Full text of "Jena glass and its scientific and industrial applications"

JENA GLASS

AND
ITS SCIENTIFIC AND INDUSTRIAL APPLICATIONS

-TC.
JENA GLASS

AND

ITS SCIENTIFIC AND INDUSTRIAL
APPLICATIONS

DR. H. HOVESTADT

TRANSLATED AND EDITED BY

J. D. EVERETT, M.A., F.R.S.

AM'

ALICE EVERETT, M.A

Bonbon
MACMILLAN AND CO.. LIMITED

NEW YORK: THE MACMILLAN ooui \s\
1902

AU rifktt rwrrr**

GLASGOW: PRINTED AT THE UNIVERSITY PRESS BY

ROBERT MACLEH08E AND CO.

AUTHOR'S PREFACE.

THIS book is mainly devoted to an account of the physical and
chemical properties of the various types of glass which have
up to the present been produced at the Jena Glass-making
Laboratory, and to an indication of their scientific and industrial
applications. The experimental and theoretical investigations
relating to these glasses which are scattered through various
journals, or have been published as separate monographs, are so
numerous that a comprehensive summary of them has for some
time been urgently needed.

When I undertook this task, I had no intention of limiting
its scope to the Jena glasses. But the number of published
investigations relating to other glasses admitting of definite
identification is so small that, though they have received the
same treatment, they form only an insignificant fraction of
the whole.

If the plan of the book is somewhat out of the common, this
is only in accordance with the special character of its subject.

II HOVESTADT.
MONSTER, \t Jan., 1900.

TRANSLATORS* PREFACE.

I N endeavouring to present Dr. Hovestadt's work in the clearest
tniin to English readers, the translators have aimed at giving
the spirit rather than the letter of the original. They have
found it convenient, in many cases, to recast sentences and to

ply missing steps in algebraic proofs. Brief explanations
have occasionally been interpolated, and condensation has been
m ployed in dealing with a few matters of very subordinate
interest ; due intimation being given of all material changes.

litions are indicated by square brackets or by the ini
of one of the translators. In many cases the original memoirs
have been consulted as a security against misapprehension.
The abbreviated designations " Reichsanstalt," " Standards Com-
iiii^sion," and "Bureau International" are substituted for the
full titles " physikalisch-technische Reichsanstalt," " Normal-

lUiiLjs-Kommission," and "Bureau International des Poids
et Mesures."

The Appendix includes a summary of more recent investiga-
tions, kindly furnished by Dr. Hovestadt for this edition; also
ili- new Catalogue of Jena Optical Glasses issued in 1902,
which introduces radical changes.

The Table of Contents is intended to give a clear idea of
scope and arrangement of the book. The Index will
permit the quick finding of any desired item.

The translators desire to acknowledge their obligations to
several friends for information and advice on various points;
especially to 'Mr. H. J. Powell and Mr. \\ lls -nliain. who

> guided them in dealing with the technicalities <>f ^lass-
making.

J. D. i \ ER]
A. EVERETT.

KM IN... "'.. 1902.

CONTENTS.

CHAPTER I.

INTRODUCTION.

16. ,,,,. 1-22

Attempts at improvement of optical glasses by Fraunhofer and by
Harcourt. Abbe's appeal for a systematic investigation. Schott's
response. Mode of carrying on their joint investigation. Its results,
as described in the first trade catalogue, 1SS6. Schott's summary of
results attained, 1888. Definite effects of different elements. Fine
annealing. Schott's sketch of the process of making ordinary optical
silicate glass. Supplementary lists, 1888 ami ivi-J. Improvement of
the microscope, 1886; telescope, 1899. Thermometer glasses. Thurin
gian glass and its alumina. Glasses for withstanding heat and chemical
attack.

CHAPTER II.

OPTICAL PROPERT 1 1 :> OF GLASS
7 -31. pp. 23-81

Abbe's mode of specifying refracting properties of a glass. n, A.
3, , a , i, a, /*, y, v=(n n - 1 )/A. List of 76 Jena glasses. Achromatizing
one glass by another. Secondary and tertiary spectra illustrated by
curves. Approximately constant relation between n and A for the old
glasses. Hypochromatic and hyperchromatic doublets. Chromatic
difference of spherical aberration. Infra-red and ultra-violet sp* t
Absorption, and its connection with dispersion. Measurements of
absorption for .lnl.-i . i.t parts of the spectrum. Calculation of coefficient*
of absorption. Influence of temperature. Optical properties of quickly
cooled glasses ; discs acting as diverging lenses. rUy-curvature, and
focal length. Double refraction of quickly cooled plates ; and iU gradual
disappearance with heating. Litmin^ temperatures. Testing

1 plates by polarised light Kllipt., poferiwf
from glass.

