
* Marshall, F. H. A., M.A., D.Sc., Physiological Department, University of Edinburgh
Marshall, Hugh, D.Sc., F.R.S., Lecturer on Chemistry and on Mineralogy and Crystallo-
graphy in the University of Edinburgh, 12 Lonsdale Terrace
Martin, Wrancis John, W.S., 17 Rothesay Place 365
Martin, Nicholas Henry, F.L.S., F.C.S., Ravenswood, Low Fell, Gateshead
Marwick, Sir James David, LL.D., 19 Woodside Terrace, Glasgow
Masson, David, LL.D., Litt. D. Dub., Emeritus-Professor of Rhetoric and English Literature
in the Univ. of Edin., H.M. Historiographer for Scotland, 2 Lockharton Gardens
* Masson, Orme, D.Sce., F.R.S., Professor of Chemistry in the University of Melbourne
Masterman, Arthur Thomas, M.A., D.Sc., Inspector of Fisheries, Board of Agriculture,
Whitehall, London 370
Matheson, The Rev. George, M.A., B.D., D.D., LL.D., 19 St Bernard’s Crescent
Matthews, Ernest Romney, C.E., F.G.8., Bridlington, Yorkshire
* Menzies, Alan W. C., M.A., B.Sc., F.C.S., Professor of Chemistry in St Mungo’s College,
Glasgow
* Methven, Cathcart W., Memb. Inst. C.E., F.R.I.B.A., Durban, Natal, 8. Africa
Metzler, William H., A.B., Ph.D., Corresponding Fellow of the Royal Society of Canada,
Professor of Mathematics, Syracuse University, Syracuse, N.Y. 375
* Mill, Hugh Robert, D.Sc., LL.D., 62 Camden Square, London
ae
*
*
*
ok
*
k
ra
:
. ae
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 6879
Election.
1905 * Miller-Milne, C. H., M.A., Rector, The High School, Arbroath, 8 Dalhousie Place, Arbroath
1905 | * Milne, Archibald, M.A., B.Sc., Lecturer on Mathematics and Science, Cliurch of Scotland
Training College, 5 Elgin Terrace
1904 | C. |* Milne, James Robert, B.Sc.. 56 Manor Place
1886 * Milne, William, M.A., B.Sc., 70 Beecberove Terrace, Aberdeen 380
1899 * Milroy, T. H., M.D., B.Sc., Professor of Physiology in Queen’s College, Belfast, 14 Ashley
Avenue, Belfast
1866 Mitchell, Sir Arthur, K.C.B., M.A., M.D., LL.D., 34 Drummond Place
S89) C! Mitchell, A. Crichton, D.Se., Professor of Pure and Applied Mathematics, and Principal of
the Maharajah’s College, Trivandrum, Travancore, India
1897 * Mitchell, George Arthur, M.A., 9 Lowther Terrace, Kelvinside, Glasgow
1900 * Mitchell, James, M.A., B.Sc., 7 Bath Street, Nairn 385
1899 * Mitchell-Thomson, Sir Mitchell, Bart.,.6 Charlotte Square
890) (C: Mond, R. L., M.A. Cantab., ES., The Poplars, 20 Avenue Road, Regent’s Park, London
NSS ui uy Moos, N. A. F., L.C.E., B.Sc., Professor of Physics, Elphinstone College, and Director of
the Government Observatory, Colaba, Bombay
1901 * More, James, jun., M. Inst. C.E., 74 George Street
1896 * Morgan, Alexander, M.A., D.Sc., Rector, Church of Scotland Training College, 1 Midmar
Gardens 390
1892 Morrison, J. T., M.A., B.Se., Professor of Physics and Chemistry, Victoria College, Stellen-
bosch, Cape Colony
1901 Moses, O. St John, M.D., B.Se., F.R.C.S.E., Captain, Indian Medical Service, 8 Lansdowne
Road, Calcutta, India
1892 | ©. |* Mossman, Robert C., 30 Blacket Place
1874 |C. K.| Muir, Thomas, C.M.G., M.A., LL.D., F.R.S., Superintendent-General of Education for Cape
Colony, Education Office, Cape Town, and Mowbray Hall, Rosebank, Cape Colony
1888 | C. |* Muirhead, George, Commissioner to His Grace the Duke of Richmond and Gordon, K.G.,
Speybank, Fochabers 395
1887 Mukhopadhyay, Asitosh, M.A., LL.D., F.R.A.S., M.R.I.A., Professor of Mathematics
at the Indian Association for the Cultivation of Science, 77 Russa Road North,
Bhowanipore, Calcutta
1894 * Munro, J. M. M., Memb. Inst. E.E., 136 Bothwell Street, Glasgow
1891 | C. |* Munro, Robert, M.A., M.D., LL.D., Hon. Memb. R.I.A., Hon. Memb. Royal Soc. of
Antiquaries of Ireland (Vice-Presipent), 48 Manor Place and Elmbank, Largs, Ayrshire
1896 * Murray, Alfred A., M.A., LL.B., 20 Warriston Crescent
1892 | C. |* Murray, George Robert Milne, F.R.S., F.L.S., Keeper of the Botanical Department, British
Museum (Natural Hist.), Cromwell Road, London 400
1877 | C. Murray, Sir John, K.C.B., LL.D., D.C.L., Ph.D., D.Se., F.R.S., Member of the Prussian
BLN. Order Pour le Mérite, Director of the Challenger Expedition Publications (Vicx-
Presipent). Office, Villa Medusa, Boswell Road. House, Challenger Lodge, Wardie,
and United Service Club
1887 Muter, John, M.A., F.C.S., South London Central Public Laboratory, 325 Kennington
Road, London
1902 Mylne, The Rev. R. S., M.A., B.C.L., Oxford, F.S.A. Lond., Great Amwell, Herts
1888 Napier, A. D. Leith, M.D., C.M., M.R.C.P.L., General Hospital, Adelaide, S. Australia
1897 Nash, Alfred George, C.E., B.Sc., Engineer, Department of Public Works, Jamaica,
Belretiro, Mandeville, Jamaica, W.I. 405
880
Date of
Election.
1887
=
v2)
ite}
lo 2)
1895
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
* Nasmyth, T. Goodall, M.D., C.M., D.Se., Cupar-Vife
Newman, George, M.D., D.P.H, Cambridge, 2 Woburn Square, London
|* Nicholson, J. Shield, M.A., D.Se., Professor of Political Economy in the University of
Edinburgh, 3 Belford Park
C. | Nicol, W. W. J., M.A., D.Sc., 15 Blacket Place
| Norris, Richard, M.D., M.R.C.S. Eng., 3 Walsall Road, Birchfield, Birmingham 410
| Nunn, Joshua Arthur, C.1.E., D.S.O., F.R.C.V.S., Barrister-at-Law, Lincoln’s Inn; Veter-
inary Lieut.-Colonel and Deputy Director-General, Army Veterinary Department,
| Pretoria, South Africa
/* Ogilvie, F. Grant, M.A., B.Sc., Principal Assistant Secretary for Science, Art, and
| Technology, Board of Education, Whitehall, London
| * Oliphant, James, M.A., 12 Murrayfield Road
C. Oliver, James, M.D., F.L.S., Physician to the London Hospital for Women, 18 Gordon
Square, London
Oliver, Thomas, M.D., F.R.C.P., Professor of Physiology in the University of Durham,
7 Ellison Place, Newcastle-upon-Tyne 415
|
1884 |C. K.| * Omond, R. Traill, 3 Church Hill
1905
1892 |
1901
1886
1889
1892
Pallin, William Alfred, F.R.C.V.S., Captain in the Army Veterinary Department, c/o
Messrs Holt & Co., 3 Whitehall Place, London
Parker, Thomas, Memb. Inst. C.E., 1B Chapel Street, Edgeware Road, London
* Paterson, David, F.C.S., Lea Bank, Rosslyn, Midlothian
C. |* Paton; D. Noél, M.D., B.Sc., F.R.C.P.H., 22 Lyndoch Place 420
| * Patrick, David, M.A., LL.D., c/o W. & R. Chambers, 339 High Street
/* Paulin, David, Actuary, 6 Forres Street
1881 PC: N.| Peach, Benjamin N., LL.D., F.R.S., F.G.S., late District Superintendent and Acting
1904 |
1889 |
1863 |
Palzeontologist of the Geological Survey of Scotland, 72 Grange Loan
'* Peck, James Wallace, M.A., Principal Assistant to Executive Officer (Education) of the
London County Council, 70 High Street, Hampstead, London
.* Peck, William, F.hk.A.S., Town’s Astronomer, City Observatory, Calton Hill, Edinburgh 425
Peddie, Alexander, M.D., F.h.C.P.E., 15 Rutland Street
1887 / C.B. | * Peddie, Wm., D.Sc., Lecturer on Natural Philosophy, Edinburgh University, 14 Ramsay
1900 |
1893
1889
1905
1886
1888
Garden
Penny, John, M.B., C.M., D.Se., Great Broughton, near Cockermouth, Cumberland
Perkin, Arthur George, F.R.S., 8 Montpellier Terrace, Hyde Park, Leeds
| * Philip, R. W., M.A., M.D., F.R.C.P.E., 45 Charlotte Square 430
|* Pinkerton, Peter, M.A., Head Mathematical Master, George Watson’s College, Edinburgh,
36 Morningside Grove
Pollock, Charles Frederick, M.D., F.R.C.S.E., 1 Buckingham Terrace, Hillhead, Glasgow
Prain, David, Lt.-Col., Indian Medical Service, M.A., M.B., LL.D., F.L.S., F.R.S., Hon.
Memb. Soc. Lett. ed Arti d. Zelanti, Acireale ; Corr. Memb. Pharm. Soc. Gt. Britain,
ete. ; Director, Botanical Survey of India, Royal Botanic Gardens, Shibpur, Calcutta
_* Preller, Charles Du Riche, M.A., Ph.D., Assoc. Memb, Inst. C.E., 61 Melville Street
|* Pressland, Arthur J., M.A. Camb., Edinburgh Academy 435
C. Prevost, E. W., Ph.D., Weston, Ross, Herefordshire
* Pullar, J. F., Rosebank, Perth
* Pullar, Laurence, The Lea, Bridge of Allan
Pullar, Sir Robert, LL.D., Tayside, Perth
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 881
Date of
Election.
1898 * Purves, John Archibald, D.Se., 53 York Place 440
1897 * Rainy, Harry, M.B., C.M., F.R.C.P. Ed., 16 Gt. Stuart Street
1899 * Ramage, Alexander G., 8 Western Terrace, Murrayfield
1884 Ramsay, I. Peirson, M.R.LA., F.L.S., C.M.Z.S., F.R.G.S., F.G.S., Fellow of the Imperial
and Royal Zoological and Botanical Society of Vienna, Curator of Australian Museum,
Sydney, N.S.W.
