50(pA^
PROCEEDINGS
OF THE
Cambritrgc ^Ijil0S0pl^ica:I Sorietg.
VOLUME XVII.
dambrttige :
FEINTED BY JOHN CLAY, M.A.
AT THE UNIVERSITY PRESS.
PEOCEBDINGS
OF THE
CAMBEIDGE PHILOSOPHICAL
SOCIETY.
VOLUME XYII.
October 28, 1912— May 18, 1914.
dTambritige :
AT THE UNIVERSITY PRESS,
AND SOLD BY
DEIGHTON, BELL & CO. AND BOWES & BOWES, CAMBEIDGE.
CAMBEIDGE UNIVERSITY PRESS,
C. F. CLAY, MANAGER, FETTER LANE, LONDON, E.C.
1914
CONTENTS.
VOL. XVII.
PAGE
The Effects of Hypertonic SoUuions upon the Eggs of Echinus. By
J. Gray. (Communicated by Mr F. A. Potts) .... 1
Preliminary Note on the Inheritance of Self-sterility in Reseda odorata.
By R H. CoMPTON 7
On the Anthropometric data collected by Professor J. Stanley Gardiner,
F.R.S., in the Maldive Islands and Minikoi. By W. L. H.
Duckworth 8
Note§ on the volatilization of certain binary alloys in high vacua. By
A. J. Berry 31
On Pulsus alternans. By George Ralph Mines. (Plate I) . . ,34
The Diffraction of Short Electromagnetic Waves by a Crystal. By
W. L. Bragg. (Communicated by Professor Sir J. J. Thomson.)
(Plate II.) (Two figs, in Text) 43
The Meres of Breckland. By J. E. Marr 58
Note on a Remarkable Instance of Complete Rock-disintegration by
Weathering. By F. H, Hatch 62
The Variation of Magnetic Susceptibility ivith Temperature. Part II.
On Aqueous Solutions. By A. E. Oxley. (Six figs, in Text) . 65
Some Experiments on the Electrical Discharge in Helium and Neon.
By Herbert Edmeston Watson. (Communicated by Professor
Sir J. J. Thomson.) (Two figs, in Text) 90
Some Diophantine Impossibilities. By H. C. Pocklington . . . 108
On the earlier Mesozoic Floras of New Zealand. By E. A. Newell Arber 122
The Mineral Compositio7i of some Cambridgeshire Sands and Gravels.
By R. H. Rastall 132
Note on the Rontgen radiation from cathode particles traversing a gas.
By R. Whiddington. (One fig. in Text) 144
vi Contents.
fAGE
The Gravels of East Anglia. By Professor Hu&hes .... 147
On the Properties of a Liquid connected with its Sxirface Tension. By
E. D. Kleeman 149
The Minerals of some Sands and Gravels near Newmarket. By R. H.
Rastall 161
Observations on Polyporus squamosus, Huds. (Preliminary Communi-
cation.) By S. Reginald Price 168
Note on the respiratory movements of Torpedo ocellata. By G. R.
Mines. (Plates III and IV) 170
The Atomic Constants and the Properties of Substances. By R. D.
Kleeman 175
Note on the effect of heating paraformaldehyde vnth a trace of sulphuric
acid. By J. G. M. Dunlop . , 180
The Oxidation of Ferrous Salts. By F. R. Ennos. (Communicated by
Mr C. T. Heycock) 182
A Simple Method of determining the Viscosity of Air. By G. F, C.
Searle. (Two figs, in Text) 18S
The Swarming of Odontosyllis. By F. A. Potts. (One fig. in Text) . 19^
Further applications of positive rays to the study of chemical problems.
By Professor Sir J. J. Thomson 201
The chemical and bacterial condition of the Cam above and below the
sewage effluent outfall. By J. E. Purvis and A. E. Rayner . . 202
On the optically active semicarbazone and benzoylphenylhydrazone of
Gjclo-heicanone-4:-carboxylic acid. By W. H. Mills and Miss A. M.
Bain ............ 20a
The ten Stereoisomeric Tetrahydroquinaldinomethylenecamphors. By
Professor Pope and J. Read ■ . 204
Experiments illustrating flare spots in photography. By G. F. C.
Searle. (Six figs, in Text) 205
Sarcocystis colii, n. sp., a Sarcosporidian occurring in the Redfaced
African Mouse Bird, Colius erythromelon. By H. B. Fantham.
(Plate V) 221
Observations on Hirneola auricula-judae, Berk. ("Jew's ear"). (Pre-
liminary communication.) By M. J. Le Goo. (Communicated by
Mr F. T. Brooks) 225
Notes on additions to the Flora of Cambridgeshire. By A. H. Evans . 229
A Note on the Food of Freshwater Fish. By J. T. Saunders . . 236.
Observations on Ticks : (a) Parthenogenesis, (b) Variation due to nutrition.
By Professor Nuttall 240
Contents. vii
PAGE
The Division of Rolosticha scutellum. By K. R. Lewin. (Communicated
by Professor Nuttall) 241
Exhibition of living Termites. By Professor A. D. Imms . . . 241
On the greatest value of a determinant whose constituents are limited.
(Proof of Hadamard's theorem.) By Professor A. C. Dixon . 242
Expressions for the remainders when 6, 6'^, sin^^, cos kd are expanded in
ascending po^ve^'s of sin 6. By Professor A. C. Dixon . . . 244
A diist electrical machine. By W. A. Douglas Eudge, (One fig. in
Text) 249
On a mechanical vacuwn tube regidator. By R. Whiddington. (One
fig. in Text) 251
Some Plants new to the British Isles. By C. E. Moss . . . 255
On some new and ra,re Jurassic plants from Yorkshire: — Eretmophyllum,
a new type of Ginkgoalian leaf By H. Hamshaw Thomas.
(Plates VI and VII) . . " 256
The Unstable Nature of the Ion in a Oas. By R. D. Kleeman.
(Two figs, in Text) 263
N'ote on the Absorption of Cathode Rays by Metallic Sheets. By
R. Whiddington. (One fig. in Text) 280
The Influence of Molecular Constitution and Temperature on Magnetic
Susceptibility. Preliminary Note. By A. E. Oxley . . . 282
A Chinese Flea-trap. By Edward Hindle. (Communicated by Pro-
fessor Nuttall.) (One fig. in Text) 284
Some methods of measuring the surface tension of soap films. By
G. F. C. Searle. (Ten figs, in Text) . . ' . . . .285
Proceedings at the Meetings held during the Session 1912 — 1913 . . 300
A possible connexion between abnormal sex-limited transmission and
sterility. By L. Doncaster 307
The Flight of the House-Fly. By Edward Hindle. (Communicated by
Mr C. Warburton) . . . . , 310
On the Dependence of the Relative lonisation in various Gases by /3 Rays
on their Velocity, and its bearing on the lonisation produced by
y Rays. By R. D. Kleeman 314
Note on a Dynamical system ilhistrating Fluorescence. By N. P.
McCleland . 321
On the Presence of certain Lines of Magnesium in Stellar Spectra. Ej
F. E. Baxandall. (Communicated by Professor Newall) . . 323
The proportions of the sexes of Forficula auricularia in the Scilly Islands.
By H. H. Brindley. (One map in Text) 326
viii Contents. msmk
PAGE
Notes on the Breeding of Forficula auricularia. By H. H. Brindley . 335
The comparison of nearly equal electrical resistances. By G.'F. C. Searle.
(Five figures in Text) 340
The Distribution of the Stars in relation to Spectral Type. By Professor
A. S. Eddington 351
The oxygen content of the river Cam hefoi'e and after receiving the Cam-
bridge sewage effluent. By J. E. Purvis and E. H. Black. (Three
figs, in Text) 353
On Root Development in Stratiotes aloides L. with special reference to
the occurrence of Amitosis in an embryonic tissue. By Agnes Arber.
(Communicated by Dr Arber.) (Plates VIII and IX) . . . 369
Amitosis in the Parenchyma, of Water-Plants. By E. C. McLean.
(Communicated by Professor Seward.) (One fig. in Text) . . 380
The History of the occurrence of Azolla in the British Isles and hi Europe
generally. By A. S. Marsh. (Communicated by Professor Seward) 383
A Simplification of the Logic of Relations. By N. Wiener. (Com-
municated by Mr G. H. Hardy) 387
A Double- Four Mechanism. By G. T. Bennett. (Two figs, in Text.)
(Plate X) 391
On the Nature of the Internal Work done du,ring the Evaporation of a
Liquid. By E. D. Kleeman. (Two figs, in Text) .... 402
The Work done in the Formation of a Surface Transition Layer of a
Liqidd Mixture of Substances. By E. D. Kleeman . . . 409
The ionisation produced by certain substances when heated on a Nernst
filament. By Frank Horton. (Two figs, in Text) . . .414
Fluctuations of sampling in Mendelian Ratios. By G. Udny Yule . 425
A Case of Repulsion in Wheat. By F. L. Engledow. (Communicated
by Professor Bipfen) 433
The determination of the best value of the coupling -ratio from a given set
of data. By F. L. Engledow and G. Udny Yule .... 436
A Contribution to the Theory of Relative Position. By Norbert
Wiener. (Communicated by Mr G. H. Hardy) .... 441
Oil an Application of the Molecidar Field in Diamagnetic Substances.
By A. E. OxLEY 450
Thompsonia, a little known Crustacean Parasite. (Preliminary Note.)
By F. A. Potts, M.A., Trinity Hall. (Two figs, in Text) . . 453
The gall-forming Crab, Hapalocareinus. (Preliminary Note.) By
F, A. Potts, M.A., Trinity Hall. (One fig. in Text) . , ,460
Contents. ix
PAGE
A A'^ote on Leaf-Fall as a Cause of Soil Deterioration. By W. Lawrence
Balls, M.A., St John's College 466
Specific Salinity in the Cell Sap of Pure Strains. By W. Lawrence
Balls, M.A., St John's College 467
Pre- Determination of Fluctuation. (Preliminary Note.) By W.
Lawrence Balls, M.A., St John's College 469
The Ammonia Content of the Waters of Small Ponds. By J. T. Saunders,
M.A., Christ's College 471
Optically active substances of simple molecular coitstitiUion. By Professor
Pope and John Read, M.A 475
Some further experiments on eutectic growth. By F. E. E. Lamplough,
M.A., Trinity College, and J. T. Scott, B.A 476
Note on the detection of Malonic Acid. By Dr H. J. H. Fenton, Christ's
College 477
On the Resolution of b-Nitrohydrindene-2-carboxylic Acid. By W. H.
Mills, M.A., Jesus College, H. V. Parker, B.A., and R. W.
Prowse, B.A 478
Proceedings at the Meetings held during the Session 1913 — 1914 . . 479
Index to Vol. xvii 485
PLATES.
Plate L To illustrate Mr Mines' paper
Plate II. To illustrate Mr Bragg's paper .
Plates III and IV. To illustrate Mr Mines' paper .
Plate V. To illustrate Mr Fantham's paper
Plates VI and VII. To illustrate Mr Thomas' paper
Plates VIII and IX. To illustrate Mrs Arber's paper
Plate X. To illustrate Mr Bennett's paper
34
43
170
221
256
369
391
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SOCIETY.
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1913
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PROCEEDINGS
OF THE
Camtrritrg^ ^Ijil0S0p]^ttaI Sorietg,
The Effects of Hypertonic Solutions upon the Eggs of Echinus.
By J. Gray, 'B.A., King's College. (Communicated by Mr
F. A. Potts.)
[Bead 28 October 1912.]
In the Proceedings of this Society for last year, a preliminary
account was given of the cytology of hybrid eggs obtained from
the two species Echinus escidentus and Echinus acidus. The
structure of such eggs was given as follows:
"In the cross esculentus $ x acutus (^ the mitotic figures of
the segmenting egg are perfectly normal, and do not differ recog-
nisably from those of the pure species. In the converse cross
acutus % X esculentus (/*, however, a striking abnormality is con-
stantly present in all the eggs examined. Until immediately
after the dissolution of the nuclear membrane in the first seg-
mentation division the behaviour is normal, and 38 normal
chromosomes can be counted. As the spindle is formed, the
chromosomes become scattered upon it irregularly, and gradually
become collected in the equatorial plate. During this process it
is seen that a considerable though variable number of them are
either swollen up, or more commonly bear vesicles attached to
their ends and sides. The staining of the vesicles is always less
intense than that of the chromosomes, and is progressively fainter,
the more the vesicle is developed, so giving the impression that
the chromosome has swollen at one point, and that the chromatin
is thus more thinly diffused in the wall of the vesicle than in the
normal part of the chromosome. In the equatorial plate stage
the vesicles may either remain attached to the chromosomes which
produced them, or become separated from them ; those which
VOL. XVII. PT. I. 1
2 Mr Gray, The Effect of Hypertonic Solutions
become separated tend to take up positions round the edge of the
equatorial plate, sometimes outside the' spindle. The normal
chromosomes, and those of which the normal shape has not
become much altered by vesicle-production, then split longi-
tudinally in the ordinary way, and begin to travel to the poles.
It may sometimes be seen that a chromosome with a vesicle
attached has split, and the vesicle, remaining attached to one half,
is being carried with it towards the pole. It is possible that a
few chromosomes, the greater part of which has become swollen
into a vesiclO; do not divide, but are carried entire to one or
other pole. The vesicles which have become separated from their
parent chromosomes appear to differ in their fate according to
their position. If they lie among the chromosomes inside the
spindle, they are carried with them to one or other pole and
become included in the daughter nuclei. If, however, they are
left on the edge of the spindle, as commonly happens with the
larger vesicles, they remain outside the mitotic figure in the cyto-
plasm, and are not included in the nuclei of the daughter cells.
In this case they usually contract and become small evenly stained
spheres, not easily distinguishable from the larger yolk-granules,
but usually recognisable after the cell-division is completed, lying
in the cytoplasm near the boundary between the two cells.
In the second segmentation division, a similar process takes
place, but is usually rather less pronounced; the vesicles are on
the whole .smaller, and we doubt whether complete chromosomes
ever become vesicular*."
A similar phenemenon within the eggs of Echinoderms has
recently been described by Konopacki. He treated the fertilised
eggs of Strong ylocentrotus lividus with hypertonic solutions of
certain strengths for half an hour, and subsequently transferred
to sea-water. Although no detailed description is given of the
behaviour of the chromatin, a study of his figures leads to the
conclusion that the effect of such solutions upon the fertilised
eggs of Echinus esculentus and E. acutus would throw some light
upon the cytology of hybrids derived from these species. The
following are the chief results of such experiments carried out
this year at Plymouth.
Eggs of E. esculentus were fertilised and allowed to remain
in fresh sea- water for one hour: they were then transferred to
a mixture of 50 c.c. sea- water -|- 6 c.c. 2| M . NaCl solution, and
after half an hour were transferred to fresh sea-water until the
first mitotic figure had been formed.
The eggs were then preserved and sectioned : the stain used
being Heidenhain's Haematoxylin. Such preparations shewed
that the most interesting effect of the hypertonic solution was to
* Proc. Camh. Phil. Soc. Vol. xvi. Pt. v. 1911, p. 415. Doncaster and Gray.
upon the Egfjs of Echinus. 3
cause the formation of one vesicle in each nucleus exactly similar
in appearance and behaviour to those seen in eggs of the hybrid
E. acutus ^ xE. esculentus ^. There was, however, this important
difference; whereas in the hybrid eggs the vesicles are formed
directly from individual chromosomes and are never present inside
the nuclear membrane, those in the hypertonic eggs oiE. esculentus
are always formed inside the nuclear membrane of the female pro-
nucleus. It was found impossible to determine whether the number
of chromosomes formed from such a nucleus was one less than
the full somatic number for the species, but what evidence there
is, is certainly not unfavourable to the view that this vesicle
represents morphologically either the whole or part of one chro-
mosome. It resembles the vesicles of the hybrid eggs in being
either omitted from or included in the daughter nuclei of the first
division.
The cytology of eggs of E. acutus which were treated in
exactly the same way as is above described for E. esculentus,
shews a marked difference between the two species. Within the
nuclear membrane of the zygote nuclei, it is only very exceptional
to find any trace of vesicles. As soon as the nuclear membrane
disappears, however, numerous vesicles are found among the
chromosomes. Their number varies from three to five, and there
is absolutely no doubt that they are formed directly from indi-
vidual chromosomes just as in the hybrid E. acutus^ xE. escu-
lentus {/", for not only is the number of normal chromosomes
correspondingly reduced, but every stage between typical chromo-
somes and fully formed vesicles has been found. If it could be
shewn that the vesicles are always derived from the same indi-
vidual chromosomes in the complex, there would be an interesting
proof of the physiological individuality of these bodies. Unfortu-
nately so far this has been found to be impracticable.
The ultimate effect of these hypertonic solutions on the eggs
of both species is to cause irregularity in segmentation of the
cytoplasm. In no case did an egg develop beyond the blastula
stage.
These experiments shew, therefore, that in the formation of
vesicles and the consequent elimination of chromosomes, which
normally takes place in the nuclei of the hybrid E. acutus '^ x E.
esculentus ^, it is essentially the female chromatin that becomes
pathological. It is extremely unfortunate that it is impossible to
test this hypothesis by a study of the hybrid eggs themselves; yet
the effects of hypertonic solutions on the eggs of the two species
gives strong support for such an assumption.
It will be remembered, however, that the mitoses of the hybrid
E. esculentus % x E. acutus ^ are quite normal, and l^herefore we
cannot explain the pathological condition of the reverse cross by
4 Mr Gray, The Effect of Hypertonic Solutions
the simple statement that the chromosomes of E. acutus are more
susceptible to changed environment than those of E. escnlentus.
In order to explain these facts I would put forward the following
suggestion in the most tentative way. It is based on the view
that the relation of a cell to electrolytes in its surrounding media
is of prime importance to the existence of that cell. The work of
McClendon and E,. S. Lillie has shewn that after fertilisation the
surface membrane of the egg is more permeable to ions than
before. It has also been demonstrated that the CO2 production of a
dividing cell changes just before each division, ie., there is a slight
increase in permeability*. It is also highly probable that the
effect of hypertonic solution upon a cell is to decrease its permea-
bility to ions. (Sutherland ; Lillie.)
The whole of the evidence in favour of the view that the
permeability changes of the egg membranes (plasmic and nuclear)
are of profound importance to the activities of the cell cannot be
discussed in full, but the following extract from a recent paper by
R. S. Lillie has a peculiar interest in connection with the phenomena
discussed in this paper.
"The conclusion that many pathological conditions have their
primary origin in abnormalities of the limiting membranes of cells
is an obvious corollary of any view that regards such membranes —
which are essentially insulating surface films of varying ionic
permeability and electrical polarization — as largely controlling the
rate and character of the cell processes. If stimulation depends
primarily upon altered polarization of the plasma- membrane
due to increased ionic permeability, it is clear that a normal
response, in the case of any cell, implies a definite condition of
the membrane. If this condition is permanently altered, the
cell processes inevitably undergo derangement, and pathological
changes follow. Such a deranged condition, if not too far ad-
vanced, may be rectified by restoring the membrane to its normal
condition The alteration caused by a toxic agent may consist
primarily either in increasing or in decreasing the permeability
normal to the membrane, or in altering in either direction the
readiness with which the latter undergoes change.... The plasma
membrane cannot undergo marked and prolonged increase of
permeability without alteration in the nature and proportion of
the cell-constituents; this involves altered chemical organization
and eventual derangement of the cell-processes."
It is, therefore, a possibility at least that the hypertonic
solutions exert a toxic action upon the nucleus of a fertilised
egg by upsetting the normal relationship of the cytoplasm to
electrolytic ions.
* The susceptibility of a dividing cell to poisons has also been shewn to be
rhythmical in the same way.
upon the Eggs of Echinus. 5
Now, the permeability of the egg is changed when a sperma-
tozoon enters, and presumably the change is constant in degree
for each species. When, however, the sperm of a foreign species
is made to enter an Qgg, is it not possible that the change in
permeability is not that which would have been caused by a sperm
of the species to which the egg belongs? If this is so, and the
degree of change in permeability of an egg when fertilised is there-
fore a function of the sperm, then the cytological behaviour of
reciprocal crosses is explicable.
Let the change in permeability for
E, acutus eggs (fertilised by) E. acutus sperm be P,
E. escidentus „ „ E. escidentus „ Pj.
Then E. escidentus „ „ E. acutus is P,
and E. acutus „ „ E. escidentus „ Pj.
Let the difference between P and P^ be about equal to the
change of permeability in normally fertilised eggs of E. acutus
which is brought about by the action of hypertonic solutions of
appropriate strength.
Now the chromatin of E. escidentus can withstand a change of
permeability in the surrounding protoplasm equal to P — P^,
without becoming abnormal*, as is shewn by its reaction to a
hypertonic solution capable of producing such a change. Hence
when the egg of E. escidentus is fertilised by the sperm of E.
acutus, and so attains the permeability peculiar to fertilised eggs
of E. acutus, no abnormality occurs.
On the other hand, when the egg of E. acutus is fertilised by
the sperm of E. esculentus, the E. acutus element becomes patho-
logical, as it cannot endure a permeability in its surrounding proto-
plasm equal to that characteristic of an egg of E. esculentus.
This suggestion is, however, in entire opposition to most of
the conclusions of other workers in hybridisation. The work of
Kupelwieser, Baltzer and Tennent all tends to shew that it is the
male chromatin which becomes abnormal in such cases. Tennent,
however, has shewn that in the cross Arbacia x Toxopneustes not
only are all the chromosomes derived from the male eliminated, but
also some of those from the female parent. Again, G. Hertwig
has shewn that fusion with an abnormal sperm can cause the
female chromatin of a normal egg to be affected.
If the abnormalities are to be entirely confined to the male
element in the egg, there is apparently no explanation for the
cytology of such reciprocal crosses as Sphaerechinus x Strongylo-
centrotus, or Echinus acutus x E. escidentus; for if, as Baltzer
* Presumably the change P-Pi is a little less than that caused in eggs of
E. esculentus by 50 c.c. sea- water + 6 c.c. 2h, M . NaCi, as in the latter case one vesicle
is produced, while in the hybrid E. acutus x E. esculentus no such abnormality
6 Mr Gray, The Effect of Hypertonic Solutions, etc.
suggests, the male chromatin goes wrong because it is "out of
tune" with the female cytoplasm, why are not both reciprocal
crosses abnormal? And in the case of E. acutus x E. escidentus
we should expect the more sensitive E. acutus chromatin to go
wrong when it enters the cytoplasm of the more resistent E. escu-
lentus, and this is not the case.
The proof of the hypothesis here put forward would be in the
demonstration of the fact that the permeability change of an &gg
when fertilised differs according to the species of sperm used, in
other words, the degree of permeability change should be a function
of the sperm*.
A more detailed account of this work will appear in the forth-
coming number of the Quarterly Journal of Microscopical Science
(Vol. LViii.), where references will be found to all the works quoted
in this paper.
* As in some cases of hybridisation there is no doubt whatever tliat it is the
male chromatin that becomes abnormal it is obvious that changes of permeability of
the cytoplasm, such as can be induced by the sperm, cannot be a sufficient explana-
tion of all the abnormalities observed in cross-fertilised eggs.
Mr Gompton, Preliminary Note on the Inheritance, etc. 7
Preliminary Note on the Inheritance of Self-sterility in Reseda
udorata. By R. H. Compton, M.A., Gonville and Caius College.
[Read 28 October 1912.]
Among the numerous examples of self-sterility recorded for
plants and animals the Mignonette is exceptional in that, as was
discovered by Charles Darwin, certain individuals are completely
self-sterile, others completely self-fertile. Clearly this affords a
favourable opportunity for breeding experiments with the object
of studying the inheritance of these obscure and puzzling pheno-
mena. Each flower is normally self-pollinated, so that it is only
necessary to exclude insects in order to ascertain whether a plant
is self-fertile or self-sterile. Further the anthers are freely exposed
before dehiscence, so that, although the flowers are small, emascula-
tion is easy.
Seed was obtained from various tradesmen, and among the
plants grown from it both classes of individuals were abundant.
Experiments are in progress, and the results of the first generation
may be described with the tentative hypothesis to which they
point.
This hypothesis is that self-fertility is a simple Mendelian
dominant character. In support of it may be mentioned the
following facts :
(1) Self-sterile plants when bred inter se throw self-sterile
offspring only. This is in accordance with the view that self-
sterility is a Mendelian recessive.
(2) Certain self-fertile plants when self-fertilised yield self-
fertile offspring only : when crossed with self-sterile plants the
same result is obtained. These are regarded as homozygous for
self-fertility.
(3) Other self-fertile plants when self-fertilised yield approxi-
mately three self- fertile to one self-sterile offspring : when crossed
with self-sterile plants about half the progeny are self-fertile, half
self-sterile. These are regarded as heterozygotes.
The publication of the data in full is deferred until the com-
pletion of the experiments, as is also discussion with reference to
the literature.
Other characters are also being studied. As regards stature it
appears that pure-breeding tall and dwarf races exist, and that the
^1 between them is intermediate in height.
An interesting pollen-character also seems to behave in a
Mendelian fashion. Orange-red colour of pollen appears to be
a simple dominant to bright yellow : self-fertilised heterozygotes
throw about three reds to one yellow.
8 Dr Duchworth, On the Anthropometric data collected
On the Anthropoinetric data collected hy Professor J. Stanley
Gardiner, F.R.S., in the Maldive Islands and Minikoi. By W. L. H.
Duckworth, M.D., Sc.D., Jesus College.
[Bead 28 October 1912.]
In the course of an expedition to the Maldive Islands and
Minikoi, Professor J. Stanley Gardiner, F.R.S., collected a number
of anthropometric data. These he handed to me, and they form
the material upon which the following report is based,
1. The total number of individuals examined is 69. All are
males. Of the 69, 20 are Minikoi men, while of the remainder
24 are from Addu Atoll. Other islets of the Maldive group
supply a few representatives each. The complete list is as follows :
Island
No. of individuals measured
Minikoi
20 (caste is said to be of little moment)
Maldives: Addu
24 (in 4 sets according to caste).
Male
11 (in 3 sets according to caste).
Hulule
9
Kaharidu
1
N. Mahlos
1
Mulaku
1
Nolewangfaro
2
Total
69
2. Professor Gardiner records 13 measurements of each of these
men. In addition to these data, five indices have been worked
out. In preparing the list of the mean values and the range of
variation I have been greatly aided by Dr Poole, of Sidney Sussex
College. Dr Poole intended to prepare the whole of the report,
but the claims of professional work made it necessary for him to
hand the material back to me when he had nearly completed the
determination (previously begun by me) of the means, the maximum
and minimum values. As a result of all this, I am able to deal
with the data re-arranged in the following list :
I. Stature.
II. Height seated, i.e. height
of torso.
III. Cephalic length.
IV. Cephalic breadth.
V. Face length.
VI. Upper face length.
VII. Face breadth.
VIII. Bigonial breadth.
IX. Nose length.
X. Nose breadth.
XI. Cephalic height.
XII. Cranial height.
XIII. Circumference of head.
in the Maldive Islands and Minikoi.
Cephalic.
Altitudinal.
Facial (Kollmann's).
B. Indices.
Nasal.
Gonio-zygomatic.
These data are arranged in three tables, of which No. I con-
tains the original measurements made by Professor Gardiner,
together with some of his comments on the same. Table II gives
the complete list of indices, while in Table III, the means, the
maxima and the minima are set forth in relation to the different
groups of individuals described in paragraph 1 {supra). The
absolute dimensions added to the indices give a total of 18
characters (cf. A and B above) for examination.
3. It is convenient to enquire first into the extent of variation
and the manner in which it is exhibited by the several groups
of men. For this purpose, the records of the maxima and minima
as set forth in Table III may be employed. An examination of
Table III leads to the following conclusions in this connection.
The maxima and minima are shared in the proportions given
as follows :
Minimum values ... Minikoi 16 out of 18 characters.
Hulule 2 „ „ (sharing the
lowest place once with Minikoi).
Addu 1 out of 18 characters.
Maximum values
Minikoi
4 out of 18 characters
Male
7
Addu
7
The tables shew clearly that the men of Minikoi are of smaller
dimensions on the whole than the men from the Maldives. In
addition to this, the Minikoi men are the most variable of the
groups into which the data have been divided.
4. The standard deviation and the coefficient of variation will
provide further evidence on the same point, viz. the relative
variability of the different groups. Here we may begin the
examination by a scrutiny of the seriations upon which the calcula-
tions of these data are based. Eight measurements and four
indices are here available for study, but the analysis is not suit-
able for discussion in this place and it is presented in a tabulated
form. Only a summary will be given here, and it is to the
following effect.
{a) Stature : The Minikoi men are nearly at the bottom of
the list in this respect. The Addu men (the most numerous group
and therefore most fitly comparable) are the tallest and thus at the
opposite end of the scale. The remaining groups are intermediate,
10 Dr Diichwoi
ih, On the
Anthl
'opo)iietric data collected
Table I.
Maldive Islands
No
1.
All <|
<D
.a
B
CD
bD oj
CrJH
h^ o
■5 -a
qi Ah
t-H
Q
CD a
to
^5
O cS
03 r^
AH CD
^ o
f3 °
=4-1
o
be 1>
be S :
XII
I
II
III
19-1
IV
V
VI
VII
VIII
IX
X
XI
1
148-9
75-8
14-0
10-5
6-1
13-2
11-5
5-1
3-8
20-5
12-4
2
156-8
73-3
17-8
13-6
11-1
6-3
12-6
10-3
5-3
3-5
19-9
12-0
3
160-4
81-1
20-4
14-6
10-8
6-1
12-5
11-1
4-5
3-4
21-8
12-6''
4
163-2
84-2
19-5
15-0
11-1
6-2
12-2
10-0
5-0
3-7
22-3
13-6
5
161-4
80-7
18-9
15-4
11-2
6-3
13-5
11-1
5-1
4-2
21-2
11-4
6
150-4
76-0
19-0
14-0
10-4
5-9
12-6
10-1
4-7
2-8
21-6
12-2
7
155-9
79-5
19-6
15-3
11-2
6-4
13-3
10-8
4-9
3-5
22-4
12-61
8
153-2
83-1
17-8
14-4
10-8
6-5
12-8
11-6
5-5
3-3
23-6
12-9!
9
147-8
79-2
18-2
14-4
10-8
5-8
12-7
10-2
4-8
3-3
20-5
12-6
1898-0
712-9
170-3
130-7
97-9
55-6
115-4
96-7
44-9
81-5
193-8
112-3
13-2
10
156-7
83-7
20-0
15-7
10-7
6-5
13-6
11-6
4-2
3-8
21-1
11
172-9
89-2
18-5
14-3
11-2
6-7
13-9
13-1
5-0
4-2
24-2
13-0
12
158-1
80-9
19-4
16-0
11-7
6-5
14-5
13-0
4-8
4-5
22-8
13-61
13
173-6
88-5
20-5
16-0
11-4
7-0
14-2
12-0
5-1
3-7
25-0
14-7i
661-8
842-3
78-4
62-0
45-0
26-7
56-2
49-7
19-1
16-2
93-1
55 -a
14
161-3
83-2
20-0
15-4
12-1
6-4
14-3
11-7
4-9
3-9
21-0
12-11
15
158-4
73-4
17-9
14-1
10-0
5-4
12-5
10-7
4-8
3-5
21-3
12-2.:
16
158-1
79-5
20-2
14-4
11-4
6-8
13-3
11-2
5-2
3-6
21-6
12-71
477-8
236-1
58-1
43-9
88-0
18-6
40 1
33-6
14-9
11-0
68-9
87 -0.
17
155-6
76-8
18-8
14-3
11-3
6-8
13-0
11-7
5-3
4-0
22-2
13-4
18
147-4
79-9
18-6
14-2
10-9
6-4
12-0
9-7
5-2
3-3
22-4
13-4 1
19
156-7
78-2
18-6
14-6
12-2
7-5
12-8
11-0
5-7
3-7
21-7
11-gi
20
161-5
79-4
19-0
14-8
11-6
6-9
12-7
10-4
4-9
3-7
21-9
12-21
621 -2
3U-8
75-0
57-9
46-0
27-6
50-5
^^•6'
21-1
14-7
88-2
50-5 :
21
150-8
72-5
19-6
14-4
11-0
6-2
13-5
12-4
4-6
3-7
19-9
12 -ii
22
156-3
74-4
18-2
14-4
10-9
6-3
11-9
10-5
4-5
3-2
21-5
1
12-1
23
153-2
75-6
19-8
14-8
10-7
5-8
13-1
11-6
4-3
3-7
21-5
13-4
24
166-6
83-3
19-3
13-8
11-6
5-9
12-7
11-8
4-3
3-5
23-1
13-3
25
163-8
82-4
19-5
13-9
10-7
5-6
13-7
11-0
5-0
3-5
22-9
14-0 ■'
790-7
388-2
96-4
71-3
54-9
29-8
64-9
57-8
22-7
17-6
108-9
''1
in the Maldive Islands and Minikoi.
11
''eas Lire) I tents in ctms. Ages approximate.
•i O c6
3 fl <U
} g-^
Name
Occupation
or caste
Island
Age
Remarks
XIII
54-7
Ahamada
Toddy Drawer
Hulule
24
Condition good.
49-8
Mohammed
)) 55
,,
22
„ thin.
5o-2
Ibrahim
Fisherman
J J
21
,, medium.
00-3
Moussa
Toddy Drawer
,,
21
,, thin.
55-2
Dongkoko
Fisherman
,,
33
,, good.
53-6
Ibrahim
5)
,,
23
,, thin. Syphilitic.
55 -2
Hassan
Toddy Drawer
, .
32
„ good.
53-8
Avakaru
Head man
"
60
,, good. Stoops but
teeth good. Deaf. (Photo.)
52-9
Hassan
Fisherman
-;
30
Condition good.
i85-7
58'2
Mohamed
Didi
Male
25
Stout. High caste. (Photo.)
56 "5
Hassan
"
"
54
Good.
Father of last. Velanama-
nihofan.
56-1
Mohamed
Chief Vizier
jj
53
Good. Best caste.
58-3
Manipul
Head of Mosque
.'
31
(Photo.)
229-1
56-3
Hosein
Overseer
35
Good, stout. Muniku.
51 -3
Hassan
Singing Boy
,j
20
Poor, thin. ,,
55-8
Ibrahim
Servant
"
40
Good. Fulu. Sloping fore-
head.
163-4
53-5
_
Fisherman
53
22
Thin.
53-0
—
)i
>)
30
Fair.
54-1
5)
,,
25
Sparse.
53-7
—
„
50
>»
214-3
55-7
Mohammed
Servant
Kaharidu
35
Good. Marked stoop and
broad jaws.
52-3
Mohammed
N. Mahlos
25
Thin.
55-2
Ismail
','
Mulaku
23
Fat. Vacant. Fool.
54-9
Hassan
Sailor
Nolewangfaro
25
I Good. My boys. Big Photos.
55-1
Hosein
>)
'>
23
)
273-2
12 Dr Duckworth, On the Anthropometric data collected
Table I {cont). Maldive Islands. No. 2.
26
27
28
29
30
31
32
33
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
161-7
169-5
160-1
158-2
156-6
165-7
155-7
1127-5
172-0
155-5
327-5
157-9
161-6
163-7
157-7
157-9
798-8
162-2
155-9
163-1
155-7
146-6
158-0
160-5
166-4
161-7
166-5
Lj<J6-6
II
81-8
82-7
79-9
79-7
76-5
82-1
82-2
564-9
82-1
78-9
161-0
79-6
75-8
82-4
75-2
76-4
389 -d
81-0
80-1
80-6
75-4
73-4
74-8
80-6
82-7
789-9
III
20-7
18-9
20-9
20-6
19-8
19-9
19-4
140-2
19-0
19-5
38-5
19-3
20-4
19-1
19-3
18-9
97-0
19-5
18-8
19-5
19-0
19-5
19-4
19-9
19-1
19-5
20-0
194-2
pq O
IV
14-8
14-1
15-2
15-1
14-9
14-8
15-9
104-8
16-2
18-8
30-0
15-4
15-5
15-3
14-1
13-9
74-2
14-4
14-0
14-3
14-3
15-7
14-4
15-2
14-4
13-8
15-6
146-1
f^ S
10-8
11-5
12-3
11-7
11-2
12-3
11-6
81-4
11-4
10-5
21-9
12-2
11-3
11-4
11-2
10-8
56-9
10-5
9-8
11-2
11-4
10-8
12-1
12-3
12-1
11-5
12-0
113-7
^-^^
VI
6-5
6-2
7-2
6-2
6-3
6-7
6-5
45-6
6-7
5-9
12-6
6-8
6-1
6-7
6-3
5-9
31-8
5-8
5-7
6-5
5-9
5-9
6-7
7-3
6-6
6-4
6-6
63-4
03 C3
VII
13-4
14-0
13-0
13-5
13-7
13-3
13-8
94-7
14-7
12-7
27-4
12-8
13-5
13-8
13-4
12-4
65-9
13-4
13-3
13-2
12-9
13-0
13-4
13-7
14-2
12-8
14-0
133-9
'3 -§
O cS
bo <p
VIII
IX
10-9
11-5
11-4
12-5
12-0
10-6
11-9
12-9
10-6
23-5
11-3
11-7
12-2
10-7
10-2
56-1
11-2
11-4
11-3
11-4
11-4
10-1
11-5
13-2
11-2
11-9
5-0
4-7
5-5
4-7
4-3
5-2
5-9
8 35-3
5-2
4-4
9-6
5-0
4-7
5-0
5-2
4-7
24-6
4-5
4-2
4-9
4-5
4-4
4-9
5-6
5-3
5-4
5-3
114-6 49-0
3-8
3-9
3-7
4-2
3-9
3-6
3-4
26-5
4-0
3-7
7-7
3-8
3-9
3-8
3-8
3-3
18-6
3-8
3-7
3-7
3-5
3-5
3-5
3-6
3-9
3-4
4-2
36-8
43 r^
6D 5
XI
23-1
22-7
23-7
23-3
22-9
22-6
22-0
160-3
23-8
20-6
44-4
22-6
22-2
21-3
22-2
20-6
108-9
20-1
21-6
21-3
21-4
20-7
21-0
23-7
23-4
21-2
23-7
21fi-l
12-
65-
12-7
13-5
13-4
132-3
in the Maldive Islands and Minikoi.
13
4 sets arranged according to castes.
,3 o :«
3 s 2
3=2 o
Name
Occupation
or caste
Island
Age
Kemarks
Ixiii
56-8
Ibrahim '
Didi
Addu
30
Good. Stout in face. Rich
man. Marked depression
right of head.
, 51-4
Ibrahim
J,
))
35
Good. Back of head quite
flat. Base nose furrow
very marked.
58-2
Hassan
,,
J J
30
Good.
56-6
Mahomed
jj
35
Good. Nose very broad.
56-3
Ali
32
Deep bridge.
Good.
55-7
Hosein
,,
, J
27
Fair, thin.
54-9
Hassan
"
"
30
Good. Nose and forehead
level, no depression at base.
1389 -9
55-6
Ahmed
Manikofanu
37
Fair but thin.
54-1
Hosein
,,
,,
24
Good.
109-7
\ 55 -fi
Ali
Thackarufanu
24
Fair.
i 57-1
Moussa
^^
40
Fair. Low receding forehead.
! .56 -2
Ali
[[
J,
42
Fair, thin.
i 54-5
Ibrahim
,,
25
Good.
i 52-2
Hassan
,,
,,
24
Good.
'275-6
\ 54-2
Mohamed
>,
45
Fair.
1 52-7
Adam
,,
18
Thin.
; 55-5
Abdurahman
,,
40
Good. Angles of jaw very fat.
54-2
55-6
Ali
Hassan
All poor men.
Boatmen,
> fishermen
and agri-
culturalists
"
22
26
Fat in lower part of face.
Good.
54-6
56-5
Hassan
Hosein
''
48
30
Good.
Good. Very thick lips and
54-5
Hassan
35
face looks long.
Stout. Head like ridge in
centre ; jaws square.
53-7
Ibrahim
^,
50
Moderate.
57-6
Hosein
J
"
26
Good. Marked negroid fea-
tures.
\ 549-1
^
^
-Si
cq
14 D7- Duchoorth, On the Anthrojjometric data collected
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15
•Table II. Indices.
No. of individual
and locality
Cephalic
Altitudiua]
Facial
(Kollmann's)
Nasal
Gonio-
Zygomatic
Maldives
/ 1
73-3
64-9
46-21
74-51
87-12
2
76-4
67-4
50-00
60-04
81-75
3
71-6
61-8
48-80
75-56
88-80
Hulule Island.
4
76-9
69-7
50-82
74-00
81-97
Nn<! 1 tn 9
5
81-5
60-3
46-67
82-35
82-22
X'lVJO. -L UU ZJ
6
73-7
64-2
47-20
59-57
80-16
7
78-1
64-3
48-12
71-43
81-20
8
80-9
72-5
50-78
60-00
90-63
\ 9
79-1
69-2
45-67
68-75
80-31
IVTfllp TQlnnrl
(10
78-0
66-0
47-80
90-48
85-29
High caste.
Not? in to m
1]
77-3
73
48-13
84-00
94-24
12
82-0
70-1
44-83
93-75
89-66
xi L/o. i.yj \iKj xo
13
78-0
71-7
49-29
72-55
84-51
Male Island.
14
15
77-0
60-5
44-75
79-59
81-82
Intermediate caste.
78-8
68-2
43-20
72-92
85-60
Nos. 14 to Ifi
16
71-3
62-9
51-13
69-23
84-21
Afqlp Tcilflnrl
17
76-1
71-3
52-31
75-47
90-00
Low caste.
Nos. 17 to 20
18
76-3
72-0
53-33
63-46
80-83
19
20
78-5
77-9
61-8
64-2
58-59
54-33
64-91
75-51
85-94
81-89
Kaharidu
21
73-5
63-3
45-93
80-43
91-85
N. Mahlos
22
79-1
66-5
52-94
71-11
88-24
Mulaku
23
74-7
67-7
44-27
86-05
88-55
Nolewangfaro
24
71-5
68-9
46-46
81-40
92-91
,,
25
71-3
71-8
44-88
70-00
■ 80-29
26
71-5
61-8
48-51
76-00
81-34
27
74-6
73-5
44-28
82-98
82-14
Addu Atoll.
28
72-7
63-1
55-38
67-27
87-69
Nos. 26 to 49. j^
29
73-3
67-4
45-93
89-36
92-59
Didi. Nos. 26 to 32
30
75-3
65-7
45-98
90-70
87-59
31
74-4
69-3
50-38
69-23
79-70
32
82-0
67-0
47-10
57-63
86-23
Manikofanu.
33
85-3
78-9
45-58
76-92
87-76
Nos. 33, 34
34
70-8
64-6
46-46
84-09
83-46
'35
79-8
67-9
53-13
76-00
88-28
Thackarufanu.
36
76-0
66-2
45-19
82-98
86-67
Nos. 35 to 39
37
80-1
69-6
48-55
76-00
88-41
38
73-1
68-4
47-01
73-08
79-85
39
73-5
63-0
47-58
70-21
82-26
'40
73-8
64-6
43-28
84-44
83-58
41
74-5
68-6
42-86
88-10
85-71
42
73-3
68-2
49-24
75-51
85-61
43
75-3
76-3
45-74
77-78
88-37
"Poor" men.
44
80-5
67-7
45 -.38
79-55
87-69
Nos. 40 to 49 i
45
74-2
63-4
50-00
71-43
75-37
46
76-4
69-8
53-28
64-29
83-94
47
75-4
66-5 1
46-48
73-58
92-90
48
70-8
69-2
50-00
62-96
87-50
49
78-0
67-0
47-14
79-25
85-00
16 Dr Duckwoj^th, On the Anthropometric data collected
Table II (cont).
No. of individual
and locality
Cephalic
Altitudinal
Facial
(KoUmann's)
Nasal
Gonio-
Zygomatic
Minikoi
,50
83-1
60-1
57-63
103-57
88-14
/51
52
76-9
68-8
51-24
66-67
86-78
78-0
81-2
40-91
85-00
82-58
53
80-8
72-3
44-11
86-05
79-41
54
70-9
63-8
47-29
84-21
82-17
55
77-2
74-5
46-34
85-37
77-24
56
78-5
74-6
43-41
78-05
83-72
57
80-3
71-9
48-28
78-57
82-09
58
, 80-3
72-7
53-85
77-08
80-77
Minikoi.
J 59
A 60
83-1
77-5
48-46
70-00
68-46
Nos. 50 to 69
78-3
66-3
45-74
82-50
80-62
61
74-7
70-9
47-20
103-57
83-20
62
77-5
69-8
48-80
65-12
84-00
63
73-0
69-9
47-37
85-00
80-45
64
78-2
71-8
50-43
65-85
86-09
65
78-5
74-6
46-09
46-15
82-03
66
83-3
72-8
64-40
71-79
84-00
67
79-1
71-2
46-51
67-44
84-50
V68
74-9
65-1
52-67
65-96
70-99
^69
79-1
76-3
48-82
70-45
86-72
if the Hulule men be excepted, for they are the shortest of all.
But they are only nine in number.
(b) Head dimensions (Length, Breadth and Cranial Height) :
The Minikoi men provide the smallest heads, whether length,
breadth or cranial height be taken. The Addu men come again
into contrast, for they have the largest heads. The contrast is
most marked in respect of length and it will be noted that this is
in accord with the fact noted above, viz. that the men of Addu are
the tallest. The other groups are again intermediate.
(c) Cephalic Index : The Minikoi men are more frequently
(21-05 per cent.) and more intensely brachycephalic. The Addu
men are more frequently and more intensely dolichocephalic.
The remainder occupy an intermediate position in regard to this
index.
(d) Altitudinal Index : The Minikoi men have higher (and
therefore more spherical) heads : the Addu men are not markedly
distinct from the other Maldive groups in this respect. It is to be
noted that the shortness of the head in the Minikoi men, as well
as their lower stature, are influential factors in the production of
this result, as are also the opposite characters presented by the
other groups.
(e) Nasal dimensions (viz. length, width), and index. The
Minikoi men present a curious series of contrasts in this respect.
in the Maldive Islands and Minikoi.
17
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VOL. XyjI. FT. I.
18 Dr Duckworth, On the Anthropometric data collected
The nasal length (Minikoi) is distinctly smaller than in the Addu
group and other Maldivian islands, of which the various subgroups
are not distinguishable. The nasal width is distinctly least in the
Minikoi group, greatest in the Addu men and in the remainder it
is intermediate. With regard to the nasal index, the Minikoi men
are disposed in equal forces above and below the mean, while
the Maldivian group (which is not subdivisible) shews a distinct
tendency to excess on the side of the narrow noses. The seriation
of these nasal characters yields some rather interesting con-
clusions.
(/) Facial dimensions (upper facial length, facial width) and
facial index. The Minikoi men have the shortest and narrowest
faces : the Addu men have much longer but also broader faces.
Moreover the Addu men are shewn by the facial index to have
relatively broader faces than the Minikoi men. The other Mal-
divian groups are intermediate between the Addu men and the
Minikoi islanders.
5. The various conclusions set out in Section 4, may be still
further summarised as follows:
(a) The Minikoi men are distinctly contrasted with the
Addu men in eleven out of the twelve characters available for
study. The exception is the head-breadth, i.e. the absolute
dimension of that name. Of the Maldive islands, Addu atoll is
the most remote from Minikoi.
(b) The remaining groups are intermediate between the
Minikoi men and the Addu men in nine out of twelve characters.
(c) The Minikoi men are distinctly contrasted with the
" remainder " (i.e. Maldive groups excepting the Addu men) in
three out of the twelve characters.
(d) From such investigations it is fair to conclude that the
Minikoi islanders really offer distinct points of contrast with the
islanders of the Maldive group. In section 3 (supra) we have
seen that the Minikoi men are more variable than the Maldive
islanders. That they should be thus more variable is perhaps
intelligible in view of their geographical position as compared
with that of the Maldivians. This matter will be discussed a little
further in the sequel.
6. The standard deviation and coefficient of varia,bility have
been determined by me for a series of some ten characters or so,
and these are set forth in the accompanying table :
Only two remarks need be made in the present connection.
First, the greater variability of the Minikoi men is (on the balance)
confirmed. In the second place, the exclusion of the curiously
formed head of No. 10 (Minikoi) has singularly little effect on the
values of the means and other determinations.
7. The variability of these islanders has now to be compared
in the Maldive Islands and Minikoi.
Table IV.
19
Measurement
Group
No.
Mean
a
C
N
1. Cephalic
index
Maldives with Minikoi
Maldives with Minikoi
(less No. 10 Minikoi)*
Minikoi rnen only
Minikoi (less No. 10)*
Maldives without
Minikoi
69
68
20
19
49
77
77
79
78
76-2
3-47
3-42
3-164
3-024
3-53
4-5
4-44
4-05
3-87
4-64
•174
•172
•501
-481
-254
2. Nasal index
Maldives with Minikoi
Minikoi men only
Maldives only
69
20
49
77
77-5
76-2
10-15
12-25
8-66
13-20
15 -80
11-40
1-490
1^225
1-530
3. Altitudinal
index
Maldives with Minikoi
69
68
4-54
6-67
-298
4. Facial index
Maldives with Minikoi
69
48
4-10
8-54
-243
5. Stature
Maldives with Minikoi
Minikoi men only
Maldives only
69
20
49
1590
1580
1590
62-55
35-10
59-50
3-93
2-22
3-70
5-69
1-95
7-22
6. Cephalic
length
Maldives with Minikoi
Maldives with Minikoi
(less No. 10)*
Minikoi only
Maldives only
69
68
20
49
190
190
182
191-2
8-995
8-27
8-20
7-26
4-73
4-35
4-51
3-80
1-173
1-006
3 23
1-07
7. Cephalic
breadth
Maldives with Minikoi
Maldives with Minikoi
(less No. 10)*
Minikoi only
Maldives only
69
68
20
49
146
146
143
147-2
6-50
6-325
4-37
6-75
4-45
4-33
3-056
4-59
•612
-558
-955
•930
8. Cranial
height
Maldives with Minikoi
Maldives with Minikoi
(less No. 10)
69
68
130
130
7-68
7-70
5-90
5-092
•854
•872
9. Nasal length
Maldives with Minikoi
Minikoi only
Maldives only
69
20
49
47
40
49-8
5-77
4-79
4-02
12-54
11-97
8-07
•482
1^146
•33
10. Nasal width
Maldives with Minikoi
Minikoi only
Maldives only
69
20
49
36
31
38-04
4-45
4-16
2-99
12-36
13-53
7-85
•287
•8665
-18
11. Upper facial
length
Maldives with Minikoi
69
63
4-485
7-12
-291
12. Facial width
Maldives with Minikoi
69
131
6-306
4-81
•574
* There is a doubt about No. 10 Minikoi. The dimensions of the head are very
unusual and Professor Gardiner has a note to the effect that the head in question
looks as though deformed, possibly through some injury.
2 2
20 Dr Duckworth, On the Anthropometric data collected
Table V.
Group
Standard
deviation
Mean
value
Eeference
Cephalic index
Moslems (Egypt)
2-86
74-00
Myers *
Corsicans
2-90
75-50
Duckworth
Amarer
3-15
77-00
Duckworth
Minikoi
3-164
77-5
Duckworth
Sundanese
8-18
85-53
Garrett t
Maldives with Minikoi
3-42
77-00
Duckworth
Javanese
3-45
85-02
Garrett t
Copts
3-48
74-26
Myers *
Maldives only
3-53
76-00
Duckworth
Amarer with Jemeni
3-56
77-00
Duckworth
Sardinians (Lanusei)
3-57
73-00 (?)
(76-40)
Duckworth
Amarer, etc.
3-72
77-00
Duckworth
Sardinians
3-98
77-50
Duckworth
Bishari
4-10
79-00
ChantreJ
Cretans
4-10
79-00
Hawes §
Greek Youths
4-18
82-50
Duckworth
Jemeni
4-25
77-00
Duckworth
Moormen
4-305
79-00
(77-00)
81-48
Eisley ||
Banjerese
4-46
Garrett f
* Journal of the Royal Anthropological Institute, 1903-1905-6.
t Ibid. 1912.
J Chantre, Recherches anthropologiques en Egypte, 1904.
§ Hawes, Rep. British Assoc. 1908.
II Bisley, Journ. Roy. Asiat. Soc. Bengal, lxii. 1893. [The index is calculated
on Flower's method and should be reduced by 2 units.]
Standard
Coefficient
Mean
Group
deviation
of variation
Nasal index
Moslems of Egypt
7-67
10-12
75-83
Moormen (Ceylon)
7-75
9-57
80-7
Sundanese
7-76
8-93
86-92
Banjerese
7-81
8-88
88-01
Copts of Egypt
8-16
10-77
75-77
Bishari
8-51
11-20
76-0
Maldives (only)
8-66
11-40
76-2
Javanese
9-18
10-72
85-67
Maldives with Minikoi
10-15
13-20
77-0
Minikoi men only
12-25
15-80
77-5
Altitudinal
Banjerese
2-81
3-84
73-09
index
Sundanese
3-22
4-27
75-31
Javanese
3-46
4-59
75-47
Maldives with Minikoi
4-54
6-67
68-0
in the Maldive Islands and Minikoi.
Table V {cont.)
21
Group
Standard
deviation
Coefficient
of variation
Mean
Facial index
Sundanese
2-65
5-76
46-00
(Kollmann)
Banjerese
2-92
6-26
46-58
Copts of Egypt
3-18
6-55
48-57
Moslems of Egypt
3-53
7-29
48-39
Javanese
3-70
7-98
45-99
Maldives with Minikoi
4-10
8-54
48
Stature
Minikoi only
35-10
2-22
1580
Javanese
40-99
2-61
1571
Banjerese
48-61
3-10
1570
Sundanese
54-07
3-40
1591
Maldives only
59-50
3-70
1590
Bishari
59-90
3-63
1646
Maldives with Minikoi
62-55
3-93
1590
Cephalic length
Javanese
4-68
2-63
178
Sundanese
5-28
2-93
177
Moslems of Egypt
6-09
3-13
195
Copts of Egypt
6-13
3-17
193
Banjerese
6-22
3-44
181
Maldives (only)
7-26
3-80
191-2
Minikoi (only)
8-20
4-51
182
Maldives with Minikoi
8-27
4-35
190
Cephalic breadth
Moslems of Egypt
4-34
3-01
144
Minikoi (only)
4-37
3-056
143
Javanese
4-57
3-03
151
Copts of Egypt
5-09
3-56
148
Sundanese
5-24
3-47
151
Maldives with Minikoi
6-325
4-33
146
Maldives only
6-75
4-59
147
Banjerese
6-77
4-59
147
Cranial height
Copts of Egypt
4-15
2-83
146*
Moslems of Egypt
4-65
2-83
146*
Banjerese
4-76
3-59
132
Javanese
4-86
3-63
134
Sundanese
6-62
4-97
133
Maldives with Minikoi
7-70
5-092
130
Nasal height
Sundanese
2-39
5-30
45-1
(or length)
Banjerese
3-19
7-18
44-3
Copts of Egypt
3-41
7-14
47-8
Maldives (only)
4-02
8-07
49-8
Javanese
4-83
9-56
45-18
Minikoi (only)
4-79
11-97
40-0
Maldives with Minikoi
5-77
12-54
47-0
Naaal width
Copts of Egypt
2-72
7-57
35-96
Maldives (only)
2-99
7-85
38-04
Sundanese
3-05
7-65
39-80
Banjerese
3-50
8-76
40-00
Minikoi (only)
4-16
13-53
40 00
Maldives with Minikoi
4-45
12-86
36-00
Javanese
4-70
11-88
39-58
Auricular height not precisely comparable with other means in this section.
22 Dr Duckworth, On the Anthropometric data collected
with that of other groups. For this purpose, I have a number of
data mostly prepared by myself from the original measurements.
As the data for the cephalic index are most numerous, they will be
considered first. For this purpose I have collected them as shewn
in Table V, where the values of the standard deviation are
arranged in their sequence of increase.
The first conclusion to be drawn from Table V is that the
Maldive and Minikoi men agree generally in presenting a higher
degree of variability than the other groups brought into comparison
with them.
BuL the Minikoi men are not always thus associated with the
Maldive islanders. For in two important characters, viz. the
stature and the width of the head, the Minikoi men are dissociated
from those of the Maldive group. Moreover the Minikoi men are
in these two respects more homogeneous than their neighbours.
Thirdly, this homogeneity as regards stature and cephalic
breadth is in strong contrast with the great variability in respect
of the nasal index shewn by the men of Minikoi.
Evidently the conclusions already formed as to the mixed
character of these island populations find confirmation in Table V.
8. Before passing from the strict consideration of such
numerical data, it is convenient to notice the values of the
coefficient of correlation for certain pairs of dimensions. They
are shewn in Table VI.
Table VI.
Characters compared
No. of individuals
"r"
p.E. of " r"
Maldives and Minikoi together
1. Cephalic length and breadth
68
•484
± ^0564
2. Cephalic length : Cranial height
68
•244
±•074
3. Cephalic breadth : Cranial height
68
•227
±•075
4. Cephalic index and length
68
-•520
±•053
5. Cephalic index and breadth
68
•475
±•056
6. Nasal length and width
69
•528
±051
7. Cephalic index : Nasal index
68
•0104
±•068
Minikoi men only
8. Nasal length and width
20
•281
±•133
The data presented in Table VI do not differ markedly from
those based upon measurements of very different origin. I have
few records available for comparison, but the values set out in
Table VII are not without interest. Yet they do not seem to
enhance the value of "r" as a discriminating agency.
in the Maldive Islands and Minikoi.
Table VII.
23
Group
Characters compared
"r"
P E. of
" r"
Reference
Maldives with Minikoi
Modern English I
n
Cephalic length and breadth
)) )) ))
)! )) )>
•484
•402
•345
± -0564
±•019
±•019
Duckworth
Lee
Lee
Maldives with Minikoi
Sardinian crania
English ,,
Naqada ,,
Cephalic index and length
-•520
-•543
-•547
-•551
±•053
± -075
?
±•041
Duckworth
Duckworth
MacDonnell
Lee
9. Thus far an endeavour has been made to deal with all
Professor Gardiner's data or at least to subdivide them into two
groups only, viz. the Minikoi men and the Maldivians. This was
necessitated by the small number of individuals observed. For in
the wider comparisons it is absolutely imperative to deal with the
largest possible number in each area.
But Professor Gardiner has grouped two series of his measure-
ments, viz. the men of Male and of Addu Atoll, according to caste,
A review of Table III will shew that even with the small
numbers to which each subdivision finds itself reduced, the in-
fluence of caste is quite distinct. Moreover it acts in the same
direction both in Male and in Addu. For in each, the higher
caste has the higher stature, and larger head-dimensions. Indeed
the mean values of the circumference of the head may be regarded
as an epitome of the rest of the measurements. It should be
noted that fishermen are in the lowest caste and class.
The indices do not yield the same contrast, though this might
be expected in regard to the nasal index at least, which indicates
that the higher caste possesses paradoxically the broader nose.
Yet the small number of examples must be recalled again, and
this influence is doubtless much more effective in obscuring differ-
ences in indices than in the absolute dimensions.
10. The possible aSinities of these natives forms the next
subject of enquiry. The statistical data shew that they are not
very homogeneous, although certain distinguishing characters do
seem to occur within their own borders.
One feature of Professor Gardiner's lists impressed me at once.
Although distinguished by caste, the natives of the Maldives and
Minikoi have Moslem names. This very paradox serves, however,
to indicate two out of the many possible sources of the popula-
tion of these islands. In other words, Hindustan is suggested at
once, and again the Moslem influence, though it may have travelled
via that peninsula, need not have done so.
24 Dr Duckworth, On the Anthropometric data collected
11. Leaving these speculations on one side for a moment, it
is convenient to consider another possibility. In many islands of
the south-eastern parts of Asia, indications are met with of the
existence of pygmy types subjected to invasion by taller and
stronger immigrants. Ceylon and the Andaman islands will serve
as examples of the phenomenon in question.
Evidently it is a matter of interest to make this enquiry as
regards the Maldives. It can be undertaken without prejudice in
the case before us, for if Ceylon and the Andamans suggest a
succession such as has been mentioned, the history of the Maldives
and Minikoi goes far to discountenance the idea.
If we commence such a search, it is necessary to fix a limit of
stature, this character having a prime value in the definition of
pygmy types. An upper limit of 1480 mm.* will not be too great
if it be understood to refer to adult males. The mean values for
Andamanese and Aetas exceed this, and the same character
among the Vedda is very considerably greater (1570).
(a) Our preliminary search yields the following results :
Adult males of stature less than 1480 mm.
1. Maldives : Hulule (No. 9), 1478.
2. „ : Male (No. 18), 1474.
3. „ : Addu (No. 44), 1466.
4. Minikoi: (No. 2), 1476.
Mean value (4 individuals), 1473"5 mm.
Consequently there is at least a prima facie case to be made
out for the existence (in these islands) of a pygmy element. Of
these individuals, the only information available (in addition to
the other measurements) is to the effect that the three Maldive
men were fishermen and therefore presumably of low caste. Two
of the three are named Hassan, the name of the third is not
recorded. The Minikoi man was named Ismail, and Professor
Gardiner makes the following noteworthy comment, " mongoloid
eyes and rather high cheek-bones " ; this individual was fat, and
none of the other three is described as thin or emaciated.
ih) The four individuals thus associated stand apart in
marked contrast to the rest by reason of their small stature. The
next stage in the enquiry is directed to the positions occupied by
the same men in the other seriations. For a pygmy type might
be expected to provide other contrasts than that of stature.
A careful search through the whole range of seriations (upon which
the standard deviations discussed in Table IV are based) shews me
that the short-statured men are remarkable in no other respect f.
* 4 ft. 10 in.
t In other words the range of variation they yield is markedly overlapped by
that given by the remainder. This of itself need not however disprove their pygmy
in the Mai dive Islands and Minikoi. 25
For in no other character are they grouped together in contrast to
the other individuals. The nasal index is not far from providing
an exception to this statement. But so far as the nasal index is
thus concerned, its evidence is distinctly against the idea suggested
by the stature of the four men. For the nasal index is in distinct
contrast with that typical of a pygmy stock.
(c) In reference to pygmy types, a good deal of stress has
been laid by some authors on the great relative length of the
torso as compared with its (relative) value in the tall races. If
we wish to take as a basis of comparison the percentage proportion
of the torso to the stature in European races, we find that the
percentage is regarded as about 52-5. According to theory, pygmy
types, in some cases at least, should provide a larger number as
i^epresentative of this percentage.
If we turn to the short-statured individuals of the Maldives
and Minikoi we shall find this percentage represented in two cases
by higher values (than 52-5), viz. 53-6 (Hulule, No. 9) and 54-1
(Male, No. 18). But on the contrary the two remaining values
are 501 (Addu, No. 44) and 48-5 (Minikoi, No. 2) respectively.
Evidently this test is of no use in the present instance ; and
though I have mentioned it here, I am convinced that it is not
a reliable test in most if not in all instances. The examination of
the existing data from various tribes scattered over all parts of the
earth will soon bring this conviction home to the investigator.
But where data of all kinds are as scanty as in the present
instance, one must try every test that is not absolutely unreason-
able.
(d) Except in point of stature, then, the proportions of the
four small men are as variable as they could well be. In such
circumstances, the onus of proof is, in my opinion, transferred to
those who elect to regard these individuals as representatives of a
pygmy stock. This may be the case, but, if so, the stock is not
directly comparable with others generally admitted to be pygmy.
If a pygmy element does exist in the Maldives and Minikoi, the
data here available do not suffice for its detection, or for a demon-
stration of its distinctness.
The circumstances demand that this criticism should be search-
ing: indeed I conceive that the existence of "genuine pygmy"
types has been proclaimed in other instances upon a basis of
evidence which is insufficient to warrant such a conclusion. In
particular, I am not confident that the Vedda would survive as a
pygmy type under sound criticism.
nature, for I find that in about a score of characters taken at random, the Seman
(an undoubtedly pygmy stock) are overlapped by their neighbours, the South Perak
Malays.
26 Dr Duckworth, On the Anthropometric data collected
12. Three great sources of immigration into the Maldives and
Minikoi can be suggested at once. These are
(i) The peninsula of Hindustan with Ceylon ;
(ii) The coasts of Arabia and possibly of Africa ;
(iii) The western shores of the Malay Peninsula, and the
islands of the Malay Archipelago.
(i) The proximity of India and Ceylon lead naturally to the
expectation that they may be called to account for some contribu-
tion at least. But again, we have to consider the seafarers of the
region. For hundreds of years mariners from the West have made
their way past these islands and have penetrated as far as the
Pacific Ocean*. They may have come from the Arabian peninsula,
and their stock might be that known as " Himyaritic." Or they
may have been accompanied by the negroes of Africa, or again by
Semites or Negrito-Susians from the head of the Persian Gulf.
There remains a counter-current setting westwards from the
great Archipelago. For it must not be forgotten that whether as
a reflux or otherwise, certain " Malayan " peoples have travelled
extensively in this direction. Prichard in particular (Nat. Hist, of
Mankind, 1844, Vol. iv. p. 190) speaks of Malay colonies on the
coast of Ceylon.
It is therefore necessary to enter upon a brief consideration of
each of the three possible sources in turn.
The task of comparing the natives of the Maldives and Minikoi
with the various races of Southern India and Ceylon would enlarge
this report to such an extent as to render it unwieldy. Only a few
selected examples will be dealt with in this place.
Taking first Ceylon, the Vedda may be eliminated at once.
The comparative rarity of a nasal index exceeding 82 in the
islands may be taken as justification for this exclusion, and it will
also rule out the Rhodias, Tamils and Singhalese. The two latter
stocks are further distinguished by stature superior to that of the
average man of the Maldives or Minikoi.
But there remains in Ceylon the very curious type known as
that of the "Moormeo" or "mariners." They present something
of an enigma. I took some pains therefore to enquire into their
physical characters. For these we are indebted to the late
Sir H. H. Risley, who has recorded anthropometric data relating
to 22 Moormen (cf. Journ. Roy. Asiat. Soc. Bengal, LXii. 1893,
p. 33). Table VIII provides the comparison between these men
and the Maldive islanders.
The concordance is admittedly small. Yet it is perhaps not
* The Maldivians themselves are said by Eeclus {Geog. Univ.) to trade in native
boats as far as Sumatra. Reelus also refers distinctly to Arabic influences among
them.
in the Maldive Islands and Minikoi.
27
altogether sufficient to justify the abandonment of the enquiry in
this direction. In view, however, of the small numbers of the
groups compared, the quest can hardly be pursued further here
with any prospect of success. The contrasts might be attributed
to the difference in circumstances. For the Maldive folk are pre-
sumably less favourably situated than the inhabitants of Ceylon.
We know little of the way in which Risley obtained his records,
and of the social status of his subjects. But the Moormen are
characteristically Moslem, a feature already remarked as distinctive
of the Maldive islanders, if their names can be held to provide
evidence on this point. And again the relation of the Moormen
to the Malay colonies mentioned by Prichard (v. supra^ p. 26),
remains to be investigated.
Table VIII.
Character
22 Moormen
(Risley)
49 Maldive men
(Gardiner)
Stature
Height sitting
Eatio : sitting height to stature = 100
Head length
Head breadth
1625
815-8
50-2
182 (186)*
144
130-2
47-7
38-5
79-1 (77-1)*
80-7
1590
795-7
50-04
191-2
147-2
130-0
49-8
38-04
76-2
76-2
Head height
Nasal height
Nasal width
Cephalic index
Nasal index
* Flower's method. About 4 mm. to be added to the cephalic length and 2 units
subtracted from the cephalic index, for comparison with groups in which the
maximum cephalic length is recorded.
The Tamils of Ceylon are even taller than the Moormen, their
heads are narrower and their noses are broader. The comparison
with the Maldive islanders fails more definitely and conspicuously
here, though it may be remarked that the Moorman probably
represents a blend into which a distinct Tamil element enters.
When the Indian peninsula is considered, a vastly greater
range of possibilities presents itself.
In the first place, our interest must be directed inevitably to
the comparison with such " aboriginal " hill-tribes of the Nilgiris
as the Irulas and Kurumbas. But in my opinion the comparison
fails conspicuously. And the failure is determined chiefly by
the difference in the nasal index, for in this respect the contrast
is very marked between the wide nose of the hill-tribe types and
the relatively narrow noses of the islanders.
28 Dr Duchvorth, On the Anthropometric data collected
Per contra, I may be allowed to make one comment in passing.
The " Mongoloid " appearance of one of the Maldive men of pygmy
stature should be recalled here in view of the fact that the
aboriginal Kurumba of the Nilgiris is alleged by some to be of
Mongolian aspect. The threads of evidence are, however, so frail
that I do not venture to insist on the comparison.
Of the great host of t}pes which still remains for discussion, I
must be content to select three only for consideration. For the
comparative data I am indebted to the admirable paper by the
late Professor E. Schmidt*, and even more to the invaluable work
by Mr Thurston (entitled Castes and Tribes of Southern India).
Of the three groups mentioned above, I have selected one, the
Linga Banajiga, on account of the similarity in head-form and pro-
portions which obtains between them and the Minikoi men.
The Mukkavan, another tribe of Southern India, must certainly
be considered, for they are the fisher-folk of the Malabar coast,
and they are also distinguished by their tendency to adopt the
Moslem religion.
The Billava are not a littoral people, so far as I can learn, but
they shew in their head-form so marked a tendency to brachy-
cephaly and thus so strong a contrast with most of their neighbours
that it seems well to include them in this comparison. The avail-
able data will be found arranged in Table IX.
Table IX.
Maldives
Linga
Group
Minikoi
with
Minikoi
Addu
Banajiga*,
Sandur
Mukkavan *
Billava*
No. of subjects
20
69
24
25
40
50
Stature
1577
1588
1604
1656
1631
1682
Head-length
182
190
196
182
190
182
Head- breadth ...
143
146
148
142
142
146
Cephalic index...
78-5
76-8
75-5
78-3
75-1
80-1
Nasal index
77-5
77-0
75-5
74-6
81-0
72-6
* Thurston, op. cit.
The result of the comparison is curiously perplexing, but the
one outstanding feature is the inferior stature of the islanders.
Apart from this the general conclusion to be drawn is that the
mainland tribes may be considered as grouped around the men of
the islands, and indeed a further draft on Mr Thurston's data
might be made easily to confirm this view. On the whole, too,
this comparison is more apt than that already instituted (cf.
Table VIII) with the Moormen.
* Schmidt, Archiv fur Anthropologie, 1911.
in the Maldive Islands and Minikoi. 29
It should be noted here, however, that, according to tradition,
both the Mukkavan and Billava natives originally came from
Ceylon. At the present time they are not widely separated, though,
as has been pointed out, the Mukkavan are a seafaring folk, whereas
the Billava are found inland.
(ii) When we turn to the second possible source of immi-
grants, viz. the western region including Somaliland and Arabia as
far as the Persian Gulf, the ground is manifestly more uncertain.
I will therefore content myself with the reminder that the possi-
bility exists, and that a comparison of the Maldivians (especially
the men of Addu) with the men of Yemen is not preposterously
absurd. Yet the shorter stature and the greater tendency to
brachycephalic heads shewn by the islanders renders the com-
parison unsatisfactory.
(iii) The third area to be considered may be described as the
Malayan one. And it is important to note once more in this
connexion that the chief difficulty hitherto encountered has de-
pended largely on the low stature and rotundity of head met with
in the islands. To match these, the South Perak Malays may be
adduced at once. The Moslem names and the sporadic occurrence
of " Mongolian " features are also in accord with this view. There
remains the contrast in respect of the nasal index, which points to
a broad nose among the Malays who are thus in contrast with the
Maldivians.
But the Malay type is extraordinarily variable, so that the
comparison need not be abandoned should one test (even though
so important as that of the nasal index) seem to fail to provide
confirmatory evidence.
Indeed there is a good deal of evidence to be brought forward
on this subject, and the following notes may serve to indicate the
general trend of my surmises in this connexion. It is in fact
known that in the Malay Archipelago the larger islands often
possess an outlying fringe of islets inhabited by native populations
differing from their neighbours. A contrast in stature at least is
noticeable. Dr Hose mentioned this to me in conversation, and
Mr Garrett, my former pupil, has just published some notes on the
Orang Balik Papan, who may serve as examples of the stunted
maritime populations in question.
Further west, they are replaced by the Orang-Laut, and these
again in turn by the Selungs of the Mergui Archipelago, and
possibly some (though certainly not all) of the Nicobarese. In all
instances the low stature*, brachycephalic head, and absence of
high degrees of platyrrhiny provide just the combination of
physical characters sought for. In conclusion, mention must be
* The Selungs described by Dr Anderson in 1890 are however taller than the
other tribes mentioned in this connexion.
30 Dr Duckworth, On the Anthropometric data., etc.
made of the Biajus or sea-gypsies of Borneo, if only on account of
a custom alleged by Prichard {Researches, etc. Vol. v. 1847, p. 87)
to be common to them and the Maldive islanders. The custom
consists in the preparation and launching of a small boat as an
offering to one of their deities. And even though the custom
be now recognised (Skeat) as of wide dispersion in Malaysia, its
practice in the Maldives would be most significant.
It remains to add that the discovery of Malayan affinities and
relations may not end with the Maldive islands and their popula-
tions. For in my opinion the question may be fairly raised as to
whether Malay invaders ever secured a hold in the Malabar district.
We read of Malay colonies in Ceylon. We find hints of Malayan
influence in the Maldives. The islanders of that group are not
without resemblance to the Mukkavan, and possibly to the Billava
and Linga tribes just studied. Is there any Malayan blood in the
latter ? I can only ask the question. The answer will depend on
the study of language and customs. In regard to the latter, it is
at least remarkable that the Mukkavan should make offerings to
the sea, though a closed vessel and not a model boat is employed
as the vehicle.
Summary.
To sum up this protracted discussion, I would conclude by
recalling the great variability in physical type shewn to exist in
the Maldives and Minikoi. A diversity of racial stocks is thus
shewn to be probable. The seriations provide two-peaked curves
in several instances, but the significance of these is not beyond
question, although they may be really evidence in the same direction.
Such approaches to pygmy proportions, as can be detected, are
not to be dissociated from the effects of local conditions upon
nutrition, etc.
Of the possibilities in the way of invasions, I have indicated
three main sources. On the whole, the resemblance to the mari-
time natives of Malabar is close enough to satisfy most require-
ments. But I feel assured that the Malabar coast is not the only
source of immigrants, and in Minikoi especially I think that
account must be taken of what I term generally Malayan in-
fluences. And these may have affected the Malabar natives also
and even before they sent immigrants into the Maldives. It is
with regi-et that I am compelled to make a statement which is so
deficient in directness. But I do not care to lay more weight on
any evidence than it can reasonably sustain, and this thought has
influenced the present report. In any case the fact that Professor
Gardiner has been a pioneer of anthropometric research in this
little-known area is a matter upon which he is to be congratulated
warmly.
Mr Berry, Notes on the volatilization, etc. 31
Notes on the volatilization of certain binary alloys in high
vacua. By A, J. Berry, B.A., of Trinity and Downing Colleges.
[Eead 11 November 1912.]
In a previous paper (A, J. Berry, Roy. Soc. Proc, 1911, 86 a,
67) it was shown that the compound MgZn,, conld be prepared by
distillation of an alloy containing excess of zinc in an apparatus
exhausted by cold charcoal. It was also shown that the com-
pound MgZng can itself be vaporized unchanged in a high vacuum.
These observations have been repeated and confirmed and experi-
ments have been performed on other pairs of metals in the hope
of isolating intermetallic compounds.
The phenomena of the vaporization of alloys when heated in
vacuo has occupied the attention of other investigators. Thus
Tiede and Fischer {Ber. Deutsch. Chem. Ges. 1911, 44, 1712) have
effected a quantitative separation of lead and tin from an alloy of
these two metals. Groves and Turner (Trans. Chem. Soc. 1912,
101, 585) have examined the behaviour of a number of alloys and
have classified them into five groups as follows :
Group I. The metals are non-volatile and the alloy is un-
altered in weight.
Group II. The volatile metal or metals are removed and a
quantitative separation results.
Group III. Any excess of volatile metal is removed and a
chemical compound remains.
Group IV. Any excess of volatile metal is removed, but the
residue is not a compound.
Group V. The metals composing the alloy volatilize together,
their relative proportions being in part dependent on the tem-
perature.
Experimental.
The experimental method already described (loc. cit.) has been
employed with but slight modifications. The distillations were
conducted in an electric furnace, and the charcoal was kept
immersed in liquid air during the initial stages of the distillation
with the object of removing gas occluded within the body of the
metal.
Copper and cadmium. An alloy containing excess of cadmium
was heated at a temperature of about 600° for several hours. On
analysis it was found that the two metals had been separated
quantitatively, A confirmatory experiment yielded identical
results.
32 Mr Berry, Notes on the volatilization of
Cadmium and magnesium. On heating an alloy containing
excess of cadmium in vacuo both metals volatilized together, but no
definite relation between the composition of the distillate and the
residue was established. From the form of the equilibrium
diagram which was worked out by Grube (Zeitsch. anorg. Chew,.
1906, 49, 72) it is probable that the compound CdMg which forms
solid solutions with both constituents would dissociate on melting.
It is clear that this pair of metals belongs to Group V in Turner's
classification.
Magnesium and lead. Since these two metals are both
moderately volatile in high vacua at temperatures of the order
of 600° according to the researches of Krafft and his collaborators,
it was thought that the compound MgaPb might under suitable
conditions be volatilized unchanged as had already been observed
in the case of the compound MgZng. The existence of the com-
pound MgaPb has been proved by the work of Grube {Zeitsch.
anorg. Gheni. 1905, 44, 117) and confirmed by Kurnakoff and
Stepanoff {ibid. 1905, 46, 177). This compound does not form
mixed crystals with either of its constituents. In the experiments
of the present author, alloys containing the two metals in
approximately equivalent proportions were distilled in vacuo at a
temperature of about 680°. It was found that the distillate
consisted chiefly of magnesium with mere traces of lead. In no
case was it possible to isolate a homogeneous portion of the
distillate for quantitative analysis. Under the microscope, steel
blue crystals embedded in a matrix of magnesium or magnesium
silicide from the glass were plainly visible, and these portions of
the distillate underwent rapid corrosion on exposure to the air
with formation of a black powder — a property of the compound
MgaPb noted by Grube {loc. cit). It is noteworthy that the
coolest portions of the tube where the distillate condensed were
practically free from lead. According to Krafft and Bergfeld
{Ber. Deutsch. Chem. Ges. 1905, 38, 254) lead commences to
volatilize at 335° in a cathode ray vacuum, while Knocke {ibid.
1909, 42, 206) has shown that magnesium under similar con-
ditions commences to volatilize at 415°. One might, therefore,
expect that at a temperature of 680° both metals would readily
vaporize and condense in the cooler parts of the apparatus. It
must be borne in mind that magnesium vapour would diffuse
nearly three times as rapidly as lead vapour, and further, although
the volatilization point of lead is apparently lower than that of
magnesium it does not follow that the same order would obtain
with regard to the vapour pressures of these two metals at higher
temperatures. In a special experiment in which 77 grams of
assay lead were heated for about five hours at 680° in a vacuum
produced by cold charcoal, it was found that only a very small
certain hinary alloys in high vacua. 33
quantity of lead in the form of a thin mirror was condensed. Such
an experiment might indicate that magnesium is the more
volatile at that temperature, but it would be premature to con-
clude that this is the case in the absence of knowledge of the
relative viscosities of the two vapours.
While the experiments recorded in the present communication
have not been successful in effecting the isolation of intermetaliic
compounds of the metals under consideration, a comparison of the
result obtained in the case of the magnesium-zinc series with that
obtained with the magnesium-lead series is not without interest.
The maximum on the freezing point curve of the magnesium-zinc
series corresponding to the compound is remarkably sharp, while
the maximum on the freezing point curve of the magnesium-lead
system is rounded. It is clear that the less sharp the summit of
the curve, the more the compound will tend to dissociate into
its constituents on heating above its melting point. It is, there-
fore, not surprising that all the author's attempts to distil the
compound MggPb resulted in showing that, in the state of vapour,
this compound is largely dissociated.
VOL. XVII. PT. I.
34 Mr Mines, On Pulsus alternaus.
On Pulsus alternans. By George Kalph Mines, M.A., Fellow
of Sidney Sussex College, and Additional Demonstrator of Physio-
logy in the University of Cambridge. (From the Physiological
Laboratory, Cambridge.)
[Read 28 October 1912.]
[Plate I.]
Introduction.
The condition of pulsus alternans, described clinically in the
first place by Traube in 1872, has long been recognised as due to
alternation in the strength of the ventricular contractions. Alterna-
tion in strength of ventricular contractions of the isolated frog's
heart was observed, described and explained by Gaskell in 1882.
After this, for nearly twenty years, the subject received
but little attention. Within the last ten years a number of
papers have appeared, dealing both with the clinical and experi-
mental aspects of the matter. Hering (1902) and Volhard (1905)
in particular have insisted on the distinction to be drawn between
true pulsus alternans, in which the ventricular contractions are
evenly spaced, and pidsus pseudo-alternayis or bigeminus pseudo-
alternans, in which the intervals between the beats, as well as the
strengths of the beats, show alternation.
In the latter condition, the variation in size of the ventricular
contractions depends immediately upon their being provoked when
the ventricular muscle is in different stages of recovery from its
last excitation and does not of necessity connote any abnormality
in the properties of the ventricular muscle.
In the present paper I am concerned only with the condition
of true pidsus alternans, that is to say, the condition in which the
ventricular beats follow regularly-occurring auricular beats at
perfectly rhythmic intervals*, but in which the musculature
behaves differently in successive responses, though in the same
way in alternate responses f.
The most important additions to our knowledge of this condi-
tion which have been made in recent years have resulted from the
* Under these circumstances, the pulse wave corresponding to the weak
contractions arrives at the wrist a little late, so that the sphygmographic tracing
shows unequal intervals between 1 and 2, and 2 and 3. Volhard shows that this is
due to haemodynamic factors.
t For convenience of discussion I shall refer from time to time to a series of
beats, 1, 2, 3, 4, etc., referring to the beats 1, 3, 5, etc. as the " odd series" and to
the beats 2, 4, 6, etc. as the "even series."
M?' Mines, On Pulsus alternans. 35
method — fruitful in so many directions — of taking simultaneous
records of the activity of the heart by two or more instruments.
In this way it has been found both clinically and in experiments
on animals, that although in many instances the alternation is
shown alike in pulse record, cardiogram and electrocardiogram,
this is by no means invariably the case. Thus it may be well
marked in the apex beat but absent from the radial pulse (Hering,
1908) ; it may be present in the electro-cardiogram but in opposite
phase to the apex beat or to the radial pulse, so that the large
excursions in the one record correspond to the small excursions in
the other. There may be similar " incongruence " between apex
beat and pulse wave and also between two cardiograms taken from
different points on the same chest wall (Hering).
The appearance of an extra-systole, whether spontaneous or
artificially provoked, may profoundly affect the course of an
alternating series of beats, while progressive changes in such a
series without intentional or perceptible change in the external
conditions is frequently noted. The interest of all clinicians has
been attracted by Mackenzie's statement that the appearance of
pulsus alternans in a patient usually means death within two
years. Such are the facts which have led Lewis (1911) in a
recent review of the subject to characterise pulsus alternans as
" one of the most mysterious and most important mechanisms of
the heart with which clinicians have to deal."
The interyretation of pulsus alternans.
I have already stated that Gaskell in 1882 gave an explanation
of pulsus altei'nans. Largely owing to the overwhelming interest
of his later work on the tortoise heart, the full significance of
Gaskell's explanation has been overlooked and another view,
superficially resembling it and really forming one special case
of it, has been widely adopted. The recent discoveries about
pulsus alternans have shown this view to be inadequate.
I shall first quote Gaskell's explanation and examine the
grounds on which its single assumption is founded ; I shall then
discuss the more recent hypothesis which makes the same funda-
mental assumption, but neglects its logical consequence, and finally
I shall show how Gaskell's original suggestion lends itself to the
interpretation of the various phenomena which at first appear so
perplexing.
Gaskell's experiments on the frog's heart showed conclusively
the following facts about alternation :
(1) that it depended on a local alteration in the condition of
the ventricle;
3—2
36 Mr Mines, On Pulsus alternans.
(2) that it could be abolished temporarily by stimulation of the
vago-sympathetic trunk ;
(3) that during the course of alternation there was a relation
between the beats such that if the even series got smaller, the odd
series got larger, and vice versa.
After describing and illustrating the last point Gaskell con-
tinued as follows :
" Now we know from the experiments of Bowditch that the
force of the ventricular contractions is independent of the strength
of the stimulus. The explanation, therefore, of this alternation in
the force of the contractions must be sought for in the muscular
tissue itself, and it seems to me that the most probable explanation
is that a larger amount of tissue contracts when the beats are
large than when they are small, and that, therefore, in all prob-
ability, certain portions of the ventricle respond only to every
second impulse, while other portions respond to every impulse.
The observations of Aubert show that by the direct action of
a blow a circumscribed area of the ventricular muscle can be
made to remain quiescent, while the rest of the ventricle is
contracting rhythmically.
"I am inclined, therefore, to suggest that, owing to some
cause in the manipulation, such as cutting open the ventricle,
or some other cause which affects the ventricle unequally, the
excitability of the ventricular muscle is at the time not absolutely
the same throughout, so that, although the impulses remain the
same in strength, yet certain parts which possess a lower excitability
are able to respond only to every second impulse, while the rest of
the tissue responds to every impulse. In this way, if the strength
of the contractions depends upon the amount of tissue contracting,
we see not only that every second beat must be larger, but also
that the size of each strong contraction must vary inversely as the
size of each corresponding weaker contraction."
The quantitative expression for the excitability of an irritable
tissue towards a particular variety of stimulus is the inverse of the
strength of stimulus needed to excite it. If a piece of ventricular
muscle is acted upon by stimuli, whether these be electric or
whether they be auricular excitations, the muscle will respond
to every stimulus, provided that a certain relation exists between
the strength of each stimulus and the degree of excitability of the
muscle when it arrives. But since the excitability of the muscle
is greatly depressed after the beginning of each excitation, and
increases after a time gradually, at first rapidly and then more
slowly, it is evident that if the stimuli arrive too frequently only
every alternate stimulus will find the heart muscle in a condition
in which it can be excited (Hofmann, 1901). In a similar way, if
stimuli of a certain strength arrive at a frequency such that each
Mr Mines, On Pulsus alternans. 37
stimulus causes a ventricular contraction, it is evident that by
lowering the excitability of the muscle, the whole cycle of changes
in excitability of the muscle may be carried out at a lower level
than before, so that, even without supposing that the process of
recovery of excitability goes on slower in the depressed than in the
normal tissue, it is clear that it will have to go on longer before
the excitability reaches the value at which the stimulus becomes
liniinal. And if the time taken to reach this value is greater than
the interval between two stimuli, it is evident that every second
stimulus must fail to excite. The range of muscular excitability
over which this state of affairs will hold for a given strength of
stimulus is considerable. In such cases the " half-rhythm " is
due to the refractory phase of the muscle. In other instances it
may be attributed to a property possessed by all excitable tissues —
the power of summation of stimuli. If the excitability of the
muscle is below a certain grade, a stimulus which is subliminal
may yet so raise the excitability of the muscle as to render the
same stimulus on repetition liminal. It appears certain from the
experiments of von Basch (1880) and others that this is the
explanation of many cases of " half rhythm." For our present
discussion it matters little which of these explanations holds in
any particular case, though it is important to note that the exist-
ence of these two well defined mechanisms, either of which may be
responsible for " half-rhythm " and both of which are known to
produce it, increases the chances of the occurrence of this type
of relation between heart muscle and a rhythmic succession of
stimuli in any particular instance and extends the range of modi-
fication of the excitability over which "half-rhythm" may occur.
That a condition of depressed excitability affecting part of the
ventricular muscle is indeed responsible for alternation, is strongly
supported by the fact that alternation is removed by just those
methods which improve the excitability of the heart muscle. Thus,
for example, bathing with Ringer's solution* or stimulation of
the vago-sym pathetic, as Gaskell showed, produces just the effects
demanded by the hypothesis.
Fig. 1 shows an instance in which alternation, here much
more marked in the electrogram than in the mechanical record,
was abolished after stimulation of the sinus venosus.
A peculiar and instructive case is that shown in fig. 2.
Examination of the two upper lines of the tracing near the
beginning, the records of the auricular and ventricular contrac-
tions respectively, would suggest that it is a case of partial
auriculo-ventricular block. But the electrogram of the ventricle
* Cf. Mines, Proc. Camh. Phil. Soc. Vol. xvi. (1912), Plate 6.
38 Mr Mines, On Pulsus alternans.
(the third line of the tracing) shows that every auricular excitation
reaches the ventricle, but apparently the alternate excitations
spread only a very short way into the muscle, affecting so few
fibres that their mechanical response is too slight to move the
lever.
After stimulation of the sinus venosus, the electrical response
of the alternate ventricular excitations which before were very small,
greatly increases in size — indicating probably that the excitation
process spreads further into the muscle, while the mechanical
response makes its appearance. We have thus the appearance
of a mechanical alternation as a result of stimulating the sinus
venosus. This condition continues some time after the stimulation
has ceased and then gradually disappears, the electric response
returning finally to the condition which obtained at the beginning
of the tracing. It is obvious that this was an extreme case of
alternation, in which nearly the whole of the ventricular muscle
failed to respond to the same alternate series of excitations. The
stimulation of the intracardiac nerves reduced the grade of the
alternation, making the alternate beats for a time more nearly
alike in extent.
The view propounded by Hering {loc. cit.), by Muskens (1907)
and by several other authors is that in the condition of alternation
the whole musculature of the ventricle contracts in one beat, while
a portion of the musculature fails to contract in the next beat, and
so forth.
This view employs Gaskell's assumption,
(1) that part of the ventricular muscle has its excitability so
depressed that it can respond only to every other auricular
excitation, but it adds the further assumption, which, as I shall
show, is not only unnecessary, but vicious, namely,
(2) that the musculature, of which the excitability is depressed,
responds all of it to the same excitations ; i.e. all of it to the first,
third and fifth excitations or all of it to the second, fourth and
sixth excitations, and so forth.
The effect on the contraction of the heart as a whole, of
depression of excitability of a portion of the musculature such
as to cause half-rhythm in this portion, will depend on the region
in which this musculature is situated. If it is placed on the sole
route by which excitations reach a large tract of musculature —
as for example in the junctional tissue between auricles and
ventricles — the effect will be to impress the half-rhythm on this
tract of musculature, the excitability of which is in reality
normal.
The differences known to exist in the mammalian heart between
the musculature of the bundle of Stanley Kent, and that of the
Mr Mines, On Pulsus alternans. 39
auricles and ventricles, make it easy to imagine that this tissue
may be affected differently from the rest of the musculature of
the heart by a change of external conditions to which the whole
musculature is exposed. But the ventricular muscle does not, so
far as we know, present any regular differences in its various parts;
though it is always to be expected that in any collection of excit-
able cells some will be above and some below the .average of
excitability. If the average excitability of the ventricular muscle
is gradually depressed, some portions of it, those namely below the
average excitability, will reach the condition in which they assume
half-rhythm before the main part of the musculature has reached
this condition. If these fibres are directly connected with each
other the chances are in favour of their contracting in response to
the same series of excitations, odd or even. For under these
circumstances, if we consider the case of two fibres A and B,
A may respond to excitation, reaching it by way of B or by
perhaps one or two other routes. If in the even series of excita-
tions of the ventricle in general, B fails to be excited, it is plain
that A has a greater chance of receiving a successful stimulus
during the odd series, when excitation arrives by way of B as well
as by other routes. And, of course, where a number of contiguous
fibres are concerned these may surround other fibres which are
never reached by excitations except those coming by way of the
affected fibres. In such cases it will be true to speak of heart
block in the ventricular walls ; fibres isolated in this way will of
necessity follow the rhythm of their neighbours, whether their own
excitability is depressed or not.
But there is no justification for the assumption that when the
excitability of the ventricular muscle is gradually depressed, the
fibres which are below the average excitability of the muscle at
the time and in which half-rhythm develops will all be situated
at a single focus. Much more likely is it that they will be
distributed in various regions. And whether there are two foci
or twenty, each one will respond either to the odd or to the even
series of excitations. The chances are obviously against all of the
foci responding to the odd or all to the even series. And if there
are more than two foci, the chances are against their being equally
divided between the two series — though both of these conditions
are possible and may be expected to arrive occasionally.
To put the position tersely we may use symbols. Let V be the
whole ventricular muscle and v the portion of it which is depressed
in excitability so as to be capable only of the half-rhythm.
Then on the view of Muskens and Hering the series of beats
runs thus,
V, V-v, V, V-v, &c (1),
40 Mr Mines, On Pulsus alternans.
while in order to give adequate expression to the possibilities of
Gaskell's hypothesis we must subdivide v, thus v = v' + v". Then
the series of beats will run
V-v', V-v", V-v', V-v", &c (2).
Series (1) then expresses only the special case of (2) in which
v'ovv" = Q.
Clearly, whenever v is greater or less than v" , as will happen
in most cases, there will be alternation in the extent to which the
ventricle contracts and so alternation in the pulse wave, if the
circulation is intact.
But while the relative force of contraction of the ventricle
in the beats V—v and V—v" as registered by the suspension
method or by the pulse wave, will depend chiefly on the relative
amounts of tissue in v' and v", the apex beat (which is due largely
to a twisting of the ventricles) and the electrocardiogram (which
is affected by the path of the excitation wave in the musculature)
will depend in even greater measure on the positions of the
portions of muscle v and v". Therefore, when v is greater than
v" , the pulse wave corresponding to V—v" will be greater than
that corresponding to V—v', while the apex beat corresponding to
V—v" may be either greater or less than that corresponding to
V—v. This may be made clearer by taking an extreme case.
Supposing that v represents a fairly large area of muscle in the
posterior wall of the ventricles while v" represents a much smaller
area in the anterior walls. The radial pulse wave produced by
V—v" will be greater than that due to V—v', but the apex beat
may easily be greater for V—v than for V—v". Thus the larger
apex beats will fall in the odd series, the larger pulse waves in
the even series.
Similarly with respect to the electrocardiogram. The failure of
excitation in a small region near the apex is likely to produce greater
modification of the detectable electric variation of the whole heart,
than is the failure of a larger amount of muscle nearer the base.
In those cases where v = v", the pulse waves or the suspension
record may show no alternation, while the apex beats or the electric
variations, or both, give clear evidence of alternation.
Such cases are of peculiar interest ; although absolute equality
of v and v" will be extremely rare, an approximation to this con-
dition is encountered fairly often, so that while the beats of the
ventricle are apparently only very slightly if at all different in
size, the electrogram exhibits marked alternation. It was through
finding several cases of this kind in the frog's heart that my interest
in the subject was aroused*.
* I have already published examples in this Journal. See Vol. xvi. Plate vii.
Figs; 8, 9, 10.
Mr Mines, On Pulsus alternans. 41
It is possible to interpret such curves as these on the assump-
tion that the path followed by the excitation wave in the ventricle
was different in the odd and in the even series of excitations. The
mechanical record, unlike the electrical, takes no count of the order
in which the various regions of the ventricle become excited.
It is interesting to note that this condition, for which I have
proposed the name pulsus alternans celatus, is frequently followed
by marked mechanical alternation. An instance of this has been
shown*. Comparison of curves (b) and (c)* illustrates once more
the fact discovered by Gaskell, that when the odd series gets
smaller the even series gets larger. Evidently this means that
a portion of the tissue which was contracting with the odd series
goes over to the even series or vice versa. To do so, it has only to
miss one beat or to take up one extra excitation.
Windle (1910) in fig. 7 of his paper gives a curve which illus-
trates the same point.
From what has been said, it is clear that an extra-systole of
the musculature as a whole, whether provoked by an idio-
ventricular excitation or by an artificial stimulus, will be expected
to influence very materially the distribution of the tissue v and v"
between the odd and the even series. Exactly what effect the
extra-systole will produce will depend on the moment of its
arrival. Theoretically it may be expected sometimes to reduce
and sometimes to increase the extent of the alternation, depending
on the phase in which it arrives. But it will generally produce
one or the other effect, for it is only for a short period in each
complete cycle of two beats that v' and v" are both refractory.
Supposing at a certain instant v' is refractory and v" is not. At
the beat about to arrive v" would respond. But if at this instant
an extra-systole occurs, v" will give a premature response and will
then miss either one or two natural excitations, depending on the
exact time relations of the extra-systole and the natural excitations.
If it missesone only it will be transferred from one series to the other.
These conclusions are precisely in accord with Windle's observa-
tions : that extra-systoles have a profound effect on the course of
pulsus alternans, but sometimes in the direction of increasing and
sometimes reducing the alternation.
Postscript. Since the above was written my attention has
been drawn to another paper by Hering (Zeitschr. f. exper. Pathol,
u. Therap. 1909, vii. p. 363). On p. 372, Hering put forward a
view which is practically identical with that advocated in the
present paper. He did not, however, recognise that this view
was implicit in Gaskell's original statement.
]}[ov. 13, 1912.
* loc. cit. Fig. 11.
42 Mr Mines, On Pulsus alternaus.
DESCRIPTION OF PLATE I.
Fig. 1. Frog's heart. Top line of record shows contractions of an
auricle (down-stroke = systole). Second line of contractions of ventricle.
Third line electrogram by direct derivation of base and apex of ventricle.
Einthoven galvanometer. .High tension of quartz fibre. Sensitiveness
— about 8 ram. deflection for 1 centi-volt. Alternation, developed
spontaneously. Signal line indicates stimulation of sinus venosus with
tetanising current of moderate strength. Time in seconds.
Fig. 2. Frog's heart. Arrangement as in Fig. 1. Description in
text.
REFERENCES.
1872. Traube. Berlin, klin. Wochenschr. 9, p. 185 (quoted by Starkenstein
and others).
1880. VON Basch. MilUer's Archiv, Suppl. Band, p. 283.
1882. Gaskell. Phil. Trans, p. 1017.
1901. HoPMANN. Pflllgei^s Arch. 84, p. 130.
1905. VoLHARD. MUnchen. Med. Wochenschr. 52, p. 590.
1907. Starkenstein. Z. exp. Path. u. Therap. 4, p. 681.
1907. Muskens. Journ. Physiol. 36, p. 104.
1908. Hering. MUnchen. Med. Wochenschr. 55 (ii), p. 1417.
1909. CusHNY, Heart 1, p. 1.
1910. Windle. Heart 2, p. 95.
1911. Lewis. Mechanism of the heart heat (Shaw & Sons), Chapter 23.
1912. Mines. Proc. Cctmh. Pkil. Soc. 16, p. 615.
I
Phil. Soc. Proc. Vol. xvii. Pt i.
Plate I.
fi't'r ,
fSjgSa!
rif ♦**•;•■ 'Jr.*--.!.
J*« *«r r^: •♦••V.'* • • ;
Mr Bragg, Diffraction of Short Electromagnetic Waves, etc. 48
The Diffraction of Short Electromagnetic Waves by a Crystal.
By W. L. Bragg, B.A., Tiinity College. (Communicated by
Professor Sir J. J. Thomson.)
[Read 11 November 1912.]
[Plate II.]
Herren Friedrich, Knipping, and Laue have lately published
a paper entitled 'Interference Phenomena with Rontgen Rays*/
the experiments which form the subject of the paper being carried
out in the following way. A very narrow pencil of rays from an
X-ray bulb is isolated by a series of lead screens pierced with fine
holes. In the path of this beam is set a small slip of crystal,
and a photographic plate is placed a few centimetres behind the
crystal at right angles to the beam. When the plate is developed,
there appears on it, as well as the intense spot caused by the
undeviated X-rays, a series of fainter spots forming an intricate
geometrical pattern. By moving the photographic plate back-
wards or forwards it can be seen that these spots are formed by
rectilinear pencils spreading in all directions from the crystal,
some of them making an angle of over 45° with the direction
of the incident radiation.
When the crystal is a specimen of cubical zinc blende, and one
of its three principal cubic axes is set parallel to the incident
beam, the pattern of spots is symmetrical about the two re-
maining axes. This pattern is shown in Plate II. Laue's
theory of the formation of this pattern is as follows. He con-
siders the molecules of the crystal to form a three-dimensional
grating, each molecule being capable of emitting secondary
vibrations when struck by incident electromagnetic waves from
the X-ray bulb. He places the molecules in the simplest possible
of the three cubical point systems, that is, molecules arranged in
space in a pattern whose element is a little cube of side ' a', with
a molecule at each corner. He takes coordinate axes whose
origin is at a point in the crystal and which are parallel to the
sides of the cubes. The incident waves are propagated in a
direction parallel to the z axis, and on account of the narrowness of
the beam the wave surfaces may be taken to be parallel to the xy
plane. The spots are considered to be interference maxima of the
waves scattered by the orderly arrangement of molecules in the
crystal. In order to get an interference maximum in the direction
* Sitzungsberichte cler Koniglich Bayerischen Akademie der Wissenschaften.
June 1912.
44 Mr Bragg, The Diffraction of
whose cosines are a, /S, 7, for incident radiation of wave-length \,
the following equations must be satisfied
aa = hj\, ap=h=^, a {1 — <y) = lu)\. (1)
where Ih Ih K are integers.
These equations express the condition that the secondary
waves of wave-length \ from a molecule, considered for simplicity
as being at the origin of coordinates, should be in phase with those
from its neighbours along the three axes, and that therefore the
secondary waves from all the molecules in the crystal must be in
phase in the direction whose cosines are a /3 7.
The distance of the crystal from the photographic plate in the
experiment was 3'56 cm. The pencil of X-rays on striking the
crystal had for cross-section a circle of diameter about a millimetre,
and the dimensions of the spots are of the same order. The plate
of crystal was only "5 millimetre thick. It is thus easy to calculate
with considerable accuracy from the position of a spot on the
photographic plate the direction cosines of the pencil to which it
corresponds, since the pencils of raj^s may be all taken as coming from
the centre of the crystal. Laue found, on doing this for each spot,
that as a matter of fact the values for a /3 1 — 7 so obtained were
in the numerical ratio of three small integers hi ho, A3 as they
should be by equations (1).
For instance, a spot appears on the photographic plate whose
coordinates referred to the x and g axes are
oc = '28 cm., y = 1'42 cm.
The distance of the crystal from the photographic plate,
3'56 cm., gives z.
Thus sin
a
ce
1-42
a :
7 _
3-56
a
•28
/3:7::
X : y : z
1
1
•28
Thus
\/(-28)'^
1-42
+ (l-42)^-H(3-
1-7
" -27 '
56)^
3-83
or
a:^: 1-7:: 1 : 5 :1.
Laue considers some thirteen of the most intense spots in the
pattern. Owing to the high symmetry of the figure, the whole
pattern is a repetition of that part of it contained in an octant.
Thus these thirteen represent a very large proportion of all the
spots in the figure. For these spots he obtains corresponding
integers Aj h^ h^ which are always small, the greatest being the
number 10. But even if one confines oneself to integers less than
10, there are a great many combinations of Aj Ag A3 which might
Short Electromagnetic Waves by a Crystal. 45
give spots on the photographic plate which are in fact not there,
and there is no obvious difference between the numbers h^ h^ h^
which correspond to actual spots, and those which are not repre-
sented.
To explain this Laue assumes that only a few definite wave-
lengths are present in the incident radiation, and that equations
(1) are merely approximately satisfied.
Considering equations (1) it is clear that when h^ h^ hg are fixed
- can only have one value. However if h^ h^ Ih are mailtiplied by
an integral factor p, equations (1) can still be satisfied, but now
by a wave-length -. By adjusting the numbers h^ h^ hs in this
p
way, Laue accounts for all the spots considered by means of five
different wave-lengths in the incident radiation. They are
\ = -OSTTa
\ = -OBQSa
\ = -OGGSa
\ = -1051a
X = •143a.
For instance, in the example given above, where it was found
that
a:/3:l-7:: 1:5:1
these numbers are multiplied by 2, becoming 2 . 10 . 2. Then
they can be assigned to a wave-length
- = •037,
approximately equal to the first of those given above.
However, this explanation seems unsatisfactory. Several sets
of numbers hj_ ^2 h can be found giving values of - approximating
very closely to the five values above and yet no spot in the figure
corresponds to these numbers. I think it is possible to explain
the formation of the interference pattern without assuming that
the incident radiation consists of merely a small number of wave-
lengths. The explanation which I propose, on the contrary, assumes
the existence of a continuous spectrum over a wide range in the
incident radiation, and the action of the crystal as a diffraction
grating will be considered from a different point of view which
leads to some simplification.
46 Mr Bragg, The Diffraction of
Regard the incident light as being composed of a number of
independent pulses, much as Schuster does in his treatment of
the action of an ordinary line grating. When a pulse falls on a
plane it is reflected. If it falls on a number of particles scattered
over a plane which are capable of acting as centres of disturbance
when struck by the incident pulse, the secondary waves from them
will build up a wave front, exactly as if part of the pulse had been
reflected from the plane, as in Huygen's construction for a re-
flected wave.
The atoms composing the crystal may be arranged in a great
many ways in systems of parallel planes, the simplest being the
cleavage planes of the crystal. I propose to regard each inter-
ference maximum as due to the reflection of the pulses in the
incident beam in one of these systems. Consider the crystal as
divided up in this way into a set of parallel planes. A minute
fraction of the energy of a pulse traversing the crystal will be
reflected from each plane in succession, and the corresponding
interference maximum will be produced by a train of reflected
pulses. The pulses in the train follow each other at intervals of
2d cos 0, where 6 is the angle of incidence of the primary rays on
the plane, d is the shortest distance between successive identical
planes in the crystal. Considered thus, the crystal actually
' manufactures ' light of definite wave-lengths, much as, according
to Schuster, a diffraction grating does. The difference in this case
lies in the extremely short length of the waves. Each incident
pulse produces a train of pulses and this train is resolvable into a
series of wave-lengths X, ^ , k , ^ etc. where X = 2d cos 0.
Though to regard the incident radiation as a series of pulses
is equivalent to assuming that all wave-lengths are present in its
spectrum, it is probable that the energy of the spectrum will be
greater for certain wave-lengths than for others. If the curve
representing the distribution of energy in the spectrum rises to a
maximum for a definite \ and falls off on either side, the pulses
may be supposed to have a certain average ' breadth ' of the order
of this wave-length. Thus it is to be expected that the intensity
of the spot produced by a train of waves from a set of planes in
the crystal will depend on the value of the wave-length, viz. 2(i cos 0.
When 2d cos is too small the successive pulses in the train are
so close that they begin to neutralize each other and when again
2d cos 6 is too large the pulses follow each other at large intervals
and the train contains little energy. Thus the intensity of a spot
depends on the energy in the spectrum of the incident radiation
characteristic of the corresponding wave-length.
Another factor may influence the intensity of the spots.
Consider a beam of unit cross-section falling on the crystal. The
Short Electromagnetic Waves by a Gnjstal. 47
strength of a pulse reflected from a single plane will depend on
the number of atoms in that plane which conspire in reflecting
the beam. When two sets of planes are compared which produce
trains of equal wave-length it is to be expected that if in one set
of planes twice as many atoms reflect the beam as in the other
set, the corresponding spot will be more intense. In what follows
I have assumed that it is reasonable to compare sets of planes in
which the same number of atoms on a plane are traversed by unit
cross-section of the incident beam, and it is for this reason that I
have chosen the somewhat arbitrary parameters by which the
planes will be defined. They lead to an easy comparison of the
effective density of atoms in the planes. The effective density is
the number of atoms per unit area when the plane with the atoms
on it is projected on the xy axis, perpendicular to the incident light.
Laue considers that the molecules of zinc-blende are arranged
at the corners of cubes, this being the simplest of the cubical
point systems. According to the theory of Pope and Barlow this
is not the most probable arrangement. For an assemblage of
spheres of equal volume to be in closest packing, in an arrange-
ment exhibiting cubic symmetry, the atoms must be arranged
in such a way that the element of the pattern is a cube with
an atom at each corner and one at the centre of each cube
face. With regard to the crystal of zinc-blende under considera-
tion zinc and sulphur being both divalent have equal valency
volumes and their arrangement is probably of this kind. It will
be assumed for the present that the zinc and sulphur atoms are
identical as regards their power of emitting secondary waves.
Take the origin of coordinates at the centre of any atom, the
axes being parallel to the cubical axes of the crystal. The distance
between successive atoms of the crystal along the axes is taken for
convenience to be 2a.