JENA GLASS.
CHAPTER III.

PERFECTING OF OPTICAL SYSTEMS BY THE NEW

< ; LASSES. THE MICROSCOPE.
32-44. pp. 82-94

Numerical apertuiv, and limits of performance. Useful magnification.
Mairnification by objective, and amplification by ocular. Aberration-
constant of objective. Old achromatic objectives. Apochromatic ob-
jectives. Less necessity for high power in objective. Increased range
of magnification. Chromatic difference of magnification corrected by
compensating eyepiece. The ray-union obtained is of the eleventh
order. Photographic and visual images in same plane ; micro-photo-
graphy. Optical properties of fluor-spar ; its introduction into micro-
scopic objectives by Abbe. Trials on test objects. Monobromouapthalin
immersion. Projection eyepieces ; projection objectives ; semi-apochro-
matics.

CHAPTER IV.

PERFECTING OF OPTICAL SYSTEMS (Continued}.

PHOTOGRAPHIC OBJECTIVES.
| 45-51. pp. 95-111

Astigmatism and curvature of image. Testing of objective for astig-
matism. Graphical representation of field-curvature and astigmatic
difference. Distortion. Miethe's use of phosphate crown and borate
flint. Steinheil's aplanat. Anastigmatic aplanat. Apochromatic
triplet. Normal and anomalous doublets, or old and new achromats.
Voigtlander's use of light baryta flints ; their transparency to chemical
rays, with flattening of primary image. Ross' concentric lens, calculated
\>y Schroder. Zeiss' unsymmetrical anastigmats, calculated by Rudolph.
Goertz' double anastigmat. Voigtlander's collinear. Zeiss' anastigmatic
lenses. Steinheil's orthostigmatics. Zeiss' spherically and chromatically
corrected objective, with hyperchromatic diverging lens. Specifications
of triple and quadruple objectives.

CHAPTER V.

PERFECTING OF OPTICAL SYSTEMS (Continued).
52-53. pp. 112-114

Achromatic diverging lenses. Rudolph's improvement, by using two
components of the same mean index.

CONTENTS. xi

CHAPTER VI.

PERFECTING OF OPTICAL SYSTEMS (Continued}.

TELESCOPES.
54-66. pp. 115-144

Hand telescopes with inverting prisms, giving 4 reflections. Porro's
invention. Field glasses, and relief binoculars. High transparency
necessary in the prisms. Resolving power, and brightness of image, as
depending on size of objective. Vogel's calculations for the Potsdam
photographic telescope. Haiting's calculations for cemented doublets.
Chromatic aberration in objectives of great focal length. Lick, Potsdam,
and Vienna telescopes. Czapski's calculation of objectives of phosphate
crown and borate flint ; and Vogel's testing of the objectives. Successful
employment of more durable glasses ; and tests by Wolf of an objective
calculated by Pauly. Cooke triple objective calculated by II. 1). Taylor,
of borosilicate flint, baryta light flint, and silicate crown. Two-part
Gaussian objective, by Hamburg, from Czapski's calculations ; it*
chromatic aberrations exhibited for central, marginal, and intermediate
zone. Lummer's Gaussian objective for collimator of spectroscope.
Description of Zeiss' objectives.

CHAPTER VII.

M IX'HANICAL PROPERTIES OF GLASS.

67-85. 1>1. 145-193

Winkelmann's list of 72 glasses. Density as dependent on chemical
npo.sition. Tenacity, and its relation to composition. Resistance to
crushing, and its relation to composition. This resistance is from 9 to
Mies the tenacity. Comparison with i-arlier experiments !

Iski. Lens strength at higher temperatures. Young's modulus,

from observations on flexure of a rod loa.l.-.l in the middle. Observations

at higher temperatures. Relation to chemical composition. Discusxion

of results at high temperatures. Hardness of glass investigated by

Uich, by an indentation method devised by Hertz. Confirmation of

/' theory, and calculation of iixl.nt.it ion-modulus. Deduction of

Poisson's ratio. Limiting amount of pressure is proportional to radius

ivMure. Best mode of expressing hardness by a single number.