1891 * Rankine, John, M.A., LL.D., Advocate, Professor of the Law of Scotland in the University
of Kdinburgh, 23 Ainslie Place
1904 Ratcliffe, Joseph Riley, M.B., C.M., Elmdon, Wake Green Road, Morley, Birmingham 445
1900 Raw, Nathan, M.D., Mill Road Infirmary, Liverpool
1883 | C. | * Readman, J. B., D.Se., F.C.S., Mynde Park, Tram Inn, Hereford
1889 Redwood, Sir Boverton, D.Sc. (Hou.), F.I.C., F.C.S., Assoc. Inst. C.E., Wadham Lodge,
Wadham Gardens, London
1902 Rees-Roberts, John Vernon, M.D., D.Sc., D.P.H., Barrister-at-Law, National Liberal Club,
Whitehall Place, London
1902 Reid, George Archdall O’Brien, M.B., C.M., 9 Victoria Road South, Southsea, Hants 450
1875 Richardson, Ralph, W.S., 10 Magdala Place
1872 Ricarde-Seaver, Major F. Ignacio, Atheneum Club, Pall Mall, London
1898 | C. Roberts, Alexander William, D.Sc., F.R.A.S., Lovedale, South Africa
1880 Roberts, D. Lloyd, M.D., F.R.C.P.L., 23 St John Street, Manchester
1872 Robertson, D. M. C. L. Argyll, M.D., F.R.C.S.E., LL.D., Surgeon Oculist to the King
in Scotland, Mon Plaisir, St Aubins, Jersey 455
1900 * Robertson, Joseph M‘Gregor, M.B., C.M., 26 Buckingham Terrace, Glasgow
1896 * Robertson, Robert, M.A., 25 Mansionhouse Road
1902 | C. | * Robertson, Robert A., M.A., B.Sc., Lecturer on Botany in the University of St Andrews
1896 | C. |* Robertson, W. G. Aitchison, D.Sc., M.D., F.R.C.P.E., 26 Minto Street
1905 | C. | * Romanes, George, C.E., Craigknowe, Slateford, Midlothian 460
1881 Rosebery, The Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L., F.R.S., Dalmeny Park,
Edinburgh
1880 Rowland, L. L., M.A., M.D., President of the Oregon State Medical Society, and Professor
of Physiology and Microscopy in Williamette University, Salem, Oregon
1902 | C. |* Russell, James, 11 Argyll Place
1880 Russell, Sir James A., M.A., B.Sc., M.B., F.R.C.P.E., LL.D., Woodville, Canaan Lane >
1904 Sachs, Edwin O., Architect, 7 Waterloo Place, Pall Mall, London, S.W. 465
1903 * Samuel, John §., 8 Park Avenue, Glasgow
1897 * Sanderson, William, Talbot House, Ferry Road
1864 Sandford, The Right Rev. Bishop D. F., D.D., LL.D., 4 Coates Crescent
1903 * Sarolea, Charles, Ph.D., D. Litt., Lecturer on French Language, Literature, and Romance
Philology, University of Edinburgh, Hermitage, Colinton
1895 Savage, Thomas, M.D., F.R.C.S. England, M.R.C.P. London, Professor of Gynecology,
Mason College, Birmingham, The Ards, Knowle, Warwickshire 470
1891 Sawyer, Sir James, Knt., M.D., F.R.C.P., F.S.A., J.P., Consulting Physician to the Queen’s
Hospital, 31 Temple Row, Birmingham
1900 | C. |* Schafer, Edward Albert, M.R.C.S., LL.D., F.R.S., Professor of Physiology in the Univer-
sity of Edinburgh
1885 | C. Scott, Alexander, M.A., D.Sc., F.R.S., The Davy-Faraday Research Laboratory of the Royal
Institution, London
882
Date of
Election.
1880
1905
1902
1872
1897
1894
1870
1871
1900
1903
1901
1891
1882
1885
1871
1904
1880
1899
1880
1889
1882
1896
1874
1891
1886
1884
1868
1888
1868
1904
1873
1877
1902
1889
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Scott, J. H., M.B., C.M., M.R.C.S., Prof. of Anatomy in the University of Otago, New
Zealand
Scougal, A. E., M.A., H.M.C.1I.S., 1 Wester Coates Avenue 475
Senn, Nicholas, M.D., LL.D., Professor of Surgery, Rush Medical College, Chicago,
U.S.A.
Seton, George, M.A., Advocate, Ayton House, Abernethy, Perthshire
* Shepherd, John William, Carrickarden, Bearsden, Glasgow
* Shield, Wm., Memb. Inst. C.E., 33 Old Queen Street, Westminster, London
Sime, James, M.A., Craigmount House, 10 Grange Road 480
Simpson, A. R., M.D., Emeritus Professor of Midwifery in the University of Edinburgh,
52 Queen Street
* Simpson, James Young, M.A., D.Sc., Professor of Natural Science in the New College,
Edinburgh, 52 Queen Street
* Skinner, Robert Taylor, M.A., Governor and Headmaster, Donaldson’s Hospital, Edinburgh
* Smart, Edward, B.A., B.Sc., Benview, Craigie, Perth
* Smith, Alex., B.Sc., Ph.D., Prof. of General Chemistry, University of Chicago, Ills., U.S. 485
Smith, C. Michie, B.Sc., F.R.A.S., Director of the Kodaikanal and Madras Observatories,
The Observatory, Kodaikanal, South India
* Smith, George, F.C.S., Polmont Station
Smith, John, M.D., F.R.C.S.E., LL.D., 11 Wemyss Place
* Smith, William Charles, K.C., M.A., LL.B., Advocate, 6 Darnaway Street
Smith, William Robert, M.D., D.Sc., Barrister-at-Law, Professor of Forensic Medicine in
King’s College, 74 Great Russell Street, Bloomsbury Square, London 490
Snell, Ernest Hugh, M.D., B.Se., D.P.H. Camb., Coventry
Sollas, W.J., M.A., D.Sc., LL.D., F.R.S., late Fellow of St John’s College, Cambridge, and
Professor of Geology and Paleontology in the University of Oxford
Somerville, Wm., M.A., D.Sce., D.Oec., Assistant Secretary, H.M. Board of Agriculture,
4 Whitehall Place, London
* Sorley, James, F.I.A., C.A., 82 Onslow Gardens, London
* Spence, Frank, M.A., B.Sc., 25 Craiglea Drive 495
Sprague, T. B., M.A., LU.D., Actuary, 29 Buckingham Terrace
* Stanfield, Richard, Professor of Mechanics and Engineering in the Heriot-Watt College
* Stevenson, Charles A., B.Se., Memb. Inst. C.E., 28 Douglas Crescent
* Stevenson, David Alan, B.Sc., Memb. Inst. C.E., 45 Melville Street
Stevenson, John J., 4 Porchester Gardens, London 500
* Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the University
of Edinburgh, 9 Learmonth Gardens
Stewart, Major-General J. H. M. Shaw, late R.E., Assoc. Inst. C.E., F.R.G.S., 7 Inverness
Terrace, London, W.
* Stewart, Thomas W., M.A., B.Sc., Science Master, Edinburgh Ladies’ College, 29 Brunts-
field Gardens
Stewart, Walter, 3 Queensferry Gardens
Stirling, William, D.Se., M.D., LL.D., Brackenbury Professor of Physiology and Histology
in Owens College and Victoria University, Manchester 505
* Stockdale, Herbert Fitton, Clairinch, Upper Helensburgh, Dumbartonshire
* Stockman, Ralph, M.D., F.R.C.P.E., Professor of Materia Medica and Therapeutics in the
University of Glasgow
eo
Date of
Election.
1903
1896
1905
1885
1904
1898
1895
1890
1870
1899
1892
1885
1905
1887
1896
1903
1887
1880
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 883
BLN.
Sutherland, David W., M.D., M.R.C.P. Lond., Captain, Indian Medical Service, Professor
| of Pathology and Materia Medica, Medical College, Lahore, India
* Sutherland, John Francis, M.D., Dep. Com. in Lunacy for Scotland, Scotsburn Road, Tain,
Ross-shire
Swithinbank, Harold William, Denham Court, Denham, Bucks 510
* Symington, Johnson, M.D., F.R.C.S.E., F.R.S., Prof. of Anatomy in Queen’s College,
Belfast
* Tait, John W., B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith
Tait, William Archer, B.Sc., Memb. Inst. C.E., 38 George Square
Talmage, James Edward, D.Sc., Ph.D., F.R. M. 8., F.G.S., Professor of Geology, Univ. of
Utah, Salt Lake City, Utah
Tanakadate, Aikitu, Prof. of Nat. Phil. in the Imperial University of Japan, Tokyo,
Japan 515
Tatlock, Robert R., F.C.S., City Analyst’s Office, 156 Bath Street, Glasgow
'* Taylor, James, M.A., Mathematical Master in the Edinburgh Academy, 3 Meleund
| Terrace
Thackwell, J. B., M.B., C.M.
_* Thompson, Dive W., C.B., B.A., F..S8., Professor of vail History in University
College, Dundee
* Thoms, Alexander, 7 Playfair Terrace, St Andrews 520
* Thomson, Andrew, M.A., D.Sc., F.1.C., Rector, Perth Academy, Ardenlea, Pitcullen,
Perth
_* Thomson, George Ritchie, M.B., C.M., Cumberland House, Von Brandis Square, Johannes-
burg, Transvaal
Thomson, George S., E.C.S., Dairy Commissioner for (ueensland, Department of
Agriculture, Brisbane, Queensland
* Thomson, J. Arthur, M.A., Regius Prof. of Natural History in the Univ. of Aberdeen
Thomson, John Millar, LL.D., F.R.S., Prof. of Chem. in King’s College, Lond., 9 Campden
Hill Gardens, London O25
* Thomson, R. Tatlock, F.C.S., 156 Bath Street, Glasgow
Thomson, Spencer C., Actuary, 10 Eglinton Crescent
Thomson, Wm., M.A., B.Sc., LL.D., Registrar, University of the Cape of Good Hope,
University Buildings, Cape Town
Thomson, William, Royal Institution, Manchester
Traquair, R. H., M.D., LL.D., F.R.S., F.G.S., Keeper of the Natural History Collections in
the Royal Scottish Museum, Edinburgh (Vicz-PreswEnr), The Bush, Colinton 530
Tuke, Sir J. Batty, M.D., D.Se., LL.D., F.R.C.P.E., M.P. for the Universities of Edinburgh
and St Andrews, 20 Charlotte Square
* Turnbull, Andrew H., Actuary, The Elms, Whitehouse Loan
* Turner, Arthur Logan, M.D., F-R.C.S.E., 27 Walker Street
Turmer, Sit William, K.C.B; MOB, FR.C-S.E., LL.D., D:C.L., D.Se. Dub., F.R.S.,
Principal of the University of Edinburgh, 6 Eton Terrace
Turton, Albert H., A.I.M.M., 45 Ribblesdale Road, Streatham Park, London 535
* Tweedie, Charles, M.A., B.Sc., Lecturer on Mathematics in the University of Edinburgh,
12 Nelson Street
Underhill, Charles E., B.A., M.B., F.R.C.P.E., F. R.C .S.E., 8 Coates Crescent
Underhill, T. Edgar, MD., PROSE, Dinedin. Barnt ee Worcestershire
884 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCTETY.