All atoms in the xz plane will have coordinates
pa qa
where p and q are integers and p -\- q is even. See fig. 1 in text.
The same holds for atoms in the yz plane. Therefore any
reflecting plane may be defined by saying that it passes through
the origin, and the centres of atoms
pa qa
7'a sa
For instance, the plane on which the triangle GAB lies passes
through the origin and
(X 3a
a a
48
Mr Bragg, The Diffraction of
The planes can now be classified by the corresponding values
of p, q, r, s as parameters.
The direction cosines of a plane p q r s will be
rq ps —pr
If these are called I m n the direction cosines of the reflected
beam are
2ln, 2mn, 27i^ — 1,
/
/
/
/
/
/
/
• /
/
1
•
•
•
*
•
•
•
•
•
•
•
•
o
X
Fig. 1.
and the position of the interference maximum on the photographic
plate can be found in terms of these quantities.
The corresponding wave-length is 2d cos where d is the
perpendicular distance between successive planes. Now is the
angle of incidence, therefore cos = n above. It is easier to find
the intercepts which successive planes cut off on the z axis, than
their perpendicular distance apart. Calling these intercepts I, then
X = 2c? cos ^ = 2 . Z cos 6* . cos ^ = 2ln\
Sliof't Electy'omagnetic Waves hy a Crystal. 49
Consider the atoms as arranged in vertical rows parallel to
the z axis in the figure. A plane for which p = l and r = 1 passes
through one atom in every one of these vertical rows (see fig. 3).
Therefore the next plane to it passes through a set of atoms all
2a above the corresponding atoms in the first plane. Thus for
this set of planes, I = '2a and the wave-length \ = 4<a7i^. The
effective density of atoms on such a set of planes is the greatest
possible.
If j9 = 1, r = 2, each plane now passes through atoms in one
half of the vertical rows. For instance, the plane through the
origin contains no atoms in those vertical rows for which r is odd.
2a
The successive planes must cut the z axis at intervals -^, since
the effective density of atoms in each is half as great as before and
the whole number of atoms in unit volume of the crystal remains
2a
constant. Similarly ii p = l, f = 3 1=-^ and so forth.
o
In the general case I = ^^ ^— .
° L.C.M. of p and r
In the tables given below planes with the same effective
density of atoms on them, and therefore the same values of I, are
grouped together.
The position of the spot reflected by each system of planes
considered has been calculated, also the wave-length of the
reflected train expressed for convenience in the form - , and when
in the photograph a spot is visible in the position calculated, its
intensity is denoted by star according to an arbitrary scale.
*;;$#* + •
When no spot appears in the calculated position, I have put
' invisible ' opposite that plane.
There is no need to go any further than the set for which
2a
l = -r , to obtain all the spots in the photograph. Indeed only
one spot is given by this last set.
Only one spot on the plate is to be assigned to planes of this
class. It is curious that the value of - corresponding to this spot
A/
should be as great as 11 "2. It is noticeable in the photograph
that all spots at any distance from the centre of the pattern tend
to become very faint, and the values of p, q, r, s which do give a
spot in Table IV are the only ones to be found giving a spot
at all near the centre. In the first three tables the parameters
VOL. XVII. PT, I. 4
50
Mr Bragg, The Diffraction of
corresponding to a value of - between 6 and 9 are represented by
the most intense spots.
Every spot in the photograph is accounted for in the following
Tables. I think it is evident that the sets of planes which actually
reflect spots can be arranged in a very complete series with few
or no gaps. Though at first sight it may appear that in the
Table I.
Planes for which p = l, r = l, l = 2a, \ = 4!an^
p
Q
r
s
a
X
Intensity
h
h
h
1
3
2-8
*
1
3
1
5
6-8
I
5
1
7
12-8
*
1
7
1
9
20-8
Invisible
1
9
3
1
2-8
*
3
1
3
3
4-8
*
3
3
3
5
8-8
3
5
3
7
14-8
+
3
7
3
9
22-8
Invisible
3
9
5
1
6-8
5
1
5
3
8-8
'If
5
3
5
5
12-8
■X-
5
5
5
7
18-8
Invisible
5
7
7
1
12-8
*
7
1
7
3
14-8
+
7
3
7
5
18-8
Invisible
7
5
1
9
1
1
20-8
Invisible
9
1
1
Range of values of -, all possible up to 15.
A/
tables the parameters are selected in a somewhat arbitrary way,
they are in reality the simplest possible. For instance, in Table
III the first values for p, q, r, s considered are 1, I, 3, 5. This
is so because 'r+s' must be positive. If r = l, s must be odd.
Short Electromagnetic Waves hy a Crystal.
51
1, 1, 3, 1 and 1, 1, 3, 3 would reflect the beam so as to miss the
photographic plate. 1, 1, 3, 5 and 1, 1, 3, 7 are considered.
1, 1, 3, 9 has already been considered as 1, 1, 1, 3, and 1, 1, 3,
11 gives a value for the wave-length outside the 'visible' range.
In fig. 3, Plate II, is given a photograph of the interference
pattern which Laue obtained. In fig. 4, Plate II, the key to the
pattern has been drawn, showing in what planes the spots are to
be considered as reflected.
Table II.
Planes for which l.c.m. of p and r = 2, l=a, X. = 2an^.
■p
<l
r
s
a
Intensity
/'I
/«2
/'3
1
1
2
4
3
•
2
4
2
1
1
2
8
9
#
2
8
2
1
1
2
12
19
Invisible
2
12
2
2
4
2
2-5
Invisible
4
2
2
4
2
4
4-5
•
4
4
2
2
4
2
8
10-5
• 1
4
8
2
1
3
2
5
*
6
2
1
3
2
4
7
#
6
4
2
1
3
2
8
13
• 1
6
8
2
2
8
2
8-5
•
8
2
2
8
2
4
10-5
.?
8
4
2
1
5
2
13
Invisible
10
2
Consider a reflecting plane which passes through the atom at
the origin and a neighbouring atom, let us suppose the atom whose
coordinates are a, o, a. As the plane is turned about the line
through these two points the reflected beam traces out a circular
cone, which has for axis the line joining the two points and for
one of its generators the incident beam. This cone cuts the
photographic plate in an ellipse. If the atom through which
the plane passes is in the X2 plane as above, the ellipse touches
the y axis on the photographic plate at the origin. Now take
a plane passing through the origin and a point 0, a, 3a. The
4—2
52 Mr Bragg, The Diffraction of
Table III.
Planes for which l.c.m. of p and r = 3, 1 = — , X= — —
o o
p
Q
r
s
X
Intensity
^1
h
/'3
1
1
3
5
3-6
Invisible
3
5
3
1
1
3
7
5-6
•
3
7
3
1
1
3
11
11-6
IiiA'isible
3
11
3
3
5
3
5
4-9
Invisible
5
5
3
3
5
3
7
6-9
*
5
7
3
3
5
3
11
12-9
Invisible
5
11
3
3
7
3
1
4-9
Invisible
7
1
3
3
7
3
5
6-9
*
7
5
3
3
7
3
7
8-9
■X-
7
7
3
3
7
3
11
14-9
Invisible
7
11
3
1
3
3
1
7-6
*
9
1
3
1
3
3
5
9-6
+
9
5
3
1
3
3
7
11-6
Invisible
9
7
3
Raoge of values of - , 5*6 — 96.
Table IV.
Planes for which the l.c.m. of p and r = 4, 1 =
^an^
A, = — -, — = an^.
2a
4 '
p
1
r
s
a
X
Intensity
h.
ht
h^
1
1
4
10
8-2
Invisible
4
10
4
1
1
4
14
16-2
Invisible
4
14
4
2
4
4
10
11-2
+
8
10
4
1
3
4
6
12-2
Invisible
12
6
4
Short Electromagnetic Waves by a Crystal. 53
locus of the reflected spot as it turns is again an ellipse, which
now touches the x axis. The intersections of the two ellipses
will give the position of a spot reflected by a plane passing
through all three points, the origin, the point a, 0, a, and the
point 0, a, 3a.
The ellipses are drawn in the figure, and the plane corresponding
to any spot can be found by noting the ellipses at the intersection
of which the spot lies. Only those ellipses have been drawn which
give the points in Table I. It will be seen that a very large
proportion of the spots in the photograph lie at the intersection
of these.
The analysis involved in this way of regarding the interference
phenomena must be fundamentally the same as that employed by
Laue. In fig. 1, suppose the phase difference between vibrations
from successive atoms along the three axes, when waves of wave-
length X fall on the crystal, to be 27r/ii, 27r/i2, ^who. Then in order
that the vibrations from those atoms, which are arranged in the
figure at the centres of the cube faces, should also be in phase,
one must have
hi ho . , ho hs
— - 2 = an mteger, -^ - -g = an integer.
This condition is simply expressed by saying that h^, h^, h^
must all be even or all odd integers. When Aj, h^, A3 are given,
the value of X, follows from
\ 2L
2a W + A^^ + As^'
since here 2a has been taken as the distance between neighbouring
molecules along the three axes.
If the three simplest values of hj, h^, h^ for a spot on the plate
are not all odd, or all even, then these numbers must be doubled
to make them even and the wave-length accordingly halved.
When this is done, it can be seen that for each value of h^ there
is a series of values of h^ and h^. These numbers all give spots in
the photograph if the corresponding value of - lies within a certain
range. The smaller the number Aj, the larger is the range of - for
A.
which spots are visible. Spots whose - lies near the extremity of
A,
the range are very faint, those whose - is in the middle of the
A/
range are intense. In the tables the values of li^, h^, A3 corre-
sponding to each spot are set down.
54 Mr Bragg, The Diffraction of
It is quite probable that the qualitative explanation put forward
here to account for the intensities of the spots is not the right one,
other explanations being possible. For instance, one might substi-
tute for the factor termed 'effective density' above, one which
expressed the fact that, other things being equal, spots nearer the
centre of the pattern were more intense than those farther out.
This, together with the right curve for the distribution of energy
in the spectrum of the incident radiation, could be made to account
for the intensities quite reasonably. This does not vitiate the
conclusion that the spots in the pattern represent a series which
is complete, and characteristic of a cubical crystalline arrangement.
The other arrangements of cubical point systems cannot, as far as
I can see, give such a complete series. The other possible arrange-
ments have for elements of their pattern (1) a cube with a molecule
or atom at each corner, the arrangement which Laue pictured, or
(2) a cube with a molecule at each corner and one at the centre.
Neither arrangement will fit the system of planes given above. It
is only the third point system, the element of whose pattern has a
molecule at each corner and one at the centre of each cube face,
which will lend itself to the system of planes found to represent
spots in the photograph.
This last system, seeing that it forms an arrangement of the
closest possible packing, is according to the results of Pope and
Barlow the most probable one for the cubic form of zinc sulphide.
In one of the photographs taken by Messrs Friedrich and
Knipping the crystal was so oriented that the direction of the
incident radiation made equal angles with the three rectangular
axes of the crystal. In this case a figure is obtained in which the
pattern is a repetition of the spots contained in a sector of angle
TT .
^. Regarding the spots as reflections of the incident beam in
planes as before, these planes can be found almost as easily as
those which reflect the spots in the square pattern, and indeed in
many cases the planes are identical. I will not give the calcula-
tions here, but one point is of especial interest. A photograph
was taken of the crystal oriented so that the pattern obtained
was perfectly symmetrical. The crystal was then tilted through
3° about a line perpendicular to the incident beam and to one of
the cubical axes. This distorted the pattern considerably, but
corresponding spots in the two patterns are easily to be recognised.
The points which I wish to consider especially are the following.
In the first place, the spots in the distorted pattern are all
displaced exactly as would be expected if they were reflections in
planes fixed in the crystal. For instance, when the reflecting
plane contains the line, about which the crystal was tilted
through 3°, it can be ascertained that the movement of the spot
Short Electromagnetic Waves hy a Orystal. 5o
corresponds to a deviation of the reflected beam through 6°. This
alone is, I think, strong evidence that the wave-length X, is elastic,
and not confined to a few definite values, and that equations (1)
are satisfied rigorously and not merely approximately.
Besides the distortion of the figure due to the tilting of the
crystal, a very marked alteration in the intensity of the spots is
to be noticed. This is especially marked for those spots which
are near the centre of the pattern, but not on or near the axis
about which the crystal is tilted. This is probably due to the
fact that for these spots a considerable change in wave-length has
taken place.
When the angle of incidence 6 of the primary beam on a set
of reflecting planes varies, the value of 2c? cos 6 is altered and the
alteration for the same hd is greater the greater 6 is.
One spot in particular changes from being hardly visible in the
symmetrical pattern to being by far the most intense when the
crystal is tilted. It is the spot reflected in a plane passing through
the origin and
3a, 0, a; 0, 3a, a.
Planes parallel to this have for d, the shortest distance between
^a
successive planes, the value -pr^ . It can easily be calculated from
the position of the spot that the value of cos 6 changes from Id
to '12 when the crystal is tilted. This corresponds to a change
in the value of - from 4*3 to 6"5, and it was found before for the
A,
square pattern that spots corresponding to the former wave-lengths
were weak, those corresponding to the latter intense.
A curious feature of the photographs may be explained by
regarding the spots as formed by reflection. As the distance of
the photographic plate from the crystal is altered, the shape of
each individual spot varies. At first round, they become more
and more elliptical as the plate is moved further away. A reason
for this is found in the following. If the incident beam is not
perfectly parallel, but slightly conical, rays will strike the crystal
at slightly different angles. Regard the crystal as a set of
reflecting planes perpendicular to the plane of the paper (fig. 2).
The rays striking the reflecting planes on the upper part of the
crystal on the whole meet them at a less angle of incidence than
those striking the planes at the bottom; the latter are deflected
more, and the rays tend on reflection to come to a focus in a hori-
zontal line. On the other hand, rays deviating from the axial
direction in a horizontal plane diverge still more after reflection.
Thus as the plate is removed from the crystal, the spots up to a
certain distance become more and more elliptical.
56
Mr Bragg, The Diffraction of
The atoms of a crystal may be arranged in ' doubly infinite '
series of parallel rows, as well as in ' singly infinite ' series of
planes. The incident pulse falls on atom after atom in one of
these rows, if the row is not parallel to the wave front, and
secondary waves are emitted, one from each atom, at definite
time intervals. Along any direction lying on a certain circular
cone with the row of atoms as -axis, these secondary waves will
be all in phase, one generator of the cone being, of course, parallel
to the direction of the incident radiation. If the row of atoms
makes a small angle with the direction, this cone with vertex at
the crystal slip may now be considered to cut the photographic
plate in an almost circular ellipse passing through the big central
L
C
G C
Lead Screen
Crystal
Positions o\ Pho1b|ra|oliic Plate
Cro55 secfions o| pencil o| rays at F) P^
Fig. 2.
spot. Drawing the ellipses which correspond to the most densely
packed rows of the crystal, a spot is to be expected at the inter-
section of two ellipses, for this means that pulses from a doubly
infinite set of atoms are in that direction in agreement of phase.
Thus it ought to be possible to arrange the spots in the photograph
on these ellipses, in whatever way the crystal is oriented, and indeed
they appear in all cases. They come out very strongly in the
photographs taken with copper sulphate crystals.
So far it has been assumed that the atoms of zinc and sulphur act
in an identical manner with regard to the production of secondary
waves, but this assumption is not necessary. What is brought
Phil. Soc. Proc. Vol. XVii. Pt. i.
Plate II.
I
i
t
Fig. 3.
103
O'll
tor
Fig. 4.
SJiort Electromagnetic Waves by a Crystal. 57
out so strongly by the analysis is this ; that the point system to
be considered has for element of its pattern a point at each corner
of the cube and one at the centre of each cube face. In the
arrangement assigned to cubical zinc sulphide and similar crystals
by Pope and Barlow, this point system is characteristic of both the
arrangement of the individual atoms regarded as equal spheres,
and of the arrangement of atoms which are in every way identical
as regards nature, orientation, and neighbours in the pattern. The
atoms of zinc, for instance, in the zinc blende are grouped four
together tetrahedron- wise, and as these little tetrahedra are all
similarly oriented and are arranged themselves in the above point
system, atoms of zinc identical in all respects will again be arranged
in this point system. Which of these factors it is that decides the
form of the interference pattern might be found by experiments
with crystals in which the point system formed by the centres of
all the atoms differs from that formed by the centres of identical
atoms.
In conclusion, I wish to thank Professor Pope for his kind
help and advice on the subject of crystal structure.
58 . Mr Marr, The Meres of BrecMand.
The Meres of BrecMand. By J. E. Marr, Sc.D., F.R.S.,
St John's College.
[Read 25 November 1912.]
The sandy heaths of south-west Norfolk and north-west
Suffolk form a type of physiographical feature unique in Britain.
Among many points of interest in the district are several small
meres, in the drainage-basin of the Little Ouse; these lie among
the heaths between Croxton and Wretham, north of Thetford.
The origin of these meres has never been explained, and
requires elucidation. These notes are only intended to direct
attention to the question of their formation, and to offer some
facts bearing upon it.
The meres above mentioned form a cluster a little way north-
west of Roudham Junction. They are noticed by Mr F. J. Bennett
in the Geological Survey Memoir of the district (Geology of the
Country around Attlehorough, Watton, and Wymondham, 1884,
p. 17). He suggests that they started as sand and gravel pipes
in the chalk, and afterwards became enlarged by chemical solution,
assisted by mechanical disintegration during rise and fall of
underground water.
An interesting paper on the meres by Mr W. G. Clarke
appeared in the Transactions of the Norfolk and Norwich
Naturalists' Society, Vol. vii (1903), p. 499 ; it contains a number
of observations, but he does not give any explanation of their
origin other than that offered by Mr Bennett.
The meres under notice occur in two shallow valleys lying
north and south of an east-west plateau. In the northern valley
lie the Devil's Punch Bowl, Fowlmere, Home Mere, and a group in
Wretham Park including Mickle Mere : in the southern one are
Langmere and Ringmere.
The meres possess several features in common. All are dry in
seasons of little rainfall, and only under very exceptional condi-
tions is any one completely filled to the brim, so that normally
they have no outlet. The sides of some are steep, at the angle
of repose of the material which composes them, and the surface
Mr Marr, The Meres of Breckland. 59
of the water usually lies at from 15 to 25 feet below the rim.
The floors are flat, and the waters shallow.
They differ in size and shape, the smaller being most regular
and approaching a circular outline : such are the Devil's Punch
Bowl, Ringmere and many nameless ponds, the latter often only
a few feet in diameter. The largest are less than half a mile in
length. These are irregular, often having sinuous shore-lines,
and in some, as Langmere, one diameter is longer than the
other.
The meres in Wretham Park have undergone considerable
modification at the hands of man, but those on the open heath
are in their natural condition.
Associated with the named meres are the above-mentioned
small ponds. These grade downward in size to ordinary swallow-
holes, such as occur in most limestone districts, and there is little
doubt that these swallow-holes mark the starting-point in the
formation of the larger meres. They are situated in chalk and,
as in the case of the meres which still hold water at times, near
the junction of the chalk with overlying glacial deposits.
Langmere and Ringmere lie in two tributary-valleys south of
the plateau. Tracing these valleys downward to their coalescence
near Roudham Junction, we find remains of similar hollows, now
nearly always dry, and with the sides sloping gently to the
floors.
That the valleys existed before the meres is indicated by a
deposit of river gravel exposed on the bank of Ringmere.
The origin of some of the meres is probably complex. The
swallow-holes may have begun as sand-pipes, as suggested by
Mr Bennett, or, like those of other limestone regions, may be
simply due to enlargement of a place on a joint by acidulated
water, or to subsidence of part of the roof of a subterranean
hollow. Such a subsidence giving rise to a pit at Rockland is
described by Mr Bennett (loc. cit. p. 21).
When sufficiently large, the surface- drainage of the little
valleys situated on the glacial clays would, when reaching the
chalk as it was exposed by the denudation of those clays, be
carried underground through swallow-holes, but the transport of
glacial clay to the floor of the swallow-hole might block it to a
degree sufficient to prevent free drainage into the subterranean
water-course, and hence the water would stand in the swallow-
hole during wet periods. The standing water would sap the sides
of the hole by solution, as suggested by Mr Bennett, slipping of
the slope above would take place, as can now be seen in progress,
and the hole would grow in circumference, giving rise ultimately
to meres like the Punch Bowl and Ringmere. Coalescence of
two or more would produce irregular meres like Langmere and
60 ilfr Marr, The Meres of Breckland.
Fowlmere, Again mechanical erosion of the watercourse above
the mere would widen the bed there, while that of the deserted
stream below the mere would be no longer lowered, and a larger
area to be filled with water would be thus produced. In other
cases, direct collapse of the roofs of underground caves might
initiate meres.
In hollows of other districts bearing some resemblances to
those of Breckland, the upward pressure of artesian waters due
to erosion of overlying impervious deposits has been regarded as
the cause of formation of the hollows. The conditions in Breckland
do not seem suitable for such occurrence.
The existence of deserted mere-hollows down-stream near
Roudham Junction is of importance. At the time of their
formation, according to the above views, the junction of glacial
clays and chalk would be situated near these sites, it having
been gradually driven up-stream to its present position by
erosion.
When the glacial clay junction was near these hollows, their
underground drainage would be partly blocked by deposit of clay
on their floors. As the junction between clay and chalk was
shifted up valley, the supply of clay would be stopped in the
lower meres, being now deposited in newly formed upper ones.
Solution would now proceed unchecked until a free underground
passage for all water draining into the hollows would be established,
and the meres would then be permanently dry.
In connexion with this question, however, is that of the mode
of infilling of the meres, and here we find conflicting views ; one,
that they are filled by the rise of the saturation-level of under-
ground water, the other that they are fed by surface streams.
(See W. G. Clarke, loc. cit.) If the latter, the supply of water
would cease when the glacial clay was denuded.
As to the age of the meres, they are clearly post-glacial in
the sense that they were formed after the accumulation of the
boulder-clay of the district. They may have been formed at
various subsequent periods, and are probably still in process of
formation. One of the meres at Wretham was drained and its
floor dug out, and the results were described by Mr C. J. F.
(afterwards Sir Charles) Bunbury (Quart. Journ. Oeol. Soc. xii.
1856, p. 355). Over twenty feet of black peaty mud was found
resting on a light grey sandy marl. In the mud were a number
of horns of the red deer, which had been sawn off just above the
brow-antlers. In connexion with this discovery Mr Skertchley
(Geol. Survey Mem. Geology of the Fenland, p. 248), refers to
the horns used for picks in the flint-mines at Grimes Graves.
These mines have been hitherto referred to the Neolithic Period,
but Mr Reginald Smith has recently advocated their assignment
Mr Marr, The Meres of Breckland. 61
to the Aurignacian stage of the Palaeolithic Period (Archaeologia,
LXII. 1912, p. 109). I have rebently found a station near Ring-
mere with implements which strongly resemble those of the last
(Magdalenian) stage of the Palaeolithic Period. If these should
prove to be Magdalenian, the horns found in the neighbouring
mere may have been cut at the same time, for bone and horn were
extensively used in the Magdalenian period.
Other remains have been found in other of the meres, and
their different ages will probably be ultimately fixed on archaeo-
logical evidence.
I hope that some one may be found who will devote himself
to a thorough study of these meres and their history.
62 Mr Hatch, Note on a Remarkable distance of
Note on a Remarkable Instance of Complete Rock-disintegration
by Weathering. By F. H. Hatch, Ph.D., Mera.Inst.C.E.
[Bead 25 November 1912.]
The material to be described occurs at Diamantina, in the
province of Minas Geraes, Brazil, where it is being worked for
diamonds. It consists of a conglomerate which, under the influence
of weathering, has been disintegrated to the condition of a loose
sandy formation capable of being dug out with a shovel at the
lowest depth yet attained in the open working.
The Pebbles. The pebbles range in size from the smallest
dimensions up to a maximum diameter of 3 inches. They have
been worn perfectly smooth by water attrition and are rounded,
generally to an ovoid shape. The materials of which they are
composed are, in the order of relative abundance:
Quartzite.
Yein-quartz.
Steatite or soapstone.
Tourmaline-quartz vein -stuff.
The steatitic material, on account of its softness and consequent
liability to pulverisation, rarely shows any smooth or rounded
surfaces ; it crumbles between the fingers to an unctuous powder,
resembling French chalk. No doubt this material has been
derived originally from the decomposition of an ultra- basic igneous
rock in which magnesian silicates (such as olivine) predominated.
The other pebbles, viz. those of the quartzite, vein-quartz
and tourmaline-quartz vein-stuff, are in a very friable condition,
crushing to powder in the hand under the least pressure. This
peculiar condition of pebbles of materials such as quartzite and
vein-quartz, which in their normal condition are characterised by
extreme hardness and unseparability, will be referred to later.
The Sand. The sand consists of a mixture of colourless
quartz and of the fine powder produced by the pulverisation of
the soapstone fragments. By careful washing with water the
slime formed by the soapstone can be removed, leaving a white
quartz sand which under the microscope is found to consist of
colourless angular grains, often presenting the characteristic
pyramidal faces of quartz crystals. Rounded grains are rare, and
Complete Rock-disintegration by Weathering. 63
there is little doubt that the bulk of the fragments has been
derived from the disintegration of the quartzite and vein-quartz
pebbles under the influence of weathering.
In order to ascertain the nature of the heavy minerals in this
sand, the whole of the sample was carefully panned, and the con-
centrates, after drying, introduced into bromoform of the density
of 2"9. By this means a separation of the minerals with a density
greater than 2*9 from the quartz which floated on the surface of
the liquid was effected. A minute quantity of a heavy powder
was obtained, the subsequent examination of which under the
microscope disclosed the following minerals :
Zircon, Chalcopyrite.
Zinc blende. Rutile.
Galena. Tourmaline.
Iron pyrites.
Of these heavy constituents, the first three constitute about
95 per cent.
In addition to the above minerals, diamonds are found in the
course of the washing operations conducted at the spot. I had
an opportunity of examining 40 of these stones : they ranged in
weight from 0*68 to 4-42 metric carats*, and showed the character-
istic rounded shape of the diamond, the prevalent forms being the
octahedron, the rhombic dodecahedron, the 3-faced octahedron
and the 6-faced octahedron, either alone or in combination. The
octahedral faces are usually smooth and brilliant, but triangular
pittings are common on them. The majority of the stones have
a characteristic greenish tint, but this is only " skin deep," and
does not appear in the cut stones. Examination under the micro-
scope shows that this colouration is due to the presence of small
spots and flecks of some green mineral (chlorite ?) in the super-
ficial layers of the stones. There is little to indicate the original
source of these diamonds. Although found in the conglomerate
they are certainly older than that rock. It appears likely that
there is some community in origin between them and the soap-
stone, which, as already stated, probably represents a decomposed
olivine-rock of igneous origin.
Origin of the Material. The material is an ancient con-
glomerate, that has suffered prolonged weathering. So com-
pletely have the weathering agents performed their work that
not only has the cement of the conglomerate been entirely
removed, but the pebbles themselves have been profoundly
affected. As already stated, many of the pebbles are rounded
fragments of an older quartzite formation. The material that
* 1 metric carat = 200 milligrams.
64 3Ir Hatch, Note on a Remarkable Instance, etc.
originally cemented the constituent quartz grains of these pebbles
has been wholly abstracted, leaving the quartz particles as a
friable, almost non-coherent mass, easily reducible to powder
between the fingers. In other cases the pebbles consist of
tourmaline and quartz, and were evidently derived from pre-
existing veins. These also have been reduced by the same
weathering action to a loose friable condition. It is clear that
the fragments of both these materials could only have acquired
their rounded character by water-attrition when they were in a
hard, compact and firmly-knit condition. Evidence is thus
afforded both of the profound nature, and the prolonged duration
of the weathering to which the conglomerate must have been
exposed since its first formation*.
* Compare : J. G. Branner, The Decomposition of Rocks in Brazil, Bull. Geol.
Soc. Amer. Vol. vii. 1896, pp. 295—300.
Mr Oxley, Magnetic Susceptibility luith Temperature. 65
The Variation of Magnetic Susceptibility with Temperature.
Part II. On Aqueous Solutions. By A. E. Oxley, M.Sc.
(Sheffield), B.Sc. (London), B.A., Senior Scholar and Coutts
Trotter Student, Trinity College.
[^Received 4 December 1912.]
( 1 ) Introduction.
In the examination of the relation between the concentration
of an aqueous solution of a salt of a ferromagnetic element and its
magnetic susceptibility*, it was hoped that some light would be
thrown on the existence of complex hydrates, in the case at least
of very dilute solutions. That such hydrates exist is now beyond
doubt. They are detected by experiments on conductivity and
absorption f and are responsible for the abnormal lowering of the
freezing point of the solutions. The examination referred to above
gave no testimony of the existence of such hydrated systems, and
the conclusion of that research was that the complex groups,
which have an ion or salt molecule as nucleus, are unstable, so
unstable in fact that the core rotates on the application of the
magnetic field independent of the surrounding shell of water
molecules.
Pascal I has examined the magnetic properties of solutions of
metallic salts in water to find if any additive law holds, but no
quantitative deductions could be made on account of the marked
characteristic properties of the metallic elements.
There is considerable evidence§|| that the liquid and solid states
of matter are consequences of complex aggregations of molecules
and not merely of a close approach of the simple molecules con-
sidered as individual particles. In other words, the transition
from the gaseous to the liquid state or from the liquid to the solid
state is of a quasi-chemical rather than of a physical nature. If
part of the solvent be united indeterminately with the solute,
then the representation of the susceptibility of the solution as the
algebraic sum of the susceptibilities of the solvent and of the
solute — a common mode of representation — corresponds to no
physical reality.
* A. E. Oxley, Proc. Gamb. Phil. Soc, Vol. xvi. p. 421, 1912.
t Vide H. C. Jones, "Hydrates in Aqueous Solutions." "Absorption Spectra
of Solutions."
t Ann. de Chim. et de Phys., Ser. vii. 19, p. 70, 1910.
§ For liquids, see the researches of H. C. Jones and his co-workers given in the
volumes mentioned in the reference above.
!l For solids, reference may be made to numerous researches on micro-structure
and on the constitution of aUoys,
VOL. XVII. PT. I. 5
66 M7' Oxley, Magnetic Susceptibility ivith Temperature.
Assuming the existence of chemically complex systems —
chemically complex excludes the cases of the ferromagnetic
elements in which the molecular field of Weiss is not negligibly
small — it has been shown* that the work of du Bois and Honda
on the temperature coefficients of paramagnetic and diamagnetic
substances is not inconsistent with the assumptions at the base
of the Curie-Laugevin theory of magnetism, providing we sup-
pose that these assumptions apply to substances composed of
simple molecules onlyf — such for example as exist in gases at a
temperature far from the point of liquefaction. Further, it does
not follow that because the differential coefficient of the suscepti-
bility with respect to the temperature is positive for some
paramagnetic elements and that the rate of variation of dia-
magnetic susceptibility with the temperature is not zero, that
there is no distinction apart from mere positive and negative
number between the nature of paramagnetism and that of
diamagnetismj.
It is important that the Curie-Langevin theory, which is the
only quantitative theory of magnetism we possess, should not be
discredited as failing to account for individual cases. Each
element has its characteristic molecular and atomic properties,
and a general theory cannot be satisfactory unless it admits of
modification to suit each peculiarity possessed by that element.
Take the case of tin, which is one of the most complex elements
from the magnetic point of view. According to du Bois and
Honda the Curie-Langevin laws of paramagnetism and dia-
magnetism do not apply. They find, indeed, that the susceptibility
of tin changes rapidly when the density changes and also during
fusion. If we could watch the rotation of the particles of tin,
under the application of the magnetic field, as the temperature is
increased, we should probably witness violent disturbances at the
points where the constitution changes. At one temperature the
groups of particles are becoming simpler, at another they are
becoming more complex. So long as the constitution of an
element does not alter as the temperature is changed, the magnetic
properties of that element will follow the Curie-Langevin laws,
the Curie constant per particle having a value dependent upon the
constitution. For another stable molecular constitution which
does not alter over ranges of temperature, there will be a new
Curie constant per particle which will now determine the variation
of the susceptibility with the temperature. In the transition
stage the Curie-Langevin laws cannot alone explain the phenomena,
* A. E. Oxley, Proc. Camb. Phil. Soc, Vol. xvi. p. 486, 1912.
t Or to complex groups of molecules whose constitution does not vary over
wide ranges of temperature.
J Loc. cit., p. 490.
I
Part II. On Aqueous Solutions. 67
for there is superposed upon the normal variation of the suscepti-
bility with the temperature (due to the change in the number of
particle collisions), the effect of chemical association or disso-
ciation. In fact, over such a range of transition the susceptibility
is dependent upon a summation of terms for the classes of particles
of definite types, the expression for each type containing a factor
regulating the rate of association or dissociation at any particular
temperature during the transition.
On this view the nature of tiie continuity of the magnetic
states of the so-called a, /3, 7 and S forms of iron is apparent.
The theory of Weiss*, which assumes all the particles to be of
equal size, cannot apply during the stage of transition.
The rule proposed by Hondaf in place of the Curie-Langevin
laws is that the effect of a slight increase of the temperature on
the susceptibility of an element is the same as that of a slight
increase of the atomic weight. This rule is quite inadequate in
the case of tin and many other elements, and even for those
elements for which it does hold it is purely qualitative, and its
application is therefore seriously limited.
In what follows we shall assume (1) that the paramagnetic
susceptibility of a substance composed of particles which do not
vary in complexity with the temperature is inversely proportional
to the absolute temperature, (2) that the diamagnetic suscepti-
bility of a substance composed of such particles is independent of
the temperature.
(2) General Theory.
Consider the solution of a salt in water. The salt will be
ionised to an extent depending upon the concentration. Moreover,
there may be present complex groups of molecules — groups of
water molecules, hydrated ions and hydrated molecules of undis-
sociated salt. (Recent work has shown that in strong solutions
multiply complex salt molecules exist, hydrated to an unknown
extent:}:.)
We shall assume that the groups of associated molecules are
unstable, and that whether they are composed of similar or dis-
similar molecules, the effect of a change of temperature on the
group is of a similar nature in the two cases. This implies that
in the groups composed of dissimilar molecules, the nucleus,
whether it be an ion or a salt molecule, merely acts as a centre
round which a shell of associated molecules is condensed, while the
nature of the forces of association is the same as it is for a group
of similar molecules.
Let there be N types of particles.
* Coinptes Rendus, t. 144, p. 25, 1907.
t Comptes Rendus, t. 151, p. 511, 1910.
X Applebey, Journ. Ghem. Soc, Trans. 11. p. 2000, Oct. 1910.
5—2
68 Mr Oxley, Magnetic Susceptibility with Temperature.
(a) Paramagnetic susceptibility.
Let Up be the number of particles of type p per unit mass of
the solution. Let ^ be the absolute temperature and Gp the
Curie constant per particle of type p. Since the susceptibility of
salt solutions, even of the ferromagnetic elements, is independent
of the intensity of the magnetic field and there is no hysteresis
effect, it is not necessary to take into account the magnetic
influences of the particles on one another.
With these assumptions we may write the specific para-
magnetic susceptibility .
XP=I'^^ (1).
There is considerable evidence that the complex groups of
molecules which are known to exist in solutions vary in com-
position as the temperature changes. Therefore Up is a function
of the temperature.
Write np = n,p.Fp{'^) (2).
n^p is the number of particles of type p which are found in unit
mass of the solution at a temperature ^o given by
Therefore xp=^'^--FA^) (3).
We shall refer to a series of researches by J. J. van Laar for
the purpose of investigating the nature of the function Fp(^).
In his work on the theory of the liquid* and solid states, he takes
into account the process of association, and shows that in the case
of a substance composed of simple and double molecules, the
degree of dissociation of the double molecules which exist at any
temperature ^ is given by the equation
-^-, = (7.^>^.e'^^.e~(^'^^^^''^\(v-6) (4),
where
{p + ^){v-b)={i+^,)R^ in
I
Here ^^ is the degree of dissociation of the double molecules,
<yJR is the change of specific heat when one gramme molecule of
double molecules passes into two gramme molecules of simple
molecules, keeping the volume large and constant. A62 is the
accompanying change in the volume of the molecules, q^ is the
quantity of heat absorbed in this change at the temperature
^ = ; P, V, a, b, R and ^ have the usual interpretation as in
van der Waals' equation.
* Arch. Teyler (2), t. 11, troisieme partie, pp. 235—331, 1909.
Part II. On Aqueous Solutions.
69
For water A62* is negative and the equation (4) is shown
graphically in fig. 1 for this case.
(o^^^ 1 , Simfale molecules.
O^J ^=0"C,p = 0-171
(3^=0-55, ^=1400.
^
00
(3 — , doutle molecules.
Fig. 1.
The portion AB of the curve, which is nearly linear, corre-
sponds to the dissociation of double molecules into simple ones
between the temperatures of 0° C. and 140° C.
The equation corresponding to (4) when the groups are on the
average of jo-fold complexity is shown to bef
/3/
■(5X
where (p + |) (^ _ &) = (1 +^ _ 1 . ^^) . J?^ (5').
We shall assume that the complex groups in solution are on
the average of ^-fold complexity. It will now be shown that
between the temperatures of 0° C. and 100° C. the curves for
all integral values of p are similar to the curve RABS, but lie
everywhere above it, so that they are flatter. Near the critical
temperature /8^
Substituting from (5') in (5) and writing
G' = G.RP-^X
a+p-i.Pp)-Abp
(v-b)
.(6).
* Loc. cit. p. 246.
t Versl. Kon. Ak. v. Wctensch., Amsterdam, Proc, May 27, p. 86, 1911.
X Loc. cit. p. 98.
70 Mr Oxley, Magnetic Susceptibility with Temperature.
As the critical temperature is approached ^8^— >1, therefore
-I p.Abp _qop
-I _ 2.A&2 _q^2
and _ = G'.'^y^ (v - b) . e (^-*).e «^.
J- P2
We shall assume that the amount of heat absorbed in the
change of molecular complexity increases as the complexity
increases, and that, further, the change of specific heat, Rjp, and
the alteration of volume which accompanies association, Abp, also
increase numerically with the degree of complexity. Referring to
the numerical values* of {v — b), q^^, R%, A62, it is seen that the
ratio
i-^:>i («'v|
on these assumptions. '
Therefore near the critical temperature I3p > ySj.
From (6), differentiating with respect to ^, we find i
dBp p(l-/g/)./3/-^ + 2;8/+^
8^- {l-^pj
= C . jp . ^Vp-i . (v - by-^ . e- (1+^-1 • ^^' ^''^ . e -^^
V — b ^ ^ ' (f^
neglecting the change in the value of A6p due to an infinitesimal
change in '^.
If ^ = 0, Tp^Jit^^'"^ = '^M'^P - D^ 2'
and therefore ^^4=1"^- (7).
Again
p (l+(j3-l).fa) A&p _gop
1-ySy
= C'.'^yp{v-b)P-Ke ^-^ .e ^^.
* (v -h)>l, qQ2 = 5000 gra. eals., JSa-=1380 gm. calories for the critical temp.
A62= - 8"26 c.c. if t?=:18'0 c.c. These values are taken from the paper referred to
at the foot of p. 68.
t S-;i/ is the temperature at which the association is greatest.
X It should be noted that ^m is not independent of p, for q^p and Ryp are each
functions of the molecular complexity. Hence the additional remarks concerning
the positions of the minima.
Part II. On Aqueous Solutions.
71
Now /3p is a fraction, and as p —> co the R.H.s. — > oo , on the
assumptions made above, because v >b, Ahp < 0.
Therefore /3p — > 1 as jl) — > oo , for all values of '^.
Hence for p >2 the curves lie between the curve for p = 2 and
the asymptote /3p = 1. They have each one minimum value, viz.
that given by the relation (7). The portions of the curves which
lie between the ordinates corresponding to 0° C. and 100° C. are
very approximately linear. The exact positions of the minima for
the curves of higher values of p do not matter, at least so far as
the first approximation only is desired, since we have proved
that the curvature of such curves is very small. On the other
hand the principle of continuity demands that for the lower values
of p the positions of the minima of ^p shall approximate with
decreasing p to the position of the minimum for p = 2.
The curves must be of the form shown in fiof. 2.
, =1, Siw>le TDolecules.
oo
A-^ = 0, ;^-fold molecules.
Fig. 2.
For all groups, the rate at which dissociation takes place over
the region 0° G. to lJfi° G. is very approximately uniform. It is to
be noted here that if we were to supercool or to superheat the
solution to a sufficient degree, this step, in taking the curves as
approximately linear, would no longer be justifiable, and the
following reasoning holds only for solutions between the tempe-
ratures 273° and 400° absolute. It is conceivable that outside
this range of temperature the formulae which will hereafter be
deduced may require to be considerably modified.
We may therefore write
Fp{^) = ,jip^-vp.^'
.(8)
* Note added. M. M. Garver, Journ. Phys. Chem. Nov. 1912, p. 669. The
experimental relation between polymerization and temperature is shown to be
approximately linear.
72 Mr Oxley, Magnetic Susceptibility with Temperature.
I
for all values of p (integral) where /*p and Vp are independent of '
the temperature.
Equation (3) now becomes H
p=l 'J p=l
_ y 'top . fJ^p.yjp , v „ P -,,
p ' i^P'
Write '^7iQp.Cp./Xp= A (9),
Xnop. Gp.Vp = B' (10).
Then %p = ^+5' (11),
where A and B' are independent of ^.
(b) Diamagnetic susceptibility.
The specific diamagnetic susceptibility of a solution may be
written
XD = lj. I Tip.hMp (12),
where ZMp is the resultant magnetic moment produced in particles
of type p, per particle, by the application of a magnetic field of
intensity H. As before Up is a linear function of the temperature.
Writing rip = n^pFp (^) = n^p (fip + Vp . ^),
1 ^
we find %D = Tr • S nop. BMp . {jXp + z^^ . ^)
\ N ^ ^
= ^. 2 Wop . SMp . /jip + -fr- 2 ^loiJ • ^^p • Vp •
u p-i n p=i
Write
jj-.Xriop. BMp . fj,p = B", ^ . 2 Mop . Sifp .Vp = G.
Therefore xb = B" + (^,
where B" and G are independent of ^.
The specific susceptibility of the solution may be written
= ^+5+a^ (13),
where B = B' + B" (14).
Part 11. On Aqueous Solutions. *JS
(3) Application of the Equation (13) to Aqueous Solutions
of Iron Salts.
It is only in the cases of strongly magnetic solutions, such as
those of salts of the ferromagnetic elements, that a satisfactory test
of the applicability of the formula (13) can be obtained. For
other salt solutions the value of the susceptibility is little different
from that of water, and in measuring such small differences as
those produced by change of temperature the errors are liable to
be large. On the other hand, in the case of strong solutions of
the salts of ferromagnetic elements, the paramagnetic suscepti-
bility is so great compared with the variation of the diamagnetic
susceptibility with the temperature that it is permissible, at least
for the strong solutions, to neglect the latter. The dependence of
diamagnetism on the temperature is expressed by the term C^ in
the equation (13), and this term will accordingly be neglected.
The diamagnetic susceptibility, in so far as it does not vary with
the temperature, is included in the constant B. The expression
connecting the susceptibility and the temperature may now be
written
X=i + B (15),
where B = (Z nop . Cp . Vp) + (rj- -^ ^op • ^^p • H'pj •
The relation (15) is hyperbolic. If the groups do not break
up with change of temperature, all the factors Vp in the first term
of the expression for B are zero, and as in this case the second
term of B represents the diamagnetic susceptibility (p const.) the
above relation (15) reduces to the unmodified Curie-Langevin
form. If the groups do break up with the change of temperature
then the first term in the expression for B will not be zero, and
the value of B may be positive or negative according as
2wo„ . C-o 'V,
■p <
-^ 2 nap . hMp . ixp
That the curves connecting susceptibility with temperature are
approximately hjrperbolae, for solutions of iron salts, can be seen
from fig. 3. This diagram is reproduced through the kindness of
Prof. J. S. Townsend*. As the numerical data corresponding to
the curves were not published, it is impossible to test equation
(15) by these observations, but from the trend of the curves it
appears that an equation of this form would be suitable for the
representation of Prof. Townsend's results.
* Phil. Trans. Boy. Soc, Vol. 187, A. p. 547, 1896.
74 Mr Oxley, Magnetic Susceptibility with Temperature.
The same remark applies to the representation of the results
of Jaeger and Meyer*, although the curvature in their diagrams
appears smaller.
5 15
Temperature
Fig. 3.
(1) Ferric Chloride -086 gm. Iron per c.cm. (see note p. 79). (2) Ferrous
Chloride. (3) Ferric Sulphate. (4) Alcoholic solution of Ferric Chloride.
In the following tables the first column represents the con-
centration of the solutions, used by Jaeger and Meyer; the
concentrations are expressed in gramme molecules per litre. The
second column gives the absolute temperature. In the third and
fourth columns the values of the constants A and B are given for
each concentration as worked out from the experimental values of
Y given in column 5. Columns 6 and 7 show the agreement
between the calculated and experimental values. For the calcu-
lations in column 6 the relation
X
+ B
is taken, for those in column 7 the empirical relation used by
Townsend and Jaeger and Meyer is taken (% = %o (1 — e • t)).
An examination of the numbers given in columns 4, 5, 6 and 7
brings a considerable amount of information to light. It will be
* Sitz. d. Akad. in Wien, cvi. II a., p. 594, 1897.
Paj't II. On Aqueous Solutions. 75
observed that the representation of the susceptibility by the
relation
holds good so long as we are dealing with concentrated solutions
and is preferable to the linear relation
% = %o(l-e.O-
But for weak solutions the linear relation is more satisfactory
than the hyperbolic one. We see, on referring to p. 73, that this
is precisely what would be expected. The approximate form
has been used instead of the accurate form
X = ^ + B + G^
for the representation ; and the term G^, which deals with the
variation of the diamagnetic susceptibility with the temperature,
has been neglected. So long as we are dealing with strong
solutions the variation of the diamagnetic susceptibility with the
temperature is insignificant compared with the large value of the
paramagnetic susceptibility, but for weak solutions this is not
the case, and it is necessary to take into account the term C^.
The figures show that for the weaker solutions the calculated
value of % on the assumption that % = ^ + 5 is in general lower
than that calculated from the equation % = %o (1 — e • 0' ^"^^ the
experimental value lies between the two calculated values.
Consider the variation of the susceptibility of water with the
temperature. Although different observers have obtained different
values for the absolute susceptibility of water, they are all in
agreement that the susceptibility decreases as the temperature
increases. This is equivalent to saying that water becomes
more paramagnetic as the temperature increases. We shall take
the expression
Xw = - 0-750 (1 - 000164i) 10-«
as representing the variation of the susceptibility of water with
the temperature.
%wo
= 1-2.
X^ioo 1-0-164
Xwm is 20 7o less than ;i^o ■ The maximum correction to be
applied to the figure in column 6 in order to take this variation
76
Mr Oxley, Magnetic Susceptibility with
Temperature.
of the susceptibility of water into account :
s 007 X 10-^ and
corresponds to a temperature of 50° C. On either side of 50° C.
the correction falls off and is zero at 0°C. and 100° C. due to the
fact that we have made the curve pass through the extreme
points. When the corrections are made there
; is a better agree-
Ferric Chloride Solutions.
Concn.
Tempr.
^.106
B.106
X (Exp.)
X (Gale.)
= Aj^ + B
X (Gale.)
= Xo(l-f«)
273+ 1-7
44-23 X 10-«
_
_
3-62
11-4
1100-5
+ 4-18
42-68
42-86
43-13
53-7
37-98
37-85
38-35
81-9
35-18
—
—
273+ 21
29-27
_
_
12-2
28-56 •
28-50
28-66
2-32
32-2
5986-3
+ 7-51
27-27
27-12
27-46
50-1
26-15
26-04
26-38
70-1
24-85
24-96
25-07
88-7
24-06
—
—
273+ 3-1
22-41
_
16-8
21-66
21-56
21-73
1-76
34-1
4930-5
+ 4-55
20-66
20-60
20-88
53-0
19-41
19-67
19-95
71-8
18-43
18-85
19-02
89-6
18-15
—
—
273+ 3-6
16-11
_
15-0
15-46
15-59
15-69
1-31
35-1
3654-8
+ 2-90
14-93
14-76
14-98
52-0
14-14
14-15
14-34
70-9
13-69
13-53
13-65
89-1
12-99
—
—
273+ 2-4
9-58
_
_
12-0
9-25
9-23
9-31
0-79
36-5
2875-3
-0-86
8-50
8-44
8-61
54-4
7-90
7-92
8-10
71-6
7-66
7-49
7-60
91-4
7-03
—
■ —
273 + 13-0
3-87
.
0-40
55-5
1190-4
-0-29
3-43
3-33
3-10
80-0
3-08
—
—
Part II. On Aqueous Solutions.
Ferrous Sulphate Solutions.
77
1
poncn.
Tempr.
4.10«
B.106
X (Exp.)
X (Calc.)
X (Calc.)
= Xo(l-fO
1-09
273+ 2-3
43-9
80-3
3566-1
+ 1-286
14-24 X 10-«
12-57
11-38
12-54
12-71
0-88
273+ 3-2
15-0
54-0
80-8
26310
+ 0-90
10-43
10-04
8-93
8-34
10-037
8-95
10-11
9-06
0-53
273+ 2-4
44-2
80-1
1849-2
-0-637
6-08
5-28
4-60
5-195
5-285
0-28
273+ 2-9
44-8
81-1
648-5
+ 0-305
2-66
2-38
2-14
2-35
2-38
Ferric Nitrate Solutions.
\
Concn.
Tempr.
^.108
B.10«
X (Exp.)
x(Calc.)
= AI'it + B
X (Calc.)
= Xo(l-^«)
0-94
273+ 3-2
44-9
83-3
5934-9
-0-161
21-28 xlO-«
18-70
16-46
18-51
18-8
0-48
273+ 2-0
44-3
83-7
2941-5
-0-226
10-47
9-14
8-02
9-044
9-20
ment between the numbers in the sixth column and the
experimental numbers, particularly with reference to the weaker
solutions. There are a few exceptions to this statement, chief
among which are the susceptibilities of a 1-76 normal solution
of ferric chloride at temperatures of 53° C. and 71-8° C. These
values are too high, but they are not so high as the corresponding
values deduced from the linear relation, and it is possible that the
irregularity is due to experimental errors in the measurement of
temperature. . .
It is to be observed that the linear relation takes the variation
of the diamagnetic susceptibility of water into account, and it is
78 ilfr Oxley, Magnetic Susceptibility with Temperature.
for this reason that the linear relation is more satisfactory for
low concentrations than for high concentrations.
If we take the complete expression deduced by the above theory
X-^ + B + G^
then we have a relation between the susceptibility and the
absolute temperature which holds for all concentrations, the
agreement, with the exception of the two values cited above,
being such as to give values within the limits of experimental
error. Jaeger and Meyer do not state the amount of their
experimental error, but it is difficult to get nearer to the true
value than ^ "/^ for the stronger solutions and 1 °/^ for the
weaker solutions, especially when working at the higher tem-
peratures.
The nature of the constant B is of greater importance than a
mere representation of numerical values. It will be seen that this
quantity, which is constant for any particular concentration for a
range of temperature from 0° C. to 80° C, but varies as the
concentration varies, throws some light on the variation of the
constitution of the liquid state with change of temperature.
The expression obtained for B (p. 73) is
B = (Z nop. Op . vp) + I -^ S Wop . hMp. Hp\.
This quantity does not vary erratically with the concentration, and
it has a higher value for the higher concentrations than it has for
the lower ones. Any factor of the type n^p . fip is essentially
positive, and as hMp is negative for anj^ particle of type p, the
second term of B must necessarily be negative. Further, we know
that over a wide range of concentration there is no appreciable
change of diamagnetic susceptibility due to the variation of com-
plexity of the molecular groups*, and therefore we may regard
the second term in the expression for 5 as a negative term which
admits of a negligibly small variation only, as we pass from one
concentration to another. This term has a value which is very
little different from the value of the susceptibility of pure water
(approx. — 7*0 X lO"'')-
The first term may be positive or negative. Any factor of the
type fiQpCp is necessarily positive, but Vp may be positive or
negative — positive if the number of particles of type p is increasing
and negative if the number is decreasing as the temperature is
raised. As we have shown that the second term is nearly constant
and lias a small negative value we attribute the large positive
values of B, for the higher concentrations, to particular values
* Townsend, Phil. Trans. Roy. Soc, Vol. 187, A. p. 543, 1896.
Part II. On Aqueous Solutions. 79
of Vp. For any concentration a definite selection of types of
particles exists in the solution and the sum total of the products
of the type ??opCp (const.) into the rate at which this particular
type associates or dissociates as the temperature is varied is
represented l)y the term B. Therefore variation in the value of
B implies variation of the stability of the molecular complexes.
For a 2'23 normal solution of ferric chloride the constant B
has a value which is 29% ^f the value of the susceptibility at
50° C. (the mean temperature). The variation of the suscepti-
bility with the temperature is well represented for this
concentration by the hyperbolic relation*
% = ^ + 5,
and it is remarkable that such a large positive quantity (the value
of B is 7'51 X 10~**, that of the susceptibility at 50° C. is
26*15 X 10~®) which is independent of the temperature should
enter into the expression for the variation of paramagnetic
susceptibility with the temperature.
For solutions of ferric chloride of concentration 3'62 normal
and 1"76 normal, the values of B are nearly equal, but are much
less than the value for a 2'23 normal solution. It appears there-
fore that a solution of ferric chloride of this concentration has a
unique constitution, and it is interesting to see if such a solution
behaves abnormally with regard to other physical properties.
(4) Measurements of the Viscosity of Ferric Chloride Solutions.
The following experiments on the variation of viscosity of four
solutions of ferric chloride with the temperature were carried out
to investigate the complexity of strong solutions of this salt and
to examine if any irregularity is shown by a 2"2 normal solution.
Experiments have been made by C. Cheneveau-j* and R. F.
D'Arcy j on the viscosity of strong solutions of sulphuric acid in
water, and they obtained evidence for the existence of complex
groups of molecules over certain ranges of concentration.
The apparatus used in the following experiments is a modifi-
cation of that used by D'Arcy and is shown in fig. 4. The ferric
chloride solution was drawn into the bulb b from the receiver B,
and when it had acquired the temperature of the water bath
inside the calorimeter C, it was driven out through the capillary
tube c" back to the receiver R under a pressure head of water
* It should be remarked that the solution referred to contains almost exactly
the same quantity of iron per c.cm. as does the solution used by Townsend, and his
results are shown graphically, fig. 3, curve 1.
t Comptes Rendus, t. clv., No. 2, 1912, p. 154.
+ PUl. Mag. Vol. xxviii., Ser. 5, 1889, p. 221.
80 Mr Oxley, Magnetic Susceptibility with Temperature.
supplied by the large bottles A and B. The pressure head was
registered in the manometer M. The time required for the ferric
chloride meniscus to fall from the mark s to the mark s' was
taken by means of a stop-watch. Care was taken to ensure that
the ferric chloride solution had acquired the temperature of the
bath before a reading was obtained, and to secure this the bulb
was filled in the following way. The solution was drawn into the
bulb till the latter was about half full, and the U-tube was shaken
by sliding the inlet and outlet tubes backwards and forwards
through the holes in the side of the calorimeter. Meanwhile the
liquid in the bath was kept well stirred. More liquid was drawn
into the bulb and the shaking repeated. Finally the bulb was
filled, and since the solution last admitted filled the capillary and
part of the outlet tube, it soon acquired the temperature of the
Fig. 4.
bath. An interval of about twenty minutes was usually allowed
for the solution to acquire the temperature of the bath, but for the
higher temperatures a much smaller interval had to suffice, on
account of radiation, while at temperatures near that of the room
an hour was frequently given*.
The method of taking an observation was as follows. The end
of the outlet tube was kept below the level of the solution in R
and the three-way cock T turned so as to shut off h and connect
B with M. The pressure head was now adjusted to a certain
value, approximately the same for all the observations. T was
turned so as to connect B, M and 6, R was lowered and the time
taken as the meniscus passed the mark s.
The following observations were made :
* The small bubbles of air which were
removed before an observation was made.
always formed in the outlet tube were
Part II. On Aqueous Solutions.
I. Water.
81
Pressure
Mean
Time
Corrected Time
(mm. water)
temperature
(seconds)
(P. 85 mm.)
86-5
89-0
84-0
85-5
86-2
80-3
87-0
88-2
84-9
78-0
88-25
88-25
86-4
73-5
90-75
92:4
85-6
71-6
100-0
100-7
86-0
66-6
97-0
98-2
86-2
55-8
107-0
108-8
86-5
51-7
113-5
115-7
86-4
46-5
116-75
119-0
1 85-8
38-9
133-0
134-2
85-8
31-3
146-5
147-9
1 86-0
18-2
185-5
187-75
i 86-2
18-0
187-0
188-5
85-1
7-55
246-5
246-5
84-9
4-15
274-0
274-0
84-9
0-4
307-0
307-0
85'0
0-4
307-5
307-5
1
II. 1'3 Normal Solution of Ferric Chloride.
Pressure
Mean
Time
Corrected Time
(mm. water)
temperature
(seconds)
(P. 85 mm.)
84-7
74-5
130-0
129-4
84-2
66-3
146-25
144-6
84-8
58-1
163-0
163-0
84-0
48-1
191-5
190-6
84-6
39-1
225-0
224-0
84-8
31-1
266-25
265-6
85-0
26-4
300-0
300-0
84-9
26-0
294-25
294-25
84-6
19-6
341-75
340-2
85-4
19-6
336-5
338-9
85-7
14-8
378-6
381-5
83-3
14-6
382-0
376-0
85-4
9 75
460-0
463-0
85-6
8-55
466-5
469-5
85-6
7-5
477-5
481-0
85-5
6-0
519-5
522-5
84-7
0-2
603-0
601-0
84-8
0-2
609-0
607-6
VOL. XVir. PT. I.
82 Mr Oxley, Magnetic Susceptihility with Temperature.
III. 2-0 Normal Solution of Ferric Chloride.
Pressure
Mean
Time
1
Corrected Time
(mm. water)
temperature
(seconds)
(P. 85 mm.)
85-8
84-6
133-25
134-7
85-5
76-8
147-25
148-0
85-9
70-3
162-25
1640
85-7
69-7
161-0
162-4
84-9
64-8
181-0
181-0
84-3
61-5
200-0
198 3
85
54-5
213-0
213-0
84-4
46-0
258-5
256-7
85-6
44-5
250-75
252-6
84-3
36-2
317-5
314-7
85-6
33-6
325-0
327-4
85-8
27-45
377-0
380-6
85-0
19-2
488-0
488-0
85-0
18-4
479-0
479
85-8
18-2
484-25
489'1
85-7
14-2
568-5
573-5
86-4
12-3
625-0
635-7
86-0
11-6
633-5
637 5
86-0
1105
647-5
651-5
85-0
8-7
704-0
704-0
86-2
8-4
710-0
718-4
85-0
7-8
742-0
742-0
85-0
6-4
742-0
742-0
85-1
4-4
795-0
794-0
84-9
0-2
900-0
9020
84-6
0-2
900-0
896-0
On account of the deliquescent nature of ferric chloride the
solutions were submitted to a chemical analysis (the permanganate
method was used) to determine their concentrations. The above
observations have been plotted and are shown in fig. 5. The
ordinates are the times given in the last column of the tables —
they are proportional to the viscosities — and the abscissae are the
temperatures in degrees centigrade.
On an examination of these curves it will be observed that the
curves III and IV show irregularities with respect to the curves I,
II and V, which are very nearly hyperbolae. Ill and IV are
parallel over a short range of temperature in the neighbourhood
of 15° C. The dotted line shows the position of the hyperbola
which passes through the end points of the curve — the position of
the points A, and the direction of the curve at the highest
Part II. On Aqueous Solutions.
IV. 2*6 No7nnal Solution of Ferric Chloride.
83
Pressure
Mean
Time
Corrected Time
(mm. water)
temperature
(seconds)
(P. 85 mm.)
84-3
78-0
183-0
181-4
83-9
67-5
216-75
214-25
84-8
58-8
256-5
256-0
84-9
49-7
294-0
294-0
85-6
432
341-0
343-2
83-4
43-0
361-0
355-0
84-5
37-5
408-0
405-5
84-1
25-9
536-5
531-0
86-1
22-9
585-5
592-5
85-0
20-5
643-0
643-0
85-0
19-5
667-0
667-0
84-6
18-0
707-0
7030
83-4
16-9
747-5
733-5
84-8
15-9
7350
733-0
85-0
15-25
740-0
740-0
85-5
15-0
730-5
734-8
85-9
8-5
925-0
.934-0
84-1
7-6
986-0
9760
84-9
0-4
1290-0
1289-0
84-7
0-2
1350-0
1345-0
V. o"22 Normal Solution of Ferric Chloride.
Pressure
Mean
Time
Corrected Time
(mm. water)
temperature
(seconds)
(P. 85 mm.)
86-2
84-9
179-5
181-9
86-1
75-5
209-0
211-7
86-1
67-8
239-5
242-5
86-2
59-1
284-0
288
86-1
47-4
372-5
377-3
86-0
40-4
441-0
446-0
86-3
33-4
527-5
535-3
86-1
27-4
631-0
639-0
85-0
21-2
792-0
792-0
85-4
17-0
924-0
930-0
86-0
17-0
906-5
916-5
85-0
3-75
1498-0
1498-0
86-5
0-45
1724-0
1739-0
6—2
84 Mr Oxley, Magnetic Susceptibility with Temperature.
15 00
1400
1100
1000
10 20 30
Temperature
40 50
Fig. 5.
60 70 80 90
Part II. On Aqueous Solutions.
85
temperature are accurately known. The deviation is admittedly
small, but it is considerably greater than the error of observation.
The deviation of the curve IV from a mean hyperbola is smaller
than that of curve III, and although the points obtained for
temperatures between 15" C. and 25° C. indicate an irregularity,
yet on account of the absence of points in the neighbourhood of
12° C. it is not considered advisable to attach importance to it.
The nature of the irregularities mentioned above is brought
out more clearly in fig. 6, where the ordinates represent the rate
of variation of viscosity with the temperature and the abscissae
are temperatures in degrees centigrade. In the following table
columns 2, 3, 4, 5 and 6 give the abscissae of those points of the
curves I, II, III, IV and V, where the slope has the value given in
column 1.
d-n
^ of
^of
3- of
3- of
S»-of
d^
curve I
curve II
curve III
curve IV
curve V
5-00
3-0
4-00
—
—
7-2 .
13-5
3-00
12-0
10-2
20-3
2-75
16-5
13-0
21-5
2-25
15-6
13-2
23-0
2-00
17-0
15-2 A 22-2
26-5
1-80
2-5
17-5
246
29-25
1-60
6-75
18-4
27-0
32-0
1-40
10-5
20-0
28-7
34-6
1-20
130
22-75
31-5
38-4
1-00
1-5
16-5
27-0
35-5
43-7
0-83
5-0
20-0
31-0
39-75
50-0
0-71
7-5
23-5
35-6
46
54-5
625
9-5
26-5
39-2
49-7
59-25
0-55
10-5
29-1
43-4
53-75
62-6
0-50
12-6
32-5
45-9
56-7
64-4
0-40
18-3
40-0
51-2
66-0
70-5
0-30
26-5
49-5
61-2
72-7
80-0
0-20
37-5
69-5
74-5
—
—
0-10
55-7
—
'^
These values were measured a second time, and a good agree-
ment was found in the two cases.
No importance is attached to the cutting of the curves IIF and
IV', since that depends upon the actual shape of the curve IV,
fig. '5, in the neighbourhood of 15" C. where the number of points
is not sufficient to enable an accurate value of the gradient to be
86 Mr Oxley, Magnetic Susceptibility with Temperature.
measured. The curves I', IT and V, which correspond to I, II and
V in fig. 5, show that the value of — ^ steadily increases as ^
decreases. This is not so with the curve IIT. At the higher
dr]
temperatures the value of —
is low, and as a temperature
—
Fig. 6.
of 20° C. is approached it assumes a more normal value. Below
dr]
20° C. the value of
a^
iir
is abnormally high, and at 15° C it
has a value equal to that of the strongest solution at a slightly
(4°) higher temperature. For temperatures lower than 10° C. the
dr)
falls off.
iir
abnormally high value of —
The general shape of the curve III, fig. 5, is evidence for the
existence of complex groups of particles in the solution at the
Part li. On Aqueous Sohitions. 8*7
concentration 2'0 normal. At the low temperatures a dissociation
of the complex particles, formed of a salt molecule or ion and its
associated water molecules, takes place. At the higher tempera-
tures the gradual recovery of the curve is probably due to the
formation of a new type of complex— a solution of ferric oxy-
chloride or ferric hydroxide in the excess of ferric chloride. All
the four solutions had sufficiently high concentrations to prevent
the formation of a precipitate at the higher temperatures.
It is not intended that this part of the investigation shall
establish a quantitative relation between the complexity of mole-
cular structure and the temperature. Indeed, it has been shown
by Cheneveau* that the viscosity and refractivity methods used
for the determination of molecular complexity in the liquid state
do not give identical results, although each indicates the presence
of groups composed of solute and solvent particles. The present
viscosity measurements have been made with the object of verifying
the prediction of the earlier part of the paper, that the high value
of the constant B, in the representation of the magnetic suscepti-
bility of a 2-23 normal solution of ferric chloride as a function of
the temperature, may be connected with an abnormal variation
of the viscosity of the solution. Since in a solution there are at
least several types of particles, the complexity of some changing
with the temperature, it seems impossible in the present state of
our knowledge of the viscosity of liquids to derive from it quanti-
tative information as to the nature of the relation between
molecular complexity and temperature. For this purpose use has
been made of the researches of van Laar who has considered the
general theory of association in the solid and liquid states.
(5) The Lowering of the Freezing Point of Solutions.
There is another interesting point in connection with the value
of the constant B for a 2-0 normal solution of ferric chloride. It
has been shown that such a solution shows an abnormal value of
the molecular lowering of the freezing pointf. Since , the latter
quantity is directly connected with the constitution of the groups
of solvent and solute particles, the molecular lowering bemg
smaller the greater the complexity of the groups of particles, the
abnormally low value of the molecular lowering produced by a 2-0
normal solution of ferric chloride indicates that the groups of
particles are abnormally complex at this concentration. These
* Comptes Rendus, t. clv., No. 2, 1912, p. 154.
t Jones and Getman, Zeits. f. Phys. Chem., xlix. 1904, pp. 426—433.
Note. The curve in fig. 7 of the research of Jones and Getman, relating to
ferric chloride solutions, is drawn inaccurately. Prof. H. C. Jones has knidly
informed me that the tabulated data are correct and an n-regularity still exists tor
a concentration 2-0 normal, when the error of representation has been allovyed tor.
88 Mr Oxley, Magnetic Susceptibility with Temperature.
groups are unstable and rapidly break up as the temperature is
increased. Hence Vp is large, and it is reasonable to expect a high
value of the constant B.
Another property of the constant B is that it never acquires a
large negative value, Values of B have been obtained for solutions
of the sulphates, chlorides and nitrates of all the ferromagnetic
elements and the largest negative value found is 086 x 10"'' for a
079 normal solution of ferric chloride. This value is only 12%
greater than the value of the diamagnetic susceptibility of pure
water. The positive values, on the other hand, have been shown
to range from zero to 7-5 x 10-« a quantity which is ten times as
great as the numerical value of the susceptibility of water. The
preponderance of large positive values of B is to be expected if
the curve of fig. 1 represents the change of molecular complexity
with change of temperature.
Conclusion.
In this paper and in an earlier investigation ("The Variation
of Magnetic Susceptibility with Temperature," Proc. Gamh. Phil.
Soc.^ Vol. XVI. p. 486) an attempt has been made to represent the
variation of magnetic susceptibility with the temperature, taking
into consideration the formation of complex aggregations of mole-
cules and the effect such aggregations have in modifying the
magnetic properties. It is believed that if due account be taken
of the characteristic properties of substances, the work of du Bois
and Honda does not prove that the foundations of the Curie-
Langevin theory are unsound.
Hitherto, the relation representing the variation of the
susceptibility of solutions with the temperature has been an
empirical one and of the simplest form — linear. Assuming the
truth of the Curie-Langevin laws for groups of particles whose
complexity does not vary with the temperature, the para-
magnetism of any substance will follow a simple hyperbolic law
X^^ ^^^ ^^^ diamagnetism will be constant as the temperature
^ varies. If the groups vary in complexity as the temperature
changes, these laws will be modified in a manner depending on
the characteristic changes of constitution possessed by the sub-
stance.
For the general case of aqueous solutions, treated in the present
paper, the rate of variation of the molecular complexity with the
temperature has been shown to be approximately linear. The
modified relations have been applied to represent the variation of
the susceptibilities of solutions of ferric chloride, ferrous sulphate
\
Part IT. On Aqueous Solutions. 89
and ferric nitrate. Taking into account the variation of dia-
magnetic susceptibility with temperature, it has been shown that
the numerical representation of the results of Jaeger and Meyer is
satisfactory, and, with the exception of two cases, specially referred
to, the relation proposed represents the observations to within the
limits of experimental error. A solution of ferric chloride, 22^
normal, whose susceptibility expressed by the relation % = -^+-S,
appeared to be due to an abnormal molecular constitution, was
examined in order to see if its viscosity varied abnormally as the
temperature was changed. Evidence of such an abnormal variation
has been obtained. The abnormal molecular constitution of such
a solution is further supported by determinations of the molecular
lowering of the freezing point.
The general theory developed in this paper includes the special
case of water. The variation of molecular association in water
with change of temperature affords a ready means of accounting
for the variation of its diamagnetic susceptibility as the tempe-
rature varies, but we are not justified in taking a linear relation
between the susceptibility and the temperature since we have no
proof that the molecules of water do not possess a paramagnetic
property smaller than the diamagnetic susceptibility and obscured
by it at ordinary temperatures. Unless we suppose that the
association modifies the magnetic properties of the water mole-
cules, it is difficult to see how the diamagnetic susceptibility of
water decreases as the temperature increases.
Note added Jan. 20, 1913.
The work of Dr G. Piaggesi {II Nuovo Gimento, Ser. V, T. IV,
1902, p. 247) has, until now, escaped my notice. Piaggesi shows
that for a given concentration of an aqueous solution of ferric
chloride, ferrous sulphate, ferric nitrate, manganese chloride,
manganese sulphate, manganese nitrate, cobalt chloride and
nickel chloride, the product of susceptibility and absolute tem-
perature is nearly constant.
90 Mr Watson, Some Experivients on the
Some Experiments on the Electrical Discharge in Helium and
Neon. By Herbert Edmeston Watson, B.Sc. (Lond.), 1851
Exhibition Scholar, Trinity College, Cambridge. (Communicated
by Professor Sir J. J. Thomson.)
{Read 11 November 1912.]
The investigation which is about to be described had as its
original object the determination of the cathode fall and the spark
potential (or minimum potential necessary to produce a spark
between two electrodes) in all the inactive gases. Unfortunately,
before it could be completed, the author was obliged to leave
England, but as several results of interest had already been
obtained, it seemed advisable to give a brief account of them.
The spark potential in helium has already been carefully
investigated by the Hon. R. J. Strutt {Phil. Trans. A. 1900, 193,
p. 379). His experiments differ, however, from those about to be
described, in that, in the former, the electrodes were brass plates
0*755 mm, apart, a Wimshurst machine was used for producing
the required potential difference, mercury vapour was allowed
access to the sparking tube, and no allowance seems to have been
made for the lag which is a very pronounced feature of the
phenomenon under consideration. His results will be referred to
later.
In 1904, Ritter {Ann. d. Physik, IV. 1904, 14, p. 118) examined
the discharge in helium between a steel plate and sphere for
pressures between 100 mm. and one atmosphere. The gas admit-
tedly contained argon, and probably, judging by the results, other
impurities as well, although it is difficult to compare experiments
carried out under widely differing circumstances. In any case,
the investigation has no bearing on the present work.
Bouty {Ann. Ghim. Phys. 1911, 23, p. 5) has made numerous
experiments on the cohesion dielectrique or rate of change of the
spark potential with pressure, for helium and neon, and has
recognised the need for the extreme purity of the gases under
examination. His results are of great interest and will be men-
tioned later.
Apparatus.
The annexed diagram shows the general arrangement of the
apparatus used. The current was obtained from a battery B of
small cells giving a maximum e.m.f. of 1000 volts, 20 cells B'
connected with the others in series were also connected with the
Electrical Discharge in Helium and Neon.
91
terminals of a 2000 ohm resistance G, contact with which could
be made at 100 different points by a sliding arm D. The current
was regulated by an adjustable water resistance A.
B
■m^y
I uj
:>Ch
B
Fig. 1.
The discharge tube F was made from a piece of wide glass
tubing 5-5 cm, in diameter, ground flat at the ends, and closed
with sealing-wax. Needless to say it was perfectly air-tight. It
contained three plane aluminium electrodes tightly fitting the
tube, and held apart, at the edges by frames of very thin glass rod
constructed so that the plates were exactly \b and 3 cm. away
from each other. They were held in position by a spring at one
end. An aperture for the admission of gas and the leads to the
centre electrode, which were soldered to its edge, was drilled
opposite the latter, and covered with a dome of glass ground to fit
the tube.
The electrodes were very carefully cleaned with glass paper,
and the middle one used as cathode. The two others could be
made the anode in turn by means of the tipping key H, the one
not in use being simultaneously connected to the cathode, which
was itself at a potential only a few volts removed from that of the
earth, E.
An accurate Weston voltmeter G was connected between the
electrodes, and since its resistance was comparable with that of
the liquid resistance A, the potential difference across the tube
could be varied by altering A. The movement of D afforded a
fine adjustment. A' telephone was included in the circuit to
enable any intermittency in the discharge to be detected.
92 Mr Watsov, Some Experiments on the
In making an experiment upon the spark potential, the
voltage was increased slowly until the discharge passed through
the tube, and the potential difference noted. This was found to
be independent of the current passing when once established, a
fact which was determined by using different voltages on the
main battery B, and consequently different values of A ; the fact
that the voltmeter was in parallel with the tube was also found to
be without influence, for the spark potential was unchanged if the
voltmeter was removed and the number of cells in the battery
reduced until there were only sufficient to give the required
voltage.
As noticed by other observers, there was a distinct lag in the
lighting up of the tube after the potential difference was applied.
This was most marked in the case of neon, and was frequently a
minute in duration. In the present experiments, which were
carried out in an indifferently lighted room, no external stimulus
was given to start the discharge, but the potential difference was
applied for three minutes, and if no discharge occurred in this
time, it was considered that the sparking potential was not
attained. This method gave very consistent results, the difference
between successive values at the same pressure being nearly
always less than one volt, and hardly noticeable on the voltmeter.
It could be detected, however, by the variation in the position of
the sliding contact D. Three observations were made at each
pressure for each side of the cathode. It was rather remarkable
that after a change of pressure, the first value of the spark
potential was always two or three volts below those obtained
subsequently. The figures given below refer to the steady values,
as the first discharge potential was uncertain.
The gases were those used in a previous investigation on
electrical discharge {Roy. Soc. Proc. A. 1912, 86, p. 168), and
were very carefully purified before every experiment. They were
first mixed with oxygen, and phosphorus ignited in the mixture
to remove hydrogen, a very convenient method when dealing with
small quantities of gas. The residue was then transferred to a
tube containing charcoal immersed in liquid air, and allowed to
stand for at least half an hour, the gas in the connecting tubes
being pumped away. After this treatment the spectrum is
perfectly clear from foreign lines, except those of mercury, at
100 mm. pressure. The gas was admitted directly from the
charcoal tube to the discharge tube, passing however through a U
tube immersed in liquid air on the way in order to remove
mercury vapour. There is little doubt that mercury vapour
exerts a considerable influence on the spark potential, especially
when aluminium electrodes are used, and for this reason the
discharge tube was shut off from the rest of the apparatus, and
Electrical Discharge in Helium and Neon. 93
no gas of any kind ever admitted except after freezing in liquid
air.
Before starting the experiments some helium was admitted to
the tube and a current run for some weeks, the gas being
frequently renewed until no change in its spectrum was observed.
As observed by Strutt {loc. cit), the minimum spark potential
is a very delicate criterion of the purity of the gas. It was also
found in the present experiments that the minimum voltage
necessarj^ to maintain the current when once started (a quantity
which will be discussed later) was likewise very sensitive to the
presence of impurities, and as this was constant over a wide range
of pressure it afforded a more convenient method of detecting
their presence.
Some of the results obtained are given below, p is the pressure
in mm. of mercury (measured by a McLeod gauge below 9 mm.),
V the spark potential between the electrodes 1'5 cm. apart, and
V between those 3 cm. apart.
In the case of helium the figures are for two very pure samples
of gas. After the first series of readings at comparatively high
pressures had been taken, the tube was pumped out and more
helium admitted directly from the charcoal, values for this gas
being marked with an asterisk. It will be observed that the first
of these for the nearer pair of electrodes is 180. As a matter of
fact, immediately the gas had been introduced into the tube, one
reading of 170 was obtained, and 180 between the other pair of
electrodes, 180 and 214 being recorded a minute or two later. It
is difficult to account for this, as the value 184 was found in a
very similar experiment, when the gas was probably just as pure.
There may possibly have been some ionising aj^ent in the vicinity
at the time. Such a low value was never obtained again, and it
seems probable that the correct figure is not far removed from 184.
The case of neon is of special interest as at comparatively high
pressures it allows an electrical discharge to pass far more readily
than any other gas at the same pressure. This was observed in
1909 by Dr Collie and the author, and some rough measurements
were made but not published. Soon afterwards M. Bouty {loc.
cit.) determined the cohesion dielectrique which is a measure of
the readiness with which a spark will pass, and ibund it to be at
least 6"1, and probably 56, the figures for helium and air being
18-3 and 419, respectively. Hence it seemed not unlikely that
the minimum spark potential would also be less than that of
helium, and it was rather surprising to find that this was not the
case, as may be seen from the figures in the table. Unfortunately
the experiments are not quite complete, especially at high pressures,
but the minimum spark potential has been examined carefully,
and certainly seems to be higher than that of helium.
94
Mr Watson, Some Experiments on the
The first set of figures, which is not reproduced in full for the
lower pressures, was obtained from an experiment with a sample of
gas which was originally very pure, but which had been pumped
into a test tube and allowed to stand a few days before use. Even
Helium
Neon
p
V
V
P
V
V
56-3
387
616
32-8
267
372
48-7
375
568
27-7
' 251
350
38-8
343
505
24-0
243
327
31-7
322
455
17-9
228
299
25-2
304
414
13-2
219
273
20-6
293
385
99-3
215
261
14-4
271
351
11-8
264
335
2-81
204t
241
9-1
246
324
1-28
216
231t
6-75
227
309
lO-li^
200
240
5-34
212
295
7-98
200
240
4-44
205
276
5-76
203
240
3-18
188
245
4-42
200
240
2-45
186
225
2-65
200
232
2-43*
180
214
2-19
200
2.30
187
186
213
1-60
204
224
1-86*
190
206
1-23
218
224
l-^U
216
201
0-96
240
229
1-15
221
198
l-87§
211
228
im-^
249
210
1-43
215
229
0-79>'f
390
230
1-01
242
235
0-69*
>1000
258
0-77
285
232
0-495.'f
309
0-59
358
231
0-475*
332
0-45
450
246
0-44#
360
0-345
?725
290
0-355*
473
0-27
?790
360
0-262*
750
0-21
0-16
0-125
>1000
435
650
830
\ Minimum
value.
§ F
rash gas.
though all the apparatus and the test tube had been previously
well rinsed with the gas, it is likely that some impurity was
introduced, as the minimum values for V were 204 and 231
respectively, those obtained later with purer gas being 200 and
224. By analogy with helium, however, it is probable that the
Electrical Discharge in Helium and Neon.
95
figures at higher pressures for the slightly impure gas are not very
far wrong. In the case of the second sample, the constancy of
the spark potential over a wide range of pressure was surprising,
although it was probably illusory, and caused by the gradual
contamination of the gas. It is rather remarkable, however, that
another sample of exactly the same gas admitted immediately
afterwards directly from the charcoal at what was assumed to be
approximately the critical pressure for minimum spark potential,
gave minimum values of 206 and 228.
600
500
400
300
200
\ I xv \ ^^-^^ -
nJ / ^v= N. ^,,~- — ""^o' ■ « —
>*^ ^-— jt *■ ■
10
20 30 40
Pressure mm. and ^th mm.
50
60
Fig. 2. The above curves show the relation between spark potential and pressure
in helium for plane electrodes 15 mm. and 30 mm. apart, the upper curve being
for the latter. The curves on the right correspond to the others, but the
horizontal scale is ten times as great to show the shape at low pressures.
Fig. 2 shows two typical curves for helium. It may be
mentioned here that the electrodes in the present experiments
were placed at a considerable distance, in order that the pheno-
menon under consideration might be studied through a wide
range without unduly increasing the pressure. Paschen's law
states that the spark potential depends only upon the mass of gas
between unit area of the electrodes, and consequently, if the
electrodes are 15 mm. apart, it will be the same as it would be in
a tube with electrodes 1 mm. apart and containing gas at 15 times
the pressure. When using a tube of small dimensions the volume
of the dead space becomes relatively large, and the total quantity
96 Mr Watson, Some Experiments on the
of gas required is more. This is always to be avoided, as the
purification of large quantities of gas is a difficult and uncertain
operation. The whole of the present experiments were carried out
with less than 15 c.c. of each gas.
There is, of course, the objection that the field obtained in this
way is not uniform, and indeed, there is about 20 volts difference
between the minima obtained with the two pairs of electrodes.
At the same time, as will be seen from the figure, the form of
curve is not altered, and indeed, if the horizontal scale of the
upper curve be doubled (the distance of the electrodes for which
this was obtained was double that of the other pair) and the
whole moved downwards, the two nearly coincide. It was intended
to make more experiments with the electrodes quite close, but up
to the present this has not been possible. It seems unlikely,
however, that the true spark potential for a uniform field between
infinite planes is more than two or three volts lower than the
minima already obtained.
On examining the curves, it will at once be seen that they are
of a type not previously observed. Below the critical pressure of
minimum spark potential they are approximately hyperbolic, and
then for a short distance linear, as is usually the case, but at a
slightly higher pressure there is a break, and the curves turn over,
and again become very nearly linear. The same thing occurs in
the case of neon. With the closer pair of electrodes, this break
begins at a pressure of 10 mm. This would correspond with a
pressure of 200 mm. in Strutt's experiments, and is beyond the
range studied by him. The bend occurred at the same point for
all samples of gas even when distinctly impure, and so is not
likely to be caused by impurities. It may however be due to the
irregularity of the field, but this in turn is improbable, owing to
the similar shape of the two curves.
At high pressures there was little difference in the spark
potential when a small trace of impurity was present, but the
niost minute amount affected to a large degree the depth of the
dip in the curve and consequently the minimum spark potential.
The pressures of minimum spark potential were, as nearly as
could be judged, 24 and 2-8 mm. for the closer pair of electrodes
in helium and neon respectively. The latter figure is probably
low, and consequently these pressures are by no means proportional
to the mean free paths of the molecules of the gases (cf Sir
J. J. Thomson, Conduction of Electricity through Gases, 2n(l
edition, p. 450) which are in the ratio 1 : 0-704 (Rankine' Rou
Soc. Proc. A. 1910, 83, p. 524). '
Since the electrodes in the present case were 20 times the
distance of those used by Strutt, it might be expected by Paschen's
law, that the slope of his curves above the critical pressure would
Electrical Discharge in Helium and Neon. 97
be about l/20th of that of the lower ones in fig. 2. As far as can
be judged from his diagram, 20 times the steepness of his flattest
curve is very slightly steeper than the first and corresponding
portion of my curve, and in fact, the agreement is as good as can
be expected. One remarkable effect observed by Strutt, namely
that the spark potential was lowered by vigorous sparking, or by
standing, was not noticed at all in the present experiments, and
in fact the reverse was the case. It has already been mentioned
that the first discharge passed more easily than the subsequent
ones, and if the gas was left standing for a few hours the spark
potential invariably rose slightly. It is quite possible that the
reverse effect may be produced by mercury vapour, which in my
experiments was completely excluded.
With regard to Bouty's experiments, it is difiicult to compare
the slopes of the curves obtained, as all the conditions in the two
sets of experiments differ so widely. Considering the closer pair
of electrodes in my experiments, the rate of change of spark
potential with pressure at high pressures where the curve has
assumed its final definite linear form is 30 volts per cm. of
mercury in the case of helium, and 22 in the case of neon. These
figures should be proportional to the cohesions dielectriques of
Bouty which are 18"3 for helium and probably less than 6*0 for
neon. It will be seen that this is not the case, but on the other
hand, for pressures not so far removed from the critical pressure,
the gradient for helium is about 90 volts per cm. while, as far as
can be judged, that for neon is not much greater than at higher
pressures. The ratio for this part of the curve would therefore be
nearer to the value found by Bouty.
The Cathode Fall.
It has recently been shown by Aston {Roy. Soc. Proc. A. 1911,
84, p. 526), that the supposed anode fall of potential measured by
many observers is probably an entirely illusory phenomenon
induced by the methods of measurement, and he concludes that,
provided there is no positive column, the cathode fall, or difference
in potential between the cathode and the negative glow, is
practically equal to the total voltage across the tube provided that
the current is not large enough for the whole surface of the
cathode to be covered with the glow. The potential fall in the
negative glow itself is negligible. In the light of these results,
the hypothesis put forward by Strutt as a theoretical reason for
the cathode fall being equal to the minimum spark potential, does
not seem very plausible, and is in no way consistent with my
experimental results. Strutt considers that the rise in spark
VOL. XVII. PT. I. 7
98 ^ Mr Watson, Some Ewperimevts on the
potential at pressures above the critical pressure is due to the fact
that a positive column of gradually increasing length has to be
maintained, while below this pressure, the negative glow is
crushed. Except at very high pressures, far above the critical
pressure, no positive column appeared in any of my experiments,
and it has been shown that moving the anode up and down in the
negative glow has no appreciable effect upon the voltage unless
the dark space is reached. Moreover, the present experiments
tend to show that the cathode fall is not equal to the minimum
spark potential at least for helium and neon, for the voltage across
the tube invariably fell when the current started.
Assuming the above mentioned results, it follows that the
cathode fall is equal to the minimum voltage at which the current
will pass when once started, and can be easily measured by
increasing' the resistance in the circuit until the discharge ceases,
and measuring the voltage. This is very constant over a wide
range of pressure, but varies greatly as already mentioned with
the purity of the gas, and also with the material of the cathode.
In what follows, whenever cathode fall is mentioned, it is to be
understood that it is measured by the minimum running voltage.
In the case of the tube already mentioned, with aluminium
cathode, the value of this quantity was 164 volts for helium, and
170 for neon, figures which are 20 and 30 volts respectively lower
than the minimum spark potentials. It is perhaps worthy of note
that they correspond approximately to the calculated fall in
potential in the Aston dark space for these gases, namely, 20 and
40 volts {Roy. Soc. Proc. A. 1907, 80, p. 45; 1911, 84, p. 535;
1912, 86, p. 172). A short consideration of the theory put
forward in these papers to explain the existence of this dark space,
will show that, if in a gas with no Aston dark space the cathode
fall is equal to the minimum spark potential, then in the gases
which do possess it, the cathode fall should be less than the
minimum spark potential by the amount of the voltage drop in
this region.
Experiments with other Electrodes.
A number of other experimental tubes were constructed, some
of which were as follows.
1. A short tube about 4 cm. in diameter with a plane circular
aluminium electrode touching the sides, and about 4 cm. from the
rounded end which contained sodium potassium alloy introduced
after complete evacuation of the tube. Some of the alloy was
shaken on to the aluminium to which it adhered. A series of
spark potentials for neon from a pressure of 11*3 mm. downwards
was taken with this electrode as cathode, and a curve exactly
Electrical Discharge in Helium and Neon. 99
similar to those in fig. 2 obtained. The bend occurred at about
6 mm. pressure, and the minimum spark potential was 150 volts
at 1'5 mm. pressure. The cathode fall luas 8-5 volts. Mey found
78'5 for helium {Verh. deut. physikal. Ges. 1903, 5, p. 72).
2. A similar tube with an aluminium disk upon which were
a few drops of sodium potassium alloy as one electrode, and a
clean aluminium wire normal to it and 1"5 cm. away as the other.
The first neon introduced was not perfectly pure and the surface
of the alloy tarnished. When in this condition at 20 mm. pressure
a 800 volt alternating current was completely rectified. After
shaking to clean the surface of the alloy, and refilling with pure
neon at 3'5 mm. the spark potential with plane as cathode was
145 and the cathode fall 85. When the tube was filled for the
first time, the minimum spark potential with the wire as cathode
was 155 and the cathode fall 130, on the second filling the latter
had risen to 142. These figures are much lower than those
obtained in the original spark potential tube, and it seems quite
possible that they are due to the freshness of the electrode which
had never been used before and was probably coated with a film
of oxide, or was evolving hydrogen. The gas in the present case
would also, if possible, be purer.
3. A tube 22 cm. long and 2*5 cm. wide, with an aluminium
strip running the whole length as cathode. A sodium rivet was
fixed in this, but by the time the tube was filled it was slightly
tarnished. The anode was a wire in the form of an inverted U
passing along each side of the strip. This tube was filled with
neon at varying pressures, and showed a minimum spark potential
of 209 at 5 mm. It was then refilled at this pressure and used
for experiments which will be described later.
4. A tube 14 cm. long, and 2 cm. wide with two copper sheets
in the same plane along its axis and their ends 3 mm. apart as
electrodes. Minimum spark potential 270 volts at 6'0 mm.
pressure of neon, and cathode fall 221 volts.
5. A tube the same size as the above with two square carbon
rods 5 mm. apart at the ends as electrodes. Constant results
could not be obtained even after frequent refilling and passing
heavy currents. The lowest values obtained for the spark potential
and cathode fall were 360 and 217 volts respectively.
6. A tube of the same size with an aluminium plate
covered with sheets of very slightly tarnished calcium as cathode.
U shaped anode. Minimum spark potential 200, cathode fall
150 volts.
7. Similar tube with spirals of magnesium wire as electrodes.
Results very inconsistent. A value of 229 for minimum spark
potential was obtained, and one of 150 for cathode fall.
7—2
100 Mr Watson, Some Experiments on the
Abnormal forms of Discharge.
Soon after starting the experiments on spark potential, a
rather remarkable occurrence was observed. It has been stated
that to determine the discharge point, the potential was gradually
raised. On several occasions it was noticed that before the dis-
charge took place, a glow appeared over the surface of the anode
and increased in brilliancy as the potential was raised. Suddenly
the discharge would assume its normal form with Aston dark
space, Crookes dark space and negative glow. This anode glow
was about 5 mm. thick, and although of quite a different order of
brightness to the normal discharge, was distinctly visible in a well
lighted room. It was more conspicuous in neon than in helium,
as would be expected from the extreme readiness with which the
former gas glows under the least electrical excitation. In helium
it could not be determined whether the glow appeared suddenly
or gradually, but in neon it seemed to be produced at a definite
potential. For pressures above the minimum spark potential
pressure this occurred at voltages often below the minimum spark
potential itself, and always below the normal spark potential.
For instance, in one case with helium at 4 mm. pressure, the
glow appeared at a potential difference of 185 volts, while the
true spark potential was 205, while in another with neon at
33 mm. the glow started at 165 volts and the spark potential was
267. Below the critical pressure, the voltage at which the glow
formed seemed identical with the spark potential at that
pressure.
It must be emphasised that this glow discharge is not a part
of the normal discharge occurring at a voltage insufficient to
produce the latter, such as takes place from a Wehnelt cathode
or in the discharge from points (Gond. of Electricity through
Gases, 2nd edn. pp. 479, 513), but an entirely different and
alternative form of discharge. It was quite impossible in any
experiment to determine a priori which form would make its
appearance, but at low pressures the glow seemed to be the more
stable form.
If the glow appeared, the potential could be raised far above
the nurmal spark potential without any change occurring, but if
the rise was sufficient, then the ordinary discharge would appear,
although the potential at which this happened was by no means
definite. Thus, in a sample of neon, at 10 mm. pressure, the
glow formed at 199 volts, and the normal discharge appeared at
voltages varying from 272 to 330. The spark potential was 200.
Owing to these circumstances the measurement of the spark
potential was a matter of some difficulty. It was found, however,
that if the normal discharge was once obtained, it tended to
Electrical Discharge in Helium and Neon. 101
reappear when the potential was reduced below the spark potential
and then raised; consequently, in practice, the potential was
raised slightly above the spark potential, causing the glow to
appear, the voltmeter was then momentarily disconnected, a pro-
ceeding which largely increased the potential across the tube (as
may be seen from fig. 1) and started the normal discharge. The
current was at once cut off and the potential reduced to just
below the spark potential. On again switching on the current
and raising the potential, the tube sometimes lit with the normal
discharge, but very often the glow reappeared and the process had
to be repeated.
Unfortunately it has been so far impossible to make any
measurements of the currents passing through the tube under
these varied conditions, and it is not easy to ascribe any reason
for the glow discharge. It has however been remarked by the
author in conjunction with F, W. Aston {Roy. Soc. Proc. A. 1912,
86, p. 176), that helium appears to conduct the discharge in two
different ways, and the occurrences under consideration appear to
be a manifestation of the same phenomenon. It seems that an
explanation might be afforded by the rather crude assumption
that if the gas be considered analogous to a metallic conductor, it
can have two (or perhaps more) different resistances. In this case
the normal discharge would be the one corresponding to the low
resistance, and the glow discharge to the high resistance, for the
latter is exactly similar to the normal discharge when the external
resistance is largely increased. The glow resembles the negative
glow and appears to be on the anode because of the great size of
the dark space owing to the low current density ; moreover four
or five Aston dark spaces are often seen at high pressures exactly
as in the normal discharge. It is noteworthy, however, that the
glow discharge could not be produced from the normal one by
decreasing the current, although at low pressures the change often
occurred spontaneously when no alteration was made in the
external conditions.
On a few other occasions, yet another type of discharge
appeared. If the potential was very slowly raised when the glow
discharge was taking place, the glow, which was approximately a
plane disk over the anode, became unstable, and bulging out at
the centre, moved bodily over to the cathode where it assumed
the form of a paraboloid having its vertex towards the cathode,
and separated from it by a small dark space. No change in
intensity occurred during this process until the potential was
raised sufficiently to produce the normal discharge. I can offer
no explanation for this.
An interesting type of discharge could also be produced as
follows. When the current was passing through the gas, the
102 Mr Watson, Some Experiments on the
voltmeter being disconnected, the pressure was reduced until the
dark space just reached the anode. If then the pressure was
very slightly further reduced or the current density lowered by
increasing the external resistance, the current ceased to pass
continuously, and passed in flashes. By careful adjustment these
could be made to succeed each other with great rapidity, or at
regular intervals as far apart as quarter of a mimite. This dis-
charge was previously noted in the experiments carried out in
conjunction with F. W. Aston {loc. cit.), and affords a beautiful
illustration of the well known although rarely concisely stated
fact, that if the anode be brought inside the Crookes dark space,
no current will pass unless an enormously increased voltage is
applied. In the present case matters are so adjusted that if the
current were to pass continuously, it would be so weak that the
dark space would be longer than the distance between the elec-
trodes. Consequently this cannot occur. Increasing the current
density, however, shortens the dark space, and a large current can
pass. To effect this, the energy seems to store itself up until
sufficient is accumulated to pass over in a burst. As the con-
denser capacity of the vacuum tube must be quite small, it is
difficult to tell how this storage takes place, and it is remarkable
that the flashes can be obtained at such long intervals as those
already mentioned. A further investigation of this point would
most certainly prove of great interest, and might throw valuable
light on the phenomenon of initial discharge in gases at low
pressure.
Another form of discharge was observed which was probably
similar to that from a Wehnelt cathode. Its characteristic was
that it occurred from a single point on the cathode, and it was
induced by traces of impurity on the surface. It only appeared
once in the carefully cleaned tube used for spark potentials, and
was exceedingly persistent in tube no. 7, with magnesium elec-
trodes. Its appearance in the case of neon was extraordinarily
beautiful, and resembled nothing so much as the sun just setting
in a perfectly clear atmosphere. Its brilliance was dazzling as
may well be imagined from the fact that currents of the order of
50 milliamperes frequently passed from this one point.
The voltage when this discharge was passing was very low,
some figures being : with helium in spark potential tube 154 volts,
neon in tube no. 3, 17"5 mm. pressure, aluminium wire cathode,
109 volts; neon in tube no. 7, magnesium electrodes, 75 volts at
18 mm. pressure, and 110 at 3 mm.; neon in tube no. 2 aluminium
wire cathode 1 mm. pressure, 85 volts. These values did not
vary greatly with the current and seemed to bear no relation to
one another. As with the other abnormal forms of discharge, it
was impossible to tell when this form would make its appearance.
Electrical Discharge in Jffeliiivi and Neon. 103
Fatigue of the Electrodes.
Some experiments were carried out to determine the effect on
the electrodes of prolonged passage of the current. Tube no. 3
with a large sodium and aluminium electrode was originally
made for this purpose. No convenient source of direct current
being available it was connected to the 200 volt alternating
mains with one carbon lamp in series. The current passing was
Jg th amp. and was sufficient to cover only about half the cathode
with glow. This glow, however, gradually spread, and at the end
of 44 hours covered the whole electrode. The tube was about as
hot as an ordinary carbon filament lamp. After about 10 hours
further running, most of the discharge took place from the
sodium, although there was still a certain amount from the
aluminium. The experiment was continued, but no further
chanujes occurred. The initial voltage across the tube was 143,
corresponding to a maximum of 200, and this rose to 154, the
glow also diminishing greatly in intensity.
From this it may readily be seen that after some time,
current passed less easily from a given portion of the electrode,
and moved towards an unused portion. Finally when the whole
of the aluminium was "exhausted" the discharge started from
the sodium which was slightly oxidised and evidently less
favourable to its passage than fresh aluminium.
A peculiar effect was observed with this tube. When the
current was cut off with a one-pole switch which disconnected the
large sheet electrode, the gas round the wire electrode continued
to glow. Presumably the leakage across the switch or its
capacity allowed sufficient current to pass to produce luminosity.
This is another striking demonstration of the minute currents
which suffice to show their presence in neon, and a tube of this
nature might well be used in testing for leaks.
Fatigue was especially noticeable in the tube no. 5 with
carbon electrodes. For instance, after running about 30 milli-
amperes through one electrode at 2-1 mm. pressure, the spark
potential rose from 400 to 530, and the running potential from
255 to 300. The tube then completely rectified a 300 volt
alternating current. In this case a large amount of gas was
evolved, and this appears to facilitate the passage of the current.
If this is the case, a new aluminium electrode which evolves
much hydrogen might be expected to give rise to a lower
cathode fall than an old one as was observed to be the case in
one experiment.
Experiments were made later on a small tube with two sheet
aluminium electrodes in the same plane, and filled with neon at
5 mm. pressure. This was connected to a 240 volt main through
104 Mr Watson, Some Experiments on the
I
a lamp. After five or six hours the glow became far paler,
and it was found that if the current were switched off and
then on again, the lamp would not light up, although it
would do so if the current were reversed. This seems to be
an effect similar to that in connexion with the initial spark
potential. It occurred in the case of both electrodes, and can
hardly be ascribed to true fatigue, since, if the current passed
only for a small fraction of a second, the tube would not again
light up. Reversal of the current, and possibly alteration of
pressure, seems to produce some molecular rearrangement of the
surface of the cathode.
This tube also showed signs of true fatigue, and after about
60 hours would not light at all with the potential difference in
question.
It will thus be seen that with helium and neon there are
considerable fatigue effects similar to the well known phenomenon
of photo-electric fatigue, and probably arising from the same
cause.
Intensity of the Illumination.
Anyone who has seen a discharge through pure neon will be
aware of the intense brilliancy which characterises it. The
brightness of the negative glow on a flat electrode at pressures in
the neighbourhood of 10 mm. is remarkable, and it was thought
that the efficiency of this light might be very high, and more-
over, as it appeared likely before starting the experiments that
the potential difference necessary to start and maintain a current
would be very low, it seemed not improbable that it would be
possible to make an efficient lamp which would run from an
ordinary lighting circuit. Nearly ail the experiments so far
described were carried out with this end in view, and this accounts
for any apparent lack of connection between them, and in many
cases their incompleteness.
A number of very rough measurements of intensity were
made with a grease spot photometer, the voltage and current
being measured simultaneously, but it is not proposed to give
these in detail. One very interesting fact was that the intensity
of the light when measured was found to be far less than when
estimated. Some tubes which were dazzlingly bright were of con-
siderably less than one candle power, and the estimated efficiency
was correspondingly reduced.
There appeared in all cases to be a maximum efficiency for
medium currents, which were of the order of 30 milliamperes for
the small tubes already described. The pressure exerted a great
influence, for example, with copper electrodes, at 8 mm. pressure
Electrical Discharge in Helium and Neon. 105
the efficieBcy was about 90 watts per candle, while at 12-'7 mm. it
was 20. A similar tube with aluminium electrodes at the former
pressure had an efficiency of about 40 w.p.c. More satisfactory
results were obtained with tube no. 2 with a sodium potassium
electrode. Here the efficiency was increased to 4 w.p.c. for
pressures between 10 and 16 mm., the volta.ge across the tube
being 90, but this of course is far above the limit required for
practical illumination. Experiments were started with a number
of other metals as cathodes, but were unavoidably broken off.
The above figures were only obtained with gas of the utmost
purity free from mercury vapour, and after a short time, in spite
of ali precautions, it invariably became contaminated, and the
brightness diminished. This was less noticeable when the cathode
was of sodium potassium alloy owing to the absorption of the
impurity, but this liquid is most inconvenient as it tends to soil
the glass, and it is almost impossible to coat a metallic surface
evenly with it.
While these experiments were in progress, I was informed
privately that similar work was being carried on by M. Claude
in Paris. Some of his results have now been published (G. R.
1910, 151, p. 1122; 1911, 152, p. 1377), and are much more
satisfactory from a practical point of view, an efficiency of 0-64
watts per candle having been attained. In his experinients no
attempt was made to keep the voltage low, 1000 volts being used,
and the light appears to be that from the positive column,
although this is not precisely stated. In my experiments the
light was derived from the negative glow, and the amount of
energy lost in the dark space is many times the amount which
produces luminosity. On the other hand, when high voltages are
utilised, the dark space loss becomes negligible.
Physiological Effects.
The light given out by helium and neon under the influence
of the electric discharge is of a peculiar nature. It has already
been mentioned that the apparent brightness is far in excess of
the actual intensity, but what is more remarkable is the acute
physiological effect of such a feeble illuminant. In the foregoing
experiments it was found that if the light from one of these
tubes emitting say Jgth of a candle power, was allowed to fall on
the unprotected eyes for about a quarter of a minute, a violent
headache was the result, followed by temporary blindness, while
on one occasion, looking at a tube of one candle power for one or
two seconds produced pain in the eyes, and a total inability to
read for two days, and these effects were not confined to one
106 Mr Watsov, Some Eorperiments on the
individual. In consequence, during the whole of the experiments
it was necessar}^ to wear very dark brown glasses.
The same effects have been noticed with argon, krypton and
xenon although the light emitted was of the faintest kind. The
most obvious suggestion is that ultra-violet light is the cause, but
an examination of the spectra of these gases fjhows that the
intensity of the ultra-vi()let spectrum as measured photographi-
cally is certainly less in all cases than that of the visible spectrum,
and indeed, in krypton, there are practically no bright ultra-
violet lines.
A property common to these gases is that their spectra all
consist of a comparatively small number of intensely bright lines,
and it would be interesting to know if these could possibly affect
the eye to the same extent as a continuous spectrum emitting for
instance the same amount of energy per yq th A.U. as is given out
by one line of the gas spectrum. The total energy of the con-
tinuous spectrum would naturally be far greater, but for certain
colour senses the two would be equal, and an equal strain on
some portion of the eye might result.
In conclusion, it may be mentioned that of the several points
which have been dealt with in this paper, there is not one, our
knowledge of which is in the least degree complete, and a further
investigation would certainly in every case be amply repaid.
I should like to take this opportunity of conveying my very
best thanks to Sir J. J. Thomson in whose laboratory these
experiments were carried out, for the great interest he has at all
times shown in them.
Summary.
1. Measurements have been made of the spark potentials at
different pressures, between plane aluminium electrodes in very
pure helium and neon, no external exciting agent being used.
2. In the case of electrodes 15 mm. apart, the normal
minimum spark potentials excluding a lower value obtained on
the first passage of the current, were found to be 184 and
200 volts for helium and neon respectively, the corresponding
pressures being 2*4 and 2'8 mm. respectively. For a perfectly
uniform field the potential differences might possibly be two to
three volts less.
3. At pressures higher than those given above, the curve con-
necting spark potential and pressure did not assume a linear form
until the pressure rose to about 10 mm. After this point, the
gradients were 30 volts per cm. pressure for helium, and 22 volts
per cm. for neon (electrodes 15 mm. apart).
Electrical Discharge in Helium and Neon. 107
4. Special attention was paid to the lag, the purity of the
gas, and the exclusion of mercury vapour.
5. The cathode fall with aluminium electrodes which have
been well "run" is at most 164 volts for helium and 170 volts for
neon. Consequently it does not appear to be equal to the
minimum spark potential.
6. With a cathode of sodium potassium alloy in neon, the
minimum spark potential is near to and not greater than 145 volts,
and the cathode fall is 85 volts.
7. The cathode fall in neon with cathodes of copper, carbon,
magnesium and calcium is approximately 221, 217, 150, and 150
volts respectively.
8. Four abnormal and alternative forms of discharge were
observed.
(a) Corresponding to a state of very high resistance in the
gas under examination.
(6) A variation of the above corresponding to a transition
stage between it and the normal discharge.
(c) An intermittent discharge, the frequency of which
could be controlled.
{d) Corresponding to the discharge from a Wehnelt
cathode.
9. Experiments were made on the fatigue of the electrodes
which was found to be considerable, and of two kinds. Firstly a
true fatigue, and secondly a reluctance to allow the current to
start for a second time when one discharge had already passed.
10. Measurements were made on the efficiency of the light
from the negative glow. This was found to be less than was
expected.
11. Peculiar physiological effects were observed, correspond-
ing to arc blindness produced by light of very feeble intensity.
108 Mr Pocklington, Some Diophantine Impossihilities.
Some Diophantine Impossibilities. By H. C. Pocklington,
M.A., St John's College.
[Received 28 October 1912.]
1. The object of this paper is mainly to discuss some
equations obtained by equating a quadratic function of x^ and 'if
to a square, either to show that they are impossible in integers or
rational fractions (§ 3 — § 10), or to completely find their solutions
in integers (§ 12). Two theorems on arithmetical progressions of
which given terms are to be squares are given in §§ 6, 11, and the
impossibility of x^'''^ + y'^^ = z^ is discussed in § 13.
2. We make use principally of three lemmas. The first is
that if xy = z^, and x is prime to y, then both x and y are nth
powers. The proof is obvious on expressing ^ as a product of
primes and their powers. For each prime that occurs in z must
occur in x or y, but not in both, and clearly occurs raised to a
power the index of which is some multiple of n. If w = 2 we
have an alternative proof in Euclid ix. 2, and if n is a power of
2 we can get our result by a repeated application of Euclid's
proposition. We have assumed that x and y are positive. If
they can be negative there is the alternative x — — u^, y=— V^.
By a repeated application we see that if xyz= w^, then x, y and z
are nth powers.
We shall also require the following application of the lemma.
Let x^ + Ny^= z^, where either x ov z is prime to Ny. Then x is
prime to z, for if p is a prime common divisor of x and z it
divides Ny^ and hence Ny. Hence the greatest common divisor
oi z ■\- X and z — x i% 1 or 2. First suppose that it is 1, i.e. that
Ny is odd. Then, writing the given equation Ny'^ ={z + x)(z — x),
we see that z + x = lu, z — x = mv, where lm = N and lu is prime
to Tnv. We now have y^ = uv whence u = ^^, v= rf and so
X = {l^^ - m7f)l% y=^v, z = (l^^ + mr}^)/2.