Scratching. Active and passive scratching hardness follow different

Hardness in relation to composition. Hardness of pis-
bodies like rock salt. rY.ppl's experiments on metals. Position of glass
in Moli*' scale of hardness. Compsruon with other mechanical properties
of glass. Poisson's ratio investigated by Straubel, using a on

Cornu's imtho.l, in u liich system i-.-rboUs are formed by

interference. Results for 29 glasses. The values range from 197 to
on with Auerbach's deduced values. Straubel's de-
ductions of volume elasticity and " nimple rigidity."

xii .IKNA CLASS.

CHAPTER VIII.

THERMAL PROPERTIES OF GLASS.
86-108. pp. 194-238

Winkelmanii's measurements of specific heat, and comparison with
composition. Paalhorn's observations on conductivity by Christiansen's
" conducting column " method. Relation to composition. Voigt's method
of comparing two conductivities by observation of isothermals. Applied
by Focke to 25 glasses. First mode of comparison with composition ;
discordant results. Second mode, in which reciprocal of conductivity is
regarded as a linear function of the percentages. Expansibility, and its
relation to composition. Influence of stress. Expansibility as a function
of temperature. Observations on the expansion of rerre dur, 16 111 , and
59 m . Thiesen and Scheel's distinction between Normal expansion and
Principal expansion. Observations up to 220 by Reimerdes. Compen-
sation vessels. Compound glass, and its use for resisting sudden changes
of temperature. Thermal endurance of various glasses, tested by sudden
changes. Theoretical discussion. Laboratory glass, and lamp chimneys.

CHAPTER IX.

AFTER-WORKING AND THERMOMETRY.

109-129. pp. 239-318

Secular rise of zero. Depression of zero by heating. Definition of
"depression-constant." Weber's investigation of its dependence on the
composition of the glass. Its large value for very fusible alkali glasses.
Greatest when the soda and potash are about equal. English thermo-
meter glass. Regnault's Choisy le Roi glass. Tonnelot's pure soda
glass rerre dur. Jena experiments with new glasses ; h'nal selection of
the "normal thermometer glass" 16 m , and the borosilicate glass 59 IIr .
Greiner's "resistance glass"; the Jena baryta-borosilicate 12'J 1 ".
Course of recovery from depression. Secular rise. Artificial ageing.
Comparisons of different mercury thermometers with air thermometers.
Depression as dependent on the degree of heating. Formulae, and values
for different glasses. Exact relation between after-working of glass and
change in reading of thermometer. Depression in boiling-point thermo-
meters is fatal, if large. Practical tests. Thermometers of 59 Iri or Hi 11 '
are fit to take the place of barometers in extended travels. Creeping up
of thermometers with long exposure to high temperatures. Comparisons.
Observations up to 500 with nitrogen above the mercury. Ei)i*<-hliix*-
f /i i // /lometer and Stabthermometer. Seasoning of high temperature
thermometers. Rise of zero as a consequence of relief of stress. Increase
of "fundamental interval." Wiebe and Bottcher's comparisons of
mercury thermometers with one another and with air thermometer.

CONTENTS. xiii

Formula for reduction to air thermometer. Griitzmacher's comparisons
ami tables of reduction to air thermometer. Thiesen's discussion of
relative expansions of liquid and envelope ; with application to diluto-
meter as observed by Mahlke. Reduction of mercury thermometers to
hydrogen thermometer. Thermometer with compensated after- working.
Elastic after- working and its relation to composition. Relation of
after-working to other physical properties.

CHAPTER X

CHEMICAL BEHAVIOUR OF GLASS SURFA< 1 >

130-146. pp. 319-371

List of references. Corrosion in spirit levels containing watery ether.
Mylius' experiments with pounded glasses. Weber's test by colour-
reaction. Mylius' colour test with iod-eosin. Soaking in of water.
Mylius and Foerster's systematic comparison of glasses. Comparison of
commercial glasses. Analysis by F. Kohlrausch of dissolved matriial.
Mylius and Foerster's titration with millinormal solutions. Application
to chemical flasks and bottles by eminent makers. Tests with u.it>r
above 100 ; gauge-tube glasses. Weathering of glass surfaces. Kohl-
rausch's tests by electric conductivity of solution; \\aUt in bottles;
]H.\vdered glass. Hygroscopic gain of weight in powdered glass exposed
to air. Improvement of glass surface by long contact with water.
I'm itication of distilled water. Action of dissolved alkali on glass.
Action of acids ; the stronger the acid the weaker the action. Lime
glasses. Lead glasses. Action of saline solutions ; carbonate of soda.
Reinitzer's use of Jena laboratory -glass for measuring small quantities
of alkali contained in large quantities of water.