Date of
Election.
1888
C. B.
Q
Walker, James, Memb. Inst. C.E., Engineer’s Office, Tyne Improvement Commission,
Newcastle-on-Tyne
* Walker, James, D.Se., Ph.D., F.R.S., Professor of Chemistry in University College,
Dundee, 8 Windsor Terrace, Dundee 540
Walker, Robert, M.A., University, Aberdeen
* Wallace, Alexander G., M.A., 154 Forrest Avenue, Aberdeen
* Wallace, R., F.L.S., Prof. of Agriculture and Rural Economy in the Univ. of Edin.
Wallace, Wm., M.A., Principal, Cockburn Science School, Leeds
* Walmsley, R. Mullineux, D.Sc., Prin. of the Northampton Inst., Clerkenwell, London 545
* Waterston, David, M.A., M.D., F.R.C.S.E., Lecturer on Regional Anatomy in the
University of Edinburgh, 23 Colinton Road
* Watson, Charles B. Boog, Huntly Lodge, 1 Napier Road
Watson, Sir Patrick Heron, M.D., F.R.C.S.E., LL.D., Surgeon in Ordinary to the King in
Scotland, 16 Charlotte Square
Watson, Rev. Robert Boog, B.A., LL.D., F.L.S., Past President of the Conchological
Society, 11 Strathearn Place F
* Watson, Thomas P., M.A., B.Sc., Principal, Keighley Institute, Keighley 550
Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professor of Obstetrics and Gynecology,
Rush Medical College, Chicago, 706 Reliance Buildings, 100 State Street, Chicago
* Wedderburn, J. H. Maclagan, M.A., 13 South Charlotte Street
Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior
Inspector of Schools, Burma, The Edueation Office, Rangoon, Burma
Wenley, R. M., M.A., D.Sc., D.Phil., LL.D., Prof. of Philosophy in the University of
Michigan, U.S.
White, Philip J., M.B., Prof. of Zoology in University College, Bangor, North Wales 555
White, Sir William Henry, K.C.B., Memb. Inst. C.E., LL.D., F.R.S., late Assistant Con-
troller of the Navy, and Director of Naval Construction, Cedarscroft, Putney Heath,
London
Whitehead, Walter, F.R.C.S.E., Professor of Clinical Surgery, Owens College and Victoria
University, 499 Oxford Road, Manchester
Whymper, Edward, F.R.G.S., 29 Ludgate Hill, London
Will, John Charles Ogilvie, of Newton of Pitfodels, M.D., 17 Bon-Accord Square, Aberdeen
* Williams, W. Owen, F.R.C.V.S., Professor of Veterinary Medicine and Surgery,
University of Liverpool, The Veterinary School, The University, Liverpool 560
Wilson, Alfred C., F.C.S., Voewood Croft, Stockton-on-Tees
Wilson, Andrew, Ph.D., F.L.S., Lecturer on Zoology and Comparative Anatomy,
110 Gilmore Place
* Wilson, Charles T. R., M.A., F.R.S., Glencorse House, Peebles, and Sidney Sussex
College, Cambridge
Wilson-Barker, David, F.R.G.S., Captain-Superintendent Thames Nautical Training College,
H.M.S. ‘‘ Worcester,” Greenhithe, Kent
Wilson, George, M.A., M.D., 7 Avon Place, Warwick 565
* Wilson, John Hardie, D.Sc., University of St Andrews, 39 South Street, St Andrews
Wilson, William Wright, F.R.C.S.E., M.R.C.S. Eng., Cottesbrook House, Acock’s Green,
Birmingham
* Woodhead, German Sims, M.D., F.R.C.P.E., Prof. of Pathology in the University of
Cambridge
.
4
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. 885
Date of
Election.
1884
1890
1896
1882
1892
1896
1900
1904
|
Woods, G. A., M.R.C.S., Eversleigh, 1 Newstead Road, Lee, Kent
* Wright, Johnstone Christie, Northfield, Colinton 570
* Wright, Robert Patrick, Professor of Agriculture, West of Scotland Agricultural College,
6 Blythswood Square, Glasgow
* Young, Frank W., F.C.S., H.M. Inspector of Science and Art Schools, 32 Buckingham
Terrace, Botanic Gardens, Glasgow
Young, George, Ph.D., Lauraville, Bradda, Port Erin, Isle of Man
* Young, James Buchanan, M.B., D.Sc., Dalveen, Braeside, Liberton
* Young, J. M‘Lauchlan, F.R.C.V.S., Lecturer on Veterinary Hygiene, University of
Aberdeen 575
Young, R. B., M.A., B.Sc., Transvaal Technical Institute, Johannesburg, Transvaal
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 130
886
LIST OF HONORARY FELLOWS.
LST
HIS MOST GRACIOUS MAJESTY THE KING.
FOREIGNERS (LIMITED TO THIRTY-SIX BY LAW xa)
Elected
1897
1897
1900
1900
1889
1895
1905
1897
1905
1902
1902
1905
1902
1905
1888
1883
1879
1864
1902
1897
1895
1888
1895
1897
1881
1905
1895
1889
1897
1905
1905
1905
1897
Alexander Agassiz,
E.-H. Amagat,
Arthur Auwers,
Adolf Ritter von Baeyer,
Marcellin Pierre Eugéne Berthelot,
Ludwig Boltzmann,
Waldemar Chr. Brogger,
Stanislao Cannizzaro,
Moritz Cantor,
Jean Gaston Darboux,
Anton Dohrn,
Paul Ehrlich,
Albert Gaudry,
Paul Heinrich Groth,
Ernst Haeckel,
Julius Hann,
Jules Janssen,
Albert von Kolliker,
Samuel Pierpont Langley,
Gabriel Lippmann,
Eleuthére-Klie-Nicolas Mascart,
Demetrius Ivanovich Mendeléef,
Carl Menger,
Fridtjof Nansen,
Simon Newcomb,
Eduard Pfliiger,
Jules Henri Poincare,
Georg Hermann @uincke,
Giovanni V. Schiaparelli,
Eduard Suess,
Wilhelm Waldeyer,
Wilhelm Wundt,
Ferdinand Zirkel,
Total, 33.
OF GON O RABY
AT OcToBER 1904.
Cambridge (Mass.).
Paris.
Berlin.
Munich.
Paris.
Vienna.
Christiania.
Rome.
Heidelberg.
Paris.
Naples.
Frankfurt-a.-M.
Paris.
Munich.
Jena.
Graz.
Paris.
Wiirzburg.
Washington.
Paris.
Paris,
St Petersburg.
Vienna.
Christiania.
Washington.
Bonn.
Paris.
Heidelberg.
Milan.
Vienna.
Berlin.
Leipzig.
Leipzig.
FELLOWS
LIST OF HONORARY FELLOWS.
887
BRITISH SUBJECTS (LIMITED TO TWENTY BY LAW X.).
Elected
1902
1889
1900
1892
1897
1892
1900
1900
1895
1883
1884
1902
1900
1905
1905
Sir Benjamin Baker, K.C.M.G., Mem.Inst.C.E., F.R.S.,
Sir Robert Stawell Ball, Kt., LL.D., F.R.S., M.R.1A., Lowndean
Professor of Astronomy in the University of Cambridge,
Edward Caird, LL.D., Master of Balliol College, Oxford,
Colonel Alexander Ross Clarke, C.B., R.E., F.R.S.,
Sir George Howard Darwin, K.C.B., M.A., LL.D., F.R.S., Plumian
Professor of Astronomy in the University of Cambridge,
Sir David Guill, K.C.B., LL.D., F.R.S., His Majesty’s Astronomer
at the Cape of Good Hope,
David Ferrier, M.D., LL.D., F.R.S., Prof. of Neuro-pathology,
King’s College, London,
Andrew Russell Forsyth, D.Sc., F.R.S., Sadlerian Professor of
Pure Mathematics in the University of Cambridge,
Albert C. L. G. Giinther, Ph.D., F.R.S.,
Sir Joseph Dalton Hooker, K.C.S.L, M.D., LL.D., D.C.L., F.R.S.,
Corresp. Mem. Inst. of France,
Sir William Huggins, K.C.B., LL.D., D.C.L., P.R.S., Corresp.
Mem. Inst. of France,
Sir Richard C. Jebb, Litt. D., D.C.L., M.P., Regius Professor
of Greek in the University of Cambridge,
Archibald Liversidge, LL.D., F.R.S., Professor of Chemistry in
the University of Sydney,
Afred Newton, M.A., F.R.S., Professor of Zoology and Com-
parative Anatomy in the University of Cambridge,
Sir William Ramsay, K.C.B., LL.D., F.R.S., Professor of
Chemistry in the University College, London,
The Lord Rayleigh, D.C.L., LL.D., D.Se. Dub., F.R.S., Corresp.
Mem. Inst. of France,
Sir J. 8. Burdon Sanderson, Bart., M.D., LL.D., D.Sc. Dub.,
E.RB.S.,
Joseph John Thomson, D.Sc, LL.D., F.R.S., Cavendish Pro-
fessor of Experimental Physics, University of Cambridge,
Thomas Edward Thorpe, D.Sc., LL.D., F.R.S., Principal of the
Government Laboratories, London,
Sir Charles Todd, K.C.M.G., F.R.S., Government Astronomer,
South Australia,
Total, 20.
London.
Cambridye.
Oxford.
Rediull, Surrey.
Cambridge.
Cape of Good Hope.
London.
Cambridge.
London.
London.
London.
Cambridge.
Sydney.
Cambridge.
London,
London.
Oxford.
Cambridge.
London.
Adelaide.
888 LIST OF FELLOWS ELECTED.
ORDINARY FELLOWS ELECTED
DurRinG Session 1904-1905.
ARRANGED ACCORDING TO THE DATE OF THEIR ELECTION.
21st November 1904.
Witriram Anperson, F.G.S. GEORGE ALEXANDER Carsz, M.A., B.Sc.
Jacos C. Haum, Ph.D.
19th December 1904.
Wm. Avex. Francis Batrour-Browne, M.A. Davip Corrig, F.C.S.
Davip Lawson, M.A., M.D., L.R.C.P. and S.E.
23rd January 1905.
Wiuuram Anperson, M.A. ArcHiBaLp Miune, M.A., B.Sc.
Joun Cameron, M.D., D.Sc. C. H. Miuier-Miuyg, M.A.
Rev. Wm. Gattoway DonaLpson | Perper Pinkerton, M.A.