Next suppose that the greatest common divisor is 2, i.e. that Ny^
is divisible by 4. Then if y is even we have
N(yl2y = ^(z + x).U^-'^),
where {z + x)/2 is prime to (z — x)/2. Treating this as before we
find x=l^^ — m7f, y=2^r}, z^l^^ + mrf. If y is odd, iV must
be divisible by 8, and Ny'^j^ = ^{z + x) . ^(z — x), whence as
before we find x = l^'^—mif, y = ^i], z=l^'^+ mif, where l^ is
prime to mrj and Im = N/4<.
Mr Pocklington, Some Diophantine Impossibilities. 109
In the case of w^ + y^= z^ we see by taking remainders to
modulus 4 that a; or 2/ is even. Supposing that y is even the
solution can be put into either of the equivalent forms x = u^ — v^,
y = 2uv, z=u? + v^ or x = uv, y = (u^ - v^)/2, z = {v?-\- v^)/2.
We have assumed that z is positive. If it can be negative,
we must prefix the ambiguous sign to its value. The proof given
above shows that it is necessary that w, y, z should be of the
forms found; we easily see by Algebra that it is also sufficient.
Our second lemma is that if ocy = uv then a; = a/3, y = 7S,
u = a<y, v= ^8. This also may be proved by expressing a; and y
as products of primes and their powers, or more readily by
noticing that a solution is to take a to be the greatest common
divisor of cc and u, and put ^ = xja, 7 = uja, which substituted in
xy = uv gives ^y = jv with ^ prime to 7. Hence /3 divides v.
Take S = v/0, then this equation gives y - /38, and the lemma is
proved, for we have already arranged that x = a.^, u = ct<^, v = p8.
It is clear that the lemma still holds if x, y, u, v may be negative.
The extension to the product of m indeterminates equated to the
product of n others is obvious.
For an example take the equation x^- + y^=u^ + V. By finding
the remainder to modulus 4 we see that x and y are both even,
both odd, or even and odd, according as u and v are. Hence we
may suppose x to be that one of the first pair that has the same
parity as u. Then \{x -¥ u) .l{x ~u)^\{v + y) . ^{v - y), where
{x + u)l% etc. are integral. Applying the lemma we have
{x + u)/2 = al3, {x-u)/2 = -/8, {v+y)l2 = ay, (v-y)/2 = ^S,
whence x = al3 + ryS, y^ay-^B, u=a^- 78, v = a'y+ ^B, which
gives a complete solution of the problem to find a sum of two
squares equal to the sum of other two squares. These values of x
and y give x^+y^= {a0 + jhy + {ay - ^Sf = {a? + 8') {^ + 7'). and
we easily see that 8 is the only one of the four that can vanish,
so that only the first bracket can be unity. This requires that
x = u, y = v,so that the squares are the same. This is the well-
known theorem that if a number can be expressed in more than
one way as the sum of two squares, it is composite*.
We can deduce the solution of x^ + y^= 2 (u^ + v^). For it is
clear that x and y are either both even or both odd, so that
^ = (x + y)l2 and 77 = (^ - 2/)/2 are integral. Substituting for
X and y, the equation reduces to the form just discussed,
|2 ^ ^2 ^ ^2 + ^2^
* The more general case x^±Ny^=u^J=Nv^ can be treated in the same way by the
extension of the lemma. The equation x^ + y^ = u^ + v^ was solved by Bachet (in his
Diophantus). See also Fermat's note (p. 133). The equation x* + y* = u* + v* also
can be solved generally, one solution being
a; = 12231, 2/ = 2903, 1*= 10381, v = 10203.
110 Mr PocMington, Some Diophantine Impossibilities.
From this we easily solve completely the problem of finding the
parallelograms that have their sides and diagonals integral. The
solution is that the sides are aj3 — <yh and ay + /3B, and the
diagonals a/S + <yS + ay — ySS and a/3 + jB — ay + /38. We may
without loss of generality take a to be positive, and then in order
that 00, y, u, v may be positive and form a real parallelogram we
must have /3, 7, 8 positive, and a> 8, /3 > 7.
The third lemma is that if ooy— uv and x is prime to v and y
to u, then x--= ±u, y=±v. For from the first condition x divides
u, and from the second u divides x.
3. Consider od^ — py^ = z^, where p is a prime of the form
8m + 3, and suppose that we have that solution in which xy has
the least value. Then x is prime to y. It is also prime to p, for
otherwise z^ is divisible by p and hence by p^, so that py^ is
divisible by p^, which is impossible, as y, being prime to x, is not
divisible by p. Also y is even, for otherwise we should have
z^= h or 6, mod. 8. Hence x^ = v? + pif; y^ = 2ww, where u is
prime to pv and one of them is even. If u is even, v is odd and
x^ = 3, mod. 4, which is impossible, so that v is even. Hence
±u=^^ — p7f, v=2^r), where ^ is prime to prj and one of them
is even, which gives y^= ± 4^9/ (p — pij^). Hence f = a^ r) = /3^
p — pr}^ = ± 7^ or a* — p^^ = ± 7^, and a or /S is even. Hence
+ 7^ = 1, mod. 4, so that the upper sign must be taken, and the
equation is of the same form as that considered. Also
that is we have found a solution in which xy has a value less than
the least that it can have, and we infer that the equation con-
sidered is impossible. In the same way we show that the equation
x^ + 2y^ = z^ is impossible, and the impossibility of a^ — hy^ = z^
can be proved similarly. The complete solutions of x^ — 2^/* = z^
and 2a;^ — y^ = z^ can be found.
4. The equation a?"* + 2/* = ^^^ is impossible if n (supposed not
divisible by any square) contains an odd prime not of the form
8??i + 1, for if it has a solution it has one in which x is prime to y,
and £c* + 2/^ is then not divisible by any odd prime that is not of
this form. If n. = 17 there is a solution x = 1, 3/= 1 and we can
prove by Fermat's* method that the number of distinct solutions
is infinite.
If possible let x, y, z be that solution of the equation
x^ — y^ — pz^,
where ja is a prime of the form 8m + 3, in which xy has the least
value. Then as before x is prime to pz and z is even. Hence
* "Doctrinae Analytieae Inventum novum" (prefixed to S. Fermat's edition of
Diophantus), p. 26 et seq.
Mr Pocklington, Some Diophantine Impossibilities. Ill
v^=v:^ -\- pv^, ±y^ = it" — pv^, where u is prime to pv and one is
3ven. But by taking residues to modulus 4 we see from the first
eq\iation that v is even, and that the upper sign must be taken in
the second. Hence solving, 2pv^ = x^— y-, 2u^ = x^ + y^. Writing
the second equation f "^ j + ( — ^1 = w^ where x — y>0, we
[have {x ± 2/)/2 = p - if, {x + y)j1 = 2^7), whence
p(v/2y^^v(^'-v')-
Now ^ is prime to 77 and so each is prime to ^^ — tf. Hence
1^=P0?, 7? = y82, |2_^2^^2or ^=5j2^ ^^^^2 p_^2 = ^£ or | _ ^2,
\.r]~ ^^, ^^—7)^ = py^ according to the factor that is divisible by p,
and in each case a, 0, y are prime to each other. These give
p^a-i — /34 = 7^, a* — p^l3* = 7^ or a* — ^^ = p<f respectively. The
first of these is impossible for p cannot divide /3* + 'f. The third
is of the form of the hypothesis, and a^^'^ :\>ol^^^j^<v^< x'^ <xY
iiwhich contradicts the assumption that xy had the least possible
value. In the second a is prime to p, for if not we can write the
jequation p^a'* - /3'^ = y'^ so that ^ is divisible by p, which is
impossible as a is prime to /3. Hence as a or /3 is even,
a^±y = \\ a^ + 7 = py\
and adding we have V + |}V*= 2a^, which is impossible, for j9 does
not divide a and 2 is a non-residue of p. Hence the given
equation is impossible. We have proved one case of the theorem
that x^ - p^y^ = z^ is impossible, and the other case gives
x^ = v?-\- v^, py"- = v? - v^,
so that u^-v* = px^y'^, which is impossible. Hence x^ - p^y* = z" is
impossible.
We have also proved that xy {x^ - y^) = pz'' is impossible if x
is prime to y, and we easily see that this restriction can be
removed, hence the area of an integral right-angled triangle
cannot be the product of a square and a prime of the form
8/71 + 3.
5. If a^ — x^y"^ -{■ y^ = z^ has any solution it has one in which x
is prime to y (and x^y unless x = y=l). Firstly let ^ or y be
even, say y, and suppose that we have that solution in which xy
has the least value, subject to y even. Writing the equation in
the form {x^ - y^f + x^y^ = z^ we see that x^ - y^ is prime to xy, so
that x^-y^=v?-- v^, xy = 2uv, where the first equation^ shows
that V is even. Dividing the last equation by 2 and using the
second lemma we have x = ap, y=2yS, u = ay, v = ^8, where
a, 13, 7, 8 are prime to each other in pairs, for x is prime to y, and
u to V. Also a, /3, 7 are odd and 8 even. Substituting in the
previous equation we have yS^ (a^ + ^) = 7^ (a^ + 4>8% Now ^ is
prime to 7 and as oc is prime to S the greatest common divisor of
112 Mr Pochlington, Some Diophantine Impossibilities. |
a^+S^ and ol^+4>^ is some divisor of the determinant formed
from their coefficients, which is 8. But 3 does not divide o?+h^,
hence the brackets are prime to each other, and applying the
third lemma we have a? + h'^ = r^^, a^ + ^h^ = ^'^. The last gives i,
a= ^^ — 7}% S = ^7) which substituted in the previous one gives ';
^4_p^2^^4_^2 rpjjjg jg Qf ^Yie original form, for ^ or 77 is i
even. Also f 77 = S < 2y8 < y < xy, which contradicts the assump- ;
tion, and we conclude that the equation is impossible \{ x ox y
is even.
Secondly if x and y are both odd, we again write the equation \
(of — y^f + x^y^ = z^ and unless x — y = ^ we find x^ — y'^ = 2uv, ,
xy = u^ — v^, whence
which is of the form just proved to be impossible, for u is prime
to V, one of them is even, and (x^ + y^)/2 is integral. Hence
x'^ — x^y^ -\- y^ = z^ is impossible unless x = y.
From this we can prove that an integral triangle with an
angle of 60° cannot be equal in area to an equilateral triangle,
unless ib is itself equilateral. For this requires
x^ — xy + y^= z^, xy = w\
where x, y are the sides about the angle of 60°. If these
equations have a solution they have one in which x is prime to y,
and then the second equation shows that x = u^, y = v^, and the
first becomes u'^ — v?v^ + v'^ = z'^, which is impossible unless u — v,
that is, x = y.
6. If we attempt the second part of the discussion of
a^ - x^y'^ -\- y^ = z^ g
by the same method as was used for the first part we get I
whence o?, rf, ^'^, 8^ are in arithmetical progression. It is possible
but troublesome to go on and complete the proof. As however
we have proved the theorem in question we can invert the
present proof and show that four squares cannot be in arith-
metical progression. For if x^, y^, z^% w^ are such squares, we have
'2xH'^ — 2y^-w^ = x^y^ — z^w^. Hence putting
u = xz, v= yw, ^ = (xy + zw)/2, rj = (xy — zw)/2,
which we easily see to be integral, we have
and hence m^ - wV + ?;* = (p + 77^)^ Also unless the squares are
all equal (when they can hardly be a progression) we have
y>x, w> z OY y <x, w< z, so that u and v are unequal, and the
Mr Pocklington, Some Diophantine Impossibilities. 113
last equation is impossible. Hence four squares cannot be in
arithmetical progression*.
Also x^ — ^x^y + 2a;y + ^xy'^ + y"^, oc* + 2x^y^ + y*,
X* + 4fX^y + 2a?Y - Aixy^ + y* and x"^ + 8a^y + 2x^y^ — 8xy'^ + y*
are in arithmetical progression, and the first three are squares.
Hence we conclude that the last expression cannot represent a
square f.
■ If a^ + \^x'^y'^ ■\- y* = z^ has any solution it has one in which x
is prime to y. If the indeterminates are odd and even we have
: {x^ — y^y + 1 Qx^y^ = z^, whence x^ — y'^ = v? — v^, Ixy = uv and so
!M^— u^v^ + v*= (x^ + y'^y, which is impossible, for u and v are odd
jand even and hence unequal. If x and y are odd and unequal,
we write the equation ( — j-^ j + x^y^ ~ ( T ) > whence
(x^ — 2/^)/4 = 2uv, xy = u^— v'^,
so that W + 14z(V + v*= (x"^ + y^yi^, where u is prime to v and one
of them is even, which we have just shown to be impossible.
Hence x^ + l^x^y^ -^ y^ = z^ is impossible unless x = y.
7. If possible let {x^ + y-f — Nx^y^ = z^, where iV is odd, not
of the form 8^ + 3 and not divisible by any prime of the form
4w + 1, and moreover iV — 4 is an odd power of a prime| (it cannot
be an even power for N cannot be the sum of two squares), and
let us suppose that we have that solution in which xy has the
least value. Then x is prime to y, and by taking the remainders
to modulus 8 we see that x and y are not both odd. Let y be
the even one. Also from its composition N is prime to x^ 4- 2/^
hence the terms of the equation are prime to each other, and
from the first lemma x^ -\- y''-= Iv? + mv"-, xy = 2uv, where Im = N
and I is prime to 7n. Applying the second lemma to the second
equation we get x = a^, y = 27S, u = ay, v = /38, where a and yS
are odd, "y or S is even. Since x is prime to y we have a prime
to 7, 8 and /3 also prime to 7, 8, and since lu is prime to mv, we
have a prime to yS and 7 to S, and also I prime to ^, B and m to
a, 7. Substituting in the previous equation we get
Now a is prime to S, and since /8 is prime to 7, the greatest
common divisor of the two brackets divides
m, — 4
* Fermat, "Inventum novum," p. 20.
t Ibid. p. 36.
J If N=l, then 2V-4= ^ §, This case is included in the proof, taking p = 3
later.
VOL. XVII. PT. I. 8
114 Mr Pocklington, Some Diophantine Impossibilities.
say, and hence must be a power of p, say 2>^ where \ if- 2k + 1.
Dividing by p'^ and using the third lemma we get
First suppose that X is even. If we take the lower sign the
first equation shows that 1=1, for otherwise I would contain a
prime of the form 4?i + 3 and could not divide jB"^ + p^h^ which is
a sum of two squares the first of which is prime to I. Hence
m = N. The first equation has become rf = ^ + 'p^h^, whence 7
is odd, and as a and /3 are odd the second equation gives
iV'-4 = -l, mod. 8,
which is contrary to the hypothesis.
If we take the upper sign the second equation shows that
m= 1, for otherwise it would contain a prime of the form 4w + 3
and so could not divide ^'y'+p^a?, where 2^ is prime to m.
Hence l = N and the second equation, ^^ =p^o? + 4^^, gives
and on substituting in the first we get {^^ + tj^Y — N^^rj'^ = p^'SK
This is of the original form, for \ being even, p^ is a square. Also
^rj = ry<: 2y8< y < xy, which contradicts the assumption.
Next suppose that \ is odd. Solving the equations for ^ and
7 we have 0? - mS^ = + p^r^'', la^ _ 4^2 ^ + ^^32^ where /i = 2/n- 1 - X
and is even. These equations are of the same form as those just
considered, with I and m, a and /3, 7 and S interchanged, and
in precisely the same way we show that the lower sign gives
a contradiction of the hypothesis, and the upper sign gives an
equation of the original form with a smaller value of the product
of the indeterrainates, which contradicts the assumption. Hence
the equation is impossible under the restriction on N stated in the
hypothesis.
The most important case of the proposition is that of iV = 1
or that x^ + x-y-^ + y* = z^ is impossible. Hence, just as in § 5, an
integral triangle with an angle of 120° cannot be equal in area
to an equilateral triangle. Also
x^ + x^-y^ + y^ = {^^ + a;y + y^) (x^ — xy+ y%
so that both brackets cannot be squares. Hence a parallelogram
with integral sides and diagonals cannot have an angle of 60°
between the sides or between the diagonals.
If a;* — 14«;^2/^ + 2/* = ^^ has any solution it has one in which
X is prime to y. If one of these is even we write the equation
{x?-\-y'^y' -\'ox^y'^ = z^, whence a?" + 3/^ = it^ + v^ 2xy = uv, and so
yi _|_ ^2^2 -I- ^4 _ ^^2 _ yiy^ which is impossible. If x and y are both
odd we write the equation
I
4
(^^y-4^y=^V4,
Mr Pochlington, Some Diophantine Impossibilities. 115
and as {x^ + 'y^)/2 is odd we have 2'^/4> = 5, mod. 8, which is im-
possible. Hence the proposed equation is impossible.
8. If possible let (x^ + y^y + Nx^y- = z^, where N is odd, not
of the form 8w + 5, and not divisible by any prime of the form
4n + 1, and iV + 4 is an odd power of a prime (it cannot be an
even power, for it is odd and not = 1, mod, 8). As before we take
the solution for which xy is least, and see that x is prime to y and
one of them even, say y, and that N is prime to x'^ + y"^. Hence
x'^ + y^ = lu^ — Qnv^, xy=2uv. As before the last gives x = a.^,
y = 278, u = ay, v = /3S, where a and /3 are odd, a, /3, 7, B prime
to each other in pairs, and I prime to /3 and 8, m prime to a and
7. Substituting in the previous equation we have
a" {If - ^') = 8' (47^ + m^').
The determinant of the coeflScients in the brackets is
say, and hence the greatest common divisor of the brackets is p^,
where \:jf> 2k + 1. Proceeding as before we have ly'-' — fi'^ = p^S-,
472 + m0^ = p^a?. First suppose that A, is even. Then the first
equation shows that I = 1 (and so w = N) and that 7 is odd.
Hence as a and /3 are odd the second gives iV+4= 1, mod. 8,
which is contrary to the hypothesis. Next suppose that \ is odd.
Solving for /3 and 7 we find la?-'^P = pi^^\ a" + mh- = p'^y"-, where
fi^2k+l —\ and is even. The first equation shows that 1 = 1
(and so m = iY) and then gives a = p ^ ??^ 8= ^rj, and on sub-
stituting in the second we get {^^ + rj^y + N^Y^ = pi'y"- = square.
This equation is of the original form, and ^v = ^< y< ^1/' which
is contrary to the assumption. Hence the equation in question
is impossible.
In a closely similar way we can prove the impossibility of
{x^ + y^y - 2NxY = z^, where N is of the form 8m + 7, is divisible
only by primes of the form 8m + 7, and iV- 2 is an odd power of
a prime; that of {x^ + y^) + 2NxY = z^ where iV -K 2 is an odd
power of a prime and N is of the form 8m -i- 1 and either divisible
only by primes of the form 8m -f 3 or only by those of the form
8m H- 7 ; that of (x^ + y'^y - 8NxY = z\ where N is of the form
4m + 3, is divisible only by primes of that form, and 2iV- 1 is an
odd power of a prime ; and that of {x^ + y'J + ^Nx'y'', where N
is of the form 4m 4- 1, is divisible only by primes of the form
4m + 3, and 2i\^-hl is an odd power of a prime. (We easily see
that in each case the power is necessarily odd,)
9. The general method can also be applied to many other
cases, the necessary exclusion of some alternatives being effected
by noticing that an equation such as ao? -^ S^ = h^"- can only hold
if some such condition as that - a and 6 are quadratic residues
8—3
116 Mr Pocklington, Some Diophantine Impossibilities.
of each other is satisfied. It is sometimes convenient to com-
mence by writing the equation in the form (w^—y^y±Nx'^y'^ = z^,
and then we must examine the equation to see if a; = y gives a
solution. Sometimes we have to use the method developed in § 12,
second case. Collecting results, we have a;* + nx^y^ + y* = z^ im-
possible if w is 0, 1, 3, 4, 5, 6, 7 (unless os = y), 9, 10, 11, 14 (unless
x=y), 15, 18, 19, 20, 21, 22, 25, 28, 29, 35, 45, 51, 59, 65, 69, 74,
81, 91, and if -w is 1 (unless x = y), 3, 5, 6, 7, 8, 10, 12, 14, 17,
18, 19, 20, 21, 22, 23, 24, 27, 29, 31, 45, 54, 55, 60, 61, 69, 75.
If n lies between - 30 and 30 the equation can be solved except
in the cases just given. If n = — 15 the least solution is ^ = 95,
y = 24, but in the other cases the values of x and y in the least
solution do not exceed 6.
10. We now propose to prove the impossibility of
(x^ - 5y^f + 1 28a;y = z% Ij
not so much for its own sake as because of a deduction we make
from it. As before, if it has a solution, take that in which xy
has the least value. Then x is prime to y. If x is divisible
by 5 let it be ox', then the equation becomes
(y2 _ 5x'J + 1 28?/V2 = {z/5y,
which is of the same form as the original equation but with a
smaller value of the product of the indeterminates. Hence x is
prime to 5 and x^ — 5y^ to x^y"^.
Firstly, suppose that x is even and y odd. Then x^—5y^=2v^—u^,
Axy = uv, where u is odd and v even, x = aj3, y = yS, u = a7,
V = 4/3S and a^ (/S^ + 7^) = ga (32^2 ^ 5^2)^ where /3 is even and 7
odd. The only possible greatest common divisor of the brackets
is unity, so that a^=82yQ2+57^ which is impossible to modu-
lus 8.
Secondly, suppose that icis odd, and y even. Then
^2 _ ^y2 — q£i — 2v^, ^xy = uv,
where u is odd and v even, x = a/3, y = yB, u = ay, v = 4/3S, where
a, j3, y are odd and 8 even and /3' (a^ + 3282) = ^ (a^ + 58^). The
greatest common divisor of the brackets divides 27, hence
a2 + 3282 = 72 or = 97^, a^ + 552 ^ ^2 qj. = 9/3^, the other cases being
excluded by using the modulus 8. Since 8 is even the second
of these equations gives in either case ± a = p — 5r}^, 8 = 2^?/, where
^ or 97 is even, and the first becomes {^^ — By^y + 128^/'j]'^ = sq.
This is of the original form, and 2^?; = 8 ^ y < 2xy, which is
impossible since we have chosen a solution for which xy has the
least possible value. Hence the equation has no solution in
which X and y are one even and the other odd, or in which both
are even but containing 2 to different powers.
Mr Pocklington, Some Diophantine Impossibilities. 117
Lastly, let both x and y be odd. Then x^ — 5y'^ is divisible
by 4, the quotient being odd. Writing the equation
fay" - 5y\' „ , ,
[ 4-^j +8^y = sq.,
we have (x^— 5y^)/4i = ± (w^ — 2v'^), xy= uv, where u and v are odd,
and x = a^, y = jS, u = ccy, v = ^S, where a, yS, 7, 8 are odd.
Taking the lower sign in the first equation we have
The greatest common divisor of the brackets must be unity, so
that a2=8/3^ + 57^ which is impossible to modulus 8. Taking
now the upper sign we have /3^ (a^ + 88^) = 7^ (4a^ + SS^). The
greatest common divisor of the brackets must divide 27, hence
a2^_8g2_y2 QY =97^, 4a^ + 5S^ = i8- or 9yS^ the other cases being
excluded by using the modulus 8. The second of these gives
+ a = (p — 5»7^)/2, B=^7}, where ^ and 77 are odd, and the other
becomes
which is of the original form. Also ^rj = 8 = xy/a/Sj < xy unless
a = ^ = 7 = 1 numerically. But then x='l, y= 8, u = l, v = B
and (x^ — 5y^)/4! = u^ — 2v^ gives S^ = 1, so that our solution is
x = y = \ numerically. Hence if we have any solution in which
X and y are odd and not both = + 1, and x is prime to 5y, we can
find another satisfying the same condition, in which the product
of the indeterminates has a smaller value. This is impossible.
Hence the given equation can be satisfied only if x = y or x=by
numerically, or \i x ox y vanishes.
11. We deduce that the first, second, fifth and tenth terms
of an arithmetical progression cannot all be squares, unless the
first term is zero or all are equal. For if possible let the squares
be those of 8, 7, /3, a (supposed positive). Then
a2/32 - 57^8^ = 4aY - S/S^S^
and if ^ = 0/8, y = <y8, u = ay,v = ^8, we have x^ — 6y^ = 4 (m^ — 2v^),
xy = uv and (x- - 5y^y + 128a;y = 16 (it^ + 2v^y. This is impos-
sible except in four cases. If x = y we have a/S = 78, which gives
- 4a2/82 = 4aY - 8^8\ Eliminating 7 this gives a.^8'^ = 28* - a^ and
so a^ = 8% whence the squares are all equal. If ^ = oy we have
a/3 = 578, which gives 5y^8^ = a.^ - 2^8^ Eliminating a. this
gives 5/3Y = 257* - 2y8*, which has no solution in integers. If
x = or y = 0, one of the numbers a, /S, 7, 8 must vanish, and
we easily see that it must be 8. Hence we have the theorem
stated above.
118 Mr Pochlington, Some Biophantine Impossibilities.
12. Some equations of the type considered can be solved
completely. We choose as an example oc/^ — ^x^y^ ■\-if = z^ and
confine our attention to the case of x prime to y, as it is clear
that when all such solutions are known the others can be
immediately derived from them. We cannot have both x and
y odd. Suppose y to be even. Then writing the equation
(a;^ + y^Y — Qx^y^ = z^ we have oc^ + y'^ odd, and either
x^ + y'^ = u^+ 6?;^, xy = 2uv, I
with u odd and (using modulus 4) v even, or
x^ + y^ = Su^ + 2v^, xy = 2uv,
with u odd and (using modulus 4) v also odd. In the first case
x^ + y^= 1, mod. 8, in the second case x^ + y^= 5, mod. 8.
In the first case x = a/3, y = 2yS, u = ay, v = ^B, with a, ^, y odd
and B even. The other equation now is yS^ (a^ — 6B^) = 'f {o? — 48^),
which gives a? — 6S^ = 7^, 0? — 4S^ = ^S^, the alternatives being im-
possible to modulus 8. From the second of these a = p + if,
B = ^t], and the first becomes (p + rff — ^l^tf = rf. Also
^7] = B< 2a^'yB < xy.
Of course ^ is prime to 77.
In the second case x = a^, y = 27S, u = ary, v = /3S, but a, /3, <y, B
are all odd. The other equation now is a^ (^^ — 87^) = 28^ (/3^ - 27^),
which gives 87^ — 0^ = 2B^, 2rf — /3^ = a^, the alternatives being
impossible to modulus 8. These give
(/3+a)(;8-a) = 4(7 + S)(7-S).
We suppose none of the factors to vanish. Each of the factors
is even, one of those on the left is not divisible by 4, and the
other must be divisible by 8. Supposing * it to be yS + a we have
where a, b, c, d are mutually prime (for a, /S, 7, B are), and c and
d are odd. Substituting in 2<f—^'^ = o?, we have
a^ (166^ - (?) - 2ad .bc + d^ (c^ - ¥) = 0.
But as ajd is rational we have
¥c^ + 16 (6^ - c^) (6^ - c^) = sq. = ^%
say. Putting 26 = 77, c= ^, this is |*— 4|V + '?*= ^^ where ^ is
prime to ij. Also numerically
I?? = 26c < 4tabcd < y^ — B^ < <y^ or < B^,
^7] < 16abcd <^^-a?<^^or < a\
* If it is /3- a we put {^ + a.)j2 = hd, (;8-a)/2 = 4a&, {y + b)j2 = ac, (7- 5)/2 = M
and get the same result as that given in the text.
Mr Pocklington, Some Diophantine Impossibilities. 119
Therefore we have ^rj either < <y^ or < ya or < 8/3 or < 8a, so
that ^T] < a^yS < xy. But if one of the factors does vanish we
find on working back that numerically a, /3, 7, h are all equal
and X = 2y.
Hence if we are given any solution in which x is prime to y
except the solution (1, 2) we can deduce a smaller one, and
repeating the process must ultimately reach the excepted solution
(1, 2), Hence we can reach any solution by retracing our steps
from this one. Let then ^rj satisfy ^^ — 4f V + V* = ^^ where rj
is even and prime to ^. In retracing the work of the first case
we see that each number can be determined, and that a is prime
to B, then that a, /9, 7, S are mutually prime in pairs, and finally
that X is prime to y. In retracing the work of the second case
we have b, c and ^ mutually prime and c odd. Then
a/cZ = (6c± 0/(166'- c^).
If we take a/d to be in its lowest terms we have a prime to b, c
and d, and d odd and prime to b and c. Then (/3 + a)/2 is prime
to (/3 — a)/2 and a is prime to /S, both being odd. The previous
equations now show that a, /3, 7, B are all odd and mutually
prime, so that x is prime to y. The ambiguous sign in the
value of a/d may be taken either way unless 6 = c = ^=l
numerically, and the values of a/d are not reciprocals of each
other. Hence in general we can deduce three solutions from
any given one, but only two can be deduced from the solution
(1, 2).
All these solutions are different. For if in retracing our steps
we arrive at the same solution in different ways, then in the
direct work there would be two alternative ways of proceeding.
But this does not happen, for the case that the work falls in can
be determined by the remainder oi a^ + y^ to divisor 8, and in each
case each step is uniquely determined.
By a method similar in principle but differing in detail we
can find the complete solution of 2x^ — y'^ = z\ From the least
solution (1, 1) we can deduce one other, but from any other we
can deduce two new ones, and by continuing the process can
reach any solution. In the case of y*—2x^=z^ we deduce one
solution from each solution of the allied equation 2x^ — y^ = z^ and
from any solution of the equation itself we can deduce one other,
and continuing can reach any solution. The arrangement of the
primitive solutions is not a dichotomously or trichotomously
branched one, as before, but consists of an infinite number of
unbranched sequences.
13. If the equation x^"" + y^'^ = z^ has any solution it has one
in which x is prime to y, one of them, say y, being even. Then
x"^ = V? — v^, y^ = 2uv, and if ii is even m + v = a"*, m - v = ;8'^
120 Mr Pocklington, Some t)iophantine Impossibilities.
u = 2'^~^7"', V = 8**, or if u is odd u + v= a'\ u- v = yS**, w = 7'^
^) = 2'*-^S^ whence a*^ + yS^ = (27)'* or «»» - yS*^ = (28)** respectively.
Hence af''^ + y^^ = z^ is impossible for all values of n for which
x'"' -\-yn— z''^ is impossible, that is according to a statement of
Fermat *, for all values of n greater than 2, or according to a
proof by Kummer-f-, for all values of n that are divisible by any
odd prime less than 100. Our equation is also impossible if n
is even,
14. We can of course apply the method of this paper to
a;" _}_ y»i _ ^2^ ]3jj^. ^g gg^ jjQ results other than those found by
AbelJ. We notice, however, that if it has any solution it has
one where x is prime to y. Hence {xyzj^ = x^y'^ (x'^ + y"^) is of
the form iv'^ =^ uv {u + v) with u prime to v, so that the problem
reduces to that of proving that an wth power cannot be repre-
sented primitively in a certain binary cubic form. We can now
apply the criterion that the number can be represented, but the
resulting condition is so complex that further progress appears
impossible.
15. Summary. We have proved or given a method for
proving that the following equations have no solutions in which
X, y, z are rational fractions or integers other than zero : —
«* — ipy^ = z^, where p is a prime of the form 8m + 3 ; x'^ + 2^/* = z^ ;
a^ — 8y* = z^ ; x'^ — y^ = pz^, where p is a prime of the form 8m + 3 ;
(x^ + y^f — Nx^y"^ = z^, where iV is odd, not of the form 8m + 3 and
not divisible by any prime of the form 4m + 1, and iV — 4 is an
odd power of a prime (including the case iV = 1) ;
where N is odd, not of the form 8m + 5 and not divisible by any
prime of the form 4m + 1, and iV -I- 4 is an odd power of a prime ;
(i»2 + 2/2)2 _ 2NxY = z^, where N is of the form 8m + 7 and is
divisible only by primes of the form 8m + 7, and iV — 2 is an odd
power of a prime ; (ic^ + y^y + '2NxY = •^^ where iV + 2 is an odd
power of a prime and N is of the form 8??i + 1 and either divisible
only by primes of the form 8m + 3 or only by those of the form
8m + 7 ; {x^ + 2/2)2 _ 8i\r^y ^ ^2^ ^fhe^e N is of the form 4m + 3,
is divisible only by primes of that form, and 2iV" — 1 is an odd
power of a prime; {x'^-\-y^y -\-SNx'^y^- = z^, where iV is of the form
,4m + l and divisible only by primes of the form 4m + 3, and
2N +1 is an odd power of a prime ; xf^ — nx^ + y^ = z^ for the
following values of n not included in the general results given
above, w = 17, 18, 20, 23, 24, 27; x' + nxY + y' = z^ for the
following values of n not included in the general results given
* Diophantus, p. 61.
t See H. J. S. Smith, Brit. Assoc. Report, 1860 (Oxford), p. 151.
J N. H. Abel, Oeuvres Completes (Christiania, 1839), vol. ii. p. 264.
Mr Pocklington, Some Diophantine Impossibilities. 121
above, n = \5, 19, 22, 91; x^'^ + y-^ = z'^ for all values of n for
which the equation x^^ -{■ y"^ = z^ has no solution in integers other
than zero. We have also indicated the proof that the following
equations have no solutions in which x, y, z are rational fractions
or integers other than zero, x and y being arithmetically unequal j
A'* + nx^y'^ ■\-y'^ = z^ \i n = 7, 14 ; oc^ — nx^y"^ -}- y^ = z'^ if n= 1; and
proved the impossibility of (x^ — 5y^y+ 128x^y^ = z^ if x, y, z are
rational fractions or integers other than zero and x=/=y ^5y
numerically. We have proved that four consecutive terms of an
arithmetical progression cannot each be square, unless all are
equal ; and that the first, second, fifth and tenth terms cannot
each be square unless the first is zero or all are equal. We have
solved the equation x* — 4ia^y^ + y^ = z^ completely and given the
nature of the complete solution of 2af — y*=z^ and y^ — 2x'^ = z^.
We have also shown that Fermat's impossibility may be made to
depend on the properties of a binary cubic form.
122 Mr Arher, On the earlier
On the earlier Mesozoic Floras of New Zealand. By E. A.
Newell Arber, Sc.D., F.G.S., Trinity College, Cambridge,
Demonstrator in Palseobotany.
[Read 25 November 1912.]
The presence of the "Terra Nova," the ship of Capt. Scott's
Second Antarctic Expedition (which is still at work in the far
South), during the winter months of the last two years in New-
Zealand waters has led to the collection of materials which are
likely to add considerably to our knowledge of the earlier fossil
floras of that island. For the seizing of this opportunity we are
indebted to Mr D. G. Lillie, B.A., of St John's College, a member
of the Biological Staff of Capt. Scott's expedition. Mr Lillie, who
previous to his departure for the South had had considerable
experience of the art of fossil plant collecting in this country, has
set himself the task of making fresh collections by modern methods
from the oldest (in a geological sense) plant-bearing beds in New
Zealand. He has also been the means whereby the best of the
fossil plant material, already collected by the Survey and other
institutions in New Zealand, has been sent on loan to Cambridge
to undergo a thorough examination for the first time. I thus
hope within the next few years to offer a fairly complete account
of the older Mesozoic floras of these islands.
In the present communication I have a two-fold object. In
the first place it is proposed to make some brief remarks on
the nature of the new material collected last year by Mr Lillie, in
conjunction with Mr R. Speight, F.G.S., of the Canterbury College,
Christchurch, New Zealand, from the celebrated Mount Potts
beds, the geological age of which has remained so long in doubt.
In the second it is proposed to revise our present knowledge of the
pre-Cretaceous floras of New Zealand.
The Mount Potts Beds.
Since the discovery in 1878 of the fossil flora of the Mount Potts
beds by McKay, a controversy has raged, on and off, in New Zealand,
as to the character and geological age of the flora of these beds in
the Rangitata Valley, Ashburton County (Canterbury), while in
Europe subsequent uncertainty has also continued until this day
on these points. In that year it was asserted, by Hector, that
Olossopteris occurred in these beds, and the impression has come
Mesozoic Floras of New Zealand. 123
to be widely held that a typical Glossopteris flora would one day
be forthcoming in this locality. This is really a matter of great
importance, for we have long been uncertain whether New Zealand,
in Permo-Carboniferous times, did, or did not, form part of the
great Southern continent of " Gondwana-land." If, as now seems
almost certainly the case, New Zealand formed no part of that
continent, then we are face to face with a fact of far-reaching
geological interest.
Mr Lillie's collections from Mount Potts show that the age
of the flora is either late Triassic (Rhaetic) or very early Jurassic.
Glossopteris itself does not occur, though a fern-like frond of
somewhat similar habit, but without a reticulate lateral nervation,
is present. This plant which has in the past been mistaken for
Glossopte7'is is a member of a new genus. The other plants
associated are all of the Mesophytic type, such as Thinnfeldia,
Gladopklebis and Baiera, and no typical Permo-Carboniferous
species are represented.
So far no Palaeozoic plants of any kind are known from New
Zealand ; which is a most remarkable fact. A Geological Survey
of the islands has been in existence for nearly half a century, and
there is little doubt that by this time the main features of the
geology of the islands are pretty well known. It is thus unlikely,
though not of course beyond the range of probability, that any
great series of Palaeozoic plant-bearing beds remains to be dis-
covered, and, bearing in mind the very wide extent of the
Glossopteris beds in Australia and other parts of Gondwana-land,
it is still more unlikely now that such rocks remain undiscovered
in New Zealand. Many new localities for fossil plants will doubt-
less be discovered in the future, but at present it seems likely
that the}'^ will only furnish Mesozoic or Tertiary plants.
A Review of our present knowledge of the earlier
Mesozoic floras of New Zealand.
At the present time our knowledge of the fossil floras of New
Zealand remains in an extremely unsatisfactory condition. It is
true that a number of Tertiary plants, and possibly also some of
Cretaceous age, were described and figured by Ettingshausen*
many years ago. From this evidence Ettingshausen drew several
startling conclusions with regard to the origin of the present flora
of New Zealand, conclusions which are now generally discredited,
and which tended at one time to throw considerable doubt on the
value of the study of fossil plants. The systematic portion of this
* Ettingshausen, Denkschr. K. Akad. Wissen., Wien (Math.-Natur. Klasse),
Vol. Liii. Pt. I. p. 143, 1887 ; see also Geol. Mag., Dec. 3, Vol. iv. p. 363, 1887, and
Trans. N. Zealand Inst. Vol. xxiii. p. 237, 1887.
124 Mr Arher, On the earlier
work, however, remains as one of the very few real contributions
to the study of the fossil floras of New Zealand.
It has been known, however, for more than half a century,
that New Zealand is rich in Mesozoic floras of pre-Cretaceous
age. Large collections of these plants were gathered together
from time to time by the officers of the Geological Survey of the
islands and by others, and several half-hearted attempts, at one
time or another, have been made to describe these floras, attempts
which generally ended in long lists of valueless nomina nuda (see
p. 130). As the literature on the subject of these pre-Cretaceous
floras stands at present, it consists of little more than strings of
names, applied to fossils which have never been described or figured,
names which are therefore meaningless.
There have, however, been some exceptions. Through the
good ofiices of Mr Lillie, Mr P. G. Morgan, the Director of the
New Zealand Geological Survey, has kindly sent me on loan all
the previously figured specimens in the Collection of the Survey.
I have also gratefully to acknowledge my indebtedness in this
matter to Mr J. Allan Thomson, Palaeontologist to the Survey,
for facilitating the loan of these specimens, and for much informa-
tion as to the localities and to the literature published in New
Zealand.
The first step in the revision of these fossil floras has naturally
been a re-examination of the specimens which have hitherto been
regarded as types. I propose here briefly to review these specimens
with the object of sorting out those which are of real value, and
of further compiling lists of imperfect determinations and of
nomina nuda (p. 130). Such names cannot unfortunately be
entirely ignored, and the lists at the conclusion of this paper have
at least the melancholy interest that they include terms which
should never again be applied to any fossil or living plants.
Osmundaceous Stems.
There are two fossil plants of which our knowledge is on
altogether a diff'erent plane to that of any other plants from
New Zealand. These are the two Osmundaceous Fern-stems,
obtained from the Jurassic rocks near Gore, Otago District,
Osmundites Gibbiana, K. and G. V,, and 0. Dunlopi, K. and G. V.,
so named in honour of their discoverers, Mr Robert Gibb, and
Mr R. Dunlop respectively. These are the only petrified plant
remains, with the exception of certain post-Jurassic woods,
so far known from New Zealand. They have recently been fully
described by Dr Kidston and Prof. Gwynne- Vaughan * conjointly.
* Kidston and Gwynne- Vaughan, Trans. Roy. Soc. Edinb. Vol. xlv. Pt. iii.
p. 759, 1907.
Mesozoic Floras of New Zealand. 125
linger Records (1864).
The earliest descriptions and figures of Mesozoic plants from
New Zealand are those given by Unger in the " Palaontologie
von Neu-Seeland " by Hochstetter and others (Novara-Expedition,
Geol. Theil, 1 Band, 2 Abtheil., 1864). They are few in number.
The present whereabouts of these specimens is unknown to me,
and I have consequently not been able to examine them.
, Polypodium hochstetteri, Unger (Plate II). This plant is no
|idoubt a Cladophlebis, allied to G. australis (Morr.). The chief
difference between the Australian and New Zealand species appears
to be that the lateral nerves in the former case fork twice, as a
rule, whereas, in the New Zealand plant, they are shown as only
occasionally forking a second time. As is well known, the species
of this genus are exceedingly difficult to discriminate, and in the
absence of any personal knowledge of Unger's type, I am, for the
present at least, inclined to include the New Zealand plant in the
older species C. australis (Morr.). In the similar British plant,
G. denticulata (Brongn.) the lateral nerves appear as a rule to fork
only once. For the present I am inclined to regard G. denticulata
(Brongn.) and C. australis (Morris) as distinct species. Unger's
plant was obtained from the Kalkmergelbanken (Calcareous marls)
of the West Coast of the province of Auckland, south of the
estuary of the Waikato river.
Asplenium palmopteris Unger (Plate I, figs. 4 — 8). This plant
appears to be a Sphenopteris, and, were the fructification known,
one would rather expect that it would be referred to the genus
Coniopteris. It appears to be a distinct species, though it bears
some slight resemblance to the Jurassic frond Sphenopteris Mur-
rayana (Brongn.). On the other hand Professor Seward* regards
it as identical with the Wealden frond, Sphenopteris Fittoni,
Seward. Whatever the correct genus may be, Unger's specific
name can hardly stand, for it had been previously used by Geinitz
in 1855 as a generic term, and I am quite in agreement with the
rule that the same term should not be used both as a generic and
specific name.
I do not, however, propose to invent a new specific name for
this plant at present, for I have yet some hopes of rediscovering
Unger's types. I will, therefore, simply term it Sphenopteris sp.
It was obtained from coal-bearing beds on the West Coast of the
province of Auckland, between the estuary of Waikato and the
harbour of Whaingaroa.
Unger also figures three obscure specimens from the coal-
bearing beds of Pakawau in Massacre Bay, in the province of
* Seward, The Wealden Flora, Part i. p. xxxiii (Brit. Mus. Cat.), 1894.
126 Mr Arber, On the earlier
Nelson. Those described as Phonicites ? sp. and Equisetites ? sp.
are too imperfect even for generic determination. That figured
as Neuropteris sp. is possibly a fragment of a frond of Glado-
phlehis.
Hectors Records (1870—1886).
The late Sir James Hector apparently made more than one
attempt at an account of the fossil floras of New Zealand, but,
for some reason or other, they all ended, with one exception,
in long lists of nomina nuda. His " Catalogue of the Colonial |
Museum, Wellington," 1870, his Progress Report for 1878 (New .;
Zealand Geological Survey, p. viii), his paper in the Trans, and I
Proc. New Zealand Inst. (Vol. xi. p. 536), 1879, and his Appendix \
to the Official Catalogue of the New Zealand Court, International
Exhibition, Sydney, 1879 (being the first edition of his Handbook ,
of New Zealand), all contain long lists, for the most part of new |
specific names, but without any figures or descriptions. The last I
but one of these papers was meant to serve as a " prodromus of !
a work on the Fossil Flora of New Zealand containing descriptions '
and figures of about one hundred species," This work however
never appeared*. (
In the " Detailed Catalogue and Guide to the Geological ![
Exhibits of the New Zealand Court of the Indian and Colonial li
Exhibition " (London) of 1886, Hector figures (pp. 65—66, figs. •
30 and 30 A) a number of plants without descriptions, in addition
to another long list (pp. 31 — 32) of nomina nuda.
Despite the lack of descriptions and the rough nature of the '
figures, I am inclined to accept most of the specimens figured as ;
types duly published, and as species to be reckoned with, though I
as I shall show here the majority of the names are synonyms of '
plants previously described. I have seen most of these types, and
I now include a brief revision of this flora here, }
The first eight specimens were derived from the Clent Hills j
(Ashburton County) in the province of Canterbury. j
Asplenites rhomboides. Fig. 30 (1) of Hector's Catalogue is an j
inaccurate drawing of a very small fragment of a Thinnfeldia, t
somewhat recalling Thinnfeldia argentinica (Gein.) from Argentina, I
For the present it may be referred to as Thinnfeldia sp. Hector's I
specific name cannot stand in relation to Thinnfeldia, since it !
approaches too closely Ettingshau sen's T. rhomboidalis.
* There are in existence, however, in New Zealand a large number of copies of
lithographed plates, many of which contain figures of fossil plants, and these no
doubt represent the beginnings of this work. No scientific names appear on the
plates and further none of them were ever published, and thus it is quite impossible
to regard these figures as having any scientific status as regards priority of nomen-
clature.
Mesozoic Floras of New Zealand. 127
Pecopteris acuta. Fig. 30 (2) of Hector's Catalogue is a small
fragment of a frond of Cladophlebis, far too incomplete to merit
specific distinction, and is thus best termed Cladophlebis sp. The
specific name 'acuta' could not stand in any case, as the term
Pecopteris acuta had been used long previously by Brongniart for
another plant.
Pecopteris linearis. Fig. 30 (3) of the same work is a reduced
and very inaccurate drawing of a frond probably identical with
Cladophlebis australis (Morris).
Vertebraria novce-zealandiw. Fig. 30 (4) is a restored sketch
of a very obscure specimen which it is quite impossible to determine
even generically. It certainly has nothing whatever in common
with Vertebraria, and this name must in future be excluded from
lists of the fossil plants of New Zealand.
Taxites maitai. Fig. 30 (5) is founded on a very small fragment
of Coniferous branch, probably identical with Palissya conferta
(Old. and Morr.) first figured in 1862.
Pecopteris ovata. Fig. 30 (6) is again a small fragment of a
frond of Cladophlebis, and, although I have not seen the original
specimen, I have no doubt that it is best described as G. sp. This
name P. ovata was also used long previously for a quite different
plant by Brongniart.
Pecopteris obtusata. Fig. 30 A (1) appears to represent a distinct
species of Cladophlebis, which will have to be renamed later on.
Hector's name P. obtusata had already been occupied by a quite
different plant, described by Presl in 1833.
Camptopteris incisa. Fig. 30 A (8) almost certainly represents
a small portion of the frond of Dictyophyllum acutilobum
(Braun).
Next, we have six specimens from the Mataura Falls, in the
province of Southland.
Macrotwniopteris lata. Fig. 30 A (4) of Hector's Catalogue is
undoubtedly Tceniopteris crassinervis (Feistm.) first described from
the Rajmahal Group of India in 1877. It is certainly not
Twniopteris lata (Old. and Morr.).
Lomarites pectenata. Fig. 30 A (5) represents a species of
Gleichenites, allied to, but perhaps specifically distinct from, the
Indian Gleichenites gleichenoides (Old. and Morr.) and may for
the present be regarded as a distinct species Gleichenites pectinata
(Hector).
Taxites manawao. Fig. 30 A (6) represents a plant which
appears to be undoubtedly Pagiophyllum peregrinum (L. and H.),
well known in the earlier Mesozoic rocks of England and the
Continent.
Pterophyllum matauriensis. Fig. 30 A (7) appears to me to
be a distinct species, though somewhat similar to some of the
1.28 Mr Arber, On the earlier
Pterophyllums of the Jurassic rocks of the Rajmahal Hills of
India, This species may thus stand for the present.
Sphenopteris asplenoides. Fig. 30 A (8) represents a small
fragment of a Sphenopteris frond, the original of which I have
not seen. The specific name cannot in any case be retained, for
it had been previously applied to another plant by Sternberg, as
far back as 1826.
Taxites kahikatea. Fig. 30 A (11) represents a small fragment
of a Coniferous branch, the type of which appears to have been
lost. Judging by the figure, it would appear to be impossible to
refer this plant with certainty to any genus, and thus I should, for
the present at any rate, be inclined to omit this determination
from any list of New Zealand fossils.
Lastly we have three species from Waikawa.
Taxites manawao. Fig. 30 A (2) represents a specimen which
I have not seen, but which I imagine is probably identical with
Palissya tenuifolia (McCoy) first described from New South Wales
in 1847. This name (see above) was applied to two quite distinct
plants by Hector in this Catalogue.
Fecopteris grandis. Fig. 30 A (3), the original of which I
have not seen, no doubt represents a portion of a frond of
Cladophlebis australis (Morr.).
Asplenites palceopteris, Unger. Fig. 30 A (10), which again
I have not seen the original of, is a fragment of a Sphenopteris,
which bears a considerable resemblance to fig. 6, Plate I of Unger's
memoir, and is very possibly correctly referred to Unger's species
by Hector. Unger's plant has been alreadj'^ discussed on p. 125.
We see therefore that even if we are inclined to accept 15 of
the 16 plants, first figured but not described by Hector in 1886,
as published types, six of them had been previously recorded from
other regions, and at the most only six others are likely to stand
as first records.
Ettingshausen s Records (1887).
In 1887 Ettingshausen* discussed the floras of five localities,
Mount Potts, the Malvern Hills, Haast Gully (Clent Hills),
Mataura and Waikawa, and included long lists consisting for the
most part of new species. All these are however nomina nuda,
and as regards the pre-Cretaceous floras this paper is best
neglected. Some of these names had been previously published
in the preceding year in a paper by Haast f.
* Vide ante. . .
t Haast, Trans, and Proc. New Zeal. Inst. Vol. xix. for 1886, p. 449, 1887.
Mesozoic Floras of New Zealand. 129
Cries Records (1888).
In 1888 Crie* published a short note on a comparison of the
earlier Mesozoic floras of New Zealand, Australia and India. He
also instituted a considerable number of new names, all of which
are nomina nuda.
■ Since 1888, no further contributions to this subject have
been made, so far as I am aware, with the exception of the recent
work of Kidston and Gwynne-Vaughan already mentioned (p. 124).
The following list sums up our present knowledge of the
pre-Cretaceous floras of New Zealand, and includes only ten
species, with the addition of three or four other types for which
new specific names must be found. I hope before very long to
publish a full account, with figures, of these plants, and of other
ispecimens from the same localities.
A List of the Valid Species (known in 1912) from the Pre-Cretaceous
rocks of New Zealand.
Cladophlehis australis (Morris).
Dictyophyllum acutilohunn (Braun).
Gleichenites pectinata (Hector).
Osmundites Duidopi K. and G. V.
Osmimdites Gihhiana K. and G. V.
Palissya conferta (Old. and Morr.).
Palissya tenuifolia (McCoy).
Pagiop)hylluin peregrinuvfi (L. and H.).
Pterophylluin matauriensis Hector.
Tceniopteris crassinervis (Feist.).
The occurrence of new species of the genera Thinnfeldia,
Gladophlebis, and 8phenopteris has been also noted.
In conclusion, I add lists of names applied to figured
specimens of New Zealand fossil plants, which are synonyms
etc., and also a list of nomina nuda.
I A list of names applied to figured specimens of Pi-e-Cretaceous
plants from New Zealand, which are rejected as being either synonyms
or names previously occupied or names founded on imperfect materials.
Asplenites palceopteris Hector.
; Asplenites rhomboides Hector.
i Asplenium palceopteris linger.
Camptopteris incisa Hector.
Pecopteris acuta Hector.
Pecopteris gra7idis Hector.
Pecopteris hochstetteri Hector.
Pecopteris linearis Hector.
Pecopteris ohtusata Hector.
* Crie, Compt. Eencl. Vol. cvii. p. 1014, 1888,
VOL. XVII. PT. I. 9
130 . Mr Arber, On the earlier
Pecopteris ovata Hector.
Polypodium hochstetteri linger.
Sphenopteris asplenoides Hector.
Taxites kahikatea Hector.
Taxites maitai Hector.
Taxites manawao Hector.
Vertebraria novca-zealandim Hector.
A List of Nomina Nuda applied to Pre-Cretaceous Fossil Plants
from jSTew Zealand, with an indication of the place of publication of
the earliest references to the names.
* First mentioned in Hector, Cat. Colonial Mus. Wellington,
1870, pp. 199—201.
t First mentioned in Hector, Rep. Geol. Explorations (1877 — 78),
Geol. Surv. JV. Zeal. 1878, p. viii.
X First mentioned in Hector, Trans, and Proc. N. Zeal, Inst.
Vol. XI. p. 536, 1879.
§ First mentioned in Hector, Official Cat.N. Zeal. Court, Intern.
Exhib. Sydney, 1879, Appendix, pp. 48—49.
II First mentioned in Hector's Detail. Catal. K Zeal. Court, Indian
and Colon. Exhib. London, 1886, pp. 31 — 32.
U First mentioned by Ettingshausen in Haast, I'rans. and Proc.
N. Zeal. Inst, for 1886, p. 449, 1887.
** First mentioned in Ettingshausen, Denkschr. K. Akad. Wissen.,
Wien (Math.-Nat. Klasse), Vol. Liii. p. 143, 1887.
ft First mentioned in Crie, Compt. Rend. Vol. cvii. p. 1014, 1888.
Alethopteris Hochstetteri Hector f.
Alethopteris insignis Hector f.
Araucarioxyion australe Crieff.
Asplenites cuneata Hector §.
Asplenites distans Hector §.
Asplenites ohlonga Hector§.
Asplenium palceo-dura Ettingshausen H.
Asjdenium Ungeri Ettingshausen H. J|
Asteroijhyllites clentii Hector §. "
Baiera australis Ettingshausen*"*.
Camptopteris haastii Ettingshausen**.
Camptopteris novoi-zealandice Hector f.
Gyperites wiivi Hector§.
Dictyophyllum huttonianwni Crieff-
Equisetum microdon Ettingshausen**.
Gleichenia waitia Hector ||.
Glossopteris haastii Hector §.
Hymenophyllites australis Ettingshausen*'*.
Lycojjodites palmo-selaginella Ettingshausen**.
Macrotceniopteris affinis Ettingshausen**.
Macrotceniopteris zeelandica Crieff.
Neuropteris stricta Hector f.
Nilssonia zeelandica Ettingshausen**.
Mesozoic Floras of Neiu Zealand. 131
Noegyerathia valida Hector ||.
Oleandridum distans Hector §.
Oleandriduni JnUtoni Hector f.
Oleandridum matauriense Hector §.
Oleandridum obtusatum Hector §.
Oleandriduini stipidatum Hector§.
Oleandridum, tceniopteroide Hector §.
Oleandridwin vittatum Hector f.
Falceozamia mataurensis Hector % .
Palissya australis Crieff.
Palissya podocarjnoides Ettingshausenll.
Pecojiteris distans Hector*.
Pecopteris gracilis Hector*
Pecopteris grandis Hector*.
Pecopteris haastii Hector §.
Pecopteris ligidatus Hector*.
Pecopteris obliqua Hector §.
Pecopteris oblongis Hector §.
Pecopteris proxiTua Ettingshausen**.
Pecopteris serratus Hector*.
Pecopteris stricta Hector §.
Pisoniaphyllites novce-zealandice Hector §.
Podozamites malvernictis Ettingshausen**.
Protocladtis lingua Ettingshausen**.
Psaronius inataurensis Crieff.
Pterophyllum dieffenbachi, Ettingshausen **.
Pterophyllum grandis Hector ||.
Sphenopteris amissa Ettingshausen**.
Sphenopte7-is clentiana Ettingshausen**.
Sphenopteris lomaroides Hector §.
Tceniopteris gramineus Hector*.
Tceniopteris Huttoni Hector jj.
Tceniopteris linearis Hector*.
Tceniopteris lomariopsis Ettingshausen **.
Tceniopteris matauriensis Hector ||.
Tceniopteris 2)seudo-simplex Ettingshausen **.
Tcenio2)teris pseudo-vittata Ettingshausenll.
Tceniopteris obtusatus Hector*.
Tceniojderis robustus Hector*.
Tceniopteris tetranervis Hector ||.
Taxites manoao Hector ||.
Taxites miro Hector §.
Taxites totara Hector §.
Taxites totara,nui Hector ||.
Thinnfeldia australis Ettingshausen**.
Tympanojyhora paradoxus Hector ||.
Zamites Etheridgei Crieff.
Zamites mataurensis Ettingshausen**.
9—2
132 Mr Rastall, The Mineral Composition of
The Mineral Composition of some Cambridgeshire Sands and
Gravels. By K H. Rastall, M.A., Christ's College.
[Read 25 November 1912.] J
It has been recognized of late years that a detailed and l|
careful study of the mineral composition of sands and gravels \\
often yields valuable information as to the sources from which '
the material was derived and frequently throws much light on i|
the geographical and other conditions prevailing at the time of '
deposition*.
Some time ago I had occasion to apply this method of
research to the Lower Greensand of Bedfordshire, Cambridge-
shire and Norfolk. The results of this investigation have not
yet been published, but they were of some interest, and it occurred
to me that it might be useful to compare with them the mineral
composition of some of the Pleistocene and Recent deposits of the
same district, in order to see whether it was possible to trace the
derivation of material from the Lower Greensand as well as from
far-travelled glacial deposits.
A careful examination of numerous specimens of the so-called
Neocomian sands showed that all possessed certain peculiar
features in common ; of these features the most important for
the present purpose are the abundance of kyanite, staurolite and
tourmaline, and the complete or almost complete absence of '
garnet, amphiboles and pyroxenes. This is not the place to >
discuss the source from which these materials were derived :
it must suffice here to say that they were certainly not of local
origin, but must have come from some distant land-area not now
exposed at the surface. The presence of tourmaline is not of
much significance, since this mineral is very stable and resistant,
and is common in nearly all sandy sediments, being often passed
on with little change from one formation to another. But the
freshness and angularity of the chips and crystals of kyanite and
staurolite in the Neocomian sands suggest that they were then
recently separated from the parent rock, and not derived from
some older sediment.
* Thomas, ' The Petrography of the New Red Sandstone of the West of
England,' Quart. Journ. Geol. Soc. Vol. xv. 1909, pp. 229—245.
some Cambridgeshire Sands and Gravels. 133
The Collection and Preparation of the Material.
The specimens on which the present paper is founded were
collected from deposits of several different ages, as follows * :
Surface Deposits.
The Gravels of the Present River System.
The Gravels of the Ancient River System.
The Plateau Gravels.
Most of the samples were collected by myself, but for some
specimens of blown sands and other surface deposits from the
Breckland I am indebted to Dr Marr. Whenever possible a
fairly large quantity of the sand was collected from different
points in the same bed so as to obtain a really representative
sample. After drying, the material was passed through a sieve,
to remove large stones, and the finer portion reserved for chemical
and mineralogical investigation.
The samples were first washed by shaking with water to
remove the fine muddy material ; after several repetitions of this
process the sand was well boiled with water, and then dried.
In this state it was then usually ready for examination with a
pocket-lens. Very commonly, however, many of the grains were
still covered with a pellicle of calcium carbonate or iron oxide,
and further treatment was required to render the constituents
visible.
Methods of Investigation.
In order to get rid of the calcium carbonate, most of which
was in the form of minute particles of Chalk, the samples were
then treated with dilute hydrochloric acid. When the effervescence
had subsided the washing and drying were repeated and notes
were then made on the general appearance of the samples.
If the sand appeared to be highly ferruginous, it was then
boiled for some time with fairly strong hydrochloric acid. This
removed the iron oxides almost completely, and after again
boiling with water, thorough washing and drying, the sand was
ready for detailed examination. No doubt this treatment would
also remove certain unstable minerals, if present, but from a
comparison of samples, some of which had been treated with
strong acid, and others not, it appears that the loss was not
serious. Most of the important minerals which are likely to occur
in sands are not affected by this treatment, and it is obvious that
* Penning and Jukes-Brown, ' The Geology of the Neighbourhood of Cam-
bridge' (Expl. quarter-sheet 51 S.W.), Mem. Geol. Surv. 1881, pp. 82—109. Marr
and Shipley, ' The Natural History of Cambridgeshire,' Brit. Ass. Handbook, 1904,
pp. 42 — 50. Eastall, ' The Geology of Cambridgeshire, Bedfordshire and West
Norfolk,' Geol. Ass. Jubilee volume, 1909, pp. 173—177.
134< Mi^ Rastall, The Mineral Composition of
a mineral grain covered by an opaque skin of haematite or limonite
cannot be identified, and is therefore useless, unless this skin is
removed. It is necessary therefore to run the risk of decomposing
some of the less stable minerals.
The separation of the heavier constituents was effected by the
heavy-liquid method, the particular liquid used being bromoform,
which when pure has a density of about 2'93. This removes all
the quartz and felspar and nearly all the glauconite. The density
of this latter mineral, however, appears to be variable since some
green grains occasionally sank in bromoform. According to the
best authorities the density of glauconite is about 2'3 only. It is
evident therefore that this point requires further investigation.
It is unnecessary here to describe the precise form of apparatus
employed, which was of the most simple nature. A very little
experience showed that any attempt at a quantitative determina-
tion by the heavy-liquid method must be absolutely unreliable,
owing to the impossibility of ensuring a complete separation. In
some cases it was found necessary to treat the heavy residues again
with acid in order to get rid of the pellicle of iron oxide which is
such a persistent feature in these sands : in a few instances this
was unnecessary. A part of each residiie was then mounted in
Canada Balsam in the usual way for microscopic examination, and
the rest reserved for any other tests required.
Detailed Description of the Sands.
A large number of samples were examined by the above
methods, but many of them were very much alike in their general
characters, and it is unnecessary to describe them all. The following
cases are therefore selected as typical examples of the sands and
finer portions of the gravels of different ages.
I. The Plateau Gravels.
Pit on Golf- Links, summit of Gog-Magog Hills,
200 ft. above O.D.
The beds exposed in this pit consist partly of gravel and partly
of a very fine-grained sand in thick beds, which often show marked
contortion. The larger constituents of the gravel comprise a great
variety of far-travelled rocks, and from pits closely adjoining the
present one, which were open a few years ago, a large number of
interesting rock-types were recorded, including abundant igneous
rocks, both Scotch and Scandinavian, Carboniferous Limestone and
Millstone Grit, several varieties of Jurassic sediments, Carstone
and Hunstanton Red Rock, together with shells of Gryphoea bored
some Gamhridgeshire Sands and Oravels. 135
by Pholas or some other rock-borer. The presence of these and
of the Cretaceous rocks of Norfolk type is of special significance,
as indicating derivation of the material from the Wash district.
Eounded pebbles of Chalk are abundant, but they are believed
to be of Yorkshire type and the large grey tabular flints are much
more like those of Lincolnshire than of any more southern
locality*.
The bed of sand, about 5 feet thick, which is now being
worked for use on the golf-links, is of very fine texture, marly
and rather tenacious, of a yellow-brown colour. It differs much
in appearance from other sands of the district. It effervesces only
feebly with dilute acid, but very large quantities of fine mud are
removed by boiling with water and subsequent washing. Chips
of white flint are common, but the most notable constituent seen
on macroscopic examination is mica, both white and brown, together
Avith glauconite. As will appear later, mica is almost completely
absent from the other sands investigated.
From a first separation, without preliminary treatment with
acid, the heavy residue was very large, and mostly of a brown
colour, owing to the presence of a coating of limonite. In this
state identification of the grains was impossible, and the residue
had to be digested with acid and again separated.
On examining a microscope-slide of the ultimate residue the
first feature to be noticed is the small average size of the grains,
which are much less than those of the other gravels of the
Cambridge district, and can only be compared in this respect
with the blown sands from the neighbourhood of Brandon, to be
afterwards described.
The following is a list of the principal minerals identified :
hornblende, augite, garnet, epidote, zircon, tourmaline, rutile,
magnetite and other iron ores, and abundant flakes of muscovite.
Kyanite and staurolite are notably rare. Hornblende is extra-
ordinarily abundant, both the common green variety and greenish
blue arfvedsonite. Tourmaline is also abundant and shows many
shades of colour, brown, pink, blue and green : the grains are as
usual very well rounded. In comparison with other local sands,
pyroxenes, epidote and zoisite are common.
The most striking features of this sand are the abundance
of hornblende and muscovite, and the strange shapes of many
of the grains, which can best be described as sharply angular
chips. It is evident that in the case of most of the constituents
there has been little rolling, either by water or wind action ; only
the grains derived from some older formation, such as tourmaline
and kyanite, are conspicuously rounded. The significance of the
* Eastall and Eomanes, ' The Boulders of the Cambridge Drift,' Quart. Jour.
Geol. Soc. Vol. Lxv. 1909, p. 254.
136 Mr Rastall, The Mineral Composition of
presence of much muscovite in this sand, and its absence in other
localities, will be discussed in the concluding section. It is at any
rate clear that this high-level deposit differs greatly from the
low-level sands next to be described.
II. Sands and Oravels of the Ancient River System.
(a) Pit on Newmarket Road, half a mile beyond Barnwell
Junction, 46 ft. above O.D.
In this pit, which is now being worked for gravel, are seen
seams of very white sand, interbedded with fine flint gravel.
On examination with a pocket-lens, the sand is seen to be very
rich in minute fragments of Chalk, flint chips and grains of
glauconite. It also contains many small white prismatic objects,
which, as Dr Bonney suggests, are probably prisms from the
disintegrated shells of Inoceramus, together with minute spines
of Echinoids.
After washing, the sand effervesced very strongly with dilute
acid, and a second washing removed a large amount of muddy
material ; hence the grains are evidently partly cemented by
calcareous matter.
In the first separation in bromoform, many brown grains
came down : the majority of these proved to be grains of light
minerals with a coating of iron oxide (limonite). After prolonged
treatment with acid this coating was removed, and many opaque
grains were left, of various colours, white, pink, green and brown.
These grains were easily separated from the true heavy residue
by shaking with water in a dish. They are very well rounded
and uniform in size, and certainly come from the Lower Greensand.
In the heavy residue the most abundant mineral is garnet,
either colourless, pink or brownish red, for the most part in very
angular chips of varying size. Green hornblende is also common,
while blue-green arfvedsonite and pale green augite also occur.
Other minerals noted are tourmaline, kyanite, staurolite, epidote,
zircon and rutile, besides opaque iron ores.
(h) Pit behind the Travellers' Rest Inn, Huntingdon Road,
1 mile from Cambridge, 83 ft. above O.D.
This large pit is opened in gravel of very variable coarseness,
with abundant seams of brownish sand. This gravel is notable
in that it yields an unusual number of large boulders, up to
one foot in diameter: the great majority of these are of sandstone,
probably Carboniferous, but other rocks are fairly common. From
this locality a large number of far-travelled erratics have been
some Gamhrtdgeshire Sands and Gravels. 137
recorded, including scratched blocks of Carboniferous limestone,
Millstone Grit, basalt, pink granite and rhomb-porphyry*.
The sand is fairly clean, of a light brown colour, and
effervescing very freely with acid. In this case a double
separation was found necessary, and the light residue from the
second separation was found to consist largely of glauconite,
which had been coated with iron oxide.
Among the heavy minerals of this specimen, the following
were identified : pink garnet, tourmaline, both brown and blue,
staurolite, kyanite, epidote, hornblende, augite and hypersthene,
together with black grains which are presumably magnetite.
Zircon is very rare. The most notable features are the extreme
angularity of most of the garnets, and the comparatively large
size of the heavy mineral grains.
(c) Furze Hill, Hildersham, 200 ft. above O.D.
This specimen was obtained from the actual bed in which a
Palgeolithic implement was found in situ by Dr Marrf. It is a
yellowish brown rather coarse sand with many small flints. After
cleaning in the usual way the sample was found to consist chiefly
of grains of clean white quartz, many of which are notably rounded.
Coloured minerals are not abundant, consisting chiefly of grains of
iron oxide. After separating in bromoform the heavy residue was
examined microscopically, and was found to contain rounded grains
of iron oxide together with brown and blue tourmaline, staurolite,
zircon, rutile, garnet, and a very little kyanite. Most of the heavy
grains are very much rounded, and they show much variation in
size.
This sand is very unlike the specimen collected at about the
same level on the Gog-Magog Golf-Links, and has evidently been
laid down in rapidly moving water, with much more rolling of
the grains. This fact helps to confirm the idea put forward by
Dr Marrj-, that these gravels and sands belong to the ancient
river- system rather than to the plateau gravels.
III. Gravels of the River Gam,
Highest or Barnwell Terrace.
(a) Gravel Pit close to L. and N. W. Railway bridge between
Trumpington and Shelford, 60 ft. above O.D.
This pit shows chiefly a moderately fine flint gravel of the
usual type, with occasional seams of sand. From the most
* Eastall and Eomanes, 'The Boulders of the Cambridge Drift,' Quart. Jour.
Geol. Soc. Vol. Lxv. 1909, p. 254.
t Marr, 'On a Palaeolithic Implement found in situ in the Cambridgeshire
Gravels,' Geol. Mag. 1909, pp. 534—537.
138 Mr Rastall, The Mineral Composition of
important of the latter the sample was collected. In the heavy
residue the dominant mineral is pink garnet, and opaque grains
of magnetite and other iron ores are also abundant. The grains
are very variable in size, many of them, especially the garnet,
being rather large.
The following is a list of the minerals identified : garnet,
tourmaline, staurolite, kyanite, hornblende, augite, hypersthene,
zircon, rutile, epidote and magnetite.
Garnet, both pink and colourless, is very abundant ; some
grains are rounded, most are subangular, while a few are very
sharply angular. The grains of brown and pink tourmaline are
generally very well rounded and appear to be derived, while the
staurolite and kyanite grains exactly resemble those of the Lower
Greensand, being almost certainly derived from that formation.
{h) Swan's Gravel Pit, Milton Road, 45 ft. above O.D.
This well-known pit, which is situated near the first milestone
on the Cambridge and Ely road, is excavated chiefly in rather fine
flinty gravel which contains a good many far-travelled rocks. The
specimen was collected from a thick seam of rather ferruginous
sand which forms the north-western corner of the pit. After
cleaning in the usual way it was found to contain abundant dark
grains together with glauconite. The proportion of grains sinking
in bromoform was unusually large and most of them were so thickly
coated with iron oxide as to require prolonged treatment with acid.
It is noticeable in this and other cases that the iron oxide is often
regularly deposited in concentric coats round some mineral nucleus,
and when these shells are only partially destroyed a regular oolitic
structure giving a black cross in polarised light can often be seen.
The final residue consisted of abundant rather large grains,
most of which were fairly well rounded, sharply angular crystals,
other than garnet, being uncommon. The list of minerals re-
cognised is as follows : garnet, tourmaline, kyanite, staurolite,
epidote, hornblende, augite, hypersthene, rutile and zircon :
possibly also brookite and anatase. The garnets vary much in
colour, being most commonly pink or brownish pink, sometimes
colourless. The tourmaline grains are very round, and include
brown, pink and blue varieties. There are many rounded grains
of yellow-green epidote, which in everything but colour have
a strong resemblance to monazite.
This sample is specially notable for the large size and rounded
form of the kyanite grains. Generally speaking, the grains of
heavy minerals are conspicuously more rounded than those of the
sands previously described.
some Cambridgeshire Sands and Gravels. 139
Second or Chesterton Terrace.
Pit near Pike and Eel, Chesterton, 24 ft. above O.D.
This pit is opened up in fine flint gravel with seams of rather
coarse sand and in it have been found a good many far-travelled
rocks, including rhomb-porphyry. To the naked eye the sand
when dry is white and chalky in appearance. It shows many
grains of Chalk and flint together with glauconite, fragments of
the thin shells of fresh-water moUusca, prisms of Inoceramus and
Echinoid spines. With dilute hydrochloric acid it effervesces
strongly, and in the cleaned sample dark grains are fairly
abundant.
The sand yields an abundant heavy residue in which nearly
all the grains are covered with brown limonite. After treatment
with strong acid many of these are found to be glauconite or a
pale brown isotropic material of uncertain character, perhaps
consisting of colloid silica. The principal minerals identified are
garnet, hornblende, rutile, zircon, kyanite, staurolite and tour-
maline. The garnets are mostly subangular and rounded, only
a few being angular. The grains of tourmaline, which are chiefly
brown, are well rounded. The minerals in general do not present
any special features of interest : they are on the whole more
rounded than in the older gravels.
IV. Gravels of the Great Ouse Basin.
Gravel Pit half a mile S.E. of Fenstanton, 36 ft. above O.D.
This pit is situated on the north side of the Cambridge and
Huntingdon road, close to the county boundary. It shows a
ferruginous gravel of the usual type, with brown 'pipes' and
seams of sand.
The sand is brown in colour, with very little muddy matter.
It was treated at once with dilute acid, giving only slight
effervescence, and yielding a remarkably white sample consisting
of clean bright colourless quartz and rounded grains of white
flint with much glauconite. In the heavy residue pink garnet
and bright grains of magnetite were conspicuous before mounting,
while a few grains of glauconite sank in the bromoform.
The heavy grains are of unusually large size and garnet is
predominant, being often extremely angular in shape ; other
transparent minerals are present only in small quantity. The
minerals recognized are as follows : garnet, generally very angular,
tourmaline, kyanite in fine large crystals, staurolite, hornblende,
epidote and rutile ; zircon is rare.
140 Mr Ra stall, The Mineral Composition of
The exact stratigraphical position of this gravel is uncertain :
it is situated near the margin of a low plateau, which slopes down
somewhat suddenly within a short distance to the alluvial flats
of the Great Oiise. In general appearance it strongly resembles
the gravels of the Cam, and it is included here for the sake of
comparison.
V. Surface Deposits.
Blown Sand, Lakenheath Warren.
This specimen, which was collected by Dr Marr as an example
of the superficial wind-transported deposits of the Brandon district,
consists of a very clean sand, remarkably free from muddy material,
but containing a good deal of black fibrous vegetable matter. The
effervescence with acid was very slight and the sample required
very little preparation. It gave a fairly large dark residue in
bromoform, and as most of this was obviously ferruginous it was
at once treated with acid and allowed to stand for some time,
washed and re-separated. The final product was small in amount
and the constituent grains were of very small size as compared
with those of the sands presumably laid down in water. The only
mineral occurring in fairly large grains is garnet, which is also
rather angular ; all the other constituents are very round (except
staurolite, which appears to remain angular under all circum-
stances).
The minerals identified are garnet, tourmaline (sometimes
blue), kyanite, staurolite, hornblende, augite, hypersthene, epidote
and r utile. Zircon is much more abundant than in any other
specimen here described.
Surface Deposit, Fowlmere, near Thetford.
This is a sandy deposit, of a curious grey colour when fresh ;
the peculiar colour is probably due to the absence of the usual
iron oxide. When washed and treated with dilute acid it is
found to consist principally of clean white quartz sand, with a
few reddish grains.
The minerals of the heavy residue are much as usual, namely,
magnetite, garnet, tourmaline, hornblende, augite, epidote, zoisite,
kyanite, staurolite and zircon. The staurolite is as usual angular,
but the other minerals are well rounded, and this is specially
notable in the garnet, which shows signs of more attrition than
in any other sample examined. This may safely be attributed
to wind action.
The particles show a wide variation in size, but the majority
are small.
some Cainhridgeshire Sands and Gravels. 141
General Conclusions.
The most abundant constituent in all the sands here examined
is, as might be expected, quartz. This is normally perfectly clear
and colourless, but sometimes shows a reddish tinge. Next in
abundance is flint, in white opaque grains, often well rounded.
In many samples Chalk is abundant, while prisms of Inoceramus
and Echinoid spines derived from the Chalk are often common.
Glauconite is generally present, although not conspicuous till the
sands are cleaned, since the grains of this mineral are frequently
covered by a skin of iron oxide, which must be removed by acid
before they become readily visible. The heavy residues, of a
density higher than 2-95, include a large proportion of opaque
grains of magnetite and other oxides of iron. Among the trans-
parent constituents of the heavy residues the following are generally
present: garnet, tourmaline, kyanite, staurolite, hornblende, augite,
hypersthene, epidote, zoisite, zircon, r utile. Of these the most
abundant is, in most cases, garnet, which occurs in angular, sub-
angular and rounded fragments often of considerable size ; tour-
maline varies much in colour, and blue varieties are common ;
other colours noted are brown, pink and green. Staurolite is
common, always in angular fragments, while the numerous
crystals of kyanite are notably more angular in the older gravels.
Hornblende is locally very abundant and includes the blue variety
(arfvedsonite) which is so characteristic of Norwegian soda-rocks.
Zircon is much less common than in most sands, e.g. the Bagshot
Sands described by Dick.
The minerals of these sands may be divided into two groups,
as follows :
A. Glauconite, tourmaline, kyanite and staurolite : these are
almost certainly derived from the Neocomian. As is well known,
staurolite nearly always remains angular, but the tourmaline and
kyanite are somewhat more rounded than in that formation. The
tourmaline especially occurs in extraordinarily well-rounded forms.
The blue variety, which is common, is almost certainly derived,
via the Lower Greensand, from the ancient Armorican land to
the south-west. Kyanite is a very common and characteristic
mineral both in the Carstone and in the Sandringham Sands, and
staurolite is also present in both of these. The abundance of
glauconite in the Neocomian hardly needs mention.
B. Garnet, hornblende, augite, hypersthene, epidote: these
minerals are almost unknown in the Neocomian, and have
certainly been derived at first hand from the disintegration of
far-travelled rocks of Scotch and Scandinavian origin during the
142 Mr Rastall, The Mineral Composition of
glacial period. They are much more angular than the first group,
especially in the older sands, and show little evidence of derivation
from pre-existing sandy deposits : in particular the angularity
of the chips of garnet is often very marked, and to use a simple
word they look very new, having undergone little rolling or
attrition : well-rounded garnets are very rare, except in the
superficial and wind-borne deposits of the Breckland.
The most striking feature of the sands here examined is the
almost complete absence of muscovite, this mineral being one of
the commonest constituents of sands of all ages, with a noteworthy
exception in the case of deposits of one class. It is stated by
Retgers* and Thouletf that mica and other minerals with very
perfect cleavage are almost completely absent from wind-blown
sands, and this observation may have some significance in this
case. The only deposit here described containing muscovite is
the high-level or plateau gravel on the summit of the Gog-Magog
Hills. This is undoubtedly much older than the gravels and
sands of the Cam system, and it is generally regarded as being
of glacial age. The great abundance and variety of far-travelled
erratics in it certainly lend support to this conclusion, and the
sand itself is of a very different character to the river and surface
deposits seen at lower levels.
On the retreat of the ice the whole country must have been
covered by vast spreads of sand and gravel, the relics of which
are still to be seen in the Breckland of western Suffolk and
south-west Norfolk, It is generally believed that the Glacial
period on the continent was succeeded by a time of warm and
dry climate, the Steppe period, and somewhat similar conditions
must have prevailed in England, It is possible that during this
time the sands were to a certain extent worked over by the wind,
removing the muscovite and other light and flaky minerals. The
chief difficulty in the way of this view is the extreme angularity
of the garnets and some other minerals in the earlier river-
gravels.
The general conclusions arrived at from a study of the mineral
composition of the sands here examined may be stated as follows :
the materials have been derived from two sources, partly from the
Neocomian sands of Cambridgeshire and the neighbourhood of the
Wash, and partly from far distant sources by ice- transit ; that is,
from the solid matter transported on and in the ice from Norway,
Scotland and the north of England. The mineral grains obtained
from the former source are almost exactly like those characteristic
* Betgers, ' Uber die chemische und mineralogische Zusammensetzung der
Diinensande Hollands,' Neues Jahrb. filr Min. 1895, p, 22,
t Thoulet, 'Etude mineralogique d'un sable du Sahara, ' jBmZZ, Soc. Min. France,
Vol. IV. 1881, p. 262.
some Cambridgeshire Sands and Gravels. 143
of the Neocomian sands of Noi-folk, the Carstone and the Sand-
ringham sands, only differing from them in their slightly more
rounded form. The far-travelled grains on the other hand are
largely such as might be obtained from igneous and metamorphic
rocks, then undergoing disintegration for the first time : they are
angular in the earlier deposits, subangular in the later, and only
in the obviously wind-borne surface deposits are all alike reduced
to a small size and a fairly uniform degree of roundness. Thus
during the deposition of the Cam gravels water action was pre-
dominant ; at a later time wind asserted its power as the principal
agent of distribution of the latest superficial accumulations of the
drier parts of East Anglia.
144 Mr Whiddington, Note on the Rontgen radiation
Note on the Rontgen radiation from cathode particles tra-
versing a gas. By R. Whiddingtojsi, M.A., St John's College.
[Bead 11 November 1912.]
It is now a commonplace that Rontgen rays are emitted from
a target struck by cathode particles, and very many researches
have been carried out with the object of determining how the
nature of the target and the velocity of the incident particles
determine the quantity and the quality of the emitted Rontgen
rays. The experiments shortly to be described bring forward
evidence to show that when very slow cathode particles traverse
a gas at low pressure, Rontgen rays are emitted all along their
path *.
The form of apparatus used is indicated in the figure. A hot
lime cathode L projects a fine beam of cathode particles down the
axis of the evacuated glass tube T, the anode being a spiral of
aluminium wire A. An insulated aluminium plate P is enclosed
in an earthed brass tube E, provided with a small opening at W.
This opening is closed by a thin blown-glass window, so thin as to
show interference colours of a low order. P is connected to the
leaf of a Wilson tilted electroscope. The arrangement of taps
shown in the diagram enables connection between T and E to be
severed after a moderate vacuum has been produced so that a
slightly higher vacuum may prevail in E than in T. This is
desirable since we wish to observe the potential to which P will
rise, and it is necessary under such circumstances to eliminate any
gas leak due to ionisation.
In the earlier experiments it was found that when the
cathode stream from L was passing down the tube there was
an enormously rapid deflection of the gold leaf in such a direc-
tion as to show that the plate P was charging up positively.
This effect was finally traced to defects in the window W, small
cracks being present which apparently allowed a diversion of the
main current into the brass cylinder, P functioning as a subsidiary
anode and becoming positively charged. When the window, how-
ever, was apparently perfect there was still an effect in the same
direction, the plate P charging up positively as before but at
a very much diminished rate. A strong magnetic field applied
across W had little or no effect upon the rate of charging of P.
Moreover, when the narrow pencil of rays from L was curled up into
a close spiral in front of the window, but not touching it, P charged
""' No rays can be detected unless the applied potential exceeds 90 volts.
from cathode particles traversing a gas.
145
up much more rapidly, an effect easily explained if P is regarded
as emitting negative electricity as the result of a radiation pro-
ceeding from the cathode stream itself. A test which conclusively
showed that the effect was really due to a radiation from the
cathode stream was devised. A solid obstacle was placed in front
of W, the effect at once disappeared ; on removal of the obstacle,
P again commenced to charge up. In the actual experiment the
obstacle was a small brass plate, which could be rotated from the
To Battery
rioEartti
Gudrd rmd
^ ^
■To E)ecTro6Co}>e
To bumb and cViarcoat tube
outside by means of the ground glass joint J. In this way P
could be given an uninterrupted view of the cathode stream or
the view could be cut off.
There is thus definite evidence of a radiation proceeding from
the path of the cathode stream. That this radiation does not
consist of charged particles of small mass is shown by the fact
that it is not cut off by a transverse magnetic field. Strong
evidence in favour of supposing it to be a very soft Rontgen
VOL. XVI I. PT, I.
10
146
Mr Whiddington, Note on the Rontgen radiation.
radiation is afforded by the observation that the velocity of the
negative particles ejected from P is not very different from the
velocity of those streaming out from the lime cathode*. This
experiment was carried out as follows. An electrostatic volt-
meter connected between L and A gives the velocity (expressed
in volts) of the cathode particles shot out from L. The potential
to which P charges up is a measure of the velocity of the
particles ejected from P. In practice it was found necessary to
keep the gold leaf in as sensitive a position as possible, and a
convenient method of ensuring this was to keep the potential
difference between the electroscope plate and the leaf very nearly
equal to V, the voltage giving instability. Thus the leaf was
charged to a positive potential v, and the plate was kept at such
a potential p (positive or negative according as v was greater
or less than V) as would satisfy the relation v — 'p = V. The
voltage across the tube was then varied until the leaf did not
drift from its zero position when insulated. We can then say
that cathode particles of velocity not greater than v are being
ejected from P. The following table gives a few of the results
obtained in this way.
Velocity of lime cathode rays
(expressed in Volts)
Velocity of particles from P
(expressed in Volts)
128
145
187
218
100
117
152
178
tj^ . , 1 ,. 1 ,, , 1 • velocity of lime cathode rays
It IS to be noticed that the ratio — -, — t^ v. —, — j. ^
velocity or particles from r
is nearly constant*.
In this connection see Proc. Roy. Soc. A. Vol. lxxxvi. 1912.
Professor Hughes, The Gravels of East Anglia 147
The Gravels of East Anglia. By Professor Hughes.
[Read 25 November 1912.]
In introducing the subject of the gravels of East Anglia the
author pointed out that too much importance must not be attached
to the absolute height and level of the river terraces, firstly because
of the rise of the valley from its mouth to its source and secondly
on account of the earth movements which have affected the area.
He showed that there had been considerable depressions in the
valley of the Cam since the deposition of some of the existing river
silt.
Only a small proportion of the flints of Tvhich the gravels were
chiefly composed were likely to have been derived directly from
the Chalk and very few from the London Tertiaries. They were
probably produced on the Miocene land surface over which the
Crag sea advanced rapidly sweeping up the old surface soils and
forming the first deposits of angular flints from which so much of
our stained gravel has been derived.
The subsequent depression of this area, while adjoining moun-
tain regions were uplifted, would account for the material of the
Norfolk cliffs which might be referred to the action of an ice-laden
sea on the land. Shore ice and pack ice early impinged upon the
sinking and afterwards the rising land, mixing up and contorting
the material upon it, and creeping up the long slopes and over the
wide plains with similar results.
He traced these glacially formed or glacially modified beds
from the coast to the hills inland, pointing out that every character
which was seen in isolated sections inland could be seen along the
coast in continuous sections. They differed from the river gravels
in their tumultuous arrangement and in their great variety of
composition.
This group, of glacial origin, were well represented by the
Whittlesford beds.
The loam of the cutting near Chesterford Station, and the
sands, gravels, loam and marl of Hildersham, Gog Magogs and
Hare Park were assigned to the same series, and connected with
the coast by the deposits of Roslyn Pit, Sedgeford and Hunstanton.
As the land rose the agents of subaerial denudation began their
work at once and the rain-wash and river-terraces thus formed,
10—2
148 Professor Hughes, The Gravels of East Anglia
being often fossiliferous, were more easily grouped in chronological
succession.
Of the newest age were the gravels of Jesus College, Little
Downham, &c. In an earlier stage he placed the gravels of
Barnwell, Stow, the Botanic Garden, Trumpington, Shelford, and
the mammoth gravel of Chesterford, and to a still earlier stage he
referred the Girton and Observatory gravels and those of the
Newmarket Road.
The Barrington beds must be considered by themselves, being
very different in composition, situation and fossil contents.
Properties of a Liquid connected with its Surface Tension 149
On the Propei'ties of a Liquid connected with its Surface
Tension. By R. D. Kleeman, D.Sc. (Adelaide), B.A., Emmanuel
College,
\_R.eceived 18 December 1912.]
Calculation of the Absolute Mass of the Hydrogen Atom.
If no transition layer were formed on a liquid surface the
equation *
^«-6">r876 ^^^
could be used to calculate the absolute molecular weight m^ of
a molecule where U denotes the energy expended against mole-
cular attraction in separating the molecules of a gram of substance
an infinite distance from one another, p^ the density of the sub-
stance, and Xa the surface tension that would exist if no transition
layer were formed. At low temperatures when the density of
a liquid is large in comparison with that of its saturated vapour
U = L the internal heat of evaporation, if the internal energy of
a molecule is practically independent of the vicinity of other
molecules, which is very likely the case. But although a tran-
sition layer is formed the equation may be used to obtain an
approximate value of the quantity in question. It was found that
if values of m^ are calculated by equation (1) for different tem-
peratures of a liquid, substituting for X^ in the equation the
values X found in practice, and plotted against the corresponding
temperatures, the points obtained lie approximately on a straight
line. Now the effect of the transition layer on the surface
tension decreases with decrease of temperature f, and at the abso-
lute zero is probably negligible. According to a formula given
by the writer | the surface tension at the absolute zero is about
sixteen times that at room temperature, and the effect of the
transition layer on the surface tension therefore small according
to the paper first quoted. An approximate value of the absolute
molecular weight is therefore given by the intercept of the straight
line on the nia axis.
* Phil. Mag. Dec. 1912, p. 883.
t Loc. eit.
X Ibid. Jan. 1911, pp. 99—101.
150
Mr Kleeman, On the Properties of a liquid
Table I.
Ether
Carbon tetrachloride
T
X
L
T
X L
1
313
363
U-05
8-63
75-36
63-31
363
423
17-60
11-21
40-62
34-42
m„ = l-34 X lO^^grm.
7n„=l-67x 10-24 grm.
Methyl formate
Benzene
T
X
L
T
i
X 1 L
i
303
363
23-09
14-29
107-5
85-1
353
413
20-28 ' 85-62
13-45 1 74-09
1
w„ = 1 -62 X 10-2^ grm. m« = 1 -62 x 10--^ grm.
i
Table I contains the values of m^ for the hydrogen atom
calculated in the way described from the values of \ for four
liquids corresponding to the temperatures given in the table*.
It will be seen that the values on the whole agree well with one
another, the only serious deviation being shown by that obtained
from ether. The mean value is
1-56 X 10-2* gyjjj^
which is very nearly equal to 1-61 x lO-^"* grm., the value deduced
by Rutherford from experiments on the a particle.
Relations connecting Surface Tension with other Quantities.
A number of relations have been found connecting the surface
tension of a liquid with its internal heat of evaporation, co-
efficient of compression, coefficient of expansion with rise of
temperature, and other qiiantities. They should have as foun-
* The values of L were obtained from a paper by Mills, in the Journ. of Phy.
Ghem. vol. viii. p. 405 (1904).
connected with its Surface Tension. 151
dation the relations that can be obtained from the fundamental
equations the writer deduced from the law of molecular attraction.
Some of these relations will be pointed out here.
From the equations *
X = K"(^)\Xcar and L^-{P^)\tcar
\mj m \ml ^
we have ■ X = A -^ (2),
where m denotes the molecular weight relative to hydrogen, and
Di is a quantity which is the same for all substances at corre-
sponding states.
The equation f
and one of the foregoing equations give
--^'^^-MlS- <«>■
where A and D^ are corresponding quantities, p denotes the
pressure of the saturated vapour, and the suffix c indicates that
the quantity to which it is attached refers to the critical point.
The coefficient of compression /3 is given by
_ 1 dv _ai
vdp p'
where a^ is a corresponding quantity, and hence equation (2)
may be written
-'^=M^)* (^).
where D^ is a corresponding quantity.
The coefficient of expansion a is given by
_ 1 dv _ a^
''~vdp~¥;
By means of this equation and the equation
_ BTcpc
equation (3) may be written
ci\ = DJ^) (5),
where A is a corresponding quantity
* Phil. Mag. Oct. 1909, pp. 491—510.
t Ibid. Dec. 1909, p. 903.
152
Mr Kleeman, On the Properties of a liquid
The different values of each of these corresponding quantities
for a number of liquids will probably not differ much from one
another for a constant temperature, if it is low, i.e. that of the
room, since the differences between the values of a corresponding
quantity for a constant temperature decrease with decrease of
temperature.
A case of special interest is the following. From one of the
foregoing equations by differentiation and elimination we obtain
-7^= B^jpf, where D^ is a corresponding quantity. This equation
d\
may be written -jm= D^Xa, by means of the equation giving the
coefficient of expansion, where Dy is a corresponding quantity.
Now the surface tension is approximately a linear function of the
temperature, and is therefore approximately given by an equation
of the form \ = Xo(l + SiT), where Bi is approximately a constant.
The former of the last two equations may therefore be written
where gi is a corresponding quantity. Since Sj is approximately
a constant and a does not vary rapidly with the temperature, gi is
approximately constant over a considerable rauge of temperatures.
This is the empirical relation connecting S^ and a proposed by
Cantor*, who showed that g^ = 2-3 approximately. Table II
Table II.
Name of substance
X
8,
a
1
di
2-6
2-9
2-5
2-4
2-2
2-5
2-2
3-3
2-7
3-1
2-0
Argon
11-7
13-5
830
610
510
29-4
34 -3 «
40-6
45-0
48-2
54-6«
0-013
0-013
0-00042
0-00027
0-00029
0-0035
0-0027
0-0029
0-0025
0-0028
0-0029
0-00491
00454
0-000170
0-000114
0-000129
0-00139
0-00124
0-00089
000092
0-00089
0-00121
Carbon monoxide . . .
Cadmium
Tin
Lead
Benzene
Ethyl alcohol
Phenol
Aniline
Nitro lienzene
Carbon disulphide
contains the values of ^1 for a number of substances selected from
a table given by Freundlich in his book on Kapillarchemie.
* Zeitschr.f.phys. Chemie, xxxix. 129 (1902).
connected tvith its Surface Tension. 153
The Influence of the Curvature of Surface of a Liquid on its
Surface Tension in Connexion with the Radius of the Sphere
of Action of a Molecule.
Since the surface tension of a liquid is due to the existence
of molecular forces we should expect that it should depend on the
curvature of the liquid surface. But the effect of curvature of
surface on the surface tension becomes appreciable only when the
radius of curvature becomes comparable with the radius of the
sphere of action of a molecule. The latter quantity may be
defined as the distance that two molecules in a liquid must be
separated in order that the energy expended in overcoming their
attraction on one another during the process is approximately
equal to that expended in separating them an infinite distance
from one another.
Consider a sphere of liquid in the centre of which is a tiny
spherical air bubble whose diameter is equal to the radius of the
sphere of action of a molecule. Suppose the air bubble increased
slightly in size by forcing an additional quantity of air into it. Now
it will be easily seen that during the increase of the liquid surface
in contact with the bubble the molecules in and near the surface
do not get out of each other's range of molecular action for an
increase of surface ds to such an extent as if the surface were
plane. The amount of work done per unit increase of surface
is therefore less than in the case of a plane surface, and the
surface tension therefore decreases with increase of the curvature
of the surface when it is concave with respect to a point outside
the liquid.
In a similar way it can be shown that if the diameter of a
sphere of liquid is equal to the radius of the sphere of action
of a molecule, less energy would be expended in producing an
increase of surface area ds than if the surface were plane. The
surface tension will therefore also decrease with increase of
curvature of the surface when it is convex. It will be observed
that these results should also hold if a liquid is incompressible
and no transition layer is formed.
Properties of Plane Liquid Films.
It can be easily shown that the average external work done
in evaporating by a reversible process a film of liquid of constant
mass, and expanding the vapour till its density is equal to a given
density, increases with a decrease of the thickness of the film.
Thus let Wi denote the external work done in one case. Next
let the process of evaporation be carried out in a different way.
Thus let the area of the film first be considerably increased by
stretching it out, and let Wg denote the work done against the
154 Mr Kleeman, On the Properties of a liquid
surface tcDsion. Let the film now be evaporated and the vapour
expanded or compressed at constant temperature till its density
is the same as that of the vapour at the end of the previous
process, and let iv^ denote the external work done. Now ac-
cording to thermodynamics the external work done at constant
temperature during a reversible process between given limits is.
independent of the nature of the path of the process. Hence
Wi = Wv—Ws, and therefore w^ is greater than W.
It follows therefore that if a film of liquid is gradually
stretched out a thickness would ultimately be reached at which
the pressure of the saturated vapour begins to increase with
decrease of thickness of film. It can be easily shown that this
thickness is equal to twice the radius of the sphere of action of
a molecule. For if a film has a thickness equal to or less than
this quantity it requires the expenditure of less energy to move
a molecule to infinity than in the case of a much thicker film.
Consequently a larger proportion of molecules will possess suffi-
cient velocity to be able to overcome the molecular attraction
and escape from the liquid surface in the former case than in the
latter, producing a corresponding difference in the pressures of
the saturated vapours. Also the attraction of one half of the
film on the other half per cm.^ of surface would in such a case
be less than the attraction of a large mass of liquid on a cm.^
of its surface transition layer. This should have the effect of
making the transition layer for the film less abrupt than for a
much thicker film. Further, the density of the liquid mid- way
between the surfaces of such a film should be less than that in
the centre of a large mass of liquid.
An inferior limit of the radius of the sphere of action of a
molecule can be obtained. When the surface of a liquid is
increased at constant temperature an amount of heat is absorbed
d\
equal to T-^ per unit increase of surface. Therefore if a c.c.
of liquid be stretched out till it consists of a film containing one
layer of molecules only the amount of heat absorbed should be
practically equal to the internal heat of evaporation Lp^ of the
c.c. of liquid, or
dX
I
2T^.dA = Lp,.
It is evident therefore that the surface tension should undergo
a change during the process before the area of the film is equal
to A, where
If A denote the thickness of the film we have A^ = 1.
connected with its Surface Tension.
155
Table III contains values of A at different temperatures for
two liquids. The inferior limit of the radius of the sphere of
action of a molecule obtained, which is equal to -^, is of the
same order of magnitude as the usually accepted radius of a
molecule.
Table III.
Ether
T
dT
L
A
"c
313
35-06
75-36
3-2 X 10-8 cm.
1-6
333
36-60
70-79
3-7
1-7
3.53
37-43
65-85
4-2
1-8
.373
37-87
60-33
4-9 „
1-8 .
(
]!arbon tetrachloride
363
40-3
40-62
3-2 X 10-« cm.
1-6
383
41-39
38-64
3-6
1-7
403
42-33
36-58
4-0
1-7
423
42-69
24-42
4-5 „
1-9
The table also contains the values of the number of layers of
molecules Uc in a film of thickness A, which is given by
n,., = A
+ 1.
The values are all less than 2, and a film therefore consists of
a single layer of molecules when stretched out till its area is
equal to A. Now the surface tension must obviously decrease
before this stage is reached. Since n^ is calculated on the
supposition that T -7™ is independent of the thickness of film, it
follows therefore that the ratio
on the average increases with a decrease of the thickness of film
when it is less than that of twice the radius of the sphere of
action of a molecule.
156 Mr Kleeman, On the Properties of a liquid
The Polymerization of Molecules in a Substance.
The equations*
Z = H,^(^^\X^m,f (7)
and p, = M'^l^y{t^m,y (8)
and the relations f connecting the internal heat of evaporation, f
surface tension, and other quantities with one another, obtained
by giving the function (<^) in the law of molecular attraction
different forms, may be used to investigate whether a substance |
is polymerized. The quantities Tc, Pe, Pc, denote the critical |
temperature, pressure, and density respectively of a substance of j
molecular weight m, m-^ denotes the atomic weight of an atom
in the molecule and H^ and M are constants. If a relation does j
not fit the facts, it signifies that the molecular weight does not j
correspond to that indicated by the chemical formula, but to |
some multiple of it. Provided the substance does not consist of j
a mixture of molecules polymerized to different extents the actual '
molecular weight can be determined by finding the factor of the ;
chemical molecular weight which gives an agreement with the
facts. Oetvos' surface tension equation has been used in this
way. By means of it Ramsay and Shields found that water,
acetic acid, and the alcohols are more or less polymerized. This
may be verified by applying to these substances the latent heat
and other relations quoted.
A few additional important cases of polymerization will be
pointed out here. By means of Dieterici's equation %
T KRT , p,
L = log '— ,
m *^ p2
giving the internal heat of evaporation L in terms of the densities
Pi and p2 of the liquid and vapour respectively, it can be shown
that MHs is considerably polymerized in the liquid state. The
constant K instead of being equal to 1*75, the value it has for
liquids that are not polymerized, varies ffom 2*6 to 8*9 when the
temperature varies from — 10° to 40° C. It will also be found
that the critical quantities of 0^ do not fit in with equation (8),
and O2 is therefore to a certain extent polymerized. Mercury
is usually supposed not to be polymerized. It will, however, be
foimd that if the internal heat of evaporation is calculated by
means of Clapeyron's thermodynamical equation, and substituted
* Phil Mag. May 1910, pp. 783—809.
t Ibid. Jan. 1911, pp. 83—102.
+ Ibid. Oct. 1910, pp. 688, 689.
connected with its Surface Tension.
157
lin the equation L=Ei (p^^ — p.^), the value of E^ is not constant
as it should be*, but increases rapidly with the temperature,
showing that mercury is in a polymerized state.
A liquid may consist of molecules whose molecular weight is
that indicated by the chemical formula, or of molecules poly-
merized in equal degrees, or of a mixture of molecules polymerized
in different degrees. The formulae discussed do not distinguish
between the last two cases. It will therefore be of importance to
develop one that does.
In a previous paper f it was shown that
p-^ m^p^
when the density of the liquid is large in comparison with that
of its surrounding vapour, where X denotes the surface tension.
Since — according to Traube is approximately proportional to
Svmi we may write
Pc
Hence the foregoing equation becomes
-^ = 3296
Pi
m
.(9).
This equation holds independently of the extent of the polymeri-
zation of a substance, provided all the molecules are polymerized
to the same extent, in which case m and S Vm^ have the same
polymerization factor. Let us apply this equation to the four liquids
mentioned in Table IV, which are known not to be polymerized.
Table IV.
Name of liquid
X
3296 (^^/"*^)^
Methyl formate
Carbon tetrachloride . . .
Benzene
Ether
27-53
399
46-5
62-92
32-6
3-25
45-66
66-11
The table contains the values of the risfht- and left-hand sides of
* Phil. Mag. Oct. 1910, p. 687.
t Ibid. Jan. 1911, pp. 99—101.
158
il/r Kleeman, On the Properties of a liquid
the equation (9) for these liquids, which, it will be seen, agree
fairly well with one another, as we should expect. The values
of the left-hand side are the mean values given in a table in a
previous paper*.
Since equation (9) holds independently of the temperature
and the values of the critical quantities of the substances under
investigation it can be easily applied to the facts. We may, for
example, use it to investigate the polymerization of fused metals
and salts. The results of such an investigation are given in
Table V.
Symbol of
substance
X
Pi
X
J?
3296 (^^/'"^)*
Pd
1339
11-4
-07929
-2935
Pt
1658
21-32
-008024
•08670
Hg
435-6
13-55
-01293
-08241
S
42
1-811
3-904
3-22
Se
70-4
4-26
-2138
•5282
Ag
782-4
9-51
•09563
•2825
Bi
381-9
10-04
•03759
•07652
Zn
812-2
6-48
•4606
•7802
Sn
587-1
7-02
■2418
•2374
Sb
244-5
6-41
•1447
•2289
Pb
448
10-37
•03877
•07691
Cd
693-5
7-975
•1713
■2628
Fe
950
6-88
•4239
1^051
Au
612-2
19-23
•004476
•08492
K
363-9
-8298
767^4
2^167
Cu
581
8-217
•1275
•8.307-
Na
519-7
-9287
699^2
6^232
P
41-15
1-7555
4^340
3^431
KBr
48-4
1-991
3^079
003787
KoCOs
160-2
1-90
12^28
•01654
KCl
69-3
1-45
15^67
•01592
LiCl
63-4
1-375
17-74
. ^04725
LiCO,
152-5
1-765
15^71
•05360
NaBr
49
2-212
2-046
•005526
NaCOs
179
1-9445
12-52
■02847
NaCl
66-5
1-500
13-13
•03251
Na.S04
182
2-065
10-02
•0115
AgBr
121-4
6-479
-0689
•0009854
* hoc. cit.
connected with its Surface Tension. 159
Table V, It will be seen that in most cases the value of — -
Pi
differs very considerably from that of
■ 3296 f^^
V m
indicating that the fused substances consist of a mixture of
molecules polymerized to different extents. We would, of course,
expect that the molecular weight of these substances is not that
indicated by their chemical formula since fused metals and salts
do not possess any appreciable vapour pressure. But this in-
vestigation gives additional information. It will be seen that in
the case of each of the four substances S, S„, Cd, and P, each
molecule is polymerized to the same extent.
i
CONTENTS.
PAGE
The Effects of Hypertonic Solutions upon the Eggs of Echintis. By
J. Gray. (Communicated by Mr F. A. Potts) ....
Preliminary Note on the Inheritance of Self-sterility in Reseda odorata.
By R. H. CoMPTON 7
On the Anthropometric- data collected hy Professor J. Stanley Gardiner,
F.B.S., in the Maldive Islands and Minikoi. By W. L. H.
Duckworth
Notes on the volatilization of certain binary alloys in high vacua. By
A. J. Berry 31
On PulsiLS alternans. By George Ralph Mines. (Plate I) . . . 34
The Di fraction of Short Electromagnetic Waves hy a Crystal. By
W. L. Bragg. (Communicated by Professor Sir J. J. Thomson.)
(Plate II.) (Two figs, in Text) 43
The Meres of BrecMand. By J. E. Marr 58
Note on a Remarkable Instance of Complete Rock-disintegration hy
Weathering. By F. H. Hatch 62
The Variation of Magnetic Susceptibility ivith Temperature. Part II.
On Aqueoiis Solutions. By A. E. Oxley. (Six figs, in Text) . 65
Some Experiments on the Electrical Discharge in Helium and Neon.
By Herbert Edmeston Watson. (Communicated by Professor
Sir J. J. Thomson.) (Two figs, in Text) . . . . . 90
Some Diophantine Impossihilities. By H. C. Pocklington . . . 108
On the earlier Mesozoic Floras of New Zealand. By E. A. Newell Arber 122
The Mineral Composition of some Cambridgeshire Sands and Gravels.
By R. H. Rastall . 132
Note on the Rontgen radiation from cathode particles traversing a, gas.
By R. Whiddington. (One fig. in Text) 144
The Gravels of East Anglia. By Professor Hughes .... 147
On the Properties of a Liquid connected with its Surface Tension. By
R. D. Kleeman 149
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PROCEEDINGS
OF THE
Camkitrgx l^ibsnpl^kal 3acut^.
The Minerals of some Sands and Gravels near Newmarket.
By R H. Rastall, M.A., Christ's College.
[Bead 10 February 1913,]
In a recent communication to this Society* a brief account
was given of the composition and characters of certain sands and
gravels of Pleistocene and Recent age found in the neighbourhood
of Cambridge. A few specimens have since been collected from
deposits of the same general age in the Newmarket district, and
the present paper embodies the results of an examination of these
by methods similar to those previously employed, with slight
modifications suggested by experience.
The deposits here described are not connected with any
streams now existing and must have been formed by rivers
belonging to an ancient drainage system which has now totally
disappeared, having undergone complete modification by capture
or other processes of a like nature. For the present purpose
however it is unnecessary to discuss in detail the origin of these
deposits; the main object is to place on record their characters
and composition for the guidance of future workers. It is hoped
that a systematic investigation of the lithological characters of the
gravels and sands of this region may eventually succeed in
establishing the existence of definite types of deposit which may
be correlated with the physical conditions prevailing at different
periods in the past.
The deposits here described are referred to very briefly in the
publication of the Geological Survey f dealing with this district,
and no detailed descriptions seem to exist. When mentioned at
* Eastall, "The Mineral Composition of some Cambridgeshire Sands and
Gravels," Proc. Gamh. Phil. Soc, vol. xvii. 1913, pp. 132 — 143.
t "The Geology of parts of Cambridgeshire and Suffolk," Mem. Geol. Surv
1891, p. 72.
VOL. XVII. PT. II. 22
162 Ml' Rastall, The Minerals of some Sands
all they are generally assumed to be similar to the " Gravels of
the Ancient River System " of Cambridge, and the field evidence,
such as it is, goes to support this vievv. In the neighbourhood of
Exning and Snailwell the gravels and sands form a ridge, no
doubt once continuous, but now cut through in places by existing
rivers. This ridge is no doubt analogous to the Quy-Cambridge-
Girton ridge, which is similarly cut through by the Cam. I have
been unable to find in the scanty literature any mention of the
loam or brick-earth here described, although brick-earth is said to
exist in some abundance at Bury St Edmunds.
It is unnecessary to describe in detail any of the methods
adopted in collecting, preparing and separating the material.
These processes were all carried out by the methods mentioned
in the paper just cited. The only addition here made was the
adoption of a new optical arrangement to facilitate the examina-
tion of the separated minerals, which may be briefly described.