( HAPTKR XI

II;K AM M \. \ETO-OPT1C PROI

PI-. :i:-j-385

ink-ally bad glasses insulate badly. Transparency for X-rays;
influence of the several components; rare earths. Small e\|.an-.il.ihty
<>f the best glasses; precautions in seal ing- in the wire. I

mts ; Starke's d uendenoe on frequency of ..

i. Absorption of electromagnetic radiut \.i.i.-'- ntant

i'-al glasses. Zeiss' standard plates for measuring field-
Recent investigation by Jungbans.

xiv JENA GLASS.

APPENDIX.
REVISED LIST OF JENA OPTICAL. GLASSES, pp. 387-393

ADDITIONS BY DR. HOVESTADT
(Besides Art. 155).

FAO*

A. Coloured glasses, - 394

B. Opal Glass, - 397

C. Durax glass for gauge-tubes, 398

D. Depression of zero by heating, 399

E. Reduction of mercury thermometers of m 16 and 59 ni to the hydrogen

scale, 400

F. Influence of temperature on thermal conductivity, - 404

G. Decomposition by air and dust, - - 405

H. Optical effects of stress, 406

NOTES BY THE SENIOR TRANSLATOR.

(a) On the name to be given to the quality represented by Abbe's symbol /, 412

(b) On the effect of employing soft pressure-plates in experiments on

crushing, * 412

INDEX, - 414

ERRATA.

p. 44, line 15, read fig. 2 (p. 41).

p. 117, line 18, for with a principal plane mirror,
read each having a plane mirror.

p. 157, line 17, for 0'2 mm., read 0'02 nun.

p. 188, lines 6, 7, 8, read entered either the camera,
or the observing telescope and apparatus for
measuring a.

p. 285, line 3 from bottom, for (100-<?)' 2 read
(100- W

JENA GLASS

AM'

ITS SCIENTIFIC AND INDUSTRIAL APl'LK . \TIONS

CHAPTER 1.
INTRODUCTION.

1. The Jena glass-works originated in successful efforts to
satisfy, by means of new glass fluxes, the increasing demands for

llence in refracting instruments. Newton 1 long ago asserted
' that it is not the spherical figures of glasses, but the different
refrangibility of the rays, which hinders the perfection of
telescopes," and this is equally true of other optical instruments.
Dollond, indeed, established the possibility (contrary to Newton's
opinion) of combining two lenses into a doublet so as to bring
pairs of colours to common foci on the axis, thus largely diminish-
ing chromatic aberration. And Gauss showed that it was further
possible, with the glasses known in his day, to render the
resulting image almost entirely free from spherical aberration.

But the development of the art of glass-making in response to

optical requirements kept, for a long time, to one narrow groove,

and no new fluxes broke the monotony of a uniform series of

us an. I Hints. 'Only* two earnest attempts were made to

produce really new and optically improved glasses, one by

inhofer, the other by Harcourt, an English clergyman. With

these two exceptions, all the efforts at improvement, and the great

prizes offered by governments and corporations, were devoted to

perfecting technical manipulation, and extending the series of

i-e flints objects undoubtedly very important in tlu-mselves.
nhofer, besides taking, in conjunction with Guinatul, a

1 Optic*, Prop. VII. (p. 4, vol. iv. t Homlcy).
'Capeki, ZeH*chr.f. In*rume*le*k. 6. 341 (1886).
A

2 JENA GLASS.

prominent part in this extension, published the results of spectro-
metric determination for seven glasses, of which two, designated
* Flint No. 1 3 ' and ' Crown Lit. M,' showed decided diminution
of the secondary spectrum. He appears, however, never to have
attempted to produce these glasses except in small quantities ;
there is no record of their having gone through the melting pot
in the way of ordinary manufacture, nor of discs for objectives
being made of them. It may be that the difficulties in the way
of producing them on a practical scale were found insuperable ; or
their mechanical properties may have rendered them unservice-
able."