Prof. Hector Munro Macponatp, M.A., F.R.S. Grorce Romanss, C.E.
ALEXANDER THOMS.
20th February 1905.
Prof. Joan Water Grecory, D.Sce., F.R.S. Wm. Atrrep Pain, F.R.C.V.S.
Ropert Buy Greic, F.Z.8. HaroLtp WM. SwWITHINBANK
Wm. Coun Mackenzin, M.D., F.R.C.S. Artruur Logan Turner, M.D., F.R.C.S.E.
15th May 1905.
JAMES CaMPpBELL Dewar, C.A. Grorce Wo. Jonzs, M.A., B.Sc.
19th June 1905.
GzorcEe AnpREw, M.A., B.A. THomas Lown Buntine, M.D.
Forrest Hay LicHTBopy.
17th July 1905.
JosmPpH Henry Carter, F.R.C.V.S. A. EK. Scougan, M.A., HM:COLS:
(Readmitted).
HONORARY FELLOWS ELECTED
Durine Session 1904-1905.
BRITISH HONORARY FELLOWS.
AtrreD Nrwrton, M.A., F.R.S., Professor of Zoology and Comparative Anatomy in the University
of Cambridge.
JosepH Joun THomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental Physics
University of Cambridge.
Sir Witr1am Ramsay, K.C.B., LL.D., F.R.S., Professor of Chemistry in the University College,
London.
LIST OF FELLOWS ELECTED, ETC.
HONORARY FELLOWS ELECTED—continued.
FOREIGN HONORARY FELLOWS.
Moritz Cantor, Hon. Professor of Mathematics, University of Heidelberg.
Witsetm Wonpt, Professor of Philosophy, University of Leipzig.
WitHetm Watpeyer, Professor of Anatomy, University of Berlin.
Epuarp Prutcer, Professor of Physiology, University of Bonn.
Epuarp Suess, Em. Professor of Geology, University of Vienna.
Pavut Esruicu, Director of the Institute for Experimental Therapeutics, Frankfurt-a.-M.
889
WaLpEMaR Cur. Broacer, Professor of Mineralogy and Paleontology, University of Christiania
PavL Herricu Groru, Professor of Mineralogy in the University of Munich.
- ORDINARY FELLOWS DECEASED
DuRING
Watter Berry, of Glenstriven, K.D.
SEssIon 1904-1905.
A. H. Japp, LL.D.
Professor RatpH CopELAND, Astronomer-Royal for JAMES Napipr, M.A.
Scotland.
Davin Derucuar, F.1.A., F.F.A.
JAMES DUNCAN.
James Duruam, F.G.S.
Patrick Nei~i FRASER,
Dr A. LockHartr GILLESPIE.
Dr CHaruns D. F. Pures.
Eyre Burton Powe tt, C.S.1., M.A.
Sir JoHn Srppaup, M.D.
Rey. Cuarues R, Taps, M.A., Ph.D.
Dr Ropert STEVENSON THOMSON.
CuHarues Winson Vincent, F.I.C., F.C.S.
HONORARY
FELLOWS DECEASED
Durine SEsston 1904-1905.
FOREIGN.
FERDINAND VON RICHTHOFEN. Orro WILHELM STRUVE.
Topras Roperr THALEN.
ca
LAWS
OF THE,
move SOC yY OF EDINBURG H,
AS REVISED 181TH JULY 1904.
is
©, 2893 4
{By the Charter of the Society (printed in the Transactions, Vol. VI. p. 5), the Laws cannot
be altered, except at a Meeting held one month after that at which the Motion for
alteration shall have been proposed. |
iL,
THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and
Honorary Fellows.
IA
Every Ordinary Fellow, within three months after his election, shall pay Two
Guineas as the fee of admission, and Three Guineas as his contribution for the
Session in which he has been elected; and annually at the commencement of every
Session, Three Guineas into the hands of the Treasurer. This annual contribution
shall continue for ten years after his admission, and it shall be limited to Two
Guineas for fifteen years thereafter.* Fellows may compound for these contri-
butions on such terms as the Council may from time to time fix.
ee
All Fellows who shall have paid Twenty-five years’ annual contribution shall
be exempted from further payment.
IV.
The fees of admission of an Ordinary Non-Resident Fellow shall be £26, ds.,
payable on his admission ; and in case of any Non-Resident Fellow coming to
reside at any time in Scotland, he shall, during each year of his residence, pay
the usual annual contribution of £3, 3s., payable by each Resident Fellow ; but
after payment of such annual contribution for eight years, he shall be exempt
* A modification of this rule, in certain cases, was agreed to at a Meeting of the Society held on
the 3rd January 1831.
At the Meeting of the Society, on the 5th January 1857, when the reduction of the Contribu-
tions from £3, 3s. to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was
resolved that the existing Members shall share in this reduction, so far as regards their future annual
Contributions.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 131
Title.
The fees of Ordinary
Fellows residing
in Scotland.
Payment to cease
after 25 years.
Fees of Non-Resi
dent Ordinary
Fellows.
Case of Fellows
becoming Non-
Resident.
Defaulters.
Privileges of
Ordinary Fellows.
Numbers Un-
limited.
Fellows entitled to
Transactions.
Mode of Recom-
mending Ordinary
Fellows.
894 LAWS OF THE SOCIETY.
from any further payment. In the case of any Resident Fellow ceasing to reside
in Scotland, and wishing to continue a Fellow of the Society, it shall be in the
power of the Council to determine on what terms, in the circumstances of each
case, the privilege of remaining a Fellow of the Society shall be continued to
such Fellow while out of Scotland.
V;
Members failing to pay their contributions for three successive years (due
application having been made to them by the Treasurer) shall be reported to
the Council, and, if they see fit, shall be declared from that period to be no
longer Fellows, and the legal means for recovering such arrears shall be
employed.
VI.
None but Ordinary Fellows shall bear any office in the Society, or vote in
the choice of Fellows or Office-Bearers, or interfere in the patrimonial interests
of the Society.
VIL.
The number of Ordinary Fellows shall be unlimited.
VILL.
The Ordinary Fellows, upon producing an order from the TREASURER, shall
be entitled to receive from the Publisher, gratis, the Parts of the Society’s
Transactions which shall be published subsequent to their admission.
ID.
Candidates for admission as Ordinary Fellows shall make an application in
writing, and shall produce along with it a certificate of recommendation to the
purport below,* signed by at least fous Ordinary Fellows, two of whom shall
certify their recommendation from personal knowledge. This recommendation
shall be delivered to the Secretary, and by him laid before the Council, and
shall be exhibited publicly in the Society’s Rooms for one month, after which
it shall be considered by the Council. ff the Candidate be approved by the
Council, notice of the day fixed for the election shall be given in the circulars
of at least two Ordinary Meetings of the Society.
* “A. B., a gentleman well versed in Science (or Polite Literature, as the case may be), being
“to our knowledge desirous of becoming a Fellow of the Royal Society of Edinburgh, we hereby
“recommend him as deserving of that honour, and as likely to prove a useful and valuable Member.”
LAWS OF THE SOCIETY. 895
DS
Honorary Fellows shall not be subject to any contribution. This class shall
consist of persons eminently distinguished for science or literature. Its number
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty-
six may be subjects of foreign states.
Xe
Personages of Royal Blood may be elected Honorary Fellows, without regard
to the limitation of numbers specified in Law X.
XI.
Honorary Fellows may be proposed by the Council, or by a recommenda-
tion (in the form given below*) subscribed by three Ordinary Fellows ; and in
case the Council shall decline to bring this recommendation before the Society,
it shall be competent for the proposers to bring the same before a General
Meeting. The election shall be by ballot, after the proposal has been commu-
nicated viva voce from the Chair at one meeting, and printed in the circulars
for two ordinary meetings of the Society, previous to the day of election.
UOTE
The election of Ordinary Fellows shall take place only at one Afternoon
Ordinary Meeting of each month during the Session. The election shall be
by ballot, and shall be determined by a majority of at least two-thirds of the
votes, provided Twenty-four Fellows be present and vote.
XIV.
The Ordinary Meetings shall be held on the first and third Mondays of
each month from November to March, and from May to July, inclusive; with
the exception that when there are five Mondays in January, the Meetings for
that month shall be held on its second and fourth Mondays. Regular Minutes
shall be kept of the proceedings, and the Secretaries shall do the duty
alternately, or according to such agreement as they may find it convenient
to make.
* We hereby recommend — z
for the distinction of being made an Honorary Fellow of this Society, declaring that each of us from
our own knowledge of his services to (Literature or Science, as the case may be) believe him to be
worthy of that honour.
(To be signed by three Ordinary Fellows.)
To the President and Council of the Royal Society
of Edinburgh.
Honorary Fellows,
British and
Foreign.
Royal Personages.
Recommendation
of Honorary
Fellows.
Mode of Election.
Election of Ordi-
nary Fellows.
Ordinary Meet-
ings.
The Transactions.
How Published.
The Council.
Retiring Council-
lors.
Klection of Office-
Bearers.
Special Meetings ;
how called.
Treasurer’s Duties.
896 LAWS OF THE SOCIETY.
XV.
The Society shall from time to time publish its Transactions and Proceed-
ings. For this purpose the Council shall select and arrange the papers which
they shall deem it expedient to publish in the 7ransactions of the Society, and
shall supermtend the printing of the same.
The Council shall have power to regulate the private business of the Society.
At any Meeting of the Council the Chairman shall have a casting as well as a
deliberative vote.
XVI.
The Transactions shall be published in parts or Fasciculi at the close of
each Session, and the expense shall be defrayed by the Society.
XVII.
That there shall be formed a Council, consisting—First, of such gentlemen
as may have filled the office of President ; and Secondly, of the following to be
annually elected, viz.:—a President, Six Vice-Presidents (two at least of whom
shall be resident), Twelve Ordinary Fellows as Councillors, a General Secretary,
Two Secretaries to the Ordinary Meetings, a Treasurer, and a Curator of the
Museum and Library.
XV
Four Councillors shall go out annually, to be taken according to the order
in which they stand on the list of the Council.
XIX
An Extraordinary Meeting for the election of Office-Bearers shall be held
annually on the fourth Monday of October, or on such other lawful day in
October as the Council may fix, and each Session of the Society shall be held
to begin at the date of the said Extraordinary Meeting.
OE
Special Meetings of the Society may be called by the Secretary, by direction
of the Council; or on a requisition signed by six or more Ordinary Fellows.
Notice of not less than two days must be given of such Meetings.
XO
The Treasurer shall receive and disburse the money belonging to the Society,
granting the necessary receipts, and collecting the money when due. _
He shall keep regular accounts of all the cash received and expended, which
shall be made up and balanced annually ; and at the Extraordinary Meeting in
October, he shall present the accounts for the preceding year, duly audited.
