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Full text of "Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences"

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 



PEOCEEDINGS 




OF THE 



CAMBRIDGE PHILOSOPHICAL 
SOCIETY. 



VOL. XVII. PAET I. 



[Michaelmas Term 1912.] 




AT THE UNIVERSITY PRESS, 
AND SOLD BY 
DEIGHTON, BELL & CO. AND BOWES & BOWES, CAMBRIDGE. 

CAMBRIDGE UNIVERSITY PRESS, 
C. F. CLAY, MANAGER, FETTER LANE, LONDON, E.C. 

1913 
Price Two Shillings and Sixpence 



14 February, 1913. 



NOTICES. 



X. Applications for complete sets of the first Seventeen 
Volumes (in Parts) of the Transactions should be made to the 
Secretaries of the Society. 

2. Separate copies of certain parts of Volumes i. — xi. of the 
Ti'ansactions may be had on application to Messrs BoWES & 
Bowes or' Messrs Deighton, Bell & Co., Cambridge. 

3. Other volumes of the Transactions may be obtained at 
the following prices: Vol. xii. £1. IO5. 6d.; Vol. xin. £1. 25. Qd.; 
Vol. XIV. £1. lls.Qd. ■ Vol. XV. £1. 12s. 6d. ; Vol. XVL £1. 10s. Od. ; 
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4. Complete sets of the Proceedings, Volumes i. — xVL, 
may also be obtained on application to the Secreta^ries of the 
Society. 

5. Letters and Communications for the Society should be 
addressed to one of the Secretaries, 

Mr O. H. Hardy, Trinity College. [Mathematical.] 
Mr A. Wood, Emmanuel College. [Physical] 
Mr F. A. Potts, Trinity, Hall. [Biological.] 

6. Presents for the Library of the Society should be ad- 
dressed to \ 

The PItilosophical Library, 

New Museums, 

Cambridge. 

7. Authors of papers are informed that the Illustrations and 
Diagrams are executed as far as possible by photographic "process" 
work, so drawings should be on a large scale and on smooth white 
Bristol board in Indian ink. 

8. Members of the Society are i-equested to inform the 
Secretaries of any change of address. 



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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in the Maldive Islands and Minihoi. 



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 



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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) . . . . . . . 



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168 
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PEOCEEDINGS 



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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, 
AND SOLD BY 
DEIGHTON, BELL & CO. AND BOWES & BOWES, CAMBRIDGE, 

CAMBRIDGE UNIVERSITY PRESS, 
C. F. CLAY, MANAGER, FETTER LANE, LONDON, E.C. 

1914 

Price Two Shillings and Sixpence 



30 January, 1914. 



NOTICES. 

1. Applications for complete sets of the first Seventeen 
Volumes (in Parts) of the Transactions should be made to the 
Secretaries of the Society. 

2. Separate copies of certain parts of Volumes i. — XI. of the 
Transactions may be had on application to Messrs BowES & 
Bowes or Messrs Deighton, Bell & Co., Cambridge. 

3. Other volumes of the Transactions may be obtained at 
the following prices : Vol. xn. £1. 10s. Qd.\ Vol. Xm. £1. 2s. 6d. 
Vol. XIV. £1. 17s. U. ; Vol. xv. £1. 12s. U. ; Vol. xvi. £1. 10s. Orf. 
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4. Complete sets of the Proceedings, Volumes i. — xvi., 
may also be obtained on application to the Secretaries of the 
Society. 

5. Letters and Communications for the Society should be 
addressed to one of the Secretaries, 

Mr G. H. Haedy, Trinity College. [Mathematical.] 
Mr A. Wood, Emmanuel College. [Physical] 
Mr F. A. Potts, Trinity Hall. [Biological] 

6. Presents for the Library of the Society should be ad- 
dressed to 

The Philosophical Library, 

.New Museums, 

CawJ>ridge. 

7. Authors of papers are informed that the Illustrations and 
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work, so drawings should be on a large scale and on smooth white 
Bristol board in Indian ink. 