" Fraunhofer's experiment was thus practically fruitless, and
Harcourt's attempts did not fare much better. Stokes, in British
Association Eeports, 1871 and 1874, has given an account of
Harcourt's work, 1 from which we learn that from 1834, for a
quarter of a century, he laboured perseveringly at his experiments,
making in all 166 different meltings. In the main he seems to
have been on the right track, though he made some mistakes.
His failure seems to have been due to want of the necessary
practical appliances. He did not succeed in producing, from his
small-scale meltings, pieces of glass sufficiently homogeneous to
enable accurate spectroscopic determinations to be made. The
uncertainty of these determinations reacted in turn upon the
experiments, by not giving sufficiently definite indications to work
from. The ultimate product of his work consisted of two ' nearly
flawless ' 3 -inch discs of ' titanium glass,' and two of borate glass.
On attempting to make a triple objective from these, it was found
necessary to reject one of the titanium discs and replace it by
a disc of ordinary crown. The completed objective, though
otherwise inferior to a good one of ordinary glass, still fully
sufficed to prove the possibility of abolishing the secondary
spectrum."

2. Some years after the publication of Stokes' reports on
Harcourt's attempts, a paper by Abbe appeared, discussing in
detail the increased requirements which must be satisfied if any
real improvement in the performance of refracting instruments
was to be obtained. Though he was speaking of the microscope,

J Czapski also refers to a report by Safarik on attempts to improve the
telescope. Vierteljahrswhr. d. astron. Ges. 17. 13 (1882).

INTRODUCTION. 3

his remarks are almost equally applicable to other refracting
instruments. He arrives at the following conclusion : l

" The future of the microscope as regards further improvement
in its dioptric qualities seems to lie chiefly in the hands of the
glassmaker. The especial desiderata are a distribution of colour
dispersion more favourable to the removal of the secondary
spectrum, and a greater variability in the relation between dis-
persion and mean index. There is now a definite basis for the
hope that these conditions will sooner or later be satisfied, and
th- way thus be opened to radical improvement in the microscope
and other optical instruments. The limitations observed in the
connection between refraction and dispersion in existing glasses
must not be regarded as a natural necessity; for among both
natural minerals and artificial products, there are plenty of
transparent substances which are known to have widely different
properties as regards refraction and dispersion, though on other
accounts they are scarcely available for optical purposes.
Further, some experiments in the production of glasses with
small secondary dispersion conducted by Stokes in England a
few years ago, though barren of direct practical result, gave
useful hints as to the specific effects of certain bases and acids on
refraction of light. The uniformity shown by existing glasses in
their optical qualities is probably chiefly due to the very limited
nuinlier of materials hitherto used in their manufacture. Beyond
lick acid, alkali, lime, and lead, scarcely any substances have
been tried, except perhaps alumina and thallium. When this
narrow groove is left, and a methodical study, on an extended
scale, is made of the optical qualities of chemical elements in
<ml.ination, we may anticipate with some confidence a greater
ty in the products.

" Unfortunately there seems little hope of material progress in
this direction in the immediate future a state of things very
<1< trimental to the interests of science. The manufacture of
optical glasses has for a long time been almost a monopoly ; so
f.-w have been engaged in it that there could be no real
competition. Since Daguet's glass-works were given up, ih. -it-
have only been two establishments which supply public demands,

1 " Die optiBchen Hilfamittel der Mikrotkopie," Bcrirkt tifor d. KM****.
OH/" d. Londoner intern. A*ut*U**g t. J. 1870, I. 417 (Brunswick,

1878).

4 JENA GLASS.

for the third (the only one in Germany), founded by Utzschneider
and Fraunhofer, is still in the exclusive service of one optical
tii in. It is true, as we are quite ready to acknowledge, that the
art has in some respects made great advances even within the
last few decades. Not only are the ordinary kinds of crown ami
Hint produced with a perfection as regards clearness, homo-
geneity, and freedom from colour, never before attained, but the
series of optical glasses has been greatly extended in one
direction by the introduction of flint glasses which far surpass
their predecessors both in refractive power and in dispersion.
But these advances are confined to traditional lines. No
inclination is shown to strike out a new departure, and endow
practical optics with materials possessing new properties. In the
absence of serious competition, it is not to the interest of the
proprietors to try experiments with doubtful hope of profit.
That an important industry, whose work is indispensable to
many of the sciences, should be dependent upon a few indivi-
duals, is a highly undesirable state of affairs. It involves the
danger (through some accident) of a complete stoppage of the
whole supply, with disastrous results. It is therefore of vital
importance, to all interests which are bound up with optics, that
there should be more workers in the field, and that a spur to
advance should be provided by increased competition.