————tt—t~s
LAWS OF THE SOCIETY. 897
At this Meeting, the Treasurer shall also lay before the Council a list of all
arrears due above two years, and the Council shall thereupon give such direc-
tions as they may deem necessary for recovery thereof.
XXIL.
At the Extraordinary Meeting in October, a professional accountant shall
be chosen to audit the Treasurer’s accounts for that year, and to give the neces-
sary discharge of his intromissions.
XXIII.
The General Secretary shall keep Minutes of the Extraordinary Meetings of
the Society, and of the Meetings of the Council, in two distinct books. He
shall, under the direction of the Council, conduct the correspondence of the
Society, and superimtend its publications. For these purposes he shall, when
necessary, employ a clerk, to be paid by the Society.
XXIV.
The Secretaries to the Ordinary Meetings shall keep a regular Minute-book,
in which a full account of the proceedings of these Meetings shall be entered ;
they shall specify all the Donations received, and furnish a list of them, and of
the Donors’ names, to the Curator of the Library and Museum ; they shall like-
wise furnish the Treasurer with notes of all admissions of Ordinary Fellows.
They shall assist the General Secretary in superintending the publications, and
in his absence shall take his duty.
DOXEN
The Curator of the Museum and Library shall have the custody and charge
of all the Books, Manuscripts, objects of Natural History, Scientific Produc-
tions, and other articles of a similar description belonging to the Society ; he
shall take an account of these when received, and keep a regular catalogue of
the whole, which shall lie in the Hall, for the inspection of the Fellows.
XXVI.
All Articles of the above description shall be open to the inspection of the
Fellows at the Hall of the Society, at such times and under such regulations
as the Council from time to time shall appoint.
OSI
A Register shall be kept, in which the names of the Fellows shall be
enrolled at their admission, with the date.
Auditor,
General Secretary’s
Duties,
Secretaries to
Ordinary Meetings.
Curator of Museum
and Library.
Use of Museum
and Library.
Register Book.
Power of
Expulsion.
898 LAWS OF THE SOCIETY.
XXVIII.
If, in the opinion of the Council of the Society, the conduct of any Fellow
is unbecoming the position of a Member of a learned Society, or is injurious to
the character and interests of this Society, the Council may request such
Fellow to resign ; and, if he fail to do so within one month of such request
being addressed to him, the Council shall call a General Meeting of the Fellows
of the Society to consider the matter ; and, if a majority of the Fellows present
at such Meeting agree to the expulsion of such Member, he shall be then and
there expelled by the declaration of the Chairman of the said Meeting to that
effect ; and he shall thereafter cease to be a Fellow of the Society, and his
name shall be erased from the Roll of Fellows, and he shall forfeit all right or
claim in or to the property of the Society.
( 899 )
THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND
GUNNING VICTORIA JUBILEE PRIZES.
The above Prizes will be awarded by the Council in the following manner :—
I. KEITH PRIZE.
The KeirH Prize, consisting of a Gold Medal and from £40 to £50 im
Money, will be awarded in the Session 1905-1906 for the “‘ best communication
on a scientific subject, communicated, in the first instance, to the Royal Society
during the Sessions 1903-04 and 1904-05.” Preference will be given to a
paper containing a discovery.
Il. MAKDOUGALL-BRISBANE PRIZE.
This Prize is to be awarded biennially by the Council of the Royal Society
of Edinburgh to such person, for such purposes, for such objects, and in such
manner as shall appear to them the most conducive to the promotion of the
interests of science ; with the proviso that the Council shall not be compelled
to award the Prize unless there shall be some individual engaged in scientific
pursuit, or some paper written on a scientific subject, or some discovery in
science made during the biennial period, of sufticient merit or importance in
the opinion of the Council to be entitled to the Prize.
1. The Prize, consisting of a Gold Medal and a sum of Money, will be
awarded at the commencement of the Session 1906-1907, for an Essay or Paper
having reference to any branch of scientific inquiry, whether Material or
Mental.
2. Competing Essays to be addressed to the Secretary of the Society, and
transmitted not later than 8th July 1906.
3. The Competition is open to all men of science.
900 APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES.
4. The Essays may be either anonymous or otherwise. In the former case,
they must be distinguished by mottoes, with corresponding sealed billets, super-
scribed with the same motto, and containing the name of the Author.
5. The Council impose no restriction as to the length of the Essays, which
may be, at the discretion of the Council, read at the Ordinary Meetings of the
Society. They wish also to leave the property and free disposal of the manu-
scripts to the Authors; a copy, however, being deposited in the Archives of
the Society, unless the paper shall be published in the Transactions.
6. In awarding the Prize, the Council will also take into consideration
any scientific papers presented to the Society during the Sessions 1904—05,
1905-06, whether they may have been given in with a view to the prize or not.
Ill. NEILL PRIZE.
The Council of the Royal Society of Edinburgh having received the bequest
of the late Dr Parrick Nem of the sum of £500, for the purpose of “the
interest thereof being applied in furnishing a Medal or other reward every
second or third year to any distinguished Scottish Naturalist, according as such
Medal or reward shall be voted by the Council of the said Society,” hereby
intimate,
1. The Nem. Prize, consisting of a Gold Medal and a sum of Money, will
be awarded during the Session 1907-1908.
2. The Prize will be given for a Paper of distinguished merit, on a subject
of Natural History, by a Scottish Naturalist, which shall have been presented
to the Society during the three years preceding the 8th July 1907,—or failing
presentation of a paper sufficiently meritorious, it will be awarded for a work
or publication by some distinguished Scottish Naturalist, on some branch of
Natural History, bearing date within five years of the time of award.
IV. GUNNING VICTORIA JUBILEE PRIZE.
This Prize, founded in the year 1887 by Dr R. H. Gunning, is to be awarded
quadrennially by the Council of the Royal Society of Edinburgh, in recognition
of original work in Physics, Chemistry, or Pure or Applied Mathematics.
APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES. 901
Evidence of such work may be afforded either by a Paper presented to the
Society, or by a Paper on one of the above subjects, or some discovery in them
elsewhere communicated or made, which the Council may consider to be
deserving of the Prize.
The Prize consists of a sum of money, and is open to men of science resi-
dent in or connected with Scotland. The first award was made in the year
1887.
In accordance with the wish of the Donor, the Council of the Society may
on fit occasions award the Prize for work of a definite kind to be undertaken
during the three succeeding years by a scientific man of recognised ability.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX). 132
( 902)
AWARDS OF THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND
GUNNING VICTORIA JUBILEE PRIZES, FROM 1827 TO 1904.
I. KEITH PRIZE.
lst BrenniaL Periop, 1827—29.—Dr Brewster, for his papers “on his Discovery of Two New Immis-
cible Fluids in the Cavities of certain Minerals,” published in
the Transactions of the Society.
2np Bienntat Pertop, 1829-31.—Dr Brewster, for his paper “on a New Analysis of Solar
Light,” published in the Transactions of the Society.
3rp Brenntat Pertop, 1831—33.—THomas Granam, Esq., for his paper “on the Law of the Diffusion
of Gases,” published in the Transactions of the Society.
47H Brenniat Pertop, 1833-—35.—Professor J. D. Forsgs, for his paper “on the Refraction and Polari-
zation of Heat,” published in the Transactions of the Society.
57TH Brenniat Psriop, 1835-37.—Joun Scorr Russex1, Esq.,for his Researches “on Hydrodynamics,”
published in the Transactions of the Society.
6TH Brenniav Periop, 1837-39.—Mr Joun Suaw, for his experiments “on the Development and
Growth of the Salmon,” published in the Transactions of the
Society.
7rH BienntaL Perron, 1839—41.—Not awarded.
87H Bienntau Periop, 1841-43.—Professor James Davin Forpes, for his papers “on Glaciers,”
published in the Proceedings of the Society.
97H BrennIAL Periop, 1843—45.—Not awarded.
107TH Bimnntat Periop, 1845—47.—General Sir THomas BrisBane, Bart., for the Makerstoun Observa-
tions: on Magnetic Phenomena, made at his expense, and
published in the Transactions of the Society.
llvxa Brennrat Periop, 1847—49.—Not awarded.
127H BrenniAL Periop, 1849-51.—Professor Kriuanp, for his papers “on General Differentiation,
including his more recent Communication on a process of the
Differential Calculus, and its application to the solution of
certain Differential Equations,” published in the Transactions
of the Society.
1378 BrenniaL Periop, 1851—53.—W. J. Macquorn Ranxinz, Esq., for his series of papers “ on the
Mechanical Action of Heat,” published in the Transactions
of the Society.
14rH Brenntau Periop, }853-55.—Dr Tuomas Anprrson, for his papers “on the Crystalline Con-
stituents of Opium, and on the Products of the Destructive
Distillation of Animal Substances,” published in the Trans-
actions of the Society.
J5vn8 Brenniat Periop, 1855-57.—Professor Boor, for his Memoir “on the Application of the Theory
of Probabilities to Questions of the Combination of Testimonies
and Judgments,” published in the Transactions of the Society.
APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES. 903
16TH Brennrau Periop, 1857-59.—Not awarded.
17TH Brenna Pertop, 1859-61.—Joun Attan Broun, Hsq., F.R.S., Director of the Trevandrum
Observatory, for his papers “on the Horizontal Force of the
Earth’s Magnetism, on the Correction of the Bitilar Magnet-
ometer, and on Terrestrial Magnetism generally,” published in
the Transactions of the Society.
18TH Brenniat Periop, 1861—63.—Professor WiLL1am THomson, of the University of Glasgow, for his
Communication “on some Kinematical and Dynamical
Theorems.”
Principal Forses, St Andrews, for his “ Experimental Inquiry into
the Laws of Conduction of Heat in Iron Bars,” published in
the Transactions of the Society.
20TH Brenniau Prriop, 1865—67.—Professor C. Prazzt Smyvs, for his paper “on Recent Measures at
the Great Pyramid,” published in the Transactions of the
Society.
21st Brenntau Periop, 1867-—69.—Professor P. G. Tarr, for his paper “on the Rotation of a Rigid
Body: about a Fixed Point,’ published in the Transactions of
the Society.
22ND Biennrat Parton, 1869—71.—Professor CLerK Maxwetu, for his paper “on Figures, Frames,
and Diagrams of Forces,” published in the Transactions of the
Society.
23RD BrennraL Psriop, 1871—73.—Professor P. G. Tair, for his paper entitled “ First Approximation
to a Thermo-electrie Diagram,” published in the Transactions
of the Society.
247H BienniaL Periop, 1873—75.—Professor Crum Brown, for his Researches ‘‘ on the Sense of Rota-
tion, and on the Anatomical Relations of the Semicircular
Canals of the Internal Ear.”
25TH Biennial Periop, 1875—77.—Professor M. Forstsr Heppue, for his papers “on the Rhom-
bohedral Carbonates,’ and “on the Felspars of Scotland,”
published in the Transactions of the Society.