The heavy residues from all the sands dealt with contain a
considerable proportion of opaque grains, all of which look very
similar when examined by transmitted light in the usual way.
Hence it became highly desirable to devise some method by which
grains of different colours could be readily distinguished. It was
important also to make such an arrangement that it was possible
to revert to the normal method of examination without disturb-
ance of the microscope or of the slide, enabling any individual
grain to be examined by each method alternatively. After some
trials it was found that the best results were obtained b)' strong
oblique illumination, and that various colours of background were
required for objects of different characters. Thus highly-coloured
transparent or semi-transparent minerals are made most con-
spicuous by a black background, while for completely opaque and
metallic grains a partially illuminated background gives the best
results. The method finally adopted was as follows : a powerful
electric lamp, of 16 or preferably of 32 candle-power, was placed to
one side of and as close as possible to the revolving stage of an
ordinary Swift petrological microscope, the light being raised very
slightly above the plane of the stage. The illumination of the
field of view was thus very nearly horizontal. The plane mirror
was arranged to reflect a beam of light up the tube in the usual
way for examination by transmitted light, with or without crossed
nicols. To obtain a dark background all that is necessary is to
insert a card of the required shade, black, grey or white, into the
space between the lower nicol and the stage. It is convenient to
have a single card, half black and half white, or with a grey strip
in addition ; this card can be moved about as desired for different
grains, and it can also have a hole cut in it to be brought to the
centre when a solid background is not desired. This card in no
and Gravels near Newmarket. 163
way interferes with the working of" the nicols, the revolving stage,
or other parts of the microscope and can be left in position
permanently. This method of examination is especially useful for
the detection of glauconite, magnetite, haematite or any metallic
minerals, and it might perhaps be of service in the search for
small traces of gold or platinum in sands and gravels and also in
the examination of soils for agricultural purposes. If a strong
source of artificial light is not available, sunlight acts as well, or
even better in the case of minerals of some shades of colour, but
unfortunately sunlight is not always obtainable when required.
The special advantage claimed for this arrangement depends
mainly on the extremely oblique illumination, which reveals
clearly pittings and inequalities on the surfaces of the grains, thus
bringing out the characteristic appearance. Among transparent
minerals it can be usefully employed for the detection of thin
flakes of mica, which always lie flat in properly mounted slides.
Since the light strikes them edgeways, owing to their thinness
they are practically invisible against the dark background, though
conspicuous when viewed by transmitted light. This complete
disappearance of a mineral may be tajjen as a proof of its occur-
rence in very thin flakes. By this means also the colours of very
minute grains are made easily visible. This simple apparatus
was employed to a considerable extent in the examination of the
specimens described in the following pages.
(1) Pit at Newmarhet Station.
Numerous shallow excavations have recently been opened on
the slope of the hill immediately adjoining the north side of
Newmarket station, behind the Coronation Hotel, and from these
numerous mammalian bones have been obtained. Among the
specimens preserved in the Sedgwick Museum, Cambridge,
Mr C. E. Gray has identified the following : Elephas, Hippopota-
mus, Rhinoceros, Bos, Bison, Ursus and Gervus. The general
character of the deposit is best described as brown, rather loamy
sands and gravels with many fairly large flints : pebbles of other
rocks are extraordinarily rare, only one or two fragments of
sandstone being observed.
After washing, the heavy constituents of the sand were
concentrated by panning and separated directly in bromoform ;
a large and very ferruginous residue was obtained, necessitating
prolonged digestion in strong hydrochloric acid. It then appeared
that a considerable proportion of the grains that sank in bromo-
form consisted of glauconite of various shades of brown, green
and bluish green, coated over with a skin of brown iron oxide.
These were so abundant that a second separation was necessary.
11—2
164 Mr Rastall, The Minerals of some Sands
The final residue was nevertheless large in amount and contained
a considerable variety of minerals. Black grains of magnetite are
very abundant, and the chief transparent minerals found are
zircon, rutile, garnet, tourmaline, staurolite, hornblende, augite
and probably spinel. Zircons are very common and rather large :
sometimes idiomorphic, but more commonly well rounded ; un-
usually so for such a hard mineral. Rutile is also very plentiful
in prismatic crystals and in grains varying in colour from yellow
to deep red. It is possible that some of the deep red grains here
assigned to rutile may really be cassiterite : this would be difficult
to prove. Pale pink and brown garnets are common in well
rounded grains rather larger than the average size. There are
also a few opaque white, yellow and brown grains of indetermin-
able nature, and a very little opaque red iron oxide, probably
haematite. Kyanite is very rare. When examined on a dark
background the most striking feature of the sample is the
abundance of magnetite and rutile, and its general appearance is
very characteristic.
(2) Dane Hill, Kennett.
At this locality, which is about four miles north-east of New-
market, there are curious patches of marl or loam resting on
gravel. The marl is very pale grey in colour, weathering pale
yellowish brown. It is very fine in texture and soft, disintegrating
readily when placed in water. By repeated washings much fine
mud can be removed, leaving a residue of pale brownish sand,
with small chips of flint and some white mica. It is difficult to
get rid of the last residue of the mud by washing, and this is
important, since separation of heavy minerals is prevented by the
presence of mud. However addition of a little acid facilitates the
process, and produces a copious effervescence, thus justifying the
designation of marl employed above. Larger elements which fail
to pass the first sieve are small in amount, consisting of pinkish
quartz and grains of iron oxide, together with chips of pale blue
flint.
The portion sinking in bromoform also for the most part
consists of iron oxide in rounded and curiously polished grains.
After further treatment with acid these are removed, and all that
remains is a very few rounded grains of garnet, together with still
fewer crystals of hornblende, zircon and rutile. These grains are
not by any means exceptionally small : in fact they are consider-
ably larger than in the sands from Newmarket station and from
the cemetery pit at Exning. This fact probably has some bearing
on the origin of the marls, as will be explained more fully in the
case of the Exning deposits.
and Gravels nea.r Newmarket. 165
(3) Cemetery Pit, Exning.
A large pit adjoining the cemetery at Exning now shows a
good exposure of sands and gravels, apparently lying in a pocket
in the Chalk. It is possible that sands and gravels of two different
ages are here seen in juxtaposition, since a good deal of variation
is to be observed in different parts of the pit. The eastern end is
excavated in brown, highly ferruginous, sand with wisps of chalky
clay and many blue flints. The north wall of the same pit
consists of a lighter coloured sand, with much more Chalk and at
the top the usual pipes filled with brown loamy material. All
over the pit large flints are numerous, but judging from a careful
examination of the piles of stones riddled out from the gravel,
pebbles of distant origin are very rare ; only a few blocks of sand-
stone were seen, ranging up to 6 inches in diameter: no pebbles
of igneous rocks could be found.
Since some doubt exists as to the identity of the sands seen
in various parts of the pit, samples were collected from different
points and treated separately by the usual methods.
(a) Eastern side of pit. This is a pale brown, clean, bright
sand, of rather fine grain, with few stones : when washed it was
found to be remarkably free from mud. The heavy portion was
partially concentrated by panning, and being obviously ferruginous
it was at once treated with acid, yielding a remarkably white
sand with much glauconite. A fairly abundant heavy residue
sank in bromoform.
This residue consists of rather small grains which are as a
rule distinctly rounded : the chief minerals present are iron
oxides, brown tourmaline, abundant zircons, rutile, epidote, stauro-
lite, hornblende in rounded grains and ragged fragments, together
with kyanite and garnet, the last-named mineral being fairly
abundant and in grains distinctly larger than the rest, suggesting
a somewhat different origin. The zircons are notably abundant
and more rounded than in samples from the neighbourhood of
Cambridge.
(h) Northern side of pit. This specimen consists of a rather
light coloured fine grained quartz sand with fairly abundant dark
grains and many very small chips of flint, A small sample when
tested with acid gave a strong effervescence. The heavy consti-
tuents were partially concentrated by panning and then separated
in bromoform without previous treatment with acid. Grains of
iron oxide were found to be so abundant as to necessitate treat-
ment with acid and a second separation in bromoform. This
process brought to light a considerable amount of green glauconite
and some pale brown grains of doubtful character. The heavy
residue after the second separation was abundant and consisted of
unusually small grains. Its general mineral composition also was
166 Mr Rastall, The Minerals of some 8ands
very similar to that from Newmarket station, and unlike the
sands near Cambridge. The chief minerals identified are zircon,
rutile, garnet, hornblende, augite, epidote and staurolite. Tour-
maline is notably scarce and kyanite was not found.
The grains of garnet, though larger than most of the other
minerals, are still small and generally a good deal rounded, while
the crystals of epidote, of a bright yellowish green, are conspicu-
ously round. The hornblende includes not only the common
green variety, but also a blue form, referable to arfvedsonite.
The most notable feature of the specimen is certainly the extra-
ordinary abundance of zircon and the extreme rounding of many
of the crystals of this very hard and resistant mineral, indicating
prolonged rolling, or derivation in a rolled condition from some
older rock. The entire absence of kyanite and rarity of tourmaline
are also notable and difficult to explain, since both these minerals
are so abundant in the sands of the same general age near
Cambridge and both occur with fair frequency in the sample of
sand taken from another part of the same pit. This fact goes to
confirm the idea that sands of two different origins and ages are
exposed in this pit.
(4) Pit near Eacning Village.
This pit is situated a short distance from the village of
Exning, on the road to Snail well, and lies on fairly high ground.
It shows a good exposure of material of peculiar character, which
is best described as brown and grey loam or marl, or the somewhat
vague designation of hrick-earth might well be applied to it.
Although the material is of very fine texture it contains a few
large flints, those of an elongated form often lying with their long
axes vertical. There are also well rounded boulders of sand up to
a foot in diameter embedded in the marl. The occurrence of the
vertical flints and of the boulders of sand suggest deposition irom
floating ice in comparatively still water. It is difficult to account
for the sand boulders unless they were frozen when deposited in
their present position, as they are well rounded and with sharp
outlines clearly demarcated from the fine marl.
Two large samples were taken from this pit, one of a brown
loamy material and the other of a fine greyish-yellow sandy marl.
The treatment of these samples presented considerable difficulties,
owing to the large amount of fine mud. However by long-
continued washing in a large porcelain dish the mud was eventu-
ally got rid of, and the sandy residue could be treated in the usual
way. Naturally this residue was of unusually fine grain, and did
not submit to the operation of panning so readily as the coarser
sands. In the case of the fine marl in particular the amount of
heavy minerals ultimately obtained was very small.
and Oravels near Newmarket. 167
(a) Brown loam. In this specimen all the grains are rather
small and even in size ; a few garnets only being somewhat larger
than the average. Among the opaque constituents magnetite is
moderately abundant and there are a few grains of red iron oxide.
Among the transparent constituents zircon and rutile are very
abundant, both in sharply angular and well rounded crystals.
Hornblende, epidote and staurolite were also noted, while flakes
of muscovite are abundant. Tourmaline is scarce, while kyanite
is very rare indeed. Garnet occurs in angular chips and also in
rounded grains.
The notable features here are the abundance of zircon and
rutile and the rarity of kyanite and tourmaline, together with the
presence of abundant muscovite.
(b) Grey marl. In this specimen the grains are all very
small indeed, and of uniform size. Magnetite is not very abun-
dant and there are a few pale yellow and white opaque grains.
Minute flakes of muscovite occur in great profusion, the other
notable minerals being zircon and rutile : the crystals of both are
for the most part sharply angular, though a few are rounded.
Other minerals are in such minute quantity as scarcely to be
worth mention. Allowing for the difference of size of grains this
specimen agrees very closely with the last.
General Conclusions.
Although the specimens here described are few in number,
and show a certain amount of variation among themselves, they
all possess certain characters in common, with the exception of the
Dane Hill marl, which is quite exceptional. In all the others the
most notable heavy minerals are zircon and rutile, while kyanite,
staurolite and tourmaline, so abundant in the gravels near Cam-
bridge, are notably rare or even completely absent. In the loam
and marl of the Snailwell road pit at Exning muscovite is also very
abundant.
From the general mineralogical composition of the sands and
gravels here examined it may be inferred that the greater part of
the material has been derived from distant sources by glacial
transport, minerals obtained at second hand from the Neocomian
series being quite subordinate in amount, and notably in less pro-
portion than in the gravels near Cambridge. Not enough evidence
is yet available to enable any explanation of the causes of this
difference to be offered, and more work is required on this subject.
As for the actual manner of formation of these deposits, the
coarser types appear to be due to rapidly moving water, either
the waters of ancient rivers, or possibly in some cases fluvio-
glacial, while as before stated the fine marls have possibly been
deposited in still or slowly moving water in which ice was floating.
168 Mr Price, Observations on Polyporus squamosus, Huds.
Observations on Polyporus squamosus, Huds. Preliminary
Communication. By S. Reginald Price, B.A., Clare College
(Frank Smart Student in Botany in the University).
[Read 10 February 1913.]
Polyporus squamosus, the " Saddle-back Fungus " or " Dryad's
Saddle," is well known as a parasite upon living trees and a powerful
timber destroyer. Perhaps the most important work which has
been done on the biology of this species is detailed in the papers
published by Prof. A. H. R. Buller* and by Mr F. T. Brooks f.
There were certa,in features, however, with regard to its biology
which merited further investigation, and the object of the work
here summarised was to attempt to throw further light on the
general life-history of the species.
The fungus has never before been grown on wood in artificial
culture. BuUer obtained some cultures on gelatine media, but
did not get infection of wood to take place.
By making use of the property of the species of forming a
spore cloud, as described by Brooks and Buller in the papers
mentioned above j, it was possible to collect the spores in large
quantities and in an uncontaminated condition. For the culture,
the usual methods, as described by Marshall Ward§ for Stereum
hirsutum and Brooks || for Stereum purpureum, were employed. The
spores were placed on the surfaces of sterilised wood blocks con-
tained in wide plugged test-tubes, the wood being kept moist by
a pad of cotton-wool saturated with water.
Two months or more elapsed before. any sign of mycelium made
its appearance, after which it gradually spread over the surface.
Generally the mycelium in older cultures formed a white felt-like
mass of very fine hyphae covering the surface of the block. Later
this became brown in colour and numerous " oidia " were found to
be produced. Drops of a brown watery liquid also exuded from
the mycelium at about this stage.
Spore cultures were made on elm wood ; further cultures were
made by mycelial transfer in many cases. The mycelium grew on
blocks of the wood of the elm, lime, sycamore, horse-chestnut, and
very feebly on that of Pinus.
* Buller, A. H. E. "The Biology of Polyporus squamosus Huds., a timber
destroying Fungus," Journ. Econ. Biol., 1906, vol. i. p. 101.
t Brooks, F. T. "Notes on Polyporus squaviosus," Neio Phyt. viii. 1909, p. 348.
X Vide also Buller, Researches on Fungi.
§ Ward, H. Marshall. "On the Biology of Stereum hirsutum," Phil. Trans.
Roy. Soc. 1898.
II Brooks, F. T. "Silver-leaf Disease," Journ. Agric. ScL, vol. iv. p. 138.
Ml' Price, Observations on Polyporus squamosus, Huds. 169
Ultimately peculiar fructifications, which were, however, always
sterile, and showed no signs of basidia formation, were produced in
many cases, so far as present observations go always on elm wood.
They took the form of rather elongated stipes with no indication
of a pileus. On the whole they resembled the natural fructifica-
tions, obtained by Buller, from logs filled with the mycelium, which
were kept in darkness*. Some were unbranched, others freely
branched and tree-like.
Cultures kept in darkness usually developed a more abundant
mycelium than those in light, but never produced any fructifica-
tions.
The mycelium penetrated the wood comparatively slowly, and
except for the outer layer the blocks remained quite hard even
after twelve months' action of the mycelium. This is very
probably a cultural effect as the decay is certainly much more
rapid in nature.
Attempts were made to grow the mycelium on a decoction of
elm wood extract solidified with gelatine and also on agar con-
taining the same decoction. The growth was slow and feeble on
both these media.
The spores germinated in hanging drops of solutions rich in
nitrogenous substances, as Buller found f. To follow out the
manner of the germina.tion of the spores on wood, and the
penetration of the hyphae, numerous spores were placed on small
sterile blocks of wood. The germination was slow, but the pene-
tration of the hyphae could be traced after four to six weeks.
Inoculations were also made on living elm trees, using both
mycelium and spores, on new and old wound surfaces. The
mycelium again penetrated slowly as determined by cutting
sections in the region of inoculation. Infection seemed to take
place more readily in autumn and winter than in spring and
summer, while old wound surfaces and especially dead twigs were
easily attacked.
This last point is probably definitely connected with the slow
germination of the spores and the relative activity of the region
on which they are placed.
The work was suggested to me by Mr F. T. Brooks, to whom
I wish to record my best thanks for his constant interest and
advice.
* Buller, A. H. E. Researches on Fungi, p. 59 sqq.
■|- Buller, "Biology of P. sqiiamostis," loc. cit., p. 116.
170 Mr Mines, Note on the 7'espiratory movements
Note on the respiratory movements of Torpedo ocellata. By
G. R. Mines, M.A., Fellow of Sidney Sussex College. (From the
Stazione Zoologica, Naples.)
[Bead 10 February 1913.]
(Plates III and IV.)
The researches of Bethe, Rynberk, Baglioni and others have
shown that in a great variety of fishes, both bony and cartilaginous,
the rhythm of the respiratory movements is very closely dependent
on peripheral stimuli. It has been remarked that the sequence
of regular rhythmic movements which are ordinarily called the
respiratory movements, is liable to be interrupted by movements
of a different type, in which the cavity of the pharynx is opened
more widely than usual and then forcibly contracted, driving the
water out through channels which ordinarily conduct an inflowing
stream. These movements can be elicited with great ease by the
introduction of any foreign solid object into the mouth cavity, and
also by the introduction of bubbles of air : they occur when a fish
is removed from water, and are called variously gasping move-
ments, Auspeirejlewe or, in the case of elasmobranchs, Spritzreflexe.
Baglioni* remarks that these spouting movements may be seen
occasionally if one watches a fish kept in a tank under conditions
as nearly as possible normal. He attributes their occurrence to
the entry into the mouth cavity of some foreign particle with the
inspired water, such as a grain of sand or a shred of mucus : such
objects are often to be seen in the jet of water shot out by the
Auspeireflex. Baglioni thus regards the sporadic appearance of
these movements as being conditioned by the chance occurrence
of some slight external stimulus. He considers them equivalent
to a cough or a sneeze.
While it is undoubtedly true that spouting movements can be
elicited by very small external stimuli, I have made some observa-
tions which seem to me to point to a tendency on the part of the
nerve cells concerned in the reflex to discharge at rhythmic
intervals which are not correlated with rhythmic external stimuli.
The development of rhythms of long period in nerve cells is a
matter of interest from several points of view, and I have therefore
thought it worth while to give a brief account of these observations,
which were made incidentally in the course of another enquiry as
yet unfinished,
* Z.f. allg. Physiol, vii. p. 177, 1907.
of Torpedo ocellata.
171
Methods. In the study of a series of rhythmic movements
three points may receive attention : these are the frequency, the
amplitude and the form of the movements. The fii^t may be
determined with sufficient accuracy by simple observation, but lor
the study of the second and third of these factors a graphic record
is required. For the accurate study of the form of the movements
the recording surface must move fairly rapidly, that is to say a,t
the rate of some centimetres per second. From such a record all
the information required as to frequency and amplitude could be
obtained, but only as the result of examining and measuring many
metres of tracing, even in an experiment of moderate duration.
As a matter of fact, in the case of respiratory movements the
factors of greatest interest are the frequency and amplitude of the
movements ; it is rare to find changes in form unaccompanied by
any change either in frequency or in amplitude. For the investi-
gation of frequency and amplitude the most usual practice is to
take a tracing on a drum travelling at such a rate that the
movements are just distinctly separated. Such a record shows at
once the amplitude, and on counting and comparing with a time
record it gives the frequency. Anyone who has had the task ot
counting up the number of movements per minute from such a
tracing knows that it is exceedingly tiresome. The tracings
moreover are very cumbersome if the experiments are prolonged,
and mere inspection gives no indication of any but relatively large
changes in frequency. Following on the work of Marey, Nogues
has elaborated an apparatus known as an odograph for the
investigation of such series of rhythmic movements. The fre-
quency of a rhythm studied by this apparatus is indicated by the
inclination of a continuous line to the horizontal axis. If the
rhythmic movements continue at a uniform rate, the line ascends
regularly: if they accelerate, the line goes up more steeply, if
they retard, less steeply. In the course of an experiment, it may
be of several hours' duration, the frequency recorder traces a single
oblique line. , .
The method which I have used differs from that of Nogues m
that the counting mechanism records each minute by a separate
vertical line the number of contractions which have taken place
in a predetermined interval of time. It is arranged as follows.
The lever shown in Fig. 1 is used to record the amplitude of the
movements, in the usual way. The recording lever is pivoted at
A. At 5 a second lever is pivoted, the screws supporting it
being insulated from the brass holder. This second lever consists
of a wire bent to the form shown. On its axis there is pressed
a piece of hair-spring which introduces sufficient resistance to
* Trav. Inst. Marey, ii. p. 31, 1910.
172 Mr Mines, Note on the respiratory movements
prevent this little lever from falling by its own weight, and at
the same time brings it into electrical connexion with the insu-
lated binding screw 0. The extremity of the second lever is bent
back on itself so as to form a pair of jaws which pass on either
side of the first lever, about 15 mm. from its axis. To the upper
jaw is fastened a small piece of platinum wire, which can make
contact with another piece of platinum wire fastened to the main
lever. The under jaw is prevented from making contact with the
first lever by a thin piece of mica. The amount of play between
the recording lever and the jaws of the second lever is made as
small as possible consistent with the making and breaking of
contact with each up and down movement of the levers. This
arrangement provides for a rubbing contact between the platinum
pieces. D is a stop.
During the ascent of the recording lever, electrical contact is
maintained between the binding screw G and the brass support ;
during the descent of the lever, the contact is broken. This holds
good for a wide range of positions of the recording lever, and the
arrangement will work even when the amplitude of the excursions
is very small : it is limited, of course, by the width of the gap
between the jaws of the second lever. This lever is connected to
a source of current of about 4 volts and to the coils of a light
relay. To obviate any sparking at the contacts a shunt may be
introduced. The intermittent movements of the relay actuate
another circuit which controls the apparatus shown in Fig. 2.
This consists of a toothed wheel (a small circular saw was used)
which is moved on, one tooth at a time, by a ratchet actuated by
an electric magnet. A difficulty in the construction of an electric
counter is that the movements of the armature of the magnet are
apt to be so abrupt that the wheel may be shot on more than one
step at a time. This difficulty is overcome by the use of a
glycerine brake, which is seen below the toothed wheel. The
ratchet actuating the wheel and that preventing it from slipping
back, are placed near together on the periphery of the wheel. A
second electro-magnet E is so arranged, that when it is energised
both these ratchets are pulled away from the toothed wheel, so
that it is free to move. On the same axis as the toothed wheel is
a small grooved pulley, on which is wound a piece of silk thread.
The other end of the thread is attached to a suitably weighted
lever. The wheel is furnished with a stop so that when the
magnet E is energised, the wheel and the lever return to a
definite zero position. The magnet E is excited for a period of
eight seconds once a minute, the circuit being made by a wire
connected to the second-hand of an ordinary clock dipping into a
pool of mercury contained in a cavity in a paraffin block on which
the clock stands.
of Torpedo ocellata. 173
The lever connected with the wheel is arranged to write under
that recording the amplitude of the movements. It gives a record
showing the number of movements which have occurred during
a period of 52 seconds in each minute and at the same time
provides a time tracing in minutes by which the upper tracing
may be read.
The general arrangement of the apparatus is shown in Fig. 3.
Records are taken on a drum moving about 10 cms. per hour, and
thus quite a short tracing shows at a glance the frequency and
amplitude of the movements over periods of several hours. Two
sources of instrumental error must be noted, though they do not
affect any of the conclusions to be drawn from the experiments to
be described. In the first place variations in frequency within
the interval of 52 seconds would escape notice in the record if
they chanced to include an acceleration and a retardation which
exactly balanced one another. In the second place, when the
frequency of the movements is quite regular, there is liable to be
a variation of one in the record from minute to minute, since the
number of movements will not as a rule be an exact sub-multiple
of the number of seconds during which they are counted.
Examples of the records obtained are shown in Figs. 4 and 5.
The method is obviously suitable for the study of the heart beat
or for counting drops.
Experiments were made on moderate sized specimens of
Torpedo ocellata. The fish was held lying with the ventral
surface uppermost by means of von UexkuU's device. A gentle
stream of sea-water wos, led into the mouth by a rubber tube.
The fish was placed in a small tank, provided with an overflow
pipe, and as a rule was covered with water. The recording lever
was connected by a thread to one of the gill clefts.
The temperature of the water varied in different experiments
from 18° to 22° C.
Observations. After the irregularity caused by the manipula-
tion involved in fixing the fish in position, the respiratory
movements became regular, and often continued so with little
change in amplitude or frequency for several hours. During this
period it was very usually found that the fish made occasional
spouting movements.
The graphic records showed that these spouting movements
tended to recur at fairly regular intervals.
Fig. 4 is an example taken from the close of a period of two
hours during which the behaviour had been practically the same
the whole time. It is to be noted that the spouting movements
do not occur at exactly equal intervals, yet sufficiently nearly so
to suggest a slightly-distorted rhythm. The period of this rhythm
was sometimes as great as 5 minutes — in other cases the movements
recurred several times in a minute.
174 Mr Mines, Note on the respiratory movements, etc.
The frequency of the spouting movements was greatly in-
fluenced by changes in the mechanical conditions. The efifect of
an increased flow of water through the pharynx always caused an
increase in the frequency of the ordinary respiratory movements
with a decrease in the frequency of the spouting movements.
These points are illustrated by Fig. 5 (<x) and (h). The tracings
are from different experiments.
In (a) the flow of water through the pharynx was reduced
during the times indicated by the white horizontal lines. In (h)
the horizontal line indicates an increase in the rate of flow.
The frequency scale at the side applies to both tracings.
I have not found any definite relationship between the
chemical composition of the water and the frequency of the
rhythm. A considerable increase in the carbon dioxide tension,
changing the hydrogen ion concentration of the sea-water from
about 10~^'^ to 10"" caused violent movements and upset the
rhythm altogether. In one case increase in the oxygen tension of
the water was accompanied by cessation of the spouting move-
ments which returned when the oxygen tension was restored to
its original value. This result was not confirmed on repetition
with other specimens. Further work on the subject is needed.
The object of the present communication is to point out that
these spouting movements do often occur in the resting fish,
separated by intervals so nearly alike as to make it improbable
that the occurrence of each movement is the result of a fortuitous
external stimulus. External stimuli will readily affect the reflex
mechanism, but it appears that when external conditions are kept
as uniform as possible the periodicity of the spouting movements
is determined by the central nervous system.
I wish to express my warmest thanks to Doctor Dohrn and
his Staff for the kindness with which they aided my work during
my tenure of the University Table at the Stazione Zoologica in
the autumn of 1912.
Phil. Soc. Proc. Vol. xvii. Pt. ii.
Plate III.
Fig. 1.
/
'4
^
i
I
fR'^gS
m
piH-.^
—
Fig. 2.
Fig. 3.
Phil. Soc. Proc. Vol. xvii. Pt. ii.
Plate IV.
Fig. 4.
Amplitude
jM'equeiicy
h
/
=^0
i^
:^
k
.0.0
-^
: iO
^
(r
///////// ,7
i !
Fig. 5.
Mr Kleeman, The Atomic Constants, etc.
175
The Atomic Constants and the Properties of Substances. By
R. D. Kleeman, B.A., Emmanuel College, D.Sc. (Adelaide).
[Eead 27 January 1913.]
The quantity — of a substance, where p denotes its density
and m the molecular weight of a molecule relative to that of the
hydrogen atom, is the volume of a gram molecule of the substance,
and accordingly proportional to the molecular volume of a molecule.
It has long been known that it is approximately an additive
quantity of the atom for substances at their boiling points at
atmospheric pressure. It is evident, however, from the investiga-
tions of the law of corresponding states in connexion with the law
of molecular attraction by the writer, that the molecular volumes
obtained for corresponding states are likely to be of greater value
and importance. Table I contains the values of — for a number
Table I.
Values of c^.
H = l, = 2-034, = 2-298, F = 2-098, 01 = 4-105,
Br = 5-805, 1 = 7-734, Sn = 8-59.
Name of substance
m
Pc
14 -062c
Name of substance
VI
Pc
14-062c„
Di-isopropyl
356-7
368-4
Stannic Chloride
351-6
351-6
Di-isobutyl
482-2
482-2 i
Benzene
256-2
256-2
Pentane
310-3
311-7
Ether
284-1
287-3
Isopentane
307-7
311-7
Propyl formate
288-5
291-5
Hexane
367-5
368-4
Propyl acetate
344-9
348-2
Heptane
427-6
425-1
Carbon dioxide
94-8
93-2
Octane
490-4
482-2
Ethyl butyrate
420-4
404-9
Fluor benzene
271-4
271-4
Methyl acetate
231-3
234-8
Bronio benzene
323-5
235-5
Carbon tetrachloride
276-2
259-4
lodo benzene
350-6
350-6
Methyl formate
172-0
178-0
Chloro benzene
307 8
299-6
Hydrochloric acid
61-4
73-7
Hexamethylene
•
307-5
340-3
176 Mr Kleeman, The Atomic Constants
of substances at the critical point — the most important corre-
sponding point — and the values of the molecular volumes calculated
from the expression K^^ , where Cy denotes the apparent volume
of an atom relative to that of a hydrogen atom. The values of c„
are given at the top of Table I. Those of the H and C were
obtained from the two substances di-isobutyl and benzene, while
the values for the other atoms are the mean values obtained from
the remaining substances. K has been put equal to 14 "06. A fair
agreement between calculation and experiment is obtained.
There is no obvious simple reason why the apparent molecular
volume of a molecule should be an additive property of its atoms,
since an increase in the volume of a substance is not attended by
an equal increase in the actual space occupied by the molecules.
The molecular volume in the case of a liquid or vapour, it may be
pointed out here, is really the outcome of the equilibrium between
the intrinsic pressure due to the attraction between the molecules,
and the pressure exerted by the molecules due to their motion of
translation. We might therefore expect that the constant c« and
the atomic attraction constant Ca should be connected with one
another. Thus the writer has shown that the attraction constant
of an atom is proportional to V^Wi, where m^ denotes its atomic
weight. Traube has shown that the atomic volume of an atom at
the absolute zero, which according to the law of corresponding
states is proportional to that at the critical point, is proportional
to V'^ii. But the values of the constants Ca and Cy (the average
values determined from the facts) agree on the whole better with
the facts than the constant \/mi, as might be expected.
The factors of \/mi that have to be introduced in both cases
to obtain a better agreement with the facts are of interest. In
the case of the constant c« we may accordingly write Ca = ji'\/mi.
The values of y^ for a number of atoms corresponding to the values
of Ca deduced from the internal heat of evaporation* are given in
Table II, the value for the carbon atom being put equal to unity.
It is very probable that y^ depends on the chemical constitution
of the molecule in which the atom occurs, and should therefore
strictly not be given the same value for each substance. Probably
it will be found when more extensive data are available that it has
the same value for all substances belonging to the same chemical
group. Further investigations of the properties of the attraction
constants in the law of molecular attraction along these lines will
probably lead to interesting results.
In the case of the constant c„ we may similarly write
Cv = 72 \/'nii. The values of 72 for a number of atoms are given in
Table II, the value for the carbon atom as before being put equal
* Phil. Mag., Oct. 1909, p. 507.
and the Properties of Substances.
177
to unity. An inspection of the table will show that the greatest
deviation from the square root law in the case of both the
quantities c„ and c„ is shown by the hydrogen atom. The
deviations are in opposite directions. This adds another anomaly
to the large number for which hydrogen is already famous.
Table II.
Atomic
Atomic
symbol
71
72
symbol
71
7-2
H
•65.3
1-70
CI
•920
M71
C
1-000
1-00
Br
•778
1-105
-974
•977
Sn
•882
1^346
F
•863
•819
I
•897
1-168
The writer has deduced two fundamental relations from the
law of molecular attraction and the laws of thermodynamics*.
These equations may now be written
T =
■in
.(2),
where p denotes the pressure of the substance at the tempera-
ture T, and Mi^ and M^^ are quantities which have the same values
for all substances at corresponding states. Thus if the chemical
formula of a substance be known the critical constants can ap-
proximately be calculated by means of the atomic constants Ca
and Cv The values of Tg for a few substances were calculated in
this way by means of equation (2) and are contained in Table III,
putting for ilfg^ its mean value 17"69. The agreement between
calculation and experiment is not quite so good as obtained in
Table I, due probably to the fact that higher powers of S^ and
Sg are involved which increases the effect of the errors in their
values on the value of Tc. But still the formulae should be useful
in obtaining approximately the values of the critical quantities.
They may be of use in chemical investigations, especially when
the properties of a new compound are being investigated whose
chemical formula can only be conjectured. Thus if the critical
constants of a hypothetical substance be calculated, its pressure,
* Phil. Mag., Oct. 1909, p. 509, and Dec. 1909, p. 903,
VOL. XVII. PT. II,
12
178
Mr Kleeman, The Atomic Constants
Table III.
Values of Ca-
H=l, C = 5-S0,
0-5-94, F = 5-76, CI = 8-40, Br = 10-65,
Sn= 14-68, 1 = 15-49.
Name of substance
-Ca
T,(Exp.)
2; (Gal.)
Chloi'o benzene
45-2
21-31
633
620-7
Octane
60-4
34-27
569-2
588-4
Ethei-
37-2
20-43
467-4
442-7
Carbon dioxide
17-2
6-63
304-3
426-5
Methane
9-3
6-03
191
141-6
Hydrogen
2
2
38-5
28-5
Ethylene
14-6
8-07
282
290-7
Carbon tetrachloride
38'9
18-45
556-1
557-2
Pentane
38-5
22-17
470-3
427-4
Heptane
53-1
30-23
539-0
637-8
Di-phenyl methane
73-6
34-41
768-6
869-2
and density of liquid and saturated vapour, can be obtained for -
any temperature from those of a known substance by means of:
the law of corresponding states. By comparing these quantities i
with those found by experiment useful information for the guid- I
ance of further experiments is obtained. As an example of the i
application of these principles let us calculate the critical and
other quantities of the substance Og, which Ladenburg believes is |
produced in a vacuum tube through which an electric charge i
passes, supposing that it exists as a pure substance, that is, not ;
as a mixture of substances whose formulae are of the type 0„. j
The critical density, temperature, and pressure in atmospheres ■
are found to be -495, 603, and 83-3 respectively. At a tempera-
ture of 16° C. (room temperature) the substance would have a
vapour pressure of 30'7 mm. of mercury, and the temperature of'
its boiling point would be 134° C.
Useful information may also be obtained by means of the
foregoing equations about the purity of a substance, that is,
whether or no it consists of a mixture of two or more substances,
a special case of which is partial polymerization of the molecules.
For example, the values of c^ and c„ for an atom of copper, deduced
by interpolation from the values of Ca and c^ for a number of atoms
given in Tables I and III are 9'81 and 5-18 respectively. The
critical temperature of liquid copper should therefore be 190° C.
and the Properties of Substances. 179
Since, however, it is undoubtedly enormously higher, it follows
that copper in the solid and molten state consists in practice of
molecules having the formula Cn,i, where n is probably quite large.
The same conclusions can be arrived at in respect to all the other
metals, and a large number of chemical compounds such as the
various salts etc.
It will be apparent from equation (2) that the value of Tc
increases with that of S^ . Therefore the partial polymerization
of a liquid should have the effect of raising its critical temperature.
An important case in point is water, whose critical temperature
would be 1.59"5°C. instead of 631° Q, if the chemical formula for
each molecule were HgO. If each molecule were polymerized to
the same extent its chemical formula would be 7'8 (H2O). It
appears, however, from surface tension considerations that water
consists of molecules polymerized to different extents. The mole-
cular weight of some of the molecules must thus be greater than
that according to the above formula. It may be pointed out here
that the determination of the extent of polymerization of a liquid
from Oetvos' surface tension equation cannot lead to very accurate
results since it is tacitly assumed that the critical temperature is
not influenced by polymerization.
Another interesting case in this connexion is the molecular
weight of liquid mercury. If we take Ca and c^ equal to V^u
which we have seen is approximately the case, we obtain 604"9° C.
for the critical temperature. But it is undoubtedly much higher,
from which it follows that mercury must be partially polymerized.
This we have shown to be the case by a different method in a
previous paper*.
* Proc. Camb. Phil. Soc, vol. xvii. p. 157.
12 2
180 ilfr Dunlop, Note on the effect of heating
Note on the effect of heating paraformaldehyde with a trace of
sulphuric acid. By J. G. M. Dunlop, M.A., Gonville and Caius
College.
[Bead 24 February 1913.]
Pratesi (Oaz. XIV. 139) described a polymeric variety of
formaldehyde, soluble in alcohol and other solvents, and to which
he gave the name a trioxymethylene. This he prepared by i
heating paraformaldehyde (trioxymethylene) with a trace of
concentrated sulphuric acid for some hours in a sealed tube at i
115° C. The a trioxymethylene was described as condensing in
the cooler portion of the tube in long needles.
The present author, having occasion to require a strong solution
of formaldehyde in alcohol (in which paraformaldehyde is in-
soluble), began to prepare a trioxymethylene in this way.
For convenience it was thought desirable to use a tube about
60 cm. long, bent in the middle into a right angle, so that the end
containing the paraformaldehyde and sulphuric acid could be
heated in a tube furnace, the a trioxymethylene being condensed
in the other limb, which was immersed in a beaker of water.
The distillate was found to consist of a very mobile liquid,
which when distilled gave two fractions, one distilling at 33° C.
and the other at about 100° C.
The more volatile fraction had an ethereal odour, and did not
react with sodium bisulphite. On investigation it was found to
be methyl formate, and this was confirmed by comparison with a
specimen of this ester, the boiling point and density being
identical. On hydrolysis with moist lead oxide it yielded lead
formate and methyl alcohol.
The yield of methyl formate is very variable, and depends on
the amount of sulphuric acid and also on the temperature. With
about six drops of acid to ten grams of trioxymethylene, a yield of
about one to two grams of ester appears to be usual. In an ex-
periment in which about five grams of acid to ten grams of trioxy-
methylene were taken, great charring took place, and practically
no ester was formed.
The reaction appears to take place by an intermolecular
exchange of linkages thus :
H,C = O H,C— O
/ I
H— C— H H 0— H, i.e. H— COOCH3.
I I
O O
paraformaldehyde with a trace of sidphuric acid. 181
It may also take place by the hydrolysis of two molecules of
formaldehyde to methyl alcohol and formic acid, (analogous to
the Cannizzaro reaction in the case of aromatic aldehydes), and
subsequent esterification in the presence of the sulphuric acid.
In this case however it would be reasonable to expect that by
using a larger proportion of acid, the yield of ester would be
increased, which does not accord with the experiment described
above.
The higher boiling fraction was found to consist chiefly of a
liquid boiling at 95 — 96° C. and which appears to be a polymer
of formaldehyde. It is still under investigation. Experiments
with other condensing agents are also being carried on.
182 Mr Ennos, The Oxidation of Ferrous Salts.
The Oxidation of Ferrous Salts. By F, R. Ennos, B.A.,
St John's College, (Communicated by Mr C. T. Heycock.)
[Bead 24 February 1913.]
The rate of oxidation of ferrous salts in aqueous solution and
in absence of free acid was studied by bubbling air or oxygen
through the solutions at a constant rate of about one litre in
three hours, portions of the solution being removed at definite
intervals and titrated with potassium permanganate or bichromate.
At the ordinary temperature ferrous sulphate and chloride are
oxidised exceedingly slowly. In the case of the former the initial
N .
rate of oxidation in an y^ solution at 25" C. is of the order '03 per
cent, per hour, and this rate is doubled roughly for a rise of 10° C.
A temperature of 60° C. was finally employed in comparing different
ferrous salts and it was found that the oxidation of the chloride is
about one-tenth and of the acetate ten times as fast as that of the
sulphate. For the sulphate the reaction appears to be of the
second order as regards the ferrous salt and also proportional to
the partial pressure of the oxygen, results agreeing with those
obtained by McBain by a different method (Jour. Phys. Ghem.
1901). It has not yet been possible to find the order of reaction
for the chloride or the acetate.
The influence of temperature, dilution and nature of the acid
radicle indicates that the oxidation depends on the non-ionised
part of the ferrous salt molecule. It remains to be seen whether
there is any quantitative relationship between the two.
D?- Searle, A Simple Method of determining, etc. 183
A Simple Method of determining the Viscosity of Air. By
G. F. C. Searle, Sc.D, F.R.S., University Lecturer in Experi-
mental Physics, Fellow of Peterhouse.
[Read 11 November 1912.]
§ 1. Introduction. The determination of the viscosity of water
by the flow through a capillary tube has, for many years, been one
of the experiments done in my practical class at the Cavendish
Laboratory. The determination of the viscosity of air was intro-
duced in October 1912 for the benefit of those students who had
already determined the viscosity of water in Mr T. G. Bedford's
class at the Cavendish Laboratory or in other laboratories. The
apparatus can be constructed at small cost and without the aid of
a highly-skilled mechanic — advantages which will appeal to many
teachers. No atteinpt has been made to introduce refinements
into the apparatus.
Air is pumped into a large vessel and is allowed to escape
through a capillary tube. The pressure of the air at the beginning
and end of a measured interval of time is determined, and it is
assumed that the temperature of the air in the vessel and in
the capillary tube is always equal to that of the surrounding
atmosphere.
In the determination of the viscosity of water the difference
of pressure forcing the liquid through the tube is kept constant
and the density of the liquid may be treated as uniform. But in
the present experiment the density of the air is not uniform along
the flow tube at any given time, and the difference of pressure
driving the air through the tube is not constant, but diminishes
as the time increases. The theory must therefore take account of
these two facts. For the convenience of those who may wish to
repeat the experiment, I give the details of the necessary
calculations.
dx
D
A ^ "
Fig. 1.
I 2. Calculation of velocity. Consider a tube AB (Fig. 1) of
radius a cm. and length I cm., through which air is passing in the
184 Dr Searle, A Simple Method of determining
direction from A to B. Let CD be a length doc of a coaxal
geometrical cylinder of radius r cm., the end G being at a distance
X cm. from the end A of the tube.
Let the velocity of the air in the positive direction at any
point defined by r and x he v cm. per sec. Then the velocity
gradient at the curved surface of the cylinder CD is dv/dr sec.~^
Hence, if the viscosity of the air be rj dynes per sq. cm. per unit
velocity gradient or 77 grm. cm.~^ sec.~^, the force due to viscous
action on the curved surface of CD in the positive direction is
7] -J- ■ 27rrdx dynes.
If the pressure at any point on the end C of the cylinder be
p dynes per sq. cm., the pressure at any point on the end D is
p + (dp/dx) dx, and thus the resultant in the positive direction of
the forces due to the pressures is
— irr'^ J- dx dynes.
When the velocity of the air at any point in the tube is very
small compared with the velocity of sound in air, the rate at which
momentum enters the cylinder CD by the end C by convection
differs from the rate at which it leaves the cylinder by the end D
by an amount negligible compared with 7rr^ (dp/dx) dx. Since the
motion is steady, the momentum within the cylinder remains
unchanged. Hence the resultant force vanishes and thus
7? ^- . 2irrdx — irr^ ~- dx = ^
dr dx
dv _ r dp
dr 2r) dx ^ ^
Since v — when r= a, because there is no slipping at the wall of
the tube, the solution of this equation is
* = -r/«'-'-'>S <2)
If the flow of air across the plane defined by ^ be U c.c. per sec,
U=\ 2'7rrvdr= — - — f- | (a^ — r^)rdr
J 2r] dx j
^_7ra^dp
877 dx • ^"^^
The mass of air crossing this plane per second is o-?7 grammes,
where a- grm. per c.c. is the density of the air under the pressure j?
at the temperature 6 prevailing at the plane x ; this temperature
the Viscosity of Air. 185
is assumed to be equal to 6^, the temperature of the surrounding
atmosphere.
§ 3. Calculation of pressure. When the motion is steady, the
mass of air crossing each section of the flow tube per second is the
same, and hence
aU=a,Uo, (4)
where cr,, and f/o are the density and volume of the same mass of
air at temperature Oq and at the atmospheric pressure Po- Thus
U = ^U, = ?^U, (5)
a p
Inserting this value of JJ in (3), we find the following differential
equation for jj, viz.
loUo^pU^_7T^ clp
a' a' Sv^dx ^"^^
In practice the radius of the tube will not be quite constant at
different parts of the tube, but it will generally vary so slowly as
we pass along the tube that the conditions of flow for any in-
finitesimal length dx may be treated as if they were those which
would exist there if the whole tube had the same radius as the
element dx. On these assumptions, equation (6) holds good for all
values of x. Integrating it with respect to x from x = to x=l,
and remembering that t) is independent of the pressure, we have
^"<'I=-^»^'C w
If the pressure in the vessel, i.e. where x = 0, be P, then
^"^•0=il?(^'-^»'> («)
since the pressure Sit x = l is the atmospheric pressure Pq. With
moderately good tubes the integral on the left differs very little
from ^/tto*, where ttOq" is the value of the cross-section deduced
from the formula
Tra.Hp^M, (9)
and M grammes is the mass of mercury, of density p grm. per c.c,
which fills the tube. The necessary calibration correction is in-
vestigated in I 6. Neglecting it for the present, the formula
becomes
_„ 4 P2 P 2
^° IQvl' Po ' ^ ^
au equation due to 0. E. Meyer.
186 Dr Searle, A Simple Method of detei^mining
§ 4. Formida for viscosity. In the experiment the mass of
the air which passes through the tube is deduced from the fall of
pressure of the air in the vessel during a time t seconds.
Let the volume of the vessel up to the end « = of the flow
tube be ;S^ c.c. and let the mass of air in the vessel at any time t be
ilf grms. Then if, as is assumed, the temperature be d^, we have
M=8a = S(ToP/Po (11)
The rate at which mass escapes from the vessel is aoUo grms. per
sec. and this is equal to —dM/dt. Hence, by (11),
_ 1 dM__S^dP
°"~ o-o dt " P, df
Using this value of U^ in (10), we obtain the following differential
equation for P, viz.
8 dP ^ -rra,' P'~Po'
P, dt ~ lQr]l Po ■
Putting 1/(P' — P,)^) into partial fractions, we have
J_ [ 1 _ 1 ] ^_ ^[^ n9^
2Po|P + Po P-Po] dt WrjlS ^ ^^
Integrating from ^ = to ^ = ^, we have
1
2P„
P + Po 1^=^_ 7ra,H
If Pi and P., be the pressures in the vessel at ^ = and at t = t,
then
TTCIq ±f)t /10\
~W8 ^^' ^ ^
where X = log, | y _p ■ p ^ p \ (^^)
He^^^ ^= w°-x ^^^^
From the last expression rj can be determined. The value of Py
on the right side of (15) must be expressed in dynes per sq. cm.
Thus, if the barometric height be K cm. and the density of
mercury at the temperature of the barometer be p grms, per c.c,
Po = gpho.
Since only ratios are involved in the formula (14) for \, the pres-
sures in that formula may be expressed in cm. of mercury.
In the experiment it is the differences Pj — Po and Pg-Po
the Viscosity of Air.
187
which are observed by means of a gauge. The quantities Pi + Pq
and Po + Po are obtained as follows: —
Pi + Po = (Pi - Po) + 2Po. p. + Po = (P. - Po) + 2P..
§ 5. Experimental details. A " tin " can C (Fig. 2) of about
10 litres capacity (price \0d.) is used to contain the air. Through
a well-fitting rubber bung a tube passes, and into this tube are
G
Fig.
soldered a cycle tyre valve V (price 4c^.), an ordinary gas-fitter's
tap T (price 8d), and a side tube. The side tube is connected
with the mercury gauge (r by a stout rubber tube. The flow
tube F is connected with the gas tap by a rubber joint. The
various joints must, of course, be air-tight.
Air is pumped into the can by means of an ordinary cycle
pump attached to the valve V, until the pressure is raised to
188 Dr Searle, A Simple Method of deterndniiig
20 to 25 cm. of mercury above the atmospheric pressure. The
apparatus is then allowed to stand for some minutes in order that
the rise of temperature due to the compression of the air may die
away. A screen should be placed between the can and the observer
to prevent the transfer of heat from his body to the can.
When the gauge readings have become steady, they are recorded.
The tap is then opened for a time t seconds — one minute or more
— and is then closed, and the new gauge readings are taken and
recorded*. This process is repeated for various initial pressures.
If the barometric pressure and the temperature remain constant,
we see, by (15), that the value of tjX should have the same value
for each of the experiments with a given tube.
The radius of the flow tube is found from the mass of mercury
required to fill the tube. It is here assumed that the bore of the
tube is uniform ; the method of obtaining the small calibration
correction is explained in § 6.
The volume of the can is best found from the mass of water
required to fill it ; small corrections are required for the various
tubes connected to the can.
§ 6. Calibration correction. We shall now investigate the
correction required when the flow tube is not of uniform radius.
By (8) we see that we have to replace Ija^ in (10) by
^ dx
(^
and thus formula (15) becomes
ttPo
dx
a*
i («>
The value oi Jdx/a^ is found as follows. Suppose that n — 1 marks
are made on the tube, dividing it into n parts, each l/n cm. in
length. Let a thread of mercury of mass ni grms., whose length
is approximately l/n cm., be introduced into the tube. Let the
thread be moved along the tube so that its centre approximately
coincides with the centre of each of the oi parts in turn, and let
^1, q,,, ... be its length in the n positions. Then, if the tube be
treated as uniform over each of the n parts, we may put
'jrpa^-^ = m/c2i, irpa^^^mlq.i, &c.,
where p is the density of mercury.
* After the tap has been closed, the pressure in the vessel sometimes rises
gradually by a few tenths of a millimetre. This indicates that, although the
thermal conduction from the walls of the vessel has not kept the temperature of
the expanding air quite constant, yet the fall of temperature has been very slight.
the Viscosity of Air. 189
If the mass of mercury filling the whole tube be ilf grms.,
M = TTp \ a^ dx.
Jo
Taking l/n as an element of length instead of doc and replacing
integration by summation, we have
M — irp I a^dx = irpXa^ . - = »iS — = — X - .
^Jo n q n q
Hence 1 = _L ^ 1 (17)
m niVl q
In a similar way we find
f"
■'o
Hence, by (17),
'^dx^^^^[^7rY[^ Tryl ^
f^ dx _ iryH" 1 /^ 1 Y^ ^
Jo"^~l^ -n'\-'q) •^'^'■
If cia^ be the mean value of the square of the radius deduced from
the mass of mercury filling the whole tube,
tto^ = MJTrpl.
Thus f^dx^± If^ 1 Y v^ 2
Hence the factor F by which Z/ao* must be multiplied to correct
for the inequality of the tube is
^-hmi-'-"' (i»)
This factor is only very slightly greater than unity when the tube
is nearly uniform.
We may exhibit the correcting factor in another form. Let q^
be the mean value of the n quantities qi, q2, ... and let
qi = qo + d,, q2 = qo + d2, &c.
Then Sdl = (ii + 4 + • . . = 0.
Hence %q^ = 2 (qo^ + 'Iq^d + d'-) = nq^ + ^d'^.
Also, since with a nearly uniform tube di,d2, ... are small compared
with qo,
^1^1 ^ /I d d^ \ n 1 K« 7.,
q qo + d \qo qo^ q,^ J qo ^o'
190
Dr Searle, A Simple Method of determining
Hence, going as far as ^d"^, we find for the correcting factor
1 + — :,=! + 2-'
nqoV nqo^
of \ qJ \ nqo-
(19)
9o
d
1 1
Since ^ - = 2 , = S „ ,, ,
^ qo + d g'o- - rt-
and since qo + d and q^ — d are both positive,
^1 1 V / 7V ?^
q qo' go
Hence
i^>i(-yo.^„-^+2(^^)>i+— ,
and thus i'' always exceeds unity.
To illustrate the practical application of the calibration cor-
rection, I give the data for the flow tube No. I used in the
measurements described in § 7. The following table gives the
length 9' of a mercury thread in 11 equally spaced positions along
the tube ; the length of the tube was 64'82 cm.
Length of
thread q
q^
1
d = q-q^
d^ i
cm.
cm."
cm.~^
cm.
cm.^
6-32
39-9424
0-158228
-0-15
0-0225
6-40
40-9600
0-156250
-0-07
0-0049
640
40-9600
0-156250
-0-07
0-0049
6-38
40-7044
0-156740
-0-09
0-0081
6-40
40-9600
0-156250
-0-07
00049
6-43
41-3449
0-155521
-0-04
0-0016
6-49
42-1201
0-154083
+ 0-02
0-0004
6-53
42-6409
0-153139
+ 0-06
0-0036
6-60
43'5600
0-151515
+ 0-13
0-0169
6-60
43-5600
0-151515
+ 0-13
0-0169
6-58
43-2964
0-151976
+ 0-11
0-0121
(?o = 6-47 S(/2=460-0491
S - = 1-701467
2(^2=0-0968
Hence, since n= 11, we find, by (18),
^ = £5^9'
^ly^ 4600491 x(1701467y^^.^P^g3
qJ 11®
The need of tables giving q'-^ and q ^ to several significant
figures may be avoided by finding F by formula (19). Thus
^■=l + 3?f = 1 + 3x^968^ 1.00063.
nqo''
11 X 6-472
the Viscosity of Air.
191
§ 7. Practical Example. The following observations were
made with two flow tubes.
Volume of can and tubes (found by mass of water) =S = 9646 c.c.
Barometric height =7/0 = 76-36 cm.
Barometric pressure =Po = f//D/io = 1-016 x 10^ dyne cm .-2.
Density of mercury z=p= 13-56 grm. cm.~3_
Length of flow tube I =? = 64-82 cm.
Mass of mercury filling flow tube I = ill = 3-671 grm.
Hence <-= M/7rp? = 0-001329 cm.^, ao^ = 1-767 x 10-« cm.^.
By § 6, " ^
If
then
ttPoV
8,SZ
00063.
iy\ -1 _ ,rPo«o* 1
8Sl 'F'
Thus, for tube I,
K=
w X 1-016 X 10" X 1-767 x 10-"
8x9646x64-82x1-00063
= 1-127x10-" dyne cm.-^.
The results obtained with tube I are shown in the following
table. The table also includes results found with tube II. The
data for tube II were
Z= 77-56 cm., rt„^= 1-386 x 10-» cm.^ i<^= ^-^^ Sg^ . (s -j =1-00467.
Hence, for tube II,
/i:=7-356xlO-'' dyne cm.-".
Tube
I
Time
Gauge readings
Pi-P,
?2-n
\
Kt
sees.
120
cm.
36-26
30-20
cm.
13-80
19-93
cm.
22-46
cm.
10-27
0-710
1-90x10-^
I
1-20
33-81
29-08
16-28
21-08
17-53
8-00
0-727
1-86x10-^
I
120
31-01
27-80
19-12
22-40
11-89
5-40
0-749
1-80 X 10-^
II
180
36-39
30-10
13-66
20-06
22-73
10-04
0-742
1-78x10-*
II
180
3015
27-40
20-00
22-77
10-15
4-63
0-751
I76x 10-^
II
180
32-49
28-30
17-65
21-88
14-84
6-42
0-785
1-69 X 10-^
192 Dr Searle, A Simple Method of determining, etc.
In the case of tube I the tap was opened for 120 seconds, so
that t= 120 sees. For tube II the tap was opened for 180 seconds.
The temperature was 13"8° C throughout.
The mean value for the viscosity of air at 13'8° C. is
7} = 1'80 X 10~^ grm. cm.~^ sec.~\
R. A. Millikan (Physical Revieiu, No. 1, 1913, p. 79) gives
r] = 1-824 X 10-* {1 + -0027 (t - 23)}
for the viscosity of air at t° 0. This gives tj = 1*779 x 10-"* for the
viscosity at 13'8° C.
Mr Potts, The Stuarming of Odontosyllis. 193
The Swarming of Odontosyllis. By F, A. Potts, M. A., Trinity
Hall.
[Bead 10 February 1913.]
Throughout the months of June and July in 1911 I had
frequent occasion to take and examine dredgings from the sea
bottom outside the harbour of Nanaimo, British Columbia. The
bottom deposits there are of a peculiar character, consisting largely
of the debris of dead Hexactinellid sponges. . The long interwoven
spicules form a matted mass which furnishes a secure retreat for
many species of Polychaet worms. One of the most abundant and
interesting of these is a species of Syllid which proved to be
Odontosyllis phosphorea described by Moore* in 1909. During
the whole period the worms of this species contained reproductive
products. The females were of a bright red colour due to the
eggs, while the males showed the natural yellow colour and trans-
verse markings of the species. Both sexes were very irritable
under handling and broke up entirely when attempts were made
to fix them with sublimate solutions or alcohol, and at the same
time an intense phosphorescence was produced.
No appearance of the mature worms at the surface Avas noticed
during these months, though a close lookout for phenomena of
this kind was maintained. On August 15th, however. Professor
McMurrich of Toronto informed me that he had observed just
before sunset hundreds of small worms swimming on the surface
of the sea in Departure Bay, a shallow inlet adjacent to the
grounds described above. Examination of a number of these
which had been brought into the laboratory showed me that they
belonged to the species found so abundantly amongst the sponge
debris.
The next night Professor McMurrich and myself followed the
phenomenon as closely as possible. Sunset was about seven o'clock,
and half an hour or more before isolated individuals began to appear.
At first these were mostly males, but as the numbers increased so
did the proportion of females to males until there was approximate
equality. On their appearance from the depths the individuals of
both sexes swam round and round in circles with swift undulatory
movements. A short time after, the movements became slower,
finally ceasing, and during spasmodic flexures of the whole body
the eggs and spermatozoa were discharged. Then the spent
individuals sank slowly beneath the surface. No approximation
of the two sexes was observed to take place, but my impression
was that each individual sought the surface without fixed plan or
* J. Percy Moore, Proc. Acad. Nat. Sci., Philadelphia, vol. lxi. 1909, p. 327.
VOL. XVII, PT. II. 13
194 Mr Potts, The Swarming of Odontosyllis.
direction, rid itself of its contents as quickly as might be, and then
lost no time in descending to its accustomed habitat. The pheno-
menon continued till the light had nearly faded, but by then there i
were only very occasional individuals to be seen, so that probably
the whole period of swarming is less than an hour.
On the following day I left Nanaimo, but I was afterwards told j
that, though a few individuals were seen on the surface on that \
night and the next, there were nothing like the numbers of the
two preceding nights.
The accompanying map shows the distribution of 0. phosphorea :
in the neighbourhood of Nanaimo. In explanation of the small |
area assigned to the swarming worms, it must be noticed that the i
short time did not allow a complete investigation of their distribu- i
tion, but doubtless future observers will be able to map out the j
area more completely. One fact is quite clear ; that the worms, j
in seeking the surface, migrate inshore in considerable numbers, |
for I never, in the course of many dredgings, found a single i
example of Odontosyllis in Departure Bay itself. i
Recently Professor McMurrich has been kind enough to send i
me very interesting information which establishes the periodic j
appearance of the swarms of Odontosyllis. The weather was very
unfavourable in 1912 and there had been a great deal of rain just ;
before August 18th. On that night, however, the weather was |
fine, and on going out at 7.30 p.m. Professor McMurrich found i
Odontosyllis swarming at the surface as in the year before, j
Dr Fraser again observed the phenomenon on the two or three I
evenings following. j
It seems certain, then, that the swarming of Odontosyllis \
phosphorea takes place at Nanaimo at approximately the same i
date every year. In 1912 it occurred three days later than in
1911, but this may possibly have been due to the unfavourable !
weather. In 1911 swarming took place during the last quarter :
of the moon and in 1912 at the beginning of the first quarter. In j
both cases the tide was full or just falling. The close proximity
of the Dominion Government Biological Station will allow of a close
watch being kept on the circumstances of the appearance from ,
year to year, and I trust that the scanty data which I give here '
will soon be supplemented. In particular I hope that enquiry j
will be made as to whether swarming takes place at any other ■
period of the year*. ]
For some time I supposed that the phenomenon witnessed at 'I
Nanaimo had not been previously described in Odontosyllis, and it I
* In the original description by Mocre {loc. cit.) he states that the type
specimens were labelled "Phosphorescent annelids caught at surface; Avalon
Bay, Catalina Island, evening, April 11, 1904." This fixes a date for the swarming
of this species in California.
Mr Potts, The SvMrming of Odontosyllis.
195
was with great interest that I discovered and read a paper by-
Galloway and Welch* on very similar phenomena in an Atlantic
species Odontosyllis enopla. In the summer of 1904 this species
was observed to appear in the surface waters of Harrington Sound,
Bermudas, in considerable numbers and with striking regularity.
The following dates of appearance are chronicled :
July 3 — 7 reaching a maximum on the 4th,
July 29—31 „ „ „ „ 30th,
August 23 (no further details),
NanaLTTio
QTeaofseoubotti7m-j''ttnrt ujAjxit czurTTZTi
C/phospKoreo. tuas cLvedgea. " ^^^^^^
LocohXsf wbeye Stoctrmtng -prms r i..„..,^,.r i
weve obsewect ^;--vxv: iJ
so that there appears to be an interval of approximately 26 days.
On the two first occasions when they were carefully observed they
appeared each day within fifteen minutes of the same time just at
twilight. The daily period of swarming lasted from 20 — 30 minutes.
"Only a few appeared at first each evening. The numbers gradually
* Trans. Amer. Micr. Soc, vol. xxx. 1911, pp. 13-39.
13—2
196 Mr Potts, The Swarming of Odontosyllis.
I
increased to a maximum when scores might be seen at once. The
display waned somewhat more suddenly than it waxed.
" The males and females differ considerably in size, the females
often being twice as long as the males.... Both sexes are distinctly
phosphorescent — the female with strong and more continuous
glow and the male with sharper intermittent flashes.
"In mating the females, which are clearly swimming at the
surface of the water before they begin to be phosphorescent, show
first as a dim glow. Quite suddenly she becomes acutely phos-
phorescent, particularly in the posterior three-fourths of the body,
though all the segments seem to be luminous in some degree. At
this phase she swims rapidly through the water in small luminous
circles two or more inches in diameter. Around this smaller vivid
circle is a halo of phosphorescence growing dimmer peripherally.
This halo of phosphorescence is possibly caused by the escaping
eggs together with whatever body fluids accompany them. At
any rate the phosphorescent effect closely accompanies ovulation
and the eggs continue mildly phosphorescent for a while.
"If the male does not appear this illumination ceases after
10 to 20 seconds. In the absence of the male the process may
be repeated as often as four or five times by one female at
intervals of 10 — 30 seconds. The later intervals are longer than
the earlier. Usually, however, the males are sufficiently abundant
to make this repetition unnecessary ; and the unmated females
are rare, if they are out in the open water. One can sometimes
locate the drifting female between displays by the persistence of
the luminosity of the eggs ; but the male is unable to find her in ■
this way.
" The male first appears as a delicate glint of light possibly as
much as 10 or 15 feet from the luminous female. They do not swim
at the surface as do the females, but come obliquely up from the
deeper water. They dart directly for the centre of the luminous circle,
and they locate the female with remarkable precision when she is
in the active stage of phosphorescence. If, however, she ceases to
be actively phosphorescent before he covers the distance he is
uncertain and apparently ceases swimming, as he certainly ceases
being luminous, until she becomes phosphorescent again. When
her position becomes defined he quickly approaches her, and they
rotate together in somewhat wider circles, scattering eggs and
sperm in the water. The period is somewhat longer on the
average than when the female is rotating alone; but it, too, is
of short duration.
" So far as could be observed the phosphorescent display is not
repeated by either individual after mating. Very shortly the worms
cease to be luminous and are lost."
This is, I submit, a very remarkable account. In its general
Mr Potts, The Swarming of Odontosyllis. 197
aspects the swarming in this species resembles that in 0. phosphorea,
i.e. in the appearance of great numbers of individuals at the surface
of the sea at definite tiaies of the year and at a definite period of
the day in the neighbourhood of sunset. But the divergencies in
the habits of the two species are very interesting. While 0. phos-
pho7-ea first reaches the surface well before sunset, 0. enopla is not
seen till dusk has fallen. In this latter species, moreover, the
phosphorescence, which is characteristic of most species of this
genus, is developed to a most extraordinary extent and is adapted
to serve as a means of sexual recognition. This is almost without
parallel in the animal kingdom. It is, however, stated that the
function of the phosphorescent organs in the Fireflies is to attract
the other sex. In the case of the common glow-worm it is generally
allowed that the male finds the female by means of her phos-
phorescence. Mr J. C. F. Fryer has told me of a Lampyrid beetle
in Ceylon, the female of which actually remains in deep holes, but
that she emits a most powerful light from organs on the underside
of the abdomen, which is the better displayed by the flexion of that
part of the body. As soon as the male approaches, however, the
light dies down as in Odontosyllis. The account of 0. enopla,
wliich I have quoted above at length, shows, however, that we
have among much lower animals almost as complex a phenomenon
in which the production of phosphorescence is equally essential for
the meeting of the sexes. It is possible, however, to make one
criticism of the interpretation which is given above. This is that
an arrangement to secure close approximation between the male
and female of a marine worm would seem in general to be un-
necessary for the successful propagation of the species. There is
none such in 0. phosphorea, and in the case of our two commonest
British species of Odontosyllis, 0. ctenostoma and gihha, the hetero-
syllids seem to occur, not in swarms, but as scattered individuals,
and probably discharge their eggs or spermatozoa when no other
member of the species is near. In the only reference respecting
the pelagic occurrence of these species that I am able to find
Gravely* says : "The brown Odontosyllis {i.e. 0. gihha) is frequently
seen in the adult condition — occasionally accompanied by 0. cteno-
stoma and sexual specimens oi Autolytus and Myrianida — swimming
at the surface of the sea at the mouth of Port Erin Bay and further
out towards the Calf on calm evenings during July." This passage,
I think, clearly points to an irregular and sporadic occurrence.
If there are these considerable differences in the reproductive
habits of the different species there must, I think, be equivalent
physiological differences in the reproductive cells of the species.
One would expect, from the elaborate devices practised by 0. enopla
to ensure fertilisation, that the independent life of the eggs and
* Q. J. 31. S., vol. Lin. p. 600.
198 Mr Potts, The Swarming of Odontosyllis.
I
spermatozoa of that species was very brief and that fertilisation
must take place very shortly after dehiscence, while probably in
0. gibba and 0. ctenostoma the genital products can survive for
a much longer time in sea-water.
In the literature of swarming amongst Annelids a majority of
the observations refer to the genus Nereis and show a great
diversity of reproductive habits. Hempelmann*, who has in-
vestigated the case of N. dumerilii very thoroughly, found that
at Naples heteronereid forms occurred at the surface of the sea
from 1st October, 1908— 15th May, 1909. From 15th May,
1909— 15th August, 1909 there were no heteronereids. The
mature worms appear at the surface indifferently in the day or
the night and usually occur not as swarms but scattered in-
dividuals which discharge their eggs or spermatozoa when no
other heteronereid is near. But on one occasion at least, on
May 2nd, 1908, there was seen in the Bay of Naples a great
swarm of N. dumerilii and N. coccinea.
Similarly attention has been lavished on the heteronereids
which are seen off the east coast of England. Sorbyf was
accustomed to observe the phenomena in the summer throughout
a long series of years. On several occasions he saw immense
numbers of heteronereids on the surface. The date, time and
place of occasion of these are indicated in the following table : —
23 May, 1885. N. dumerilii. In the evening at the
mouth of the Colne.
16 July, 1898. „ „ At 5 o'clock in the morn-
ing at the mouth of
the Stour and Orwell,
the sea being covered
with millions of worms.
11 May, 1882. N. longissima. In the evening near Sheer-
ness.
24 May, 1889. „ „ At the mouth of the
Orwell.
9 September, 1889. „ „ In the evening at Queen-
borough.
In twenty years Sorby only saw five such great swarms of
nereids. He does not state that he ever observed isolated hetero-
nereids on the surface of the sea, and for this reason the record
of these English occurrences is lamentably incomplete. But his
observations go to establish several facts which Hempelmann's more
thorough, but less extended, investigations give no clue to, viz. : —
* " Znr Naturgeschichte von Nereis dumerilii," Zoologica, Bd. xxv. Heft 62, 1911,
pp. 92 ff.
t Sorby, Journ. Linn. Soc, London, vol. xxix. 1906.
Mr Potts, The Swarming of Odontosyllis. 199
(1) that these great swarms of nereids are only seen rarely ;
(2) that they occur at almost any time of the day (at early
morning, at midday* or in the evening) and nearly any period
of the summer ;
(3) that the date of swarming has no definite relation to the
full moon.
On the whole I think we are justified in stating that in N.
dumerilii and probablj^ other species the swarming habit is not
fixed. Hempelmann has noticed a slight correlation between the
appearance of the heteronereids and the phases of the moon, but
this is by no means marked. There is no doubt from Hempelmann's
observations that the ascent of the sexually mature worms is due
to a combination of causes which act throughout a long period and
whose eflScacy fluctuates considerably.
Enough has been said to indicate the irregularity in period and
time of the swarming of Nereis dumerilii and other associated
forms. There is, however, at least one good case in the genus
where an absolute periodicity has been established. I refer to
N. (Ceratocephale) osawai of Japan f, the heteronereids of which
regularly issue forth four times in the year in the months October
and November, in 3 — 4 day periods. Their date of appearance is
absolutely fixed for the days following the new moon. Their
presence on the surface is limited to from one to two hours in
the evening, but the time of appearance is by no means so
definitely fixed as in the case of Odontosyllis phosphorea and
enopla (sunset). They appear in fact well after sunset and often
after moonset, so that the immediate stimulus would appear to
be independent of the action of light.
Other cases might be quoted, but I think my main contention,
the diversity of swarming habits in Nereis, is sufficiently proved.
The phenomenon of swarming, at least in its final form, does
appear to be of a definitely adaptive nature. The object is the
fertilisation of the maximum number of eggs, and this is gained
by the simultaneous emission of eggs and spermatozoa from a
crowded mass of male and female individuals. Galloway and
Welch found in 0. enopla that of eggs collected in connection
with the swarming worms from 45 — 80 °/^ were already fertilised.
In the case of the Atlantic Palolo worms, which turn the clear
blue waters of the Tortugas into a thick milky mass with their
eggs and spermatozoa, it is difficult to imagine how any of the
eggs escape fertilisation. Yet Professor Mayer tells me that the
* Mr William Brockett in the month of June, 1910, collected a rather large
number of heteronereids off Mersea Island on the Essex coast between midday and
two o'clock in the afternoon.
t Izuka, "Observations on the Japanese Palolo Ceratocephale osaioai," Journ.
Coll. So., Tokio, T. xxxvi. 1903.
200 Mr Potts, The Stuarming of Odontosyllis.
eggs laid by females on the borders of the swarm are certainly not
developed.
How, then, does it come about that a species like N. dumerilii,
the heteronereids of which become sexually mature at any time
within a widely extended period, and in which the swarming habit
is very indefinitely developed, is able to maintain its great numbers
and wide distribution. Not only is there no arrangement to ensure
the simultaneous swarming of the sexes, but it has frequently been
observed in this and related species that large swarms consist of a
single sex*. Under these circumstances there must be an enormous
waste.
There is, however, one obvious explanation. JV. dumerilii is a
polymorphic species, and according to the results of von Wisting-
hausen and Hempelmann all individuals have more than one
period of sexual maturity. When they first reach a certain
length the female lays eggs, within the tube she normally in-
habits, to the number of 1000 or more. These are generally
fertilised in the most economical manner by the male, who creeps
into the tube and spreads his sperm over the eggs. It would seem
probable that this is the method most responsible for the main-
tenance of the species, the production of sexually ripe heteronereids
at a later period of life being a subsidiary (possibly incipient or
degenerate) phenomenon.
These comments on swarming in Odontosyllis and Nereis are
only intended to illustrate the diversity in the habit existing
among related forms. I have not attempted to discuss the thorny
question of the part played by external stimuli or the possibility
of an inherited rhythm in the organism.
Note. Since writing the above I have had access to a paper
by Lillie and Just (Biol. Bull, Feb. 1913) on the breeding habits
of Nereis limhata. In this species swarming takes place quite
regularly in four runs during the summer corresponding to the
lunar cycles in the months June, July, August, September, occur-
ring on many successive nights shortly after sunset and lasting
little longer than an hour. This is, then, an advanced case of the
swarming habit, but the great interest lies in the fact that the
female produces a substance which acts on the male causing the
emission of sperm. It will be of great interest to see whether the
distribution of this phenomenon is at all general or whether it
is a peculiar development of the swarming habit to ensure fertili-
sation, like the mating relations in Odontosyllis enopla.
* Cf. Sorby, Hempelmann, loc. cit.
Prof. Thomson, Further applications of positive rays, etc. 201
Further applications of positive rays to the study of chemical
problems. By Professor Sir J. J. Thomson.
[Read 27 January 1913.]
The author described the application of positive rays to the
detection of the rare gases in the atmosphere. Sir James Dewar
kindly supplied two samples of gases obtained from the residues
of liquid air ; one sample which had been treated so as to contain
the heavier gases was found on analysis to contain Xenon, Krypton,
Argon, there were no lines on the photograph unaccounted for,
hence we may conclude that there are no unknown heavy gases
in the atmosphere in quantities comparable with the known gases.
The other sample which had been heated so as to contain the
lighter gases was found to contain helium and neon and in addition
a new gas with the atomic weight 22, the relative brightness of
the lines for this gas and for neon shows that the amount of the
new gas is much smaller than that of neon.
The second part of the paper contains an investigation of a
new gas of atomic weight 3 which this method of analysis had
shown to be present in the tube under certain conditions. The
gas had occurred sporadically in the tube from the time of the
earliest experiments but its appearance could not be controlled.
After a long investigation into the source of this gas, it was found
that it always occurred in the gases given out by metals when
bombarded by cathode rays, a trace of helium was also usually
found on the first bombardment. The metals used were iron,
nickel, zinc, copper, lead and platinum ; the gas was also given off
by calcium carbide. Various experiments were described which
illustrated the stability of the gas.
202 Messrs Purvis and Rayner, The chemical, etc.
The chemical and bacterial condition of the Cam above and
below the sewage effluent outfall. By J. E. Purvis, M.A., and
A. E. Rayner, M.A.
[Read 24 February 1913.]
The river was investigated at various points extending from
100 feet above the outfall and at 8 feet from the outfall : and at
^ of a mile, \ a mile, f of a mile, 1^ miles, 2 miles, 2^ miles,
3 miles and 4 miles below the outfall.
Chemically, the river purifies itself moderately well from the
contaminating effluent ; for at about f of a mile below the effluent,
tlie albuminoid ammonia and the oxygen absorbed figures were
lower than at 100 feet above the effluent outfall.
Bacterially, the dangerous pollution, as indicated by B. coli,
is well-marked at between 3 and 4 miles below the outfall. The
potential danger of such contamination is in the direction of cattle
quenching their thirst, of bathers, and of watercress.
Mr Mills and Miss Bain, On the optically active, etc. 203
On the optically active semicarbazone and benzoylphenylhydra-
zone of cjc\o-hea;anone-4!-carboxylic acid. By W. H, Mills, M.A.,
and Miss A. M. Bain.
[Read 24 February 1913.]
The semicarbazone of C2/cZo-hexanone-4-carboxylic acid can be
obtained in an optically active form by crystallising its morphine
salt from dilute alcohol, the highest value obtained for the
molecular rotation in alkaline solution being [M\j, 38*8°. The
benzoylphenylhydrazone of the acid can similarly be obtained in
an optically active form by crystallisation of its quinine salt from
aqueous alcohol, the highest value found for the molecular rotation
in alkaline solution being [il/]^ 238'6°.
These optically active compounds agree so closely in their
behaviour with the optically active oxime of this acid previously
described by the authors that there can be little doubt that the
optical activity is due to similar causes in the three cases.
The observations accordingly lend great support to the view
that stereoisomerism in the sense of the Hautzsch- Werner hypo-
thesis exists in the case of semicarbazones and phenylhydrazones.
204 Prof. Tope and Mr Read, The ten Stereoisomeric, etc.
The ten Stereoisomeric Tetrahydroqumaldinomethylenecamphors.
By Professor Pope and J. Read,' M.A.
[Bead 24 February 1913.]
The two enantiomorphously related tetrahydroquinaldines con-
dense readily with the two similarly related oxymethylenecamphors
y 08X114
yielding products of the constitution, C10H12N. CH :C\ | . Since
each component of the condensation can be obtained in a dextro-
and a laevo-rotatory form, four simple optically active condensation
products can be obtained ; the configurations of these may be
described by the following symbols, in which d- and 1- represent
the configurations of the tetrahydroquinaldine residue and D- and
L- that of the oxymethylenecamphor nucleus.
(1) d— D. (2) 1— L. (3) d— L. (4) 1— D.
The two members of a pair of enantiomorphously related
isomerides, (1) and (2), or (3) and (4), combine to form a double
or racemic compound, so that the following externally compen-
sated substances can also be prepared.
(5) [d-D, 1-L], (6) [d-L, 1-D].
Amongst substances such as these, which contain two dissimilar
centres of asymmetry, six stereoisomerides of the above types are
the only ones ordinarily obtainable but in the present instance
four more can be prepared. These are the two pairs of partially
racemic compounds of the configurations stated below.
(7) [d— D, d— L], (8) [1— L, 1— D],
(9) [d— D, 1— D], (10) [1— L, d— L].
No case has been previously recorded of the formation of
partially racemic compounds in the manner just described and
it would be anticipated that no resolution of externally compen-
sated tetrahydroquinaldine into its optically active components
would be possible with the aid of d- or 1-oxymethylenecamphor.
It is shown, however, that on treating externally compensated
tetrahydroquinaldine with less than one-half an equivalent of
d-oxymethylenecamphor a resolution can be effected because the
1-base condenses more rapidly than the d-isomeride with d-oxy-
methylenecamphor ; under these conditions the condensation
yields about 80 per cent, of the partially racemic compound (9)
and 20 per cent, of the simple optically active substance (4) from
which 1-tetrahydroquinaldine may be separated.
Dr Searle, Experiments illustrating flare spots, etc. 205
Experiments illustrating flare spots in photography. By G. F.
C. Searle, ScD., F.R.S., University Lecturer in Experimental
Physics, Fellow of Peterhouse.
[Read 24 February 1913.]
§ 1. Litroduction. When light strikes a refracting surface, it
is partly refracted and partly reflected. For glass of refractive
index /x, the ratio of the intensity of the reflected light to that of
the incident light is (fi — 1)V(/* + 1)^ foi' normal incidence and this
ratio increases as the angle of incidence increases. For glass of
refractive index I'S the ratio is 1/25. If the light suffers a second
reflexion, the ratio of the intensity of the twice reflected light to
that of the original light is 1/(25)- or 1/625. For 2n reflexions
the ratio is l/(25)2'^ which diminishes very rapidly as n increases.
If a luminous point be placed on or near the axis of a lens, an
image will be formed by rays which have passed through the lens
without suffering reflexion. This is the ordinary image used in
photography. A second and fainter image will be formed by rays
which have been twice reflected and there are other images
formed by rays which have been reflected 4, 6, ... times, but the
latter images will be very faint unless the source of light is very
powerful.
When there are 7i lenses, the rays which suffer their first
reflexion at the last air-glass surface can be reflected a second
time at any one of the 2n — 1 air-glass surfaces in front of the
last surface. The rays which suffer their first reflexion at the
last surface but one can be reflected a second time at any one of
the 2n — 2 surfaces in front of that surface, and so on. Henc6, if
iV be the total number of images formed by twice reflected rays
iV = (2n - 1) + {2n -2)+ ... + 2 + 1 = n{2n-l).
Thus we have the results
Number of lenses
1
2
3
4 5
Number of images formed by
twice reflected rays
1
6
15
28 45
In many photographic lens systems, two or more pieces of
glass are cemented together with Canada balsam. The light
206
Dr Searle, Experiments illustrating
reflected at the cemented surfaces is inappreciable, and for the i
present purpose such a cemented component of a lens system is '
to be considered as a single lens. It is only the air-glass surfaces i
which count.
The image of any object formed by rays which have not
suffered reflexion in their passage through the lens will be called \
the primary image of that object, and any image formed by rays
which have suffered two reflexions will be called a secondary image
{Nebenhild) of the object. jj
§ 2. Ghosts in photography. In photography the sensitive '
plate is adjusted so that the primary image of an object, i.e. the
image formed by rays which have not been reflected in their
passage through the lens system, is sharply focussed upon it. <
Thus, if >S> (Fig. 1)* be an object point on the axis of the lens
system, the plate is placed in the plane GH which is normal to
the axis and passes through the conjugate primary image point T.
If To be a real or virtual secondary image of S formed by twice
reflected rays, the cone of rays which meet in T^ will be cut by
the plane through T in a circle of diameter GH. If T2 is so far
from T that the diameter of this circle is greater than that of the
sensitive plate, the intensity of illumination due to T^ will be very
small and the only effect will be a slight uniform fogging of the
plate. The effect is so small that the number of air-glass
surfaces has to be considerable before there is any serious fogging
due to all the cones of twice reflected light whose sections by the
plane GH have diameters greater than that of the plate.
If, however, T2 be close to T, the illuminated patch GH will
be small and the illumination may then be sufficient to cause
trouble. This small patch is known as a "ghost."
If a secondary image T2 coincides with T, any object in a plane
normal to the axis and passing through S will have its corre-
sponding secondary image in the plane GH. But the secondary
* Fig. 1 is merely diagrammatic and does not show accurately the paths of
the rays.
flare spots in photography. 207
image will not generally be of the same size as the primary image
and may even be erect when the latter is inverted.
Thus when T, coincides with T, a faint secondary image of the
obiects to be photographed will be impressed upon the plate in
addition to the primary image. Chapman Jones {Science and
Practice of Photography, p. 248) states that he " has seen a
. portrait spoiled by an inverted image of the shirt front appearing
; over the model's head."
1 The position and magnitude of any secondary image can be
i determined when we know the positions of the corresponding
cardinal points, viz. the principal (or unit) points and the principal
foci. To each pair of surfaces which act as reflectors there corre-
sponds a set of cardinal points. When the lens system is of
considerable length, the cardinal points corresponding to any pair
' of surfaces may occupy all sorts of positions.
In the case of the secondary image described by Chapman
Jones, the system behaved as one of negative focal length with its
cardinal points so placed that it formed a real erect image of a
distant object. A system of two thin convex lenses separated by
a distance greater than the sum of their focal lengths behaves in
the same manner with respect to a primary image. The system
has a negative focal length and forms a real erect image of a
distant object.
I 3. Flare spots in photography. The rays which have been
twice reflected may give rise to trouble in another way. The
primary image of the stop R (Fig. 1) will be so far from the plate
that its effects may be disregarded ; the image will generally be
virtual. But when the camera is directed towards any landscape
or other scene, an infinite number of rays passes in all directions
(within limits) through every point of the opening of the stop,
and thus this opening will behave as if it were a self-luminous
disk which, however, only emits light towards one side. One or
more of the secondary images of this equivalent disk, formed by
rays which have suffered the first reflexion at some surface
between the stop and the plate and a second reflexion at any
other surface of the lens system, may be accurately or nearly
focussed on the plate and so give rise to a well defined bright
i spot in the centre of the plate. This spot is known as a " flare
spot."
For a given background, the flare spot image of the stop
aperture will be of the same intensity whatever the size of the
stop, at least in those cases where the second reflexion takes place
at a surface behind the stop. But the intensity of the primary
image of the background will be proportional to the area of the
stop. Hence, although the flare spot image of the stop may be
1
208 Br Searle, Experiments illustrating ^
too faint to produce a noticeable effect during the short exposure
employed with a large stop, it may be quite strong enough to
produce a deleterious patch upon the plate during the long
exposure required to obtain an image of the background with a
small stop. There are many lenses which cannot be used with a
small stop for this reason. A flare spot may be detected by
watching the focussing screen as the opening of the stop is
diminished, the camera being pointed towards the sky or other
bright background.
If the edges of the stop are bright, they may reflect light
forwards and this light after being reflected at one of the surfaces in
front of the stop, may come more or less nearly to a focus on the
plate. Since this light has suffered only one reflexion at an air-
glass surface, it may produce a strong image or at least a consider-
able fogging of the plate. The same remark applies to the tops
of screw threads, which may have been worn bright, and to the
edges of the lenses themselves. The defect may be cured by
properly blacking the surfaces with good optical black.
§ 4. Experiment with spectacle lens. A virtual flare spot
is easily seen when a positive (convex) spectacle lens of focal
lengthy" is placed before the eye. If a bright object such as a gas
flame or the bright sky is viewed through a small hole cut in a
sheet of paper, a well defined secondary image of the hole will be
seen when the distance between the lens and the hole is about
//7 (see § 7). The secondary image of the hole is virtual and at a
considerable distance from the eye. By adjusting the position of
the hole the secondary image may be seen clearly at the same
time as the flame. This corresponds to the case where a secondary
image of the stop of a camera is focussed on the plate at the same
time as the primary image of distant objects.
If two pairs of spectacles are worn, six secondary images can
be seen.
§ 5. Thin lenses in contact. The positions and magnitudes
of the secondary images of any object formed by a system of any
number of thick or thin lenses can be calculated by repeated
applications of the formulae for reflexion and refraction at spherical
surfaces. When, however, the system consists of a single thin lens
or of two thin lenses in contact, the positions of the secondary
images can be very readily calculated by the method of least time.
The experimental tests of the formulae can be made with simple
apparatus and form interesting exercises for students who have
made a little progress in practical optics.
§ 6. Focal length of thin lens. The application of the principle
of least time to find the focal length of a thin lens is well known,
flare spots in pliotography.
209
|)ut it will be convenient to give it here as the mathematical
inethods can be transferred, with little change, to the solution of
|}he other problems considered.
Let AKB (Fig. 2) be a thin lens. Let >Sf be a point source of
Fig. 2.
ight on the axis of the lens and let T be its image. Let the
•adii of the faces AK, BK be a, b cm. and let the refractive index
|)f the lens be fi. The radii are counted positive when the faces
lire convex, as in Fig. 2. Let the focal length be / cm.; we shall
iiollow the rule of the practical opticians and count /positive when
,he lens is a converging one. Where convenient, capital letters
<vill be used to denote " powers " or reciprocals of distances. Thus
1
/
= F,
vhere F cmr^ or 100 F dioptres is the " power " of the lens.
When spherical aberration is negligible, any spherical wave
ront G, which expands from S as centre, becomes, after passing
ihrough the lens, a spherical wave front I), contracting to T as
;entre. Hence the time taken by light in passing from aS to T is
\ie same for every ray — an example of the principle of Least (or
Stationary) Time.
I Let M be the point in which the plane of the edge of the lens
fntersects the axis.
Let SM = u, MT = v and KM = h.
The position of T is found by equating the optical length of the
)ath from 8 to T for the ray which starts along 8K to that for
he ray which starts along SA. If X, Y be points on SK, TK
such that 8X = 8A and TY = TB, the optical length of the path
from X to Fis equal to that of the path from A to B. Since the
speed of liglit in glass is only fM~^ times its speed in air, the optical
ength of AB is [lAB. Hence the optical equation is
XK+KY^^xAB (1).
VOL. XVII. PT. II.
14
210 Dr Searle, Experiments illustrating
Since the distance of M from the centre of curvature of AK is j|
{a? — h^Y, we have
AM^ail-Jl-hya"],
and similarly for BM. Expanding as far as Ji^, we find
AM=^h'/a, BM=\h^lb.
Hence AB = hji^{lla + \lh) (2).
Now, as far as It",
SK = sluF+Ji? - '^ + i h'lu, TK = VvMT^ = v + ^h'/v,
8X = SM-AM^u-^ h'/a, TY=TM-BM=v- \h?lh. \
Hence XK = 8K- 8X=\h^{llu + lla) (3),
KY=TK-TY=\h^{\lv-\-llh) (4).
Multiplying the optical equation (1) by 2/^^ and substituting from
(2), (3) and (4), we have
{Iju + Ija) + (1/v + 1/6) = fM (1/a + 1/6), i
or l/w + l/?; = (/^-l)(l/a + l/6) (5). '
Hence, the focal length is given by
l//==(;.-l)(l/a + l/6) (6),
and the " power " i^ by
F={^Ji-l){lja-\-l|h) (7).
§ 7. Secondary image with thin lens. Some of the light from
8 (Fig. 2) which falls on BK will be reflected and will strike AK.
Here it will be again reflected and then, on refraction at BK, it
will pass out of the lens, forming a secondary image of 8 at T,^.
Let M2\^v^.
If Fg lie on T.2K and if ^2 5^2= T.^B, the optical equation is
XK + KY, = ^^lAB (8),
since the light which moves along the axis has traversed the
thickness of the lens three times. This equation only differs from
the optical equation (1) corresponding to the primary image by
having 3yu. in place of fx and Vo, in place of v. Hence the method
of § 6 gives at once
l/w + l/v,3=(3/i-l)(l/a + l/6) (9).
Hence, if f.^ be the focal length and F^ the power of the lens for
the secondary image,
1 ,„ ,,/l 1\ 3/A-l 1 ,,„,
and F,= '^^F (11).
ilare spots in photoffraphy. 211
The symmetry of (9) shows that if Tg is the secondary image of S,
then S is the secondary image of To. If ytt = 1"5 we have /a = }f.
If we measure both / and f^, we can find /* — 1 from the
equation
2/2 2F
^~^ ^flsf.^Fo- SF ^^^^*
The method can be applied at once to rays which have suffered
4, 6 ... reflexions. If Fon be the power for rays which have been
reflected 2n times,
/x- 1
§ 8. Images hy once reflected rays. Two images of S will be
formed by rays which suffer a single reflexion. One image will
be formed by reflexion at the surface AK. With this we are not
here concerned except when that surface is concave ; in that case,
if S be placed at the centre of curvature of AK it will coincide
with its own image.
A second image, 81 (Fig. 2), will be formed by rays which have
suffered one reflexion at BK and two refractions at AK. Let
8-^M = Ui and let u^ be positive when the image, S^ , is real.
If Xi lie on S^K and if 8iX^ = SiA, the optical equation is
XK + KX, = 2ixAB.
Multiplying this equation by 2/A^ and using the results of § 6, we
have
{llu + 1/a) + (1/iii + 1/a) = 2ya (1/a + 1/6),
or 1/u + 1/mi = 2 (/^ - 1) (1/a + 1/6) + 2/6 = 2// + 2/6.
If 8 be adjusted so that the image 8-i, coincides with 8, and if
p denote the common value of u and u-^ in this case,
^ = i/p = Hi/^ + iM) = i//+i/& (13)-
Similarly, if an object at a distance q from M on the other side of
the lens coincides with its image formed by rays reflected once at
AK and refracted twice at BK,
Q^llq = llf+V^ (14).
Adding (13) and (14), we have
lip + Ijq = 2//+ (1/a + 1/6) = {2 + l/(^ - 1)} . II f.
Thus, if^, q and /are known, we can find /* — 1 from the equation
^_1= 1// ^ (15)
^ llp + llq-2lf P+Q-2F ^^''^•
The value of yu, — 1 found by (15) fromy, p and q can be compared
212
Dr Searle, Experiments illustrating
with that found by (12) from / and /g. If we equate these two
vahies of fi — 1, we obtain
2(P + Q) = F+F,.
.(16).
Fior. 3.
Equation (13) can also be obtained as follows: — Since S coincides"
with its own image, the ray >S'G^^ (Fig. 3) must be normal to the
surface BK. Hence the emergent ray HZ is directed from 0, the
centre of curvature of BK, and thus and S are conjugate
points. When the lens is thin, we may put MO — h and MS =p. ,
Then I
1/^-1/6 = 1//
which agrees with (13). The method of determining the radius b
by making an object S coincide with its image by reflexion at BK •
is due to C. V. Boys.
If BK be so strongly concave that l/f+ 1/& is negative, p will
be negative and then it will be impossible to make a real object
coincide with its own image, and Boys's method cannot be
applied. Since, however, the surface BK is concave, the radius b
can be found directly by making an object on the ^-side of the
lens coincide with its image by reflexion at BK. If AK be
smeared with vaseline, no image will be formed by reflexion at
AK and thus confusion will be avoided.
I 9. Experimental details. A spectacle lens (price 9d.) is
suitable for the experiment ; its primary focal length should be
considerable — say, a metre, — so that its thickness may be neg-
lected without much loss of accuracy. The primary focal length/"
is found by aid of a very distant object (500 metres) or of a good
plane mirror, or by measuring the distances of an object and its
image from the lens. An ordinary optical bench will not be long
enough to allow the focal length to be conveniently found by the
minimum distance method.
The secondary focal length f^ is found on an optical bench
(Fig. 4). One of the sliding carriages of the bench carries a tube
flare spots in photography.
213
blackened internally, and the lens is attached to this tube*. A
second carriage bears a plate pierced by a pinhole and furnished
with cross-wires 8. The hole is illuminated by a flame. The
third carriage bears a pin T which may conveniently be adjustable
in a plane perpendicular to the length of the bench, and T is
adjusted to coincide with the secondary image of S. In making
the adjustment, a lens of about 15 cm. focal length, held in a clip,
is of much assistance.
"■*1
i
CZ
TTiiTCTTTil^ i i i| Ii i| i ii| i i i i | i ii i|i ii i|i iii| i iiii. i ii | .i i.|i i i i | ii ii |i ii i| . i i>| i i i| i i >il i ii | ii i i |i i n | . ' m ii i ii|i ii i| i i ii imi|iiiiiii.i| i i i iiiii i |m |iimii.ii|i
Fig. 4.
The secondary focal length is best found by the minimum
distance method. The minimum distance between the cross-wires
and the secondary image is 4/2 + t, where t is the distance between
the principal points corresponding to the secondary image. The
lens being "thin," t is negligible and hence the minimum distance
may be taken as 4/3.
The measurement is very quickly made if 8 is placed at about
2//7 from the lens ; the secondary image of the cross- wires will
then be at a distance of about 2//7 from the lens on the other
side. The minimum distance is then easily found.
The distance p is found by making a well illuminated pin
coincide with its own image when the face AK of the lens is
turned towards the pin. A black surface should be placed behind
the lens. The distance q is found in a similar manner.
§ 10. Practical example. The following results were obtained
in an experiment by J. L. Barritt. A double convex spectacle
lens of a nominal power of one dioptre was used.
Primary focal length (found by plane mirror) =/"= 101 "85 cm.
Hence, power = i?^= 1//= 0-009818 cm.-i = 0-9818 dioptre.
Minimum distance between object and secondary image = 4/, = 59-62
cm. Hence /,= 14-905 om. and F.,= llf. = 0-06709 cm.-\ Thus, by
(12), § 7,
2/; , 29-81
/x- ■ ■
1 +
/-3/; ^ "^57-135
1-5218.
* Fig. 4 shows hvo lenses attached to the tube for the experiments described
in § 12.
14—3
214
Dr Searle, Experiments illustrating
Distance from lens of pin and coincident image formed by light
reflected at BK ^p = 51 -90 cm. Hence P= Ijp = 0-019268 cm.-^.
Distance from lens of pin and coincident image formed by light
reflected at AK=q=52-:i8 cm. Hence ^=1/^=0-019091 cm.-\ Hence,
by (15), §8,
/>i= 1 -h
F
P+Q-2F
= 1 +
0-009818
0-018723
= 1-5244.
This value agrees closely with that obtained from the secondary image.
Also 2 (P+e) = 0-07672 cm.-i and F+ F^= 0-07691 cm.-\ By
(16), § 8, these two quantities should have the same value.
§ 11. Secondary focal lengths for a system of two thin lenses
in contact. Let AKB, OLD (Fig. 5) be two thin lenses in contact.
Let the radii of the faces AK, BK, CL, DL be a, h, c, d, the radii
being counted positive when the surfaces are convex, as in Fig. 5.
Let the planes KM, LN through the edges of the lenses cut the
axis in M, N, and let MK = NL = h. Let )S be a luminous object
point and let T^ be one of its secondary images formed by rays
which have suffered two reflexions in their passage through the
system. Let SM=u, NT,^ = v.2. Let the refractive index of the
lens AKB be /z and let that of the lens OLD be jj! .
Xv-^
¥1
\V\
MBCN D
FiR. 5.
The position of T^ is found by making the optical length of
the path from S to T^ for the ray which starts along SK equal to
that for the ray which starts along 8 A.
Since the lenses are " thin " and since the angle KSA is
" small ", the ray between K and L is never inclined to the axis at
more than a " small " angle, and consequently the optical equation
will be, to the accuracy required, the same as if the path of the
ray were actually SKLT^ .
If X, F2 be points on SK, T^L such that SX = SA and
T2F2 = TJ), the optical length of the path from X to Y^ is to be
equal to that from A to D.
fiare spots in photography. 215
fNow, by the methods of § 6, we have
8K=u^- ^h^/u, ToL = v, + ^h^/v^
SX = SM-AM = u- ^¥/a, T, Y, = TM -DN = v,- ^h^d.
J— I p"npp
XK = SK-SX = i/i^ (1/w + 1/a)
LY, = T,L-T,Y, = ^h\llv, + Ijd).
We have also
AB = :^h^{\la+\lh), KL = ^h^l/b + l/c), CD = ^h'(l/c + l/d).
When we equate the optical length of the path via K to that
via A in each of the six cases, we obtain the following six
equations; the symbols [i)C], [DB] ... indicate the two faces which
have acted as reflectors*.
[DG] XK + KL + LY, = ^AB + Sf^'CD
[DB] XK + KL + LY, + 2KL= fiAB + Sfj,VD
[DA] XK + KL + L Y, + ^KL = S/xAB + Sfi'CD
[GB] XK + KL + LY, + 2KL= ,xAB + /x'GD
[GA] XK+KL + LY, + 2KL = 3puAB+ fx'GD
[BA-] XK + KL + LY, =3fMAB+ ^'GD
Let the primary focal lengths of AKB, GLD be m, n cm. and let
the corresponding powers be M, N cm.~^. Then
(/x-l)(l/a+l/6) = l/m = ilf, (/_l)(l/c + l/c^)=l//^=i\^.
Let the secondary focal lengths of AKB, GLD be m2, ih cm. and
let the corresponding powers be M^, N.2 cm.~\ Then, by § 7,
(3/i - 1) (1/a + 1/6) = 1/m, = M^, (3/ - 1) (1/c + Ijd) = 1/n, = N,.
Let -2(l/6 + l/c) = l/w=F.
It is worth noting that w is the secondary focal length of a " thin "
lens of refractive index unity and radii h and c, the surfaces being
concave in the case of Fig. 5. The primary focal length of such
a lens is infinite. An optical system formed by air enclosed
between two spherical soap films is a very close approximation
to such a lens.
Let /o be one of the six secondary focal lengths and F^ the
corresponding secondary power of the system, so, that
F,= llf,= \lu + llv,.
Then, when the six optical equations are multiplied by 2/A-, we
obtain the following values for the six secondary powers: —
* A more general method, applicable to any number of thin lenses in contact,
is given in § 14.
216 Dr 8earle, Experiments illustrating
[DC] Fj,a = VfDc = M +N, ■
[DA} Fj,^ = 1/fj,^ = M, + N,+ W
[CB] FcB = VfcB = M +N +W
[GA] F,^ = \|f,^ = M,^-N + W
[BA] Fs^ = l/f^^^M, + N.
If the lenses are such that each of the six secondary powers of
the system is positive, it will be possible to_obtain six real secondary
images of a real object.
A convenient system is obtained by using two meniscus lenses
of positive powers, and placing them in contact so that their
concave surfaces face each other. Then M, N, M^, No. are positive
and, since h and c are negative, W is positive. To avoid coin-
cident images, M and N should be unequal. Meniscus lenses are
used in spectacles, under the name of " periscopic " lenses.
I 12. Experi^nental details. The six secondary images are
readily observed if the system consists of two positive meniscus
spectacle lenses (price dd. each) placed in contact, with their
concave surfaces facing each other. The following description
refers to this case.
The primary and secondary focal lengths of each lens are
found just as in § 9.
The radius of curvature of the concave surface of each lens is
found by making a pin coincide with its image formed by reflexion
at that surface. The convex surface is smeared with vaseline to
stop reflexion there. The common distance of the pin and its
image from the surface is equal to the radius. Since the surface
is concave, a square- ended scale cannot be used to measure the
distance ; a proper appliance must be used.
The two lenses are then mounted on the tube as in Fig. 4.
When 8 is sufficiently far from the lenses, the six real secondary
images of S will be easily seen on looking through the system
towards 8, provided the eye be far enough from the lenses. If
the images are very small, they may be increased in size by
bringing the lenses nearer to 8. If, however, the distance is
made too small, some or all of the six secondary images will
become virtual.
The six secondary focal lengths are best found by the minimum
distance method. It is best to begin with the one of shortest
focal length.
It is impossible to tell by the appearance of any particular
secondary image which two surfaces have acted as reflectors for
that image, as long as the lenses are fixed together. But if we
flare spots in photography. 217
calculate the six secondary focal lengths from the quantities
M, N, M^, i\^2 and F by § 11, we shall find that one of the
observed values of the six secondary focal lengths will agree with
any selected one of the calculated values, and so we can decide
which two surfaces acted as reflectors in each case.
§ 13. Practical example. The following is a record of
measurements made by G. F. C. Searle, using two meniscus
spectacle lenses of nominal powers of one dioptre and of one-half
dioptre. Barlow's tables of reciprocals were used ; the powers are
given to the nearest O'OOOOl cm.~\
The primary power of each lens was found from the distances of
an object and its image from the lens.
The primary power of AKB; ti— 767 "6 cm., v — 111 "36 cm.
Hence
M= 1/u + 1/v = 0-001303 + 0-008980 = 0-01028 cm.-^ = 1-028 dioptre.
For primary power of CLD ; u = 633-5 cm., v= 306-7 cm.
Hence
iV' = 1/u + 1/v - 0-001579 + 0-003261 - 0-00484 cm.-^ = 0-484 dioptre.
The secondary power of each lens was found on the optical bench
by the minimum distance method.
For secondary power of AKB; minimuin distance = 4?-% = 56-48 cm.
Hence if^^ l/mj^ 1/14-12 = 0-07082 cm.-^.
For secondary power of OLD; minimum distance =^n^= 120-58 cm.
Hence N.^= l/7^2 = 1/30-145 =0-03317 cm.-\
Radius h of lens AKB — — 46-44 cm.
Radius c of lens CLD = — 35-18 cm.
The signs are negative since the surfaces are concave.
Hence r= - 2 (1/6 + 1/c) = 2 (0-021533 + 0-028425) = 0-09992 cm.-^.
By § 11, the six secondary powers of the system are given by
the following equations :
Fi>c = M+N^ =0-01028 + 0-03317 =0-04345 cm."
Fj,s = M +N^+ W = 0-01028 + 0-03317 + 0-09992 = 0-14337 cm."
Fj)^^ ^M^ + N^+ W = 0-07082 + 0-03317 + 0-09992 =0-20391 cm.-^
FaB = M ^N + r= 0-01028 +0-00484 + 0-09992 = 0-11504 cm.-
FcA = M.^ + N +W= 0-07082 + 0-00484 + 0-09992 =0-17558 cm."
Fs^ = M^ + N =0-07082+0-00484 =0-07566 cm.-i
The following table gives the minimum distance between the cross-
wires and each of the secondary images. The corresponding focal
length, /"o, is one-quarter of this distance and the corresponding power
i^o is l/Za- The power calculated from M, N, M^, N^, W is entered in
218
Dr Searie, ^Experiments illustrating
the last column but one and the last column shows which two surfaces
acted as reflectors.
Minimum
Focal
Observed
Calculated
distance
length
power
power
Eeflectors
cm.
cm.
cm.-i
cm.~i
19-46
4-865
0-20555
0-20391
DA
22-82
5-705
0-17528
0-17558
CA
27-91
6-978
0-14331
0-14337
DB
34-76
8-690
0-11507
0-11504
GB
53-22
13-305
0-07516
0-07566
BA
91-86
22-965
0-04354
0-04345
DC
It will be seen that there is fair agreement between the observed
and the calculated values of the secondary powers.
§ 14. Secondary focal lengths for a system of n thin lenses
in contact. The method of | 11 is easily extended to n thin
lenses in contact. Let P (Fig. 6) be the object and Q a secondary
image. Let the lenses be A^K^B^, A.jt.^B^ . . . AnK^Bn- Let
fXi, ... fin be the refractive indices and F^, ... F^ the powers of the
lenses. Let the radii of the surfaces of the lenses be a^yb-^ ... a^hi,
the radii being counted positive when the surfaces are convex as
in Fig. 6. Let the distance of the edges /tj . . . K^ from the axis
be h. Let X, Y be points on PKi, QKn such that PX = FA^,
QY= QBn. Let the planes of the edges of the first and last lenses
cut the axis in Mi, M^', let PM^ = u, and let QM^ = v.
Ki K
Fig. 6.
Since Fi = (yu,i - 1) {Ija^ + l/6i) and since A^B^ = ^h^l/a^ + l/b^),
we have
A,Bi = yi^F,l{f,i-l),
and similarly for the other lenses.
flare spots in photography. 219
If W,, = -^l/b, + lla,), W,, = -2(l/b, + lla,),..., we have
Further, as in § 11,
XK^ = ^h%l/u + 1/a,), YKn = ^h%\lv + l/6„).
Now let X denote summation for all the quantities of any type
and let S denote summation for only those quantities which refer
to spaces through which a ray has passed three times.
The optical length of the path from X to F is equal to that
from J.1 to Bn (see § 11) and hence, if we omit the common factor
^h^, the general optical equation becomes
l + i + ^ + i-S*F-SF=S^+S^,
u a^ V On " /"- — i A*- ~ J-
1 1 ^ /I IN „Tir V ^i^ « 2yt6^
'It V \a 0/ fjb — I. y"-— 1
Since for any lens
we have
and hence
1 1 i^
- +
a b y"- — 1 '
For any lens
yu. — 1 \a b
l + l = v^+S^ + SF (17).
U V fJb— \
F+ ^ , = '- — F= secondary power of lens.
/ci-l f^-l
Further, by § 11, W-^^, W23, ... are the secondary powers of the
successive air spaces, and hence the result (17) can be expressed
in words as follows :
Secondary power of system = [Sum of primary powers of
lenses traversed once] + [Sum of secondary powers of lenses
traversed three times] + [Sum of secondary powers of air spaces
traversed three times].
The six secondary powers found in § 11 for a system of two lenses
are particular cases of this general result.
If the lenses are so chosen that the primary power of each is
positive and the value of every W is positive, all the secondary
powers of the system will be positive.
When the lens used in § 10 is placed between the lenses used
in § 13, the fifteen secondary images are easily seen.
CONTENTS.
PAGE
The Minerals of some Sands and Gravels near Newmarket. By E. H.
Rastall . . .
Observations on Polyportis squamosus, II%ids. Pi-eliminary Communi-
cation. By S. Eeginald Price
Note on the respiratory movements of Torpedo ocellata. By G. R
Mines. (Plates III and IV) .... . . ' .
The Atomic Constants and the Properties of Substances. By R. D
Kleeman . . . .
Note on the effect of heating paraformaldehyde with a trace of sidphuric
acid. By J. G. M. Dunlop .......
The Oxidation of Ferrous Salts. By F. R. Ekkos. (Commmiicated by
Mr C. T. Heycock)
A Simple Method of determining the Viscosity of Air. By G. F. G
Searle. (Two figs, in Text)
The Swarming of Odontosyllis. By F. A. Potts. (One fig. in Text)
Further applications of positive rays to the stiidy of chemical problems
By Professor Sir J. J. Thomson . . . .
. The chemical and bacterial condition of the Gam above and belmv the
sewage ejfluent outfall. By J. E. Purvis and A. E. Rayner .
On the optically active semicarbazone and benzoylphenylhydrazone of
cjc\o-hexanone-A-carboxylic acid. By W. H. Mills and Miss A. M
Bain . . .
The ten Stereoisomeric Tetrahydroquhialdinomethylenecamphors. By
Professor Pope and J. Read .......
Experiments illustrating flare spots in photography. By G. F. C
Searle. (Six figs, in Text) . . . . . . .
161
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PEOCEEDINGS
OF THE
Camkitrg^ ^j^ibsnpljkal cSomtg.