8. Members of the Society are requested to inform the 
Secretaries of any change of address. 



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.] 




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CAMBRIDGE UNIVERSITY PRESS, 
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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 

oxygen taken 

up in 5 days 

in grams per 

100,000 



The 
rainfall 



inches 



o-Soo 






































(.00 


o-iiW 




















1 


















0-9^ 


o-4ii> 






































o.</o 


o-uis 






































o?.c 








































oW. 


o-3<ts 






















1' 




h 










o.yy 


oiso 


















. 




■ 




1 < 
/ » 










o-Y" 


0-3iS 






















■1 


1 


' » 








/ 


o.«y 


0-3oo 






















; 
1 




', / 




\ 






/ 
/ 


o-fo 


o.jyr 






















1 




1 1 




\ 




J 




o-«- 


0-3.SO 






















v/ 1 




i 




V 




y 






o-sa^s- 




















1 


















o-i/s 


O-loo 




























A 










O-Ha 


o-ifi- 


















\ 
\ 








}\ 










o-is 


O.ISo 


\ 
















1 








I 












OSo 


b.iiS 












h 






1/ 








/ 


I 










ff.<y 


o-ioo 


\; 




>\ 






l\ 










1 




/ 


' 




A 


k / 


/ 


OIO 


. a.ofs 


\ 


J 


^ 






\ 




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I 


, 


1 


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O-OSO 






\ 


sy 


1 


k 


V- 


.J 1 














/ 








O- 10 


oais- 








V 


--7 


\ 


















y 








o-s- 


O-OOo 












1 


U 
















V 








O'O 




1 


* 
'"^ 


3 
13 


t. 






1 




9 


6t< 


II 

1? 


11 


13 

hrtr 


14 


ir 

If- 


I* 


n 
■Rtt 

3 


%% 





dissolved oxygen absorbed in five days in grams per 100,000. 

"— ^ rainfall in inches during the four days previous to that on which the sample 
was taken. 

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 





lO-o 






-r 














Ao 




as 




















1? 


a 

g 


OO 


\ 


1 


1 \ 

/ ^ 


\ 

\ 












/6 


o 

CO 


P-^ 


\ 


y 


/ 










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1^ 


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o 


S'O 




/ 




\\ 

\\ 

\\ 




^ 




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I 

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/ 




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\ 


\ 

\ 


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o 

6 




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/ 








\ 








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\ 
\ 
\ 


/ 


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CO 

m 

s 

IB 


6-0 










\ / 
\ ' 

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// 


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O 


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1^ 


J 








ci 




S'O 










1/ 

















\ 


a. 


3 


h' 






V 


3 







- w 



dissolved oxygen in c.c. per litre at 0° C. and 760 mm. 

— ^— 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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Camkiirgt ^l^iksopl^kal Sorirfg, 



Thom^psonia, a little known Crustacean Parasite. (Preliminary Note.) 
By F. A. Potts, M.A., Trinity Hall. 

[Read 4 May 1914.] 

Thompsonia is a genus of Cirripedia belonging to the parasitic 
family the Rhizocephala, and was first noted by Kossmann* in 
1874 as a parasite upon the small crab Melia tesselata from the 
Philippines. Since that time it has been described by Coutieref 
under the name of Thylacoplethus as a parasite of Alpheids in East 
Indian and Australian waters, and by Hafelej and Kruger§ from 
the crab Pilumnus and the hermit crab Eupagurus middendorfii 
off the coasts of Japan. I have little hesitation in including all 
these forms in the same genus, even though Thompsonia thus 
enjoys a far greater diversity of hosts than any other Rhizocephalan, 
for as a rule each genus is strictly confined to the same subdivision 
of the Decapoda. In 1913 I accompanied the expedition of the 
Carnegie Institution of Washington to Torres Straits at the kind 
invitation of Dr A. G. Mayer, and during a short stay at Murray 
Island I collected nearly twenty individuals of a speci