26TH BienniaL Periop, 1877—79.—Professor H. C. FLeemine JENKIN, for his paper “on the Appli-
cation of Graphic Methods to the Determination of the Efii-
ciency of Machinery,” published in the Transactions of the
Society; Part II. having appeared in the volume for 1877-78
277TH BienntaL Periop, 1879—81.—Professor Grorcn Curysrat, for his paper “on the teen
Telephone,” published in the Transactions of the Society.
28rH Brenniat Periop, 1881—83.—TuHomas Muir, Esq., LL.D., for his “ Researches into the Theory
of Determinants and Continued Fractions,” published in the
Proceedings of the Society.
297H BiennraL PERiop, 1883- 85.—Joun AITKEN, Esq., for his paper “on the Formation of Small
Clear Spaces in Dusty Air,” and for previous papers on
Atmospheric Phenomena, published in the Transactions of
the Society.
30TH BrennraL Period, 1885-87.—JoHn Youne Bucuanan, Esq., for a series of Communications,
extending over several years, on subjects connected with
Ocean Circulation, Compressibility of Glass, &c.; two of
which, viz., “On Ice and Brines,’ and “On the Distribution
of Temperature in the Antarctic Ocean,” have been published
in the Proceedings of the Society.
31st BrenniaL Periop, 1887—89.—Professor E. A. Lurrs, for his papers on the Organic Compounds
ot Phosphorus, p:ablished in the Transactions of the Society.
32ND BrenniaL Periop, 1889-91.—R. T. Omonn, Esq., for his Contributions to Meteorological Science,
many of which are contained in Vol. XXXIV. of the
Society’s Transactions.
53RD BiennraL Prrtop, 1891—-93.—Professor THomas R. Frasmr, F.R.S., for his papers on Strophan-
thus hispidus, Strophanthin, and Strophanthidin, read to the
Society in February and June 1889 and in December 1891,
and printed in Vols. XXXV., XXXVI., and XXXVILI. of
the Society’s Transactions.
197 BrenntaL Periop, 1863-65.
904 APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES.
34vH BrennraL Perrop, 1893-95.—Dr Careitt G. Knorr, for his papers on the Strains produced
by Magnetism in Iron and in Nickel, which have appeared
in the Transactions and Proceedings of the Society.
357H Brenniau Periop, 1895-97.—Dr Tuomas Murr, for his continued Communications on Deter-
minants and Allied Questions.
367TH Brennrat Periop, 1897-99.—Dr James Bureuss, for his paper “on the Definite Integral
Dr fe :
= 3 e “dt, with extended Tables of Values,” printed in
0
7,
Vol. XX XIX. of the Transactions of the Society.
379H Brenniau Pgriop, 1899-1901.—Dr Huen Marsnatt, for his discovery of the Persulphates,
and for his Communications on the Properties and Reactions
of these Salts, published in the Proceedings of the Society.
38TH BrenntaL PeEriop, 1901—03.—Sir Witi1am Turner, K.C.B., LL.D., F.R.S., &e., for his
memoirs entitled “A Contribution to the Craniology of the
People of Scotland,” published in the Transactions of the
Society, and for his “Contributions to the Craniology of
the People of the Empire of India,” Parts I., II, likewise
published in the Transactions of the Society.
Il. MAKDOUGALL-BRISBANE PRIZE.
lst Breyniat Perriop, 1859.—Sir Roprrick Impry Murcuison, on account of his Contributions to
the Geology of Scotland.
2np Brenniat Periop, 1860—62.—Winiiam Setter, M.D., F.R.C.P.E., for his “ Memoir of the Lite
and Writings of Dr Robert Whytt,” published in the Trans-
actions of the Society.
3RrD BienniaL Prriop, 1862—64.—Jonn Denis Macponatp, Esq., R.N., F.R.S., Surgeon of H.MS.
“Tearus,” for his paper “on the Representative Relationships
of the Fixed and Free Tunicata, regarded as Two Sub-classes
of equivalent value; with some General Remarks on their
Morphology,” published in the Transactions of the Society.
475 Birnniat Prriop, 1864—66.—Not awarded.
5rH BiennraL Prrtop, 1866-68.—Dr AtExanper Crum Brown and Dr Tuomas Ricnarp Fraser,
for their conjoint paper “on the Connection between
Chemical Constitution and Physiological Action,” published
in the Transactions of the Society.
6TH BipnntaL Prriop, 1868—70.—Not awarded.
7tH BrienniaL Psriop, 1870—-72.—Gerorce James Anuman, M.D., F.R.S., Emeritus Professor of
Natural History, for his paper ‘‘ on the Homological Relations
of the Cclenterata,” published in the Transactions, which
forms a leading chapter of his Monograph of Gymnoblastic
or Tubularian Hydroids—since published.
8TH Brennrat Periop, 1872—74.—Professor Lisrmr, for his paper ‘‘on the Germ Theory of Putre-
faction and the Fermentive Changes,” communicated to the
Society, 7th April 1873.
9TH Bienntat Periop, 1874-76.—Atexanper Bucuan, A.M., for his paper “on the Diurnal
Oscillation of the Barometer,” published in the Transactions
of the Society.
107H BienniaL Periop, 1876—78.—Professor ArcHIBALD GeEIKIE, for his paper “on the Old Red
Sandstone of Western Europe,” published in the Transactions
of the Society.
llvn Brenniat Periop, 1878~80.—Professor Prazz1 Smyru, Astronomer-Royal for Scotland, for his
paper ‘fon the Solar Spectrum in 1877-78, with some
Practical Idea of its probable Temperature of Origination,”
published in the Transactions of the Society.
APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES. 905
127H Bienntat Pertop, 1880—82.— Professor JAMES GEIKiE, for his “Contributions to the Geology of
the North-West of Europe,” including his paper “on the
Geology of the Faroes,” published in the Transactions of the
Society.
137H Brenniat Periop, 1882—84.—Epwarp Sane, Esq., LL.D., for his paper “on the Need of
Decimal Subdivisions in Astronomy and Navigation, and on
Tables requisite therefor,” and generally for his Recalculation
of Logarithms both of Numbers and Trigonometrical Ratios,
—the former communication being published in the Pro-
ceedings of the Society.
147H Brennrat Periop, 1884—86.—Joun Murray, Esq., LL.D., for his papers “On the Drainage
Areas of Continents, and Ocean Deposits,’ “The Rainfall of
the Globe, and Discharge of Rivers,” “The Height of the Land
and Depth of the Ocean,” and “The Distribution of Tem-
perature in the Scottish Lochs as affected by the Wind.”
157 Bienniat Periop, 1886—88.—ArcuipaLp Geikin, Esq., LL.D., for numerous Communications,
especially that entitled “Wistory of Volcanic Action during
the Tertiary Period in the British Isles,” published in the
Transactions of the Society.
167H Brenn1at Preriop, 1888-90.—Dr Lupwie Brcxer, for his paper on “The Solar Spectrum at
Medium and Low Altitudes,’ printed in Vol. XXXVI.
Part I. of the Society’s Transactions.
177H Brenniau Periop, 1890—92.—Hven Rosert Miu, Esq., D.Sc., for his papers on “The Physical
Conditions of the Clyde Sea Area,” Part I. being already
published in Vol. XXXVL. of the Society’s Transactions,
18rH Brennrau Periop, 1892—94.—Professor James WaukeER, D.Sc., Ph.D., for his work on Physical
Chemistry, part of which has been published in the Pro-
ceedings of the Society, Vol. XX., pp. 255-263. In making
this award, the Council took into consideration the work
done by Professor Walker along with Professor Crum Brown
on the Electrolytic Synthesis of Dibasie Acids, published in
the Transactions of the Society.
19ra Brennrat Periop, 1894—96.—Professor Joun G. M‘Kenprick, for numerous Physiological
papers, especially in connection with Sound; many of which
have appeared in the Society’s publications.
20rH Bienniat Periop, 1896—-98.—Dr Wriiniam Perpopisg, for his papers on the Torsional Rigidity
of Wires.
21sr Brennrau Periop, 1898—1900.—Dr Ramsay H. Traquair, for his paper entitled “Report on
Fossil Fishes collected by the Geological Survey in the
Upper Silurian Rocks of Scotland,” printed in Vol.
XXXIX. of the Transactions of the Society.
22np Bimnntau PeEriop, 1900—02.—Dr Arraur T. Masrermay, for his paper entitled “The Early
Development of Cribrella oculata (Forbes), with remarks on
Eehinoderm Development,” printed in Vol. XL. of the Trans-
actions of the Society.
23RD Brennrat Periop, 1902—-04.—Mr Joun Doveatt, M.A., for his paper on “An Analytical
Theory of the Equilibrium of an Isotropic Elastic Plate,”
published in Vol. XLI. of the Transactions of the Society.
III. THE NEILL PRIZE.
Isr Trimnniat Periop, 1856—59.—Dr W. Lauper Linpsay, for his paper “ on the Spermogones and |
Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens,”
published in the Transactions of the Society.
2np TRIENNIAL PERIOD, 1859-62.—Rosert Kaye Grevinie, LL.D., for his Contributions to Scottish
Natural History, more especially in the department of Cryp-
togamic Botany, including his recent papers on Diatomacez.
906 APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES.
3rd TrrenntaL Psriop, 1862—65.—Anprew Crompre Ramsay, F.R.S., Professor of Geology in the
Government School of Mines, and Local Director of the
Geological Survey of Great Britain, for his various works and
memoirs published during the last five years, in which he
has applied the large experience acquired by him in the
Direction of the arduous work of the Geographical Survey of
Great Britain to the elucidation of important questions bear-
ing on Geological Science.
4va Trienniat Periop, 1865-68.— Dr Wititam Carmicnart M‘Inrosu, for his paper “on the Struc-
ture of the British Nemerteans, and on some New British
Annelids,” published in the Transactions of the Society.
508 TRIENNIAL Periop, 1868—71.—Protessor Wittiam Turner, for his papers “on the great Finner
Whale ; and on the Gravid Uterus, and the Arrangement of
the Foetal Membranes in the Cetacea,’ published in the
Transactions of the Society.
6TH TRIENNIAL Periop, 1871-74.—Cuartes Wintiam Pracu, Esq., for his Contributions to Scottish
Zoology and Geology, and for his recent contributions to Fossil
Botany.
7TH TRIENNIAL Pertop, 1874-77.—Dr Ramsay H. Traquair, for his paper ‘on the Structure and
Affinities of Tristichopterus ulatus (Egerton),” published in
the Transactions of the Society, and also for his contributions
to the Knowledge of the Structure of Recent and Fossil Fishes.
87H TrienntaL Parton, 1877-80.—Joun Murray, Esq., for his paper “on the Structure and Origin
of Coral Reefs and Islands,” published (in abstract) in the
Proceedings of the Society.