Sarcocystis colii, n. sp., a Sarcosporidian occurring in the
Red-faced African Mouse Bird, Colius erythromelon. By
H. B. Fantham, D.Sc. Lond., B.A., Christ's College, Cambridge.
[Read 5 May 1913.]
(Plate V.)
Introduction.
The " red-faced " African mouse bird, Colius erythromelon, is
of interest to the naturalist on account of its creeping habit. This
small bird is a forest dweller, is not particularly shy, has a general
greenish coloration in harmony with its surroundings and
possesses buff feathers on the head, while the eye is surrounded
by a scarlet ring of bare skin. A fine crest is on the head of the
bird.
It has a new interest to the parasitologist, for I have in my
possession a skinned specimen of the bird showing a heavy infec-
tion with a new Sporozoon, which I name Sarcocystis colii, since
it presents several morphological features distinct from those found
in the Sarcosporidia of other birds. Further, as Colies are con-
sidered by Kaffirs as good eating, it is possible that they are
a source of sarcosporidiosis in man.
The Sarcosporidia are most frequently found in mammals
(including man), but they have been noted as occurring in fowls,
ravens and blackbirds, and the spores of the species {S. rileyi)
occurring in the duck have been described in some detail by
Crawley (1911). A few other avian hosts have been recorded by
Stiles (1893), but details are not known.
VOL. XVII. PT. III. 15
222 Dr Fantham, Sarcocystis colli, n. sp., a Sarcosporidian
Macroscopic Appearance of the Parasite. Its Distribution
in the Host.
The Golius was sent to me for examination by Mr J. W.
Outmore, taxidermist to the Liverpool Museum, to whom my best
thanks are due. The bird had been skinned recently and was
quite fresh. Superficially it showed a number of elongate, white,
opaque patches or streaks, distributed over the body surface, in
the muscles (PI. V). Teased in normal saline solution, one of these
patches showed large numbers of perfect Sarcosporidian spores.
The opaque bodies, then, were the large trophozoites of the Sarco-
sporidian, commonly known as Miescher's tubes or sarcocysts.
The parasites were seen superficially scattered over almost the
entire body surface. Concentrations occurred along the cervical
muscles near the oesophagus, the inter-coracoidal region, the in-
sertion of the humerus and scapula, the muscles around the maxilla
and near the preen glands of the tail. The areas around the
insertion of the limbs were more heavily parasitised than their
distal extremities, the dorsal surface containing more Miescher's
tubes than the ventral. Parts bearing long quills, such as the
muscles around the ulna, contained few or no parasites.
When the bird was opened the whole thickness of the breast
muscles was seen to contain numbers of tubes, lying parallel to the
long axis of the muscles. They had also penetrated the inter-
costal muscles and formed whitish streaks on the endothelial lining
of the body-cavity. The bases of the abdominal muscles showed
parasites on their peritoneal surfaces. The pericardium, connective
tissue around the carotid arteries and jugular veins and the
mesentery of the intestine also contained a few scattered tropho-
zoites. The cardiac muscles contained a large number of tubes
of smaller size than those in the pectoral muscles.
The most heavily parasitised region of the body was the large
pectoral muscles. The right and left sides of the body seemed to
contain about the same number of Miescher's tubes. The general
dorsal surface (PI. V) showed rather more trophozoites superficially
than the ventral, but the enormously increased volume due to the
pectoral muscles gave a preponderance of parasites on the ventral
part of the body.
The effect of the parasite on the host is doubtful. While the
bird showed no very obvious external signs of disease, yet there
was no fat on the body nor around the viscera. The walls of the
heart appeared somewhat thin, compared with those of an un-
parasitised bird. It is known that Sarcosporidia produce a toxin,
sarcocystin, lethal to rabbits.
occurring in the Red-faced African Mouse Bird, etc. 223
I am informed that the bird was not noticeably infected with
ectoparasites, and so no indication as to the transmission of the
parasites is available from that source.
^ Structure of the Parasite.
A brief account of the morphology of the parasite may now be
given. When a fresh preparation of a teased Miescher's tube is
examined the spores, sometimes known as Rainey's corpuscles,
appear as elongate, sickle-shaped bodies with a clear centre and a
distinct refractivity. The general cytoplasm seems homogeneous,
though a vacuole may be present. One end of the organism is
more pointed than the other. The spores examined by me
exhibited very little power of progression.
Stained smears and sections show that the trophozoites present
an elongate, tubular body with a definite envelope and a chambered
or trabeculate structure. Various stages of the organism can be
recognised. The large trophozoites contain numerous spores.
Certain of them are solid owing to the spores practically filling their
interior, but the oldest and longest of them show a hollow centre,
as the spores there die and degenerate, leaving only the trabeculae.
By the dehiscence of the tubes of the muscular system, invasion of
the connective tissues is brought about.
Large Miescher's tubes are 2'5 mm. in length and have a
breadth not exceeding 1 mm. They occur in the skeletal muscula-
ture. The cardiac muscle contains much smaller tubes, possibly
the result of the less size of the cardiac muscles invaded, as well
as the possibility of younger trophozoites being present there.
The Miescher's tubes are easily seen in sections of infected tissue
as they show great affinity for basic stains. Further details of the
parasite as seen in sections will be given in a later publication.
The internal structure of the sickle-shaped spore, as seen in
stained preparations, may be briefly outlined. Polymorphism
occurs among the spores, at least two types being distinguishable :
the one, narrow with more deeply staining contents, the other
broader with paler contents. These spores are about 5 /u. to 7 yu
long, while their breadth varies from 1'5 jjb to 2*5 /x. The dimor-
phism may be due to growth and division. Occasionally "giant"
spores are seen. The nucleus is not central but is near the blunter
end. The structure of the nucleus varies. Sometimes it is vesicular
with a karyosome, which may be central or excentric. At other
times the chromatin is evenly distributed in granules throughout
the nucleus. The differences in arrangement of the chromatin
are due to cyclical development. Near the more pointed end of
the spore a polar vesicle is often seen, and sometimes the remains
15—2
224 Dr Fantham, Sarcocystis colli, n. sp., a Sarcosporidian, etc.
of a capsulogenous nucleus can be distinguished. A few well-
stained specimens have shown portions of probable polar filaments.
The commencement of protrusion of a filament has been followed.
The polar capsule is seen as a vacuole in preparations stained
intra vitam. Some spores show a curious sinuous line which might,
perhaps, be compared with the sutural line of § Myxosporidian
spore. Such a sinuous line is not to be confused with longitudinal
division, which has been clearly followed in numerous, broad, bean-
shaped spores. It should be mentioned that the spores show no
marked metachromatic granules, nor have they the complicated
structure described by Crawley for S. rileyi from the duck (see
Fantham and Porter, 1912).
On account of the polymorphism and somewhat small size of
the spores, the lack of marked metachromatic granules, and the
presence of a definite polar vesicle, I propose the new specific
name colii for this example of the genus Sarcocystis. Perhaps
in the future, when our knowledge of the Sarcosporidia is more
complete, it may be found advisable to place S. colii in an older
species, but at present it certainly possesses several clear, distin-
guishing features.
References.
Crawley, H. (1911). "Observations on Sarcocystis rileyi (Stiles)."
FroG. Acad. Nat. Sci., Philade^jhia, Yol. LXiii, pp. 457 — 468,
1 plate.
Fantham, H. B. and Porter, Annie (1912). "The Structure and
Homology of the Microsporidian Spore, as seen in Nosema apis."
Froc. Gamb. Fhilosoph. Soc, Vol. xvi, pp. 580 — 583.
Stiles, C. W. (1893). "On the Presence of Sarcosporidia in Birds."
Bulletin o, Bureau of Animal Industry, U.S. Dept. Agric.
EXPLANATION OF PLATE V.
Dorsal aspect of Colius erythromelon, showing the distribution of trophozoites
of Sarcocystis colii. Approximately natural size.
m
Phil. Soc. Proc. Vol. xvii. Pt iii.
Plate V.
SARCOSPOEIDIA in COLIUS ERYTHROMELON.
i
Mr Le Goc, Observations on Hirneola auricula-judae, etc. 225
Observations on Hirneola auricula-judae, Berh (" Jeiu's ear").
(Preliminary communication.) By M. J. Le Goc, B.A., Fitzwilliam
Hall (University Frank Smart Prizeman, 1912). (Communicated
by Mr F. T. Brooks.)
[Bead 28 April 1913.]
Fries refers to the Jew's ear fungus as " antiquitus celebrata."
This celebrity of the fungus was due to its supposed medicinal
properties ; for, on account of its fanciful resemblance to the fauces,
it was frequently used as a cure for sore-throats in the days when
the external form of a plant was thought to be a sufficient guarantee
for its therapeutic quality. According to Berkeley, it was occa-
sionally sold at Covent Garden for such a purpose as late as
1857.
The Jew's ear fungus received several different names : Tremella
auricula-judae^', Exidia auricula-judae^, Exidia auriformis, Auri-
cularia sambucina\, etc., until Fries and Berkeley fixed the name
Hirneola auricula-judae'^. Hirneola is derived from " hirnula,"
a small jug; "judae" refers to the host, the Elder tree, on which
the legend represents Judas as having hanged himself; while the
name " auris," ear, has been attached to it throughout its history
on account of the ear-like form it often assumes. The popular
name of "Jew's ear" is a corruption of Judas' ear.
The only person who has hitherto investigated the biology of
this fungus is Brefeld, whose work was confined to a study of the
germination of the spores and the structure of the fructifications ||.
Mr F. T. Brooks suggested that I should attempt to establish pure
cultures of this fungus and investigate some points of its biology
which have hitherto been obscure.
As is well known, the Jew's ear fungus belongs to the
Auriculariaceae, a group of the Basidiomycetes characterised by
transversely-septate basidia arranged in a definite hymenium which
becomes freely exposed during spore formation IT.
This fungus is of world-wide distribution and is of frequent
occurrence in the neighbourhood of Cambridge. Most of the
* Lin. spec. (1625).
t Fr. Syst. II. p. 221; Berk. Gryptogamic Botany (1857), p. 355.
+ Mart. Erl. p. 459.
§ Fr. Fung. Nat. p. 24 ; Hym. europaei, p. 695 (1874) ; Berk. Outl. of Brit.
Fung. p. 289 (1860).
II Brefeld, Untersuchungen aus dem GesammtgeUete der Mykologie, vii. Heft,
pp. 70-76.
1[ Fuckel, Symbolae, p. 29 ; Winter, Pilze, p. 283.
^26 Mr Le Goc, Ohservations on
material used has been collected from the vicinity of Byron's Pool.
It is found abundantly on Elder bushes both living and dead, and
also on dead branches and trunks of Elm trees in moist places. It
has been suggested that the Hirneola growing on Ehn is not
perhaps identical with the Hirneola which lives on Elder: the
hymenium is decidedly freer from folds, but as a matter of fact
spores from Hirneola on Elder have germinated quite easily and
are growing qidte happily on blocks of Elm wood. It is usually
stated that the fructifications reach a size varying from 4 cm. to
7 cm. in diameter*; but it is often much larger and a specimen
collected in this locality measured 21*6 cm. by 12 cm.
The fructifications which are gelatinous under moist conditions
shrivel to black, horny masses in a dry atmosphere. In this form
the fungus remains alive for at least five months, because after
this interval it revives again when moistened and produces an
abundant supply of spores — as in the case of Stereiim purpureum
and some other fungif.
If a fructification which has been moistened is suspended over
a sterilized glass slide, spores are produced after an interval of
some 10 hours and fall on the slide where they form a thick white
deposit. They can then be transferred into tubes of sterilized
water or directly picked up with a platinum needle and used for
cultures.
Germination of spores on the fructification.
If the fruit body is kept moist for two or three days and the
spores allowed to accumulate on its surface, it is often found that
the spores germinate in situ. The mycelia reach a considerable
length and in time form roundish protuberances projecting from
the surface of the fructification. These projections prove to be
webs of hyphae entangled together and enclosing a large number
of ungerminated spores in a good state of preservation. The
hyphae themselves soon undergo a process of disintegration ; the
glycogen contained in them breaks into small globules, regularly
arranged in a chapelet which simulates a chain of " oidia." The
ungerminated spores look healthy after an interval of more than
three months and are capable of germination.
Germination of spores in liquids.
The spores can be cultivated in hanging drops in sealed
cells and easily observed under the microscope. Under these
* Massee, Diseases of Cultivated Plants, p. 404.
t Brooks, F. T., "Silver-leaf Disease," Journ. Agric. Set. Vol. iv. p. 143;
BuUer, A. H. E., Researches on Fungi, p. 106.
Hirneola auricula-judae, Berk. {"Jeiv's ear"). 227
conditions germination has not been observed in distilled water, but
in Elder-wood decoction it occurs occasionally. However, if a drop
of the decoction is laid at the bottom of the same cell instead of
being suspended from the cover glass, germination occurs regularly.
The probable explanation of this anomaly is that the spores, being
heavier than the liquid, fall to the bottom ; thus in the case of
the hanging drops the spores are only partially immersed, and
osmosis is not carried out in the proper manner. In tubes or
watch glasses the spores germinate very readily in Elder-wood
decoction and occasionally in distilled water.
The hyphae grow rapidly, reach a considerable length, branch
freely, and when the food and aeration have become deficient, they
undergo disintegration ending in the formation of abundant drops
of glycogen.
Here I must note some divergences with Brefeld's results. In
the first place, Brefeld found that eight days immersion or more
were required for the germination of spores*, while my observations
show that two or three days are suflficient ; after this interval large
drops of glycogen develop in any ungerminated spores which at
a later stage become ruptured and emit their contents. Secondly,
Brefeld describes as of regular occurrence the formation of conidia
on the germ tubes of the spores f. Such bodies have never been
observed during the whole series of my experiments.
Pure cultures of the fungus.
(a) Cultures in decoctions of Elder-wood + agar or gelatine.
The Elder-wood decoction has been solidified with 2°/^ agar or
10 7o gelatine, after previous sterilization by the usual methods.
In the case of agar cultures the spores germinate quite easily
and after some 15 days patches of mycelia become visible ; these
mycelia grow with some difficulty and not always with equal
success. In my cultures they are still developing without any
apparent attempt to produce fructifications.
The gelatine cultures are more interesting, showing an almost
luxuriant growth. At first a woolly mass of mycelium appears on
the surface : but the gelatine is soon liquefied and the fungus
sinks into the medium, assuming a definite form and developing
into bodies which imitate in shape and structure the fructifications
of the Jew's ear fungus. At this stage a number of hyphae become
very stout, irregular in form and branch freely in all directions.
It has not yet been possible to determine the ultimate fate of these
* Brefeld, loc. cit. p. 72.
t Brefeld, loc. cit. pp. 73—76.
228 Mr Le Goc, Observations on Hirneola auricula-judae, etc.
interesting structures. The production of a fruit body within
a liquid is at least unusual in the case of fungi.
(b) Cultures on wood. Pure cultures of the fungus have been
established on blocks of Elder, Lime and Elm wood, about 5 cm. in
length and from 1 cm. to 4 cm. in diameter. These blocks of wood
are enclosed in tubes or flasks containing a certain amount of
water, and sterilized in the usual manner. Inoculation of the
blocks of wood has been effected by transferring to them the
spores of the fungus by means of a sterilized platinum needle.
With few exceptions germination has always occurred. After
about 20 days a white woolly growth appears on the spots infected
and spreads all round forming a thick envelope. These woolly
hyphae show at present signs of active growth, indicated by large
drops of liquid which are oozed out as in the well-known example
of Pilobolus. Also large, stout, irregular hyphae are being formed
as in the case of the culture on gelatine. In some of the cultures
on wood blocks fructifications have begun to appear, more especially
on blocks exposed to a fair amount of light. The formation of
fruit bodies on artificial cultures of one of the higher fungi is as
interesting as it is rare.
The penetration of the hyphae inside the wood has been tested
at intervals. It is very rapid, and after three months the hyphae
have run all through the tissues. The path followed is along the
vessels and tracheids, with penetration through the pits and more
frequent branching in the medullary rays. For some time the
fungus seems to be satisfied with the food found inside the cells,
but from examination of material found in nature, it is evident
that when hunger presses hard on the fungus, it encroaches on the
cell walls : the xylem is then delignified, the hyphae bore their
way locally through the walls which are gradually consumed and
the ultimate result is that the whole tissue becomes spongy,
crumbles when rubbed with the finger, and consists more of the
hyphae than of the original tissue of the tree.
Inoculations of healthy Elder bushes with the fungus.
Inoculations of mycelia and spores have also been tried on
living branches of Elder bushes. The spores have germinated, and
the mycelia have penetrated the wood in the manner just described,
but the process of penetration is slower than on dead wood and no
further details are at present available.
I wish, as a pleasant duty, to express my hearty thanks to
Mr F. T. Brooks for his kind guidance as well as for his repeated
suggestions during these investigations.
Mr Evans, Additions to the Flora of Cambridgeshire 229
Notes on additions to the Flora of Cambridgeshire. By A. H.
Evans, M.A., Clare College.
[Read 28 April 1913.]
The publication last year in onr Proceedings (Vol, xvi., Pt. iii.)
of my " Short Flora of Cambridgeshire " has resulted, according
to expectation, in a further revival of the interest now taken in
Field Botany, and in considerable accessions to the county list.
We are naturally much indebted to our senior botanists, several
of whom are specializing in various divisions of the Cryptogams,
but we feel that even more stress should be laid on the co-operation
of the undergraduate members of the University, who have much
time at their disposal in which to range the country, and keep
submitting to us specimens of the plants with which they meet,
so that it becomes possible to determine the exact forms, and
settle whether they are new to Cambridgeshire or to any of its
districts. The excursions under the guidance of Mr Moss come
in the same category, while, extending as they do beyond the
county limits, they enable us to institute comparisons between
our Flora and that of the immediate neighbourhood, as well as to
familiarize our students with rare plants that might not otherwise
come under their notice. The extreme north of the county,
however, is still in need of careful exploration.
Species which had been lost to sight have been rediscovered,
and several that are new to our area met with, though, as will be
seen from the subjoined list, new varieties are no less common
than new species. It is most important to decide which of the
varieties recognised on the Continent are also to be found in
England, and we have been able to contribute to this desirable
result, chiefly through the penetration of Mr Moss, who will
incorporate the information in his forthcoming British Flora.
The genera Arctium, Lycium and Bartsia, as well as the
aggregate Polygonum avicidare, have been entirely reconsidered
in the light of recently published work, while several of the Latin
names in the catalogue below have been corrected. As regards
the Cryptogams we have been able to add somewhat to the lists
furnished by our former coadjutors. Mr B. S. Adamson has
sent a large number of notes on the Musci, in addition to remarks
on the Phanerogams, and Mr Compton has given us the results
of his year's work on the Hepaticce. Mr F. T. Brooks is still
studying the Fungi, but wishes to delay the publication of his
results until he has examined further material.
I
230 Mr Evans, Notes on additions to the
The most striking occurrence of the year has been the discovery
of a considerable quantity of Prunella laciniata in a fallow at
Hardwick by an undergraduate (Mr A. W. Graveson of King's
College), followed by the further discovery by Mr Moss that it w'as
accompanied by a still greater quantity of the putative hybrid
between it and P. vulgaris. This is new to the British Isles.
The field furnished several other interesting plants, among others
the radiate form of Gentaurea nigra, found by the writer. The
last-named was new to the county, as were Epilobium roseum from
the town of Cambridge (Mr Compton), Sparganium neglectum from
Waterbeach_(MrMoss),and Anthoxanthum Puellii from Gamlingay
(Mr J. E. Little). The wonderfully productive greensand at the
village just mentioned was also responsible for Helianthemum
Ghamoicistus subvar. viridis, and the rare Arnoseris pusilla was
found there in abundance in the corner of a field, which had
previously escaped investigation. Two uncommon forms of
Orchids were met with at Dernford Fen by Mr Moss, Orchis
maculata var. O'Kellyi, and Habenaria (Gymnadenia) Wahlen-
bergi; while the Babington Herbarium proved to contain H. (G.)
densiflora from the same place. These two forms of Habenaria
are new to the British Isles. Juncus bufonius var. fasciculatus
was determined from Upware by Mr Adamson, who also found
Quercus sessiliflora in Gamlingay Wood.
We have ascertained that a green as well as a glaucous form
of Stellaria Dilleniana (=S. glaitca or palustris auct.) grows in
Wicken Fen, but it is too early to state definitely how many of
the phases of this variable species the county really possesses.
Myosotis collina var. Mittenii from Chippenham and the hybrid
Willows Salix alba x pentandra and ;S^. cinerea x viminalis must
further be placed to the credit of Mr Moss.
Not one of our extinct plants has been rediscovered, but Ranun-
cidus parviflorus has been met with, after the lapse of many years
at Hardwick and Caldecot ; Mr Moss has found Acorus Galamus
at Upware; Mr Shrubbs Myosurus minimus near Ickleton and
Muscari racemosum near Hinxton ; and the present writer a whole
field_ of Thlaspi arvense near Pampisford, besides a quantity of
Pedicularis sylvatica and new stations for Glaytonia perfoliata
and Malva moschata at Gamlingay. Both Lycium chinense and
L. barbarum have been proved by Mr Moss to occur in the county ;
the same may be said of Bartsia verna and B. serotina and several
of Professor Lind man's segregates of Polygonum avicidare, while
various difficulties concerning the genus Arctium have' been
solved by the writer, who finds all the British forms in Cambridge-
shire. Mr Adamson has named tentatively some of the Rosee
and Rubi, which will probably prove to be additions to our list.
Flora of Cambridgeshire 281
ADDITIONS AND CORRECTIONS OF THE GENERAL
LIST OF SPECIES.
I. ANGIOSPERMiE,
Ranunculus trichophyllus var. Godronii Gren. 1.
R. auricomus 4.
R. parviflorus. Refound at Hardwick and Caldecot.
Erophila virescens 1. (The East Anglian plant seems to be
rather E. glahrescens Jord. than E. virescens.)
Lepidium Draha 4.
Thlaspi arvense 4. (Also in profusion near Pampisford.)
Helianthemum Chamcecistus awhw s,r. viridis Irvine 4 (Gamlin-
gay, Moss).
Viola sylvestris var. punctata 3, 5.
Stellaria palustris must now stand as S. Dilleniana. We have
in Wicken Fen both a green and a glaucous form.
Arenaria trinervia. Our form is var. typica Moss (var. nov.
ined.).
Claytonia perfoliata 4 (Evans).
Malva moschata 4 (the typical plant).
[Oeranium lucidum. Refound by Mr A. W. Graveson, at Linton.]
Ononis spinosa 4.
Rubus sylvaticus Wh. and N. 5 (fide Adamson).
R. macrophyllus Wh. and N. 4, 5 {fide Adamson).
Rosa canina var. lutetiana (hem.) 1, 2, 3, 5 (fide Adamson).
„ „ dumalis (Bechst.) 1, 3, 5 (fide Adamson).
„ „ dumetorum (Thuill.) 1, 5 (fide Adamson).
„ urbica (Lem.) 2, 5 (fide Ada,mson).
Sawifraga granulata 4.
Epilobium roseum 1 (Cambridge, Coinpton).
Smyrnium Olusatrum 6.
Matricaria suaveolens 4.
Arctium majus must stand as A. Lappa L. (see Journ. of Bot.
April 1913).
A. nemorosum (auct. plur.) must stand as A. vidgare subvar.
pycnocephalum (Evans).
A. pubens Bab. must stand as A. vulgare (Evans).
Centaurea nigra forma radiata 5 (Evans).
Arnoseris niinima. Found in quantity at Gamlingay by
Mr J. E. Little of Hitchin.
Primida veris var. suaveolens 5 (Moss, Evans).
232 Mr Evans, Notes on additions to the
Vinca minor 4.
Blackstonia perfoUata 4.
Myosotis collina var. Mittenii (Baker) 6 (Moss).
Lycium barbarum L. and L. chinense (Mill), both occur, not
uncommonly, in the county.
Bartsia verna 5. ) m ^ ■ r> >-> 7 ^ •.
Bartsia serotina 1, 5, etc./ ^^^'^ "^^'* ^^P^^°^ ^- 0^«^^*^^^-
Pedicularis sylvatica. In some quantity at Gamlingay in 1912
(Evans).
Prunella vulgaris x laciniata 5 (Hard wick, Moss).
P. laciniata 5 (Hardwick, A. W. Graveson).
Lamium hybridum 6.
Atriplex patida var. erecta. Babington's plant is merely a
variety o( patula and not the plant of Hudson or Smith.
Polygonum aviculare. This aggregate must now stand as follows
for the county :
P. aviculare L. (=P. heterophyllum Lindman) 1, 5, etc.
P. rurivagum Boreau 3.
P. cequale Lindman 1, 5, etc.
P. macidatum 4.
Ulmus procera Salisb. must stand as U. nitens Moench., the
former proves to be a synonym of U. campestris L.
Myrica gale. In quantity at a new station in Wicken Fen
(Evans).
Alnus glidinosa Gaertn.
var. typica Moss (the common form of southern England),
var. macrocarpa (Loudon) 1 (Chippenham Fen, Moss).
Quercus sessiliflora 5 (Gamlingay Wood, Adamson).
8alix alba x pentandra 1 (Moss).
Salix cinerea x viminalis 1 (Moss).
Populus canadensis. Our common tree should stand as x P.
serotina. It is always male, and always planted ; x P. canadensis
is rare in gardens near Cambridge, though " sub wild " in Suffolk ;
it is always female.
Liparis Loeselii. The specimen mentioned in our former list
as from Gamlingay has no doubt been accidentally transferred
from one sheet of the Power Herbarium at Beigate to another:
for a similar case has occurred with a specimen of Malaxis
paludosa labelled Burwell Fen, where the same explanation may
be given. In other words the specimens have probably been
interchanged.
Orchis maculata var. O'Kellyi, Sawston Fen (Moss).
Habenaria (Gymnadenia) Wahlenbergi, Sawston Fen (Moss).
H. (G.) densiflora, Dernford Fen (Bab. Herbarium, yic^e Moss).
Iris foetidissima. Several plants at Pampisford (Evans).
Juncus bufonius var. fasciculatus 1 (Upware, Adamson).
Flora of Gambridgeshir-e 233
J. compressus. Again found in quantity at Fulbourn and
Waterbeach (new stations) 1.
J. effusus 6.
J. subnodulosus 2.
Sparganium neglectum Beeby. 1 (Waterbeach, Moss).
Acorus Calamus 1. Add Upware (Moss).
Gar ex vulpina var. nemorosa 2.
Anthoxanthum Puellii 4 (Gamlingay, J. E. Little).
II. Gymnospekm^.
Jimiperus communis. Add Roman Road, near Linton (Comp-
ton).
III. Bryophyta.
Musci.
The following list contains a few additions by Mr R. S. Adamson
to the list of mosses of the county recorded by Rev. P. G. M.
Rhodes in 1911.
The nomenclature followed is that of Dixon and Jamieson's
Student's Handbook of British Mosses, Ed. 2, published in 1904.
The divisions of the county are the geological ones used in our
former list.
The following species are new to the county list with the
exceptions of the species of Sphagnum, which, however, were only
recorded on old authority. A species of Sphagnum also occurs on
Chippenham Fen ; but this Mr Adamson has not seen :
Sphagnum cymbifolium Ehrh. var, squarrulosum Nees and
Hornsch. 4.
S. acutifolium Ehrh. var. subnitens Dixon 4,
Polytrichum gracile Dicks. 4.
Pottia intermedia Ftirn. 3.
Tortula muralis Hedw. var. aestiva Brid. 6.
Ba7-bula cylindrica Schp. 3.
Orthotrichum cupulatum Hoffm. 3.
Aulacomnium androgynum Schwaeg. 6.
Bryum inclinatum Bland. 4, 6.
B. intermedium Brid. 2.
B. erythrocarpum Schwaeg. 4.
Mnium afine Bland. 5, 6.
Brachythecium rivulare B. and S. 3, 4.
B. glareosum B. and S. 3.
Eurhynchium murale Milde 3.
Hypnum polygamum Schp. 1.
H. commutatum Hedw, 1.
234 Mr Evans, Notes on additions to the
In addition to the above, the following have been found in
divisions of the county additional to those mentioned in the Flora
or are confirmations of old records :
Oatharinea undulata W. and M. 5.
Polytrichum juniperinum Willd, 6.
Dicranella heteromalla Schp. 4.
D. varia Schp. 4.
Pottia truncatula Linbd. 3.
P. minutula Lindb. 5.
Tortula Vahliana Wils. 6. On a bank near Kennett.
T. subulata Hedw. 4.
T. ruralis Ehrh. 1, 6.
Barhula fallax Mitt. 5.
B. unguicidata Hedw. 5.
Bryum ccespiticum L. 1. Recorded by Relhan.
B. capillare L. 5.
Mnium cuspidatum Hedw. 1, 6. Recorded by Relhan.
M. rostratum Schrad, 1. Recorded by Relhan.
Brachytheciu7n albicans B. and S. 1. (Wisbech).
B. velutinum B. and S. 5.
B. plumosum B. and S. 2. Recorded by Relhan.
Eurhynchiuni swartzii Schp. 1.
E. striatum B. and S. 2. Recorded by Relhan.
Hypnum elodes Spruce 5.
Hypnum aduncum Hedw. var. paternum Sanio 5.
H. cupressiforme L. 1.
H. molluscum Hedw. 5.
H. sohreberi Willd. 4. Previous record 5, Relhan.
Hylocomium splendens B. and S. 6. Previous record 5, Relhan.
H. squarrosum B. and S. 1.
H. triquetrurn B. and S. 5.
HepaticcB.
Owing to the combined influences of the low rainfall, the
absence of hard rocks and the frequency of soils containing a
high percentage of soluble salts, Liverworts are relatively rare in
Cambridgeshire. The result of researches by Mr R. H. Compton
of Gouville and Caius College is that no new species are added
to the County List prepared by the Rev. P. G. M. Rhodes. Certain
records, however, have been confirmed and new localities added,
as the subjoined supplementary list will show.
Riccia fiuitans L. L In ditches by the river and railway
near Clayhithe.
\
Flora of Cambridgeshire 235
Lunularia criiciata Dum. 1. At the water's edge, Byron's
Pool, Trumpington.
Marchantia polymorpha L. 1. On walls and bridges, Backs
of the Colleges, Cambridge.
Metzgeria furcata Lindb. 3. Wood on the Gog-Magog Hills,
near Roman Road, Cambridge.
Pellia epiphylla Dum. 1. Hobson's Conduit, Cambridge ;
Bourn Brook, Grantchester. 4. Great Heath Wood, Gamlingay.
Lophozia turbinata Steph. 3. On bare chalk, Cherryhinton
Chalk Pit.
Lophocolea bidentata Dam.j ^,.^^j distributed. 4. Great
L. Iieteropliyiia Dum. J -^
Heath Wood, Gamlingay. 5. Madingley Wood. 6. Kennett, banks
and hedgerows.
FruUania dilatata Dum. 5. Gamlingay Wood.
236 Mr Saunders, A Note on the Food of Freshwater Fish.
I
A Note on the Food of Freshwater Fish. By J. T. Saunders,
B.A., Christ's College.
[Read 5 May 1913.]
Very little is known about the food of freshwater fish, records
in the past being very scanty and, owing to the difficulty of
identifying remains in the stomach, sometimes inaccurate. Again,
if an animal happens to be found two or three times in the stomach
this was recorded as the chief food of the fish, without having
any regard to the season of the year and the natural conditions
under which the fish was living. This fault is very noticeable in
semi-popular works like those of Tate Regan {British Freshwater
Fishes, London, 1911) and Yarrell (A History of the British
Fishes, London, 1836). Here we find it recorded that certain fish
will eat such things as insect larvae, shrimps, small bivalves and
the fry of other fishes. The natural conclusion that one draws
from a statement such as this is that the fish swim about in search
of food and snap up anything palatable that they meet. But this
is far from being the case.
On opening up the alimentary canals of some sticklebacks
{Gasterosteus aculeatus, L.) caught at Madingley, I found that their
stomachs were full of Diatoms, but it was only one species of
Diatom, viz. Nitzschia sigmoidea, Ehbr. It is true that there
also occurred a few trichomes of Oscillatoria nigra, but they were
so few that it is reasonable to suppose that they were ingested
accidentally when the fish was seizing a Diatom. I have examined
the stomachs of a great many sticklebacks at all times of the year
caught in this pond and I found in them nothing but this Diatom,
Nitzschia sigmoidea. All the specimens whose stomachs were full
of Diatoms were caught with a worm and were large individuals,
probably full grown. But finding it rather arduous to catch them
singly with a worm I adopted the device of luring a number of
sticklebacks over a net in the water by means of a worm. A great
number of sticklebacks came to bite at the worm, and on quickly
withdrawing the net fifteen to twenty could be caught at once. In
this way fish of all sizes were taken.
An examination of the stomachs of fish that were not fully
grown gave very different results from the examination of those
that were full grown. I found at once that the younger fish do
not exhibit such an exclusive preference for N. sigmoidea as do
the older fish. N. sigmoidea is found only sometimes in their
stomachs and it seems that the larger the fish the more restricted
is its preference. The smaller ones are not so particular as the
Mr Saunders, A Note on the Food of Freshwater Fish. 237
larger and tend to be carnivorous ; the smaller the fish the greater
are its carnivorous propensities. Thus one finds that in a fish of
about 4 cm. long the stomach and intestine will be full of insect
larvae and small Crustacea, while the rectum is distended with
Nitzschia sigmoidea shells. In one of a smaller size the whole of
the alimentary canal was full of insect larvae and small Crustacea
only, or we may find insect larvae and Crustacea in the stomach
and Peridinians in the intestine.
Two points are worth noticing here. The first is that the fish
does not pick up anything digestible that comes handy but it
confines its attention to one food only, or rather to one class of food.
The stomach never contains a mixture, but is always full of one
thing only. The second point is that it is capable of eating both
animal and vegetable food.
As regards the animal food that is found in the stomach, it is
a mixture of insect larvae and small Crustacea of all kinds. These
the fish evidently hunts for and catches by the use of its eyes only
and not by the sense of smell. This may be amply proved in the
following manner. If some sticklebacks be kept in an aquarium
with some small waterbeetles, they will never attack the beetles,
which are not an article of their diet. But if a number of
Copepods are introduced into the aquarium the fish will at once
attack them and eat them, at the same time they will often attack
a waterbeetle by mistake, but they let the beetle go immediately,
never swallowing it. It is only for a moment after the Copepods
have been introduced that the beetles get attacked, the stickle-
back very soon learns to leave them alone. Sticklebacks will also
snap at Copepods enclosed in a glass tube if this tube be placed in
their aquarium.
But as regards the ves^etable food I think that the stickleback
must hunt for this by the sense of smell. It is difficult to see how
the fish could get a meal that entirely consists of Peridinians or
N. sigmoidea using only his eyes. And if he swam through the
water with his mouth open he would surely engulf a mixture of
organisms, and this is found to be not the case.
But so far I have been speaking of sticklebacks taken from one
pond only, and from an examination of the contents of the stomachs
of specimens caught in this pond we might assume that all young
sticklebacks of about 4 cms. long are carnivorous, while the adults
are vegetarian. This pond of which I have just been speaking is
one of a series of ponds which have been formed in the excavations
made by a former brick industry. They are all very close together,
the banks between them being not more than a few yards wide.
Yet in one pond it is found that ail the adult sticklebacks feed
only on a Diatom, Nitzschia sigmoidea, and in another all the
adults are carnivorous and hunt for insect larvae and small
VOL. XVII. PT. III.
16
238 Mr Saunders, A Note on the Food of Freshwater Fish.
Crustacea. Thus we see that the food of the stickleback may
vary, but the variation is not a haphazard one for it effects equally
all the individuals that live in one pond. It is something in the
conditions under which a fish lives that determines its preference
for a certain kind of food.
Under artificial conditions I found that the feeding habits of
the fish completely changed. I could never get the large forms
which fed on Diatoms to eat Diatoms, and I suspect this was
because the Diatoms did not grow in their natural manner. These
larger forms would however become carnivorous in aquaria and
gave the impression that this was their natural method of feeding.
Experiments in the laboratory are therefore useless to determine
this point.
The fisherman, who catches fish with bread paste and gaudy
flies, will probably ask how it is that such a thing as his bait
which the fish cannot possibly have ever seen before proves so
attractive. But the bait is not an article of diet. Every fisher-
man knows that there are times when the fish are feeding and
times when they are not. Now my experiment of introducing
Copepods into an aquarium and thus getting sticklebacks to snap
at waterbeetles, shows that when fish are " on the feed " they will
snap at anything that catches their eye, but unless they seize
something palatable they will not swallow it. Therefore the
fisherman angles when the fish are " on the feed," that is moving
about in search of food, and he uses as a bait something that is
likely to catch the fish's eye. The fish snaps at the bait and the
fisherman strikes so as to drive the hook into its mouth. If the
bait used were something that the fish ordinarily ate there would
be no need for the exercise of any skill, for the fish would swallow
it and inevitably get hooked. As it is the fisherman has to strike
at the moment the fish snaps and before it has a chance to reject
the bait. Herein lies the sport of fishing, for the more tentative
the snap the greater will be the skill required to hook the fish ; the
fish that snap so vigorously that they will hook themselves provide
little sport for the angler.
We therefore come to two conclusions.
(i) Fish may feed on different things, but a meal always
consists of one class of food only. This means that in order to
ascertain the food of a fish we must open stomachs of fish taken
at different seasons and under different conditions.
Additional evidence on this point is afforded by an observation,
Dakin and Latarche {Proc. of Royal Irish Ac, Vol. xxx. Sec. B,
No. 3). They examined the contents of the stomachs of large
numbers of Pollan (Coregonus pollan) and they remark: "The
most extraordinary thing however was that on most occasions
when Daphnids were found in the alimentary canals, practically
\
Mr Saunders, A Note on the Food of Freshwater Fish. 239
nothing else was present." I myself opened the stomachs of two
pike (Esox lucius, L.) which were brought to me and found two
roach in the one and one roach in the other. Other kinds of fish
besides roach lived in the pond from which the pike were taken.
This shows that both Pollan and pike as well as the stickleback
like their meals to be composed of one thing only.
(ii) Preference for a certain kind of food varies according
to locality.
Since all my observations have been made on sticklebacks
taken from only three localities, I refrain from giving a list of the
things they are capable of eating. It would be necessarily very
incomplete.
16—2
240 Professor Nuttall, Observations on Ticks, etc.
Observations on Ticks: (a) Parthenogenesis, (b) Variation due
to nutrition. By Professor Nuttall.
[Eead 5 May 1913.]
The occurrence of parthenogenesis in ticks was recently
observed by Aragao, in Brazil, in a new species of Amblyomma
(A. agamum), the males of which have not as yet been discovered.
Three complete generations of this tick have been raised experi-
mentally and thousands of females were brought to maturity in
the absence of males. This constitutes the first record of partheno-
genesis in ticks.
The author described how he had succeeded in obtaining a
partbenogenetic offspring from Rhipicephalus bursa, a species
(prevalent on sheep in countries bordering the Mediterranean) in
which both sexes occur in fairly equal numbers upon the host.
Larval ticks issued in limited numbers from the eggs laid by
unfertilized females.
Experiments were further recorded in which it was shown that
the genus Rhipicephalus shows a considerable natural variation in
size, and that imperfect feeding of the tick in its immature stages
leads to the development of very srnall adults which, whilst fertile,
are so different from the normal forms, that they could readily be
taken for other species. It is only by determining the range of
variability in a species under experimental conditions that the
limits of a species in this respect can be determined and the
making of bad species prevented.
Mr Lewin, The Division of Holosticha scutellum. 241
The Division of Holosticha scutellum. By K. R. Lewin, B.A.
(Communicated by Professor Nuttall.)
[Bead 5 May 1913.]
The account of the behaviour of the micronuclei at division,
given by A. Gruber (" Weitere Beobachtungen an vielkernigen
Infusorien," Ber. Naturf Ges. zu Freiburg I.B. Bd. ill. (1887),
pp. 57 — 70) is not confirmed. In the period between divisions,
H. scutellum possesses only a small number of micronuclei of
about the size of the meganuclear segments, with which they have
been confused. There is therefore no necessity to assume that
numerous micronuclear divisions occur at the fission of the in-
fusorian. Over the very limited series of preparations in which
the micronuclei have been counted, a tendency is evident for the
smaller numbers to occur at or near the stage of maximum con-
centration of the meganucleus. If this is significant, a reduction
in the number of micronuclei must take place before division.
There is, however, no evidence, nor any need to assume, that
fusion of micronuclei is the way in which such a reduction would
be accomplished.
Exhibition of living Termites. By Professor A. D. Imms.
[Read 5 May 1913.]
The author exhibited tabes containing living examples of the
Termite Archotermopsis wroughtoni Desn. The Termites were
obtained by him from the Kumam Himalayas, where they occur
in dead trunks of the Chir pine {Pinus longifolia) at an altitude
varying from about 4500 to 5800 ft. This species was described
by Desneux in 1904 and was only previously known from Kashmir
where it occurs in stumps of Pinus excelsa. The most interesting
features are seen in the length of the cerci, which are composed of
7 — 8 joints in the sexual forms and of 6 — 7 joints in the soldiers
and workers, in the possession of 5 -jointed tarsi, and in the great
development of the eyes. In the possession of these characters it
is to be regarded as one of the most primitive of living Termites.
Its nearest relationships are with two fossil species from the
amber of Oeningen (Prussia) and the N. American genus
Termopsis, Heer.
242
Prof. Dixon, On the greatest value of a
On the greatest value of a determinant whose constituents are
limited. (Proof of Hadamard's theorem.) By Prof. A. C. Dixon,
F.R.S.
[Received 9 April 1913— i?eac? 28 April 1913.]
Let there be an array || a,.., || of m rows and n columns (n > m) ,
the constituent in the rth row and .sth column being a^s, a complex |
quantity, whose conjugate is 6,.g.
Multiply the two arrays || a'rs\\, |1 Kft \\ according to the ordinary \
rule, that is, form the determinant G, of order m, which has in its i
ith row and_yth column the constituent \
n
Cij= 2 aisbjs (^■, j = 1, 2 ... m). I
1
G must be positive since it is the sum of products each formed
with a determinant from || a^sH and the corresponding determinant „
from ||6rs||> that is, products of conjugate complex quantities. ■
The theorem to be proved is that G cannot exceed its leading term
m
Ucii, or say IT.
Assume this for ni — 1, and let (7^ be the coefficient of Cy in G,
that is, the product of the matrices
Otr.Q
id \\hr
with the *th and yth rows left out respectively, with the sign
(- 1)^+^.
Thus the construction of Gij is the same as that of cij, the
places of ars, hs being taken by the first minors of the deter-
minants of j|a,.s|| and ||6j.s|| ; the value of n is now different, being
the number of determinants in a matrix of n columns and m — 1
rows.
Since the theorem is true for on — 1 we have
Gii^U ^di (i = l,2 ... m)
and also
^32 ^3!
V>7W,9 ....
Go
Gn
< G»» Go.
On
determinant whose constituents are limited. 243
that is, Cn G^-^ ^ H'^-^ - {c^^C,, . . . Cm,n),
whence C^-^ ^ 11"*-^
and if m > 2, C ^U,
for both are positive.
Hence if true for m — 1 the theorem holds for m when m > 2.
But when m = 2,
\j = Gil C22 Cjo C21
= CuCo^2-\c,.\^
^ Cn C22-
The theorem therefore holds when m = 2, 3, 4 . . . and universally.
When 71 = ni, the result gives the theorem of Hadamard used
by Fredholm in the theory of Integral Equations, that the absolute
value of a determinant of order m cannot exceed the mth power
of the absolute value of its greatest constituent multiplied by m^"\
24*4 Prof. Dixon, Expressions for the remainders when 6, 6^,
Expressions for the remainders when 6, 6^, sin kd, cos k6 are
expanded in ascending powers of sin 6. By Prof. A. C Dixon,
F.R.S.
[Received 9 April mS—Bead 28 April 1913.]
1. Take | sin k (d — t) sin^Hdt, say w^,
Jo
and integrate twice by parts. Thus
fC tlqi
k cos k (6 — t) sin** t
— kn cos k{6 — t) sin**"^ t cos tdt
Jo
k sin'*^ +
n sin k{6 — t) sin"~^ t cos t
i
re
- n sin k{e - t)[{n - l)sin'^-2^ co&H-Bn\'H\dt
Jo
= k sin**^ — n{n — 1) Un-2 + nhi^.
This holds when ?i = 2, 3, 4 ... but when n — l,Q we have
k'^Ui = k sin ^ — sin kd + Ui,
k^Uo = k{l — cos k6).
The general formula may be written
k
Un—z —
sin" +
-k^
n (n — 1)
Un.
n {n — 1)
Hence
sin kd = ks,v(x6 — (k^ — 1) u^
= Z; sin ^ ^-^-j — - sm^ 6 + ^^j u^
^,.„,-My).„,,,...,(-i).. ^(^--iy^^-f"-iyi
\
Sin^n+l Q _
A;^-(27r + l)^
A;
U^n+i
■in
cos A;^ = 1 — A;Wo
^ k^ . ,^ k(k"--2^)
sin kd, cos k9 are expanded in ascending powers of sin 6. 245
= l-|^sin^^ + ^'^^'7^'^ sin^^...
2! 4!
+ (-1)'
2. Similarly let
y^2(fc2_2^)...{A;^-(272-2)^|
2??,!
sm^** O ; u^
.(2).
V,, = {9-t) sin'^ tdt,
Jo
and integrate by parts. Thus
wWrt =1 n{6 — t) sin"^~^ ^ . sin tdt
Jo
~\e
n (6 - t) sin"-i t cos t
Jo
re
+ n [{n - \){e - 1) sin"-2 ^ cos- ^ - sin^^-i t cos ^]cZ^
Jo
?i (^ - 1) sin'^-1 i cos i + sin" ^
Jo
-\-n{n-l)\ (0- 1) sin"-2 1 cos- ^(^^
Jo
= - sin" 6 + n (n — 1) (v„_2 - -y^),
1
and w
sin" 6" +
Vn.
n{n — \) " ' n—\
This holds when ?i = 2, 3, 4 . . . , but when ?i = 1, we have
Wi = ^ — sin 6, Vq = -1^1
Hence 6 — sin ^ + Vi
. . sin^^ 3
= sin^ + -g^+-^;3
. . 1 sin^ ^ 1.3 sin^ 6
+
1.3... (271-1)
2.4...2n
sin-"+i 6
2/1 + 1'
+ (2?i + l)v2,
•(3),
and
\o^ = \ sin^ ^ + 2v.
Avf 6 2 sin' 2.4
246 Prof. Dixon, Expressions for the remainders when 6, 6^,
sm^6 > 2 &m'd 2.4 sin«
~2~ ''" 3~T~ "^375~~6~"^'"
2.4... (2w- 2)
—Tz 1- 2n Vo
'In
3.5...(2w-l)L 2n ' """"''" \ ^^^•
3. In (1) (2) (3) (4) we have the expansions of sin kd, cos kd,
6 and 6^ in ascending powers of sin 6, with expressions for the
remainders.
Now 1 . 3 < 2^ 2 . 4 < 32,
3.5 < 42, 4.6<52,
{In - 1) (2n + 1) < (2w)^ 2?z (2w - 2) < (2w ~ 1)1
Hence by multiplication the coefficient of v^^+i in (3) is
< V(2w + 1) and that of v^n in (4) is < 2 sjn.
Thus the remainders in (3) (4) tend to zero if Vn\fn does so,
when n— >oo .
Now if 6 is between and -^ inclusive 6 — t does not exceed
TT
— — ^ which does not exceed cot t.
Hence Vn<l sui'^~'^ t cos t dt or sin'^d/n,
Jo
Vn \Jn < sin" 6l\Jn
which tends to zero when n increases even when 6 = Jtt.
Thus the infinite series given by (3) (4) converge to 6 and
^6^ respectively when 6 is any real angle between + ^tt inclusive.
4. In the series (1) (2) when k is real, if the factor
-nv" (to=1, 2, 3...2W + 1)
is put in the place of k^ — w? in the coefficients of Wan+u kuo,n they
reduce to those of ^3,1+1, v^n in (3) (4). Hence these coefficients
in (1) (2) increase in a less ratio than those in (3) (4), at any rate
when n > ^k.
Also \sm k(e - t)^ k \ < (6 - 1),
so that Un< kvn.
Hence the validity of the infinite expansions (1) (2) follows
when k is real and a real angle between + ^tt inclusive.
5. The above is the elementary case. When k is not real,
but is restricted as before, we can say that
I sin k{0-t)\< k(0- t),
where /c is a finite quantity, but generally is > | ^ | ; then
I W^ I < /CVn.
sin kd, cos kO are expanded in ascending powers of sin 6. 247
The coefficient of Un or ku^ in (1) or (2) is that of Vn in (3)
k^
or (4) multiplied by the product of factors of the form 1 -:
these are known to form a convergent product. Hence the results
are still true when k is imaginary.
6. When 6 is imaginary, tin and Vn may be treated by the
following method, which would also apply if 6 were real.
Un = \ sin A; (^ — t) sec t . sin** t cos tdt
Jo
sin k{d-t) sec t . sin"+i ^/(w + 1)
re (1
s\n''+Hjr{smk{0-t)sect]dt.
71+1
The terms at the limits vanish, and if g is the greatest value
d .
of -^ {sin A; (^ — ^) sec ^ } on the path of integration, which is
finite, we have
provided that | sin 6 \ is the greatest value of | sin t \ on the path
of integration, which may be the straight line from to 0.
Now if 6 = (f) + lyjr, \ sin^ 6 \ = sin" cfj + sinh^ -v/r which increases
with the numerical value of <^ or -yjr, so long as ^ is between + ^tt.
Thus the remainders in the series (1) (2) (3) (4) tend to zero
when ?i— »oo provided that [sin^l^^l and the real part of d is
between + ^tt.
7. It is curious that the coefficient of sin^"+- 6 in (1) tends to
equality with ^n~^ 7r~^k cos ^kir and that of sin^**^ in (2) to
equality with —^n~^ 7r~^A;sin ^kTr.
The expressions (1) (2) may be used to give a proof of the
factorial expressions for the sine and cosine. In (1) (2) put ir
for e. Thus
k(2'-k'')(4^^-k')...(4^n'~-t-)
1 - cos Ajtt = -^ '-^ — ^r--^ ^ ' U^n,
In I
. , (l^-k'^(S'--k'^)...l(2n + iy-kn
sm k.= (2n+l)! ''"-'^
Now when n tends to infinity the elements of Un for which t
is not nearly ^tt may be neglected and thus Un tends to equality
with
sini-A;7r 1 sin" tdt.
I Sll
Jo
248 Prof. Dixon, Expressions for the remainders, etc.
This step is further examined below (§ 8). Thus
sin ^kir or (1 — cos k7r)/2 sin ^kw
is the limit when n—^xi of
k (22 - t) (¥ -k^)... Un^ - k") 1 f . „ ,
I
2n\ 2
k(2''-k')...{4!n'-k'') '7r 1 . 3 . 5 ... (2w - 1)
°^^ 2w! 2" 2.4.6... 2w
Also cos I^JTT or sin ^tt -^ 2 sin :^ kir
is the limit when w— >oo of
(1^ - A;^) (3^ -k')... {(2n + If-Jf} 2 . 4 . 6 . . . 2?i
(2^1 + 1)! ' S.5.7 ...{2n + l)
or of |i_|:Ui_gV fi_. ^'
IV V 3V ■■■ [ (271+1)'
I
8. To justify the statement made as to u^ when w— >oo , take
the difference
Un — sin A- k^r I sin*^ icZ^
Jo
and write tt — i for t in it^. The difference is then
/,
'^ sin kt — smA kir . ^ ^ ^ ,^
^ sm'* t cos ^ a^
cos t
sin A;^ — sin | ^tt sin'^^^^ t
cos i ' 71 + 1
1 /"".„,,, c? sin A;^ — sin 4- A;7r ,,
71 + 1 j ' dt cos i
The terms at the limits vanish, and thus the difference bears
r»r _ h .
to sin" tdt a ratio less than where h is the greatest abso-
J n + \ *=
lute value of -7- — ^ between the limits. Since h is
dt cos i
finite, this proves the statement, unless k is an even integer, in
which case the product expressions for sin ^kir and cos ^kir are
evidently true.
Mr Douglas Rudge, A dust electrical machine. 249
A dust electrical machine. By W. A. Douglas Rudge, M.A.,
St John's College.
[Read 19 May 1913.]
In the course of some work on atmospheric electricity carried
on during the past three years, the author has shown that very
considerable charges of electricity are given to the air during
the raising of dust-clouds, whether by wind blowing over the
surface of the earth, or by the motion of motor cars, etc. along
dusty roads, or in general by raising a dust by any method. The
kind of electrification varied with the nature of the dust itself,
and the magnitude of the charge depended to some extent upon
the fineness of the state of division. During dust-storms, hollow
insulated vessels arranged to catch the dust may be charged to
a potential of some thousands of volts. In a systematic study of
the methods used for raising clouds, and determining the charge
upon the dust particles and upon the air accompanying them, it
was noticed that small sparks could occasionally be obtained
from insulated vessels used to collect the dusts. Some simple
pieces of apparatus have been constructed, by which it is possible
to obtain considerable charges of electricity from the raising of
a dust cloud. As shown in a previous paper* any kind of dust
can be made to \ield charges of electricity, and in the apparatus
to be described, sand, road dust, flour, sulphur, iron filings, etc.
may be employed as the working substance of the machine. The
apparatus may be constructed very simply, but the form shown
in the figure is the most satisfactory.
The machine consists of a chamber A in which the dust is
raised by sending into it a current of air from the bellows. The
dust is carried into the chamber B. This consists of a brass
tube about 25 x 5 cms. insulated from the rest of the apparatus
by an ebonite plug E. The dust escapes through 0. In the
dry African climate, the chamber B can be dispensed with, the
tube leading from A serving as a collector and sparks will fly from
it when a rapid current of dust is passing.
The effects produced by the machine are very remarkable
with dry dust and a dry atmosphere, as the dryness allows of a
very fine state of division of the dust. With an apparatus of
the dimensions shown sparks up to 5 cms. in length have readily
been obtained, aud " brush " discharges will fly from the tube if
the atmospherical conditions are suitable. The air escaping from
* Phil. Mag., April, 1913.
250 Mr Douglas Rudge, A dust electrical Tnachine.
is very strongly charged, readily giving a potential gradient
in a room of several hundred volts per metre. This charge upon
the air is readily detected by aid of an insulated wire tipped
with a radioactive substance, the wire rapidly taking the potential
of the air in its neighbourhood, and if discharged will quickly
become charged again. The air in a room may remain charged
for more than half an hour after the dust has settled, so that it
may be concluded that the air itself is actually charged.
S^
J
air from bellows
The charge acquired by the apparatus has probably a two-
fold origin (1) that due to the raising of the dust, and (2) that
due to friction of the dust particles against the walls of the tube.
At first it appeared as though only one charge was present upon
the dust but recent experiments have shown that both kinds of
electricity are present, one of them however predominating.
Further experiments are now in progress.
Mr Whiddington, On a mechanical vacuum tube regulator. 251
On a mecha7iical vacuum tube regidator. By R. Whiddington,
M.A, St John's College.
[Read 19 May 1913.]
In several of the writer's previous papers mention has been
made of a particular form of vacuum tube regulator. It is the
object of this short paper to give a few experiments in connection
with this device which not only serve to indicate the range of its
usefulness but may perhaps help to throw a little light on its
mode of action.
The usual method of altering the hardness of a vacuum tube
is to vary the gas pressure within the tube. Under ordinary
circumstances a diminution of pressure produces a hardening
effect, or in other words the lower the pressure the faster the
cathode rays shot off from the cathode — the more difficult it is
to force current through the tube. This is only true however
when the gas pressure is below a certain amount depending on
the dimensions of the tube and its electrodes.
Winkelmann appears to have been one of the first to recognise
the fact that the size, form, and position of the cathode in a
discharge tube exerted a profound effect on the discharge. He
found that it was possible by using tubes of small dimensions
with the cathode in a confined space to produce quite fast cathode
rays even when the pressure within the tube was as high as
several mms. of mercury.
Of the many mechanical regulators based on this effect in-
vestigated by Winkelmann and others, perhaps the most useful
is the one in which a sliding glass tube tightly fitting the cathode
slides in and out, the position of this sheath determining largely
the velocity of the rays. It is possible in this way to produce
very considerable variations in the speed of cathode rays without
in any way altering the gas pressure. This device was first
described by Campbell S win ton and later by Wehnelt in 1903.
There are many possible methods of varying the position of the
sheath and one of the most convenient is to attach a small piece
of iron to the sheath and influence it from without by a magnet.
In this kind of way the sheath may be instantly adjusted to any
desired point, the further the sheath is outdrawn the faster the
cathode rays emitted from the cathode.
The graph gives some idea of the range of hardness to be
expected from a tube fitted with such a regulator. The tube in
this case was a litre bulb fitted with a cathode 1*5 cm. in diameter
252 Mr Whiddington, On a mechanical vacuum tube regulator.
mounted so as to project well within the bulb. The glass sheath
was closely fitting and was controlled magnetically. It is im-
portant to select the glass sheath so that it is entirely free from
air lines as otherwise the discharge passes along the lines and the
tube runs unsteadily. The tube was evacuated to a convenient
point and driven by a Mercedes influence machine which proved
a fairly steady source of current, the voltage across the tube being
measured by a Braun electrostatic voltmeter. In the graph the
abscissae represent lengths of sheath outdrawn while the cor-
responding ordinates are the corresponding voltages across the
tube. The pressure of gas within the tube was maintained con-
stant throughout the experiment. Accurate readings could not
Length of Sheath (in mms.)
(Diameter of Cathode = 15 mms.)
be continued above 10,000 volts with the voltmeter but an
equivalent spark gap indicated that the tube at its hardest was
working at about 40,000 volts, beyond this point the tube became
very unsteady in action.
It is noteworthy that beyond the point P on the graph the
curve rises far more steeply. Observations carried out to above
10,000 volts with a spark gap indicate that the curve continues
practically straight up to about 30,000 volts.
It seems very difficult, if indeed it is at present possible, to
give an adequate explanation of the action of the sheath. This
is a difficulty common to very many problems in connection with
discharge tubes. What I propose to do then is to give a brief
J/r Whiddington, On a mechanical vacuum tube regidator. 253
account of a few experiments with the regulator which suggest
one explanation and then to point out the complications which
stand in the way of its complete acceptance.
The tube with which the following experiments were carried
out was coil driven with a Lodge rectifier in series to prevent
reversal of the current.
(1) When a vacuum tube is hardened by diminishiug the gas
pressure the hollow cylindrical cathode beam becomes more con-
centrated about its axis, which in the case of a circular plane
disc cathode passes normally through the centre ; at the same
time the dark space lengthens out receding from the cathode.
This further is exactly what happens when the sheath is drawn
out over the cathode at a constant gas pressure, the cathode
beam narrows down — a smaller part of the cathode functions —
and the dark space lengthens out. If the pressure be not too
low the sheath as it is caused to travel out may ultimately over-
take the boundary of the dark space which is also travelling but
at a slower pace. The interesting point to notice is that when
once the sheath has overtaken the dark space boundary and is
projecting into it no additional hardening effect can be produced
by further drawing out the sheath.
(2) If the sheath is not too heavy and is running easily it
will travel out of itself when the discharge is passing — in fact it
may be made to rise against gravity if the tube be tilted so that
the cathode points slightly upwards. If now the Lodge rectifier
be cut out the coil may partly reverse and produce a spot of
positive column on the cathode, if this happen the sheath will
commence to slide back again to its original position the tube
at the same time becoming softer. On switching in the rectifier
again the sheath once more slides out and the tube hardens. It
is sometimes necessary to tap the tube to get these mechanical
effects but usually the vibration set up by the coil is sufficient
to ensure easy movement.
(3) The effects described in both the above experiments can
be obtained if the inside of the sheath is lightly silvered, not
heavily enough to introduce the complications of an additional
discharge but heavily enough to ensure that the sheath is at the
same or nearly the same potential as the cathode itself.
(4) If the sheath be cut longitudinally into halves and only
one half is used, the cathode beam is apparently repelled from
the sheath, the rays pursuing a curved path when in the neigh-
bourhood of the glass and proceeding in straight lines when
beyond its influence.
These experiments taken alone without further evidence lead
to the very natural conclusion that the sheath being negatively
charged on the inside repels the cathode rays towards the centre
VOL. XVII. PT. III. 17
254 Mr Wliiddington, On a mechanical vacuum tube regulator.
on being drawn out thus increasing the resistance of the tube.
Bat even this apparently simple statement becomes complicated
when we remember that the cathode beam is travelling in a
strongly ionised gaseous layer so that the individual particles
will be shielded from electrostatic action in some directions more
than in others. It seems obvious in fact that any individual
particle in the stream will only be repelled by the nearer portions
of the charged sheath. No mere electrostatic explanation how-
ever can be sufficient for the system under consideration is not
in electrical equilibrium.
Now the generally accepted theory of the discharge tube has
it that the cathode and positive rays are inseparably connected.
The cathode rays in their passage through the gas produce positive
ions which move towards the cathode thus becoming the positive
rays. When these positive rays strike the cathode they liberate
electrons which shoot off under the electric force at the cathode
and become cathode rays and the process is repeated so long as
the potential difference between cathode and anode is maintained.
The difficulty now arising is that if the sheath repels the negative
rays towards the axis of the discharge it should also attract the
positive rays outwards away from the axis. Unfortunately there
is not sufficient data as to the velocity of these positive rays
at different distances from the cathode for the question to be
discussed quantitatively, but it is important to notice that the
positive rays will always be under the action of the sheath for
a very short distance for they acquire their velocity a short
distance from the cathode and in any case a positive ray is not
so long lived as a cathode ray owing to the ease with which it
may become an uncharged atom by recombination. It would not
be surprising therefore if the effect of the sheath on the cathode
rays swamped the opposite effect on the positive rays. It is
possible that this is the explanation of the sudden rise in the
curve at P in the graph.
To summarize in conclusion the more obvious complicating
effects which must be taken into account when attempting an
explanation of this hardening action :
(1) The electrostatic screening action of the cathode beam.
(2) The similar screening action of the positive bundle
which surrounds the cathode beam.
(3) The attraction which must exist between the positive
and negative streams.
3Ir Moss, Some Plants new to the British Isles. 255
Some Plants new to the British Isles. By C. E. Moss, B.A.,
Emmanuel College.
[Bead 28 April 1913.]
The following plants were briefly described and their geo-
graphical distribution indicated :
Alnus glutinosa.
(a) var. macroca7"pa. Chippenham Fen, Cambridgeshire.
(h) var. typica (comb, nov.; ined.). The common form of
the alder in southern England.
(c) var. microcarpa. The common form of the alder in
northern England and in Scotland.
Ranunculus ficariceformis. Jersey, first found by Mr S, Guiton,
and specimens sent to me by Mr E. W. Hunnybun.
Cheiranthus cheiri.
(a) var. hortensis (var. nov.; ined.). The cultivated form
of the wallflower, and the one commonly occurring as a garden
escape on old walls and sea-cliffs.
(b) var. fruticulosus. Perhaps the wild form of the wall-
flower. Hare, on old walls, e.g., Jersey.
(c) var. angustior (var. nov.; ined.). Closely allied to var.
fruticulosus. Walls, Pevensey Castle, Sussex.
Arenaria trinervis.
(a) var. typica (var. nov.; ined.). The common form in
Cambridgeshire.
(6) var. pentandra. Devonshire, Surrey.
Primula veris var. suaveolens. Suffolk and Cambridgeshire.
P. scotica var. orkniensis (var. nov.; ined.). First found by
Mr Grant, of Orkney, and the characters of the fruit first elucidated
by Mr E. W. Hunnybun.
Brunella laciniata x vulgaris. Hertfordshire, Cambridgeshire,
Somerset.
Gymnadenia wahlenbergi. Cambridgeshire.
G. densiflora. In Herb. Babington, from Cambridgeshire.
17—2
256 Mr Hamshaw Thomas, On some new and i'are
On some new and rare Jurassic plants from Yorkshire: —
Eretmophyllum, a new type of Ginkgoalian leaf. By H. Hamshaw
Thomas, M.A., Downing College. Curator of the Botanical
Museum, Cambridge.
[Read 28 April 1913.]
[Plates VI and VII.]
In the well-known Gristhorpe plant-bed, a number of isolated
leaves occur, belonging to a type which has not been previously
recognised. The plant-bed belongs to part of the Middle Estuarine
Series of the Middle Jurassic and is exposed on the shore at the
adjacent ends of Gristhorpe and Cayton Bays near Scarborough.
I found most of my specimens in Cayton Bay, where they
are locally plentiful. Two or three portions of leaves which
appear to be closely allied to the Cayton forms have also been
obtained from the Lower Estuarine beds at Whitby and though
these exhibit some differences they may well be included in the
same genus. All the leaves are beautifully preserved in shale,
they were originally of firm texture and they can be readily
detached from the shale, though the detached leaf is brittle and
is easily broken into pieces. The examples shown in figs. 1 and 2
PI. VI. were detached from the rock, gummed on to glass and
photographed by transmitted light.
Description.
The leaves from the Gristhorpe bed, which I propose to call
Eretmophyllum* pubescens, vary somewhat in shape but are usually
oblanceolate sometimes becoming almost linear. They may be
straight but are often slightly falcately curved or at least un-
symmetrical with one margin straight and the other curved
(cf. figs. 1 and 2), They are broadest towards the apex and taper
gradually towards the base, the lamina passing mto a broad
petiole of varying length. The leaves differ somewhat in size ;
of the few complete examples the smaller are about 7 cms. long
and 1 cm. broad, the larger 10 cms. long and about 2*5 cms. broad.
Fragments of leaves more than 3 cms. broad have been found,
which, when complete, may have exceeded a length of 10 cms.
The average leaf is about 1*7 cms. broad and 9*5 cms. long,
* From epeTpLov = an oar or paddle and (pvWoi' — a leaf. I am indebted to Mibs W.
M. L. Hutchinson for suggesting this name.
Jurassic plants from Yorkshire, etc. 25*7
includiag the petiole which measures from 1—3 cms. The margins
of the lamina are entire and the apex either bluntly rounded or
somewhat retuse (cf. fig. 2), in the latter case the apical notch is
obliquely placed. Towards the base of the lamina the margins
are frequently thickened on one face, the thickened portions
passing into the petiole in the way usually seen in the leaves of
the recent Ginkgo hiloha. The petiole is somewhat expanded at
its base.
The venation is usually very distinct. Two or three veins
coming up from the petiole become distinguishable at the base
of the lamina and soon dichotomise several times, the resulting
divisions run parallel to each other through most of the length
of the leaf (fig. 1), though in the more obovate forms they may
again fork occasionally. Near the apex the veins converge some-
what. The veins are large and widely separated ; they are from
1 mm. to 1"5 mm. apart. In a leaf of average size 13 veins occur
in a width of 16 mm. Some of the leaves are now in a peculiar
brown translucent condition and their veins can be often seen
under the microscope to consist of a number of fine parallel dark
strands, no doubt representing the original xylem or sclerenchyma
strands.
Between the veins in some of the larger specimens a row of
small spots or short lines may be observed which are visible to
the naked eye and are 2 — 3 mm. apart. These are the secretory
tracts which are seen in the corresponding position in recent
Ginkgo leaves, which have been figured in the Jurassic Ginkgo
Ohrutschewi by Prof Seward* and which I found to be present
in some Ginkgo leaves from the Yorkshire Jurassic collected by
Prof. Nathorst and now in the Stockholm Museum. When the
leaves are macerated, these little secretory tracts yield small
groups of cell-like structures which resist the action of the acid
and might in some circumstances be taken for groups of spores.
The Gidicular Structure.
As is usually the case with stout leaves that separate readily
from the matrix, the present specimens yield excellent cuticular
preparations in which the outlines of the epidermal cells and the
stomatal openings are clearly seen. In E. pubescens the upper
and lower cuticles are very distinct. The upper epidermis was
composed of more or less uniform cells and was devoid of stomata.
The cells were irregularly angular or polygonal in shape, becoming
somewhat elongated above the veins. Their walls, which are
usually straight, sometimes show the slight undulations of the
* Seward (11), p. 46, PL iv. figs. 42, 43.
258 Mr Hamshaw Thomas, On some new and rare
I
type seen in some receat Ginkgo leaves. In the centre of each
cell is a short but conspicuous papilla (cf. fig. 4) and the presence
of these structures gives to the cuticle a very characteristic
appearance.
On the cuticle from the lower epidermis, the papillae are still
more marked (fig. 3); the epidermal cells were again irregularly
polygonal in shape. In these preparations we see the stomata
very clearly, they are confined to the areas between the veins.
The stomata are arranged in irregular rows and are easily dis-
tinguishable on account of the thickened subsidiary cells. The
guard cells do not seem to have been thickened and were somewhat
sunken, their outlines are now only indistinctly seen. Above and
around them lie the subsidiary cells (fig. 5) four to seven in
number, regularly arranged and with clearly defined walls ; they
are more or less uniformly thickened and sometimes possess small
papillae, they show more clearly after staining with Fuchsine.
These stomatal structures show close resemblance to those of
other Jurassic leaves allied to Ginkgo, and also to the stomata of
the pi'esent-day leaves of this form*; the recent stomata, how-
ever, are less deeply sunken and not so much covered by the
subsidiary cells.
The Whitby specimens.
In one of the plant beds on the Scar at Whitby I have found
several portions of leaves which seem to belong to this gonus.
The largest piece is about 7 cms. long, 12 mm. broad and slightly
falcate ; though neither end is seen, it tapers slightly above and
below. Another well-preserved fragment belonged to a some-
what broader leaf. The veins in these examples are about 1 mm.
apart but do not clearly show any forking; a portion of one
margin is slightly thickened as near the base of E. puhescens;
secretory tracts have not yet been observed. The leaves were
again stout and can be readily detached from the matrix. The
epidermal structure of this form, which I propose to call E. Whit-
hiense, differs considerably from that of E. puhescens. When
viewed under the binocular microscope, the upper surface is seen
to be rough, the individual cells being more or less visible as
convex projections. The areas above the veins are distinguishable
by their more elongated cells but in addition to these, interstitial
strands of elongated cells are seen between the veins, which
sometimes appear to anastomose with each other, and may have
corresponded with thickened hypoderm strands or small veins.
* Cf. Seward (11), PI. v. figs. 59-62.
Jurassic plants from Yorkshire, etc. 259
Similar interstitial strands have been recorded in Ginkgodium
by Yokoyaraa* and in some Baierasf,
The cnticnlar preparations made from the leaves of this species
are generally somewhat thicker than those from E.puhescens. The
cells of the upper epidermis were strongly cuticularised above the
veins and somewhat elongated (cf. PI. Vil. fig. 8), while the areas
between the veins were composed of more rounded cells with a
convex outer surface ; in this region stomata are frequently seen
(fig. 9,5^), which are much smaller than those on the lower epidermis.
The distinction between the cells above and between the veins is
much greater than in the Gristhorpe specimens. The lower
epidermis consists of fairly uniform squarish or hexagonal cells
all considerably thickened (fig. 6). The stomata are seen in the
areas between the veins but are smaller and fewer in number
than in E. pubescens, they show five or six subsidiary cells of the
same type as in that species (fig. 7), and these sonietimes possess
small papillate projections though they are not specially thickened.
The guard cells were sunken, being just visible through the pore
in the centre of the overarching subsidiary cells.
It will be seen from the foregoing description that the Whitby
and Gristhorpe specimens exhibit some well-marked differences,
chiefly in cuticular structure, but also in external appearance in
well-preserved specimens. The resemblances and differences may
be summarised as follows.
Eretmophyllum gen. nov.
Leaves oblanceolate to linear tapering into a distinct petiole.
Apices rotmded or retuse. Veins distant, dichotomising near base
of lamina and more or less parallel above, slightly convergent near
apex. Epidermal cells more or less rectangular or polygonal.
Stomata with group of angular subsidiary cells regularly arranged
round and above the guard cells.
Eretmophyllum pubescens sp. nov.
Surface of leaves appearing more or less smooth. No inter-
stitial veins or strands. Secretory tracts present between the
veins. Epidermal cells of upper surface uniform, without stomata.
Cells of upper and lower epidermis with short papillae. Stomata
numerous on lower side of leaf.
Eretmophyllum Whitbiense sp. nov.
Upper surface of leaves rough. Interstitial veins or strands
present between the veins. Cells of upper surface elongated
* Yokoyama (89), PI. vm. figs. 1, \a, 14, 14 «.
t Krasser (05), p. 24.
260 Mr Hamshaw Thomas, On some new and rare
above the veins, stomata present in areas between the veins.
Papillae absent. Lower epidermis smooth. Papillae only on
subsidiary cells of stomata. Stomata small and not very
numerous.
Relationship with other forms.
The genus Eretmophyllum, as has been already .mentioned,
possesses a number of" features in common with the leaves of
Ginkgo and must undoubtedly be classed among the Ginkgoales.
The points of resemblance may be here summarised. Leaves
broadest towards the apex, the lamina merging gradually into
the petiole at the base, apical portion sometimes with a notch.
Margins of the leaf thickened at the base. Veins distant, dicho-
tomising. Secretory tracts between the veins. Epidermal cells
rectangular or polygonal, their walls sometimes slightly sinuous.
Stomata with sunken guard cells surrounded by five to seven
somewhat thickened subsidiary cells arranged in a regular radial
series.
The leaves differ from those of Ginkgo in being oblanceolate
or linear, but approach those of Ginkgodium in outline. Many
examples of the latter have been figured by Yokoyama* and I
have also described specimens from South Russia "f^ which may be
referred to the same genus. Ginkgodium, however, is distinct in
possessing shorter and comparatively broader leaves often deeply
divided at the apex. A much more impoitant distinction is seen
in its nervation, the veins being fine, very numerous and parallel
instead of spreading, they occasionally fork but do not converge
at the base of the leaf, apparently springing from the thickened
margin; interstitial nerves occur, but the venation is entirely
different in character from that of the present genus.
Li their form, their slightly falcate shape, and to some extent
in their nervation, my leaves resemble those of Feildenia described
by Heer| from the Miocene of Grinnell Land. The leaves of this
genus, however, differ considerably from mine in their smaller size,
closer venation and less distinct petiole. Feildenia Mossiana Hi*,
in its more ovate shape and coarser venation is the most com-
parable, but the curious convergence of the veins at the apex (if
correctly figured) is very distinct. The veins in Eretmophyllum
usually converge somewhat at the apex but never join in any
way resembling Heer's f]gure|.
Fontainell has figured a leaf of somewhat similar character to
* Yokoyama (89), p. 56, PI. ii. fig. 4c, m. 7, viii., ix. 1—10, xn, 14, 15.
•'- Thomas (11), PI. iv. figs. 9—11.
+ Heer (78), p. 21, PL i. figs. 3—11, viii. 2a, 3a, 4, 5.
§ Idem, PL viii. figs. 2a, 3a, 4.
II Fontaine (89), PL lxxxv. figs. 6, 5a.
Jurassic plants from Yorkshire, etc. 261
F. Mossiana from the Potomac beds of Virginia, with veins which
fork in the lower part of the leaf, then run parallel and near
the apex converge and join up on a central line. This type may
be perhaps related to the Yorkshire form but the peculiar course
of the veins at the apex, which according to Fontaine is clearly
seen, is quite a distinguishing feature.
The only leaf bearing a close relationship to those before us,
which I have found already figured, is the form recently described
by Prof. Seward* from Afghanistan under the name of Pot^o^a-
mites Saighanensis. This leaf had a similar form and size to some
of our examples, with a well-defined petiole and parallel veins
1 mm. apart, which branched near the petiole and converged
slightly near the apex.
In referring this form to Podozamites, Prof. Seward pointed
out that it could be compared with the leaves of Ginkgoales
especially with the Oinkgodium type. It is extremely probable
that this leaf should be placed in the genus Eretmophyllum, though
until more material is forthcoming it is impossible to determine
whether it is specifically as well as generically identical with
either of the Yorkshire species.
It probably provides another example of a Jurassic genus
with very discontinuous distribution.
Among the numerous examples of Podozamites which have
been figured, a few show some slight resemblance to our present
form, but none show the gradual narrowing of the lamina into a
distinct petiole. Some of the examples of P. lanceolatus possess
similar nervation and a small petiolef. The sporophylls recently
described by Nathorst| as Cycadocarpidium Swabii possess
distant veins which fork near the base of the lamina and thus
allow of a somewhat limited comparison.
A comparison may also be made with the isolated leaves
figured by Fontaine§ from Cape Lisburne, Alaska, under the name
oiNageiopsis longifolia ? Font., but which according to Berry |1 are
in nowise related to Migeiopsis. Fontaine's figure 5 might possibly
be an Eretmophyllum leaf figured upside down, and the shape
of the other fragments, their distant veins almost parallel but
sometimes forking, present some points of similarity.
It seems then that we are justified in regarding these York-
shire leaves as types of a new genus of Ginkgoalian plants, which
f(^rm a connecting link between Ginkgo or rather Oinkgodium
and Feildenia or Phoenicopsis (if indeed these latter genera are
members of the Ginkgoalian alliance).
* Seward, (12), p. 35, PI. iv. fig. 53.
t Heer (77), PL xxvii. figs. 3, 4, 5c.
X Nathorst (11), p. 5, PI. i. figs. 11—15.
§ Fontaine in Ward (05), PI. xlv, fig. 1—5.
II Berry, (10), p. 190.
262 Mr Hamshaw Thomas, On some new and rare Jurassic plants.
REFERENCES.
Berry, E. W. (10). " A Revision of the Fossil Plants of the genus Nagdopsis
of Fontaine." Proc. U.S. Nat. Mits. vol. 38, p. 185.
Fontaine, W. M. (89). " The Potomac or Younger Mesozoic Flora." Rep.
U.S. Geol. Survey, 1889.
Hber, 0. (77). " Beitr. zur Jura Flora Ostsibiriens und des Amurlandes, I."
Flor. Foss. Arct. Bd. iv. pt. 2.
Heer, O. (78). "Die Miocene Flora des Grinnell-Landes." Idem, Bd. v.
pt. 1.
Krasser, F. (05). " Fossile Pflanzen aus Transbaikalien, Der Mongolei und
Mandschurei." Denk. Nat. Naturw. Kl. der K. Akad. Wien, Bd. Lxxviir.
Nathorst, a. G. (11). " Palaobotanische Mitteilungen No. 10." K. Svenska
Vet. Akad. Hand. Bd. 46, No. 8.
Seward, A. C. (11). "Jurassic Plants from Chinese Dzungaria." Mem.
Com. Geol. St Petershourg, Liv. 75.
Seward, A. C. (12). "Mesozoic Plants from Afghanistan and Afghan-
Turkestan." Mem. Geol. Sur. hid. Palaeontologica Indica, N.S. vol. iv.
No. 4. Calcutta.
Thomas, II. Hamshaw (11). "The Jurassic Flora of Kamenka." Mem. Com.
Geol. St Petershourg, N.S. Liv. 71.
Ward, L. F. (05). " Status of the Mesozoic Floras of the United Stiites."
Rep. U.S. Geol. Survey, 1905.
YoKOYAMA, M. (89). "Jurassic Plants from Kaga, Hida and Echizen." Jown.
Coll. Sci. Univ. Japan, vol. iii. pt. 1.
DESCRIPTION OF FIGURES.
Plate VI. E. puhescens.
Fig. 1. Upper portion of a leaf of average size showing parallel
venation, secretory tracts and shape of apex. Reduced to fths.
Fig. 2. Almost complete small leaf showing unsymmetrical shape,
retuse apex and forking venation. Like fig, 1 this photo was taken,
by transmitted light, of the actual leaf which had been removed from
the rock, x |-.
Fig. 3. Cuticle of lower epidermis showing stomata and papillate
cells. X 40.
Fig. 4, Cuticle of upper epidermis showing papillae and slightly
sinuous walls of cells, x 150.
Fig. 5. Cuticle of lower epidermis showing stomata with thickened
subsidiary cells, x 150.
Plate VII. E. Wkitbiense.
Fig. 6. Cuticle of lower epidermis, x 40.
Fig. 7. Part of the same more highly magnified, showing stomata
with surrounding subsidiary cells, x 150.
Fig. 8. Cuticle of upper epidermis showing rows of elongated
cells above veins or hypodermal strands, x 40.
Fig. 9. Part of the same more highly magnified, showing thickened
elongated cells above a vein and thinner portion with stomata (.s^).
xl50.
Phil. Soc. Proc. Vol. xvil. Pt iii.
Plate VI.
*/^ ^ %
♦ %i*
f
:if^
'% *♦ ' .
"1' :->".:t.--*:.Mi:ifJ
. V. .ti2k;'>S^::*:>K7li>l*i^*
J?. H. T. phot.
EEETMOPHYLLUM PUBESCENS.
Phil. Soc. Proc. Vol. xvir. Pt iii.
Plate VII.
H. H. T. phot.
ERETMOPHYLLUM WHITBIENSE.
Mr Kleeman, The Uiistable Nature of the Ion in a Gas. 263
The Unstable Nature of the Ion in a Gas. By R. D. Kleeman,
D.Sc. (Adelaide), B.A., Emmanuel College.
[Bead 19 May 1913.]
Theoretical considerations.
The ions in a gas are usually assumed to be stable at constant
temperature. The writer has pointed out*, however, that it follows
from thermodynamical considerations that this can by no means
be the case. It is shown that an ion cluster should be continually
changing in complexity, the changes being governed by the same
laws as chemical dissociation, namely by the laws of thermo-
dynamics and the law of mass-action.
Some of the principal deductions made in the paper quoted
will be mentioned here as an introduction to the experiments
described in this paper. If Vq denote the velocity of a free ion,
Vi that of a cluster formed by the elementary ion and a molecule,
^2 that of a cluster formed by the elementary ion and two molecules,
and so on, and Cq, Cj, Ca, ... denote respectively the concentrations
of the ion clusters and the elementary ions, then the average
velocity V, the quantity^ measured in practice, is given by
Tr / C, Co
C(\ Co / 1 I Ci , ^2
Cn Cn
This equation may also be written
- f^ (IT - {—' dT
f^ dT
where H^ denotes the energy of formation of a chister 1 from an
elementary ion and a neutral molecule at the temperatiu'e T,
i/2 the energy of formation of a cluster 2 from an elementary ion
and two neutral molecules, and so on, and J.,, A^, ... are constants
which depend only on the nature of the gas.
From considerations based upon the kinetic theory of gases it
follows that the velocity of a stable cluster in a gas must depend
on its mass, and decrease with an increase of its mass. The result
obtained by Blanc and Wellischf that the velocity of an ion in a
gas does not depend much on the nature of the molecule from
* Proc. Camh. Phil. Hoc. vol. xvi. pt. iv. p. 285.
t C. R. cxLvii. July 1908, pp. 39—42 ; Proc. Roy. Soc. Ser. A, lxxxii. July 31,
1909, pp. 500—517.
264 Mr Kleeman, The Unstable Nature of the Ion in a Gas.
which it is derived may therefore be explained by the ion duster
continually changing in complexity, the effect of which might be
to produce approximately the same average velocity in each case.
The ions made in a gas are initially elementary ions, and a
certain time must therefore elapse after their production before
all the possible kinds of clusters are formed and they are in equi-
librium with one another. Therefore if the ionic velocity of freshlj^
made ions is measured over a distance of such magnitude that all
the possible clusters have not time to form, the velocity will be
greater than that obtained over much larger distances. Moreover,
the velocity will depend on the magnitude of the electric field
applied. By means of this result the increase of the ionic velocity
greater than inversely proportional to the pressure of the gas at
low pressures was explained.
Experiments on the lonisation by Collision with Positive Ions.
In the experiments on ionisation by collision the initial ionisa-
tion usually takes place in the powerful electric field in which
new ions are produced by collision. The elementary ions are then
seized upon by the electric field before they have time to attach
themselves to neutral molecules, and given a velocity sufficiently
large that ions by collision are produced, after which their chance
of attaching themselves to neutral molecules is small. Therefore
if the initial ions are made in a weak electric field so that they
have a chance of forming clusters, and they are then drawn into
the powerful field, we should expect that results would be obtained
which differ in many respects from those obtained in the former
case. The writer has carried out a set of experiments of this
nature*. Fig. 1 indicates the experimental arrangement used,
-d is a plate connected to an electrometer, and B a wire gauze at
a distance "5 cm. from the plate. The chamber C, which was in
electrical connection with the gauze, was connected with a battery
of cells. Ions were made in the part a of the chamber and drawn
through the gauze by the weak field existing between gauze and
chamber due to some of the lines of force which end on the plate
threading through the gauze on to the chamber wall. Negative
or positive ions were drawn through the gauze accordingly as the
chamber was raised to a negative or positive potential. It was
found that the admixture of a gas to a gas of a different kind
produced an effect which could only be explained by the nature
of the positive ion depending on the nature of the atom or mole-
cule from which it is produced. This result is of importance
* Proc. Camb. Phil. Soc. vol. xvi. pt. 7, p. 621.
Note. In the figures of this paper containing curves read 200 volts per division
instead of 40, the small divisions not having come out in the photographs.
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 265
in connexion with experiments on the nature of the ions in a
discharge tube. It is found that hydrogen atoms and molecules
positively charged are always present in the tube, and their
apparent number may even be increased by the addition of a gas
whose molecules do not contain hydrogen. At first sight this
would seem to indicate that the nature of the positive ion is
independent of the nature of the atom from which it is produced.
But this explanation is not conclusive, since the increase in the
number of hydrogen atoms can also be explained therraodynaraic-
ally. Hydrogen is always given off by the electrodes in the tube
due to the discharge, and is therefore always initially present.
Evidence was also obtained that a molecule when ionised is
sometimes split into its constituent atoms.
<x
Fig. 1.
Experiments on the lonisation by Collision with Negative Ions.
Further experiments were carried out along the same lines,
especially with the negative ions, which will be described in this
paper. For the experimental details (the same apparatus as before
was used) the reader must consult the paper quoted.
Fig. 2 shows two curves obtained with negative ions when
ether vapour was in the chamber. The curve A was obtained
with the ions drawn through the gauze from the space adjacent
to its lower side. The curve B was obtained after placing a
quantity of radium near the chamber, in which case additional
initial ions were made in the space between the gauze and plate
by the 7 rays of the radium. These ions are not given an oppor-
tunity of forming clusters. In the latter case the curve should
be situated nearer to the zero than in the former, because in that
case we are dealing with a larger amount of initial ionisation.
That this must be so will at once be seen on doubling all the
ordinates of the curve A, which amounts to doubling the number
266 il^/r Kleeman, The Unstable Nature of the Ion in a Gas.
of ions drawn through the gauze. It will be seen that the curve
B is nearer to the zero than the curve A, as required. But the
difference in position is much greater than warranted by the
increase of the initial ionisation on bringing the radium near
the chamber, which is very small since' the curves almost coincide
for small fields. It follows therefore that only a small proportion
of the ions drawn through the gauze are in a state fit for the
production of ions by collision, or the proportion of free ions to
clusters is small in a number of ions in equilibrium in ether.
The following vapours were also examined in this way: ethyl
propionate, methyl butyrate, acetylene, hydrogen, oxygen, nitrous
oxide, carbon dioxide, air, carbon tetrachloride, ethyl chloride,
chloroform, pentane, benzene, hexane, aldehyde, methyl formate.
/•
1
A
/
/
J
/
-
»=J
^"^
— — -
200 400 600 800 1000 1200 1400
Volts per cm.
Fig. 2.
methyl bromide, methyl iodide, ethyl bromide, ethyl iodide, and
carbon disulphide. The results obtained could to a certain extent
be compared with one another, as will be explained. From the
theory of clustering referred to at; the beginning of the paper it
follows that the number of free ions to clusters is independent of
the pressure of the gas. The writer* has shown that the relative
ionisation in gases whose molecules do not contain atoms of higher
atomic weight than that of the chlorine atom is the same for 7
and a rays, and in the case of the other gases the ionisation is
greater in the latter case than in the former, but the ratio is
always less than two. The initial numbers of free ions introduced
by the 7 and a rays respectively are therefore always proportional
* Vroc. Rmj. Soc. A, vol. lxxix. p. 220, 1907.
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 267
to one another in the case of the former gases. It follows there-
fore that the ratio of the abscissae of two points one on each of
the steep part of two curves of the type A and B corresponding
to a common ordinate, should be approximately independent of
the pressure of the gas. This was found to be the case. We may
therefore as a first approximation take this ratio as a relative
measure of the proportion of free ions to clusters in a gas. It was
found that in the majority of the gases mentioned this ratio was
approximately the same as that obtained with ether. The gases
which showed a considerable deviation from this were carbon
tetrachloride, carbon disulphide, benzene, air, oxygen, chloroform,
and hydrogen, whose ratios were coUvsiderably greater than the
ratio obtained with ether. Especially was this the case with
carbon tetrachloride, carbon disulphide, and benzene ; for these
three gases the curves obtained almost coincided with one another.
It follows therefore that the proportion of free ions to clusters in
these particular gases is considerably greater than in the case of
the other gases in which the relative ionisation for 7 rays is the
same as for a rays.
The separation of the curves obtained with the gases con-
taining bromine and iodine atoms in their molecules was about
the same as that obtained with ether. This separation is in part
due to the greater relative ionisation of these gases with 7 rays
than with a rays. But the difference in ionisation accounted only
for a small part of the separation. We may therefore conclude
that these gases fall into line with the majority of the other gases.
It will be of interest here to consider theoretically the be-
haviour of ion clusters in gaseous mixtures. In one of the papers
quoted it is shown that Cn = tnUn, where c„ denotes the concentra-
tion of the ion clusters of the type n, tn the period of life of a
cluster, iin the number of clusters changing into other clusters
per second. Now the quantities tn and iin depend directly on
the nature of the collision between a cluster and the surrounding
molecules. Thus when a cluster collides with a molecule the
latter will have a dissolving or dissociating action upon the cluster
due to electrostatic induction, chemical attraction, etc., apart from
the kinematical effect of the collision. Therefore when two gases
are mixed the ratio of free ions to clusters is not likely to be the
mean of the ratios of the constituent gases, but may be much
greater or much smaller, even if no new kinds of clusters are
formed after mixture of the gases. Thus the behaviour of a
mixture of gases can hardly be predicted from that of its con-
stituents. If new kinds of clusters are formed after mixture of the
gases, matters are still further complicated, and we may be quite
sure then that the ratio is different from the mean of the ratios of
the constituent gases.
268 Mr Kleeman, The Unstable Nature of the Ion in a Gas.
Some experiments by Latty, Frank, and Townsend on the
velocity and diffusion of ions have a bearing on the clustering
effect under consideration. Thus Latty* found that the velocity
of the negative ion in air specially dried is much greater than that
usually observed. Moreover, the velocity did not vary inversely as
the pressure of the air under these circumstances. For example,
a velocity of 173 cm. per second was obtained for the negative ion
in air at a pressure of 10 mm. of mercury on applying an electric
force of "5 volt per cm., which is about 100 times the velocity
obtained under ordinary conditions. On increasing the electric
field to "9 volt per cm. the velocity rose to 1845 cm. per second.
It appears therefore that a cluster in air composed of an elementary
ion and water and possibly air molecules, is much more stable
than when the cluster is composed of air molecules only.
Frankf found that the velocity of a negative ion in carefully
purified argon is 206"3 cm. per second, but that it falls to 1*7 cm.
per second on adding about one per cent, of oxygen. A cluster in
argon composed of argon molecules only is thus very unstable and
has a correspondingly short period of life, but its stability is
greatly increased when oxygen molecules enter into its com-
position.
Townsend :|: found that when a gas has been subjected to a
drying process for several days the rate of diffusion of the negative
ions greatly increases, and does not obey the ordinary laws of
diffusion. The effect seems to be greater with Hg than with O2,
and much greater with these gases than with CO2. A cluster in
CO2 composed of an elementary negative ion and CO2 molecules
thus seems to be comparatively stable.
When the ions are drawn through the gauze (see fig. 1) in
experiments of the nature described in a previous part of the
paper, a certain fraction (which may have any value lying between
unity and — ) should be, as we have seen, in the elementary state,
and thus be in a state fit for the production of ionisation by
collision if the electric field be sufficiently large. Further ions
become elementary on their passage from the gauze to the plate,
and the number of initial ions available for the production of
ionisation by collision is thus increased. It will be of importance
therefore to obtain a formula for the current observed under these
conditions when the field is sufficiently large to produce fresh ions
by collision of ions. The case when fresh ions are produced by
collision of the negative ions only will be considered first.
Let K denote the total number of ions drawn through the
* Proc. Roy. Soc. A, vol. lxxxiv. 1910.
t Verh. d. Deut. Phys. Gesell. March, 1910, pp. 291—298.
X Proc. Roy. Soc. A, vol. lxxxv. pp. 25—29, 1911.
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 269
gauze of which k^ are elementary negative ions and k^ chisters of
various complexities, and thus K = k^-\- k^. The quantity K can
be measured directly. The elementary ions give rise to a current
A^ie'" by collision with neutral molecules*, where I denotes the
distance between gauze and plate, and a the number of fresh ions
produced by a negative ion per cm. of its path.
There is an additional current produced by some of the clusters
becoming elementary ions during their passage from gauze to
plate. Let N denote the number of clusters in a c.c. at a distance
dJSf
X from the plate. We then have dc = — -7^ . dec . e'^, where do
denotes the current from a strip of gas of thickness doc and unit
dN
area in which -j- . dx clusters become elementary ions per second.
dN
Now -^r- = — vN, where ri denotes the fraction of clusters he-
dt
coming elementary ions per second. Integrating this equation
we have N — ^e~*'^, where t denotes the time the clusters take
to pass over the distance {I — x), and Fj the average velocity of
a cluster. The value of t is given by ^ = -^^ . Therefore
dN h -''-^
= ^ve
dt " Fi
F,
k^v , «.v--
and thus do = '-^ .dx.e ^' .
Integrating this equation between the limits x=l and a; = we
obtain
c = T^ e^« - e ^' .
The total current G is therefore given by the equation
FiO + t;
If 7} is small in comparison with Fjtt, rj ^ is small in com-
parison with la, and the equation becomes
«={^„+''^'" (2).
It will be seen that in the latter case the effect produced by the
* The Theory of lonisation by CQlUsion, p, 4, By Prof. J. S. Townsend.
VOL. XVII. PT. III. 18
270 Mt^ Kleeman, The Unstable Nature of the Ion in a Gas.
dissociation of the clusters is equivalent to an additional number
of free ions equal to -r^ being drawn through the gauze.
In the paper on clustering of ions quoted it is shown that
tn = c, where c denotes the concentration of the clusters per c.c,
71 the number changing into other clusters and elementary ions
per second, and t the life of a cluster. If the clusters are con-
sidered in a body so that t denotes the average life of a cluster,
77C = n, and therefore t = -.
^ . . .
It appears also that the dissociation of a cluster takes place
after it has undergone a certain average number of collisions, and
the time required for these collisions therefore varies inversely as
the pressure of the gas, or rj increases with increase of pressure
of the gas. But the value of 77 probably also depends on the
electric field applied to the gas when of great intensity. The
field increases the violence of collision of the cluster with other
molecules and consequently decreases its period of life. Since the
kinetic energy given to a cluster between two consecutive collisions
is proportional to the electric field and inversely proportional to
the " mean free path " of the cluster, the effect of the field on the
value of 77 may be expressed as a function of — . We may there-
P
fore write 77= j9.</)i( — ), where the value of 0i [ — j increases with
an increase of X, and consequently decreases with an increase of ^.
If 7 denote the fraction of elementary ions becoming clusters
per second of a number of ions in equilibrium we have 7^^! = rjkz,
since the number of elementary ions becoming clusters per second
must be equal to the number of clusters becoming elementary
ions. The ratio of k^^ to k^ is independent of the pressure of the
gas when the ions are not subject to any external force such as an
electric field. The effect of the electric field may as before be
expressed in terms of — , or 7;^ = 02 ( — ) • It follows therefore
/X\
that we may write 7 = |) . ^3 ( — ] .
The foregoing considerations will now be applied to some of
the experimental results obtained. Let us first calculate the
fraction of elementary ions drawn through the gauze that would
have to be in the elementary state to account for the current due
to ionisation by collision on the supposition that no clusters be-
come elementary daring their passage from gauze to plate. Thus
in the case of COg at a pressure of 9'5 mm. of mercury a current
of 187 in arbitrary units was obtained corresponding to a field of
ilfr Kleeman, The Ui^stahle Nature of the Ion in a Gas. 271
1860 volts per cm. From the curve for CO2 giving* the relation
between — and - we obtain - = 1*62 correspondinor to
P P P L O
^ = i||? = 140.
p 9 5
and hence a = 15*39. Let ??.„ denote the initial ionisation that
would account for this current. Then we have 187 = 7^oe'^^^•''^^
and hence n^ = "064. The actual number of ions drawn through
the gauze corresponding to a field of 1360 volts can most ac-
cuiately be obtained by reversing the field and measuring the
positive leak obtained. This leak was found to be equal to 25.
Thus about 2 °/^ only of the ions drawn through the gauze need
be in the elementary state to account for the current obtained.
Actually a smaller fraction is in the free state since some of the
clusters become elementary ions during their passage from gauze
to plate, and augment the current due to collision of ions. The
result obtained fits in with experiments described in a previous
part of the paper, v/here it was shown that the position of the
collision curve (fig. 2) with respect to the axes is greatly in-
fluenced by radium brought near the chamber, though the initial
ionisation was not increased by an appreciable degree.
In the case of air (dried by bubbling it through strong H2SO4)
at a pressure of 15 mm. of mercury a current of 172 was obtained
corresponding to a field of 1440 volts per cm. Now - = "85
corresponding to — = 96, and hence a = 12"75. The value calcu-
lated for Uq is thus "37. The total current through the gauze
corresponding to 1440 volts per cm. was equal to 20. Thus less
than 2y of the ions drawn through the gauze were in the free
state. In a similar way it was shown that a small fraction only
of the negative ions drawn through the gauze when H2 was in the
chamber are in the free state.
It might be suggested that the meshes of the gauze in causing
the electric field to be non-uniform in its immediate neighbour-
hood give rise to the results obtained. Thus the effective distance
between gauze and plate may be smaller or greater than that
which actually exists. If however the distance between the plate
and an imaginary plane corresponding to the collision current for
a constant voltage per cm. is calculated, it is found to be only
•14 of the actual distance between gauze and plate. It is quite
certain from this number that the effect is not due to the meshes
of the gauze.
* The Theory of Ionisation by Collision, pp. 19—21. By Prof. J. S. Townsend.
18—2
272 Mr Kleeman, The Unstable Nature of the Ion in a Gas.
f
The fraction of clusters drawn through the gauze that become
elementary ions on their passage from gauze to plate must be
small if the calculated fraction is small of the ions drawn through
the gauze that must be in the elementary state to account for the
total current observed due to ionisation by collision. If all the
clusters were to become elementary ions before reaching the plate
the current obtained would be very nearly equal to that obtained
on the supposition that all the ions drawn through the gauze are
in the elementary state. Since only a small fraction of the ions
are in the elementary state it follows that the life of a cluster in
the gases under consideration is greater than the time the cluster
takes to pass from gauze to plate. If the velocity of a cluster is
taken equal to the velocity of an ion measured in the usual way
(strictly it must be less) the time of passage of a cluster in the
'OX Q*^
experiments just mentioned is for CO2 ;ok = '00735 sec. and
■5 X 15
for air ^t^ — ^z^-r = "00554 sec. Thus the average periods of life
of the clusters must be greater than these values, and the values
of'/; consequently less than 66"45 and 90*2 respectively.
The values of Fitt in the cases under consideration are 1047
and 1150 respectively, and thus the values of rj are small in
comparison with the values of Via. Equation (2) may therefore
be used to calculate the values of 77, if -^ is not small in com-
aVj
parison with k^.
Thus for example in the case of air a current of 172 and 80
was obtained corresponding to a field of 1440 and 1320 volts
a. X
respectively. The values of - corresponding to the values of —
are "85 and "715 respectively. The positive leaks corresponding
to the above voltages were 20 and 18'5 respectively. If ki denote
the number of free ions and k^ the number of clusters corre-
sponding to the leak 20, the number corresponding to the leak
18'5 are k^ -^^ and k^ -^^^ . The two simultaneous equations
obtained from equation (2) and the equations A;] + yfc2 = 20 and
t,'n = l then give A;i = -196, h = ld'S, 77 = 1134, and ^1 = '89 sec.
Thus about 1 ^ of the ions in equilibrium in air are in the
elementary state ; and the period of life of a cluster at a pressure
of 15 mm. of mercury is of the order of one second. The value of
7 is 115, and the corresponding period of life 4 of an elementary
ion therefore "00872 sec. Since ^1 and t.^, are inversely proportional
to the pressure, their values at atmospheric pressure are "0176 and
"000172 second respectively.
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 273
It is of interest to obtain a value for the average number of
collisions a negative cluster undergoes before becoming a simple
ion. From the kinetic theory of gases we find that the number
of collisions an air molecule undergoes with other molecules at a
temperature of 30° is 1'6 x 10" per second, A negative ion cluster
in air at standard pressui'e therefore undergoes on the average a
number of collisions of the order 10® per second before becoming
a simple ion, and an elementary ion undergoes a number of
collisions of the order lO*' per second before it successfully forms
a cluster.
The above calculations cannot be carried out with success in
k .
the case of CO2; very likely 17 — is small in comparison with 77.
Townsend's experiments on diffusion suggest that 77 is probably
smaller in CO2 than in other gases. Better results might be
obtained after making some improvements in the experimental
arrangement. These would consist in having the distance be-
tween gauze and plate as large as is convenient, and using as
large a potential difference as possible, the pressure of the gas
being regulated to suit these conditions.
The numerical results obtained for air can only be approxi-
mately correct because the calculations are subject to considerable
errors, as small errors in the data may appear as large errors in
the ultimate results. Moreover, we have seen that the period of
life of a cluster and elementary ion depends greatly on the dryness
of the air. Latty's experiments suggest that the period of life of
an elementary ion in air specially dried is much greater than that
obtained by the writer. It appears also that under these circum-
stances the values of a would be very different from those obtained
by Townsend. The dryness of the air in Townsend's and the
author's experiments was however probably approximately the
same, and as the velocity of an ion and other quantities are
approximately independent of the dryness when it is not ex-
ceptionally great, the use of Townsend's values of a was not
objectionable. Further the values of rj and ti are probably also
seriously affected by the electric field when it is so large that new
ions are produced by collision. However, the results obtained
give one some idea of the processes going on in an ionised gas,
and the order of magnitude of the quantities involved.
The conclusions of a general nature that can be drawn from
the author's experiments and those of other investigators are as
follows. The period of life of an elementary negative ion or a
cluster depends very much on the nature of the gas in which it
is formed. It depends also very much on slight admixtures of a
different gas. The period of life of a cluster in a gas at standard
pressure may have a value lying between a few seconds and a
274 3Ir Kleeman, The Unstable Nature of the Ion in a Gas.
small fraction of a second. The order of magnitude of the period
of life of an elementary negative ion is about j^q that of a
cluster.
The results obtained have an important bearing on the motion
of a negative ion in a gas under the influence of an electric field.
The average velocity V of the ion under unit electric field is
obtained from an equation given at the beginning of the paper
which may also be written |
rr Co "Wo T" (^a'^a
Co T Ca
where Ca denotes the concentration of the clusters (considered in
a body) and Va the average velocity of a cluster, and Cq and Vq these
quantities corresponding to the elementary ions. The experiments
of Latty on the velocity of the negative ion in air specially dried
suggest that Va is of the order 100 F. ^ince Ca, vve have seen,
is of the order r-^ . the order of magnitude of CoVq is the same as
that of CaVa, and the presence of free negative ions in a gas thus
affects the average ionic velocity. Thus the various expressions
for the velocity of an ion through a gas that have been obtained
by different physicists on the supposition that the ion consists of
a definite unchanging cluster of molecules cannot be regarded as
representing what actually happens in the gas, but have value
only as useful empirical formula. It is conceivable that the effect
of the passage of the ion through cycles of clustering on its
velocity might be the same as that of a cluster of average mass.
It should also be noticed that these formulae usually rest on one
or more additional assumptions, which are not likely to be
realized in practice. One of them is that the motion of an ion
due to the electric field is reduced to zero on each collision with
a neutral molecule.
The results obtained have also an interesting bearing on the
interpretation of the results obtained on ionisation by collision in
the usual (Townsend's) experimental arrangement. We have seen
that T^ = <^2 ( — ] , where ^2 ( — ) increases with an increase of the
field and consequently decreases with an increase of the pressure.
But it probably varies only appreciably with the field when its
strength is comparable with that necessary to produce ionisation
by collision. But even when ionisation by collision occurs k^ may
not be zero, for sometimes the collision of an elementary ion with
a molecule must be favourable for the formation of a cluster. But
the life of such a cluster will of course be much smaller than
when the field is weak. Thus the current when ionisation by
collision takes place may be divided into two parts, a current
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 275
of elementary ions and a current of clusters. But the elementary
ions only produce further ions by collision. Now the quantity a
in the ordinarj'- theory of ionisation by collision is calculated on
the supposition that the whole current consists of elementary ions.
The quantity a when it refers to the partial current of elementary
ions is however the important one, it will in this case be denoted
by «!. The a's are connected by the equation CeCCi = a{Ge+ Gg),
where Gg denotes the current of elementary ions and Gc that of
the clusters. Since Gg increases while Gc decreases with increase
of electric field, the value of otj differs most from that of a when
ionisation by collision begins to come in, being always greater
than «!, while for much greater fields they may be practically
equal to one another. The curves connectinsf — and — would
n ^ p p
X
therefore be less concave towards the — axis near the origin than
p
the curves connecting — and - obtained by Townsend. We can-
° p p
not obtain any information about the relative values of Ge and Gc
from measurements of the ionisation current, and it does not seem
possible to devise a simple experiment by means of which they
could be directly measured.
The velocity with which an electron is ejected from its parent
atom has little influence on the ionisation by collision. It is
practically only the first collision of the electron with a neutral
molecule that would get the benefit of the initial velocity of the
former, if the motion of the electron is in the same direction as
that given to it by the electric field. On the average the electron
undergoes hundreds of collisions before it reaches one of the
electrodes, and the first collision is therefore comparatively of no
importance.
But the ionisation by collision should be considerably affected
by the direction of motion of the ejected electrons relative to that
given to them by the electric field. Consider the two cases when
the electric field acts in the same direction as the ejected electron
is moving, and when it acts in the opposite direction. In the
latter case the electron must be reduced to rest before a velocity
can be given to it sufficiently large to produce ionisation by
collision. The chance of a cluster being formed is therefore much
greater in the latter case than in the former. On a cluster being
formed it must run a distance x depending on its period of life
and velocity before it becomes an elementary ion again, after
which it can be used by the electric field for the production of
new ions by collision. Thus in the latter case the collision current
is smaller than in the former. The effect may roughly be said to
276 Mr Kleeman, The Unstable Nature of the Ion in a Gas.
correspond to a distance A between the electrodes in the former
case and a distance A—x in the latter. Since the collision current
increases rapidly with the distance of separation of the electrodes
and the value of a, the asymmetry in the leaks obtained by re-
versing the field should also increase with these quantities. The
writer* has carried out experiments on the ionisation by the a
particle involving the foregoing principles, and found that the
ejected electron has a component of motion in the same direction
as the ionising a particle.
The case when the initial ionisation is produced on the surface
of one of the electrodes in the field producing ionisation by collision
requires consideration here. Since all the ions start out as simple
ions, their condition near the surface is different from that some
distance away, where there is equilibrium between the clusters
formed and the simple ions. It is evident that when the breadth
of the region in which equilibrium is produced between the
clusters and simple ions is comparable with the distance between
the electrodes, the value of the collision coefficient a should
depend on the distance between the electrodes and the pressure
of the gas. But a. would obviously not vary abruptly with the
distance of separation of the electrodes because the region in
question has no well defined boundary.
Now Campbell f has carried out an investigation on the de-
pendence of a on the distance of separation between the electrodes.