97H TRIENNIAL Pertop, 1880—83.—Professor HerpMan, for his papers “on the Tunicata,” published
in the Proceedings and Transactions of the Society.
10Ts TrienntaL Periop, 1883-86.—B. N. Peacu, Esq., for his Contributions to the Geology and
Paleontology of Scotland, published in the Transactions of
the Society.
11lta TrrenniaL Periop, 1886—-89.—Roserr Kinston, Esq., for his Researches in Fossil Botany, pub-
lished in the Transactions of the Society.
127TH TrrenntaL Periop, 1889-92.—Jonn Hornu, Esq., F.G.S., for his Investigations into the Geolo-
gical Structure and Petrology of the North-West Highlands,
137m TrienntaL Pertop, 1892—95.—Roserr Irving, Esq., for his papers on the action of Organisms
in the Secretion of Carbonate of Lime and Silica, and on the
solution of these substances in Organic Juices. These are
printed in the Society’s Transactions and Proceedings.
141m Trrenntau Psriop, 1895—98.—Professor Cossar Ewart, for his recent Investigations connected
with Telegony.
15ta Trrennrau Periop, 1898-1901.—Dr Joun S. Fuzrt, for his papers entitled “The Old Red
Sandstone of the Orkneys” and ‘‘The Trap Dykes of the
Orkneys,” printed in Vol. XXXIX. of the Transactions of
the Society.
16TH TRIENNIAL PeERiop, 1901—04.—Professor J. GRanam Kerr, M.A., for his Researches on
Lepidosiren paradoxa, published in the Philosophical Trans-
actions of the Royal Society, London.
IV. GUNNING VICTORIA JUBILEE PRIZE.
Ist Trienntat Periov, 1884—87.—Sir Wintiam Tuomson, Pres. R.S.E., F.R.S., for a remarkable
series of papers “on Hydrokinetics,” especially on Waves
and Vortices. which have been communicated to the Society.
2nd TripnniaL Pertov, 1887—90.—Professor P. G. Tarr, Sec. R.S.E., for his work in connection with
the “Challenger” Expedition, and his other Researches in
Physical Science.
APPENDIX—KEITH, BRISBANE, NEILL, AND GUNNING PRIZES. 907
3rd TRIENNIAL PaRiop, 1890—93.—ALExanDER BucHan, Hsq., LL.D., tor his varied, extensive, and
extremely important Contributions to Meteorology, many of
which have appeared in the Society’s Publications.
47H TripnniaL Periop, 1893-96.—Joun Aitken, Esq., for his brilliant Investigations in Physics,
especially in connection with the Formation and Condensation
of Aqueous Vapour.
1st QUADRENNIAL PeRiop, 1896-1900.—Dr T. D. Anpsrson, for his discoveries of New and
Variable Stars.
2nD QuUADRENNIAL PerRiop, 1900-04.—Sir James Dewar, LL.D, D.C.L, F.RS., &., for his
researches on the Liquefaction of Gases, extending over the
last quarter of a century, and on the Chemical and Physical
Properties of Substances at Low Temperatures: his earliest
papers being published in the Transactions and Proceedings
of the Society.
T
)
PROCEEDINGS
OF THE
STATUTORY GENERAL MEETING,
24TH OCTOBER 1904.
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (APPENDIX).
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STATUTORY MEETING.
HUNDRED AND TWENTY-SECOND SESSION.
Monday, 24th October 1904.
At the Annual Statutory Meeting,
The Hon. Lord M‘LAREN in the Chair,
The Minutes of last Annual Statutory Meeting of 26th October 1903 were read
approved, and signed.
>
On the motion of Dr Crum Brown, Dr R. M. Fercuson and Dr B. N. PEACH were
appointed Scrutineers, and the Ballot for the New Council commenced.
The TREASURER submitted his Accounts for the year. These, with the Auditors’ Report,
were read and approved.
The Scrutineers reported that the following New Council had been duly elected :—
The Right Hon. Lord Ketviy, G.C.V.O., LL.D., D.C.L., F.B.S., President.
Professor JAMES GrEIKIn, LL.D., F.R.S.,
The Hon. Lord M‘Laren, LL.D.,
The Rev. Professor Ftrnt, D.D.,
Rosert Munro, M.A., M.D., LL.D.,
Sir Joun Murray, K.C.B., LL.D., F.R.S.,
Ramsay H. Traquair, M.D,, LL.D., F.R.S.,
Professor GrorGE Curystat, LL.D., General Secretary.
Professor Crum Brown, F.R.S.,
Professor D. J. CunnincHam, M.D., LL.D., F.R.S.,
Parure R. D. Mactaean, F.F.A., Treasurer.
Aurx. Bucuan, M.A., LL.D., F.R.S., Curator of Library and Museum.
Vice-Presidents.
| Seoretaries to Ordinary Meetings.
912 APPENDIX—PROCEEDINGS OF STATUTORY MEETING.
COUNCILLORS.
JoHN Horns, LL.D., F.R.S.
D. Non Paton, M.D., F.R.C.P.E.
CarciLt G. Knort, D.Sc.
Professor Jonn Curene, C.B., M.D., LL.D.
Professor RaueH Stockman, M.D., F.R.C.P.E. Professor J. GRanam Kerr, M.A.
Professor JAMES WALKER, D.Sc., Ph.D., F.R.S. Wituram Peppiz, D.Sc.
Professor ANDREW Gray, M.A., LL.D., F.R.S. Lronarp Dossin, Ph.D.
Rosert Kipsron, F.R.S., F.G.S. Professor J. C. Ewart, M.D., F.R.S.
On the motion of Professor Crum Brown, thanks were voted to the Treasurer.
On the motion of Dr Traquair, thanks were voted to the Scrutineers.
On the motion of Professor Crum Brown, thanks were voted to the Auditors, who
were reappointed.
On the motion of Professor CHRysTAL, thanks were voted to the Chairman.
JOHN M‘LareEn, V.P.,
Chairman.
( 913 )
PN Dib Xx.
A
Aleohol and Chloroform, Effect on Heart. By
E. A. ScHArer and H, J. ScHaruigs, 338.
Alcyonarians collected by the Scottish National
Antarctic Hxpedition. By J. A. THomson
and Jas. Ritcuin, 851-860.
Arctic Plant Remains in the Peat Mosses of the
Scottish Southern Uplands. By Francis J.
Lewis, 699-723.
Arteries, Effect of Chloroform on. By E. A.
ScuArer and H. J. Scwarvigs, 311.
Atropine, Effect of, on Vagus Action,
ScHArserR and H. J. Scuaries, 328.
By E. A.
Lb
Band- and Line-Spectra, On the Structure of the
Series of. By J..Hatm, 551-598.
Bathyate and Linlithgow Hills, Igneous Geology of.
By J. D. Fatconsr, 359-366.
Bdelloida, New Family and Twelve New Species
of. By James Murray, 367-386.
Beckrer (L.). On the Spectrum of Nova Persei
and the Structure of its Bands as photographed
at Glasgow, 251-290.
Bruges (Epwarp J.). The Life-History of Xenopus
levis, Daud, 789-821.
Boulder-Clay with Marine-shells in Pembrokeshire.
By T. J. Jesu, 63-68.
Bryce (THomas H.), The Histology of the Blood
of the Larva of Lepidostren paradoxa, Part I.
Structure of the Resting and Dividing Cor-
puscles, 291-310.
—— Part II. Hematogenesis, 435-467.
C
Chloroform, Action on Heart and Arteries. By
K. A. Scuarer and H. J. Scuariies, 311-
341,
Chloroform, Antagonising Agents (Atropine, Adren-
alin, Ammonia, Alcohol). By E. A. ScHArsr
and H. J. Scuaruiep, 335,
Curystat (G.). On the Hydrodynamical Theory
of Seiches, 599-649.
Curystat (G.) and Ernesr Macnacan-WEpDER-
BURN. Calculation of the Periods and Nodes
of Lochs Earn and Treig, from the Bathy-
metric Data of the Scottish Lake Survey, 823—
850.
Coker (E, G.). On the Measurement of Stress by
Thermal Methods, with an Account of some
Experiments on the Influence of Stress on the
Thermal Expansion of Metals, 229-250,
CoE (Frank J.). A Monograph on the General
Morphology of the Myxinoid Fishes, based on
a Study of Myxine. Part I.
of the Skeleton, 749-788.
Continuants Resolvable into Linear Factors. By
THomas Muir, 343-358.
The Anatomy
D
Devonian (Lower) Fishes of Gemiinden.
ment. By R. H. Traquarr, 469-475.
Doveatt (Jonny). An Analytical Theory of the
Equilibrium of an Isotropic Elastic Plate, 129-
Sr
Supple-
Drepanaspis Gemiindenensis, Schl. Traquair:
Supplement to the Lower Devonian Fishes of
Gemiinden, 469-475.
E
Elastic Plate, Mathematical Theory of Equilibrium
of. By J. Dovearn, 129-228.
Elastic Plates, Thin, Theory of, deduced to a Second
Approximation from an Exact Solution. By
J. Doueatn, 129-228.
Eniot, Sir Coarves, Nudibranchiata of the Scottish
National Antarctic Expedition, 519-532.
Elliptic Functions, Expressions in Terms of General-
ized Bessel Functions: Series obtained from
Generalized Hixponential Function: Bessel
Function of Double Order m, n. By F. H.
Jackson, 399-408.
914
By T. J. Jenv, 77-8
Evratics in Pembrokeshire. 2
By aod.
Estuaries, ria-like, in Pembrokeshire.
JEHU, 59.
F
Fatconer (J. D.). The Igneous Geology of the
Bathgate and Linlithgow Hills, 359-366.
Forests submerged on the Pembrokeshire Coast. By
T. J. Janu, 60.
G
Grorgonia studerit, n. sp. J. A. Tomson and J.
Ritcuie: Alecyonarians of the Scottish National
Antarctic Expedition, 858.
Gorgonia wrighti, n. sp. J. A. THomson and J.
Rircuie ; Aleyonarians of the Scottish National
Antarctic Expedition, 857.
H
Hexmatogenesis in Lepidosiren paradoxa. By T. H.
Bryce, 425-467.
Hatm (J.). Spectroscopic Observations of the
Rotation of the Sun, 89-104.
—— On the Structure of the Series of Line- and
Band-Spectra, 551-598.
— Ona Group of Linear Differential Equations of
the 2nd Order, including Professor CorysTav’s
Seiche-equations, 651-676.
Heart, Effect of Chloroform on.
and H. J. ScHaruies, 322.
By E. A. ScuArer
if
Igneous Geology of the Bathgate aud Linlithgow
Hills. By J. D. Fauconer, 359-366.
Interglacial Plant Remains in the Scottish Peat
Mosses. By Francis J. Lewis, 699-723.
di
Jackson (Ff. H.). On Generalised Functions of
Legendre and Bessel, 1-28.
[The simpler properties of functions which are
natural extensions of the Bessel and Legendre
functions: associated functions: extension of
the function I. Properties of derivatives of
functions P,Q and J. Recurrence formule:
some examples of expansions in series of the
functions. |
Certain Fundamental Power Series and their
Differential Equations, 29-38,
[Series SA,” in which(r) =p, +pot+.... +P,
specially the Hypergeometric series of this type,
reducing when (p,p,p,....)=(1,1,1....)
to the series F(a By de.... 2). Coefficients
INDEX.
Ga! ; -
(nr) Pry! with properties analogous to _,C,
reducing fo ,,C, whem (@ip.p, 2... Je
QUEUE Wee ee eae lp
Jackson, (F. H.). Theorems relating to a General-
ization of the Bessel-Function, 105-118.
—— Theorems relating to a Generalization of
Bessel’s Function. II., 399-408.
Jenu (T. J.). On the Glacial Deposits of Northern
Pembrokeshire, 55-87.
K
Karyokinesis in Red Blood Corpuscles of Larva of
Lepidosiren paradoxa. By TT. H. Brycs,
295-303.
Kerr (J. GranwAm). On some Points in the Early
Development of Motor Nerve Trunks and
Myotomes in Lepidosiren paradoxa, Fitz.,
119-128. .
Kipston (Ropert). On the Internal Structure of
Sigillaria elegans of Brongniart’s ‘‘ Histoire
des végétaux fossiles,” 533-550.
Kworr, C. G. Magnetization and Resistance of
Nickel Wire at High Temperatures, 39-52.
L
Lepidosiren paradoxa, Structure of Red Blood
Corpuscles of ; Karyokinesis in; Structure and
Character of Leucocytes. By T. H. Brycs,
291-310.
Hematogenesis in. By T, H. Bryon, 425-467.
Leucocytes of Lepidosiren paradoxa, Structure and
Characters of. By T. H. Brycu, 303-310.
Origin of. By T. H. Brycs, 425-467.
Lewis (Francois J.). The Plant Remains in the
Scottish Peat Mosses. Part I.—The Scottish
Southern Uplands, 699-723.
Line- and Band-Spectra, On the Structure of the
Series of. By J. Haum, 551-598.
Linear Differential Equations of the 2nd Order, in-
cluding Professor CurysTa’s Seiche-equations.
By J. Hau, 651-676.
Linlithgow and Bathgate Hills, Igneous Geology of.
By J. D. Fatcongr, 359-366.
Lymphoid Tissue of Kidney in Lepidosiren, Develop-
By T. H. Brycs, 446-449, 458-460.
ment of.
M
Magnetization and Resistance of Nickel at Higr
Temperatures. By C. G. Knorr, 39-52.
Metals, Experiments on the Influence of Stress on
the Thermal Expansion of. By E, G. Coxmr,
229-250.
INDEX.
Microdinadx, A New Family of Bdelloid Rotifera.
By James Murray, 367-386.
Mollusca found Inland in Sands and Gravels, Pem-
brokeshire. By T. J. Jenu, 72-73.
Muir (THomas). Continuants Resolvable
Linear Factors, 343-358.
— The Eliminant of a Set of General Ternary
Quadrics (Part III.), 387-397.
Murray (JAmgs).
into
collected by the Lake Survey, 367-386.
— The Tardigrada of the Scottish Lochs, 677-
698.
Muscles, Early Development of, in Lepidosiren.
By J. Granam Kerr, 119-128.
Myzxinoid Fishes, The General Morpholegy of, based
on aStudy of Myxine. Part I.—The Anatomy
of the Skeleton. By Frank J. Cotz, 749-788.
N
Nerves, Karly Development of, in Lepidosiren. By
J. Grawam Kerr, 119-128.
— Regeneration, Suggestions as to, based on
developmental features in Lepidosiren. By J.
GraHamM Kerr, 119-128.
Nickel at High Temperatures, Magnetization and
Resistance of. By C. G. Knorr, 39-52.
Normal Curve, determining the Seiches in a Lake.
By G. Curysrat, 607, 614.
Notaeolidia, gigas and purpurea.
519-532.
Nova Perse,
251-290.
Nudibranchiata of the Scottish National Antarctic
Expedition. By Sir C. Extotr, 519-532,
By Sir C. Exrort,
Spectrum of. By L. Becxmr,
P
Paramuricea robusta, n. sp. J. A. THouson and
J. Rircnie: Aleyonarians of the Scottish
National Antarctic Expedition, 856.
Pembrokeshire (Northern), Glaciation of,
JeHu, 82-87.
Pennella balenopterx: a Crustacean, parasitic on
the Fiuner Whale, Balxnoptera musculus. By
Sir Wm. Turner, 409-434.
Peridinex of the Scottish Plankton.
and G. 8S. Wzst, 493-495.
Phytoplankton, Table of Scottish, By W. Wesr
and G. S. Wsst, 481-492.
Summary of Knowledge of Scottish. By
W. West and G. 8. West, 509-515.
Plankton, Freshwater, of Scottish Lochs.
West and G. S. West, 477-518.
By T. J.
By W. West
By W.
On a New Family and Twelve |
New Species of Rotifera of the Order Bdelloida, |
Sg)
Primnoella scotix, n. sp. J. A, THomson and
J. Rrrcoar: Alcyonarians of the Scottish
National Antarctic Expedition, 854.
Primnoisis ramosa, n. sp. J. A. THomson and
J. Rircam: Alcyonarians of the Scottish
National Antarctic Expedition, 851.
Q
Quadrics, The Eliminant of a Set of General
Ternary Quadrics. Part II. By TxHomas
Muir, 387-397.
R
Red Blood Corpuscles of Lepidosiren paradoza,
Structure of. By T. H. Brycz, 292-295.
—— Origin of. By T. H. Brycg, 425-467.
Resistance and Magnetization of Nickel at High
Temperatures. By C. G. Knorr, 39-52.
Ritcwi£ (James) and J. ARTHUR THomson. The
Alcyonarians of the Scottish National Antarctic
Expedition, 851-860.
Rotation of the Sun, Spectroscopic Observations of.
By J. Haun, 89-104.
Rotifera, New Family and Twelve New Species of
Bdelloid. By James Murray, 367-386,
Rubbly Drift in Pembrokeshire. By T. J. Jenu,
74-77.
S
Sands and Gravels, High Level and Marine-beds,
in Pembrokeshire. By T. J. Jenv, 68-74,
ScHirer (E. A.) and H. J. Scuarures, The Action
of Chloroform upon the Heart and Arteries,
311-341.
Somarnies (H, J.). See ScHirer, H, A,
Scottish National Antarctic Expedition, Nudibran-
chiata. By Sir C. Euior, 519-532.
—— Alcyonarians, By J. A. THomson and Jas.
Ritcars, 851-860.
Seiche, True Acoustic
CurystaL, 609-615.
— Forced. By G. Curysrat, 608.
— Longitudinal, General Mathematical Theory
of. By G. Curysrau, 613-616.
Seiche Functions : Seiche Cosine, Seiche Sine, Lake-
By G. Curysrat, 617-620,
Analogy for. By G,
Function.
632-635.
Seiche Periods, in General not Harmonic. By
G. Curystat, 602.
—— Quartic Approximations for. iy (Ge
Curystrat, 604.
Ratio T,/T, in Concave and Convex Lakes.
By G. Carysrau, 606.
—— Du Boys’ Approximation for,
CurysraL, 606.
By G.
916 INDEX.
Seiche Periods, Ratios of, in Parabolic Lakes.
By G. Curysran, 626.
—— Ratios of, in Rectilinear Lakes.
Curysta, 639.
—— by Du Boys’ Rule. By G. Curysran and
Ernest MacnaGan-WEDDERBURN, 829-842.
By G.
Seiches, Bibliography of. By G. Curysrat,
644-649.
in Parabolic Lakes. By G. Curysrat,
620-635.
——— in Rectilinear Lakes.
635-641,
——- in Quartic Lakes. wy Ce
641-643.
Experimental Analogies and Illustrations. By
G. CurystaL, 609-612.
—— Nodes and Ventral Points of, numerical data.
By G. Curysrat, 624, 628, 640, 641.
caused by Lisbon Earthquake. By G.
Carystat, 599.
--~~— Longitudinal, in a Lake of Varying Section.
By G. Curystat, 602.
By G. Curystat,
Curystat,
—— Calculation of the Periods and Nodes of
Lochs Earn and Treig. By G. Curysran and
Ernest Macuacan-WEpDDERBURN, 823-850.
—— On Group of Linear Differential Equations,
including Professor CurysTaL’s Seiche-equa-
tions. By J. Haun, 651-676.
Sigillaria eleyans of Brongniarts “ Histoire des
végétaux fossiles,” Internal Structure of. By
Ropert Kinston, 533-550.
Skeleton of Myxine. By Frank J. Coun, 749-788.
SomMERVILLE (Duncan M. Y.). Semi-regular Net-
works of the Plane in Absolute Geometry,
725-747.
Spectroscopic Observations of the Rotation of the
Sun. By J. Hato, 89-104.
Spectroscopy, Ou the Structure of the Series of
Line- and Band-Spcctra. By J. Hato, 551-
598.
Spectrum, Nova Persei. By L. Becker, 251-290.
Spleen, Histogenesis of, in Lepidosiren paradonxa.
By T. H. Brycz, 454-458.
Stress, On the Measurement of, by Thermal
Methods, with an Account of some Experi-
ments on the Influence of Stress on the
Thermal Expansion of Metals. By E. G.
Coker, 229-250.
Sun, Spectroscopic Observations of the Rotation of
the. By J. Hatm, 89-104,
a
Tardigrada of Scottish Lochs.
677-698.
Tuomson (J, Arvuur) and Jamus Rivcure, The
Aleyonarians of the Scottish National Antarctic
Expedition, 851-860.
Thouarella brucei, n. sp.
By James Murray,
J. A. THomson and J.
RitcHie : Aleyonariaus of the Scottish National
Antarctic Expedition, 652.
Traquair (R. H.). Supplement to the Lower
Devonian Fishes of Gemiinden, 469-475.
Tritonia appendiculata. By Sir C. Extor, 519-
532.
Tritonia pallida, By Sir C. Evtor, 519-532. ,
Tritoniopsis, By Sir C. Enior, 519-532.
Tonner (Sir Wurriam). On Pennella Bale-
nopteree: a Crustacean, parasitic on a Finner
Whale, Balenoptera musculus, 409-434.
}
W
WEDDERBURN (Ernest Maciacan-). See CHRYSTAL,
G.
West, W., and Wes?, G. 8S. A further Contribu-
tion to the Freshwater Plankton of the Scottish
Lochs, 477-518.
x
Xenopus levis, Daud, Life History of. By Ep. J.
Burs, 789-821.
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