The object of the investigation was to distinguish between two
hypotheses as to the changes an ion undergoes when producing
ionisation by collision, viz. (1) that the simple ion never forms a
cluster during collision, (2) that sometimes a cluster is formed
which is not broken up subsequently. If the latter hypothesis is
true a. should depend on the distance between the electrodes and
the pressure of the gas. Campbell concludes from his experiments
that no clusters are formed. Interpreting these experiments from
the point of view that the ion cluster is unstable, it follows that
either the region in which equilibrium between the simple ions
and clusters is produced is small, or, that the period of life of a
cluster is small in comparison with that of a simple ion in an
electric field of intensity sufficiently large to produce ionisation
by collision. It will be easily seen that in the latter case the
effect of the region under discussion is negligible for all distances
of separation of the electrodes. The latter explanation is probably
the correct one.
It was found impossible to obtain any definite information
about the period of life of an elementary positive ion or cluster.
* Proc. Boy. Soc. A, vol. lxxxiii. p. 195, 1909, and Phil. Mag. p. 198, July,
1912.
t Phil. Mag. p. 400, March, 1912.
I
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 277
B
This was principally due to the fact that the values of — required,
where ^ denotes the coefficient of collision for the positive ions,
could not be obtained from Townsend's curves for small values of
— . There is good reason to believe, however, from other experi-
ments, that the period of life of a positive cluster is greater than
that of a negative. The behaviour of the positive and negative
rays in a discharge tube, which has been studied in great detail
by Sir J. J. Thomson, Wien, and others, is evidence in support of
this. Obviously we should obtain evidence of those clusters only
whose period of life is greater than the time it takes them to
travel the length of the tube under the electric field. The number
of different clusters obtained would in that case depend on the
pressure of the gas in the tube, its dimensions, etc., and this has
been found in practice. Now as a rule the number of different
negative clusters obtained is much smaller than the number of
positive clusters, and may be explained by a difference in the
period of the clusters. It will be of interest, however, to give the
formula here by means of which the period of life of a positive
cluster could be calculated. The production of dark and luminous
spaces in a discharge tube under certain conditions must be in
part regulated by the fact that the proportion of free ions to
clusters increases as the ions pass into a stronger field. The
principles involved will be brought out in deducing the formula
in question.
Let K denote the number of positive ions drawn through
the gauze when at a positive potential, of which ki are in the
elementary state and ki clusters, so that K = ki + k2. The ionisation
current Ci produced by the free ions ki is given by
h( ^-cc)e^-^^
•
where /3 denotes the number of new ions made by a positive
ion per cm, of its path. This formula is obtained by inter-
changing a and ^ in the formula used by Townsend in his
investigations of the ionisation by collision of positive ions.
The ionisation produced indirectly by the clusters will be
considered separately. Let S denote the number of clusters that
cross per second a plane parallel to the plate at a distance x, and
5 the fraction of the number of clusters becoming elementary
f/Sf
ions per second. We then have -%— = — 8h, which on integrating
az
becomes S = k2e~^K Now ^ = -,, , where V^ denotes the average
' 9.
278 Mr Kleeman, The Unstable Nature of the Ion in a Gas.
velocity of the positive clusters per second. Hence
&{l-x)
_js &^
where A = e ^2 and z ■= e'^^.
Let r' be the number of negative ions produced by collision
in the layer of gas between the plate and the parallel plane at
a distance x, and r the number of positive ions produced by
collision between this plane and the gauze. Let c denote the
current crossing the plane which gives rise to further ionisation
by collision. Then we have
G = h{l - Az'^) -\- r + r' .
The number of ions dr generated between the two planes at
distances x and x-\-dx is given by the equation
-dr= [[k^ (1 - Az'^) + r} y8 + r'a] dx.
Substituting for r' from the foregoing equation we obtain
(It*
^ + (;S-a)r = (/3-a)A;,(^^'«-l)-ca.
Multiplying by e^^~'^^^ and integrating we obtain
where G is an arbitrary constant. The value of the constant is
obtained from the condition that ?' = when x = l, which gives
^ ( ca + h{^-a )\ _ ]c:{l3~a)Ae^'^^'"'y
From one of the foregoing equations we have c = k^(\ — A) + r,
when x = 0, where r is given by equation (4), and hence on sub-
stituting for r we obtain
The total current Ct is given by
Ct = c + Ci (6),
I
Mr Kleeman, The Unstable Nature of the Ion in a Gas. 279
where Ci and c are given by equations (3) and (5) respectively.
If 8 is small in comparison with (/3 — a)F2, ^ is small in com-
parison with (/3 — a) I, and in that case
C,
Bk, , \ (y8-a)e'^-'^
The effect of the unstability of the positive ion is then as if an
8k
additional number of free ions equal to „ .^ — r were drawn
through the gauze.
In conclusion I wish to express my thanks to Prof. Sir J. J.
Thomson for his kind interest in these experiments. It should
also be mentioned that the expense of the principal apparatus
was defrayed out of a grant of the Royal Society.
280 Mr Whiddington , Note on the Absorption
Note on the Absorption of Cathode Rays by Metallic Sheets.
By R. Whiddington, M.A., St John's College.
[Received 17 June 1913.]
Last year I published an account of some experiments on the
transmission of cathode rays through matter which showed that
the law determining the diminution of velocity of cathode rays
through matter was expressed by the relation
'^o'' — Vx* = a . X,
where
Vo = the velocity of a beam of rays incident on a sheet of
material of thickness x,
Vx= the greatest velocity in the emergent stream,
and a = a constant depending on the material of the sheet.
We are thus led to the conception of range of cathode rays, for
if in the above expression we put Vx=0 the value of Vo^ja is the
thickness of the material through which cathode rays of velocity Vq
can just penetrate.
In fact by using this expression we can easily determine the
constant a by measuring the velocity Vq, below which no appreci-
able effect is produced on the emergent side of a sheet of thickness
d ; we can then substitute these values in d = Vo'ja.
I have recently been making experiments with cathode rays of
definite speeds in order to determine the number of the rays
absorbed during their passage through metals.
Lenard, Seitz and others many years ago showed that using
rays of a more or less definite speed, the law of absorption was
exponential, being expressed by the relation
where
/o = the cathode ray current incident on a metal sheet of
thickness x,
I = the corresponding emergent cathode ray current,
and X = the absorption coefficient, a constant for any definite
speed but varying inversely as the fourth power of
the speed of the incident cathode rays.
I have found that in all cases I have examined this law is by
no means universally applicable. In fact the experiments were
originally commenced with the idea of discovering whether X
suffered an abrupt change when the material of the absorbing
screen commenced to give out its fluorescent Rontgen radiation.
So far, experiments have been carried out using screens of Au,
Ag, Cu and Al.
of Cathode Rays hy Metallic Sheets.
281
The curves given below are typical of two classes of absorption
which have been obtained. In these curves Ijv"^ is plotted along
the y-axis while the corresponding values of log IqJI are plotted
Log 7o/I
along the a;-axis. The simpler type is the lower one obtained
with Ag and Au sheets. It is clear that A, oc Ijv^ for velocities
greater than that corresponding to the point A. The value of v
for the point A is given quite as accurately as could be expected
by the expression quoted above — d = v^ja, and thus depends on
the thickness of the sheet.
The other type has been obtained with Cu and Al sheets
and shows in addition to the bend at A already explained another
bend at B. The velocity corresponding to this point is in the
case of Cu 6 . 2 x 10'' cm./sec, which is the velocity above which
the fluorescent X-radiation of Cu is excited. This is the effect
which was being looked for, but it is not possible just at present
to ascribe it definitely to the excitation of the fluorescent radia-
tion since Al also shows a similar effect though not at the same
velocity.
The experiments are being continued.
282 Mr Oxley, The Influence of Molecular Constitution
The Influence of Molecular Constitution and Temperature on
Magnetic Susceptibility. Preliminary Note. By A. E. Oxley, B.A.,
Coutts Trotter Student, Trinity College.
[Received 14 July 1913.]
In a former paper* the author has shown how the observed
departure from the Curie-Langevin laws for paramagnetism and
diamagnetism may be explained in terms of the variation of the
nature of the molecular complexes with temperature. Later, the
influence of such aggregations has been considered by Holm-f-,
Weiss and Piccard^, and Piccard§; the last physicist showing that
the variation of the diamagnetic susceptibility of water with the
temperature can be interpreted as due to the presence of two
types of complexes. The idea of the coexistence of different types
of complexes has been satisfactorily applied to the case of aqueous
solutions of salts of the ferromagnetic elements||.
The present note is intended to contain a preliminary account
of further experiments which have been made to test the effect
of the presence of molecular complexes on the susceptibility.
We shall denote the specific diamagnetic susceptibility by %.
About thirty organic and several inorganic substances have
been investigated and the variation of % with temperature has
been examined over a range of 250° C. It is found in generallf
that there is a decrease in the value of % during the passage from
the liquid to the crystalline state. This decrease amounts to
5°/q (approx.) of the value of ^. If the substance supercools or
passes into a gel as the temperature is lowered there is no dis-
continuity, but when crystallisation does take place the value of %
is found to decrease. If the substance is now heated % remains
constant until the normal melting point is reached but increases
during fusion. A hysteresis loop due to temperature is thus
obtained, similar to those which Hopkinson** discovered for the
passage from the paramagnetic (non-crystalline) to the ferro-
magnetic (crystalline) state in the case of nickel-steels, the critical
temperature in the latter case corresponding to the temperature
of fusion of the diamagnetic crystals in the former case.
With regard to the continuity found when the substance passes
* Proc. Canib. Phil. Soc, Vol. xvi. p. 486, March 1912.
t Ark. for Mat., Stockholm, 8, 16, 1912.
X Comptes Rcndus, t. 155, p. 1234.
§ Comptes Rendus, t. 155, p. 1497.
II Proc. Camb. Phil. S'oc, Vol. xvii. p. 65, Dec. 1912.
II There are a few exceptional cases which are not discussed here.
** Proc. Roy. Soc, Vol. xlviii. p. 1, 1890 ; or Ewing's Magnetic Induction in
Iron and other metals (third edition), p. 184 et seq.
i
and Temperature on Magnetic Susceptibility. 283
from a liquid into a gel, it is interesting to note that Chaudier*
has found that the specific magnetic rotation of such substances is
continuous, a discontinuity appearing only when crystallisation
sets in.
On the theory of diamagnetism developed by Langevinf, the
above experiments indicate that in the quasi-chemical compounds
formed during aggregation or crystallisation the internal structure
of the molecule or atom is modified. This result was assumed in
the investigation cited at the beginning of this note.
It will be observed that an exact interpretation of the experi-
mental facts must necessarily be highly speculative in view of the
present state of the electron theory of valency and further dis-
cussion of the quantitative results is reserved until an early
date.
* Comptes Rendus, t. 156, p. 1529, May 1913.
t A complementary theory to that of Langevin has recently appeared dealing
with the diamagnetism of conducting substances and the part played by free
electrons (Schrodinger, Sitz. d. k. Akad. Wien cxxi. p. 1305, 1912). In dealing
with organic liquids the diamagnetic effect due to this source is negligibly small.
Note. In the paper "The Variation of Magnetic Susceptibility
with Temperature. Part ii. On Aqueous Solutions" {Proc. Camb.
Phil. Soc, Vol. XVII. p. 65) the temperature coefficient given at
the foot of p. 75 is due to du Bois. The recent work of Weiss
and Piccard, referred to above, shows that this value is incorrect,
but the change does not affect the numbers given in the tables
on pp. 76 — 77.
It should be mentioned that the susceptibilities given by
Jaeger and Meyer are referred to unit volume of the solutions.
As, however, the density of a solution is very approximately a
linear function of the absolute temperature, over the interval
considered, the specific susceptibility is correctly expressed by the
formula
X = ^ + B + C^,
where A, B and G are independent of the absolute temperature (^),
The conclusions reached concerning the presence of molecular
complexes are of course unmodified.
284 Mr Hindu, A Chinese Flea-trap.
A Chinese Flea-trap. By Edward Hindle, B.A., Ph.D.,
Magdalene College, Cambridge, Assistant to the Quick Professor
of Biology. {Communicated by Professor Nuttall.)
[Read 5 May 1913.]
Through the kindness of Mr Stanley A. Stericker, we have
recently been able to obtain from Cheng-tu, the capital of Sze-
Chwan, an example of a flea-trap much used by the natives in
that part of China.
The apparatus consists of two pieces of bamboo one inside the
other. The outer bamboo is about one foot in length and 2^
inches in diameter and is fenestrated in the manner shown in the
accompanying photograph. The inner bamboo is of equal length
but only about one inch in diameter, and is kept in position
within the former by means of a short wooden plug.
The manner in which the apparatus is employed is as follows :
The two pieces of bamboo are first separated by removing the
wooden plug. The inner bamboo is then coated with bird-lime,
or some similar sticky substance, and put back in position within
the fenestrated bamboo. The function of the latter is protective and
prevents the sticky surface from coming in contact with any large
objects. The whole trap can now be placed under bed-clothes, or
amongst rugs, etc., and any fleas that get on to the surface of the
inner bamboo at once stick to the bird-lime and are thus caught.
The apparatus is said to be a very efficient flea-trap, and
considering its simplicity it might be used with advantage during
plague epidemics, in order to catch any fleas, rat or human, within
houses. Considering the importance of the rat-flea in the trans-
mission of plague, the employment of a simple and effective flea-
trap, such as the one described above, would probably have a
decided effect on the spread of the disease.
Dr Searle, Some methods of measuring the surface tension, etc. 285
Some methods of measuring the surface tension of soap films.
By G. F. C. Searle, Sc.D., F.R.S., University Lecturer in Ex-
perimental Physics, Fellow of Peterhouse.
[Read 19 May 1913.]
§ 1. Introduction. The following paper gives an account of
some methods employed in my practical class at the Cavendish
Laboratory for the measurement of the surface tension of films
of soap solution. The first two methods have been in use for
some years, but I have included them in the hope of making the
paper more useful to teachers of practical physics. The apparatus
may, without loss of efficiency, be constructed in quite '■ home-
made" style or may be built up of elements at hand in most
laboratories.
§ 2. Torsion balance method. Let A BCD (Fig. 1) be a
rectangular frame of thin wire, the plane of the rectangle being
^c=^
Kg. 1.
vertical. If the frame be dipped into a soap solution and then
be partially withdrawn so that the horizontal surface of the
solution cuts the frame at E and F, a film will be formed, which
will fill the area ABFE. This film will pull the frame down-
wards. If the surface tension of the solution be T dynes per
centimetre*, and if the distance EF be Z cm., the .downward pull
on the frame will be 2TI dynes, each surface of the film con-
tributing Tl dynes. If the downward pull be measured, the
surface tension can be calculated.
The pull of the soap film is easily measured by aid of the
simple torsion balance shown in Fig. 2. This was designed, in
conjunction with Mr W. G. Pye, as a more convenient form of the
apparatus originally constructed at the Cavendish Laboratory.
The base of the balance is a tripod stand furnished with a
levelliuor screw. From this stand rises an adjustable vertical rod
• •11*
carrying a stiff metal frame, across which is stretched a torsion
wire ; the tension of the wire can be adjusted by a screw. A
double-ended beam is attached to the wire. The long arm of the
* So many elastic constants are expressed in dynes per square centimetre that
students easily fall into the error of stating surface tensions in dynes per square cm.
VOL. XVII. PT. III.
19
286
Dr Searle, Some methods of measuring
beam is pointed to serve as an index, and this index point moves
near a vertical scale divided to millimetres ; the short arm carries
an adjustable counterpoise for bringing the beam to a horizontal
position. To secure a good connexion of the beam to the wire,
the beam is clamped to a short metal tube of small bore, through
which the wire passes and to which the wire is soldered. Near
the pointed end of the beam is cut a small notch which serves
to define the position of a hook supporting a small scale pan.
Below the scale pan hangs the wire frame on which the film is
formed. This frame is about 8 cm. in length and 3 cm. in
height.
The sensitivity of the torsion balance depends upon the
thickness of the torsion wire ; by using wires of different thick-
nesses a wide range of sensitivity can be covered. For the
present purpose, it is convenient to use a torsion wire such that
one deci-gramme in the scale pan gives a deflexion of about
2*5 mm.
A beaker containing soap solution is placed so that the frame
dips into it, and the height of the torsion balance is adjusted
so that when the frame is drawn down by the film, the film is
one or two centimetres in height. There must be enough solution
in the beaker to allow the frame to be completely immersed when
necessary.
The measurements are taken as follows : — The end of the
balance arm is depressed so as to completely immerse the frame.
The arm is then allowed to rise, when a film will be formed
between the emergent part of the frame and the horizontal
surface of the solution. The solution will then begin to drain
off from the wire and from the film itself, and the scale reading
the surface tension of soap films
287
of the index will change slightly, but will reach a steady value
after a short time. This steady reading is recorded. The
reading must be taken to -^ mm. ; a short focus lens mounted
in a clip may be used to give the necessary optical assistance.
The film is now broken. The arm then rises but is brought
back to the position it had when the film was intact by placing
a mass m ofrras. in the pan. If necessary, the exact mass required
is obtained by interpolation from two scale readings, the mass
being a little too large for one reading and a little too small for
the other. A "rider" may also be used to obtain the fine adjust-
ment. If its mass be r grms., its effect is equivalent to that of
a mass rxjd grms. placed in the pan, where d and x are the
distances from the axis of the torsion wire to the notch and to the
point of suspension of the rider. Since the volume of the wire
below the surface of the solution is the same as when the film was
intact, the upward thrust of the solution is the same in each case.
Hence the weight, mg dynes, of the mass in the pan is equal
to the force which was exerted by the film. Thus
mg^2Tl
or
T
_ mg
~2l
dynes per cm (1),
where I is the distance EF (Fig. 1) between the points where
the frame cuts the solution. This is the shortest distance
between the two circles in which the plane of the surface inter-
sects the two wires.
After each pair of readings, the height of the torsion balance
may be slightly changed or a small mass may be placed in the pan.
In this way a number of independent readings may be obtained.
§ 3. Practical example. The following results were obtained
in an experiment :
Width of frame = ^ = 8-00 cm. Temperature about 19° C.
Beading with
film UD broken
Readings with film broken
0-40 grm. in pan -45 grm. in pan
m
3-83 cm.
3-87
3-90
4-00
3-79 cm. ; 3-85 cm.
3-82 ' 3-88
3-85 3-90
3-94 4-00
0-433 grm.
0-442
0-450
0-450
Meau value of m = 0-444 grm.
Hence
T'-
mg
'"21 '
0-444 X 981
2x8-00
- = 27-22 dynes per cm.
19—2
288
Dr Searle, Some methods of measuring
§ 4. Measurement of surface tension of water. The balance
may also be used to determine the surface tension of water or any
other transparent liquid which will not form persistent films. A
thin rectangular glass plate is held in a clip (Fig. 2) by which it
is suspended below the scale pan instead of the wire frame. The
glass slips sold for microscope slides are convenient. The plate is
adjusted in the clip so that when it is suspended its lower edge
is horizontal. The plate is then allowed to dip into the liquid in
the beaker and the balance is raised until the lower edge of the
plate is exactly in the plane of the undisturbed part of the
surface of the liquid; the fine adjustment is conveniently made
by the levelling screw in the base of the instrument.
The scale reading of the index is now taken and then the
beaker of liquid is removed and the plate is dried by filter paper.
A mass m grms. is then placed in the pan to bring the index to
the first reading. If the length of the plate be I cm. and its
thickness be a cm., the surface tension is given by
1
T =
mg
2 (^ + a)
dynes per cm.
(
If water be used, the surface should be free from grease.
The beaker should be cleaned with potash and should be filled
with water freshly drawn from the tap. The glass plate should
also be cleaned with potash.
§ 5. Thread method. The surface tension of a soap solution
can be found by this method with very simple apparatus.
P n
Fig. 3.
On the horizontal arm QR (Fig. 3) of a bent glass rod PQR
slide two rings A, B. Through eyes on these rings passes a
thread whose ends are attached to a glass rod CD. By adjusting
the rings and the thread the distances AB and CD can be made
equal, and the rod can be made to hang with its axis horizontal.
the surface tension of soap films 289
The points G, D should be at equal distances from the corre-
sponding ends of the rod. The distance AG should be three or
four times the distance AB.
If the whole system be dipped into soap solution and be then
withdrawn, a film will be formed in the area bounded by the
thread and the lower rod GD. The threads now take the form
of curves AGG, BHD, which we shall show are arcs of circles.
The vertical part PQ of the bent rod is fixed in a clamp and
a horizontal scale 8 is placed close to the film, and the distance
GH between the two points on the threads where the tangents
are vertical is determined from the scale readings of the threads.
The film is then broken and the scale readings of the threads are
again taken. Before the first pair of readings is taken as much
as possible of the solution adhering to the low^er rod is removed
by filter paper so that the supported mass may be as nearly as
possible the rod alone.
Let the distance EF (Fig. 3) between the threads when they
are vertical be a cm. and let the distance between the points
GH when the threads are curved be h cm. Let the mass of
the rod GD be m grms. ; the mass of the threads and of the film
may be neglected. Let the tension of the threads at G and H
be N dynes.
The weight of the part of the system below a horizontal
plane through G, H is mg dynes, and this is supported by the
stresses which act across the plane. The force due to the film
is 2T6 dynes, since there are tivo faces to the film, and the force
due to the threads is 2iY dynes. Hence the equation of equi-
librium is
2Tb + 2N=77ig (2).
Since the weight of the threads is negligible and since the
force exerted by the film on any element of either thread is at
right angles to the element, it follows that the tension of each
thread is constant and equal to iV dynes.
Fig. 4.
Let P, Q (Fig. 4) be two neighbouring points on the thread,
and let the radius of curvature of the arc PQ be p cm. Let PQ
290
Dr Searle, Some methods of measuring
subtend an angle 6 radians at 0, the centre of curvature.
Then PQ = pO.
The force which the other parts of the thread exert upon PQ
is 2iV"sin ^6 in the direction KO, where K is the point of inter-
section of the tangents at P and Q. The force which the film
exerts on PQ is in the direction OK and lies between 2T .PQ and
2T.PQ cos ^d dynes or between 2Tp0 and 2Tpd cos ^d dynes.
Since the force due to the thread balances the force due to the
film, we see that N lies between '
'^"l^e -^ '^''S^e
cos ^0.
When 6 approaches zero, the limit of ^d/sm^6 is unity and the
limit of cos ^6 is also unity. Hence
N'=2Tp dynes (3).
Since N and T are constant, p also is constant and hence the
threads form arcs of circles.
The equilibrium equation now becomes
T{2b + 4/j) = mg,
or
T =
mg
W+Jp
.(4).
Fig. 5.
The radius of curvature, p, of the threads must now be found.
Let a; = i(a - 6) so that (Figs. 4, 5) a; = HF = EG. Then, from
Fig. 5, if BD = h cm.
X {2p — x)= Ih^,
or P=oZ + ^ (5).
The vertical distance h = BD is measured while the film is un-
broken.
the surface tension of soap films
291
If the length of each thread, i.e. the length of the arc BUD,
be I cm., the radius can be found from an approximate formula (6).
Thus, if the angle BHO be ^, we have = Ij^p. But
-;=i-co.,.i-(i-iL.^-^^
2
-fi-
'-8p
Hence
- J--
8x
1-
48p'
+
The first approximation is p = I'^Sx. Using this in the term
Pj^^p^, we have as a second approximation
P
P^8x
4 x^
SP
+
_ P X
(6).
§ 6, Practical example. The following is a record of an
experiment by Mr C. E, Simmons.
Distance ^i^ between threads when vertical = a = 1 '68 cm.
Minimum distance GH between threads when curved = 6 = l'15cm.
Vertical distance BD when film is unbroken = A=7"40 cm.
Mass of fflass rod CZ)=to = 2-94 grms.
Hence
and
'a^-"*" 2 ^8x0-265
^ = i(a-6) = 0-265cm.,
7-402 0-265
+ -
= 25-83 + 0-13 = 25-96 cm.
Hence, by (4),
mg
2-94x981
26 + 4p 2-30+103-84
= 27-17 dynes per cm.
§ 7. Viscosity potentiometer method. In this method the
pressure excess due to a spherical soap film is measured by
aid of what may be called a " viscosity potentiometer." Air from
a gasometer G (Fig. 6) flows through two tubes AB, CD, which
are connected in series by the joint BG. The pressure at A
®
f
%J
Fig. 6.
292 Dr Searle, Some methods of measuring
is measured by the water manometer* M\ the end D is open
to the atmosphere. From the junction BG a side-tube leads to a
cup K with a horizontal circular rim on which a soap film is
placed. On account of the viscosity of the air there is a fall
of pressure along each tube, and for a given flow of air, the fall of
pressure in either tube is proportional to the length of the tube
and inversely proportional to the fourth power of its internal
radius, provided the flow is so slow that stream-line motion exists.
The excess of the pressure in the cup K above that of the
atmosphere causes the film to rise above the rim and to take
the form of part of a spherical surface. From the distance, h cm.,
of the highest point of the film above the plane of the rim and
from the radius, c cm., of the rim, the radius, r cm., of the spherical
surface is deduced. Thus
h(2r-h) = c'',
C + h^ .K,
If the length of the tube DG be li cm. and its internal radius
be tti cm. and if 4, ci.^ be corresponding quantities for the tube BA,
and if the pressure excess at B he p and that at A be P, then
J^ — P _ tti h^ ,Q\
p ~ h ' tta"
It is sometimes convenient to form the portion AB of two or more
tubes arranged in series. If the lengths and internal radii of these
be 4, hi •■• cm. and ttg, a^, ... cm., then the equation becomes
P-p_a^*fh _(.A_^_ A /gy
p li \a2^ as
From (8) or (9) the value of p can be found in terms of P,
the pressure excess observed on the gauge M. It is convenient
to arrange the tubes so that P is about 100 times p. The internal
radii of the tubes may be found by means of mercury. For
accurate work they should be calibrated f.
The gasometer G is formed of a cylindrical can 16 cm. in
diameter and 24 cm. in height. Part of its weight is supported by
a string which passes over a ball-bearing pulley and carries a pan
and weights. By varying these weights the pressure excess in the
gasometer can be adjusted. The can is furnished with two gas-
fitter's taps, as shown in Fig. 6. The lower rim of the can is
* A petroleum manometer Avould be better, but the density of the liquid must
be found.
t For details of this process see G. F. C. Searle, " A simple method of deter-
mining the viscosity of air." Pj'Oc. Camb. Phil. Soc. Vol. xvii. p. 183.
the surface tension of soap films
293
loaded with lead so that the equilibrium of the can is stable when
the can is floating with its axis vertical. The can is connected to
the joint J. by a piece of flexible rubber tube. Since the walls
of the can are thin, the pressure excess diminishes only very
slowly as the can sinks in the cistern.
The internal radii of the flow tubes must not be too small.
With tubes of small radii, the flow of air is so small that a con-
siderable time elapses before the film reaches its full height, and
there is a danger that the film may break before the necessary
measurements can be made.
§ 8. The bubble holder. The details of the arrangement on
which the spherical film is formed and measured are shown in
Fig. 7. A brass plate 8'5 cm. in diameter is carried by a tripod ;
Fig. 7.
a central opening in the plate communicates with the tube
by which a connexion is made with the joint BG (Fig. 6). A ring
rests upon this plate. The upper end is bevelled so that the edge
lies on the internal cylindrical surface of the ring ; this secures a
definite base for the spherical film. The joint between the ring
and the plate is made air tight by a little of the soap solution.
This arrangement allows a number of rings of different radii to be
used and also allows the ring to be adjusted on the table. A rod
rising from the tripod base is furnished with an adjustable hori-
zontal arm which carries a clamp holding a glass scale divided to
millimetres. It is convenient to adjust the scale and ring so that,
when the spherical film is formed, the lower edge of the scale may
be as near as possible to the highest point of the film. There is
then little error due to parallax if the film and scale are observed
through a telescope set at the same level as the top of the film,
and the film and the scale will be both in focus at the same time.
A flame placed behind the film at a sufficient distance to avoid the
\
294 Dr Searle, Some methods of measuring
effects of its heat or a mirror reflecting the sky light may be used
to give the necessary illumination.
A film is formed on the ring by dipping a card into the
solution and then drawing the edge of the card gently across the
ring.
The position of the zero of the glass scale relative to the plane
of the rim of the ring is found by placing a steel scale of known
width on the rim with the plane of the scale vertical and then
observing the reading of the upper edge of the steel scale on the
glass scale.
An alternative method of determining the height of the vertex
of the film is to use a horizontal microscope provided with a
vertical motion and to "set" the microscope first on the vertex of
the film and then on the rim of the ring. The difference of the
readings gives tlie distance k
§ 9. Practical details. A series of measurements may be
taken by varying the counterpoise of the gasometer, and deter-
mining r, the radius of the spherical film, in each case. The value
of Mr, where M cm. is the difference of level of the manometer
columns, is found in each case, and the mean of these values is
used in calculating the surface tension. Since the pressure in the
gasometer slowly diminishes, the observations for r and M should
be made as nearly as possible simultaneously.
§ 10. Geometry of the curved film. When a curved film is
formed on a circular rim by a pressure excess p, it must be a
surface of revolution about the axis of the rim, and this surface is
easily shown to be part of a sphere. Let VMO (Fig 8) be the axis
Fig. 8.
of the rim of the cup, and Fthe vertex of the film ; the figure is
a section of the system by a plane through VO. Let NMN' be
the trace of a plane normal to VO and let MN=x and VM=y.
Let the tangent at N to the section of the film make the angle d
with MN. Since the force on the film NVN' due to the surface
tension on both sides of the film acting along the circle NW, in
which the plane NMN' cuts the film, is equal to the force due to
the pressure excess p acting on the circular area of radius MN,
the equation of equilibrium is
22" sin 6 . 27rx = p . -irx^,
the surface tension of soap films 295
or x = — sin 6 = r sin 6,
P
where r=4'T/p. But dy/dx= tan 6 and hence
dy sin 6 __ oc
da; Vl— sin^^ Vr^ — cc"
Thus y = - ^r^ - x'' + K.
Choosing the constant K so that y^O when ;» = 0, we have
{y — ry + x^ =r",
which represents a circle of radius r whose centre lies on VO at
a distance r below V. Hence the film is spherical and has the
radius
r = 4T/p.
The surface tension is therefore given by
T=lrp (10).
As the height, h, of the vertex of the film above the rim of the
ring is gradually increased from zero to c, the radius of the rim,
the radius of the bubble diminishes from infinity until it reaches c.
If h be further increased, the radius of the bubble increases also.
Hence the pressure excess must not be greater than 4T/c, for if
the height of the bubble be made to exceed c, the pressure which
it can resist will become smaller as the radius of the bubble
increases, with the result that, if the bubble be supplied with air,
it will swell until it bursts.
§ 11. Practical example. The following results were obtained
by G. F. C. Searle and A. J. Berry. Two tubes in series were used
between the manometer and the bubble stand.
Length of tube (1) or CD (Fig. 6) = Zi = 28-8 cm.
Mass of mercury filling tube = 81 '8 grms.
Density of mercury = 13"55 grms. per c.c.
Square of radius of tube=ai2=——-^i^—— - = 0-06672 cm.2
^ 13"55 X 7rx28-8
Hence «! = 0-2583 cm. and aj* = 4*452 x 10' ^cm.*
m «i* 4-452x10-3 ^ ^^^ _^_, ,
Thus -y- = —— = 1-546x10 "icm.s
tj Zo'o
By similar measurements on tubes (2) and (3)
^2 = 120-0cm., a2 = 0-1437cm., a2* = 4-259 x lO-^cm.*
Z3 = 158-2cm., a3 = 0-1479cm., a3* = 4-784x lO-^cm.*
296
Hence
Dr Searle, Some methods of measuring
^: = 2-817xl05cm.-3 and -^ = 3-307 x lO^ cm.- ^
"2*
a<i*
Thus, by (9), § 7,
^ = T^ Mi + ^ =1-546 X 10-* X 6-124 X 105 = 94-66.
Hence
V .
1
P 95-66
Eadius of rim of cup = c=2-90 cm,
:l-045xl0-2.
i
The table gives the results of a number of observations for various values
of the difterence of level, if cm., of the water in the limbs of the manometer.
Difference of
Height of vertex
Eadius of bubble
water levels
above rim
c2+/j2
Mr
M
h
'- 2h
2-53 cm.
1-28 cm.
3-92 cm.
9-93 cm.2
2-64
1-42
3-67
9-69
2-93
1-73
3-30
9-66
2-99
1-68
3-34
9-99
3-11
1-90
3-16
9-84
3-29
2-38
2-96
9-73
3-36
2-31
2-97
10-00
Mean 9-83
Since P=981.pJ/, vphere p = density of water=lgrm. cm.-^,
Pr=981i/r, and hence, by (10),
we have
T^^rp^-l^. /'r=|x 1-045 X 10-2x9-83x981 = 25-19 dynes per cm.
It will be seen that there are some inconsistencies among the readings.
They probably arise from small variations of pressure in the gasometer due
to friction in the pulley or capillary action : these variations do not instanta-
neously cause changes of the radius of the bubble. Better results would
probably be obtained with a larger gasometer. Greater steadiness would be
obtained by inserting a piece of small bore tube between the gasometer and
the manometer joint and then using a higher pressure in the gasometer.
A petroleum gauge would be better than a water gauge as it is less affected
by capillarity.
§ 12. Buoyancy method. This method was suggested by the
plan adopted by Mr J. D. Fry in the calibration of his new Micro-
manometer*; it depends upon the difference of density between
cold and hot air at the same pressure. The method is instructive
as it helps the student to realise the presence of the atmosphere.
A metal tube ABGJD (Fig. 9) has the two portions AB, CD, each a
J. D. Fry, Philosophical Magazine, April 1913, p. 494.
the surface tension of soap films
297
few centimetres long, at right angles to the main portion BG which
is about one metre in length. This bent tube is surrounded by a
second tube FG which is used as a steam jacket for heating the
tube A BCD. The parts AB and CD are horizontal and the tube
may, if desired, be rotated about CD as a horizontal axis. The
inner tube passes out of the steam jacket through rubber bungs.
The opening D is connected by a horizontal rubber tube DE to
the cup K on which a bubble is to be formed ; the same bubble
holder is used as in | 8. The end A remains open.
izzz^
^^7m
Fig. 9.
Let the temperature of the atmosphere in the neighbourhood
of the apparatus be t-^ K., i.e. ^i° on the Kelvin or "absolute" scale,
and let the temperature of the air in the tube BG be t^ K. Let
P dynes cm."^ be the atmospheric pressure at the level of A. Let
the density of air at the normal pressure p^ and the normal tem-
perature ^0° K- be po grm. cm.~^, let the density of air in the atmo-
sphere at the level of A be pi and that at B in the tube be p^. Let
the height of D above ^ be ^^ cm. Then, if we neglect the very
small changes of density due to differences of level, the pressure
in the atmosphere at the level of GD is P — gp^z*, while the
pressure in the tube at C is P — gp^z. If the horizontal tube DE
is long enough to ensure that the bubble stand K is not heated by
the steam jacket, the fall of pressure between E and the bubble
is, to all the accuracy required, the same as that which occurs in
The exact expression is Pe ^P^^'-^.
298
Dr Searle, Some methods of m^easuring
the atmosphere over the same difference of level*. Hence p, the
pressure excess within the bubble, is given by
p = gz(pi-p.2) dyne cm.-'- (11),
where
PoPto
P-2 =
Po
Pto
Po h Po h
When the radius, r cm., of the bubble is known, the surface
tension is calculated by
T=irp.
§ 13. Practical details. The bends at B and G are formed as
in Fig. 10. The end of the long tube is soldered into a block of
brass. The short side tube screws into the block, the joint being
made tight by a flange and a leather washer. The short tube
must be stout to withstand the strain involved in making the
joint tight. The side tubes are screwed into the blocks after the
long tube has been placed within the steam jacket. Steam is
supplied by a small boiler; the waste steam from the jacket should
be led away clear of the apparatus. The inner tube is about 0"8
cm. in diameter and the tube forming the steam jacket about
2*5 cm. in diameter.
The bubble is formed on the ring and the observations for its
radius are made just as in §§ 7, 8. The temperature of the sur-
rounding air is observed by a thermometer.
If, as suggested by Mr J. D. Fry, the tube ABGD be turned
about CD as a horizontal axis, the difference of level, z, between
D and A can be changed and with it the pressure excess in the
bubble. The difference of level can be calculated in terms of the
distance AD if the tube be mounted so that the inclination of the
plane AGD to the vertical can be measured.
* It will be easily seen that no care need be taken to ensure that those parts of
the tube BE ivhich are at atmospheric temperature shall be in the same horizontal
plane as CD.
the surface tension of soap films
299
To ensure that the interior of the tube ABGD is dry, air may
be blown through it while it is heated.
§ 14. Practical example. The following results were obtained
by G. F, C. Searle and A. J. Berry.
Barometric height = 76-53 cm.
Temperature of atmosphere = t■^ — 273 + 19-5 = 292-5° K.
Temperature of steam = iJ, = 273 + 100-2 = 373 -2° K.
Height of heated cokimn = « = 95-8 cm.
Density of air at normal pressure and temperature =po==l '293 x 10"
grm.
Hence
Pi-
1-293 X 10-3 X
P2
= 1-293 xlO-3x
76-53
76-00
76-53
273
292-5
273
= 1-2152 X 10-3 grm. cm.
= 0-9524 X 10 "3 grm. cm.
76-00 373-2
The pressure excess in the bubble is thus
p =gz (pi - Pa) = 981 X 95-8 x 0-2628 x 10-^ = 24-70 dyne cm.-2
The following values of the distance, h, of the vertex of the bubble from
the plane of the rim were found with five different films :
1-09, 1-10, 1-09, 1-10, 1-10 cm.
Mean value of A = 1 -096 cm.
Eadius of rim = c= 2-90 cm.
Mean radius of bubble=r = (c2 + /i2)/2/i=4-385cm.
Hence we find for the surface tension
7^=|rp = Jx 4-385 x 24-70 = 27-07 dynes per cm.
§ 15. Comparison of results. The results given by the various
methods are as follow^s :
Method
Surface tension
Torsion balance
27-22 dyne cm.-^
27-17
25-19
27-07
Thread
Yiscosity potentiometer...
Buoyancy
PROCEEDINGS AT THE MEETINGS HELD DURING
THE SESSION 1912—1913.
ANNUAL GENERAL MEETING.
October 28th, 1912.
In the Coraparative Anatomy Lecture Room.
Dr Duckworth, in the Chair.
The following were elected Officers for the ensuing year :
President :
Dr Shipley, Master of Christ's College.
Vice-Presidents :
Prof. Hopkinson.
Prof. Wood.
Prof. Pope.
Treasurer :
Prof. Hobson.
Secretaries :
Mr A. Wood.
Mr F. A. Potts.
Mr G. H. Hardy.
Other Members of the Council :
Mr R. H. Rastall.
Dr Lucas.
Dr Newell Arber.
Prof. Sir J. J. Thomson.
Mr J. E. Purvis.
Mr R. P. Gregory.
Dr Cobbett.
Mr J. Mercer.
Dr Marshall.
Mr G. R. Mines.
Dr Barnes.
Mr F. J. M. Stratton.
I
^
Proceedings at the Meetings. 301
The following were elected Fellows of the Society :
J. W. Lesley, B.A., Emmanuel College.
J. T. Saunders, B.A., Christ's College.
P. G. M. Dunlop, M.A., Gonville and Caius College.
The following were elected Associates :
J. K. Robertson, Emmanuel College.
S. N. Maitra, Emmanuel College.
The following Communications were made :
1. Anthropometric data collected by Professor Stanley Gai'diner
in the Maldive Islands. By Dr Duckworth.
2. Preliminary Note on the Inheritance of Self-Sterility in Reseda
odorata. By R. H. Compton, M.A., Gonville and Caius College.
3. The effects of hypertonic solutions upon the eggs of Echinus.
By J. Gray, B.A., King's College. (Communicated by Mr F. A. Potts.)
4. Pulsus alternaiis. By G. R. Mines, M.A., Sidney Sussex
College.
November llth, 1912.
In the Cavendish Laboratory.
Professor Sir J. J. Thomson, in the Chair.
The following were elected Associates :
G. B. Hony, Christ's College.
H. Smith, Emmanuel College.
The following Communications were made :
1. On the theory of the motion of charged ions through gases.
By Professor Sir J. J. Thomson.
2. On a simple method of determining the viscosity of air. By
Dr G. F. C. Sbarle, Peterhouse.
3. Note on the Rontgen Radiation from Cathode particles tra-
versing a gas. By R. Whiddington, M.A., St John's College.
4. The Diffraction of Short Electromagnetic Waves by a Crystal.
By W. L. Bragg, B.A., Trinity College. (Communicated by Professor
Sir J. J. Thomson.)
5. Experiments on the Electrical Discharge in Helium and Neon.
By H. E. Watson. (Communicated by Professor Sir J. J. Thomson.)
VOL. XVII. PT, III. 20
302 Proceedings at the Meetings.
6. Some Diophantine Impossibilities. By H. C. Pocklington,
M.A., St John's College.
7. A class of Integral Functions defined by Taylor's Series. By
G. N. Watson, M.A., Trinity College.
8. Notes on the Volatilization of certain Binary Alloys in high
Vacua. By A. J. Berry, B.A., Downing College.
November 25th, 1912.
In the Sedgwick Museum.
Dr Shipley, President, in the Chair.
The following was elected a Fellow of the Society :
H. Hartridge, M.A., King's College.
The following were elected Associates :
R. Rossi, Trinity College.
S. P. Heath, Fitzwilliam Hall.
The following Communications were made :
1. The Gravels of East Anglia. By Professor Hughes.
2. The Meres of Breckland. By Dr Marr.
3. On the earlier Mesozoic Floras of New Zealand. By Dr
Newell Arber.
4. The mineral composition of some Cambridgeshire sands and
gravels. By R. H. Rastall, M.A., Christ's College.
5. A remarkable instance of complete rock-disintegration by
weathering. By F. H. Hatch.
January 27th, 1913.
In the Cavendish Laboratory.
Mr J. E: Purvis, in the Chair.
The following were elected Fellows of the Society :
J. Gray, B.A., King's College.
T. C. Nicholas, B.A., Trinity College.
The following was elected an Associate :
S. Manlik, Non-Coil.
I
Proceedings at the Meetings. 803
The following Communications were made :
1. Further applications of positive rays to the study of chemical
problems. By Professor Sir J. J. Thomson.
2. The Atomic Constants and the Property of Substances. By
R. I>. Kleeman, B.A., Emmanuel College.
3. Some Diophantine Impossibilities. By H. C. Pocklington,
M.A., St John's College.
4. Magnetic Susceptibility with Temperature. Part II, On
aqueous Solutions. By A. E. Oxley, B.A., Trinity College.
5. The Properties of Liquids connected with the surface Tension.
By R. D. Kleeman, B.A., Emmanuel College.
February lOth, 1913.
In the Comparative Anatomy Lecture Room.
Dr Shipley, President, in the Chair.
The following were elected Fellows of the Society :
W. H. Mills, M.A., Jesus College.
R. Thirkill, M.A., Clare College.
The following was elected an Associate :
F. Balfour Browne, M.A. (Oxon.).
The following Communications were made :
1. Note on the respiratory movements of Torjjedo ocellata. By
G. R. Mines, M.A., Sidney Sussex College.
2. The swarming of Odontosyllis. By F. A. Potts, M.A., Trinity
Hall.
3. Observations on Polyporus squamosus. By S. R. Price, M.A.,
Clare College.
4. Note on the Composition of some Pleistocene Sands near
Newmarket. By R. H. Rastall, M.A., Christ's College.
February 2ith, 1913.
In the University Chemical Laboratory.
Professor Pope, Vice-President, in the Chair.
The following were elected Fellows of the Society :
John Christie, B.A., Trinity College.
G. J. Hill, M.A., Peterhouse.
304 Proceedings at the Meetings.
The following Communications were made :
1. The ten Stereoisomeric Tetrahydroquinaldinomethylenecam-
phors. By Professor Pope and Mr J. Read.
2. The chemical and bacterial condition of the Cam above and
below the sewage effluent outfall. By J. E. Purvis, M.A., St John's
College and A. E. Rayneb, M.A., Gonville and Caius College.
3. Some experiments on the slow combustion of Coal Dust. By
F. E. E. Lamplough, M.A., Trinity College and Miss A. M. Hill.
4. The Oxidation of Ferrous Salts. By F. R. Ennos, B.A.,
St John's College. (Communicated by Mr C. T. Hey cock.)
5. On the optically active semicarbazone and benzoylphenyl-
hydrazone of c?/cfo-hexanone-4-cai'boxylic acid. By W. H. Mills,
M.A., Jesus College and Miss A. M. Bain.
6. Experiments illustrating "Flare Spots" in Photography. By
Dr G. F. C. Searle, Peterhouse.
7. Note on the effect of heating Paraformaldehyde with a trace of
sulphuric acid. By P. G. M. Dunlop, M.A., Gonville and Caius College.
Ajjril 28th, 1913.
In the Botanical Laboratory.
Dr Shipley, President, in the Chair.
The following were elected Fellows of the Society :
E. H. Peters, B.A., Gonville and Caius College.
C. M. Sleeman, M.A., Queens' College.
The following were elected Associates :
C. G. L. Wolffe, M.D. (McGill University).
J. Burtt-Davy, Non-Coil.
The following Communications were made :
1. Notes on additions to the Flora of Cambridgeshire. By A. H.
Evans, M.A., Clare College.
2. On some new and rare Jurassic plants from Yorkshire. By
H. Hamshaw Thomas, M.A., Downing College.
3. Some Varieties of Plants new to the British Isles. By C. E.
Moss, B.A., Emmanuel College.
i
Proceedings at the Meetings. 305
4. Observations on Hirneola auricula-judae Berk (Jew's ear).
By the Rev. M. J. Le Goc, B.A., Fitzwilliam Hall. (Communicated
by Mr F. T. Brooks.)
5. (1) On the greatest value of a determinant whose con-
stituents are limited.
(2) Expressions for the remainders when 6, 0', sin k6, cos kO
are expanded in ascending powers of 6.
By Professor A. C. Dixon.
May 5th, 1913.
In the New Medical Schools.
Professor Nuttall, in the Chair.
The following was elected a Fellow of the Society :
N. P. McCleland, M.A., Pembroke College.
The following Communications were made :
1. Observations on Ticks :
(a) Parthenogenesis,
(6) Variation due to nutrition.
By Professor Nuttall.
2. Exhibition of a Chinese flea-trap. By E. Hindle, B.A.,
Magdalene College. (Communicated by Professor Nuttall.)
3. Exhibition of living Termites. By Professor A. D. Imms.
4. The Division of Holosticha scuteUum. By K. R. Lewin, B.A.,
Trinity College. (Communicated by Professor Nuttall.)
5. Sarcosporidia in an African Mouse Bird. By H. B. Fantham,
B.A., Christ's College.
6. Note on the food of freshwater Fish. By J. T. Saunders,
B.A., Christ's College.
I
306 Proceedings at the Meetings.
May \^th, 1913.
In the Cavendish Laboratory.
Dr Shipley, President, in the Chair.
The following were elected Fellows of the Society :
P. G. Bailey, M.A., Clare College.
Franklin Kidd, B.A., St John's College.
Rev. M. J. Le Coc, B.A., Fitzwilliam Hall.
0. Udny Yule, M.A , St John's College.
The following were elected Associates :
F. E. Baxandall.
C. P. Butler.
W. Moss.
W. E. Rolston.
The following Communications were made :
1. (1) Some methods of measuring the surface tension of soap
films.
(2) A simple method of testing lens systems for aberration.
By Dr G. F. C. Sbarle, Peterhouse. J
2. On the Unstable Nature of the Ion in a Gas. By R. D. ^
Klebman, B.A., Emmanuel College.
3. A Dust Electrical Machine. By W. A. Douglas Rudge,
M,A., St John's College.
4. A mechanical vacuum tube regulator. By R. Whiddington,
M.A., St John's College.
5. The hydrodynamical theory of lubrication with special reference
to air as a lubricant. By W. J. Harrison, M.A., Clare College.
CONTENTS.
PAGE
Sarcocystis colli, oi. sp., a Sarcosporidian occurring in the Red-faced
African Mouse Bird, Colius erytliromelon. By H. B. Fantham.
(Plate V) . . . . . . . . . . . . 221
Observations on Hirneola auiicula-judae, Berl. {"Jew's ear"). (Pre-
liminary communication.) By M. J. Le Goc. (Communicated by
Mr F. T. Brooks) . . . . . . . . . .225
J}^otes on additions to the Flora of Cambridgeshire. By A. H. Evans . 229
A Note on the Food of Freshwater Fish. By J. T. Saunders . . 236
Observations on Ticks: (a) Parthenogenesis, (b) Variation due to nutrition.
By Professor Nuttall ......... 240
The Division of Holosticha scutellitm. By K. R. Lewin. (Communicated
by Professor Nuttall) . .241
Exhibition of living Termites. By Professor A. D. Imms . . . 241
On the greatest value of a determinant whose constituents are limited.
(Proof of Hadamard's tbeorem.) By Professor A. C. Dixon . 242
Expressions for the remainders wlien 6, 6^, sinX'^, cosX'^ are expanded in
ascending powers of sin 6. By Professor A. C. DjxoN . . . 244
A dust electrical machine'. By W. A. Douglas Rudge, (One fig. in
Text) . 249
071 a mechanical vacuum tube regulator. By R. Whiddington. (One
fig. in Text) ... . .251
Some Plants new to the British Isles. By C. E. Moss , . .255
On some new and rare Jurassic plants from For/^'sAM-e;— Eretmophyllum,
a new type' of Oinkgoalian leaf By H. Hamshaw Thomas.
(Plates VI and YII) ... . . . . . . 256
The Unstable Nature of the Ion in a Gas. By R. D. Kleeman.
(Two figs, in Text) 263
Note on the Absorptioti of Cathode Rays by Metallic Sheets. By
R. Whiddington. (One fig. in Text) . . . . . ,280
The Influence of Molecular Constitution and Temperature on Magnetic
Susceptibility. Prelimhiary Note. By A. E. Oxley . . . 282
A Chinese Flea-trap. By Edward Hindle. (Communicated by Pro-
fessor NuTTALL.) (One fig. in Text) .- . . . . . 284
Some methods of measuring ' the surface tension of soap flms. By
G. F. C. Searle. (Ten figs, in Text) . . . . . . 285
Proceedings at the Meetings held during the Session 1912—1913 . . 300
PKOCEEDINGS
OF THE
CAMBRIDGE PHILOSOPHICAL
SOCIETY.
VOL. XVII. PART IV.
[Michaelmas Term 1913.]
aDambritige:
AT THE UNIVERSITY PRESS,
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DEIGHTON, BELL & CO. AND BOWES & BOWES, CAMBRIDGE,
CAMBRIDGE UNIVERSITY PRESS,
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1914
Price Two Shillings and Sixpence
30 January, 1914.
NOTICES.
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EREATA
Sarcocystis colli, n. sp.
Page 224, line 14, for "lack of," read " apparent lack of."
Explanation of Plate V. After "Dorsal aspect... (Sfn-cocj/sfis colii," insert
rt. = trophozoites. (Miescher's tubes.) Approximately natural size.
PROCEEDINGS
OF THE
A possible connexion between abnormal sex-limited transmission
and sterility. By L. Doncaster, Sc.D., King's College.
[Bead 17 November 1913.]
In a recent paper* I suggested that the rare tortoiseshell
male cat might be produced by the failure of the normal sex-
limited transmission of the yellow factor from the male parent.
When a yellow (orange) male cat is mated with a black female,
the normal result is that all the female offspring are tortoiseshells,
all the males black, showing that the yellow factor is sex-limited
in its transmission by the male, and goes only into gametes which
will give rise to females. Some cases, however, are recorded
of tortoiseshell males being produced from yellow sires, and I sug-
gested that these arise by the occasional failure of the sex-limited
transmission, with the result that the yellow factor is transmitted
to a male. Such a male, receiving yellow from the male parent
and black from the female, would be a tortoiseshell. If the black
factor is also sex-limited in the male, as suggested by Little f,
then a tortoiseshell male could also arise, by failure of the sex-
limited transmission, from a black male by yellow or tortoiseshell
female, some cases of which have been recorded. It therefore
seem.s probable that the rare tortoiseshell male is produced only
by the abnormal transmission from the sire to a male child of
a character which normally goes into female producing gametes,
and that the tortoiseshell male contains two positive factors (those
for both yellow and black), instead of either one or the other as in
normal male cats.
* "On Sex-limited Inheritance in Cats." Journ. of Genetics, iii. 1913, p. 11.
t C. C. Little, Science, May 17, 1912.
VOL. XVII. PT. IV. 21
308 Dr Doncaster, A possible connexion heUueen
In the paper referred to, I mentioned that I had in my
possession a tortoiseshell tom, which I was mating with black
females in the hope of testing this hypothesis. The experiment
has now been in progress for about nine months ; the tom has
mated, apparently successfully, with each of four females several
times, but none of them have become pregnant. (The females
have had respectively two, three, five and five periods of ' heat '
during the time, and at each period there have been one or more
apparently normal copulations.)
It seems fairly clear, therefore, since three of the four females
have previously borne kittens to other sires, that the tom-cat
is sterile. This is confirmed by facts pointed out to me by Dr
F. H. A. Marshall. On examining one of the females about four
weeks after the last pairing, he found that the mammae were
swollen and on pressure exuded a small amount of milk. This
continued for about two weeks, after which the exudation became
less and finally disappeared. Now it is known that there may be
correlation between the development of corpora lutea and mam-
mary hypertrophy, and Marshall and Hammond have found that
in rabbits from which the uterus has been excised so that preg-
nancy is impossible, slight lactation may supervene after ovulation,
owing, apparently, to the presence of corpora lutea in the ovary,
and that a period of ' heat ' does not recur until this lactation has
ceased. Further, Longley* has shown that in the cat ovulation
only occurs after copulation. If, then, the slight lactation ob-
served was caused, as in the rabbit, by the presence of corpora
lutea consequent on ovulation, the copulation must have been
sufficiently normal to cause ovulation, which does not take place
in its absence. That ovulation occurred is also suggested by the
rather widely separated periods of heat. Cats in the breeding
season usually come on heat every three weeks or oftener; my
females, after pairing with the tortoiseshell tom, did not come on
again as a rule for at least five weeks, and usually not for six
weeks or even more. When all these facts are taken together,
there seems to be little doubt that the tom is sterile, although he
is normally formed and has the sexual instincts strongly developed.
If this were an isolated case, it might be of no importance, but
there are hardly any records of offspring of tortoiseshell males, and
the few that exist are perhaps not wholly above suspicion. I
believe that two such cats at least are well known never to have
become parents, and I know of another case in addition in which a
tortoiseshell tom was paired but no pregnancy followed. It seems,
therefore, that the abnormal constitution of a tortoiseshell tom
with regard to its inherited characters may be connected with
* W. H. Longley, " Maturation of the Egg and Ovulation in the Domestic Cat."
Amer. Journ. Anat. xii. 1911, p. 139.
abnormal sex-limited trxinsmission and sterility. 309
sterility. If the sterility is due, directly or indirectly, to the
failure of sex-limited transmission on the part of one of the
parents, we should expect other eases in which there is an ex-
ception to the normal sex-limited transmission to be sterile also,
and this summer I have bred two specimens of this kind in
l-'ye moth Abraxas grossidayHdta. Usually the grossulariata
female transmits the g7'oss. character only to her sons, ^o that
when mated with a lacticolor male (from which the gross, charac-
ter is absent), the male offspring are gross., the females lact.
I have had very rare exceptions to this rule in preceding years,
but none in which I could entirely exclude the possibility that the
gross, females ■were really wild females of which the larvae had
accidentally been introduced with the food. This year, however, I
have in one family from the mating gross. $ x lact. (/ in addition to
21 gross, males and 14 lact. females, two gross, females to which it
is impossible to ascribe such an accidental origin, for they have
peculiar features which I have only seen in the strain to which the
family belongs. I intend to discuss elsewhere the importance of
these exceptions to the normal sex-limited transmission ; in
the present connexion, the interesting fact about them is that
both were quite sterile. Both paired normally ; one laid no
eggs at all, and the other laid only 22 eggs, none of which
developed. Sterility in the strain to which they belong is not
very rare ; this summer, in 56 matings with females more or less
related to the moths in question, 10 were nearly or quite sterile.
On the other hand, I paired four normal sisters of the exceptional
females, and all were fully fertile. It is thus not very probable
that both the exceptional females should have been sterile, if the
sterility had no connexion with their abnormal hereditary consti-
tution. The facts, therefore, seem to indicate that when, by
failure of sex-limited transmission, an individual arises which
receives from one parent a character which it normally receives
only from the other, that individual tends to be sterile.
21—2
310 Dr Hindle, The Flight of the House-Fly,
The Flight of the House-Fly. By Edward Hindle, B.A.,
Ph.D., F.L.S., Assistant to the Quick Professor of Biology ;
Magdalene College, Cambridge. '(Communicated by Mr C. Wap-
BURTON.)
[Read 17 November 1913.] if
During the months of July, August, and September, 1912,
the author, in conjunction with Mr Gordon Merriman, conducted
an extensive series of experiments on the range of flight of Musca
domestica Linn, in the town of Cambridge. In the course of these
experiments upwards of 25,000 flies have been hberated under
very variable meteorological conditions, and about 50 observation
stations were employed for their recovery.
In all cases the flies used in these experiments were either
caught in balloon traps, or directly netted. The method of
obtaining flies by breeding was abandoned, as it was almost
impossible to obtain them without numerous other species of
insects, and also on account of the possible objections to such
artificially bred flies.
Prior to being liberated the flies were kept for about 24 hours
in cages made of mosquito netting and were fed on brown sugar,
the moisture being supplied by a layer of damp sand. By this
method it was assured that they had emerged sufficiently long to
allow the full development of their chitinous exoskeleton, neces-
sary in order to obtain the full power of flight.
Preparatory to colouration the insects were transferred from
the mosquito cages into wire balloon traps. This transference
was effected as follows : — the loose sides of the mosquito netting
cage were tied round the bottom of the balloon trap. The latter
was then held towards the light and the whole of the cage sur-
rounded with a black cloth. Owing to the strong attraction of
the light, the flies all made their way towards the brightly
illuminated balloon trap and in passing through the small hole
in the bottom of the latter, it was possible to make accurate
counts of them, as not more than two or three were able to pass
through at the same time, When about 1500 flies had entered
the balloon trap it was closed, then removed and another trap
fixed in its place.
The most satisfactory mode of marking the flies was found to
be that devised by Nuttall (vide Jepson, 1909), and this was
employed in all these experiments. The balloon trap containing
the flies was placed in a large brown paper bag containing a
handful of powdered blackboard chalk, coloured either red, orange.
Dr Hindu, The Flight of the House-Fly. 311
or yellow. The mouth of the bag was then closed and the whole
gently shaken for one or two minutes so that the flies were
thoroughly dusted with the chalk. The balloon was then removed
and, after being taken to the point selected for the liberation, the
trap was opened and the flies allowed to escape in any direction
they chose. The flies were recovered either by means of fly-papers
or balloon traps, several of which were exposed at the various
observation stations. The traps and papers were examined for
several successive days after the liberation of a number of coloured
flies and as the observation stations extended as far as 900 yards
from the point of liberation, comprising both thick and sparsely
populated localities, an accurate idea of the distribution of the
insects was thus obtained. Full meteorological data were kindly
supplied by Messrs W. E. Pain, Chemists, Sidney St., Cambridge.
Their observations were made in the centre of the town and in
consequence indicate the exact conditions under which the flies
travelled.
Discussion of results.
Unfortunately, nearly all our experiments in Cambridge were
seriously handicapped by the great difficulty of obtaining flies
in sufficient numbers and also by the adverse meteorological
conditions. Throughout August the weather was so bad that
from the nineteenth to the thirty-first not a single fly could be
liberated. During the early part of September nearly all the
flies became infected with Empusa muscae and this, in conjunction
with the .cold weather, brought the investigation to a sudden end.
In the earlier experiments we should have preferred to have
liberated at least double the number of flies, but owing to the
difficulty of procuring them this was impossible. Our results,
therefore, are not as complete as we could have wished.
Nevertheless, owing chiefly to the large number of stations
employed for the recovery of the flies and their being situated
in every direction, we have been able to obtain certain definite
results.
The most striking feature is the marked effect of the direction
of the wind on the courses taken by the flies. After a careful
examination of all our results, we can state definitely that flies
tend to travel either directly against or across the wind. The
only exceptions to this rule were those recovered within a radius
of about 150 yards from the point of liberation and probably
these flies were individuals that had merely selected the first
shelter they could find. These results diff"er considerably from
those of Copeman, Hewlett and Merriman (1911) who found that
the flies tended to go with the wind, but it should be remembered
312 Dr Hindle, The Flight of the House-Fly I'
that not only were these investigators working in open country,
but also their traps were set solely at stations to the west of the
point of liberation and consequently none of the flies that flew
in other directions would be recovered.
Owing to lack of opportunities we have been unable to decide
why, in our experiments, the flies tended to travel either against
or across the wind. Two explanations seem possible.
(1) The flies may direct their flight against any current of
air to which they are subjected. This property is known as
positive anemotropism and is possessed by some obher insects
and birds. In view, however, of the contrary results obtained by
Copeman, Howlett and Merriman (1911) we cannot come to
definite conclusions on this point and further expei-iments are
required to determine if other factors than wind-direction may
influence the direction of flight.
(2) The flies may travel against the wind, being attracted
by any odours it may convey from a source of food. A point in
favour of this supposition is the nature of the stations at which
flies were recovered after they had travelled any distance. These
comprised a butcher's shop, public-houses and a restaurant, all
of which places gave off odours that are notoriously attractive
to flies.
The maximum distance travelled by aay of the flies we
liberated in Cambridge was 770 yards, which is considerably less
than that covered by those liberated in the open country at
Postwick, in one case as much as 1700 yards. This difference
may be attributed to the absence of shelter in the case of the
Postwick flies, whereas in Cambridge food and shelter were
always plentiful. On the whole, we do not think it likely that
as a rule flies travel more than a quarter of a mile in thickly
housed areas. Throughout our experiments the only individual
that exceeded this distance had travelled 770 yards, of which
a large part was across open fen land.
The chief factors influencing the dispersal of the flies are
temperature, weather, and the time of day when the insects are
liberated. The effect of temperature is very marked, as when
it is low the flies become torpid and seek the first available
shelter. Fine weather is also a necessary condition for long
flights, as rain at once drives the flies under cover. The ideal
conditions for an experiment are two or three days of fine warm
weather, during which the flies can make their flight, succeeded
by a wet or showery day, when they are driven indoors and thus
can be recorded at the various stations.
With regard to the altitude of the point of liberation, flies set
free from the roof* tended to disperse slightly better than those
■" A height of about 45 feet.
Dr Hindu, The Flight of the House-Fit/. 313
liberated from the ground, but the differences were not very
considerable.
When the insects are liberated late in the afternoon, they do
not disperse in as great numbers as those liberated during the
morning, but the distances travelled are not inferior.
With regard to the vertical flight of the house-fly, although
we have found no means of estimating the maximum, nevertheless,
when liberating them from the ground, we have frequently ob-
served the flies at once mount almost vertically upwards to a
known height of 45 feet.
Summary.
(1) House-flies tend to travel either against or across the
wind. This direction may be directly determined by the action
of the wind, or indirectly, owing to the flies being attracted by
any odours it may convey from a source of food.
(2) The chief conditions favouring the dispersal of flies are
fine weather and a warm temperature ; the nature of the locality
is another considerable factor, as in towns flies do not travel as
far as in open country, this being probably due to the food and
shelter afforded by the houses.
(3) Under experimental conditions, the height at which the
flies are liberated and also the time of day influence the dispersal
of the insects. When set free in . the afternoon they do not
scatter so well as when liberated in the morning.
(4) From our experiments the usual maximum flight in thickly
housed localities seems to be about a quarter of a mile, but in one
case a single fly was recovered at a distance of 770 yards. It
should be noted, however, that part of this distance was across
open fen land.
REFERENCES.
CoPEMAN, S. M., HowLETT, F. M. and Merriman, G. (1911). "An
Experimental Investigation on the Range of Flight of FJies.'^
Reports to the Local Government Board on Public Health and
Medical Subjects. New Series, No. 53, pp. 1 — 10, with map.
Hewitt, C. G. (1912). "Observations on the Range of Flight of
Flies." Reports to the L.G.B. New Series, No. 66, pp. 1 — 5, with
map.
HiNDLE, E. and Merriman, G. (1913). "The Range of Flight of
Musca domestica. Experiments conducted in Cambridge." Reports
to the L.G.B. New Series, No. 85, pp. 20—41, with 13 charts.
Howard, L. O. (1911). The House-Fly — Disease Carrier. New York:
F. A. Stokes & Co.
Jepson, F. J. (1909). "Notes on Colouring Flies for Purposes of
Identification." Reports to the L.G.B. New Series, No. 16, pp.
4—9.
314 Mr Kleeman, On the Dependence of the Relative lonisation
On the Dependence of the Relative lonisation in various Oases
by y8 Rays on their Velocity, and its hearing on the lonisation
produced by y Rays. By R. D. Kleeman, B.A. (Emmanuel
College), D.Sc. (Adelaide).
[Received 9 October 1913. Bead 27 October 1913.]
Experiments which give some information whether the rela-
tive ionisation by yS rays in various gases depends on the velocity
of the rays have already been carried out by the writer*, who
measured the relative ionisation per c.c. in various gases by the
yS rays of actinium and uranium. The experiments shewed, as
far as they went, that the relative ionisation is independent of the
velocity of the /3 ray. Further experiments have been carried
out on the subject and will be described in this paper.
A beam of heterogeneous ^ rays was obtained by placing a
quantity of radium in a thin glass tube at one of the entrances of
a bore-hole "6 cm. in diameter passing through a lead block about
7 cm. square. The beam was allowed to pass into an ionisation
chamber through an aluminium window '16 mm. thick. By
means of a magnetic field whose lines of force were at right
angles to the bore-hole the beam of rays could be " hardened " to
any desired extent by bending some of the slower moving rays
aside. It was found that the gradual hardening of the beam
produced no change in the relative ionisation of the gases in the
chamber. The ionisation of methyl iodide and hydrogen in
terms of that of air was measured, since these gases differ from
one another considerably in the nature of the atoms they contain.
As an illustration of the experiments it may be quoted that in
one case the ionisation of hydrogen in terms of that of air was
•156 without the magnetic field, and '151 with the magnetic field.
The magnetic field in this particular case reduced the ionisation
in air and hydrogen to about one-half of their previous values.
In the experiments the ionisation of air and hydrogen were first
measured without a magnetic field on, putting air into the
chamber first. Then leaving the hydrogen in the chamber and
putting the magnetic field on, the ionisation of the hydrogen was
measured under the new conditions. Lastly, putting air into the
chamber its ionisation was measured with the same magnetic
field on. This process was repeated several times and the mean
of the results taken. When methyl iodide mixed with a certain
proportion of air was used instead of hydrogen in the experiment
* Proc. Roy. Society, A, vol. 83, p. 530 (1910).
in various Gases by ^ Rays on their Velocity. 315
mentioned, the relative ionisations with and without a magnetic
field were 1"97 and 1*82 respectively. The relation between
velocity and number of /3 rays from radium has been investigated
b}' Pashen, It appears from this that in my experimental
arrangement the velocities of the rays producing the larger
part of the ionisation probably lay between 1 xlO^" and 2-9 x 10^" cm.
per second. It would of course have been preferable to obtain a
spectrum of the rays by means of a magnetic field and investigate
the ionisation produced at different parts. If any indications
had been obtained that the relative ionisation depended on the
velocity of the /3 ray, an elaborate experiment of this nature
would have been carried out. It would, however, be desirable
to carry out experiments on relative ionisation, using the cathode
rays obtained in a discharge tube, or those ejected from metals
by X rays, since their velocity is considerably less than the
majority of the /3 rays from radium. An experiment of this nature
is about to be carried out.
The results obtained have an important bearing on the nature
of the process of the ionisation in a chamber through which
7 rays are allowed to pass. _ The ionisation in question may be
divided into three parts, viz. (a) the ionisation produced by the
/3 rays given off the walls of the vessel, (6) that by the secondary
7 rays given off the walls, (c) and that due to the absorption of
the primary 7 rays by the gas in the vessel. The ionisation
under (c) consists of the ions produced by the /3 rays ejected
from the molecules of the gas under the action of the primary
7 rays, and possibly of direct ionisation by the primary 7 rays.
According to some experiments of C. T. R. Wilson*, however, the
latter part is comparatively small or non-existent. We shall return
to this point later. It can be easily shewn that the ionisation
under (c) is small in comparison with that under (a). For the total
absoi'ption of the primary 7 rays by the gas is very much smaller
than that by the walls of the vessel. And since the mass of
matter per cm.^ of the walls of the vessel through which a /3 ray
is able to penetrate corresponds to probably hundreds of times
that of the mass per cm.^ of the gas in the vessel, a much larger
number of /3 rays will cross the chamber which originate in its
walls than which originate in the gas. The ionisation under
(6) has usually not been deemed worthy of much or any con-
sideration by physicists who have worked with 7 rays. It is
by no means of negligible magnitude. This will appear from
a study of the ionisation by 7 rays of different hardness. The
writerf has shewn, using secondarj^ 7 rays, that the ionisation in
methyl iodide relative to that in air greatly increases with the
* Proc. Roy. Society, A, vol. 87, p. 277 (1912).
t Ibid., vol. 82, p. 358 (1909).
316 Mr Kleeman, On the Dej^endence of the Relative lonisation ^,j
softness of the rays. This fact has recently been used by ■
Rutherford to isolate the different groups of the 7 rays of radium. >i]
Now according to the results obtained in this paper this could
not be due to differences in the nature of the /3 radiation given off j
the walls of the vessel. It could not have been due to some of the
soft /S radiation from the walls being totally absorbed by the gas,
since the total ionisation depends little on the nature of the gas*.
Therefore since the ionisation under (c) is small in comparison
with that under (a), this increase must be due to an increase of
the ionisation under (b).
It appears from the experiments by C. T, R. Wilson mentioned
that /3 rays produce secondary /3 rays of small velocity only,
i.e. 8 rays. Bragg f and the writer | have shewn that the velocity
of the secondary $ rays produced by 7 rays decreases with the
absorbability of the latter. It follows from this that if the /3 and
7 rays of radium are allowed to fall upon a plate of material,
and soft 7 radiation is produced in it, soft /3 radiation should
emerge from the surface of the plate due to this soft 7 radiation.
The writer§ has shewn the existence of this soft yS radiation, some
of which is totally absorbed in about 2 cm. of air at atmospheric
pressure. The energy of the soft' 7 radiation producing the
ionisation under (b) is probably much less than that of the primary
7 rays. But since it is much more absorbable the ionisation it
produces could easily be greater. It is to be expected then that
if a narrow beam of 7 rays is sent through an ionisation chamber
and the /3 rays curled up by meaus of a magnetic field, an experi-
ment the writer II has carried out, there should still be con-
siderable ionisation left in the chamber. Bragg has objected to
this experiment, because it is difficult to curl up all the /3 rays
to the same extent owing to their cutting the lines of magnetic
force at different angles. Undoubtedly this objection might be
raised, but still I think that the diminution with increase of
magnetic field should have been greater under the particular
circumstances than that obtained. Bragg and MadsenlF have
carried out some experiments which they thought incidentally
shewed that the ionisation produced by secondary 7 rays in the
vicinity of material on which primary 7 rays are allowed to fall is
small in comparison with that produced by the secondary /3 rays.
They placed plates of material of different thicknesses in in-
creasing order of magnitude across a beam of 7 rays and measured
the ionisation produced on the side of the plate where the 7 rays
* Proc. Roy. Society, A, vol. 84, p. 17 (1910).
t Phil. Mag., Dec. 1908.
+ Proc. Roy. Society, A, vol. 82, p. 128 (1909).
§ loco. cit.
II Proc. Camb. Phil. Society, vol. xv. Pt ii. p. 169 (1909).
II Phil. May., Dec. 19Q8, p. 932.
in various Gases hy ^ Rays on their Velocity. 317
emerged. Since they got no further increase in ionisation after
a thickness of material giving the maximum /3 radiation had
been reached, they concluded that the secondary 7 rays produce
no appreciable ionisation. But it must be taken into account
that since the energy of the secondary 7 radiation is pro-
bably smaller than that of the jB radiation, the absorbability of
the secondary 7 rays must be of the same order of magnitude
as that of the ^ rays to produce an appreciable ionising effect.
This secondary 7 radiation would thus reach a maximum for
a thickness of material certainly not much greater than that
giving the maximum ^ radiation. An increase in the ionisation
with the thickness of material cannot therefore be expected, and
Bragg and Madsen's conclusions do not therefore definitely
follow from these experimental results. It should be pointed
out that the soft secondary 7 rays, whose coefficient of absorption
is the same as that of the /3 rays, are eliminated in measurements
of the coefficient of absorption of secondary 7 rays. For the
thickness of the wall of the ionisation chamber is usually such as
to absorb all the ^ rays falling ujDon it and consequently all the
secondary 7 rays of the same absorbability. Measurements by
various observers have shewn that the secondary 7 rays as a
whole are much more absorbable than the primary 7 rays. Thus if
carbon is taken as the radiating and lead as the absorbing material
the writer* has shewn that the coefficient of absorption for the
secondary 7 rays is about 10 times the magnitude of that of
the primary rays. Much softer rays are thus likely to exist
which are eliminated in the way explained. However, taking all
the evidence into account, there is no doubt that the ionisation
produced by the secondary 7 rays from the walls of the ionisation
chamber is less than that produced by the /3 rays when a gas
containing atoms of low atomic weight such as air is in the
chamber. Probably in that case it is of the order of 20 per cent.
of the total ionisation. The percentage probably increases with the
softness of the primary 7 rays. When, however, a heavy gas like
methyl iodide is in the chamber it may be very much greater,
since the ionisation of heavy gases relative to air increases greatly
with the softness of the rays ; thus the ionisation of methyl iodide
relative to that of air is about 6 for the primary 7 rays of radium
calculated from absorption data, while for X rays it is about 80.
Bragg "f" has given a formula which expresses the ionisation in
a chamber through which 7 rays are allowed to pass in terms of
other quantities. This formula does not take into account the
production of secondary 7 rays in the walls of the vessel. It is
necessary to add two terms to the formula, one term expressing
* PUl. Mag., May 1908, p. 652.
t Ihid., Sept. 1910, p. 402.
318 Ml' Kleeman, On the Dependence of the Relative lonisation
\
the ionisation due to the absorption of the secondary <y rays by
the gas in the chamber, and the other the ionisation produced
by the /S rays produced by the secondary y rays in the walls of
the chamber.
When the softness of the primary j radiation is increased,
that of the secondary radiation from the walls of the chamber
must be increased also. Thus the behaviour of the relative
ionisations of the gases in the chamber with a variation of the
softness of the primary 7 rays, is an index of a general nature of
the variation of the chance of an atom becoming the source of a
/3 ray under the influence of y pulses with the softness of the
latter. Some experiments* that I have carried out previously
have a bearing on this point. It was found that the ionisation of
a gas relative to that of air increased with the softness of the
7 rays when the molecules contained atoms heavier than those in
air. But it decreased with the softness of the rays in the case of
hydrogen. This fits in with the results obtained by Orowtherf
with X rays of different hardness. The results are thus evidence
of the identical nature of 7 and X rays.
It will be of interest here to consider more closely the nature
of the process of the ionisation by 7 or X rays. According to the
experiments of C. T. R. Wilson mentioned the ionisation is
produced by the ^ rays ejected by the rays. In these experi-
ments photographs of the ions were obtained by making them
serve as nuclei to a fog in a cloud-producing apparatus of
appropriate construction. Previously, however, Crowther| had
shewn that the ionisation by X rays is largely direct ionisation.
The method he used involved the principle that the ionisation
produced, varies directly as the pressure, while that produced
by the secondary /B rays varies as the square of the pressure.
Beattyl later found that the amount of direct ionisation
greatly depended on the nature of the gas and hardness of
the rays. These experiments do not fall into line with those of
C T. R. Wilson. But the disagreement is, I think, more ap-
parent than real. An inspection of the photographs obtained by
C. T. R. Wilson will shew that a blotch occurs at the beginning of
each streak which shews the ions produced along the course of a
yS or cathode ray. It may be mentioned that a blotch also occurs
at the end of each streak, being due to the zig-zag path and
intense ionisation by the cathode particle before it ceases to
ionise. In the former case it seems to be most likely due to
the cathode particle ionising one or more atoms of its parent
* loco. cit.
t Proc. Roy. Sociehj, A, vol. 82, p. 115 (1909).
+ Ibid., p. 103 (1909).
§ IWd., vol. 85, p. 230(1911).
in various Gases hy j3 Rays on their Velocity. 319
molecule. Besides, the recoil atom may also help to ionise the
atoms of the molecule and to break it up, and also to ionise other
molecules like an a particle. Now all the ions that are made from
the molecules which give rise to the cathode rays appear as
direct ionisation since it varies proportionally to the pressure. So
does all the ionisation produced by the recoil atom, since its path
would be extremely short in comparison with the diameter of
chamber even at very low pressures. Thus the ionisation that
varies directly as the pressure may not be of negligible magnitude
in comparison with the whole ionisation, especially at low pressures.
Bragg* has used a method to investigate the point under dis-
cussion which is entirely different from that used by Crowther
and Beatty. He concludes that all the ionisation is produced by
the secondary cathode rays ejected by the X rays. His method
would not shew as direct ionisation that produced from the
parent molecules of the cathode particles. Thus a discrepancy
between his and Crowther's and Beatty's experiments may be
expected.
Some experimenters have investigated the variation of the
ionisation by 7 rays of a gas with its pressure over a great
range of pressures. But this can furnish little if any reliable
information about the exact nature of the process of ionisation.
For the ionisation produced by the secondary /S rays from the
walls of the vessel, that of the molecules producing the secondary
/3 rays, and the ionisation produced by the recoil atom, if any,
varies directly as the pressure. The experiment does not isolate
these different ionisations. The remainder of the ionisation varies
as the square of the pressure.
But this subdivision of the ionisation holds only if all the
/3 rays end their life in the walls of the vessel. Strictly the
ionisation produced by the secondary jS rays from the gas which
do not cross the chamber or are reflected by the walls of the
vessel and end their life in the gas, varies approximately pro-
portionally to the pressure over small ranges of pressure. It
increases strictly somewhat more rapidly than proportionally to
the pressure. The ionisation by the /3 rajs from the walls of the
vessel which end their life in the gas of the vessel is approximately
constant for small variations of the pressure, but strictly increases
with the pressure.
Thus one part of the ionisation produced by the soft 7 rays
from the walls of the vessel varies as the square of the pressure of
the gas, and the other part approximately directly as the pressure.
The latter part would increase with increase of the softness of
the rays and the pressure of the gas. That part of the ionisation
* Phil. Mag., Sept. 1910, p. 406.
320 Mr Kleeman, Dependence of Relative lonisation, etc.
varies as the square of the pressure does not violate the con-
clusions drawn by the writer from the experiments on soft
secondary <y rays. It was found that the ionisation was pro-
portional to the pressure over the range of pressures used. Any
deviation from this at other pressures could not seriously affect
the results, since the ionisation in a gas was compared with
approximately the same mass of air and then reduced to standard
pressure. Thus the scattering and absorption of the /8 rays by
the gas was approximately the same in the two cases. The
principal reason for doing this at the time was that it rendered
the ionisations in most cases nearly equal to one another.
I have carried out some experiments with the object of
detecting the ionisation that is probably produced by the recoil
atom or molecule when a /3 ray is ejected. They depended on
the principle that the ions produced by the recoil atom would
probably shew initial recombination like those made by the
a particle. The difficulty is to get rid of the ionisation by jS rays
from extraneous sources. The experiments were not a success,
probably owing to this difficulty not having been overcome to
a sufficient extent. A shallow cylindrical ionisation chamber was
used whose walls consisted of tightly stretched tissue-paper over
a skeleton chamber of thin aluminium wire. A mixed beam of
/3 and 7 rays from a quantity of radium was passed through
the chamber. The current was measured for fields of different
strengths when the beam was largely freed from ^ rays by means
of a strong raaguetic field, and when it was not so modified. The
current saturation curves obtained were the same in the two
cases. It could be shewn from energy considerations that when
the beam was free from /3 rays the ionisation due to the recoil
atom must have been less than 10 °/^ of the whole ionisation. From
the outset, therefore, the experiment had not much chance of
success. Another method is about to be tried.
ilf/r McGleland, Dijnaviical system illustrating Fluorescence. 321
Note on a Bi/namical system illustrating Fluorescence. By
N. P. McCleland, M.A., Pembroke College.
[Bead 27 October 1913.]
The characteristic feature of the phenomenon of fluorescence
is that the period of the exciting force differs from that of the
induced vibration.
No simple dynamical system appears to have been brought
forward hitherto in which this condition is fulfilled, consequently
it appears of interest to suggest the following, which is founded on
a well-known model of the atom.
Suppose a particle (of unit mass) revolves in a circular orbit
about a fixed point, there being no resistance to the motion,
but that forces exist which damp vibrations along the radius
vector.
The law of attraction is here taken to be that of the inverse
square but a similar result will be obtained under any law which
permits stable motion. Let this system be acted on by a periodic
force in its own plane, the disturbance being small.
Let this force be A sin (p^ + e), acting parallel to ^ = 0.
Let r = ro + p, d — (ot + -ylr be the coordinates at time t. A, p
and -v/r are supposed always small.
We have for the disturbed motion
r ->tkf- r6" =• - -^ + A sin (jJt + e) cos (cot + ^jr)
1 d
+ ~-r (r"d) = -A sin (pt + e) sin (cot + -v/r).
7' CtZ
Substituting /•„ + p for r, cot + -ylr for and keeping in only terms
of the 1st order we obtain
p + kp — pco^ — 2roco'^ = 2pco^ + A sin (pt + e) cos cot . . .(i),
and rojr + 2a)p = — A sin (pt + e) sin (at (ii).
The last becomes on integration
A f sin Up - co) t + e] sin {(p + m) t + e]
^ ^2V p- CO p + oo
+ const (iii).
322 Mr McCleland, Bynamical system illustrating Fluorescence.
Substituting for i^ in (i) we obtain
A
"sin {( jj — (o)t-\- e] sin {( p + w) < + e]
p — (i) p + (O
— 2cop + const, j = ^ sin (pt + e) cos cot . . .(iv)
which easily reduces to
p + kp + co-p =
A
^ sin {(p - o})t + e]
.P
+ ^ — - sin [(/> + co)t + e} \+ const. . . .(v).
p + ft) J
The disturbance therefore consists of two trains of waves of
different period, and it can be seen that these do not combine to
give a single train of the same period as the initial disturbance.
Mr Baxandall, On Lines of Magnesium in Stellar Spectra. 328
On the Presence of certain Lines of Magnesium in Stellar
Spectra. By F. E. Baxandall, A.RC.Sc. (Communicated by
Professor Newall,)
[Read 24 November 1913]
In a recent paper* by Professor Fowler on "New Series of
Lines in the Spark Spectrum of Magnesium/' four magnesium
spark lines are recorded which do not belong to the series. The
same four lines had previously been given by Fowler and Paynf,
but in the later paper more accurate wave-lengths are given.
The series lines, with the exception of X.4481'3, are outside the
region usually obtained in photographs of stellar spectra, but the
four lines mentioned occur in a part of the spectrum available for
investigation, their wave-lengths being 4384-86, 4390-80, 4428-20
and 4434-20. In a " Catalogue of 470 of the Brighter Stars," pub-
lished in 1902 by the Solar Physics Committee, a record is given
of the wave-lengths of lines in the spectra of various stellar types.
Reference to this shows that weak lines are recorded at or near
the positions of Fowler's magnesium lines in the spectra of a Cygni
and a Canis Majoris, as follows :
Mg. Spark
Lines (Fowler) a Cygni a Canis Majoris Remarks
4384-86 — 4384-7 (1)
4390-80 4391-0 (2-3) 4391-0(2) Stellar line probably chiefly due
to proto-titanium 4391*19.
4428-20 4428-7 (1) 4428-7 (1)
4434-20 4434-4(1) 4434-4 (<1)
Although the magnesium line 4390-80 may enter into the
composition of the stellar line 4391-0, the latter is probably due
chiefly to proto-titanium line 4391'19, as all the other prominent
enhanced lines of titanium are represented in these stellar spectra.
The remaining lines have not hitherto been assigned to a terrestrial
source, and it seems highly probable that they are the stellar
analogues of the magnesium lines. The largest divergence in
wave-length is 0-5 tenth-metre (line 4428*20), but there is a
possibility of such an error occurring in the measurement of weak
stellar lines which, under the magnification used in the measuring
instrument, are very difficult to see.
Since the publication of the stellar records referred to, better
photographs of the spectra have been obtained at South Kensing-
ton, and new measures of the wave-lengths of the lines have been
made. The fiducial lines used in the determination of the posi-
tions are Fe 4383-72, pFe 4417-00 and pTi 4444-0, all of which are
* Proc. Roy. Soc. vol. lxxxix. p. 133, 1913. f ib, vol, lxxii, pp. 253—257,
VOL. XVII. PT. IV. 22
324 Mr Baxandall, On the Presence of certain Lines
I
i1
sharply defined lines in the spectrum of a Canis Majoris. Fron:
measures on these and the stellar lines under discussion and'
subsequent use of Hartmann's interpolation formula the resulting
wave-lengths for the three unknown lines measured are
4384-7, 4428-4, 4434-3.
Fowler's wave-lengths for the three magnesium lines are
4384-86, 4428-20, 4434-20.
The differences here are no greater than one would expect,
allowing for the weakness of the stellar lines. As a check on the
accuracy of the resulting wave-lengths, another line was measured
which was known to be identical with the laboratory line
Fe 4404-88. The deduced wave-length for this stellar line was
4404-9. It is fairly certain, then, that the wave-lengths estimated
for the weaker unknown stellar lines are correct to within + 0-2
tenth-metres.
Fowler's line 4384-86 falls in position between two well-
authenticated lines in the a Canis Majoris spectrum. The first
is 4383-72, a very strong arc and spark line of iron, the other
4385*55, an enhanced iron line. In the stellar spectrum these
two lines are nearly equal in intensity, and the line 4384-7 between
them makes a close and almost equally spaced triplet with them,
and there is no doubt about the separation of these lines in the
best spectra of Sirius photographed at South Kensington with two
Henry prisms of refracting angle 45° and aperture 6 inches.
Reference to the best spectra of this star in the Cambridge series
of photographs used for radial- velocity work abundantly verifies
the existence of the extra line.
The line at wave-length 4384-7 was not recorded in the a Cygni
spectrum in the publication previously referred to, but an examina-
tion of the most recent Kensington photographs and the Cambridge
radial-velocity plates leaves no doubt as to its occurrence in that
spectrum. Taking the three lines (4383-72, the extra line, and
4385-55) as they occur in stellar spectra, the interval on the red
side is a little smaller than the other and the wave-length of
the middle line is 4384-7. There can be no doubt about the
wave-lengths of the two outside lines, which are identical with
the two solar lines 4383-72, 4385'55. If the wave-length recorded
by Fowler for the magnesium line is correct, and if this line really
does occur in the stellar spectrum, the resulting stellar triplet
formed by this line and the iron and proto-iron lines should be
spaced in the proportion of 11-4 to 6-9, the larger space being on
the more refrangible side. As previously stated, the space on the
violet side is greater than the other in the stellar spectrum, but
certainly not in the required proportion, assuming that Fowler's
wave-length is correct.
of Magnesium in Stellar Spectra. 325
It would appear then that either (1) the laboratory line
and the stellar line are not identical, or (2) the wave-length
of the laboratory line as recorded by Fowler is from O'l to 0'2
tenth-metre too high. In stating these alternatives, it is as-
sumed that the two outside stellar lines are identical with the
solar lines mentioned, but there is practically no doubt on this
point.
The 4481 line of magnesium, which is a very strong line
in Fowler's spectrum giving the magnesium lines under discussion,
is, in stellar spectra, about at its maximum in such stars as
a Cygni and a Canis Majoris, in which these other magnesium
lines appear to exist.
22—2
326
Mr Brindley, The proportions of the sexes
The proportions of the sexes of Forficula auricularia in the Scilly
Islands. By H. H. Brindley, M.A., St John's College.
[Read 17 November 1913]
In the Proceedings, vol. xvi. pt. 8, 1912, p. 674, I summarised
the results of enumerating the sexes of adult individuals of For-
ficula auricidaria, the Common Earwig, in collections obtained from
29 localities in the British Isles. It was explained that this study
of the proportions of the sexes arose incidentally to an enquiry,
of Forficula aiiricularia in the Scilly Islands. 327
still in progress, on the dimorphism of the forceps in the adult
male. In the table showing the proportions of the sexes in collec-
tions made up to 1911 the extreme instances are both from the
Scilly Islands ; Round Island, the granite islet at the north of the
group, having 16"1 per cent, of males; while the comparatively
large and cultivated island of Tresco has the highest male per-
centage so far observed, viz. 59"7. Both collections were made in
August and September 1911. Mr E. J. Burgess Sopp, F.E.S ,
had kindly sent me the sex proportions of several collections made
by himself in four English counties, and in his list also Tresco
has the highest male percentage, 55 '5 (collection made in 1903).
In view of these results I went to the islands in the second
half of August in 1912, in company with Mr F, A. Potts of Trinity
Hall and Mr J. T. Saunders of Christ's College, to whom I am
indebted for great assistance in the task of collecting as many
earwigs as possible. Collections were made in all the inhabited
and in five of the uninhabited islands. We have to thank
Mr T. Algernon Dorrien-Smith, the Lord Proprietor of the islands,
for his kind hospitality and for local information which much facili-
tated the earwig collecting and the other zoological work which
partly occupied the time of Messrs Potts and Saunders.
The figures in the sketch map show the percentages of males
in the collections made in August 1912, and also in one islet,
Rosevear, which we did not visit, and in one locality, Perth Cressa,
the S.W. inlet of St Mary's. These were searched for me by our
boatman and his family in September 1913. The following table
includes the collections shown in the sketch map and also all
others from the Scilly Islands which are in my hands.
From certain of the islands the total number of adult speci-
mens is too small to accept the proportions of the sexes calculated
therefrom without reserve. It has been a frequent experience
that the proportions vary a good deal when the sexes are taken
haphazard from a collecting bottle in which they have been mixed
together, at least until a total of 300 has been exceeded. But on
the islands which yielded a low total it was obvious that prolonged
search woidd be necessary to capture say a thousand adults. A
little experience keeps the searchers to the right spots and we left
the smaller islands feeling that the hunt had been thorough : our
boatman and his son were provided with a killing bottle on each
occasion and they added considerably to our collections.
If we set aside the islands in which the total number of adults
collected is less than 300, there is still much evidence that the
proportions of the sexes vary widely, and in the group as a whole
the range is as considerable as in collections made in Great Britain
in localities between Edinburgh in the north and Poole Harbour
and West Cornwall in the south.
328
Mr Brindley, The proportions of the sexes
Total
Percen-
Locality
Year
,? and
tage of
? adults
males
Round Island
1911
3655
16-1
JJ 5) • • • • • ■ • • • • • •
1912
2016
17-4
Samson
1912
172
19-2
St Agnes and G ugh ...
1912
466
37-8
St Helen's
1912
120
38-3
St Mary's; between Oarn Morvel and Signal
Station
1912
587
39-9
,, between Forth Hellick and Old
Town ...
1912
368
40-0
„ total collections ...
1912
1610
42-0
,, Forth Cressa
1913
1330
42-4
Northwethel ...
1912
206
42-7
St Martin's
1912
823
43-3
St Mary's; Newford Strand and Island
1912
655
45-2
Rosevear
1913
2153
48-5
Tresco; New Grimsby
1912
1650
48-5
„ total collections
1912
2020
48-8
Tean
1912
196
49-5
Tresco; Abbey Gardens
1912
370
50-3
JJ JJ JJ ... ... ...
1913
356
50-6
Bryher
1912
1052
50-7
Tresco; Abbey Gardens
1911
330
59-7
It was pointed out in my previous paper* that the percentage
of males from the same locality is found to vary for different
years in collections made in the same months and large enough
for reliance to be placed on the percentages. In some cases
the variation is greater than might be expected, thus in collec-
tions kindly made for me by Professor H. C. Punnett, at Bobbing,
Kent, in 1903, 1904 and 1906 there was a range of 9'2. In Tresco
Abbey Gardens, Scilly Isles, the male percentages for 1903, 1911,
1912 and 1913 were 55-5 f, 59-7, 50-3 and 50-6. This range is
considerable, but in all cases the male percentage is above the
average, and forms a striking contrast with 16'1 and 17"4 in the
large collections made for me at Round Island by the light-keepers
in two successive years. The collection from Porth Cressa in
St Mary's in 1913, 42'4, agrees closely with the average 42*0 of
collections from three other localities in the same island in 1912.
* Loc. eit. p. 677.
t Figure kindly furnished to me by Mr E. J. Burgess Sopp from a small
collection (146 adults) made in August, 1903.
of Forficiila auriciilaria in the Scilly Islands. 329
The variation between different years is not wide enough to
discredit the conclusion that in some of the Scilly Islands the
percentage of males is habitually low, while in others it is above
the average.
The proportions of the sexes observed in Scilly have very little
relation to the mutual positions of the islands. Comment on these
points may be deferred till after a brief mention of the situations
in which earwigs were found most abundantly. The Scilly Islands
are granite with much blown sand, which is especially abundant
on Tresco. There is an outcrop of altered Killas on White Island,
N.W. of St Martin's, and on the latter a patch of gravel which is
possibly of Eocene date. Glacial deposits occur on the larger
islands, especially in the north of the group. There is a little
alluvium on St Mary's*.
The whole group of islands is included in a parallelogram of
6x8 miles, and St Mary's, the largest island, does not exceed two
miles in its longest diameter.
Taking the islands in an order which is roughly N.E. to S.W.,
the most northerly is
Bound Island. — This dome-like mass of granite is 185 ft. high
and inaccessible save for the Trinity House steps cut on the
S. side. Its only inhabitants are the three light-keepers. The
commonest plants are Armeria maritima, Cochlearia officinalis
and Mesembryanihemum edule. There is no turf The light-
keepers throw their potato peelings and other kitchen refuse down
the N.E. slope, and this midden swarms with earwigs under
detached stones and in old meat tins. They are not numerous
on the rest of the islet and there is no doubt that their food is
mainly the kitchen refuse. They are mostly large-bodied and the
high male is exceedingly common. The presence of man has
apparently favoured their increase in this spot. (In the above and
other references to the average size of body in adults, the state-
ment covers both sexes)
St Helens. — This island is also dome-like, but is about twice
the size of Round Island and has much turf with scattered stones,
while the rocky shore of its S. side has a fringe of bracken fern
which grows high and thickly. On this fringe is the ruined
" Pest House," an old quarantine hospital. There are now no
inhabitants. Prolonged search all round the island discovered
earwigs only in this neighbourhood. They were not numerous
and nearly all were found under fallen slates and masonry in and
about the Pest House. These earwigs were mostly fairly large and
high males were common.
Tean. — A low irregular island uninhabited save by grazing
cattle. It is nearly all turf-covered and has a fringe of blown
* G. Barrow, Geological Survey Memoir; Isles of Scilly, 1906.
380 Mr Brindley, The 23ro2Jortions of the sexes
sand as well as a large beach on its N.E. side. The comparatively
few earwigs were chiefly under stones on the sand near the margin
of the turf High males were not infrequent, but there were more
small-bodied individuals than on the two above islands.
St Martins. — This inhabited island is well cultivated on its
S. side, where the slopes are cut up into small root fields and
pastures by numerous stone walls. There are Escallonia shelter
hedges at the S.W. end. The higher land is largely pastures.
The second highest point in the islands is on St Martin's, a spot
160 ft. high at the E. end, on which the Day Mark is erected.
Earwigs were numerous in the stone walls. They were on the
average much smaller than those of the islands already mentioned,
and *' low " males were common. The sand beaches on the N.
side were not searched.
Northwethel. — This islet resembles Tean in its general features,
but has less turf and more blown sand. Earwigs were not very
numerous and all were found under stones lying on the sand. In
size they resembled the specimens from Tean.
Tresco. — This large and inhabited island is chiefly pasture
with many root fields, and it possesses a special feature in the
sub-tropical gardens of The Abbey at the S. end. Collections
were made in two localities, (i) New Grimsby, the western village.
Earwigs w^ere fairly abundant in the stone walls above the houses
and very numerous in the scattered pieces of rotting wreck wood
lying on the turf near the beach. Breaking open the wood with
a chisel turned out swarms of earwigs. The majority had large
bodies and " high " males were common : " low" males were much
more frequent than on Round Island, (ii) The Abbey Gardens.
Here earwigs have been caught for me for three successive years
by Mr James Jenkin, the head gardener. They do not appear to
be specially numerous, and, compared with those from New
Grimsby, half a mile distant, they are small-bodied, with few
if any " high " males.
Bryher. — This island is inhabited and is chiefly pasture with
scattered stones and a certain number of root fields. It has one
turfy hill. Earwigs were caught in numbers under stones in and
near the cultivated fields and less abundantly under stones on the
turf. They were of medium size, and the " high " male was not
conspicuous.
Samson. — An island composed of two turfy hills with scattered
stones. Each hill is about 100 ft. high. They are divided from
each other by an extensive beach of blown sand with numerous
stones which runs across from shore to shore. There is a wide belt
of very thick and high bracken on the E. side, in and near which
are the ruins of four or five houses, one of which was inhabited till
1855. Salsola kali is abundant on Samson. The island is now
I
of Forficula auricnlaria in the Scilly Islands. 331
used only for grazing. The earwigs were found under stones on
the turf on the S.W. part of the island and on the blown sand
beach in the middle. They were much the same size as those on
Bryher.
>S^^ Mary's. — In this, the largest island, much of the land is
under cultivation and almost all the remainder is pasture. There
is a good deal of bracken on the N.E. side. Almost all the likely
spots were searched for earwigs, and they appeared to be most
numerous in the following districts : —
(i) Between Carn Morvel and the Coast Guard Signal Station,
which is placed on the highest point, 165 ft., in the Scilly Islands.
The walls of the pastures and turnip fields on the slopes up from
Carn Morvel to the Signal Station were full of earwigs.
(ii) Neiuford Strand and Island. The Strand is a beach of
blown sand followed by flat turf with a few houses. Earwigs were
fairly plentiful under stones where sand and turf meet, as on Tean.
Newford Island is connected with the Strand at low water. It is
a small pasture walled round, and a certain number of earwigs
were captured in the wall and under stones on the turf.
(iii) Between Forth Hellick and Old Town. A few earwigs
were found under stones on the sandy beach of Perth Hellick, the
majority were captured in the walls of pastures by the road side.
(iv) Forth Cressa. This bay is surrounded by gardens and
pastures. The earwigs from all localities on St Mary's included
many " high " males, and the average size of body probably
exceeds that of individuals from St Martin's and Tresco Abbey.
St Agnes and Gugh. — The latter is a turfy, uninhabited islet
connected with St Agnes by a sandy beach save near high water,
thus it may be regarded as part of St Agues. Earwigs were found
under stones on the sand and turf near their meeting point.
St Agnes has many houses and is like St Mary's in its cultivation.
The walls of the pastures and root fields were fairly populated
with earwigs, which were on the whole of about the same size
as those from St Martin's and therefore smaller than the St Mary's
individuals.
Annet. — This island of 90 acres has no high land. It is un-
inhabited. It is chiefly turf with much Armeria maritima. The
north end is rocky and there are outcrops and stones lying about
in many places. The whole of the soil is undermined by puffin
burrows, for it is the regular breeding place of this bird in the
Scilly Islands. Here no earwigs at all were found after prolonged
searching by five persons. If there are any on Annet they are
certainly in very small numbers.
Rosevear. — This rocky islet, with the smaller Rosevean and
Gorregan, forms an isolated group about two miles E. of the
Bishop Rock. Mr C. J. King, of St Mary's, informs me that when
332 ilfr Brindley, The pr^oportions of the sexes
he visited Rosevear in October 1912 the giant mallow (Lavatera
arhorea) was so high that a short man could walk hidden among
it. Armeria marttima is one of the commonest plants. Rosevear
bears the ruined huts of the builders of the present Bishop Light-
house, who inhabited it from 1850 to 1858. In 1912 and when
he made a collection for me in September 1913 my boatman,
Mr S. Jenkin, reported the islet swarming with earwigs. The
specimens are nearly all large and the males conspicuously "high."
Among them is the longest pair of forceps which I have obtained
or heard of, viz. 12'25 mm. The Round Island collection of 1911
contained one male with forceps ll'O mm. In Mr W. Bateson's
collection from the Farn Islands in 1892, by which he showed that
the male earwig is dimorphic in respect of its forceps, the highest
males have the value 90 mm.*
The dimorphism of the male does not fall within the scope of
the present paper; all that need be said is that in the Scilly
Islands both " low " and " high " males occur, and that in some of
the islands the " high " individual is strikingly in excess. The
necessary measurements are as yet too incomplete for saying
anything about the extent to which the two kinds of males are
present in the Scilly Islands, and it should be borne in mind that
the above notes on both the dimorphism of the forceps and the
general size of body are from a comparatively superficial examina-
tion of the collections.
It is obvious that the Common Earwig is very abundant in
the islands and that it exhibits well-marked local differences in
respect of (a) numerical proportions of the sexes, (b) body size of
adult, (c) percentage of " high " males, (b) and (c) naturally to
some extent vary together : as pointed out by Bateson, the
" high " male has a large body and the " low " male a small one,
but the body dimensions give a monomorphic curve ; the male
earwig appears to be dimorphic only as regards its forceps. No
explanation is at present forthcoming of the local variations
mentioned above and we remain in the dark with regard to their
causes as to those of local races in general. As remarked on p. 329,
the percentage of males bears very slight or no relation to the
mutual positions of the islands. Bryher and Tresco yielded collec-
tions large enough to indicate the sex proportions with probable
accuracy, the islands are contiguous and in both the male per-
centage is high. On the other hand Samson, almost as near and
separated from Bryher by very shoal water, has very few males. The
estimate is based on a small total collection, but I am inclined
to believe that the male percentage is really particularly low
on this island, for we made it the object of prolonged search
* Bateson and Brindley, Proc. Zool. Soc. Lond., Nov. 15, 1892, p. 585.
of Forficula auricularia in the Scilly Islands. 333
and came away with the conviction that its earwig population
is sparse. The sketch map renders it unnecessary to particularise
other instances of the same kind. The thought arises as to
how long the Scilly Islands have had their earwig population.
The mainland is 25 miles away at its nearest, and though the
Common Earwig hardly ever uses its wings it is conceivable that
individuals have been blown across from Cornwall now and then.
But an earwig with furled wings, though it readily drops in order
to seek shelter, is not easily blown from a spot it intends to hold
on to. Floating vegetable matter and soil on the feet of birds
may have helped to introduce earwigs into the islands along with
other non-flying invertebrates, such as woodlice and earthworms.
Probably, however, man has been an important factor in carrying
earwigs to the Scilly Isles : their habit of concealing themselves in
folded clothes and in crevices of all kinds greatly assists their
passive transport. We do not know how long ago man settled on
the larger islands, one can say no more than that bis arrival was
pre-historic. With regard to Round Island and Rosevear the
suggestion may be hazarded that the extraordinary abundance of
earwigs they possess may be partly the result of recent human
settlement. On Round Island there is little doubt that they
find abundant nourishment in the light-keepers' rubbish heap,
but on Rosevear there has been no such food supply for more
than sixty years. I am unable to say anything as to what the
Rosevear earwigs feed on at the present time. It is striking
that these two islets should stand out as inhabited by earwigs
with large bodies and great frequency of " high " males, while
the numerical proportions of the sexes differ so much. It does
not appear likely that food more varied than the wild vegetation
is a cause of the greater size, for in the Farn Islands in 1907
Mr Potts and myself found that earwigs from the two unin-
habited Widerpens were larger than those caught on the Inner
Farn, which at that time had a poultry farm as well as the light-
keepers' houses. Again, on Tresco, the specimens from New
Grimsby were large while those from the Abbey Gardens com-
paratively small, both were living near human habitations but
in different conditions as regards vegetation and soil. No more
can be said with approach to certainty than that the specimens
obtained from cultivated ground were generally smaller than those
from rocky and wild localities. It may well be that local races
are in process of evolution. The absence of earwigs on Annet is
peculiar. Our search was sufficiently thorough to convince us that
either earwigs have not obtained a footing there or that they
exist in quite small numbers in isolated spots. Its nearness to
a large island well stocked with earwigs and its vegetation gave
the expectation that plenty would be found. This island furnishes
334 Mr Brindley, The proportions of the sexes, etc.
\
an argument against wind-carriage being an important factor in
distributing them. Though uninhabited it is frequently visited
by man, so that from time to time earwigs must be imported
accidentally. It may be that this insect is a parallel case with
that of cockroaches, which are apt to occur in vast numbers in one
spot and yet spread slowly from village to village and even from
house to house. The expectation is, however, that earwigs as
indigenous European insects living normally in the open would
spread more easily than cockroaches, which for the most part seem
to have followed man from warmer regions. Annet is the island
specially chosen by puffins as their breeding place: it is just
possible that in some unknown way the presence of this bird is
inimical to earwigs.
We had no opportunity of searching the Eastern Isles lying
between St Martin's and St Mary's. All are small, but many of
them have turf and plenty of other vegetation.
The present study of the earwigs of the Scilly Isles as a whole
does no more than bring to light the facts recited, but they suggest
that the group is a favourable and easily accessible locality for
a full investigation as to sex-inheritance, influence of parasites and
of environmental conditions.
About eight earwigs were taken, most of them on St Martin's,
which were infested by a large Nematode or Gordiid worm, at
present unidentified. This worm had its two ends hidden in the
abdomen and its coiled body projecting from between the terga,
which were much forced apart. The hosts seemed fairly active
and well nourished.
In the latter part of August the earwigs of the Scilly Islands
are, as on the mainland, nearly all adult. Nymphs were collected
by us, but not with so much care as the adults ; their smaller size
renders them more difficult to secure.
Mr Brindley, Notes on the Breeding o/Forficula auricularia. 335
Notes on the Breeding of Forficula auricularia. By H. H.
Brindley, M.A., St John's College.
[Read 17 November 1913]
In a previous paper* I summarised what is known with
regard to the oviposition, hatching and the duration of the imma-
ture life of the Common Earwig. It was mentioned that no record
could be found of this species being raised to maturity from the
egg in captivity, and that Mr Potts and myself had failed to do
so with eggs laid by earwigs brought to Cambridge from the Farn
Islands in 1907 and 1908.
In October 1912 I received a large number of living adults
from Round Island, Scilly Isles. They were collected in September,
and probably most of the females had paired, for while searching
Gunwalloe Cove on The Lizard, in the same month of 1912, it was
very common to find a male and a female together under stones.
About 110 females were isolated in plaster of Paris cells
averaging 2|- in, wide by 1^ in. deep, and covered by watch glasses.
20 more were isolated in flower pots. In an endeavour to diminish
the risk of septic infection and attack by fungi, coconut fibre was
the only substance used for lining the cells and flower pots. The
coconut fibre was kept fairly damp and as far as possible uniformly
so. A small piece of washed potato without any skin adhering was
the only food given, and this was renewed twice weekly. This
diet was suggested by the quantity of potato peelings in the light-
keepers' rubbish heap from which the earwigs were captured.
All the cells and flower pots were kept in a room in the
Zoological Laboratory, Cambridge, as far, as possible from the hot
air supply, though the temperature was on the average consider-
ably above the winter temperature in the open on the Scilly
Islands. The isolated earwigs were somewhat sluggish and did
not eat the potato slips much. Some hid under the latter, some
buried themselves first below the surface of the coconut fibre,
while a good many remained on its surface.
It was not possible to examine all the cells daily, but an
endeavour to look at all at least twice a week was made. So the
days which follow should no doubt in many cases be slightly ante-
dated. Counting the number of eggs in a clutch was rather
neglected, in the fear that much disturbance of the heap in which
they were laid might diminish the chances of hatching.
* Proc, CamJ). Phil. Soc. vol. xvi. p^rt 8, 1912, p. 674,
336
Mr Brindley, Notes on the Breeding
\
Id the following table, showing the results obtained, in the
second column indicates that the eggs disappeared without hatch-
ing (some were attacked by mould, but the disappearance of the
rest could not be explained). The figures in brackets after dates
indicate the approximate number of eggs or individuals.
The young when first observed were very small, having a body
length of about 5 mm. Thus they were probably all in either the
first or second instar, as newly hatched earwigs are 4 mm. long as
a rule.
Eggs
Eggs found
seen
hatch-
ing
Young found
Young last
seen alive
Adult stage
attained
1
_
_
Jan. 18 (23)
Feb. 7 (1)
2
—
—
Jan. 18 (8)
Apr. 10 (2)
_
3
—
—
Jan. 19 (8)
Feb. 17 (1)
—
4
—
—
Jan. 20
Mar. 8 (1)
—
5
—
-^
Jan. 23
Feb. 3 (several)
6
—
—
Jan. 23
May 9 (1)
—
7
Jan. 24
June 17 (1 cT , 1 ¥ ) ;
June 23 (3 more ? s);
July 4 (1 more ? )
8
—
—
Jan. 27
Mar. 22 (1)
—
9
—
—
Jan. 28 (12)
—
July 17 (1 ? )
10
—
—
Feb. 3 (c. 10)
—
June 25 (1 ?)
11
—
—
Feb. 7 (1)
Apr. 29 (1)
—
12
—
Jan. 21
Jan. 21
Feb. 7 (several)
—
13
—
Jan. 31
Jan. 31
June 23 (1 ? )
14
Jan. 19 (37)
—
—
Jan. 31 (1)
15
Jan. 19 (19)
—
Feb. 13 (1)
Feb. 18 (5)
Mar. 15 (several)
—
16
Jan. 19
—
Jan. 31 (7)
May 9
—
17
Jan. 19 (12)
—
18
Jan. 24
19
Jan. 24
20
Jan. 25
21
Jan. 30
—
—
I
Thus greater success was obtained than in the previous
attempts, for in four families all stages from oviposition to maturity
occurred in the laboratorj^
I am indebted to Mr C. B. Williams, of Clare College, for
details of a case in which he was successful in obtaining mature
individuals from the egg, hatching and subsequent stages being
passed through in the laboratory of the John Innes Horticultural
Institute, Merton. The year was the same, 1913, as my own
observations. The dates were :
March 8 : female and 20 to 30 eggs found in a pine stump.
of Forficula auricularia. 337
March 14 — 16: hatching took place, and the young were fed
on potato and flower petals.
August 20 : 4 became adult.
(In 1912, April 28, Mr Williams found two very small and
apparently newly hatched young, and by August 28 both were
adult. They lived till about March 17, 1913)
The table of results obtained in the Cambridge Laboratory
shows that out of about 130 Round Island females 21 certainly laid
eggs (probably more did so and the fact escaped observation, but
the examination of the cells was sufficiently frequent to render it
unlikely that more than a very few clutches were missed). Four
of the broods observed produced adult earwigs. The adults were
nine in number, one male and eight females, which is curiously
near the proportions given by Round Island earwigs collected in
large quantities. The usual number of eggs laid by one female
may be calculated very roughly by taking the average of 37, 19,
and 12, the instances in which the eggs were counted with
approximate accuracy; this average is 23 and is about the number
usually found. Supposing that all the 130 females which were
put into cells had laid 23 eggs each, there would have been 2990.
Actually, 21 females laid eggs, and if 23 was the average number,
potentially 483 adults were produced. But only nine were actually
found, which is 1'86 per cent, producing adult individuals of all
the eggs laid. Supposing that all the 130 females which were
isolated in cells had each laid 23 eggs, that all had hatched and
all the young had reached maturity, 2990 adults would have been
produced : nine in 2990 is 03 per cent. So great a failure to lay
eggs at all and so great a mortality in infancy as appear in this
case might be attributed to the artificial conditions under which
the females were placed in October and continued in for five
months or more before they began to lay : the conditions of
moisture, ventilation, diet and the substances they lived among
were all more or less abnormal. On the other hand, is it likely
that the mortality among the immature is to any high degree less
among earwigs in the wild state ? I am inclined to doubt it.
Again, in the artificial conditions of a laboratory the eggs and
insects were out of the reach of various factors, both physical and
organised, which affect adversely their development under natural
conditions. On the other hand it seems probable that the artificial
conditions had something to do with the great failure to lay eggs,
only 21 doing so out of 130 females presumably fertilised seems
a very low proportion. Still, a certain number died in the first
two or three weeks of their life in the cells, some may never have
been fertilised and the new conditions may have inhibited the
power of laying. As regards the failure of several of the clutches
to hatch, the premature oviposition probably brought about by the
338 ilfr Brindley, Notes on the Breeding
high temperature and other special features of life in confinement
may have rendered the eggs incapable of development. We do not
know the usual month for oviposition or how long is the period
of immaturity in the Scilly Islands, apparently these facts are not
established on extensive evidence for any country. A brief review
of the published statements in this connection was attempted in
my previous paper. In the neighbourhood of Cambridge it is
likely that oviposition takes place in March or April, that the eggs
hatch in May, and that the offspring become adult in July or
August. There is little doubt that the appearance of eggs as
early as January is premature for even so temperate a climate as
that of the Scilly Islands, especially when it is borne in mind that
a fair number of nymphs are found there in the latter half of
August. That laboratory conditions encourage premature oviposi-
tion is well known for more than one order of insects. Many of
the earwigs brought to Cambridge from the Farn Islands began to
lay about the middle of October. The same acceleration is well
shown by the further history of case 7 in the above table. The
male and the five females, which became adult between June 17
and July 4, were placed together in a large dish on coconut
fibre and supplied with green food as well as potatoes. On
November 4, 13 young were found, apparently in the first instar.
The eggs were not observed, so it is uncertain if the offspring of
one or of more of the females was found, for all the latter were living
and apparently healthy on this day. The young were isolated and
four at least were alive and active on December 21 — there is no
doubt that some had died. Thus these graud-children of a female
brought from Round Island in September 1912 were hatched
probably seven or eight months earlier than the third generation
would be in a wild state. A batch of living adults was procured
from New Grimsby, Tresco, early in October 1913, and about
44 females were isolated on coconut fibre in flower pots. On
October 28 a batch of eggs was found. So far these have not
hatched.
Survival of males through the winter.
In my previous paper (p. 678) the doubt as to what extent this
occurs under normal circumstances was alluded to. In the subse-
quent experiments the point has not been examined in detail,
partly because a large number of the males have been killed and
preserved for measurements of the forceps, and partly because the
artificial conditions of a laboratory militate against a satisfactory
conclusion.
q/ Forficula auricularia. 339
Maternal care of the eggs.
I
The eggs of earwigs laid in the wild state are usually found in
a little pit excavated and covered in about an inch below the
surface, or else in convenient crevices in vegetation. In the cells
and flower pots in which the Round Island females were kept most
of the clutches were laid on the surface of the coconut fibre, but
in many cases the mother protected them by a thin covering of
fibre so that they lay in a small pit immediately under the surface.
Whether she made the excavation before or after oviposition was
not ascertained, the act of laying itself was not observed in any
case. There is no doubt that the mother watches over the eggs,
as has been stated by various authors, but the assertion, made
from time to time, that she guards the young seems to have no
foundation. The newly hatched are active and begin feeding in
a few hours, possibly less, after becoming free from the egg
membrane, while the mother displays no interest in them. Before
hatching her behaviour is very different. The female either covers
the little pile of eggs with her body or else keeps her head towards
them with the antennae playing over them. Possibly the second
attitude is the result of her being disturbed rather than the natural
one. If driven away from the pile of eggs, for they are usually laid
in a heap resembling a pile of round-shot, in a few minutes she has
returned and is seen diligently bringing the eggs together with
the first pair of legs. This accords with Camerano's observation*
quoted in my previous paper.
Hatching.
This was observed in the case of two clutches of eggs. Shortly
before rupture of the egg membrane the position of the head is
seen easily by the black eyes, the only pigmented part of the
young earwig, showing through the membrane. The young
appears to bite through the latter and it comes out head first,
aiding its emergence with the first pair of legs. As more of the
body is freed the other legs in succession push away the egg
membrane. In more than one case there was evidently great
difficulty in discarding the membrane, which was eventually done
by catching it against obstructions,
* Boll. d. Soc. Entom. Itah, 1880, p. 46.
VOL. XVII. PT. IV. 23
340 Dr Searle, The comparison of nearly
The comparison of nearly equal electrical resistances. By
G. F. C. Searle, Sc.D., F.K.S., University Lecturer in Experi-
mental Physics, Fellow of Peterhouse.
[Bead 24 November 1913.]
§ 1. Introduction. The ratio of the resistances of two very
nearly equal coils can be determined most accurately by finding
the very small difference between their resistances. The method,
which, perhaps, is most widely known, is that of Carey Foster.
In that method the difference is expressed as the resistance of
a measured length of the graduated wire of the Carey Foster
bridge. It is therefore necessary to know the resistance of each
centimetre of this wire and to have a table of calibration corrections,
since it is impossible to procure an absolutely uniform wire. Even
if the wire were initially uniform, it would by use become non-
uniform through the wear caused by the contact of the sliding
contact piece.
In the bridge designed by Dr J. A. Fleming and used for
many years at the Cavendish Laboratory by Dr R, T. Glazebrook
and others in the comparison of resistance coils with the standards
of the British Association, the wire is about 1 metre in length and
has a resistance of about 1/20 ohm. Thus to measure a difference
of resistance of 1/200,000 ohm a movement of the contact piece
of 1/10 mm. has to be observed and measured.
In recent years the use of Carey Foster's method has been
abandoned for resistance comparisons of the highest precision and
a method of shunting is now employed. This involves the use of
a resistance box capable of furnishing high resistances, and, in
strictness, the coils in this box should be compared with a standard
resistance. But the resistance boxes now supplied by any good
instrument maker are so accurately adjusted that it is quite un-
necessary to calibrate them if they are only to be used as shunts.
The great advantage of the method of shunting is that instead
of dealing with the resistance of one or two millimetres of the
wire of the bridge — a length which could not be easily read to
less than -^ mm. — we have to deal with shunting resistances
ineasured by many hundreds or thousands of ohms, these re-
sistances not differing from their nominal values by as much as
one part in a thousand, if the resistance box has been well
adjusted.
The method of shunting has been in use for some years at the
National Physical Laboratory and in other standardising labora-
tories, but it has hardly made its way into the laboratory courses
intended for elementary students of physics. It has, however, so
equal electrical resistances.
341
many advantages both as regards accuracy and as regards the in-
struction of students that it may be useful to other teachers to
give an account of the method as employed in my practical class
at the Cavendish Laboratory.
§ 2. General theory. The theory of the method is as follows :
Let G, i)(Figs. 1, 2) be two nearly equal resistance coils; in practice
they would not differ by as much as one part in 1000.
Fig. 1.
The two coils A, B, which are to be compared, are first con-
nected with the coils G, D to form the four arms of a Wheatstone's
bridge, as in Fig. 1, the exact balance being obtained by shunting
A with a high resistance a^ and B with a high resistance h^. The
coils A and B are then interchanged, so that they are now arranged
as in Fig. 2, and the balance is obtained by shunting A with a^
and B with b^.
It will not, as a rule, be necessary to shunt both A and B at
the same time*, so that two of the four resistances ai, a^, h, b^
will be infinite. But it will be convenient to consider the mathe-
matics of the problem without this restriction.
Which of the two coils A and B will require shunting in
either of the two arrangements will depend upon the relative
values oi A, B, C, D. The four possible cases are as follows :
A shunted in both arrangements.
B shunted in both arrangements.
A shunted in the first arrangement, B shunted in the second
arrangement.
B shunted in the first arrangement, A shunted in the second
arrangement.
* If no very high resistances are available, it may be necessary to apply shunts
to both A and B in order to secure a satisfactory balance.
. 23—2
842 Dr Searle, The comparison of nearly
Let Ai, A-^hQ tlie effective resistances of A when it is shunted
by tti, ftg and B^, B^ the effective resistances of B when shunted by
61, 62. Then
ir A^ a,' A,~ A^ a.^ ^ ^'
1 = 1+1 1.1+1 _ .
i?i 5^61' B, B^ b, ^ '
G D , 1) G ,.,^
si"«^ A^-B^ irB, ^''^'
when the bridge is balanced in the two cases, we find, by elimi-
nating G and D,
-' ^-^ (4)*.
A,A, B,B, ^^
Talcing the square root of each side of (4), we have
vz;t,^v A^, ^^^'
The left side of (5) is the geometric mean of 1/J.i and 1/^2-
When J.1 and Ao, are nearly equal, this is very nearly the same as
the arithmetic mean. Thus, if
A^~ A'o a' A.,~~A^, a'
so that 1/^0 is the arithmetic mean of 1/J.i and IjA^, we have
mi /in= L/^i -ii-'-n
Hence, if A^ and A^ are so nearly equal that A^^j'loP is negligible
compared with unity, we may use the arithmetic mean IjA^ instead
of the geometric mean. For example, if A^ja is 1/1000, A^j'ia^ is
only 1/2,000,000, which is negligible in all but the most precise
work. In that case, however, the resistances would, probably,
have been so well adjusted that A^ja is less than 1/1000. The
same remarks, of course, apply to B^ and B.2. Replacing the
geometric means in (5) by the arithmetic means, we have
ifi+iUVi+^
2 Ui A J 2 \B, B,
"* Equation (4) is a quadratic for IjA in terms of 1/-B. If we solve it, we find
which can be used in any case where a^, a^, \, b.2 are not very large compared
with B.
I
equal electrical resistances.
343
or, by (1) and (2),
1 1
1 1
- + -
a, a.,
1
= 5 +
1/1 i\
.(6).
From this equation the difference between 1/A and 1/B is found,
when the shunts a^, a^, bi, 62 are known.
We also have, from (6),
A-B 111/1111^
^1/1^ 1
AB ~ B A~2\a^'^ a, b, b.
Hence
A
.(7).
1_1
2 Vc/i ' a2 ^1 h
When A and B are very nearly equal, it will be sufficient to use
A^ or B^ instead of AB on the right side, or merely to use the
nominal values of A and B on that side.
§ 3. Practical details. The measurements are easily made
when suitable connecting pieces are used. In laboratories where
serious comparisons of resistance are made, mercury cups formed
in massive blocks of copper would be used in making the con-
nexions. But mercury cups are out of place in a crowded practical
class where the students have only a limited time in which to do
the experiments ; from the demonstrator's point of view the most
important thing is that there should be nothing which can "go
wrong."
Fig. 3.
In Fig. 3, L, M, N, 0, P, Q represent six strips of stout copper
with forked ends for clamping under the terminals of the coils.
The pieces L, are connected by about 15 cm. of stout copper
wire and the pieces N, Q are connected in a similar manner*.
Short wires are soldered to L, M, N, P, as shown in Fig. 3, and by
"■ Copper wire is preferable to any stiffer connexion, since its use allows L and
N to be moved without straining the terminals of the coils C and D.
344 Dr Searle, The comparison of nearly
these wires connexions are made to the battery, the galvanometer
and the resistance boxes supplying the shunts, coupling screws
being used. A more convenient plan is to fit the copper pieces
with proper terminal screws. The four coils A, B, C, D are
inserted in the gaps as shown diagrammatically in Fig. 3.
The resistance of the part of the copper connector OL, which
lies between the coil G and the point where the battery wire is
attached to L, together with the resistance of the part of P, which
lies between C and the point where the galvanometer wire is
attached to P, counts as part of G itself and is therefore eliminated
in the equations. Similar remarks apply to the copper connectors
which are joined to the coil D. The effect of the finite resistances
of the connectors joined to A and B is discussed in § 9 and is
shown to be negligible in practice.
To prevent undue heating of the coils, a sufficiently great
resistance R should be placed in series with the battery. The
galvanometer should be permanently connected to M and P, and a
tapping key K should be placed in the battery circuit. In this
way errors due to thermoelectric effects are avoided. The in-
ductances of the coils are too small to give rise to trouble on
making or breaking the battery connexion.
In order that, after a balance has been obtained, it should not
be upset by changes in the resistances of the coils due to rise of
temperature brought about by the passage of the current, it is
necessary that the coil A should be similar to the coil B and that
the coil G should be similar to the coil D. When the bridge is
arranged as in Figs. 1 and 2, this similarity secures such constancy
of the ratios A/B and G/D that the passage of the current does
not upset the balance when once it has been obtained.
The " Sub-standards " of resistance (Fig. 4) supplied by
Mr R. W. Paul have proved very suitable for the experiment.
These coils are wound with wire of small temperature coefficient
and are well ventilated so that they carry comparatively large
currents without serious rise of temperature. Using four of these
equal electyical resistances. 345
sub-standards for A, B, C, D, in Figs. 1 and 2, the students at the
Cavendish Laboratory are able to make reasonably good com-
parisons in a room where there is much vibration due to moving
machinery, the galvanometer being a table instrument having a
pointer moving over a divided scale.
The results given below are not intended to illustrate the
power of the method when used under favourable conditions; they
are intended rather to show how well the method works under
unfavourable conditions.
§ 4. Practical example. The following results obtained by
G. F. C. Searle and A. L. Hughes will illustrate the working of
the method. Four " sub-standards " A, B, C, D, each of nominally
one ohm resistance, were employed.
Position 1.
Coil A not shunted. Hence ai = Qo ohms and l/ai = Oohm~i.
Coil B shunted with 2800 ohms. Hence l/6i=0-000357 ohm-i.
Position 2.
Coil A not shunted. Hence a2 = <^ ohms and l/a2 = ohm~i.
Coil B shunted with 4800 ohms. Hence l/b^ = 0-000208 ohm - K
Hence, using (6),
A'^ 2\a,'^ a.2) ~ B'^ 2\b, hj'
we have
4 = 4 + J (0-000357 + 0-000208) = 4 + 0-000282 ohm-i
A B 2 B
or B-A=ABx 0-000282 ohm.
The difference between A and B is so small, and each is so nearlj^ one ohm,
that we may put AB=\ ohm^ and thus obtain
i?- 4 = 0-000282 ohm.
§ 5. Intercomparison of three coils. A useful test of the
accuracy of the method is obtained if three coils A, B, C are used.
First A and B are compared as described in §§ 2, 3, using and D
as the auxiliary coils whose ratio is eliminated. Then A is com-
pared with C, using B and D as the auxiliary coils. Finally B is
compared with C, using A and D as the auxiliary coils. In this
way the values of the three differences
A-B, A-C, B-C
are found. The accuracy of the work may be tested by comparing
the value oi B-C found directly with that found from the two
differences A-B and A-C. The shunts on C may be denoted
by Ci, C.2.
346 Dr Searle, The comparison of nearly
§ 6. Practical example. The intercomparison of three coils
is illustrated by the following results obtained by G. F. C. Searle
and A. L. Hughes. Sub-standards each of nominally one ohm
resistance were used.
Comparison of A and B.
ai = QO, l/ai = 0, 61 = 2800, l/6i = 0-000357
a2=ao, 1/^2 = 0, 62 = 4800, 1/62 = 0-000208.
Hence 1 "" i + 5 (0-000357 + 0-000208) = i + 0-000282
and A-B= -^5 x 0-000282= -0-000282 ohm.
Comparison of A and C.
ai = QO, l/ai = 0, Ci = 4000, 1/Ci = 0-000250
^2=785, l/a2=0-001274, C2 = oo, l/c2 = 0.
Hence t + s x 0-001 274 = 4 -H ^ x 0-000250
and A - (7=^Cx 0000512 = 0-000512 ohm.
Comparison of B and C.
fei = 2700, l/5i = 0-000370, Ci = oo, l/ci =
62=760, 1/62 = 0-001316, C2=Q0, 1/C2 = 0.
Hence ^ + i (0-000370 + 00013 16) = ^
and B-C= ^Cx 0-000843 = 0*000843 ohm.
The vahie oi B-C deduced from the two differences A—B and A-C is
B-C={A-C)- (4 -5) = 0-000512 + 0-000282 = 0-000794 ohm.
Thus the two vahies oiB-C only differ by 0-000049 ohm.
§ 7. Intercoviyarison of four coils. When the student has
sufficient time he may determine directly, by the method of § 2,
each of the six differences
A-B, A-G, A-D, B-C, B-D, C-D.
When this has been done, it will be found that the six differences
are not quite consistent. Thus, in the example recorded in § 6, it
was found by direct comparison of B and G that B — G = 0"000843
ohm but that
{A-C)-{A-B) = 0-000794 ohm.
We have, then, to decide how to combine the six results so as to
obtain the most probable values of the three differences A—B,
A — C, A — D, it being supposed that each of the six observed
differences has been found with the same care.
The method employed to obtain the desired result is the
method of least squares.
Ao,
we
have
the
+ ^
= A,
+ z
-A,,
egita? electrical resistances. 347
Let us put
A-B = x, A-C=y, A-D = z.
Then
B-G^y-x, B-D = z-x, C-D = z~y. .
Then the six observed differences A — B, A —G, &c. give us six
equations for the determination of the three quantities x, y, z.
These equations are, however, not quite consistent and we employ
the method of least squares to reduce the six equations to three,
which when solved will give us the most probable values of
X, y, z. _
Denoting the six differences by Aj, A2, ...
following six equations
a- = Aj —x-\-y
2/ = Ao — X
z = ^, -y
The method of least squares directs us to multiply each one of
these equations by the coefficient of x in it and then to add the
six equations together to form a single equation. In our case the
coefficients of x taken in order are 1, 0, 0, — 1, — 1, 0. A second
equation is formed by multiplying each one of the six equations
by the coefficient of y in it and then adding the six equations
together. A third equation is formed in like manner by adding
together the six equations after each has been multiplied by the
coefficient of z in it. When this is done in our case, we obtain
the following three equations :
3x — y — ^ = A] — A4 — Ag = T/i ,
-x + Sy- ^ = Ao + A4- Afi = ?72,
-X- 2/ + 3^ = A3 + A5 + As = 7/3.
The values of x, y, z — say, X, Y, Z — derived from these last three
equations are the most probable values. We obtain
X = l(2,;i+ V-2+ Vs),
Y=l( Vi + ^V2+ v.),
We can now determine the most probable values of A, B, G, D in
terms of M, the mean value of these four quantities. For
M = l{A+B + G + D) = A-i{X+r+Z).
Thus A=M + i{X + Y + Z) = 3I+iivi + V2 + vA
B = A-X, G^A-Y, D = A-Z.
¥
348
Dr Searle, The comparison of nearly
§ 8. Practical example. The following results were obtained
by G. F. C. Searle and A. L. Hughes, using four sub-standards
each nominally of one ohm resistance.
The six direct determinations of differences gave the values
Ai = A-B= -282x10-% A2 = J-C= 512x10-" ohms,
A3 = A-I)= 458x10-6, Ai = B-C= 843x10-6 ohms,
A,=B-I)= 732x10-6, Ae=C-D=- 65x10-6 ohms.
Hence »7i = Ai - A^ - A5= - 1857 x 10^6 ohms,
j;2 = Aa + A4 - Ao = 1 420 X 10 - « ohms,
^3 = A3-|-A5-|-A6= 1125x10-6 ohms.
Then X=i(2rji+ rj2+ ^3)= -292x10-6 ohms,
y=H m + ^V2+ Vs)^ 527xl0-6ohms,
^=i( m+ l2 + ^i)= 453x10-6 ohms.
We can now find A, B, C, D in terms of M, the mean value of the four
resistances. Thus
^ = ilf + |(j;i + ,;2 + '?3) = J/+ 1 72 X 1 - 6 ohms,
5=^-Z=i/+464xlO-6ohms,
C=A- r=M- 355 x 10-6 ohiris,
£>= A -Z = M-2Sl X 10-6 ohms.
If we assume that M is accurately one ohm, we have the values
^ = 1-000172, i5=l-000464, (7=0-999645, i)=0-9997l9 ohms.
The discrepancies between the observed and the calculated differences are
shown in the table. The differences are given in millionths of an ohm.
f
A-B
A-G
A-D
B-C
B~D
C-D
Observed
Calcidated
-282
-292
512
527
458
453
843
819
732
745
-65
-74
The greatest discrepancy only amounts to 24 millionths of an ohm.
§ 9. Effect of finite resistance of connectors. If we treat the
copper connectors as linear conductors, we can easily modify the
equations so as to take account of the resistances of the various
parts of the connectors*. When the connectors are treated as
* Methods of dealing with non-linear conductors are given in my paper " On
resistances with current and potential terminals," The Electrician, March 31,
April 7, 14, 21, 1911. The paper is also published separately by The Electrician.
equal electrical resistances.
349
linear conductors the arrangement may be represented diagram-
matically by Fig. 5. The resistances of the parts of the connectors
are represented by p, q, r, s, h, k, as shown in Fig. 5, and these
resistances are very small compared with A or B.
Fig. 5.
When A is in the left gap with a shunt a^, while B is in the
right gap with a shunt h^ the resistances of the compound con-
ductors between JJ and W and between Fand W are
^^ ^ A+p + q^a,' B + r + s + h,
When the coils A and B are interchanged and the new shunts
are fts and h^, the corresponding resistances are
A, -"' + A+r + s+a,'
B + p + q + b,
Since
A^' 5/ . 4l_^
— = ^ and ^ - ^
we have JA,'A.' = JB,'B,' (8).
On replacing the geometric means in (8) by the arithmetic
means, the quantity ^{h + k) cancels and we have
(A+pJ^ a, (^ij-r-fsKl
A+p + q + a, ATrTsTa^ }
_^({B + r + s) b, (B+p + q)h,
" 2 \~B + 7+s + ¥, B+p + q + h
^j A+p + q A+r + s
or
2 |i + (^ +p + q)/a, "^ l+{A + r + s)la^
B+r + s , B + p + q
_ i
~" 2
+
r+ (5 + r + s)/b\ l+(B+p + q)/h
350 Dy Searle, Comparison of nearly equal electrical resistances.
Expanding each of the denominators as far as the second term, we
have
' \[A + 'p + q-{A+p-\- qY/a^ + A+r + s-{A+r + sfja^]
= \\B+r^s-{B-\-r + sf/b^ + B+p + q-(B+p + qf/b,] .
Since p, q, r, s are very small compared with A or B, we may
neglect 2Ap/ai, Ipqja-^, p^/a^ and similar terms. We then obtain
Here we may write AB for A^ and for B^, and then we find
, „ AB fl 111
2 \ai 0-2 Oi Og
which is identical with equation (7) of § 2.
Mr Eddington, The Distribution of the Stars, etc. 351
The Distribution of the Stars in relation to Spectral Type. By
Professor A. S. Eddington, Trinity College.
[Bead 24 November 1913]
It is well known that the concentration of stars to the galactic
plane is not shown equally by the different spectral classes.
Type B is the most condensed, and the others follow in the order
A, F, G, K, M, i.e. the sequence coincides with the usually
accepted order of evolution. Formerly it seemed probable that
this result was due to a progression in the average distance of
these classes of stars, for, on the hypothesis that the stellar system
is of oblate form, the greater the distance the greater will be the
concentration to be expected. This explanation fitted in well with
certain direct evidence as to the luminosities of the different
spectral types. Recent determinations by Boss and Campbell
of the average distances of the stars of different spectral types
negative this explanation in a most decided manner. It appears,
for instance, that the M stars are on the average more remote and
more luminous than Type A. We have to return to the view
that there is a real difference in the distribution of the spectral
types. Apparently the stars have been formed mainly in the
galactic plane ; the earliest type with their small velocities have
not strayed far from it ; the latest type with their large velocities
have had time to become much more uniformly dispersed.
There is an outstanding question of great difficulty. In
parallax investigations it is found that the M stars are the faintest
of all the types ; in statistical discussions of proper motions, etc.,
they are found to be the brightest except Type B. Similar
difficulties occur with the other types. Russell has put forward
the theory that Type M consists of two divisions, one being the
very earliest and the other the latest stage in evolution. Against
this it may be urged that both divisions of Type M are charac-
terised by very high velocities in space ; this seems to indicate
a close relation between them. Further, as far as statistical
investigations are concerned, Russell's theory inverts the usually
accepted order of stellar evolution. The result arrived at in the
previous paragraph would thus have to be reversed, — the stars as
formed are fairly uniformly dispersed and have high velocities;
afterwards they lose their velocities and become concentrated to
the galactic plane. This is not so intelligible as the previous
conclusion.
CONTENTS.
PAGE
A possible connexion between abnormal sex-limited transmission and
sterility. By L. Doncaster . ... . . . . 307
The Flight of the House-Fly. By Edward Hindle. (Communicated by
Mr C. Warburton) . . .310
On the Dependence of the Relative lonisation in various Oases by fi Rays
on their Velocity, and its bearing on the lonisation produced by
y Rays. By R. D. Kleeman . ... . . . . 314
Note on a Dynamical system illustrating Fluorescence. By N. P,
McCLEtAND .
On the Presence of certain Lines of Magnesium in Stellar Spectra. By
F. E. Baxandall. (Communicated by Professor Newall) .
The proportions of the sexes o/Forficula auricularia in the Scilly Islands
By H. H. Brindley. (One map in Text)
Notes on the Breeding of Forficula auricularia. By H. H. Brindley
The comparison of nearly eq^ial electrical resistances. By G. F. C. Searle
(Five figures in Text) . . . ....
The Distribution of the Stars in relation to Spectral Type. By Pi'ofessor
A. S. Eddington .
321
323
326
335
340
351
PROCEEDINGS
OF THE
CAMBRIDGE PHILOSOPHICAL
SOCIETY.
VOL. XVII. PAET V.
[Lent Term 1914.]
(JDambrttige :
AT THE UNIVERSITY PRESS,
AND SOLD BY
DEIGHTON, BELL & CO. AND BOWES & BOWES, CAMBRIDGE.
CAMBRIDGE UNIVERSITY PRESS,
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1914
Price Two Shillings and Sixpence
5 May 1914.
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PROCEEDINGS
OF THE
Camkitrge ^Ijibsopl^kal Soxietjr.
Tlie oxygen content of the river Gam before and after receiving
the Cambridge sewage effluent. By J. E. Purvis, M.A., Corpus
Christi College, and E. H. Black, M.B. (Edin.).
[Read 23 February 1914.]
The 8th Report (1912) of the Royal Commission on Sewage
Disposal, Vol. i., deals with the standards to be applied
to sewage and sewage effluents discharging into rivers and
streams, and the tests which, in the opinion of the Commis-
sioners, should be used in determining those standards. They
discuss also the connection between the physical and the
chemical conditions of streams receiving sewage liquids, the
various tests which are now employed, such as the amount of
ammoniacal nitrogen, the amount of oxygen absorbed from
permanganate of potassium in four hours, and the amount of
dissolved oxygen taken up in five days. Finally they selected
the amount of dissolved oxygen which is consumed in five days at
18° C. as the basis of a standard.
It is obvious that there are local and seasonal variations in
the conditions of rivers and streams receiving sewage or sewage
ieffluents ; but they conclude that if 100,000 c.c. of a river water
:do not normally take up more than 0*4 gram of dissolved oxygen
in five days, the river will be free from signs of pollution ; and
that if the river gives a higher figure than this, it will show
signs of pollution, except perhaps in very cold weather. They
therefore decided that this figure ought not to be exceeded by the
mixture of the rivers and the polluting streams discharging into
them. The experiments were carried out at 65° F. (18"3°C.), for
when the five days' test was carried out at the various tempera-
tures of different seasons, varying results were obtained. They
•also adopted the normal dry weather flow of the river.
VOL. XVII. PT. V. 24
354 Messrs Purvis and Black, Oxygen content of the river Gam
The quality of the river or stream as the receiver of sewage
or an effluent is a very important factor to be considered in the j
disposal of sewage or sewage effluents ; and the Commissioners f
have classified rivers into groups so that, for example :
Very clean take up 0"1 gram of dissolved oxygen in 100,000 parts of the <
stream in 5 days. ;
Clean ,, 0*2 „ of dissolved oxygen in 100,000 parts of the ]
stream in 5 days, i
Fairly clean ,, 0-3 „ of dissolved oxygen in 100,000 parts of the (
stream in 5 days. {
Doubtful „ 0-5 „ of dissolved oxygen in 100,000 parts of the I
stream in 5 days. j
Bad „ 1*0 „ of dissolved oxygen in 100,000 parts of the '
stream in 5 days. |
They consider that, under ordinary conditions, the average \
quality of the diluting water, for the purpose of arriving at i
a standard, should be represented by 0'2, that is, by a "clean I
river." '
But the most important factor is the degree of dilution
afforded by a river receiving the discharge ; because there are i
numerous instances in which the degree of dilution is sufficient to
dispose of the sewage by natural agencies without cost or injury
to the community.
Considering, however, the various methods of sewage treat-
ment, as, for example, tank treatment with or without chemical!
precipitation, or artificially constructed filters or sewage farms,
the Commissioners recommend that, in those cases where a
complete system of sewage disposal is necessary, the sewage
effluent shall not contain more than 3 grams of suspended matter
per 100,000, and that, including its suspended matters, it should !
not take up more than 2 grams of dissolved oxygen in five days
at 60° F. (18-3° C).
Tbe Report also discusses the cases where, owing to the
relatively small volume of the river, a more stringent standard is ■
necessary ; and, on the other hand, conditions of dilation which
indicate that a relaxation of the normal standard may be allowed. .
For example, a claim for a relaxed standard may be considered 1
when (1) the particular river water when mixed with sewage or
sewage effluent does not take up more than 0'4 gram of dissolved
oxygen per 100,000 in five days, and (2) when it can be shown ■
that the river will receive no further pollution until it has
recovered itself so far as not to take up in five days an amount
of dissolved oxygen much in excess of that which it took up before
receiving the first discharge.
In view of this Report, the authors have studied the con-
dition of the sewage effluent poured into the Cam from the
before and after receiving the Cambridge sewage effiiient. 355
Sewage Farm on Milton Road, and also the Cam itself above
and below the effluent outfall, to see how far the conditions of the
river and the effluent are comparable with the standards suggested
by the Commissioners.
A very extensive research would be necessary for a complete
survey. It would mean a daily examination of the river and the
effluent, and perhaps twice a day. But a fairly comprehensive
view may be obtained by obtaining an analysis once a week,
during the summer and winter months. The condition of the
river can be investigated in the dry and wet seasons; and the
dilution, as well as the varying pollution, should give a fair
indication of the general conditions of the river and the
effluent.
In connection with the condition of the Cam above and
below the sewage effluent outfall, reference may be made to a
paper by Purvis and Rayner*. In the investigation it was
shown that the chemical purification, as distinct from the bacterial
purification, was moderately good, as determined by the estima-
tion of the two ammonias and the amount of oxygen absorbed
from potassium permanganate in four hours. At two miles below
the outfall, the river showed a definite amount of purification
notwithstanding the fact that at | of a mile below there was some
contamination from another source. They also proved that above
this contaminating influence, at half a mile below the outfall,
the chemical purification was fairly good.
The method of analysis of the present investigation was that
used by Letts and Blake f. The process is simple, and the details
can be obtained in these publications. The results of the various
determinations are given in the tables (pp. 363^ — -368).
The more important facts which arise from a comparison of
these analyses are the following : (a) The solids in suspension in
the effluent were, on several occasions in the summer months,
above the standard of 3 grams per 100,000 ; and on these occasions
an offensive smell was noticed after five days' incubation. On four
occasions during the winter months the suspended solids were
also above the standard ; but, on the other hand, there was no
smell after five days' incubation. On examining these solids
microscopically it was found that they chiefly consisted of zoogloea
masses of a filamentous bacillus which had developed and had
grown on the inside of the drain pipes and inspection chambers.
They were not faecal substances which produced an unpleasant
smell like those noticed in the summer. The appearance of the
* Journ. Roy. Sanitary Inst., 1913, vol. xxxiv. p. 479.
t Proc. Roy. Dub. Soc, vol. ix. (N.S.) pt. iv. No. 33. Also the 5th Beport,
Koyal Commission on Sewage Disposal, Appendix 6, p. 221, and the 8th Beport,
vol. II. Appendix.
24—2
356 Messrs Purvis and Black, Oxygen content of the river Gam
masses of bacteria when floating or suspended in water resembled
flakes of shredded paper or pieces of cotton wool in size from
a three-penny piece to a two-shilling piece. They were con-
stricted at one end, the point of attachment of the growth ; the
Dissolved
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Fig. 1. Curves showing the degree of pollution as indicated by the rise and fall of
the amount of oxygen absorbed in five days by the river Cam 150 feet above the
effluent outfall, and its relation to the rainfall.
other end and body of the mass was spread out fan-wise, and
when held up to the light resembled frost on a window-pane.
Microscopically they consisted of long chains of rod-shaped
before and after receiving the Cambridge sewage effiuent. 357
bacteria, resembling closely the antliracoid group. Each rod
was attached to the next, and no free members were seen ; they
had the appearance of spore formation in the centre of each
rod ; they were more abundant in the effluent in cold weather.
It is proposed to study them in more detail later, (b) The
amount of oxygen absorbed by the river above the outfall was
always above the standard of a clean river water (02 gram) in the
winter months from October to December inclusive, whereas in
the summer months, from May to August inclusive, it was
always below the standard. It cannot be said, therefore, that
the river itself always satisfies the standard of the Royal Com-
mission, (c) Only on two occasions (August 14 and October 10)
was the amount of oxygen taken up by the effluent below the
standard of the Commissioners. (d) On the other hand, the
purification which takes place when the effluent mixes with
the river water is fairly rapid ; and, although the mixture of
the effluent and river at 50 feet below the outfall gives a figure
which is sometimes above and sometimes below the standard of
0'4 gram of oxygen absorbed in five days at 18° C, yet the
river | mile down as regards its cleanliness compares fairly well
with the standards of a diluting water suggested by the Com-
missioners. For example, five of the analyses would grade the
river as " clean," ten as " fairly clean " and three as " doubtful "
at I mile below the effluent outfall.
Three factors at least may be suggested to explain the
difference in the results of the summer and winter months.
They are (1) the rainfall, (2) the number of hours of sunshine
and their influence upon aquatic vegetation, and (3) the tem-
perature. The curves in Fig. 1 show that as the rainfall increases,
the amount of oxygen absorbed in five days also increases ; and,
it will be noticed, that this takes place at the beginning of the
rainy season in October. An increase in the rainfall is accom-
panied by an increase in the pollution of the river, and a corre-
sponding increase in the oxygen absorbed, and this is well shown
by the two curves rising and falling together. The second factor
is the presence of aquatic vegetation influenced by the number
of hours of sunshine ; and the curves of Fig. 2 illustrate the
variation in the amount of dissolved oxygen which rises and falls
with the number of hours of sunshine in the summer months.
It is well known that aquatic plants give off more oxygen under
the influence of the sun than in its absence, and this fact
explains the increase in the dissolved oxygen. Such an ex-
planation is confirmed by the curves of Fig. 3 for the winter
months, where there is no regularity like that indicated by the
curves in Fig. 2. Although there is a decrease in the number of
hours of sunshine, and an almost entire absence of aquatic plants,
358 Messrs Purvis and Black, Oxygen content of the river Cam
which had died or been removed, the iucreasing amount of
dissolved oxygen observed from November 12 to December 8
(see Fig. 3) is explained by the diminution in the amount of
pollution which follows the decrease of the rainfall between those
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— ^— hours of sunshine for the two days preceding that on which the sample was
taken.
Fig. 2. Curves showing the connection between the number of hours of sunshine
and the amount of oxygen dissolved in the Cam in c.c. per litre, 150 feet above
the effluent outfall.
two dates, together with the fall in the temperature of the water
from 20° C. on May 29 to 5° C. on December 8. The deter-
minations by Winkler of the number of c.c, of oxygen held in
solution in one litre of water are quoted in the 8th Report of
before and after receiving the Cambridge sewage effluent. 359
the Royal Commission on Sewage Disposal, Vol. ii. Appendix, p. iv.
From this reference it will be seen that the temperature exhibits
a controlling influence on the amount of oxygen dissolved. For
example, at 5° C, 8*9 c.c. of oxygen are held by 1 litre of water,
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«— — hours of sunshine for the two daj's preceding that on which the sample
was taken.
Fig. 3. Curves showing the relationship between the diminution in the pollution
and the gradual increase in the amount of oxygen in the river between
Nov. 12th to Dec. 8th, and the gradual decrease in the temperature of the '
water whereby more oxygen was dissolved from the atmosphere than in the
warmer months. The faU of the oxygen figure on Oct. 29th was caused by an
ii increased pollution of the river after rain.
and 6'4 c.c. at 20^ C. The Commissioners consider that at about
16° C. a clean river water may be taken as containing 7 c.c. of
I oxygen per litre ; but the authors found, at 16° C. (60° F.) and
360 Messrs Purvis and Black, Oxygen content of the river Cam
767 mm., on June 13, for example, 10086 c.c. of dissolved oxygen
in the Cam water above the effluent outfall. On reference to
Fig. 2 this corresponds to the maximum amount of sunshine for
the two preceding days.
To sum up this investigation as it affects the disposal of the
sewage effluent into the Cam, it is evident that (1) the seasonal
variations had an important influence on the composition of the
river as the receiver of the effluent, for the oxygen absorbed
figure was below the standard in the summer months and above
the standard in the winter months; (2) the suspended solids in
the effluent were above the standard on several occasions, par-
ticularly in the summer months, when they were fsecal solids and
not masses of bacteria ; (3) the oxygen absorbed in five days by
the effluent satisfied the standard of the Commissioners only
twice in eighteen times ; (4) with the increased pollution of the
river as the diluting medium during the winter months, although
the sewage effluent was of much better quality than that dis-
charged into the stream during the summer months, the oxygen
absorbed figfures of the mixture of the polluting discharge and
the river 50 feet below the effluent outfall exceeded the standard
oxygen absorbed figure of 0*4, at the rate of 89*2 per cent, of the
samples taken from October to December, as compared with
25 per cent, of those collected from May to August ; (5) on the
other hand, there is the important fact that the recovery or self-
purification of the river is fairly rapid as shown by the figures
for the oxygen absorbed at \ mile down the river below the
effluent outfall. Such purification is brought about partly by
the rapid absorption of the dissolved oxygen from the air and
which is being continually replenished, partly by the oxygen
given off by aquatic plants under the influence of sunlight, and
to some extent by the nitrates, when present in the effluent,
which are produced from the oxidation of the sewage as it passes
through the filter beds ; and these influences come into action as
oxidisers of the dissolved organic matters. It -should also be
remembered that the river receives no further sewage pollution
till it reaches Clayhithe, If miles below the effluent, where
there is some contamination ; but after that there is no
pollution till the river reaches Stretham, 8^ miles down.
However, accepting the effluents as fairly representative,
and without considering the rapid purification when they are
mixed with the river, an increase in the volume of the river so
that the ratio of the effluent and the river should be about 1 to
20 in the summer, and about 1 to 25 in the winter, it is probable
that the effluent discharged into the stream would satisfy the
standards of the Royal Commission. It will be seen from the
tables that the dilution of the effluent varied between 1 of
hefo7'e and after receiving the Cambridge setvage effluent. 861
the effluent to 12 and 20 of the river water. It is obviously
impossible to increase and maintain a larger volume of the river,
even if it were desirable from other considerations ; and, it
cannot yet be decided whether it will be necessary to spend
more money on a larger area of filter beds, until it is clearer
that the additional settling tanks in course of construction and
the beds now in use are giving their best results. For the
present, it is more important to aim at the production of an
eflSuent, which shall contain fewer suspended solids and consume
less oxygen in five days. This can be accomplished by a more
complete separation of the solids in the settling tanks, and the
filtration of all the liquid through the beds. The various sections
of the filter beds should always be kept in good condition by
periodic scarifjang, ploughiug and resting, in order to break up
the surface of the soil, and thoroughly aerate the subsoil and the
gravelly sand below.
In connection with this investigation it is desirable to re-
member that the disposal and purification of the sewage effluent
is concerned with " the harm caused by allowing unpurified, or
" imperfectly purified, sewage to flow into streams, thereby causing
" the de-aeration of the water of the river, and consequent injury
" to fish ; the putrefaction of organic matter in the river to such
" an extent as to cause nuisance ; the production of sewage fungus
" and other objectionable growths ; the deposition of suspended
" matter, and its accumulation in the river bed or behind weirs ;
" the discharge into the river of substances, in solution or
" suspension, which are poisonous to fish or to live stock drinking
" from the stream ; the discoloration of the river ; and the dis-
" charge into the river of micro-organisms of intestinal derivation,
" some of which are of a kind liable, under certain circumstances,
" to give rise to disease " (5th Report of the Royal Commission
on Sewage Disposal, p. 217). It has not yet been very closely
concerned with the bacterial purification as distinct from the
chemical purification. Like all effluents, the effluent from the
Cambridge sewage farm is polluted with all kinds of bacteria,
and is therefore potentially dangerous. It has been shown, for
example, by Purvis and Rayner (loc. cit.) that the Bacillus coli,
an intestinal bacillus found in the sewage effluent, can be traced
down the Cam for at least four miles below the effluent outfall.
Whether it will be necessary to sterilise sewage effluents before
they are discharged into streams is a question which has not yet
received adequate attention ; but if a river, which is the receiver
of sewage pollutions, is the source of supply of water for drinking
purposes, it should undergo an elaborate system of bacterial puri-
fication. The researches of Dr Houston, the Director of the
Laboratories of the London Metropolitan Water Board, are of the
greatest value in this direction.
362 Messi's Purvis and Black, Oxygen content of the river Cam.
Description of the Flora, etc., in the river Gam.
During the sumraer months, an abundance of aquatic vegeta-
tion grows and flourishes in the river Cam. A long ribbon-
shaped weed, the Sparganium sp., grows most profusely every-
where across the whole bed of the river for miles above and
below Cambridge. Where there are deposits of soft mud,
especially below the sewage effluent outfall, Zannichellia palustris
grows well, as does an imported weed Elodea canadensis.
Confervas are also abundant, and grow well on the soft mud
below the effluent outfall.
From October to December the vegetation had almost entirely
disappeared or it had been removed from the river bed. On
several occasions shoals of live fish were seen both immediately
above and below the outfall ; and at no time from May to
December were any dead fish seen below the effluent outfall.
Mud Deposits from the Sewage Effluent in the river Gam.
Deposits of black mud were found in patches below the
effluent outfall. On December 8, before collecting the sample
of river water at ^ mile below the outfall, two barges passing
along the river stirred up a quantity of filamentous bacteria and
sludge from the bottom. It could be traced along the whole
\ mile below the outfall. The total solids in the sample taken at
^ mile below were estimated to be 9'4 grams per 100,000 ; and at
^ mile below the cord to which the thermometer was attached in
midstream became coated with a gelatinous deposit of masses
of the same bacteria which had apparently been stirred up by
the passing barges. Similar filamentous bacteria have been
shortly described above as having been found in the effluent
itself.
We are indebted to Mr Lynch, the Curator of the Cambridge
Botanic Gardens, for identifying the aquatic flora, and for supply-
ing the meteorological data.
363
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Mrs Arher, On Root Development in Stratiotes aloides L. etc. 369
On Root Development in Stratiotes aloides L. luith special reference
to the occurrence of Amitosis in an embryunic tissue. By
Agnes Arber, D.Sc (Lond.), F.L.S., formerly Fellow of
Newnham College. (Communicated by Dr Arber.)
(Plates VIII and IX.)
[Read 9 February 1914.]
I. Introduction.
On August 11th, 1910, I collected a few plants of the Water
Soldier, Stratiotes aloides L., at Roslyn Pits, Ely, with the intention
of examining them in connexion with a general study of water
plants, on which I have been engaged for some time. On cutting
sections of the stems, I noticed certain peculiarities in the
young adventitious roots embedded in the tissues of the axis,
the chief of which was the occurrence of apparent amitosis.
These plants had merely been preserved in methylated spirit, with
no idea of using them for cytological purposes, but in the following
year (May 80th, 1911) a number of further examples from Roslyn
Pits were dissected and fixed on the spot in Flemming's strong
solution, acetic-alcohol, and methylated spirit. In 1912, for the
sake of having a control from some other locg-lity, two plants were
obtained from Perry's Hardy Plant Farm, Enfield. Hand sections
were stained with methyl green in 1 °l ^ acetic acid, Ehrlich's acid
haematoxylin diluted with an equal volume of potash water,
borax carmine, etc., while for microtome sections, Flemming's
triple stain and Heidenhain's iron-alum haematoxylin were used.
The hand sections, especially those stained with methyl green and
mounted in dilute glycerine, were found on the whole to be the
most favourable for the particular purpose.
I have pleasure in expressing my indebtedness to the Committee
of the Balfour Laboratory, where this work has been carried out,
and also to my friend, Mr E. Aveling Green, who kept records for
me of the rate of growth of the roots in the case of some plants of
the Water Soldier cultivated in a pond in his garden.
Before describing: the observations on the nuclei which form
the main subject of the present paper, I wish to draw attention to
a few points concerning the general structure and development of
the adventitious roots of Stratiotes aloides.
VOL, XVII. PT, y, 25
370 Mrs Arber, On Root Development in Stratiotes aloides L.
II. The Structure and Development of the Adventitious
Roots of Stratiotes aloides L.
The rosette of aloe-like leaves, which characterises the Water
Soldier, arises from an abbreviated stem, which is represented in
radial longitudinal section in PL VIII, Fig. 1. A series of adven-
titious roots is shown, becoming progressively younger towards the
stem apex. They arise at the outer limit of the central vascular
region of the axis.
Van Tieghem and Douliot* describe the young root as
enclosed externally in a digestive sac arising from the stem
endodermis, which is followed internally by a root-cap derived
from the pericycle. I cannot, however, confirm this description,
as it appears to me quite impossible to demonstrate that the
digestive sac is cortical and the root-cap stelar in origin, since no
distinct endodermis and pericycle can be seen in the stem, and
there is also no visible distinction between root-cap and digestive
sac in the root. My observations agree with those of Miss D. G.
Scott -f-, who also failed to distinguish a root-cap and digestive sac,
and who reports that the endodermis of the stem, if present, could
not be determined. In the present paper I shall use the term
" root-cap " for the entire covering of the root apex (the outer part
of which functions as a " digestive sac " in passing through the
stem), without regard to the distinction drawn by Van Tieghem
and Douliot.
The piliferous layer is marked out extremely early. In the
youngest roots, which have not yet emerged from the stem
tissues, it is visible as a columnar layer rich in contents and with ij<
large nuclei. The same is true of the apical region of the long J
roots. Near the root-tip, while it is still enclosed in the root-cap,
the future root-hair cells are already marked out by their very
large size and relatively gigantic nuclei (PI. VIII, Fig. 3). Before
these cells begin to protrude outwards to form hairs they become
considerably enlarged on the inner side, displacing the cells of the
layer internal to them. The cells of this layer divide more fre-
quently than the rest of the cortex, with the result that the base - |
of the root-hair cell becomes enclosed in what may be described |
as a jacket of small cells (j, PI. VIII, Figs. 3 and 4).
In the mature root the cortex is sharply separated into two
regions, an inner region in which the cells are radially arranged
and an outer region in which the cells, which are larger, are
* Van Tieghem, Ph. and Douhot, H., "Eecherches comparatives sur I'origine
des membres endogenes dans les plantes vasculaires," Ann. des Sci. nat., 7 ser.
Bot. T. 8, pp. 337, 338 and PI. 36, Figs. 557—560, 1888.
t Scott, D. G. , " Tlie Apical Meristems of the Eoots of Certain Aquatic
Monocotyledons," New Phyt., vol. v. p. 119, 1906.
with special reference to the occurrence of Amitosis, etc. 371
irregularly placed. The inner region is differentiated into a
lacunar part which may be called the middle cortex, and a com-
pact part to which the name of inner cortex may be confined.
The lacunar zone is characterised by large air spaces separated by
radial plates of cells, as a rule only one cell wide in the tangential
direction. These radial plates are continuous with the radial files
of cells which make up the inner cortex. The origin of the lacunae
is of some interest. The whole inner region of the cortex must be
visualised as consisting of radially arranged plates, one cell wide,
which in the early stages are so placed as to leave no spaces
between. The cells composing the plates divide very rapidly, and
a number of new cell-walls are formed, all in planes at right angles
to the long axis of the root. The result is that each plate elon-
gates in the direction of growth of the root, but, owing to the
rapidity of its cell-divisions, the plates grow in length faster than
the rest of the root, and are thus forced into undulations, since
they become too long to retain their normal vertical position. The
possibility of their taking up this sinuous form is due to the fact
that the root enlarges in diameter and thus allows room for the
separation of the plates. It will readily be seen that a series of
plates, side by side, elongating independently, and at the same
time prevented from stretching to their full length, will naturally
become detached from one another at certain points, leaving spaces
between. The result of these processes is that the middle cortex,
as seen in transverse section, consists of radial plates of cells, like
the spokes of a wheel, separated by lacunae, whereas in tangential
section the plates are found to meet their neighbours at intervals
so as to form a network (PI. VIII, Fig. 2).
The structure of the mature root of Stratiotes aloides has been
described by Van Tieghem and Douliot*. These authors must
have selected an unusually small specimen for study, for they
describe the root as pentarch, whereas I have found as many as
eight protoxylem elements and about eight metaxylem vessels
alternating with eight phloem groups, each consisting of one to
three sieve-tubes with their accompanying companion cells. Lignifi-
cation is extremely slight ; the metaxylem elements bear delicate
scalariform thickenings.
In young roots the embryonic vessels are represented by files
of large elements with correspondingly large nuclei (PL IX, Fig. 6).
The young sieve-tubes are narrower in lumen than the young
i vessels. They consist, at an early stage, of segmented tubes,
poor in contents and without nuclei. The segments are shorter
than in the case of the young vessels, and the partition walls are
horizontal instead of oblique. The accompanying cells are not
, typical companion cells, since they are much shorter than the
* I.e. p. 337.
25—2
372 Mrs Arher, On Root Development in Stratiotes aloides L.
adjacent segments of the sieve-tube. Their horizontal walls bear
no relation to those of the sieve-tube, showing that they have not
been derived from the same mother-cell.
Like those of so many water plants, the roots of Stratiotes in
their young stages are green in colour. The chlorophyll grains
occur chieHy in the cortex, especially in its inner region, and
also very richly in the root-tip, both in the root-cap and internal
tissues. Starch occurs abundantly in the inner cortex. A small
quantity also occurs in the central cylinder, especially in the
developing vessels and sieve-tubes.
III. The Nuclei.
(i) Observations. ■
The young adventitious roots of Stratiotes aloides, while still ;
enclosed in the stem tissue or just emerging from it, show two |
very marked cytological peculiarities — firstly, that the cells, j
especially those of the root-cap and cortex, not infrequently i
contain more than one nucleus, and secondly, that the nuclei j
themselves, both in the cortex and the stele, are often bilobed.
Multinucleate cells also sometimes occur in the adjacent tissues of '
the parent stem. PI. VIII, Fig. 5 shows one of the most extreme
cases I have observed, as regards number of nuclei. Here the j
outer cells of the root-cap of a young root, and also certain cells j
of the stem cortex through which it was dissolving its way, are j
characterised by numerous nuclei, one cell of the root-cap contain- ;
ing at least 12. This case is however of minor interest, since the ,
tissues in question may well be held to be in a decadent condition, !
but in the examples figured in Plate IX, the cells concerned belong :'
to the normal tissues of the leaf, root-cortex and root-stele, which i]
are still undergoing development. In PL IX, Fig. 7 a, cells belong-
ing to the root cortex and containing more than one nucleus are '
shown, while PI. IX, Figs. 6 and 9 a — e represent lobed nuclei and \
binucleate cells occurring in the xylem parenchyma and other
tissues of the central cylinder. Lobed nuclei are notably frequent i
in the cells immediately surrounding the vessels; in PI. IX, Fig. 6, ,'
three cases will be seen in which these xylem parenchyma elements ^
were binucleate, while in one of these cells {oc) each member of the \
pair of nuclei was itself bilobed. Lobed nuclei and cells with more
than one nucleus are not confined to the root and the adjacent stem
tissue, but are also to be found, though comparatively rarely, in
the meristematic apical region of the stem and in the leaf (PI. IX, ,
Figs. 8 a and h). In the latter organ they occur more frequently
towards the base, where growth is presumably taking place, than i
in the upper part where the tissues are mature. It is, however, ,
only in the young root that these nuclear peculiarities become a
really conspicuous feature. /
with special reference to the occurrence of Amitosis, etc. 373
Various instances of lobed nuclei have been described in the
higher plants, especially among the Monocotyledons, but the case of
Stratiotes differs from all those previously recorded in two points —
firstly, that the lohing is of a markedly regular and uniform type,
and secondly, that it occurs, not only in the root-cap, which may
well he regarded as a somewhat abnormal tissue, hut also in the
developing cortex and stele.
The appearance of a lobed nucleus will be more clearly under-
stood by reference to PI. IX, Figs. 6 — 9, than from description. It
is better shown in PL IX, Figs. 7 — 9, which were drawn from hand
sections, than in PI. IX, Fig. 6, for which microtome sections were
employed. In studying amitosis it is important to view the
nucleus as a whole, but in microtome sections the knife is apt
to mutilate it, and there is also more danger of distortion, owing
to the necessary preliminary treatment and the heating in the
paraffin. The result is that hand sections, though so little used
in general cytology, become of special value in this particular
case. A comparative study of the lobed nuclei, as seen in micro-
tome and hand sections, shows that in almost every instance there
is originally an indentation on one side only, the nucleus retaining
its convex form on the opposite side and presenting the general
appearance of a so-called "resting" nucleus (PI. IX, Fig. 9 e). The
two lobes appear, at early stages, to be unequal in size, the one
which contains the nucleolus being the larger. At later stages
the two lobes seem to become equalised, and the nucleus ultimately
has the appearance of being almost bisected. There is generally
a nucleolus in each lobe, due possibly to the division of the original
single one, while sometimes a third occurs in the median plane
(of. the cell marked x in PI. IX, Fig. 9 a). The nuclei in the cells
marked y, y , x and z in PI. IX, Fig. 6 show different stages in the
lobing of the nucleus, and similar stages can be followed in PI. IX,
Fig. 9. Occasionally two nuclei are seen lying closely side by side
as if one of the lobed nuclei had just separated completely into two
(PL IX, Fig. 9 c).
(ii) Interpretation.
The first questions which arise, in considering the observations
(recorded above, are whether the phenomenon which I have de-
scribed as " lobing " of the nucleus is natural or artificially induced,
and, if it is natural, whether it is normal or pathological. I think
we may conclude that it is natural, since I have observed it in
material fixed in methylated spirit, acetic alcohol, and Flemming's
strong solution. It has however been suggested to me that it may
be an abnormality, possibly due to the poisoning of the roots during
life by some substance present on the water, such as marsh gas.
This is, of course, conceivable, but it seems to me unlikely. It is
374 Mrs Arber, On Root Development in Stratiotes abides L.
true that Miss Kemp* has shown that nuclei of abnormal shape
may be produced experimentally by poisoning young roots, but the
results are far from being so uniform and regular as those just
described for Stratiotes. The plants in which I have observed the
lobing of the nuclei were obtained from two different localities
in three different years ; it is scarcely likely that identical toxic
effects would occur independently in three sets of material, which,
in each case, appeared to be quite healthy. It should also be
remembered that the young adventitious roots, in which the
multinucleate cells and lobed nuclei were observed, were still more
or less completely embedded in the stem tissues of the parent,
and thus presumably protected to some extent from adverse
external conditions.
The presence, in the young roots of Stratiotes, of nuclei
bilobed in various degrees, and also of certain cells containing
more than one nucleus, seems to indicate that the lobing cul-
minates in complete bisection. I believe that this is the case,
and that amitosis takes place ; I am inclined to go further and
to think that these amitoses may be followed directly, or after
an interval, by cell-wall formation, and that amitosis thus actually
plays a part, supplementary to karyokinesis, in the development
of the embryonic root of Stratiotes f. It is naturally almost im-
possible to prove that cell-walls are formed in connexion with
these direct nuclear divisions, but I have more than once seen
appearances decidedly suggestive of such an occurrence. The
fact also that, in the young roots, bilobed nuclei are much more
frequent than multinucleate cells, and, again, that the mature
roots are not characterised either by bilobed nuclei, or by a number
of multinucleate cells corresponding with the numerous bilobed
nuclei seen in the younger stages, is difficult to explain unless
wall formation has occurred between daughter nuclei formed by
direct division, for there is no evidence that any nuclei are
resorbed.
It is, in the nature of the case, very difficult, if not impossible,
to offer a convincing proof of the contention that amitosis plays
an active part in the growth of the young roots of Stratiotes,
and I have hence allowed more than four years to elapse since
I made my first observations on the subject, as I felt reluctant
to put forward such a heretical opinion in any haste, I am aware
that cytologists may prefer to regard the occurrence of these lobed
nuclei as a mere meaningless anomaly. However, each time that
* Kemp, H, P., "On the Question of the Occurrence of ' Heterotypical Re-
duction' in Somatic Cells," Ann. Bot., vol. xxiv. p. 775, 1910.
t I have observed a nucleus dividing by karyokinesis in a section of a root-stele
in which lobed nuclei also occurred.
with special reference to the occurrence of Amitosis, etc. 375
I have returned to the subject, my original impressions have been
strengthened, and I think it is perhaps now advisable to publish
a preliminary account of my conclusions in the hope that they
may receive confirmation or correction from other workers.
It has been suggested to me that, even if the facts are as I
suppose, it is not necessary to regard this form of nuclear division
as genuine amitosis, but that it may be interpreted as a masked
form of karyokinesis, due to incomplete separation of the chromo-
somes. I think this view is somewhat strained, and would be
difficult to accept in any case, but in regard to Stratiotes it is
certainly untenable. It could only hold good if the chromosomes
were few and large, whereas in this plant they are small and
numerous. This point can readily be observed in the case of the
nuclei dividing by normal karyokinesis, which are frequently to
be found in the root-tips.
The remarkable difference in size between the ordinary vege-
tative nuclei and those of the young root-hair cells and vessels
(cf. PI. VIII, Figs. 3 and 4, and PI. IX, Fig. 6) suggests that the
nuclei of Stratiotes aloides are unusually plastic, — thus partaking
in the general plasticity which is so marked a feature of water
plants, and which has probably been a primary factor in de-
termining the possibility of any particular group or species
adopting the aquatic habit. Assuming that amitosis does actu-
ally occur in the young roots, we may, I think, interpret it as
a special adaptation to the unusual requirements of the species.
It is well known that the young plants of the Water Soldier,
produced at the ends of stolons arising from the parent rosette,
pass the winter at the bottom of the water and rise to the surface
in the spring or early summer. Roots are not needed so long as
the plant is submerged, but, when it rises to begin its floating
phase, a quantity of remarkably long roots are produced with great
rapidity. The use of these very long roots is probably to maintain
the equilibrium of the rosette. I noticed, in the case of two
plants which I' cultivated, that the loss of their roots, through the
depredations of water-snails, deprived them of all power of keeping
upright in the water, so that they were generally to be found
floating on their sides. The young plant rises to the surface in
the form of a rosette> not, as in the case of the related Hydrocharis,
in the form of a compact winter-bud ; being, as it were, full-
fledged, it requires its roots at once. That the growth of the
roots is unusually rapid is proved by some measurements which
Mr Aveling Green has kindly taken for me. He kept records,
during part of July and August 1911, of the growth of eleven
roots belonging to three plants of Stratiotes aloides cultivated in
a pond in his garden, and several times observed an increase of
over 2 inches in 24 hours; on one occasion, even 2| inches was
376 Mrs Arher, On Boot Development in Stratiotes aloides L.
recorded. The tentative suggestion which I wish to bring forward
is that amitosis has been adopted in the young roots of Stratiotes
as a means of very rapid nuclear multiplication*, which supple-
ments karyokinesis and thus renders possible a period of extremely
rapid growth. It may, further, in this case be associated with the
somewhat peculiar conditions under which the young roots de-
velope. Owing to the corm-like form of the short main axis of the
plant, the adventitious roots arise at some little depth from the
surface and have to force their way for an appreciable distance
through solid cortical tissue (PI. VIII, Fig. 1), which must act as a
temporary check upon their expansion. Luxuriant growth-activity
is a well known characteristic of water plants, but under the con-
fined circumstances in which the adventitious roots of Stratiotes
aloides are initiated, this energy of development does not seem
to find an adequate outlet in actual increase in size. It is perhaps
conceivable that it may be temporarily diverted into other channels,
and find its expression in amitosis.
IV. On the Significance of Amitosis.
Amitosis, or direct nuclear division, seems to be generally
regarded at the present time as a degeneration process, at least
where it occurs among the higher plants. This, which we may
describe as the orthodox view, has been championed by Stras-
burgerf, who held that karyokinesis and "fragmentation" were
two entirely different processes, the former taking place under the
influence of the surrounding protoplasm, and the latter occurring
when the influence of the protoplasm was on the wane, so that the
nucleus " seinen eigenen Gestaltungstrieben folgen kann J." He
stated that he knew no case in which cell division followed
amitosis, which he regarded as a phenomenon of senility. The
same view has been taken by Zimmermann§ and other writers.
Johow|l, on the contrary, who was the first to point out that
amitosis is a wide-spread phenomenon among Monocotyledons,
protests against the use of the word " fragmentation " on account
of its pathological implication. It was Johow who drew attention
to the pith cells of Tradescantia which are now so widely used for
teaching purposes to illustrate amitotic nuclear division, and he
* Cf. Shibata's work on amitosis in mycorhizal tubercles, referred to in the next
section of the present paper.
t Strasburger, E., "Einige Bemerkungen iiber vielkernige Zellen und iiber die
Embryogenie von Lupinus," Bot. Zeit. 1880, p. 845 etc. (See also Ibid., "Die
Ontogenie der Zelle seit 1875," Progressus Rei Bot., Bd. i. Heft i., p. 22 etc., 1907.)
+ I.e. p. 852.
§ Zimmermann, A., "Die Morphologie und Physiologic des pflanzlichen Zell-
kernes," p. 49, Jena, 1896.
II Johow, F., " Untersuchungen iiber die Zellkerne in den Secretbehaltern und
Parenchymzellen der hoheren Monocotylen," Inaug. Dissert., Bonn, 1880.
with special reference to the occiLrrence of Amitosis, etc. 377
remarks on the fact that these cells, though advanced in age, still
retain their living, streaming protoplasm, and include chlorophyll
and starch.
Some very remarkable results bearing on the meaning of
amitosis have been obtained in connexion with the study of
mycorhiza. Werner * showed that in the case of certain cells
of infected roots of Listera and Orchis there is a kind of fragmen-
tation which is not a dying condition, but a special adaptation in
an actively working nucleus. Shibataf also, who studied the
mycorhizal tubercles of Podocarpus, demonstrated that in the
infected cells, which are digesting the fungus, the nuclei divide
]*epeatedly by amitosis. This is not a death phenomenon, but
must be regarded as a rapid means of nuclear multiplication.
After the digestion of the fungus is ended, normal karyokinetic
figures can often be seen in the multinucleate tubercle cells,
showing that the nuclei, after repeated amitotic divisions, still
retain the power of dividing by mitosis. I am not aware that
these results of Shibata's have actually received confirmation
from more recent workers, but, if they are correct, they are of
fundamental importance, since it is scarcely possible to reconcile
them with the theory of the permanence of the chromosomes —
a theory which already shows symptoms of crystallising into a
dogma.
The amitosis in the cortex and stele of Stratiotes aloides,
described in the present paper, seems to be unique among re-
corded cases in respect of bhe immature condition of the tissues in
which it has been observed. It lends support to the view that
amitosis is by no means always a senile phenomenon — a view
which has, in recent years, been upheld by certain zoological
writers +. This opinion has hitherto received little acceptation
on the botanical side, perhaps because the attention of cytologists
has been, of late, so closely riveted upon karyokinesis and, more
particularly, meiosis, that other phases in the life of the nucleus
have suffered comparative neglect.
* Magnus, W., "Studien an der endotrophen Mycorrhiza von Neottia Nidus
avis L." Jahrb. f. luiss. Bot., vol. xxxv. p. 205, 1900.
t Shibata, K., " Cytologische Studien iiber die endotrophen Mykorrhizen, "
Jahrb. f. tviss. Bot., vol. xxxvii. p. 643, 1902.
J See for instance Child, C. M., "Studies on the relation between Amitosis and
Mitosis," Biol. Bull., Woods Holl, Mass., vols. 12 and 13, 1906 and 1907; Glaser,
0. C, "A statistical study of Mitosis and Amitosis in the Entoderm of Fasciolaria
tulipa var. distans," Biol. Bull, Woods Holl, Mass., vol. 14, p. 219, 1908; Walker,
C. E., The Essentials of Cytology, London, 1907, p. 30; Foot, K. and Strobell, E. C,
"Amitosis in the Ovary of Protenor belfragei and a Study of the Chromatin
Nucleolus," Archiv f. Zellforschung, Bd. vii. p. 190, 1912.
378 Mrs Arber, On Root Development in Stratiotes aloides L.
V. Summary.
In the present paper an account is given of certain features
in the general development and the cytology of the adventitious
roots of Stratiotes aloides L., which may be briefly summarised as
follows : —
A. Anatomical Results.
(i) The apex of the young adventitious root is clothed in a
uniform cap of tissue, in which no distinction can be recognised
between a pericyclic root-cap and an endodermal digestive sac.
In this respect the results agree with those of D. G. Scott, and are
opposed to those of Van Tieghem and Douliot.
(ii) The origin of the lacunae of the middle cortex is shown to
be due to differences in the rate of growth of the different tissue
regions of the root.
B. Cytological Results.
(i) The nuclei of the young vessels and of the young root
hairs are shown to be relatively of great size — a feature which
possibly indicates unusual plasticity in the nuclei of this plant,
(ii) In the stem and leaf, bilobed nuclei and cells with more
than one nucleus are shown to occur, but this peculiarity is much
more important and conspicuous in the young adventitious roots
where it occurs in the root-cap, cortex and stele. These observa-
tions have been made upon plants collected in 1910, 1911 and
1912 from two different localities. It is suggested that amitosis
supplements karyokinesis in the early development of the adventitious
roots. The behaviour of the nuclei is considered in relation to
the life-history of the species, and the paper concludes with a brief
discussion of the significance of amitosis.
Explanation of Plates.
Plate VIII.
Stratiotes aloides L.
Fig. 1. Semi-diagrammatic sketch of a stem, as it appears in
August, bisected longitudinally, {v.c. = vascular central region of stem;
G. = stem cortex ; l.t. = leaf trace ; I. = leaf ; f.b. = young stolon ; s. =
squamula intra vaginalis ; r. = adventitious root.) (Nat. size.)
Fig. 2. Tangential section through the middle cortex of a young
root to show the origin of the lacunae [lac), (x 318.)
Phil. Soc. Proc. Vol. xvii. Pt v.
Plate VIII.
AAM.
Phil. Soc. Proc. Vol. xvii. Pt v.
Plate IX.
-z S>.
0>
?
A. A. del
tuith special reference to the occurrence of Amitosis, etc. 379
Fig. 3. Edge of a transverse section through a root near the apex
to show the relatively large size of the nucleus (r.h.n.) in a cell which
is destined to form a root hair. One layer of dying root-cap tissue (r.c.)
remains outside the piliferous layer (p.l.). The base of the root-hair
cell is enclosed in a jacket of small cells (j.). (x 318.)
Fig. 4. Edge of a transverse section between 1 and 2 cms. from
the apex of a root for comparison with Fig. 3 (on a smaller scale). No
root-cap tissue is present, and one cell of the piliferous layer (p.l.) has
begun to grow out into a root hair. The jacket of cells (j.) at the base
of the root hair has become more conspicuous, (x 198.)
Fig. 5. Small part of a longitudinal section of an adventitious
root embedded in stem tissue, to show multinucleate cells in the root-
cap (r.c.) and in the stem cortex (c). The arrow indicates the
direction of the root-apex. *S^. = space between root-cap and stem tissue
which contains nuclei and other remains of disintegrating cells (c?.).
(x 318.)
Plate IX.
Stratiotes aloides L.
Fig. 6. Part of the stele from a longitudinal section of a young
adventitious root of a plant collected August 1 1th, 1910, passing through
two embryonic vessels {v.) and their associated parenchyma cells {x.p.),
many of which have lobed nuclei. In the cells marked y, y', x and z,
different stages of amitosis can be observed, while the cell marked x is
also an example of a binucleate cell. Drawn from three successive
microtome sections, (x 318.)
Fig. 7 a. Cells of the outer cortex containing more than one
nucleus, from a transverse section of a young adventitious root.
(x318.)
Fig. 7 6. A cell of the outer cortex containing a lobed nucleus from
a longitudinal section of an adventitious root, (x 318.)
Figs. 8 a and h. A binucleate cell and a lobed nucleus from a
longitudinal section of the base of a leaf, (x 318.)
Figs. 9 a — d. Parts of the stele from a transverse hand section of a
young adventitious root of a plant collected August 11th, 1910, showing
lobed nuclei in the pericycle and stelar parenchyma, and, in 9 c, a case
of actual division of the nucleus in a xylem parenchyma cell, (x 900.)
(c. = cortex ; e. = endodermis ; p. = pericycle ; px. = 1 protoxylem ;
v. = metaxylem vessel; s.t. =1 sieve tube.)
Fig. 9 e. Two lobed nuclei from a transverse section of the stele of
a young root, showing the lobing in greater detail, (x 900.)
380 Mr McLean, Amitosis in the Parenchyma of Water-Plants.
Amitosis in the Parenchyma of Water-Plants. By R. C. McLean,
B.Sc, Lecturer in Botany at University College, Reading.
(Communicated by Professor Seward.)
[Read 9 February 1914.]
It is desired to recoi'd the observation that the amitotic or
direct process of nuclear division commonly occurs in the cortical
parenchyma of aquatic angiosperms.
The phenomenon was first noticed in Myriojphyllum proser-
pinacoides and afterwards in Hippuris vulgaris. This suggested
that it might be characteristic of aquatics, and several other
species, both Dicotyledons and Monocotyledons, were investigated
from this point of view, with the result that a wider distribution
of the phenomenon was discovered than had been presupposed
to be the case. The transverse section of the stem-internode of
Myriophyllum exactly resembles a wheel in its general outline.
The hub is formed by the stele, which consists of a central mass
of pith, around which lie a small number (six or seven) of vascular
bundles which are simply collateral, neither xylem nor phloem
being strongly developed, while around all this lies a well-marked
endodermis. The cortex consists of three parts, an inner zone,
enclosing the stele, an outer zone immediately under the epidermis,
forming the rim of the wheel, and an intermediate zone which
consists of long strands of parenchyma — the spokes of the wheel,
which separate the large air-lacunae from one another. It is in
the innermost zone, that immediately surrounding the stele, that
amitosis is most easily observed, although it has been seen in the
outer cortical zone and in the trabeculae between them as well,
only more seldom. In these latter cases the nuclei show the
common spheroidal form. In Hippuris the stele is central as in
Myriophyllum, but the cortex shows only one zone, consisting of a
wide zone of reticulate trabeculae surrounding numerous large air-
lacunae. Of all the plants so far examined, Hippuris shows the
phenomenon more clearly and more widely spread in the tissues
than any other.
In order to see the nuclei well it is best to use fairly thick
sections, transverse or longitudinal, which include at least the
thickness of one whole layer of parenchyma cells. These may
then be observed unstained in glycerine, or stained carefully with
carbol-fuchsin, acetic acid, methyl-green, or other direct acting
nuclear stain. If the chloroplasts take the stain it will be difficult
to distinguish the nuclei among them.
The general distribution of amitosis in the tissues follows the
general distribution of growth. Cells showing it are commoner in
Mr McLean, Amitosis in the Parenchyma of Water-Plants. 381
young stems than in older ones ; they are much more frequent in
sections taken close to a node than in those taken about the middle
of the internode. They are also more frequent in the inner zones
of the cortex, and the frequency diminishes towards the periphery
of the stem.
The appearances presented are somewhat peculiar. Irregu-
larity of outline is a well-known characteristic of nuclei in amitosis
and these are no exception to the rule. The prevailing form,
however, is an elongated spindle-shape, often twisted until it
appears sigmoid. Sometimes the nuclear outline is amoeboid,
the nucleus appearing to send out pseudopodia, its own diameter
or more ^ in length. These pseudopodia are distinctly acute and
taper off insensibly into the cytoplasm. They are not mere lobes.
Paired nuclei in cortical cells of Hippuris vulgaris. In all cases the
two nuclei lay in the same focal plane, x 240.
So common is the sigmoid form, resembling in outline the diatom
Pleurosigma, that even when stages of actual amitosis are not
found the existence of amitosis may be inferred from the nuclear
form in the tissue under observation. Sometimes the length
of these nuclei is as much as ten or twelve times their diameter.
It must be noted in conjunction with the last remark that cell-
division does not follow nuclear division for some time, so that the
sigmoid forms above referred to are almost always to be found
associated together in pairs in the same cell. Rarely three may
be met with in one cell, and not infrequently the nuclei in each
pair may be twisted round one another, although not in any way
united, recalling the appearance presented by the alga Raphidium
which both resembles these nuclei in form and in the way which
382 Mr McLean, Amitosis in the Parenchyma of Water-Plants.
they twist round one another. Apparently the separation of the
nuclei from one another after division is very slow. Large and
conspicuous nucleoli are always present, either one or, occasionally,
two in each nucleus. The nucleolus sometimes causes a bulging-
out of one side of the fusiform nuclei.
Stages in the actual separation of the two daughter-nuclei may
be observed. No constriction is formed, but the process proceeds
like the longitudinal fission in the Flagellata, from end to end, by
gradual separation of the two daughter-nuclei. Amitosis is the
only form of nuclear division which has been recognized in the
tissues investigated, and from its exceeding frequency in the
constituent cells it may be inferred that it is the only form
occurring there.
Besides the two plants — Myriophyllum and Hippuris — men-
tioned above the following plants show the same phenomena in
their cortical tissues.
Dicotyledons Monoeotyledons
Trapa bifida. Elodea canadensis.
Jussieuia sp. Potamogeton lucens.
(Hippuris). Limnocharis sp.
(Myriophyllum). Aponogeton sp.
All the above are aquatics, but two land plants have also been
noted as showing resemblances to the aquatics in the above
respects. These are Dioncea muscipula and Polypodium ireoides.
The first is of course a marsh plant, but the second is an epiphyte,
and as far removed from an aquatic as may well be. This suggests
that the phenomena of amitosis in plants may well be much more
widespread than has hitherto been supposed, and opens up a new
field for thought in regard to its theoretical importance in cytology.
It is generally admitted that amitosis represents only a fragmen-
tation rather than a qualitative division of the nuclear substance,
and that the complex phenomena of mitosis are adapted to the
segregation of the histogenetic characters resident in that sub-
stance. Mitosis should therefore be the characteristic form of
nuclear division in tissues which are undergoing ontogenetic
growth. If, however, growth continues in a tissue which has
already become fully differentiated, it is hard to see what further
need there is for mitosis to take place. Amitosis may therefore
be the constant form of nuclear division between sister-cells in all
fully differentiated tissues which remain alive and continue to
grow in bulk, although this does not preclude the possibility of its
occurrence in meristematic tissues as well.
Mr Marsh, The History of the occurrence of Azolla, etc. 383
The History of the occu7Tence of Azolla in the British Isles
and in Europe generally. By A. S. Marsh, B.A., Trinity
College. (Communicated by Professor Seward.)
[Bead 9 February 1914.]
In the middle of October 1913 a species of Azolla was found
in Jesus Ditch, Cambridge, by Mr H. Jeffreys of St John's
College. Mr Moss called my attention to the fact, and at his
suggestion and with his frequent kind assistance I have identified
the species and collected a few notes on the distribution of plants
of this genus in Europe generally and the British Isles in
particular.
The Cambridge plant I found to be Azolla filiculoides Lam.
It was growing among the Lemna, but two or three large patches,
several metres broad, bore Azolla almost pure, the dull brownish
colour of the plant as seen in large masses showing up markedly
against the bright green of the duckweed. When first found
the plants seemed to be without reproductive organs, but on
November 2nd it was bearing micro- and macro-sporocarps in
some quantity. On November 26th, after several sharp frosts,
the Azolla was growing vigorously, still with sporocarps, and had
spread over larger areas, at the eastern end of the ditch becoming
the dominant species of the aquatic vegetation. At the present
time (February 9th) it is very abundant, but very red in colour
and broken up into small pieces.
As to means of introduction of this fern into Cambridge we
are completely ignorant. The nearest of the previously recorded
stations is the Norfolk Broads area, while the obvious suggestion,
that we are dealing with a Botanic Garden escape, is untenable,
since there was before this discovery no Azolla except A. caroliniana
being grown at the Cambridge Botanic Garden.
Azolla, according to Baker*, is a genus with five species
inhabiting the tropics and warm temperate regions of both hemi-
spheres. Of these species two have been introduced into Europe,
and both occur in the British Isles. These two are A. caroliniana,
which occurs native in America from Lake Ontario to Brazil, and
A. filiculoides, from South America f.
The characters of these two species have been well summed
up in two recent papers on the occurrence of A. filiculoides in
* Baker, \F>m Allies, p. 137, London, 1887.
+ The distributions are as given in Coste, Flore de France, in. pp. 702, 703,
Paris, 1906, and Aseherson u. Graebner, Synopsis der mitteleuropaischen Flora,
I. p. 114, Leipzig, 1896.
384 Mr Marsh, The History of the occuri'ence of Azolla
Europe, and from the accouuts of these authors (viz. Bernard* and
Beguinot and Traversoi*), from Baker| and from von Martius§,
the following details of the principal differences between the
species are taken.
Azolla filiculoides (Lamarck, Encyclopedie Methodique:
Botanique, T. I. p. 343 and plate 863, 1783). The plants are
in dense tufted masses, the ends of the shoots being porrect and
often protruding, not lying flat on the surface of the water as in
the other species. The whole shoot is much larger and thicker,
the branching is more compound and the branches are closer
together. The upper lobes of the leaves have a broad distinct
margin and bear numerous unicellular trichomes on their upper
surfaces. The reproductive organs show the most distinctive
characters. The glochidia or hooked hairs which are attached to
the massulce or microspore masses have non-septate stalks. The
macrospore wall' is furnished with large, deep, circular pits.
Azolla caroliniana (Willdenow, Species Plantarum, v, p. 541,
1810). The plants are much smaller with much less dense branch-
ing. They lie flat on the surface of the water. The roots are
not as numerous or as conspicuous as in A. filiculoides. The
margin of the upper leaf lobe is not as broad as in the other
species, and the trichomes of the upper surface are said to be
bicellular, though I have not been able to observe this character
satisfactorily. The glochidia have 3 — 5 transverse septa in the
stalk, and the macrospore wall is not pitted but merely finely
granulate.
The history of the genus in Europe began in 1872, when
A. caroliniana was introduced into continental botanic gardens,
whence it soon escaped into neighbouring ditches and ponds, and
multiplied enormously. In 1878 De Bary described it as a "new
water-pest " in Kassel, and in 1885 it was very abundant at
Leyden and Boskoop in Holland ||. It was also found at Bonn,
GiessenlF and Strassburg in 1885, and in Berlin in 1887**. In
Bohemia it was found by Celakovsky near Pilsen in 1895, and it
had spread much earlier into England (1883), France (1879) and
Italy (1886) tf.
* Bernard, Recueil des Trav. Bot. Neerland., i, pp. 1 — 14, 1904, quoted in the
Report of the Botanical Exchange Club for 1912, p. 186.
t Beguinot e Traverse, "Azolla filiculoides Lam. nuovo inquilino della flora
italiana," Bull. Sac. Bot. Ital, pp. 143—151, 1906. J Baker, loc. cit.
§ von Martius, Flora Brasiliensis, vol. i. part ii, p. 657, plate 82, Leipzig, 1884.
II Kittel, Gartenjiora, 1885.
11 Dosch u. Scriba, Excursionsflora Hessen, 3'<= Auflage, p. 24.
** Luerssen, Farnpflanzen, p. 598.
ft This account is taken chiefly from Ascherson and Graebner, loc. cit., but see
also Saccardo, Gronologia della Flora Italiana, Padova, 1909; Ibid.,"De diffusione
Azollffi carolinianaa per Europam," Hedwigia, 1892, p. 217; Beguinot and Traverso,
loc. cit., where many additional references are given.
in the British Isles and in Europe generally. 385
In England A. caroliniana was first obtained at Pindon
(Middlesex), and an account of this is published in Science Gossip
for 1883. It has been recently reported from various spots in the
Thames valley, between Oxford and London, but it must be
remembered that until Ostenfeld* pointed out the fact in 1912
(from specimens found in 1911) it was not realised that we had
any Azolla other than A. caroliniana. For instance, Drucef
(1908) gives only one species, A. caroliniana. The following
records for the British Isles have been published, though, until
the material has been re-examined in the light of Ostenfeld's
discovery, they must be considered records for the genus rather
than for the species. Azolla described as A. caroliniana has been
found at Hayes Place (Kent), Oxford, Sonning, Henley, Enfield,
Sunbury and Suleham|. Of these I have been able to examine
material from Sunbury and Enfield kindly sent by Mr C. E. Britton.
The Sunbury plant is A. filiculoides, the Enfield specimen A. caro-
liniana. Another Azolla from Enfield was sent by Mr Holloway,
but this was A. filicidoides. The Norfolk Azolla, which is good
A. filiculoides, has also been several times referred to as J., caro-
liniana. I have seen A. caroliniana from one other British locality,
viz. Godalming, where it was found in 1913.
The species is described by Ascherson and Graebner (1896)
as fruiting only very rarely, they knowing of only one case of fruit
being produced in Europe — a record from Bordeaux. No fruiting
material has been found in the British Isles, although fruiting
A. filicidoides has more than once been described under the wrong
specific name.
Azolla filiculoides was introduced into Europe in 1880 by
Roze§, who naively remarks, " Le climat de Bordeaux parait, du
reste, assez bien convenir a ces deux especes americaines, car
quelques poignees de la premiere \^A. caroliniana'] en 1879, et de
la seconde \^A. filicidoides] en 1880, jetees 9a et la dans les fosses
des marais de cette ville, ont donne naissance a une legion in-
nombrable de ces plantes, qui ont envahi presque tous les fosses,
mares et etangs du departement de la Gironde."
: It spread over many parts of France and then into other
il countries. In 1896 Ascherson and Graebner knew of it only in
western and northern France. In 1900 it had reached Italy ||.
In the British Isles A. filiculoides was first noticed as a distinct
I * Ostenfeld, "Floristic Eesults of the International Excursion," New Pliyt. xi.
Ip. 127, 1912.
! t Druce, -List of British Plants, p. 88, Oxford, 1908.
' X Reports of the Botanical Exchange Club, 1910, p. 609 ; 1911, p. 56 ; 1912,
pp. 186, 220; Jo2irnal of Botany, xl. p. 113, 1902; xlviii. p. 332, 1910.
§ Eoze, " Contribution a I'^tude de la fecondation chez les Azolla," Bull, de la
Soc. hot. de France, xxx. p. 198, 1883.
II Saccardo, Gronologia, loc. cit. ; Beguinot e Traverse, loc. eit.
VOL. XVII. PT. v. 26
386 Mr Marsh, The History of the occurrence of Azolla, etc.
species by Ostenfeld * in 1911, who found it at Woodbastwick,
Norfolk, and at Queenstown Junction, Co. Cork. It was, however,
present in this country before that time. The Sunbury record of
A. caroliniana in 1910 f should certainly be ascribed to the other
species, while the Azolla was noticed in the Norfolk Broads J
before Ostenfeld's identification.
I have also seen fruiting v=;pecimens of A. filiculoides found in
1912 at Almondsbury, West Gloucestershire, and kindly sent me
by Miss I. M. Roper. The same species now occurs at Reading,
where it is peculiar in being without the endophytic blue-green
alga, Anabcena, which usually inhabits the cavity of the upper
leaf-lobe.
At present A. filiculoides seems to be growing in importance
as a constituent of British vegetation, for, as the result of the
floods of 1912, it has been distributed over large areas in Norfolk.
It is described as occupying a definite position as a member of the
association of Typha angustifolia, especially in South Walsham and
Ranworth Broads §.
A. filiculoides fruits quite readily in Europe. Both the
specimens found by Ostenfeld were fruiting, the Almondsbury
and the Sunbury plants were in fruit, and I obtained fruit last
autumn, not only from Cambridge but, by the kindness of
Mr W. Fi. Palmer, of St John's College (the author of the
article in Nature), also from Norfolk. Ascherson and Graebner||
also describe it as a freely fruiting species.
In conclusion, I should like to suggest that it is of some
importance to keep a look-out for Azollas in the British Isles as,
in the event of their becoming important factors in our vegetation,
as full a knowledge as possible of their early history in the country
would be of great interest and value.
* Ostenfeld, loc. cit.; Report of the Bot. Exch. Club for 1912, pp. 220, 301.
t Rep. Bot. Exch. Club for 1910, p. 609 ; Journ. Bot. xlviii. p. 332, 1910.
X Rep. Bot. Exch. Club for 1910 and 1911, loc. cit.
§ Palmer, "Azolla in Norfolk," Natxire, xcii. p. 233, 1913. The plant is wrongly
named A. caroliniana, but I have seen fruiting specimens, which prove it to be
A. filiculoides.
II Loc. cit., p. 115.
Mr Wiener, A Simplification of the Logic of Relations. 387
A Simplification of the Logic of Relations.
By N. Wiener, Ph.D. (Communicated by Mr G. H. Hardy.)
[Read 23 February 1914.]
Two axioms, known as the axioms of reducibility, are stated on
page 174 of the first volume of the Principia Matheniatica of
Whitehead and Russell. One of these, *12'1, is essential to the
treatment of identity, descriptions, classes, and relations : the
other, *1211, is involved only in the theory of relations. *12*11
is applied directly only in
*20-701-702-703 and *21-12-13-151-3-701-702-703.
It states that, given any propositional function of two variable
individuals, there is another propositional function of two variable
individuals, involving no apparent variables, and having the same
truth-value as for the same arguments, or in symbols :
^■:(a/):<^(^. 2/)■ = ■/J(^>2/)•
In *20 and *21-701 •702-703 all that is done with *12-11 is to
extend it to cases where the arguments of ^ and /are classes and
relations : *12'11 is essential to the development of the calculus of
relations only owing to its application in *21'12'13"151'3. Here
it is needed to make the transition between the definition of a
binary relation and its uses. This is due to the fact that a binary
relation itself is not defined, but only propositions about it, and
*12*11 is needed to assure us that these propositions about it
behave as if there were a real object with which they concern
themselves. The authors of the Principia wish to treat a binary
relation as the extension of a propositional function of two
variables : that is, when they speak about the relation between x
and y when ^{x, y), they mean to speak of any propositional
function which holds of those values of x and y, and only those
values, of which ^ holds. Now, as it leads one into vicious-circle
paradoxes to speak directly of " any propositional function which
holds of those values of x and y, and those only, of which ^ holds,"
they first define a proposition concerning the relation between x
and y when (^{x, y) as a proposition concerning a propositional
function involving no apparent variables which holds of x and y
when and only when (^{x, y). Then they need to use *12'11
to assure us that, whatever ^ may be, there always is some such
propositional function. Now, if we can discover a propositional
function T^ of one variable so correlated with ^ that its extension
26—3
388 Mr Wiener, A Simplification of the Logic of Relations.
is determined uniquely by that of ^, and vice versa — if, to put it
in symbols, when -v/r' bears to 0' the same relation that yjr bears
to (f),h :.<j)' (cc, y) .=a;,y^ (^, y)' = '- ^f'^ • =a ■ ^« — ' we can entirely
avoid the use of *12-11, and interpret any proposition concerning
the extension of <^ as if it concerned the extension of yjr ; for the
existence of the extension of a prepositional function of one
variable is assured to us by *12-1, quite as that of one of two
variables is by *]2-ll. Now, is such a i/r the prepositional
function
(g«, y) .<^{x, y) .0L= L^i'l'a; \j l'A) \j I'l'i'y.
For it is clear that for each ordered pair of values of x and y there
is one and only one value of a, and vice versa. On the one hand,
as i'{L'i'x w l'A) is determined uniquely by x, and L'l'i'y is deter-
mined uniquely by y, L'(i'i'x u i'A) w i'i't'y is determined uniquely
by X and y. On the other hand, if
i'{i'i'x yj t'A) u L'i'i'y = l\l'l'2 \j i'A) u l'l'l'w,
either i'i'y=i'l'2!^L'A or i'l'y = i'l'w. The former supposition
is clearly impossible, for, as l'z^A, I'l'z u t'A is not a unit class.
From the latter alternative we conclude immediately that y = w.
Similarly, x = z.
Therefore, when x and y are of the same type, we can make
the following definition :
xy(l> {x, y) = oi {{'^x, y) . (f>(x,y) .a= i\iH'x w t^A) w I'l'i'y] Df.*
It will be seen that in this definition of xy(^ (x, y) it is essential
that the x and the y should be of the same type, for if they are
not i'{ih'x\Ji'A) and lUH^yviiW not be, and i'(i'i'x \j i'A) u L'l'i'y
will be meaningless. To overcome this limitation, and secure
typical ambiguity for domain and converse domain of xy(f) (x, y)
separately, we make the following definitions :
a^<^ (a. 2/) = « {(a«. y) • 4> («' y) •
K = L\i'i'a vj I' A) u i'L'(L'i'y u I' A)] Df.
f^y<}> (f^, y) = P {(a«. y) ■ (>^> y) •
ii = l\i'i'K u i'A) w iH\L\i'L'y u I'A) u t'A]| Df.
etc.
K = L'[t'{i'L'x yj L'A) w t'A] yj i'i'i'jS} Df.
^\(f) (x, X) — fi {(a^, ^) ■
fM = L'{L'[i'(L'i'x yj L'A) yj t'A] u t'A} w l'l'l'X} Df.
etc.
* This may seem circular as i is a relation, defined in the Principia as I, but it
really is not circular, for \,'x may be defined directly as the class, y (y==x).
Mr Wiener, A Simplification of the Logic of Relations. 389
Though these definitions may seem to conflict with one
another, they really do not conflict, for where one of them is
applicable, the others are meaningless, since they define relations
between objects of different types. Moreover, it is easy to see
that our definitions are so chosen that
h : pv(f> (/u., v) = OT^-v/r (ot, p) .^ . t'T>'fji.v(f) {fM, v)
= t'D'^Pf (ot, p) . fa^ixvcj) {fji, v) = t'a'^Pf («r, p).
This is important, as we might easily have defined relations so that
they might have several domains or converse domains of different
types. This is why we did not define a^(/>(«, y) simply as
K {(ga, y).(f>{a,y).K = L'(i'i'a w t'A) u i'i'ih'y],
for this would also represent
«^ 1(32/) ■</>(«> 2/)- /3 = t'2/l-
It will be seen that what we have done is practically to revert
to Schroder's treatment of a relation as a class of ordered couples.
The complicated apparatus of i'b and A^s of which we have made
use is simply and solely devised for the purpose of constructing
a class which shall depend only on an ordered pair of values of x
and y, and which shall correspond to only one such pair. The
particular method selected of doing this is largely a matter
of choice : for example, I might have substituted V, or any other
constant class not a unit class, and existing in every type of classes,
in every place I have written A.
Our changed definition of xy(l> {x, y) renders it necessary to
give new definitions of several other symbols fundamental to the
theory of relations. I give the following table of such definitions :
ne[ = 1c[icQmx = x.y = y)] Df.
xRy . = . zw {z = x.w = y]CR.R6 Rel Df.
0i? . =.. (ga) .a = R.oiene\.(f>a Df.*
(i?) . (/)E : = : a 6 Rel . Da . </>« Df.
(ai?) .(f>R: = . (aa) . a e Rel . </>a Df.
The first two and the last two of these definitions replace *2r03"02
and *21-07-07] respectively. From these definitions and the laws
* We shall understand in this way any propositional functions containing
capital letters in the positions proper to their arguments. Thus no0iJ shall be
understood as
(ga) .a = R . cc€ Rel . <-«-' (fxx,
and not as
a = R . 0.6 Rel . D^ ■ '^ <^ol.
We make this definition as well as the two following ones because a propositional
function of a class of the sort we have defined as a relation may significantly take
as arguments classes of the same type which are not relations, and we wish to
define propositional functions of relations in such a manner as to require that their
arguments be relations.
390 Mr Wiener, A Simplification of the Logic of Relations.
of the calculus of classes it is au exceedingly simple matter to
deduce any of the propositions of *21 which are not explicitly
used for the purpose of deriving the properties of relations from
the particular definition of relations given there, and from this
it is easy to prove that the formal properties of the objects I call
relations are essentially the same as those of the relations of the
Principia.
But it is obvious that since they are also classes, our relations
will possess some formal properties not possessed by those of the
Principia. I give in conclusion a table of some of the more
interesting of these :
\-.R\jS = RyjS
\-.Rn8 = Rn8
\-:RCS. = .R(i8
\-.R-8. = .R-S
h.VCV
l-.A = A
h . Rel C Cls
\- : RpK . = . RpK
h : RsK . = . RsK
h . a + /S sm s'a | ^
\- . a X ^sm a^ ^
\
Phil. Sue. Fruc. Vol. xvii. Pt. v.
./
Fig. 3. The # n
Phil. Soc. Proc. Vol. xvji. Pt. v.
Plate X.
Fig. 3. Tlu- # miuks ihe centre uf similitudf of the three pairs of isograiub.
\
larks
Mr Bennett, A Double-Four Mechanism.
391
A Double-Four Mechanism. By G. T. Bennett, M.A.,
Emmanuel College.
(Plate X.)
[Read 24 November 1913.]
§ 1. A plane mechanism of eight pieces may suitably be called
a double-four when each of four pieces 1, 2, 3, 4 is linked to all
the four pieces 1', 2', 3', 4' except to 1', 2', 3', 4' respectively.
A schematic form of diagram may conveniently be drawn as in
Fig. 1, differing not greatly in appearance from a double-four
of straight lines arranged in chequer fashion. Each of the eight
Fig. 1.
pieces is represented by a triangular plate, whose vertices are
linked by pins to three other plates. The notation to be used
here may be described as follows. The vertex of plate 1 which is
linked to plate 2' will be called 12', and the vertex of 2' which is
linked to 1 will be called 2'1 ; so that points 12' and 2'1 coincide
392 Mr Bennett, A Double-Four Mechanism.
when the plates are assembled as a mechanism. The side of
plate 1 opposite to vertex 12' will be denoted by 12. These rules
of notation are to be followed for all the twenty-four vertices and
all the twenty -four side.s. (The numerals assigned to any vertex
have always one accented, and those assigned to any side have both
accented or neither.)
If the pins at points 12', 21', 34', 43' are removed, the whole
divides into separate mechanisms. One of these consists of plates
1, 3', 2, 4' consecutively linked at the vertices of a deformable
quadrilateral which may be denoted 13'24'. Its sides are 12, 3'4',
21, 4'3', and the free vertices of the four triangles form a quadrangle
12', 3'4, 21', 4'3. The other mechanism consists of plates 2', 4, 1', 3
consecutively linked at the vertices of a deformable quadrilateral
2'41'3 with sides 21', 43, 1'2', 34 ; the free vertices of the triangles
forming a quadrangle 2'1, 43', 1'2, 34'. The two quadrangles are
congruent, and coincide when the mechanism is reassembled.
Such a division into two parts may be effected in three different
ways ; and there are thus three such pairs of quadrilateral linkages.
Mechanisms of the type described are singular in possessing one
degree of freedom ; for the connectivity gives, normally, fourfold
stiffness. They were first discussed by Kempe ("Conjugate four-
piece linkages," Proc. Land. Math. Soc. 1878, Vol. ix. pp. 133 —
147), who gave five different species, and afterwards by Darboux
("Recherches sur un systeme articul6," Bulletin des Sciences Math.
2 s6rie, t. ill. 1879, pp. 151 — 192), who carried out an exhaustive
analysis and completed the catalogue by the addition of a species
in which the three pairs of quadrilateral linkages are all contra-
parallelograms (here called isograms). He shows that the material
of the mechanism depends upon six parameters only, and that the
three pairs of isograms are similar in pairs ; but, for the rest,
leaves the figure dependent for its precise description upon
thirteen simultaneous equations in complex variables. It is this
mechanism which is to be further discussed here. As a con-
sequence of some investigations the following cardinal properties
offer themselves, (a) The centre of similitude for each pair of
isograms is the same. (/S) The feet of the perpendiculars from
this centre upon the axes of symmetry of any two pairs of isograms
are the vertices of an isogram. (7) This isogram is similar to
the third pair of isograms of the mechanism, and with the same
centre of similitude. These results being found, a simple means
arises of constructing the mechanism ah initio. As it has been
somewhat elusive, and as its geometry is a little uncommon, kine-
matically, there seems sufficient reason for a short study such as
is here presented.
§ 2. An auxiliary diagram (Fig. 2), not itself a mechanism,
may be described first. It consists of an axis of symmetry x,
Mr Bennett, A Double-Four Mechanism.
39^
four points A, B, C, D on one side of x, and A', B', C, D' their
images in x, on the other. The figure contains six isograms, such
as ABA'B'. Each gives a ratio, such as ABjAB' (less than unity),
for the lengths of the pairs of equal sides. The figure depends
for its shape on only six parameters, so that, if the six ratios are
kept constant, normal expectation indicates an invariable form for
the figure, its size alone remaining variable. A porism, however,
^B
D
X
Fig. 2.
upsets this presumption. The six ratios are subject to a relation
which may be found thus : —
Taking any point P it is possible (owing to the coUinearity
of the middle points of AA', BB', GO', DD') to find constant
multipliers a, h, c, d such that the equation
a (PA' + PA'') + h {PB"' + PB'^) + c {PC + PC)
+ d{PD' + PD'') = (i)
= (v).
394 Mr Bennett, A Double-Four Mechanism.
is identically true for all positions of P. Taking P at ^,
a . AA'^ + h (AB' + AB") + c{AC' + AC')
+ d(AD'' + AD'') = (ii),
and putting (A BjABJ = {k^.^ - l)/(h, + 1),
so that k,^ = {AB' + AB'')/AA' . BB' (iii),
(ii) becomes
a . AA' + h . BB'. h, + c. GG'. k,s + d. DD'.ku = 0.. .(iv).
By taking P in turn at B, G and D three other such equations are
obtained, and hence by elimination
.1 Ki2 fCis '<!u
h, k^ 1 k,,
h, k,, k,, 1
The six ratios, such as AB/AB', remain all constant, therefore, if
any five are kept constant ; and the figure may therefore assume
a single infinity of different shapes while each of the six isograms
retains a constant value for the ratio of its sides.
The variation of shape may be obtained from any arbitrary
initial form by inverting the figure of eight points from a varying
point on the axis of symmetry x. If the radius of inversion
is R, the lengths AB and AB' become, after inversion,
R^.AB/OA.OB and R\AB'/OA .OB',
the ratio of which is AB/AB', the same as before. Inversion
leaves each of the six isograms with an unaltered value for the
ratio of its sides. Specially, when passes to infinity on x, and
the circle becomes a line normal to x, inversion becomes reflexion
in this normal and produces an image of the original figure.
It will be convenient to suppose that the arbitrary size of the
figure is kept always such that the iproduct A A'. BB'.CC'.DD'
remains constant. This is secured by making R* proportional to
OA . OB . OG . OD. An equivalent form of the constant is
{AB"" - AB') (GD'' - GD%
and hence AB.GD is constant and also AB'.GD, AB.G'D and
AB' . G'D. The product of any two sides taken one from each of
a companion pair of isograms remains constant.
§ 3. From the figure of § 2, which may be called a sytnmetro-
gram, may now be constructed the isogram double-four. The
geometry is best expressed in terms of vector multiplication ; the
product of two vectors being equal to the product of two others
if the product of their lengths and the sum of their angles are in
each case the same
Mr Bennett, A Double-Four Mechanism.
395
Let the lines joining D to the six points A, B, G, A', B', C be
taken as vectors, and let all the vector-products of these he taken
in pairs, omitting only the products DA. DA', DB.DB' , DC. DC.
The extremities of these twelve vectors give a figure of twelve
points. The vector DA .DB' gives a point 12', DA' . DB gives a
point 21', and so on, in accordance with the tabular scheme
1'
2'
3'
4'
1
AB'
CA
B'C
2
A'B
—
BC
CA'
3
CA'
B'G
—
A'B'
4
BC
CA
AB
—
where, on joining D to the extremities of any line of the symmetro-
gram entered in the table, the vector-product is to have its
extremity named by the numerals of the same row and column.
(It may be understood that an arbitrary unit vector divides all
the products in common, maintaining the vector dimensions
correctly and giving an arbitrary scale and orientation to the
resultant figure.)
Consider the triangle formed by the points 41', 42', 43'. Its
sides 41, 42, 43, as vectors, are given by the differences of the
vector-products DB.DC, DC. DA, DA.DB, and are therefore
equal to DA.BC, DB.CA, DC.AB (with zero sum). The lengths
of these vectors have appeared as constants in § 2, and hence the
triangle 41', 42', 43' has sides of constant length. Similar results
hold for each of eight triangles 1, 2, 3, 4, 1', 2', 3', 4'. The sides
of each triangle have lengths equal to those of the vector-products
of pairs of sides of an associated quadrangle of the symmetrogram ;
the four points consisting of the three points named in the row
or column of the above table, together with D. A mechanism
is therefore obtained, of the double-four type, with a notation
corresponding to that of Fig. 1. Further, the three pairs of
deformable quadrilaterals are all isograms. One is derived from
the isogram ABA'B' by multiplying it, from D as centre, by the
vector DC; and the companion isogram is got by multiplying
by DC. These are both similar to the isogram ABA'B'; the
ratio of their linear dimensions and the angle of inclination of
their axes being given by the ratio and inclination of the vectors
DC and DC. A list of the lengths of the twelve pairs of equal
lines of the mechanism figure is as follows :
896
Mr Bennett, A Douhle-Four Mechanism.
2S = \DA'.BG'
SI =\DB'.GA'\
12 = \ DC. AB'
2':y =\DA. BC
3'!' = \DB. GA'
V2' = \DG .AB'
14 =
24 =
DA.BG
DB.CA
34 = \DG. AB
1'4' = ! DA'. BC
2'4' = I DB'. GA
S%'=\DG'.AB
\)
.(vi).
Six relations should connect these twelve lengths. It appears
immediately that
23 . 14 = 2'3'. 1'4', 31 . 24 = 31'. 2'4', 12 . 34 = 1'2'. 3'4'
(vii),
giving three relations. Further (using lengths and not vectors)
'' 23^ - 2'3'2 = (DA'' - DA^)BG'' = AA' . DD'. BC'%
142 - l'4'2 = (DA^ - DA'') BG' = -AA'. DD'. BG%
and hence
(232 + 14^) - (2'3'- + 1'4'2) = AA'. BB'. GG'. DD'
(viii),
the constant of § 2, giving two further relations. The sixth
relation is supplied by the determinantal equation (v) on putting
for ki2 its value in terras of the sides given by (iii), and by
AB/ AB' = S4t/r2' = S'4<'/12 jointly; and similarly for the other
elements of the determinant.
The angles of the two sets of plates are also simply related.
The angle of plate 1 opposite to the side 12 may be denoted
by 12, and similarly for the rest. Then at the paint 12' the sum
(or difference) of the angles 12 and 2'1' is equal to the sum
(or difference) of the angles of two of the isograms ; and this
same sum (or difference) occurs for the angles at the points
21', 34', 43'. Similar results hold for the rest of the angles. The
angles of the plates 1, 2, 3, 4 thus serve to determine those of the
other set of plates ; and one method of derivation may be put
thus : — Let angles a, y8, 7 be taken such that
2a = 14 + 23 + 32 + 41,
2yS =13+24 + 31+ 42,
27 = 12+21 + 34 + 43.
Then on subtracting from a, /S, 7 the angles of any one plate
(those namely which occur in a, ^, 7 respectively) the angles of a
plate of the second set are obtained.
I 4. A deforming isogram, starting from any arbitrary form,
may pass through a cycle of fresh forms and revert to its original
Mr Bennett, A Double-Four Mechanism. 397
form, the relative rotation of adjacent sides being four right
angles. Among the forms occur two in which the vertices and
sides are all in one straight line ; and the original form itself
appears in all four times, on two pairs of occasions which alternate
with the rectilinear forms. This simultaneous cyclic performance
of all the six isograras of the mechanism may be followed by
observing the effect on the symmetrogram of inverting from the
travelling point 0. As regards the isogram ABA'B', it inverts
into coUinear points when crosses the circumference of the
circumcircle ; and it inverts into an isogram similar to ABA'B'
when is at either diagonal point N or N' , or at the centre
of the circle, or at infinity. Moreover the two isograms 1'32'4
and 24'13', similar to ABA'B' , will have parallel axes when
crosses the circumference of the circle circumscribing CDC'D';
and when passes the centre of this circle the axes are inclined
at the same angle as originally (with at infinity).
As regards the kinematics of the instantaneous movement,
any two of the eight pieces have a centre of relative rotation,
and the three centres associated with any three pieces, taken in
pairs, must be collinear. The figure necessarily possesses the
requisite collinearities, and they may be readily accounted for.
Let the instantaneous centre for plates 1 and 2 be denoted
by (12), and similarly for all others. Of centres such as (12')
there are twelve, these being permanent centres given by the
connecting pins themselves. Of centres such as (12) and (1'2')
there are altogether twelve. The centre (12) is collinear with
(13') and (23'), and is also collinear with (14') and (24'); and
similarly for all such others. For any pair of equal sides of an
isogram, that is, the plates they carry have as instantaneous
centre the (diagonal) point of intersection of the other two equal
sides.
Of sets of three plates there occur three different types, of
which 123', 1'2'3' and 144' may be taken as representative. For
the first, the collinearity of (12), (13') and (23') has already been
noticed. For the second, the collinearity of (1'2'), (2'3'), (3'1')
may be seen thus. The vector from D to (1'2'), a diagonal point
of the isogram 1'32'4, is given by the product-vector DC .DN,
where N is the intersection of AB and x ; (2'3') is given similarly
by DA . DL and (3'1') by DB . DM. These are the three products
of pairs of vectors drawn from a point D to the three pairs of
vertices of a complete quadrilateral, formed by the sides of the
triangle ABC and the line as; and hence the extremities of the
three product-vectors are collinear.
There remain only the points (11'), (22'), (33'), (44') to be
considered. The last should be collinear with three pairs such
as (14) and (14'), and also with three pairs such as (1'4) and (1'4').
398 Mr Bennett, A Double-Four Mechanism.
It may be found without difficulty that a vector from B equal
to the vector function
{DA'.DB'. DC -DA.DB. DC)I{AA' + BB' + GC)
gives a point (44') satisfying all six conditions. Exchange of A
and A' in this formula gives (11), and similarly for (22') and (33').
The twenty-eight instantaneous centres are thus all accounted for,
and their collinearity in sets of three.
I 5. The double-four mechanism described so far is not the
only one derivable from the symmetrogram of § 2. The point B
has, specially, been used as a centre for vector-products, and the
mechanism thus associated with D may be named {D). The use
of D' in place of D gives a mechanism {D') which is merely the
image of (D) in x. But three fresh pairs of mechanisms {A) and
{A'), (B) and (B'), (C) and (C") complete a set of eight, consisting
of four distinct mechanisms (A), (B), (C), (D), each accompanied
by its image. These four may now be compared.
Among the eight triangular plates of which (G) is composed
there occurs one whose vertices are the extremities of product-
vectors CA.GB, GB.GD, GD.GA. The sides of this triangle, as
vectors, are given by GD.BA, GA.DB, GB.AD; and this triangle
is identical in dimensions with the plate 4; and similarly for all
the rest. The mechanism (C) is composed of the same material
as (D), but it is differently put together. One of the isograms
of (G) is obtained by multiplying the isogram ABA'B' from G by
GD ; and one of the isograms of {D) is got by multiplying the
same isogram ABA'B' from D by DG. These isograms are there-
fore congruent, with parallel sides, and a half-turn rotation would
bring them into coincidence. The triangles on corresponding
sides, moreover, ai'e both congruent and homothetic. The other
pair of congruent isograms of {D) and (C) are got by multiplying
the isogram ABA'B' by BG' from B and CD' from G. Compare
with each the isogram of (C) got by the multiplier G'B. The {G)
and (C) isograms, with the triangles on their sides, are images
in X ; and the {B) and (C) isograms have the triangles on their
sides congruent and homothetic, and would themselves come to
coincidence by a half-turn. There results the following method
of converting the mechanism {B) into {G), namely :— (i) Separate
(D) into the two isogram mechanisms 13'24' and 2'41'3. (ii) Ex-
change two vertices of each plate 1, 3', 2, 4' by giving it a half-
turn about the middle point of the side of the isogram on which
it stands, (iii) Exchange two vertices of each plate 2', 4, 1', 3
in the same way. (iv) Turn either of these new four-piece
mechanisms upside-down ; i.e. give it a half-turn about some line
in its own plane, (v) Unite the free vertices of 1, 3', 2, 4' with
those of 1', 3, 2', 4 respectively. The double-four (C) thus formed
Mr Bennett, A Double-Four Mechanism. 399
i has for its tetrads of plates 1, 2, 3, 4 paired with (and so not
\ linked to) 2', V, 4', 3' respectively. The double-fours (A) and (B),
which may be similarly obtained from (D), have 1, 2, 3, 4
I associated, the one with 4', 3', 2', 1' and the other with 3', 4', 1', 2'.
! A double exchange of numerals suffices to convert the list of
[ connections used for (D) into those necessary for (A), (B) or (G).
\ Thus, in passing from (D) to (A), any vertex of 1, 2, 3, 4 is
replaced by some fresh vertex in making attachment to any the
same vertex of 1', 2', 3', 4'; and the rule is to exchange the
numerals 1 with 4 and 2 with 3. Since, ex. gr., in (D) 12' is
; attached to 2'1 (according to the original notation itself), so for
^ (A) 43' is attached to 2'1. The rule holds for all twelve pins.
It may be observed that, taking the aggregate of all four
; mechanisms, any particular plate 1, 2, 3 or 4 is connected in
i turn with all the twelve vertices of the plates 1', 2', 3', 4', and
I conversely. The two tetrads remain distinct throughout, and
connections occur only between members of opposite tetrads ; but
the different pairings which distinguish the double-fours are
peculiar to each mechanism in turn. The mechanism given in
; Fig. 3 is the mechanism (D) derived from the symmetrogram of
Fig. 2.
§ 6. Some of the special forms of the isogram double-four
i mechanism (D) may be briefly noticed, arising from special forms
' of the symmetrogram from which it is derived.
(i) li A,B,G,D are coney clic, the triangular plate 4 becomes
a straight bar.
(ii) I{ A, B, G, D are coney clic, and also A', B', G, D, then
both plates 3 and 4 become bars,
(iii) If A, B', G', D and A', B, G', D and A', B',G, D are
concyclic, then plates 1, 2, 3 are bars. In this case the
symmetrogram is obtainable from the figure of any
triangle ABG, with A', B', G' as the feet of its perpen-
diculars, and D as orthocentre, by inverting from any
a point on the polar circle,
(iv) If A, B, G, D are on a circle with diameter ^, then
A', B', G', D' are also on the circle. All eight pieces
are then bars, and the axes of the three pairs of
isograms are concurrent. The figure occurs in a
paper of the author's (Land. Math. Soc. 1911, Ser. 2,
Vol. X. p. 333). The eight points of the symmetro-
gram of Fig. 2 are approximately concyclic ; and as
a consequence the plates of Fig. 3 take an elongated
form differing not greatly from bars,
(v) If D and D' coincide, the double-four is symmetric
about cc, and pairs of its plates are images in cc.
(vi) If D and D' are coincident in case (iv) the eight-bar
400 Mr Bennett, A Double-Four Mechanism.
mechanism becomes symmetrical. This is the figure
given, apparently, by Darboux (loc. cit. p. 174).
(vii) If D and D' are at infinity on x, the product- vector
extremities may (as a limit) be taken at the middle
points of the sides of the isograms ABA'B', BCB'G',
GAG' A'. The mechanism is the same as in case (v),
but at a different stage of its deformation. Since
the plate given by the middle points of triangle ABG
is similar to ABG and of half the size, and similarly
for others, it follows that the material for such a
mechanism may be supplied by the eight triangles
whose vertices are A or A', B or B', G or G' in the
symmetrogram.
(viii) If C and G' coincide with D and D', the isogram 1'32'4
of (D) becomes evanescent in size, and the pieces
1', 2', 3, 4 become bars linked together at a common
extremity.
In all these cases peculiarities affecting the mechanisms (A),
(B), (G) will accompany those of (D).
Note. Fig. 1 has served a purely schematic purpose in the
foregoing treatment of the isogram double-four : its three pairs
of quadrilaterals are drawn as parallelograms instead of isograms.
But, as a consequence, it is itself a double-four mechanism of
another species, and is included in his list by Darboux {loc. cit.
p. 164). He identifies it with a last case of Kempe ; but with
some confusion, for the latter has a connectivity different from
that of the double-four type. The freedom of the mechanism is a
simple consequence of the parallelogram construction. It may be
noticed that if the pins are removed, the set of plates 1, 2, 3, 4
may, without rotation, be brought together so that pairs of equal
sides coincide, the vertices of the four triangles forming a quad-
rangle ; and similarly for 1' 2' 3' 4'. So that the material for the
mechanism may be supplied by the eight triangles given by two
arbitrary quadrangles. (In Fig. 1 these quadrangles are made,
unessentially, and for simplicity, two equal parallelograms.)
But this mechanism, though ostensibly a double-four, should
in strictness be classified as spurious or improper ; for the pairs of
pieces that are not linked have centres of relative rotation which
are not variable but permanent, and for which the missing pins of
connection may be supplied. The centre for 1 and 1' is such that
it completes the figure of the first quadrangle when associated
with the vertices of 1 ; and with the vertices of 1' it forms the
figure of the second quadrangle ; and similarly for the other three
pairs. The completed mechanism consists then of four rigid
quadrangles linked by their points to four other quadrangles;
Mr Bennett, A Double-Four Mechanism. 401
each separate set of four being congruent and homothetic. Such
a parallelogram link- work may be generalized, obviously, to include
any number of pieces linked to any number of others. A lattice-
work, if made of two separately equal sets of arbitrarily curved slats,
would afford a representative example.
The parallelogram case and the isogram case above examined
stand somewhat as companions among the species of double-four.
For all other species the angles of the plates are equal or supple-
mentary at every pin ; and of these the most interesting has been
specially treated by Fontene (Nouvelles Annates de Math. 1903,
pp. 529—549, 1904, pp. 8—29).
VOL, XVII. PT. V,
27
402 Mr Kleeman, On the Nature of the Internal Work
On the Nature of the Internal Work done during the Evapora- .
tion of a Liquid. By R. D. Kleeman, D.Sc. (Adelaide), B.A.,
Emmanuel College.
[Beceived 13 March 1914.]
When a molecule passes from the liquid into the gaseous
state it absorbs energy in overcoming the attraction of the
molecules of the liquid, and in changing its internal energy. No
energy is absorbed or evolved which is due to a change in the
kinetic energy of translation. This can be shown to follow from
the observed fact that the temperature indicated by a thermometer
is independent of the nature of the material of the bulb, and
consequently of the attraction it exerts upon the surrounding
substance. The velocity of translation of a molecule in a substance
when it passes through a point where the forces due to the
surrounding molecules neutralize one another, is then independent
of the density of the substance*. The average distribution of the
molecules in the substance corresponds to each molecule being
situated at a point possessing the property mentioned. It follows
then at once that in separating the molecules of the substance by
an infinite distance from one another energy can only be expended
in the way described. Thus the internal heat of evaporation L
of a molecule when the saturated vapour behaves as a perfect gas
may be written
L=U+(u-Ua) (1),
where U denotes the work done against molecular attraction, and
u — Ua the change in internal molecular energy, where Ua denotes
the internal energy of a molecule in the gaseous state. Therefore
if the liquid undergoes a small change in density the corresponding
changes in the potential energy of attraction and internal molecular
energy are d U and dii.
The quantity du has usually not been considered by most
investigators of the properties of matter, or has been assumed
to be small in comparison with dU. Thus for example the equation
of state of van der Waals does not take it into account. It must
however occur in the equation of state f. On the other hand, other
investigators have supposed that du is of the same order of magni-
tude as dUX- I have brought forward circumstantial evidence that
du is small in comparison with dU^, but more direct evidence is
* Phil. Mag., July 1912, pp. 101—118.
t loc. cit., Sept. 1912, pp. 391—401.
t loc. cit., Jan. 1912, p. 111.
§ Proc. Canib. Phil. Soc, xvi. Pt. 6, pp. 540—559 (1912).
done during the Evaporation of a Liquid. 403
desirable. We shall see later that the point in question is of more
than passing importance. Accordingly I endeavoured to obtain
an expression for u — Ug, in terms of other q uantities. An expression
was obtained corresponding to matter in the critical state as
follows.
It will be convenient to consider first the exact meaning of
the quantities on the right-hand side of equation (1). When a
molecule is ejected from the surface of a liquid and passes out of
the sphere of influence of attraction of the liquid molecules, it may
undergo a change in the configuration of its atoms during the
journey. This we would in fact expect since each molecule in the
liquid state is under the action of the forces of attraction of the
surrounding molecules whose resultant effect is a more or less
radial force, whose centre is in the molecule, tending to separate
the atoms from one another, and from which the molecule is
relieved when passing into the gaseous state. This change in
configuration may modify the law of attraction between the
molecules. When the molecule is out of the sphere of action
of the molecules of the liquid, or in the perfectly gaseous state,
it may not yet be in a state of internal equilibrium. And the
adjustment of equilibrium may give rise to a displacement of
energy some of which may be algebraically communicated to the
surrounding molecules. Thus an evolution or absorption of heat
may occur when the molecule undergoes bombardment by other
molecules after it has passed out of the influence of the molecules
of the liquid. This heat is evidently the quantity u — iia- It will
be obvious that the same reasoning applies if the molecule passes
into the gaseous state in stages, due to the existence of a surface
transition layer. During each stage a change in internal energy
equal to du will take place. But Xdu may then not be exactly
equal to the value that u — w« would have in the absence of the
transition layer.
Next it will be necessary to consider briefly the equilibrium
of a substance. When in equilibrium the external pressure and
force of contraction due to molecular attraction, called the intrinsic
pressure, is balanced by the pressure due to the motion of trans-
lation of the molecules. We may suppose, as in the kinetic theory
of gases, that the motion of translation of the molecules takes place
parallel to three lines at right angles to one another, one-third of
the molecules moving parallel to each line. If n denote the
number of molecules crossing a cm.^ per second of a plane at right
angles to one of the lines, and j> and Pn denote respectively the
external and intrinsic pressure in dynes, I have shown* that
p.+ P, = 7i2-534xlO-^«\/l^ (2),
* Phil. Mag., July 1912, pp. 103—109.
27—2 ,
404 Mr Kleeman, On the Nature of the Internal Work
A
a relation which is independent of the density of the substance,
where T denotes the temperature and m the molecular weight of
a molecule relative to that of hydrogen. Its deduction was based
on the fact that the temperature indicated by a thermometer is
independent of the nature of its bulb, and consequently of the
molecular attraction it exerts on the surrounding molecules.
Now let us consider the behaviour under certain conditions
of a substance which is contained in a cylinder as
shown in figure 1, in which slides a piston A. Tlie
system is kept at constant temperature. Suppose
that the substance is a liquid and that the piston is
in contact with its surface. Also suppose that the
material of the piston consists of solidified liquid, in
which case there is no change in density of the liquid
as we pass from it into the material of the piston.
Now suppose that the piston is instantaneously
removed from the liquid surface to some distance
away. Then initially an molecules will leave the
liquid surface per second, namely those that are able
to overcome the attraction of the liquid, where a is
a fraction. The substance may also be in such a state that a is
unity, in which case the liquid surface is bodily projected after
the piston. The properties of the substance corresponding to
different values of a will now be considered.
It will first be shown that if a = 1 the substance cannot give
rise to another phase of the substance which is in contact with it
in equilibrium. For suppose that A and B in figure 2 are two
Fig. 1.
/^
B
Fig. 2.
homogeneous slabs of the substance which are in equilibrium in
contact with one another under the same external pressure, and
that for the slab A the value of a is unity. It follows then that
at any instant all the molecules in the boundary surface of the
slab A move bodily into the slab B, And since there is equilibrium
an equal number must move from the slab B into A. But this
can only be the case if the density of the slab B is the same as
that of A. It will be easy to see that this also holds if in the
beginning we suppose that a transition layer exists at the boundary
of the slabs. For this transition layer may be cut up into an
infinite number of homogeneous slabs, each pair of which may be
treated in succession in the same way, beginning from the A side.
done during the Evaporation of a Liquid. 405
If a is a fraction it can be shown that the substance can exist
in two phases. Thus suppose that some of the substance is con-
tained in the cylinder of figure 1 in contact with the piston, and
let the piston be displaced in the same way as before. The surface
of the substance will go on shedding molecules till the density of
the vapour is such that the same number of molecules are received
upon the surface per second as leave it. This number must be
larger than an, since the attraction of the vapour helps the molecules
to get away from the liquid surface. But it must be smaller than
n, for if equal to n it follows in the same way as before that both
phases must have the same density, and hence there would be
only one phase. The condition that another phase could exist
in contact with the substance is therefore that a should be less
than unity. When this condition is satisfied the phases are
realizable in practice. Thus let Oj denote the value of a for a
quantity of the substance w^hose density is less than that just
considered. Now the value of n increases with increase of density
of the substance, while that of a decreases, since the attraction
the kinetic energy of a molecule has to overcome increases with
increase of density. If the two surfaces of the substances which
are of different densities are placed in contact, the values of
«!, Wi and an are increased along the boundary, since the attraction
of each substance helps the molecules of the other substance to
get away from it. But the increase is greater in the case of the
less dense substance than in the case of the other, on account of
it being bounded by a substance of greater density than itself, and
the opposite applies to the other substance. Thus it should be
possible to find a density for the second substance which is less
than that of the first, so that when the substances are placed in
contact with one another the number of molecules passing from
one into the other is the same, in which case they will be in equi-
librium. Upon reflection it will be evident that the existence
of a surface transition layer does not invalidate the foregoing
conclusions.
The foregoing considerations show that when a substance is in
the critical state a= 1. Now a molecule could get away from the
surface of a mass of substance and out of the influence of its mole-
cules after displacement of the piston in the process described only
when its kinetic energy is equal to the energy expended in over-
coming the attraction of the substance. The kinetic energy of a
molecule in the substance that could be expended in this way is
that which it has when passing through a point at which the forces
of the surrounding molecules neutralize one another. For we have
seen that when a substance is converted at constant temperature
into the perfectly gaseous state this kinetic energy remains con-
stant, the heat being expended in overcoming external and internal
406 Mr Kleeman, On the Nature of the Internal Work
molecular forces. This kinetic energy therefore represents available
energy, since it is evidently available for being converted into other
forms of energy when the substance is in the perfectly gaseous
state. It follows therefore that at the critical point — ^ — = IT,
where V denotes the velocity of a molecule in the gaseous state
and ma its absolute mass. From the kinetic theory of gases we
have F^ = , where m is the molecular weight of a molecule
ni
relative to that of a hydrogen molecule and R = 8*26 x lO''. Hence
at the critical point
£^=(^")i-5 (3).
In a previous paper* I have shown that at the critical point
JJ-^u-xi^ = \t[^-^ -p|w«w (4),
where v denotes the volume of a gram of substance. This
equation was deduced from thermodynamics without introducing
any assumptions. It was also shown that according to the facts
the right-hand side of the equation may be written maVpQ'o.
Thus the equation may be written
U+u~u, = (?^)l-76 (5),
since according to Young and Thoma's law pv = -^r^ — at the critical
point. Equations (4) and (5) then give at once
fRTma^
m
u-Ua = [^^^Z^]-^ = -l^U (6).
It appears therefore that when a molecule passes from a substance
into a less dense substance it absorbs heat in the latter substance
on being bombarded by the surrounding molecules till it is intern-
ally in equilibrium. The amount of heat absorbed is about 10 "/o
of the total heat absorbed or energy spent in the transference of
the molecule. The change in internal energy of the molecule is
thus small in comparison with other energy changes as we might
expect.
As has been remarked before, it is of importance to obtain
some definite information about the quantity u — Ua- Thus I
have shown in a previous paper-f* that if u — Ua is small in com-
parison with U the attraction between two molecules decreases
* loc.cit., Sept. 1912, p. 395.
t Proc. Camb. Phil. Soc, xvi. Pt. 6, pp. 540—559 (1912).
done during the Evaporation of a Liquid. 407
with increase of temperature, and that it follows from the Joule-
Thomson effect that it varies approximately inversely as the
temperature. This effect is more likely to be brought about, as
pointed out in the paper quoted, by a relative displacement of the
atoms of each molecule with change of temperature than by a true
change in the forces of attraction. It follows therefore that the
intrinsic pressure term in the equation of state is a function of
the temperature as well as the volume of the substance. Also the
variation of the viscosity of a gas with change of temperature is
not due only to a change in the velocity of translation of the
molecules but also to a variation of the forces of attraction between
them.
A formula for the intrinsic pressure was also obtained which
gives the quantity to the same degree of approximation that
U + u — Ua is equal to U.
Since u — Ua is small in comparison with U it is possible to
obtain some information about the law of molecular attraction
from a study of the internal heats of evaporation of liquids. This
I have carried out in previous papers assuming the foregoing.
It was shown* that if no other assumption is made besides the
one mentioned it is mathematically impossible to determine com-
pletely the law of molecular attraction from internal heat of
evaporation data, in other words the law obtained should contain
an arbitrary function of the temperature and distance of separation
of the molecules. This arises from the fact that we do not know
a priori how the attraction varies with the temperature, other
conditions remaining the same. And this point cannot be deter-
mined from the data in question because we cannot say how much
of the change in internal heat of evaporation with rise of tempera-
ture is due to a separation of the molecules of the liquid due to
its decrease in density, and how much due to a change in the
attraction of the molecules. But even if this point were deter-
mined the law would still contain an arbitrary function. For the
internal heat of evaporation is the difference of two quantities,
viz. the potential energies of attraction in the states of liquid and
saturated vapour, and we evidently cannot recover a curve given
the difference between certain ordinates. It is therefore of primary
importance to obtain the law of attraction in the form involving
an arbitrary function for we can then be sure that the part of the
law outside the function is correct. On the other hand if we obtain
a definite law by the help of assumptions, say assuming the form
of the law, an agreement with the facts does not mean that our
assumptions are correct. This follows from the mathematical
theorem so often ignored by scientists that an infinite number of
formulae can be found to express a set of facts equally well, each
* Phil. Mag., Jan. 1911, pp. 83—102.
408 Mr Kleeman, On the Nature of the Internal Work, etc.
of which corresponds to a different hypothesis. It is evident
therefore that there is only one way to obtain reliable information
about the law of molecular attraction from internal heat of evapo-
ration data. Any other way might lead to the discovery of
excellent formulae for the internal heat of evaporation, but could
by no means give any definite information about the law in
question.
I have obtained* in the way described the law I
where z denotes the distance of separation of the molecules which
are at the temperature T, x^ that of the molecules in the liquid
state at the critical temperature, and ^(^, — ) is a function of
these quantities left arbitrary. The quantity SVm^ denotes the
sum of the square roots of the atomic weights of the atoms of a
molecule; and the attraction of "cohesion " of an atom is thus pro-
portional to the square root of its atomic weight. Since I have
shown in this paper that w - w« is small in comparison with JJ, the
deduction of the law is placed on a perfectly sound basis. It is
evident that each of the definite laws that have been obtained by
introducing assumptions correspond to certain forms of the arbitrary
function. This connection has been discussed at length f. It was
also deduced j that the function 9 does not vary much with z and
roughly inversely as T from other data than those relating to the
internal heat of evaporation.
Note. It will be convenient here to correct two misprints.
Equation (27) on page 639 of the Proc. Camb. Phil. Soc, vol. xvi."
Pt. /, should read r] = kj~^^- and equation (2) on page 177,
vol. XVII, Pt. 1, should read T = M^' ^?^' .
* loc. cit. and papers quoted therein,
t loc. cit., Oct. 1911, pp. 566—586.
t loc. cit.. May 1910, p. 807 ; and Proc. Camb. Phil. Soc, xvi. Pt. 6, 1912
pp. 553—559. '
Mr Kleeman, The Work done in the Formation, etc. 409
The Work done in the Formation of a Surface Transition Layer
of a Liquid Mixture of Substances. By R. D. Kleeman, D.Sc.
(Adelaide), B.A., Emmanuel College.
[Received 16 March 1914.]
In a previous paper* I have shown that the surface tension
which a pure substance would have if no surface transition layer
were formed would be given by
l + ^'+^ + .-l
2 3
i^;^,,^... j«^=g">.v (1).
where U denotes the energy expended in overcoming molecular
attraction on separating the molecules of a gram of the substance
ian infinite distance from one another, p denotes the density of the
'substance, and m^ the absolute molecular weight of a molecule.
This equation is based on Laplace's definition of surface tension
according to which it is the work done against molecular attraction
per unit increase of surface on cutting a slab of a substance into
two slabs and separating them an infinite distance from one another.
Besides the assumption is made that the attraction between two
imolecules separated by a distance z is given by a law of the form
k
— , where k and r are constants or functions of T, the temperature.
The constants C2, Cs, c^, ... Cn in the expression
hhh-\
1 + C2 + C3 + ...
are then functions of r. Since the molecular attraction is approxi-
mately given by a law of the above form, and the foregoing
expression is not sensitive to variations in the values of the
constants c.2, C3, Ci,...Cn, the value of the expression may be
calculated with fair accuracy by means of a law of attraction
which has been found to fit approximately the facts. In this
manner I obtained "876 for the value of the expression putting
r = 5, and equation (1) accordingly became
Umr,:^
Phil. Mag., Dec. 1912, pp. 876—885.
410 Mr Kleeman, The Work done in the Formation of a
Before considering the application of this equation to mixtures it
will be useful to reconsider its deduction.
The true law of molecular attraction is probably not given by \
a law of such simplicity as the foregoing. But there is nothing
against supposing for purposes of calculation that the molecules
are replaced by a set of molecules obeying such a law pro- j
vided that the surface tension in question and the value of U'\
remain unaltered. This can be realized since we have two '
variables at our disposal, namely k and r. Equation (1) is thus:,
fundamentally correct. It then remains to find the equivalent !
law of molecular attraction of the form given. This need only I
be approximately realized for the reasons given. To see how I
the value of the expression depends on the value of r it was \
calculated for the case r = 2, which gave "71. When r=oo it!
will be easily seen that it is equal to unity. The correct value I
thus lies between "7 and 1. The attraction varies much more
rapidly with the distance of separation of the molecules than !
corresponding to r = 2, r being approximately equal to 5*. or 4 to ;
which corresponds van der Waals' equation of state. It is evident i
therefore that the approximately correct value of 5 for r should jj
give within a few per cent, the correct value of the expression. 1
When we are dealing with a mixture of substances we may '|
suppose as before that the molecules are replaced by a set of :
molecules equal to one another and which obey a law of attraction .
of the form given. This is evidently possible for the same ;
reasons as stated above. The equivalent law of attraction will j
obviously be very approximately the same as for a pure substance, \
and the value of the expression discussed practically not altered, j
The molecular weight m^ occurs in connection with the number i
of molecules in the substance. In the case of a mixture it is i
therefore only necessary to substitute for m^ the average mole-
cular weight. The quantity U refers in all cases to a gram of the
substance.
When the ingredients of the mixture consist of liquids whose
heats of evaporation in the pure state are known for temperatures
at which their vapours approximately obey the laws of a perfect
gas, the values of tl may be approximately calculated corresponding '
to this region of temperatures. The heat of evaporation of a
substance whose vapour approximately obeys the laws of a perfect
gas is equal to the energy expended in separating the molecules
an infinite distance from one another. This heat is expended in
overcoming the attraction between the molecules and producing
changes in their internal energy. I have shown f that the latter
* loc. cit., May 1910, p. 807.
t Previous paper in this volume.
Surface Transition Layer of a Liquid Mixture of Substances. 411
ipart of the heat expended is small in comparison with the former
part, and the internal heat of evaporation may therefore be taken
as approximately equal to the energy expended against molecular
attraction. By definition U for a mixture is equal to the energy
.expended in overcoming the molecular attraction on separating
;the molecules of a gram of the mixture an infinite distance from
one another, and hence approximately equal to the heat of
mixture of the ingredients and their internal heats of evaporation
in the pure state. If the ingredients of the mixture consist of
the substances a and h in the proportion of w^ and njj by weight,
iwe have
i TT Lana + L^ni, „ ..-.,
U= h ilm {o),
I na + Vf,
I where La and L^ denote the internal heats of evaporation of a gram
of substance a and b respectively^ and Hm the heat of mixture of
the iijgredients of a gram of the mixture. H^ is usually small in
j comparison with both La and Lj^ and may therefore be neglected.
j I have calculated the surface tension X^ of a few mixtures of
i substances of which Ramsay and Aston* have measured the ordinary
surface tension Xj. The constituent substances are not associated
in the pure state and according to the experimenters mentioned
do not undergo any radical chemical change on mixing, that is, the
resultant substance is more or less a pure mixture. The results
I obtained are given in Table I. The values of U were calculated
by means of equation (3) neglecting H^, and using the internal
heats of evaporation La and L^ given in the Table, which were
interpola.ted from the values calculated by Mills f. The absolute
mass of the hydrogen atom is taken as in the previous paper equal
to 1"61 X 10~^^ gram, the value obtained by Rutherford from ex-
periments on the a particle. The difference Xg — ^i is the external
work done in the formation of the transition layer.
It will be seen that the value of A.., for a mixture of CgHs and
CC14 is practically independent of the relative concentrations of
the ingredients. This is probably intimately connected with the
fact that this holds also for the values of \. The results I obtained
previously with pure substances are given in Table II for comparison,
i] denoting the internal heat of evaporation. It will be seen that
in the case of pure substances Xg — ^i is practically independent of
the temperature. But for mixtures this does not hold, its value
increases with increase of temperature. At low temperatures
X2 — Xi is smaller for a mixture than for each of the ingredients in
the pure state. The difference in the behaviour of mixtures and
pure substances is no doubt due to adsorption effects.
* Zeit.f. Phys. Ghemie, 15, 1894, p. 88.
t Jourii. of Phys. Chem. viii. p. 405 (1904).
412 Mr Kleeman, The Work done in the Formation of a
Table I.
Mixture of 1 CgHe to 1 CCI4. Average m„ = 116 x 1-61 x 10-2* grm.
T
P
^1
i„.(C6H6)
L, . (CC14)
U
^2
X2-Xi
289
318-2
351-2
1-2597
1-2095
1-1596
27-70
23-50
19-71
97-11
91-8
85-3
46-97
44-39
41-64
63-84
60-27
56-27
34-0
31-3
28-4
6-31
7-75
8-73
10 CeHg to 17 CCI4. ???„= 125-8 x 1-61 x lO-^* grm.
286-2
319-6
351-4
1-3509
1-2942
l-2ill
27-66
23-51
19-52
97-75
91-20
85-00
47-24
44-35
41-60
58-86
55-09
51-56
33-75
30-70
27-94
6-09
7-19
8-42
2 CeHe to 1 CClj. m„ = 103 3 x 1-61 x lO-^* grm.
283-8 1-1384
319-2 l-0ci77
351-2 1-0431
28-55
23-99
20-00
98-12
91-80
85-30
47-40
44-39
41-64
72-76
68-09
63-47
34-83
31-64
28-67
6-28
7-65
8-67
1 CHCI3 to 1 CS^. m„ = 97-7 x 1-61 x IQ-^* grm.
282
317-9
334
1-4026
1-3406
1-3128
29-16
24-49
22-23
61-41
57-30
55-49
81-78
76-79
74-29
69-36
64-88
62-82
37-48
34-02
32-48
8-32
9-53
10-25
Surface Transition Layer of a Liquid Mixture of Substances. 413
00 00 05 05 05 oi a;
05 Ci o o o o o
t- to lo ■<* CO oa ■-!
O OS 00 to »0 -^ CO
Tt( CO ^ <M O O W5
U5 ■<*< (M O 00 «5 .-(
»C CO >H Oi ^ ■* Oq
^ ■rJH -^ CO CO CO CO
»0 tH t^ 05 (N 00 o
r-l ^ (M O 05 O ■<*(
-<lf O OS 00 O »0 Ttl
00 00 t- c- t- t- t-
CO M CO CO CO CO CO
so t- 00 05 O --H OS
CO CO CO CO Ttl -^ -*
CO CO CO CO CO CO CO
»0 «5 t- 00 OS O rH
CO CO CO CO CO -tH ■*
65
pq
OS OS OS OS Ci OS OS
us K5 -^ ■* CO CO CO
-* <N i-H O OS 00 C-
s
-^ '^ OD <M IM O in
OS 5D lO CO O lO o
00 t^ «0 lO -* IM tH
CO to ?D to to CD to
00 t- ^ CO 00 CO to
OS -^ OS CO to O CO
U5 '^ (M 1-1 OS 00 to
OS OS OS OS 00 00 00
CO CO CO CO CO CO cc
1— I (M CO -* m to t-
CO CO CO CO CO CO CO
CO CO CO CO CO CO CO
O 1— I (N CO rt< »C to
CO CO CO CO CO CO CO
414 Dr Frank Horton, The ionisation produced by certain
The ionisation produced by certain substances when heated on
a Nernst filament. By Frank Horton, Sc.D., St John's College.
[Read 9 March 1914.]
The ionisation produced by heated solids has been investigated:
by many observers in recent years, but at the piesent time noned
of the theories which have been put forward to explain the
origin of the emission of either positive or negative electricity is
universally accepted. The substance upon which most experi-
ments have been made is platinum, but other metals, and many
compound substances, have also been used. As a rule, in testing
compound substances they have been supported upon a strip or
wire of platinum, and the view has been put forward that the
observed effects are due to the metal support rather than to the
layer of substance under test. Thus certain oxides— those of the
alkaline earth metals— give a large emission of negative electricity
when heated upon platinum in an exhausted tube, and it has
been suggested that this effect is merely an increased electron
emission from the platinum itself; the increase being caused by
the lime lessening the energy required to enable an electron to
escape through the metal surface. The emission of positive
electricity from various salts has also usually been studied when
the salt under test is heated upon a platinum strip. Dr W.
Wilson failed to detect any positive ionisation from aluminium
phosphate heated on a Nernst filament, although the positive
emission from this salt when heated upon platinum has been
investigated by several experimenters. Dr Wilson has therefore
concluded that "the leak observed when the salt is heated on
platinum is either mainly a leak from the platinum itself, or the
latter plays an important role in its production*."
The author has recently been studying the thermal ionisation
produced by Nernst filaments and, having the apparatus at hand,
it was thought desirable to test these views as to the origin of the
ionisation from glowing solids by ascertaining (a) whether lime
heated upon a Nernst filament gives a negative emission com-
parable with that obtained when it is heated upon platinum, and
(6) whether the positive emission from a glowing Nernst filament
is increased. by placing sodium phosphate upon it. It has already
* W. Wilson, Phil. Mag. 6, xxi. p. 634, 1911.
substances when heated on a Nernst filament. 415
been shown that sodium phosphate heated upon platinum gives
a large positive ionisation which is more permanent than that
given by aluminium phosphate*.
The discharge tube used in these experiments is similar to
that described in an earlier paper*, the only difference being
that the two parallel platinum plates which form the anode are
rather further apart in the present apparatus. These plates are
situated vertically, 1'5 cms. apart, at the centre of the small bulb
which forms the discharge tube. The Nernst filament when in
position is parallel to the plates and mid-way between them. It
can be heated by an alternating electric current led in through
stout platinum wires, and the filament and its leads can easily be
removed from, or replaced in, the bulb. The alternating current
was obtained from the secondary of a transformer, the primary
icoil of which was connected to the alternating town supply (100
volts), and the current through the filament could be varied by
changing the resistance in both primary and secondary circuits.
One of the fine iron wire resistances supplied with Nernst lamps
was always kept in series with the filament. As this resistance
(has a large positive temperature coefficient, it tends to keep the
temperature of the filament more steady than would otherwise be
the case.
I In order to start the filament glowing it was taken from the
Idischarge tube and heated by holding it above, and near to,
a glowing " heater " of the kind supplied with an ordinary Nernst
lamp. It was then placed in the apparatus which could be
rapidly exhausted, when required, by means of a water-pump,
mercury-pump, and charcoal tube cooled in liquid air. In this
way the gas pressure in the apparatus could be reduced to
'0001 mm. within twenty minutes from the time that the glowing
filament was placed in position.
I The temperature of the filament was determined by means of
a Fery optical pyrometer, which was very kindly lent to the
Cavendish Laboratory by Professor T. Mather, of the City and
Guilds College, London. This instrument was standardised by
using a platinum tube of about the same diameter as a Nernst
filament, with a thermo-couple of fine wires of platinum and
platinum-rhodium welded to it. In order to have the surface
of the tube exactly similar to that of the filament, a filament
was finely powdered and mixed with water, and the platinum
tube was then covered with a thin layer of Nernst filament
material by evaporating this mixture upon it. This platinum
tube was fitted up in the place of the filament in the discharge
bulb, and observations of the thermo-electromotive force and
* F. Horton, Proc. Roy. Soc. A. lxxxviii. p. 117, 1913.
416 Dr Frank Horton, The ionisation produced by certain
readings of the optical pyrometer were taken at several tem-
peratures between 900° C. and 1600° C. From these observa-
tions the temperature of a Nernst filament corresponding to any
reading of the pyrometer between these limits can be ascertained ■
with fair accuracy. In most of the experiments described in this !
paper the actual temperature of the filament is of little consequence, :
for the pyrometer was usually employed simply to adjust thel
temperature to a constant value.
The negative emission from Lime.
A Nernst filament was heated in a good vacuum (the residual;
gas having a pressure of 'OOOl mm.) until the negative current i
obtained from it under a potential difference of 214 volts had
become fairly constant, a condition which is obtained in a much
shorter time than when platinum is being experimented on.
A series of observations of the thermionic emission from the
filament at different temperatures was then taken, and the results
are shown in the curve of fig. 1. In this ordinates represent
1
150
/
/
/
/
/
100
/
i
/
/
/,
/
50
/
/
/
/
y
/"
^
^
-©-
Temperature, Degrees centigrade
Fig. 1.
current, one division = 3'78 x 10~^ ampere, and abscissae repre-
sent temperatures on the centigrade scale. The curve given
shows that at temperatures above about 1500° C. the thermionic
current increases directly with the temperature and not in the
1
substances when heated on a Nernst filament. 417
exponential manner usually obtained with substances heated at
lower temperatures. Most of the current-temperature curves
obtained with Nernst filaments at high temperatures showed
this approximately linear relation, but the curve selected for
fig, 1 is that in which the experimentally determined points lie
most nearly on a straight line. A negative ionisation of about
the magnitude represented by this curve was always obtained
when a Nernst filament was heated in a good vacuum. The
large potential difference of 214 volts was used to swamp the
alternating potential difference of the heating current, which,
between the ends of the filament, was about 60 volts when the
filament was at 1500° C.
In the first experiments with lime-covered filaments, the lime
was obtained by evaporating a strong solution of calcium nitrate
on the filament and then igniting, but this process was found to
spoil the filament, which became very difficult to start glowing,
and when glowing would sometimes suddenly go out during the
observations ; a filament so treated also broke through after being
used for a short time. Pure lime (Kahlbaum, prepared from
marble) was therefore powdered very finely in an agate mortar,
and some of this powder was stirred up with distilled water.
The lime in suspension in water was then placed upon the
filament, a drop at a time, and the water was evaporated away by
warming over the heater. The drops were all placed near the
centre of the filament, and care was taken not to allow any of the
liquid to go on to the platinum leads, although this precaution
was probably unnecessary, for the leads never became visibly hot
during the experiments. The evaporation of the lime water was
continued until a uniform layer of lime was obtained over about
7 mm. of the middle of the filament. When obtained in this
manner the layer of lime did not peel off on heating, and the
filament could be started glowing just as easily as a new one. It
should be mentioned that the filaments used were all of about the
same dimensions, the length of the glowing portion being about
9"5 mm. and the diameter "78 mm.
The glowing lime-covered filament was placed in the apparatus
and the air-pressure was reduced. It was at once obvious that
under these conditions the lime gives an enormous negative
emission, for as the pressure was reduced to a few millimetres
a brilliant glow appeared in the discharge tube, without the
application of any electromotive force except that of the heating
circuit. One of the platinum wire leads to the filament was kept
earthed, and from the appearance of the discharge it was seen
that the bare end of this wire, near the filament, was acting as an
anode. By lowering the temperature of the cathode the luminous
discharge could be stopped, but at the lower temperature it could
VOL. XVII, PT. V, 28
418 Dr Frank Horton, The ionisation produced by certain
be started again by earthing the parallel plate anodes of the dis-
charge tube by touching with the finger.
In a previous paper* the author has drawn attention to the
different appearances of the luminosity obtained with a hot
lime-covered platinum cathode. Under certain conditions of
temperature, gas-pressure, and potential difference, the luminosity
surrounds the anode only, and this luminosity always appears
gradually when the conditions are slowly changed (e.g. the tem-
perature slowly raised), and there is no sudden increase in the
current passing through the tube. If the temperature is still
further raised, or the potential difference increased, a point is
reached when the luminosity suddenly leaves the anode and
surrounds the cathode, and then, in some cases, luminous pencils
of cathode rays are seen. These effects were also obtained with
the lime-covered Nernst filament. With the temperature at
1500° C, and the gas-pressure '0001 mm., a current of 28 milli-
amperes was obtained. In this case 210 volts were put on from
the high potential battery, but the magnitude of the discharge
current was limited by a wire resistance of about 5500 ohms
included in the circuit. The passage of the discharge greatly
increased the temperature of the filament, which became much
hotter near its lower end than at any other point. The gas-
pressure in the apparatus was so low that no definite pencil of
cathode rays could be seen, but there can be little doubt that
the discharge was taking place mainly from the hottest point
of the filament. The whole bulb was filled with a bluish glow
(Hg vapour and CO), which could be best seen by looking in such
a direction that the light from the filament itself was screened
by one of the platinum plates forming the anode. The applied
P.D. was lowered to 40 volts and the filament became cooler and
equally luminous all over. The glow could still be seen in the
bulb, but as the current was now very much reduced, this
luminosity was doubtless an " anode glow." With 40 volts applied
through a resistance of 5500 ohms to the terminals of the dis-
charge tube, the following measurements of the thermionic current
at different temperatures were taken :
Temperature (° C.)
1510
1626
1698
1780
Current (niilli-amps.)
2-3
3-3
4-3
5-3
These currents do not increase so quickly with the temperature
as is usually the case with the negative emission from glowing
*■ Phil. Trans. Roy. Soc. A. ccvii. p. 149, 1907.
I
substances luhen heated on a Nernst filament. 419
solids, but the values given cannot be taken as measuring the
corpuscular emission from the lime-covered filament, for the
following reason. A resistance of 5500 ohms was included in
the circuit to prevent damage to the high potential battery, and
while this resistance remains constant during the experiments
the resistance offered by the discharge tube diminishes greatly
with increasing temperature. Thus the fall of potential across
the tube decreases as the temperature of the filament is raised,
and as the current is not saturated, its values at the different
temperatures are not proportional to the number of corpuscles
emitted by the filament. The potential difference required for
saturating a thermionic current increases as the temperature
rises, and at the same time the energy required to produce
ionisation by collisions in the gas decreases. At the temperatures
obtained with a glowing Nernst filament ionisation by collisions
occurs under quite small electric forces — much smaller than that
due to the heating circuit in these experiments — and even at the
low pressure used it was not possible to obtain a saturation
current.
A comparison of the results in the above table with those
recorded in the curve of fig. 1 shows that the negative ionisation
produced by a glowing Nernst filament is enormously increased by
coating the filament with lime. It is difficult to say whether the
emission is as large as that from lime-covered platinum, but the
experiments at all events show that the order of magnitude is
the same in both cases. To make a careful comparison of the
two it would be necessary to work at much lower temperatures
so as to avoid the complications introduced when the discharge
becomes luminous. It was found to be extremely difficult to
maintain the lime-covered filament at a constant temperature
much less than 1500" C, and after several attempts the idea of
trying to make an exact comparison was abandoned. The results
described above are, however, sufficient to show clearly that the
large negative emission obtained from lime heated on platinum
cannot be attributed to the metal with which it is in contact.
The positive emission from Sodium Phosphate.
A new filament was used in these experiments, and the
positive emission from this was first investigated. It was found
that the emission in a good vacuum decreased on continued
heating of the filament, but the decrease was not nearly so great
as that obtained when platinum is first heated in a vacuum. The
author has shown that the positive emission from platinum is
largely due to absorbed gas, and in the case of a Nernst filament
it may also be due to gas evolved during the heating, in which
28—2
420 Dr Frank Horton, The ionisation produced by certain
case the falling off with time in the case of a freshly heated
filament would not be expected to be so large as in the ca.=e
of metals, for no doubt a great deal of the absorbed gas is driven
off while the filament is being fitted into position and during the
evacuation of the apparatus. When a filament had once been
heated until the positive emission had been reduced to a steady
value it was found that the emission quickly became steady on
re-heating and re-testing, and the value under given conditions
remained fairly constant. With the filament at about 1450° C,
and with a potential difference of 205 volts (in addition to that
due to the heating circuit), a positive thermionic current of
1"36 X 10"'' ampere was obtained at atmospheric pressure, and on
gradually pumping down, the current increased to a maximum
value, generally at about 30 mm. pressure, after which it decreased
to a minimum at about 2 mm. pressure, and then rapidly increased
again as the pressure was still further reduced. Sometimes, how-
ever, this final increase in the current did not occur, and the
current decreased to a minimum value at the lowest pressure.
The form of the current pressure curve for the positive emission
from a Nernst filament is thus exactly similar to that given by
platinum*.
The filament was next covered, except for about 1 mm. at
each end, with a layer of pure sodium phosphate by evaporating
a water solution of that salt upon it, a few drops at a time. It
was then fitted into the discharge tube and the positive emission
was re-tested. In the earlier experiments it was found that the
phosphate volatilised away from the filament and condensed on
the walls of the discharge tube. The heating current was there-
fore regulated so as to keep the filament glowing at as low
a temperatui"e as possible. Under these conditions it was rather
difficult to start the filament glowing, and it often "went out"
before the observations were begun ; but ultimately I succeeded
in obtaining a series of values of the positive emission at 1422° C.
over a fairly wide range of gas-pressures. Before this series was
obtained the filament was heated for about two hours in a pressure
of '002 mm. At the end of this time the emission had been
reduced to a steady value. The gas-pressure in the apparatus
was gradually raised to 56 mm., observations of the positive
emission being taken at several pressures. After each alteration
of pressure a few minutes were allowed for the current to become
constant. The pressure was then gradually reduced again, and
the observations of the current were repeated. Throughout the
series the temperature of the filament was maintained at 1422° C.
by adjusting the resistance of the heating circuit. The results
* i\ Horton, Proc. Roy. Soc. A. lxxxviii. p. 117, 1913.
substances when heated on a Nernst filament.
421
obtained with decreasing pressures are plotted as a curve in
fig. 2. In the following table some results at various pressures,
S loof
^
3— C
' ■
>— .
-©-
Soc
'/i//7-
ph
'Sph
1
!
0/1
f-lla
me
It
<?)
_
' —
>—
T
M
~~-
~<3^
"
f\\i
trie
il^
^
*« — ,
-^
)
^
I
Ff
@^
^
Pressure mm.
Fig. 2.
both increasing and decreasing, are given. The close agreement
between the values in the two series shows that the emission had
really been reduced to a steady state.
Pressure (mm.)
•0024
13-25
15-0
45-0 ; 56-5
Thermionic curi'ent :
Increasing pressures
Decreasing pressures
92
160
163
123
114
95
162
160
120
114
The curve in fig. 2 is similar to that which represents the
connection between positive ionisation and pressure for sodium
phosphate heated upon a platinum strip. In both cases the
emission at first increases with decreasing pressure to a maximum
value at a pressure of a few mm., after which it decreases rapidly
as the pressure is still further reduced. In some earlier experi-
ments* the maximum value of the positive emission from sodium
phosphate heated upon platinum at 1190° C, under an applied
potential difference of 200 volts, was 2-25 x lO"'' ampere per
sq. cm., and occurred at about 10 mm. pressure. From the curve
in fig. 2 the maximum current is obtained at about 3 mm.
pressure, and its value is 1-97 x 10"" ampere per sq. cm., the latter
* loc. cit.
422 Dr Frank Horton, The ionisation produced by certain
figure being obtained on the supposition that the part of the
filament which had been covered with phosphate was still covered
when these observations were made. Since the current per
sq. cm. calculated on this supposition is rather less than that
given by platinum coated with sodium phosphate at a much
lower temperature, it seems probable that in places the salt had
volatilised away from the filament, so that the area covered when
the observations were taken was really much less than that
assumed in the calculation. The fact that the maximum emission
is obtained at a lower pressure in the case of the Nernst filament
is in agreement with the general characteristic of the positive
emission from glowing solids, namely, that the pressure of
maximum emission is lower the higher the temperature of the
anode.
After these experiments with sodium phosphate, the filament
was taken down and repeatedly washed in distilled water to
remove any remaining sodium salt. It was then replaced in the
apparatus and the positive emission at 1422° C. was again tested.
The current-pressure curve obtained is also shown in fig. 2.
This curve is similar to that given by a new filament after
heating to a steady state, but the values of the currents shown in
the curve are rather larger than those generally obtained. The
difference in the form of this curve and that obtained with sodium
phosphate on the filament is very marked. A similar difference
is shown by the curves for platinum covered with sodium phosphate
and for platinum alone. Evidently the increase of the emission to
a maximum value at a few mm. pressure is due to the presence
of the sodium salt on the anode ; and the large emission obtained
from sodium phosphate heated upon platinum is due to the salt
itself and not to the platinum.
Dr W. Wilson, in his experiments*, could detect no positive
emission from a Nernst filament covered with aluminium phos-
phate, but he obtained an emission while the heater connected
with the filament was kept glowing, and he concluded that
the latter effect was due to the fine platinum wire of the heater.
In an earlier paper the author has shown that the activity of
ordinary aluminium phosphate is due to sodium impurity which
would immediately sublime away at the high temperature of the
fully glowing filament, but would probably give a steady emission
at the much lower temperature of the heater; so that the current
obtained in Wilson's experiments while the heater was in operation
may have been due to the material of which it is made, or to some
of the phosphate which had fallen upon it.
The form of the current-pressure curve given by salts contain-
ing sodium is very interesting. In my paper on the discharge of
* W. Wilson, Phil. Mag. 6, xxi. p. C34, 1911.
substances when heated on a Nernst filament. 423
positive electricity from sodium phosphate heated in different
gases*, it is pointed out that this curve is similar to those obtained
when the negative emission is under test, which suggests that
ionisation by collisions comes in at certain pressures. In the
paper referred to this view is ruled out because, at that time,
it was generally thought that much larger electric forces than
those employed were necessary to obtain ionisation by collisions
with positive ions. Some experiments recently made by Dr
Pavloff in the Cavendish Laboratory have, however, shown that
ionisation by collisions with positive ions occurs even with
potential differences of about 10 volts. It is thus possible that
the shape of the curve obtained with sodium phosphate is due to
ionisation of the gaseous molecules present, by collisions with the
positive ions from the glowing anode.
The experiments made with uncoated filaments showed a
pressure of maximum emission at about 30 or 40 mm. pressure,
but near this maximum the thermionic current was very unsteady,
varying capriciously over a range of as much as 50 per cent, in
some cases. It was at first thought that this unsteadiness was
due to the cooling effect of convection currents, but the emission
at higher pressures was very much steadier, so it does not seem
probable that convection is the cause. The points plotted in this
part of the curve in fig. 2 represent the means of many deter-
minations. In the case of the particular filament to which this
curve refers, the pressure of maximum emission was at about
30 mm. The effect of placing sodium phosphate upon the filament
is to reduce this pressure of maximum emission very considerably,
so that at pressures of a few millimetres there is a very much
greater ionisation from the phosphate covered anode than from
the filament alone. The ionisation at all pressures is increased
by the presence of the sodium salt, but the increase is most
marked at pressures of a few millimetres.
The form of the current-pressure curve for a clean filament
is similar to that given by a platinum strip which has been
heated for a long time. In the latter case there are strong
reasons for believing that the ionisation is due to gas evolved
from the heated platinum, and it would appear probable that
the ionisation from the Nernst filament is due to a similar cause.
The question arises : can the form of the current-pressure curve
be due to ionisation by collisions ? The high pressure at which
the maximum value of the current is obtained would seem to be
against this view, but it must be remembered (a) that the electric
force near the filament is very great; (6) that at the temperature
employed, the mean free path in the surrounding gas or vapour
* Proc. Gamh. Phil. Soc. xvi. p. 89, 1911.
424 Dr Frank Horton, The ionisation produced by certain, etc.
is much larger than at ordinary temperatures, and the pressure of
maximum current increases with both these quantities, I think,
therefore, that the shape of the curves given by pure platinum
and by a clean Nernst filament can be explained by ionisation by
collisions coming in at certain pressures.
The effect of sodium phosphate is probably twofold : (1) it
increases the formation of positive ions at the surface of the
anode, and (2) it changes the nature of the gaseous material
through which the discharge takes place ; for the space round the
anode now contains molecules of volatilised salt, or the products
of dissociation of that salt. The pressure of maximum current
is now much lower than before, and if ionisation by collisions is
the cause of the existence of this maximum, it follows that the
vapour now surrounding the anode is not so easily ionisable by
collisions as was the gas previously in contact with it. On this
view the increase of energy required for ionisation must be
considerable to account for the large decrease in the pressure of
maximum emission. If we may assume that an increase of tem-
perature of the anode increases the percentage of difficultly
ionisable molecules surrounding it (by increasing the volatilisation
or dissociation of the salt) to a greater extent than is necessary to
counterbalance the effect of the increased mean free path, we
should expect that the higher the temperature of the anode the
lower would be the pressure at which the maxiniuni emission
occurs. This is what is actually found to happen when series
of observations of the positive emission are taken at different
temperatures. In the case of the negative emission from glowing
solids, the pressure of maximum current increases with the tem-
perature, a fact which is explained by the larger mean free path
in the surrounding gas at higher temperatures. If the above
explanation of the effects obtained with the positive ionisation is
correct, it follows that the difficulty in ionising the salt vapour
(or its dissociation products) is experienced by the positive ions
but not by electrons.
So far nothing has been said about the increase in the positive
emission from the clean filament as the pressure is reduced below
1 mm. An exactly similar increase was noticed when pure
platinum was being experimented upon, and it has been attributed
to the mercury vapour which comes over from the pump. It is
intended to test this view by taking precautions to prevent mercury
vapour from entering the discharge tube.
The author wishes to acknowledge his indebtedness to the
Government Grant Committee of the Royal Society for the means
of purchasing some of the apparatus used in these experiments.
Mr Udny Yvle, Fluctuations of samjjUng in Mendelian Ratios. 425
Fluctuations of sampling in Mendelian Ratios. By G. Udny
Yule, M.A., St John's College, University Lecturer in Statistics.
[Head 9 March 1914.]
In any series of Mendelian experiments, the observed propor-
tions always exhibit greater or smaller deviations from expectation.
In the material as a whole, if it be considerable, the deviation may
be small : but if it be broken up into small sub-groups — e.g. the
offspring of individual matings — the fluctuations may be very large
indeed. For example, in the series of matings of Japanese
waltzing mice x albino hybrids inte?' se, cited in Table A below, the
expectation of albinos is 25 per cent., and the average proportion
137/555 = 24"68 per cent, is extremely close to this: but in the indi-
vidual litters the percentages cover the whole range from to 100
per cent. The question whether such fluctuations have any signifi-
cance or whether they are merely the result of " pure chance,"
corresponding to the fluctuations that might be expected in the
number of black balls drawn from a bag containing both black and
white, is one that must no doubt have occurred to most workers in
the subject. Mr Bateson and Miss Saunders, writing in the First
Report of the Evolution Committee of the Royal Society (1902),
were careful to emphasise that the numerical results are irregular
and that the laws represent only an average result (pp. 10 and
127 — 8). In the Second Report (1905) a long series of results
with peas (Pisum) is tabulated and it is stated that " the possi-
bility that departures from the expected F2 ratios might not be
purely fortuitous was a special subject of enquiry " (p. 55). The
conclusion given is that " the ratios found in individual plants,
62 for shape and 85 for colour, are not enough for full discussion,
and a study of them does not, so far, suggest the presence of any
disturbing factor" (p. 77). But this brief statement hardly seems
to make the most of the material given in the Report.
It is difficult in fact to understand why more use has not been
made of well-known results in the theory of sampling in order to
compare the fluctuations observed in Mendelian experiments with
those to be expected if the individual families, fruits — or what-
ever the sub-groups may be — are simply random samples of the
whole possible material. If p be the chance of obtaining one of
the two alternative characters (e.g. the dominant), q the chance of
obtaining the other (e.g. the recessive), the relative frequencies of
426 Mr Udny Yale, Fluctuations of sampling
samples of n individuals 0, 1, 2, etc. of whom shew the first
character, are given by the terms of the binomial series {q — pj^ or
n n-i n(n-l) n(n-l)(n-2)
The mean of the series is np : its standard deviation is (npq)^. If,
for example, data are available for a number of litters of moderate
size, litters of the same size n may be grouped together and for
each such group the numbers of litters with 0, 1, 2, etc, recessives
may be compared with the frequencies to be expected as given by
the binomial series.
Where the sub-groups are of considerable size but not very
numerous, as in counts of peas on diiferent plants or of maize
grains on different cobs, this complete comparison becomes
impossible and we have to fall back on a simple comparison of the
standard deviation of the observed proportions with expectation.
So far as I know, not even this has been done in many instances.
The work of R. H. Lock on maize, referred to further below, is a
notable exception. For a number of samples, all of the same size
n, the standard deviation of the proportion is {pqjnY : if the sizes
of the samples vary, for n should be substituted the harmonic
mean H of the numbers in the samples where -^=-=r^S(-j* if
JSf be the number of samples. With the use of Barlow's Tables
(Spon), for giving the reciprocals, 1/H is readily evaluated : the
values of Ijn are written down straight from the tables, their
arithmetic mean r = l/H is formed, and the expected standard
deviation is (pqr)^.
The following illustrations of these theorems were for the most
part obtained some years since and have frequently been used as
examples in lectures, but with one exception they have not hitherto
been published. I have put together these notes in the hope that
they may stimulate those who are carrying out actual experiments
to make more extensive and detailed tests on the same general
lines. The work seems to me well worth doing.
I know of no data sufficiently extensive to give a thoroughly
satisfactory test against the binomial distributions. From
A. D. Darbishire's data respecting his crosses of Japanese waltzing
mice with albino mice {Biometrika, ill., 1904, p. 1) tables can be
compiled in the required form, but there are only 121 litters for
the case in which the expectation is 25 per cent., and 132 for the
expectation 50 per cent. These numbers are too small for any
close agreement with theory to be expected in the case of the
Cf. Yule, Introduction to the Theory of Statistics, xiii. § 11.
1
ill Mendelian Ratios.
427
few litters of each individual size, but a fair comparison results
when the figures for litters of all sizes are totalled together.
Table A shews what is meant. The figures in ordinary type give
Table A. Hybrids of Japanese waltzing mice x albinos jpaii^ed
together : expectation of albino 25 °/^. Observed {ronian) and
calculated {italic) numbers of litters of each size with 0, 1, 2,...
etc. albinos. Data from Darbishire, Biometrika, in.
Number of albinos in the litter
Size of
litter
Total
litters
1
2 3
4
5
6 or
more
1
7
5-25
1-75
7
2
3
6-19
7
4-12
1
0-69
11
3
7
6-75
5
6-75
4
2-25
0-25
16
4
5
5-39
9
7-18
3
3-59
0-80
0-04
17
5
9
6-17
9
10-28
3
6-86
3
2-28
1
0-38
1
0-03
26
6
8
5-52
9
11-03
8
920
6
4-09
1-02
0-14
0-01
81
7
1
l-i7
4
3-43
3
3-43
2
1-90
1
0-63
0-13
0-01
11
8
0-10
0-27
1
0-31
0-21
0-09
0-02
—
1
9
0-08
0-23
1
0-30
0-23
0-12
0-04
0-01
1
Total obs. :
calc. :
40
36-92
43
45-04
24
26-63
11
9-76
2
2-28
1
0-36
0-03
121
121-02
the observed numbers of litters of each size with a specified
number of albinos ; the italic figures are those calculated from
the respective binomial series. The expectations being 3/4 and
1/4, the expected proportions of litters of 1 with no albinos and
1 albino are 3/4 and 1/4 : the expected proportions of litters of 2
with 0, 1, and 2 albinos 9/16, 6/16 and 1/16— and so on. The
428
Mi' Udny Yule, Fluctuations of sampling
frequencies in the individual compartments of the table are too
small to shew close agreement between observation and theory,
but if the observed and calculated frequencies are totalled for all
sizes of litter, as in the bottom row of the table, the agreement
shewn is \Qvy close indeed — closer than would be found as a rule.
If Professor Pearson's test be applied {Phil. Mag., July 1900, and
Elderton's tables, Biometrika, I.), ;^^= 0"780, P = 0'94, or a worse
fit between observation and theory is to be expected 94 times out
of 100. Reducing the cases for which the expectation is 50 per
cent, in the same way, I find the figures for all sizes of litters given
in Table B. Here the agreement is not quite so good, as the
observed data for litters of five or more are ii'regular, but it is
quite fair. I find ')^ = 8003, P = 0'238, or a worse fit might be
expected nearly one time in four'*. The same data may be other-
wise dealt with by working out the percentage of albinos in every
litter and comparing the standard deviation of such percentages
with {pqlHy. I find :
Data of Table A.
H = 3-53 ; s.d. theo. 23-04 ; actual 2309 ± 1-00.
Data of Table B.
^=4-73; s.d. theo. 22-98 ; actual 21-63 ±0-90.
The agreement here is very close.
Table B. Waltzing mice x albino hybrids crossed with albinos.
Observed numbers of litters with 0, 1, 2,... albinos and numbers
calculated (as in Table A) from expectation 50 °/^. Data from
Darbishire, Biometrika, ill.
Number of
albinos in
litter
Number of litters
1
Number of
albinos in
litter
Number of litters
Observed
Calculated
Observed
Calculated
1
2
3
4
5
6
21
30
37
18
18
6-14
19-98
31-71
32-90
23-41
11-83
6
7
8
9 or more
1
1
4-48
1-28
0-26
0-03
Total
132
132-02
Turning now to the data for peas (Fisum) tabulated by indi-
vidual plants in the Second Report of the Evolution Committee
* In calculating P the frequencies of 4 albinos and upwards in the first case,
and of 6 albinos and upwards in the second, were grouped.
in Meiidelicm Ratios.
429
referred to above, it is evidently no longer possible to give the full
comparison with the binomial series as the range in number of
seeds per plant is too great and the plants too few, and a com-
parison of the actual standard deviation of the percentages for
individual plants with the standard deviation {pqjHY is all that
can be effected. Table C shews the results. The first four lines
Table C. {Data from Second Report of the Evolution Committee
of the Roy. Soc. ( W. Bateson and Miss Killhy).) Comparison
of actual and calculated standard deviations of percentages of
recessive seeds in Fo on different 'plants in peas. Expectation
• 25%.
Table in
original
Characters :
dominant first
Number
of
plants
Mean
percentage
of recessive
seeds
Standard
deviation and
probable error
(per cent.)
sIpqjH
(per cent.)
I
III
II
III
Yellow and green
Bound and wrinkled
84
86
64
86
25-4
24-3
23-8
24-3
6-55 ±-34
4-86 ±-25
6-05 ±-36
5-59 ±-29
7-31
5-30
6-48
5-30
I, III
II, III
Yellow and green
Kound and wrinkled
170
150
24-8
24 1
5-79±-21
5 -80 ±-23
6-39
5-84
Omitting from Tables I anc
plants with less than 100.
I II plant
s with less tl"
lan 50 seeds, anc
1 from III
I
III
11
III
Yellow and green
Round and wrinkled
52
43
42
43
24-9
24-3
25 1
23-8
4-40±-29
4-23±-31
4-24±-31
3-57 ±-26
4-40
3-71
4-38
3-71
of the table give the standard deviations of the percentages of
yellows for the plants included in Tables I and III of the original,
and of the percentages of rounds for the plants tabulated in
Tables II and III. In three cases out of the four the observed
standard deviation is less than that calculated, though the
differences are within the possible limits of fluctuations of sampling
(taking the probable error of a standard deviation as given ap-
proximately by the formula for the case of normality 0-6745o-/v/27?).
Grouping together the data respecting yellows and greens from
Tables I and III, and similarly the data respecting rounds and
wrinkleds from Tables II and III, the results shewn in the next
two lines are obtained : the observed standard deviation is less
430
Mr Udny Yule, Fluctuations of sampling
than that calculated in each case, and for yellows and greens the
difference is nearly three times the probable error. Speaking
generally, however, the agreement is fairly close, and the data hardly
suggest any fluctuations of physical significance. The range of
the number of seeds per plant is, however very high — from a
mere half-dozen seeds up to two or three hundred — and it was
suggested to me by Mr Darbishire that the poor plants might be
exceptional, and that it might be worth while to try the effect of
their exclusion. Excluding plants with less than 50 seeds in the
case of Tables I and II of the original, and plants with less than
100 seeds in the case of Table III, the standard deviations obtained
are given in the last four lines of Table C. Here the agreement is
distinctly closer than before. Finally use may be made of the
fact that Table III of the Report deals with the two characters
yellowness and roundness in combination. The expectation of
yellow-rounds is 9/16 or 56-25 per cent, and the mean percentage
given by all the plants of Table III of the Report is close to this.
Including all plants the actual standard deviation (Table D) is
lower than that calculated by 2-8 times the probable error:
omitting plants with less . than 100 seeds the agreement is
extremely close. In the case of the combination of characters as
in the case of the single character there is no evidence of any
significant fluctuation.
Table D. {Data from Table III, loc. cit. above.) Standard devia-
tions of percentage of the pair of dominant characters, yellow-
round seeds, in i\. Expectation 9/16 or 56-25 °/^.
Number
of plants
Percentage of
yellow-rounds
Standard deviation
and probable error
sIpqjH
All plants
Excluding plants with
less than 100 seeds...
86
43
56-51
56-77
5 -36 ±-28
4-27±-32
6-13
4-25
I turn now to Mr Lock's paper on his experiments on maize
{Annals of the Botanic Gardens, Peradeniya, iii. 1906). Mr Lock
himself worked out for one of his most extensive tables (Table 33)
for a DR x RR cross the probable error and its theoretical value
for simple sampling, calculating the actual value by a graphic
method : he also pooled together all the cases of expectation
50 per cent, and made the same comparison. In both cases the
actual somewhat exceeded the expected value of the probable
error though the difference was not great. The results of my
own work on Mr Lock's data are shewn in Table E. For three
I
in Mendelian Ratios.
431
tables in which the expectation is 25 per cent, the agreement is
good, very good considering the small number of cobs available.
When these three tables are pooled together (without respect to
the fact that they deal with different characters) the actual s.d. is
2*05 per cent, against an expected value 1*99.
Table E. {Data from Lock, Annals of the Botanic Gardens,
Peradeniya, ill. 1906.) Comparison of actual standard
deviations and s.d.'s of sanipling in experiments with maize.
1
; Table in original
Characters
No.
of
plants
Mean per-
centage of
recessive
grains
Standard
deviation and
pi'obable error
(per cent.)
sIpqjH
(per cent.)
I
XXXIV
Starchy and sugary
Yellow and white
18
22
30
24-8
23-4
2-5-5
2 -04 ±-23 .
l-96±-20
l-62±-14
2-20
2-28
1-63
I, II, XXXIV
—
70
24-7
2-C5±-12
1-99
2-60
2-72
2-16
II, IV, V, VI, VII
III, IX, X, XI, XII
j XXXIII
Starchy and sugary
Yellow and white
74
49
95
50-9
50-2
50-0
3-17 ±-18
3 -16 ±-22
2-48 ±-12
r ._.„„.„
„i? j-u„ no w DC
> „
!,„„,„..
In the case of the DR x RR crosses, however, the agreement is
by no means so good, the actual exceeding the expected standard
deviation by two to three times the probable error in each case.
The divergence in the second group is largely due to the five
plants of Table IX which give percentages of whites ranging from
43'3 to 56*6 and 56'9 on 644, 648 and 515 grains respectively :
with standard errors of 2 to 2"2 per cent., such deviations are not
probable as the results of random sampling. But, as pointed
out by Mr Lock, the data as a whole shew a rather greater
variation than one would expect, and the result cannot be
attributed merely to one or two particular tables. The difficulty
is to imagine any cause for such excessive variation (such
as fertilisation by pollen from DD's or DRs instead of RR's, in-
correct sorting of doubtful yellows or unsuspected heterogeneity
of the whites) which would not also affect the means obtained,
and the means agree very well with expectation. The contrast
between the DR's selfed and the DR x RR crosses is curious.
The former certainly do not suggest anj' significant fluctuation :
the latter do, on the whole, suggest some source of disturbance
or possibly error. I wish more data, for other plants or for
432 Mr Udny Yule, Fluctuations of sampling in Mendelian Ratios.
animals, were available for this cross. It seems to me of especial
interest as it is only on the heterozygote that there are differences
between the gametes.
Some years ago Miss E. R. Saunders was good enough to put
at my disposal extracts from her records of experiments on stocks
to test the question whether the proportions shewed any significant
fluctuation when they were based on the seeds from individual
fruits, and not merely on seeds from each plant as a whole. To
avoid possibly serious disturbance of the proportions recorded,
I excluded in the case of the plant characters all pods in which
less than 70 per cent, of the seeds survived. The following are
the results :
Characters
Expected
ratio
No. of
fruits
Actual s.d. of
the percentages
JpqjH
(per cent.)
Hoariness and smoothness
1 : 1
3 : 1
9 : 7
20
102
236
6-39 ±-68
7-11 ±-34
9 -01 ±-28
8-62
6-80
8-92
Singles and doubles
8 : 1
105
8-64±-40
8-09
Seed colours : Green, not-green
27 : 37
9:7
8 : 1
28
53
40
9 -46 ±-85
8-13±-53
5-84±-44
7-80
7-28
6-70
In five cases out of the seven the observed are greater than the
predicted standard deviations, but the excesses are within the
limits of sampling. Even in spite of the restriction mentioned
the observed percentages of the plant characters may be somewhat
disturbed by losses, so that even if the excessive variation be
regarded as significant it does not follow that in these cases it
represents a deviation from pure chance in the distribution of the
gametes amongst the fruits. In the case of the seed colours
Miss Saunders informs me that the classification was carried out
chiefly for reasons of convenience, and as it was not the main
object of the experiments the time and labour that would have
been entailed by the strictest accuracy was not given to the
sorting of difficult cases — and there are difficult cases, such as
parti-coloured seeds and seeds which have remained green because
they have died before ripening. Hence there may be a small
proportion of mi.ssorted seeds, tending to increase the fluctuation.
If the results cannot be said definitely to disprove the existence of
significant fluctuation, apart from fluctuations due to varying
death-rates in different groups of plants, neither do they give any
certain evidence of its existence.
Mr Engledoiu, A Case of Repulsion in Wheat. 433
A Case of Repulsion in Wheat, ^y F. L. Engledow, B.A.,
I St John's College. (Communicated by Professor Biffen.)
[Read 9 March 1914.]
The plants which supplied the evidence of repulsion comprised
; the second generation (^2) of the cross
Smooth Black x Essex Rough Chaff
and the two characters concerned were :
(1) Roughness of Chaff,
(2) Black Colour of Chaff.
The term chaff, as used here, refers to the glumes only of the ear.
It is, however, practically certain that an examination of the outer
paleae would justify the inclusion of these parts with the glumes
jas far as the experimental characters are concerned.
I The following details concerning the parents suffice for the
purposes of this paper.
" Smooth Black " is a variety of wheat obtained by Professor
\ Biffen as one constituent of the second generation of the cross
jl Rivet X Fife.
I Its genetic constitution has not yet been determined but, as two
years of growing have shown, it breeds true.
The glumes are glabrous and of a deep and burnished black
colour, the black pigment occurring in the sub-epidermal tissues.
Types which possess glumes of this nature will be referred to
as " Smooth Black."
'Essex Rough Chaff" is, agriculturally, a very familiar variety.
In common with most other types of wheat it has glumes entirely
devoid of the black colour which characterises the other parent.
There is a further distinction between its glumes and those of
Smooth Black, viz. the presence of numerous hairs. This com-
bination of characters in the glume is designated by the term
" Rough White."
In all, the second generation which resulted from the crossing
of these two varieties contained 213 plants. Sorting by eye —
which was fully confirmed by an examination with the dissecting
microscope — furnished the following classification :
29
Rough Black Rough White
Smooth Black
Smooth White
120 43
47
•1
OL. XVII. PT. v.
2
484 Mr Engledoiu, A Case of Repulsion in Wheat.
If repulsion occur on a 1 : 3 : : 3 : 1 basis between "Ptoughness"
and " Blackness," the theoretical expectation for this case is :
109-8 49-9 49-9 S'S
The results of the single cliaracter classifications are as follows :
Rough : Smooth :: 163 : 50
Black : White :: 167 : 46
the expectation being in each case 160 : 53. The probable error
of the number of dominants is 4'3 and hence the agreement with
expectation is satisfactory. I
In another note* there appears a method of determining the '
best coupling or repulsion series for a set of observed data.
Employing that method for this case, the best series is found
to be :
1 : 2-56 ::2-56 : 1.
In the paper already referred to, the results are examined by'
Pearson's Method f for the probability of the fit of an observed to
an expected series. It is apparent from the examination that the
probability of the existence of repulsion on the 1 : 3 : : 3 : 1 basis
between "Roughness" and "Blackness" in wheat is quite as'
great as that of the existence of coupling and repulsion which has'
been described in the cases of other plants.
A point of some interest lies in the fact that blackness appears
not to be a simple character — not simple in the sense of not being
present always to the same extent. Some of the second generation ;
plants are so black that they are indistinguishable from the black'
parental type, while others show merely a small black patch on !
the glume. The interval between these extremes is fairly i
uniformly filled by plants of intermediate blackness. It must,'
however, be remarked that blackness v/hen present is readily
detected. White glumed plants which have been discoloured by
disease sometimes resemble plants with small black patches but!
the patches caused by disease are not similarly placed on all the '
glumes of the ear and they may be almost completely removed by
scraping gently with a sharp knife.
The presence of blackness to so varying a degree can with
difficulty be conceived to be produced and controlled by one
factor only. One factor or combination of factors common to all
the black plants and accompanied in some cases by an intensor or
partially inhibitor factor is the explanation which at once suggests
itself
* Yule and Engledow, Proc. Camb. Phil. Soc, Vol. xvii., Part 5, "The Dete^;
mination of the Best Value of a Coupling Ratio from a given set of data."
+ Pearson, Phil. Mag. vol. l, 1900.
Mr Etigledotv, A Case of Repulsion in Wheat. 435
That still other factors must be assumed to be concerned in
this colour effect is clear from an examination of the parentage
of " Smooth Black." The black appeared in the second generation
of a cross in which neither of the parents showed the black colour.
This, of course, would lead us to assume that in each parent is a
factor which alone cannot produce blackness but united with the
other has this effect. No simple explanation can, however, be
furnished on these lines and it seems probable that before the
question can be settled more knowledge will have to be obtained
of the nature of true " black " and " grey." Transverse sections of
the glumes may be of some assistance in this respect. Meantime,
the repulsion above described seems certain and from the nature
of the case there appears to be a strong probability that Rivet
" 8'"^y " ^^d ^"cViQ " black " are very closely related. It is hoped to
elucidate this matter by further crosses next summer.
A double confirmation of the existence of repulsion between
blackness and roughness seems possible. The doubly heterozygous
members of the second generation ought to exhibit repulsion ;
and coupling between the two characters should result from the
crossing of " Rough Black " and " Smooth White." These two
types can, of course, be obtained from the second generation which
exhibited the repulsion.
29—2
436 Mr Engledow and Mr Udny Yule, The determination of
The determination of the best value of the coupling -ratio from a
given set of data. By F. L. Engledow, B.A., St John's College,
and G. Udny Yule, M.A., St John's College, University Lecturer
in Statistics.
[Read 9 March 1914.]
Many workers in Mendelism who have come across cases in
which coupling or repulsion occurred must have felt the necessity
for some general method by which to determine from their data
the best value to assign to the coupling-ratio, apart from any
theory as to the ratios that are possible. Mr G. N. Collins {Am.
Nat., vol. XLVL, 1912) is, so far as we are aware, the only writer who
has suggested any such method. He worked out the value of a
coefficient of association for the whole series of possible ratios,
1:1:1:1, 2:1:1:2, etc., and then used the observed value of
the same coefficient to decide which ratio gave the best agreement
with the facts. While this method is very simple and convenient,
it does not seem to lead to the most advantageous value for the
ratio.
The test to be used for the closeness of agreement between the
theoretical and observed frequencies seems clearly to be that
developed by Professor Pearson (Phil. Mag., vol. L., 1900). If
FiF^FsFi etc. are a set of theoretical or expected frequencies and
FiF^'Fs'Fi' etc. are those observed, and if
^ ^ F '
the probability P that in random sampling deviation-systems of
equal or greater improbability will arise is a function of p^;^ which
decreases continuously as %^ increases. The values of this function
for any number of frequencies from 3 to 30 have been tabulated
by Mr Palin Elderton (Biometrika, vol. i.). In order to measure
the closeness of agreement between an observed set of the four
frequencies for any pair of characters, and the expectation based
on any assumed ratio, it is only necessary to work out the value of
;t^2 and turn up in Mr Elderton's table the column headed n' = 4,
where the probability that an equally bad or worse set of deviations
might arise in sampling will be found. If P is high, the agree-
ment is good ; if low, it is bad. That value of the ratio, then,
which gives the most satisfactory agreement with the data is the
value which makes the probability P a maximum or y^^ a minimum.
The value of P is not accurate if any frequencies are small, as a
the best value of the coupling -ratio from a given set of data. 437
normal distribution of errors is assumed in the calculation of the
tables, but even from the empirical point of view the method
suggested seems much better than any now in use.
Suppose the two factors to be A and B, and let the gametes
be produced by the heterozygote in the following proportions :
AB Ah aB ah
p (0'5—p) {0'5 — p) p
then, assuming random mating, zygotic forms will be produced in
the proportions :
AB Ah aB ah
(p^+0-5) (0-25 -p') (0-25 -p^) p\
Let the observed proportions of zygotes be fifififi, where
/i +/2 +/3 + /4 = 1- Then we have to make a minimum the
quantity
p^ + O-0 0-2o-p^ 0-25 -p2 "^ _p2
Differentiating with respect to p and equating to zero, we
find
if^' + fi - A' - A') f + (o-5/i^ + A' + fi - 0-5//) p^
+ {0-25 fi + 0-25 f,' + 0-1875 // - 0-0625 f^')p'
+ 0-0625/4>^ -0-01 5625 /;-^ = (1).
This is an equation of the fourth degree for p^. A first approxi-
mation to the root required may be obtained by Collins' method
or from the formula
^^ = 0-25(/,+/,-/,-/.) (2)
(which gives the value of p that makes the sum of the squares of
differences least), or by comparison with various calculated series,
and the solution is then readily obtained by Newton's method.
To take the data of the preceding note as an illustration, the
values of the proportions /are 0-5634, 0-2207, 0'2019, and 0-0141;
writing x for p'^, this gives the equation
- 0-228147^^ + 0-248083«=' + 0-002566^^
+ 0-00001 244« - 0-0000031094 = 0.
The data suggested a gametic ratio 1:3:3:1, which gives
p = 0-125, j92 = 0-015625. Trial shewed that 0-0156 was not a
very close approximation to a root ; 0-02 proved nearer to a
solution, and Newton's method gave by two approximations
p2= 0-019715.... Hence p = 0*1404 and this gives a ratio 1 : 2-56.
The observed frequencies were then compared with the frequencies
438 Mr Engledoiv and Mr Udny Yule, The determination of
to be expected from this ratio, and from the ratio 1:3:3:1.
The results obtained were
Ratio 1 : 3 x^ = 2-0974 P = 0-554
„ 1:2-561 ;(;2^ 1-9918 P = 0-574
It will be observed that while the calculated ratio does give the |
better agreement, the difference is slight. In both cases results j
equally or more divergent from expectation would occur nearly as
often as not owing to mere fluctuations of sampling. The result
is an illustration of the now recognised fact that a considerable i
alteration in the coupling-ratio may mean but a small alteration i|
in the closeness of fit. j
Two other cases have been tried and gave the following results.
Collins (loG. cit., p. 579) gives the following data for the characters !
coloured aleurone and horny endosperm in maize. '
Coloured-horny 1774
Coloured-waxy 263
White-horny 279
White- waxy 420
We find p = 0-3891 or a ratio 3509 : 1. For this value of the !
ratio x^ is 0-60435 or P = 0-947, the calculated frequencies 1782, ]
270, 270, 414 being in very close agreement with those observed. I
For the 3 : 1 ratio, x^ is 9-106 or P = 0-028, and the divergence is '
therefore one that would only be likely to occur once in some |
36 trials owing to the fluctuations of random sampling. I
Finally we took the data given by Bateson, Saunders and |
Punnett in the Fourth Report of the Evolution Committee (p. 16) j
for coupling between dark axils and fertility in sweet peas. Here i
we find p = 0-4745, which is equivalent to a ratio 18-608 : 1, as j
compared with the ratio 15 : 1 suggested in the Report and a j
value "about 20 : 1 " by Collins. The relative merits of the I
ratios are apparent from the following:
Ratio 18-608 : 1 x' = ^'^^'^^ P = 0-294
„ 15:1 x^= 5-9226 P- 0-116
„ 20:1 ;;^2 = 3 8975 P = 0*275
The ratio 15 : 1 is clearly much the poorest of these three: a worse
fit is only likely to occur, owing to fluctuations of sampling, some
12 times in 100. A worse fit than that given by 20 : 1 may occur
some 27 times in 100, and a worse fit than that given by our
calculated ratio some 29 times in 100. The figures again shew, |
however, how great differences may be made in the coupling-ratio !
assumed without creating an impossible discordance between
assumptions and fact. The mere agreement of the data, within '
the possible limits of fluctuations of sampling, with the frequencies
tlie best value of the coupling-ratio from, a, given set of data. 439
deduced from some assumed ratio — as in the case of the above
data for peas and the ratio 15 : 1 — is very slight evidence in favour
of the truth of the assumption, especially where the coupling-ratio
is higb, at least with such moderate numbers of observations as
are at present available. Some light might, however, be thrown
on the theory of reduplication l)y carrying out an examination of
all the available cases, determining p or the coupling-ratio for each
by equation (1). Such an examination we hope to carry out.
As p is not expressed explicitly as a function of the propor-
tionate frequencies f by equation (1), we do not see our way to
give its probable error by this method of determination. The
value given by (2), however, is in some cases close to the value
given by (1), viz, if no one of the frequencies is very small (cf. the
data below), and its standard error can be determined without
difficulty on the usual, though hardly quite justifiable, assumption
that deviations in the frequencies are small compared with their
mean values. As the standard errors by the two methods of
detertuination are likely to be of the same order of magnitude, it
seems worth while stating the result as at least a rough guide to
the possible magnitude of fluctuations. Ditferentiating both sides
of equation (2), squaring and summing, we have, utilising known
results for the sums of squares and product sums (cf. e.g. Yule, Jl.
Stat. Soc. 1912, p. 601),
where Cp is the standard error of p (to be multiplied by 0'6745 to
obtain the probable error) and N is the number of observations.
If there is coupling (p >0-2o), the coupling-ratio r =p/{0-5 — p).
Differentiating, squaring and summing again, we have
1
e,r = e
^ 4^{0o-py
.(4).
Number
of obser-
vations
Value of p from
r from
Standard error of the
values from (2)
Case
(1)
(2)
(1)
(2)
P
r
Wheat
Maize
Peas
213
2736
885
0-1404
0-3891
0-4745
0-1968
0-3885
0-4744
2-56
3-51
18-6
1-54
3-48
18-5
0-0430
0-0049
0-00385
0-56
020
2-94
If there is repulsion (p<0-25), the repulsion-ratio is (0-5—p)/p
and p* must be read for (0-5 -pY in the denominator of the above
440 ilfr Engledow and Mr Udny Yule, The determination, etc.
expression. The table shews for comparison the values of p and
r given by equation (1) and equation (2) respectively, and the
standard errors of p and of r as obtained by the latter method.
In the first case the two equations give very divergent results,
the unsuitability of equation (2) for general use being shewn by
its failure to give a good approximation to the best value of the
ratio. In this case, no doubt, we must also regard the standard error
of r (0"56) as of very uncertain validity. The magnitude of the
standard error of r in the last case — nearly 3 units — again
emphasises the caution that must be used before attaching
importance to the precise values of these high coupling-ratios.
I
ifr Norhert Wiener, A Contribution to the Theory, etc. 441
A Contribution to the Theory of Relative Position*. By Norbert
Wiener, Ph.D. (Communicated by Mr G. H. Hardy.)
[Received 14 March 1914.]
The theory of relations is one of the most interesting depart-
ments of the new mathematical logic. The relations which have
been most thoroughly studied are the series: that is, relations
which are contained in diversity, transitive, and connected or, in
Mr Russell's symbolism, those relations R of which the following
proposition is true:
RdJ .R'(LR.Rk)RkjI\C'R = C'R'\C'R.
Cantor, Dedekind, Frege, Schroder, Burali-Forti, Huntington,.
Whitehead, and Russell, are among those who have helped to
give us an almost exhaustive account of the more fundamental
properties of series. There is a class of relations closely allied to
series, however, which has received very scant attention from the
mathematical logicians. Examples of the sort of relation to which
I am referring are the relation between two events in time when
one completely precedes the other, or the relation between two
intervals on a line when one lies to the left of the other, and does
not overlap it, or, in general, the relation between two stretches
a and /S, of terms of a series R, when any terra lying in a bears
the relation R to any term lying in /3. Relations of this sort,,
which I shall call relations of complete sequence, differ in general
from series in not being connected: that is, for example, it is not
necessary that of two distinct events, each of which wholly
precedes or follows some other event, one should wholly precede
the other, for the times of their occurrence may overlap. But in
all the instances we have given, the relation of complete sequence
is closely bound up with some serial relation : the relation of
succession between the events of time is intimately related to the
series of its instants, the relation between two intervals on a line
one of which lies completely to the other's left is intimately related
to the series of the points on the line, and so on. These con-
siderations lead us to the general questions, (1) what are the
formal properties which characterise relations of the sort we have
* The subject of this paper was suggested to me by Mr Bertrand Russell, and
the paper itself is the result of an attempt to simplify and generalize certain notions
used by him in his treatment of the relation between the series of events and the
series of instants.
29—5,
442 Mr Norhert Wiener, A Contribution to the
called relations of complete sequence ? and (2) what is the nature ■■
of the connection between relations of complete sequence and \
series ? i
One very general property which belongs to relations of the |
sort we have called relations of complete sequence is that they i
never hold between a given term and itself. This property — that !
of being contained in diversity — they share with series proper. !
Writing cs for the class of relations of complete sequence, we can ;
represent this fact in the symbolism of the Principia Mathematica \
of Whitehead and Russell by the formula
csCRVJ.
Another property they share with series is that of transitivity. ',
If, for example, the event x wholly precedes the event y, while i
the event y wholly precedes the event z, the event cc wholly
precedes the event z. But they possess another property more
powerful logically, which may be called a generalized form of
transitivity. If the event x wholly precedes the event y, and
the event y neither wholly precedes nor wholly follows the
event z, while the event z wholly precedes the event w, then !
the event cc will wholly precede the event w. All the other \
relations which we have mentioned as examples of relations of |
complete precedence Avill be found to possess the same property, i
which, moreover, will be satisfied by all those relations which we i
would naturally call relations of complete precedence. We may, :
then, so define "relations of complete precedence" as to regard j
this as a property common to all such relations. In symbols, we i
shall then have
The relation {^R^R\ with its field limited to that of R, is j
what we ordinarily know as simultaneity. In most theories of :
time and of relations of complete precedence, it has been thought
necessary to treat precedence and simultaneity as coordinate -
primitive ideas. Nevertheless, those who hold such theories have
to assume such propositions as the following, in order to make i
simultaneity and precedence possess the appropriate formal '
properties * :
\-.SnP = A,
\-.scis,
V.C'S=G'P.
* In the following list of propositions, S stands for 'is simultaneous with,'
and P for ' precedes.'
i
Theory of Relative Position. 443
From these it is an easy matter to deduce that
V.8 = {-P-P)IG'P,
while on the hypothesis that P dJ, the converse deduction can
readily be made. Therefore, we may define simultaneity as that
relation which holds between x and y when both either follow or
precede something and neither precedes the other. The second
property of relations of complete sequence may, then, be inter-
preted to state that if R is such a relation, then if xRy, y-is-
simultaneous-with-respect-to-i? to z'*, and zRw, then xRw.
We shall find that most of the properties of relations of the
sort of complete temporal succession between events follow from
the two conditions which we have mentioned above — indeed, many
of the most important ones follow from the second alone — so that
we shall define a relation of complete succession as one which
satisfies those two conditions : in other words, we shall make the
following definition :
*001t. Q& = ^VJ t^R[R\{^R^R)\R(iR] Df.
Moreover, as we shall have frequent cause to refer to the relation
{ — P — P)l, C'P, and as this expression is rather unwieldy, we shall
abbreviate it as follows :
*0-02. P^^ = {J-P^P)1 C'P Df.
Now the question arises, how are the members of cs related to
series ? How, for example, is the relation between an event and
another that completely succeeds it related to the relation between
an instant and another that follows it ? Two methods of procedure
are open to us ; we may define an event as a class of instants, and
derive succession between events from that between instants, or we
may define an instant as the class of all the events that occur at it.
Both these methods seem to have certain inherent disadvantages :
if we choose the first method, then we cannot consider the possi-
bility of several events occurring with the same times of beginning
and ending, whereas if we choose the second alternative, we cannot
consider the possibility of all the events of one moment happening
also at another and vice versa. However, we shall choose the
latter method of procedure, since cs is a more general notion than
ser. This can be proved as follows :
h . R K^R^R) \R = R\ [(^R^R) ^ C'R] \ R
= R\xy {x — Ry .y — Rx .x,y eG'R)R (1)
* In this paper, 'ar-is-simultaneous-with-respect-to-ii to?/' will be interpreted
as meaning x\G{-R^R)l G'R] y.
t I follow the method of the Principia Mathematica of Eussell and Whitehead.
444 Mr Norbert Wiener, A Contribution to the
\-:Reconnex.D.R\{-R-R)\R = R\ccy(a; = y)\R
= R\I\R
= R\R (2)
[■: R eser. D.R\{-R-R)\R a R.ReRV J.
D.Recs (3)
I- . (3) . D h . ser C cs.
Moreover, it has been shown by Mr Russell that it is advan-
tageous for purposes of methodological simplicity to regard the
instants of time as constructions from its events. This is an
additional reason for starting from the members of cs and forming
certain members of ser as functions of them. Let us, then, agree
that an instant, for example, is to be regarded as a class of events,,
and a point on a line as a class of the segments of the line, for the
purposes of this paper. The question then arises, when is a class
of events an instant, and when is a class of segments a point ? It
is obvious on inspection that not every class of events is an instant :
all the events which make up a given instant must be simultaneous-
with one another, and all the events which are simultaneous with
every member of the instant must belong to that instant. More-
over, A must not be an instant. It can also be seen readily that
any class satisfying these conditions will be an instant. That is,
if P is the relation of an event to an event which completely follows
it, it is a simple matter to show that the class of all instants is
One instant precedes another when and only when some event
belonging to the one entirely precedes some event belonging to
the other. That is, calling the relation of precedence between
instants inst'P, we can easily show that we have
\-.inst'P = (^''P)ta{a = p'F,^"a}.
Let me now make the following definitions for any value
of P:
— *
*0-03. Tp = a {a = p'P,^"a} Df
*0-04. inst = QP{Q^(^'^P)tTp} m
I wish to show that
1- . inst"P {R\R,^\R(1R}C ser,
* This definition is due to Mr Kussell.
Theory of Relative Position. 445
; and hence that
h . inst"cs C ser.
: This shows us how we can construct a serial relation from any
relation of the same sort as complete succession ; or, indeed, from
' any relation agreeing with it in only one respect.
*0-l. V . inst"^ [R\R^^\RQ.R]Q ser.
Proof.
It is easy to show that
\ H:ainst^P/3. = .
— > — >
a = p'Pse"^ ■ ^ = P'Pse"^ ■ (a^-S y).ocea.ye/3. xPy (1)
from the definitions of inst and xp. From this we can deduce
h : a inst'P/9 .D./3 = p'Pg/'^ . (3^, y) .xe a.y e 13 .'^ ^PseV^
since, by the definition of Pge, xPy and xP^^y are incompatible.
This reduces to
V : a inst'P/3 . D . ;S =p'P^^''^ . (g-^) .cc6a.^(x ep'P,^''/3),
from which we can deduce
t- : a iust'P/3 . D„,^ . aJ/3
or h . instep € m'J (2)
Also, we find from (1) that
h : a inst'P/9 . ;8 inst'P7 . D .
a=p'P,/'a . ^ = p'P,,''^ . 7 = l>'Ae"7 •
(a^' y,u,v) . X € a . y,u € ^ .V 6<^ . xPy . uPv.
This implies
h : a inst^P/3 . /3 inst^P7 . D .
— > -^
a = p'P^^"ci . 7 = p'Pse"'y ■ (a^, ■«) . a; e a . v 6 7 . a;P | Pgg | Pv.
This, together with (1), gives us
h . instep {R\R,^\R(iR}C trans • (3)
By the definitions of inst and rp, we find that
h : a, ^ e O'inst^P . D . a=p'P,^"a . /3=p'Pse"/3.
By an easy deduction, we can arrive, from this proposition and
the definition of Pgg, at the proposition
h : : a, /9 6 C^nst'P . D : . a = p'PJ'a . /3 = p'PJ'/3 : .
xea.ye/S: Dx,y ■ ^Py • v . yPx . v . xP^^y,
446 Mr Norhert Wiener, A Contrihutiun to the
whence we get
h :: a,/S e C'insL'P . D :. a=p''pj'a . /S^p'P./'/S :.
or h :: a, /3 6 (7'inst'P . D :. a=p'P,^"a . /9 =p'P^^"^ :.
X eOL .y e ^ .'^x,y •'^ ^Py • '^ 2/-^*' : 15 . a C /5.
By an exactly similar argument,
h :: a, y8 6 C'^inst'P . D :. a=p'P,^"a . ^ = p'P,^"/3 :.
X e a . y e /3 . Dx,y • '^ ^Py ■ '^ 2/-f ^ : "D . /S C <x.
Combining these, we get
h :: a, /3 e C'inst^P . D :. a = p'Pj'oi . /3 = p'P^^"^ :.
X e a . y € /3 . D^, y ■ '^ *-P3/ ■ "^ 2/-P^" : 3 ■ « = /3.
This we may write as
h ::a,/3e C'mst'P . D :. a=p'P,^"a . ^8 = fPJ'^ :.
(g^, y) .xea. y € . xPy : v : (ga?, y) . x ea . y € ^ . yPx : v : a = /3.
By (1), this becomes
h :. a, yS 6 C'inst'P . D : a inst'P/3 . v . /3 inst'Pa .v .a = /3,
or h . instep e connex (4)
Combining (2), (3), and (4), we get the desired conclusion :
namely,
I- . inst"P {P I P,e I ^ G P} C ser.
From this we can easily conclude that
h . inst"cs C ser.
It will be noticed that two of the three serial properties of
inst'P — its being contained in diversity and its connexity — are
independent of the properties of P itself. It is especially notice-
able that no use is made of P QJin proving inst'P G J, nor, indeed,
in deducing any of the serial properties of inst'P. inst is a valuable
tool for what Mr Russell calls "fattening out" a relation: i.e.
deriving from a non-serial relation a relation with many of the
properties of series*.
It is interesting to consider under what conditions inst'P will
be compact. If we define csd as follows :
*0-2. csd = cs r% P {P G P I P,e I ^ ■ ^ I ^se G P I min^j j R,^} Df,
* Since writing this article, I have discovered an operation which will turn any
relation into a series (though not necessarily au existent one) and will leave un-
changed the relation -number of any series to which it is applied. It is the
operation which transforms P into inst'[(inst'P)pj,].
;ne i
I
Theory of Relative Position. 447
[ivve shall find that R e csd is a sufficient condition for the density
of msi'R. This condition says that (1) i? is a relation of complete
sequence, (2) if x precedes y by the relation R, there are two
members of the field of R neither of wiiich bears the relation R
to the other, while x precedes the one by R, while the other
precedes y by R, (3) if x follows by R some i^-contemporary of y,
it follows some initial i^-contemporary of y. This latter condition,
which was first formulated by Mr Russell, ensures that if xeC'R
|and J?ecsd, minji' R^e' a; e Tj{. This I now wish to prove.
I — > —>
1*0-21. h : P 6 csd . X e C'P . D . minp'P,,'x e rp.
Proof.
— >
It follows from the definition of p'k and miup'a that
h . p'P,,''^np''PJx = §{ae 'PJ'['P,,'x n G^P-P''?,,'x] .X.yea}.
Since it follows from the definition of Pgg that h . CPg^ C C'P,
, this reduces to
I }- . p'P,e"tmnp*P,e'^ = y{oie 'Pse'W^ - P'^Pse'^] ■ ^a ■ 2/ 6 a}.
This becomes by a little manipulation
h . p'P,e"minp'P,e'^ = y {zP,^ x . z-P\P^^x .D,. yP^^ x] (1)
On the other hand, it follows from the definition of minp'a that
— > — > ^
h . minp^Pge'^ = y {yP^^ x.y^P\P^^x].
Since by definition any R which belongs to csd satisfies the
condition, R \ Pgg G R \ miup j Pgg, we get
— » — > w — >
h : P e csd . D . miup^Pgg'a; = y {yPge x . y — P\ miup | P^g x].
From this we may deduce
I f- : P 6 csd . D . minp'Pgg'a; = y {yPge oc :.
zP^^ X .z — P\ Pgg ^ : D^ : yPz . v . y — Pz . z — Py . y, z e C'P].
But when yPz is the coirect alternative in the conclusion of the
second proposition in the brackets, together with yPseOC, this gives
us ^P|Psea;, which contradicts the hypothesis. Hence, by the
definition of P^g, we have
h : P 6 csd . D .
— » — » w
minp'Pgg'^ = y {yP,, x : ^P^g ^ . ^ - P j P^g d; . D, . yP^^ z] (2)
448 Mr Norhert Wiener, A Contribution to the
Now, it is part of the hypothesis F e cscl that PQ.J. From this it
is easy to deduce that / [^ C'F G Pgg, or that a; e G'P . "^^ . xP^^x.
Moreover, it follows from the definition of P^^ that yPx and yPs^a^
are incompatible hypotheses, and hence that x — P\ Pgg x. This
fact, combined with (1), gives us
hiPecsd.xeC'P .D . p'P,^''mmp'P,^'x
= y [y^se ^ ' ^Pse x.z-P\P^^x.D,. yP^^ z] (3)
From (2), (3), and the definition of xp, we have
h : P e csd . *• 6 O^P . D .
-:> -> —►-:>-♦ -:> — >
minp'Pgg*^ =p'Pge"minp'Pge'« ■ ^ ■ minp'^Pgg'^ e Tp.
This is the desired proposition.
It will be observed that the only portions of the hypothesis
of P e csd of which we actually make use in this theorem are
^-' v-/ y
P dJ and P| Pgg GP| miup | Pgg. The theorem ensures us that
f- . G'P C s^Tp : that is, in the case of time, that each event shall i .
be at some instant — the instant at which it begins. For, since {'
—> \
PQ.J, I [ G'P QPgQ. This ensures that xeP^^x. Moreover, as
'-' '-' — ^
we have just seen, ^ — PlPgga;, or x e — P"P'x. Therefore, if !
— > ^ — > -^ ^ J
X e G'P, X e Ps%x r\ G'P — P'^P^^'x, or ic e miup^Pge'*'. As we have ;
~^ — > I
proved in *0*21 that minp'Pgg^^ e Tp, we get the formula
l-.C^PCsVp. 1
I now wish to prove that inst^'csd C comp.
*0"22. H . insf'csd C comp.
Pnoof.
As we saw in *0*1, (1),
h : a inst^P/3 . = . a =p'P,e"^ ■ ^ =p'P,e"^ ■
(a«, y) .xea.ye ^ . xPy.
Since R e csd, by definition, implies Rd R\ i^gg | R, this gives us
h:.Pecsd:D:ainst^P/g.D.
CL = p'PJ'a . /3 =p'PJ'^ . i'^x, y) . A- 6 a . 2/ e /3 . aP I Pge I Py.
Theory of Relative Position. 449
w \j — >
Since R e csd also implies R\R Q. R\ min^ | R^^, this becomes
> : . P e csd : D : a inst^P/3 . D . a = p'Pse"" ■ /3 = fP^s'^ ■
— »
(a«, y).xea.ye^.xF\ [miiip ] P^^] | P^/.
icP I [minp I Pse] j Py says that there are a ii and a v such that
— >
a;Pit, ■yPy, and wminpjPge?*. This latter proposition is equivalent
to ?; e minp^Pge^'i*. We have just seen, moreover, that u e minp'Pge u,
— » — >
land that minp^P^e u e rp. This gives us
|-::Pecsd:. D :.ainst'PyS: D :
(aw, v) : a=p''pj'a . /9 = p'P«e"/3 . rdup'^e'u e^/P,e"nmip'P,/w :
-^ — >
'(3*) y) -xea.y e ft .u,ve mmp'P^^'u . xPu . yPv.
■From this and *0'1, (1) it is an easy matter to deduce that
> :. P e csd : D : a inst'PyS . D . (37) . a inst'P7 . 7 inst'P/S.
This gives us immediately
h . inst"csd C comp.
It will be noticed that it is not true that csd C comp. For
example, if P is the relation of complete succession between one-
inch stretches on a line, P will be a member of csd, and an inch
stretch beginning half an inch after the end of another will bear
the relation P to it, yet there will be no inch stretch to which the
first bears the relation P and which bears the relation P to the
second. P G P | Pgg | P is a weaker hypothesis than P G P", which
implies it if P G J.
450 -Mr Oxley, On an Application of the Molecular Field
On an Application of the Molecular Field in Diamagnetic\
Substances. By A. E. Oxley, B.A., Coutts Trotter Student;
Trinity College.
[Bead 23 February 1914.]
It is well known how Nernst and Lindemann* have extended i
the formula, given by Einstein, fur the variation of the specific!
heat of substances with temperature. Although the new formula [
expresses the experimental results with moderate degree of ac-!
curacy, yet, in the neighbourhood of the fusion point, there is an '
abnormally large departure, the experimental value of the specific ;
heat being always greater than the calculated value. The j
empirical expansion term, a^^ (^^ coefficient of expansion ; ^, |
absolute temperature), used by Lindemann does not satisfactorily j
account for the discrepancy f.
Later DebyeJ has modified the Planck-Einstein theory and \
given a relation between the thermal properties and the elastic
constants of a substance.
In a crystalline substance we must regard the molecules as
subjected to large local forces which hold the molecules in position
in the crystalline structure, and if at the higher temperatures
the molecules begin to vibrate under the control of these forces,
then we should expect the experimental value of the specific heat
to be greater than that calculated on Debye's theory §.
It has been shownlj that we may interpret the forces which i
hold, the molecules in position in a diamagnetic crystalline struc-
ture, magnetically, and if we do so the magnetic energy associated
with one gramme of the substance may be written If
"i^ (!)■
* Sitz. d. i^reuss. Akad. d. Wiss., p. 347, 1911.
i- See the memoirs by Nernst and Einstein, La Theorie du Rayonnement et les
Quanta, Paris, 1912 ; particularly p. 272.
+ Ann. der Phys., iv. vol. 39, p. 789, 1912.
§ See Jeans, Phil. Mag., vi. vol. 17, p. 771, 1909. I am indebted to Mr Ezer
Griffiths for pointing out the work of Jeans in this connection.
II A. E. Oxley, Phil. Trans. Roy. Soc, 1914 (Unpublished).
1[ On the electron theory of magnetism developed by Langevin, a diamagnetic
molecule has no initial magnetic moment and the resultant force due to it will be
negligibly small except at points whose distances from tbe molecule are comparable
with molecular dimensions.
If i be the local magnetic moment between any two molecules and h the local
intensity of the magnetic field, then the magnetic energy associated with one c.c.
of the substance is
- 2 I i 1 1 /j I
in Diamagnetic Substances. 451
where aj is the cuustant of the molecular held of the diamagnetic
substance, / is the aggregate of the local intensities of magnet-
ization per unit volume, and p is the density of the substance.
This is analogous to the case of ferro-magnetism, given by Weiss*,
where the magnetic energy term is
NT'
~2jj ^^'g^^ P^'^' g^'^"^-
N is the constant of the ferro-magnetic field, / the saturation
intensity of magnetization and D the density of the substance.
I If, as the diamagnetic crystalline substance is heated, the
molecules perform rotational vibrations under the influence of
the intense local forces, more heat must be supplied for a given
rise of temperature than would be necessary if the molecules did
not rotate. The corresponding increase of specific heat is given
by the term
ttc Id I .„.
2Jp- d^ ^ ^'
where J is the mechanical equivalent of the calorie.
The molecular field, by which we may interpret the forces
within the crystalline structure, is a//, and is of the order of
: magnitude of the ferro-magnetic field of Weiss (IC gauss). Hence,
, as in the case of ferro-magnetic substances, we may expect that
the above term will form an appreciable fraction of the specific
heat. Moreover, the expression (2) passes through a maximum
in the neighbourhood of the fusion point.
In so far as we can test the above experimentally, there seems
to be evidence in favour of the additional specific heat represented
i by (2). For sodium^ and mc-rcury'l there is a decided maximum
of the specific heat in the neighbourhood of the fusion point such
as (2) demands. A large number of substances have been in-
vestigated by Nernst and Lindemann§, and they found that in
general the specific heat is abnormally high as the fusion point
is approached.
This work will be continued in a future paper.
if all the contained elementary systems are independent. Let n be the number of
molecules per c.c, then we may write |S| i 1 1 /* !=|«t/i. h corresponds to the
molecular lield in ferro-magnetism. If we write ni — l and ]i = a^ .1, we find that
the energy associated with one c.c. of the substance is ~- — .
* Journ. de Phys., Ser. iv. vol. 7, p. 249, 1908.
t Ezer Griffiths, Proc. Roy. Soc, vol. 89 A, p. 561, 1914.
+ The values for mercury were taken from the Tables of Physical Constants
published by the Societe Frangaise de Physique, 1913, p. 305.
§ La Theorie dii Rayonnement et les Quanta, Paris, 1912.
CONTENTS.
PAGE
The oxygen content of the rivet' Cam before and after receiving the Cam-
bridge seivage effluent. By J. E. Purvis and E. H. Black. (Three
figs, in Text) . . . . 353
Oh Root Development in Stratiotes aloides L. vnth special reference to
the occurrence of Amitosis in an embryonic tissue. By Agnes Arber.
(Communicated by Dr Arber.) (Plates VIII and IX) . . . 369
Amitosis in the Parenchyma of Water-Plants. By R. C. M'^Lean.
(Communicated by Professor Seward.) (One fig. in Text) ; . 380
The History of the occurrence of Azolla in the British Isles and in Europe
generally. By A. S. Marsh. (Communicated by Professor Seward) 383
A Simplification of the Logic of Relations. By N. Wiener. (Com-
municated by Mr G. H. Hardy) . 387
A Double-Four Mechanism. By G. T. Bennett. (Two figs, in Text.)
(Plate X) . . .391
On the Natitre of the Internal Work done dioring the Evaporation of a
Liquid. By R. D. Kleeman. (Two figs, in Text) . . . . 402
The Work done in the Formation of a Surface Transition Layer of a
Liquid Mixture of Substances. By R. D. Kleeman . . . 409
The ionisation produced hy certain sxibstances when heated on a Nemst
filament. By Frank Horton. (Two figs, in Text) . . .414
Fluctuations of sampling in Mendelimi Ratios. By G. Udny Yule . 425
A Case of Repulsion in Wheat. By F. L. Engledow. (Communicated
by Professor Biffen) . . . . . . . . . 433
The determination of the best value of the coupling -ratio from a given set
of data. By F. L. Engledow and G. Udny Yule . . . . 436
A Contribution to the Theory of Relative Position. By Norbert
Wiener. (Communicated by Mr G. H. Hardy) . . - . . 441
On an Application of the Molecular Field in Diamagnetic Substances.
By A. E. OxLEY . . . 450
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