" It is scarcely to be expected that private initiative, without
strong backing, will supply the necessities of the case in time to
prevent things from becoming much worse. The difficulties
connected with such undertakings are so great, the initial outlay
required is so heavy, and success, if attained, lies so far in
the future, that there is little inducement to enterprise. A
revolution of the industry can scarcely be brought about in
any other way than by the means for its advancement being
provided, in liberal measure, either by corporations or public
authorities.

" This is a field in which learned societies, in a position to
furnish material help for scientific requirements, could discharge
a peculiarly useful and grateful office; for very important and
diversified interests are dependent on the glass-making industry,
its continued efficiency, and its further improvement. It is not
microscopy alone that is here affected, but all sciences and arts
that need optical appliances."

INTRODUCTION. 5

3. These remarks of Abbe's induced Schott, who, from personal
study as well as from family tradition, was interested in glass-
making, to take the work in hand. He accordingly communi-
cated with Abbe, and they began in 1881 a joint investigation of
the difficult problem. The results which ensued were narrated as
regards their main features by the co-workers themselves, when,
live years later, they placed their success at the disposal of the
public. The preface to the first Trade Catalogue of the Jena
Glass Laboratory, issued in July, 1886, runs as follows:

" The commercial undertaking hereby brought under public
ii"tice is the result of a scientific investigation into the
dependence of the optical properties of amorphous combinations
nn their chemical composition, which was undertaken by the
undersigned in order to bring to light the chemico-physical
principles which underlie the manufacture of optical glass. This
work was begun in January, 1881, and, in accordance with the
plan laid duwn, Dr. Schott carried out the experimental meltings
at Witten i. \V., where he then resided ; while the spectrometric
examination of the specimens obtained was made in Jena by
Professor Abbe, assisted by Dr. Kiedel.

" The meltings at this stage were on a very small scale not
more than 20-60 gin. and were solely directed to the purpose of
studying, as accurately as possible, all chemical elements that
enuld enter in any form into the composition of glasses, as
regards their influence on refractive power and dispersion.

In this way, towards the end of that year, a series of facts, as
to the specific optical effects of certain substances, had been
ascertained, which opened up prospects of obtaining new kinds of
glass, better for some purposes than ordinary crowns and flints.

In order to render these results as far as possible available for
practical optics, it was resolved to adopt an enlarged programme,
and, on the basis of the chemico-optical knowledge already
ae<|imvd, systematically to form combinations of ingredients which,
in their optical properties, most completely satisfy the optical
desiderata, and at the same time fultil the necessary practical
ennditinns, as to hardness, durability, and freedom fmni eolour.
With this view, in the spring of 1882, I M-. s hott removed to
Jena, where, in a building taken for the purpose, we set up a
special laboratory provided with all the necessary apparatus.
With the help of gas-furnaces and motor Mown-, \\e were able

6 JENA GLASS.

to make experimental meltings on the larger scale required, up to
about 10 kgm.

"With the assistance of a young chemist for the analytical
researches, which must necessarily go hand-in-hand with the
synthetical work, and of a regular skilled operative, the experi-
ments in this laboratory were continued to the end of 1883 ;
mainly for the purpose of solving two independent problems
arising from the requirements of practical optics.

" One was the problem of. producing crown and flint pairs with
as nearly as possible proportional dispersion throughout the
different sections of the spectrum, in order to render possible a
higher degree of achromatism than the glasses hitherto in use
permitted, and thus abolish or diminish the strong secondary
chromatic aberration which silicate glasses, by reason of the
different distributions of dispersion in crown and flint, are never
able to remove in achromatic combinations.

" The second problem, which we considered not less important
than the first though its importance has not hitherto been so
generally recognised was the attainment of greater diversity in
the two chief constants of optical glass mean index and mean
dispersion.

" As a consequence of the uniformity of their chemical consti-
tution, the silicate glasses hitherto in use could be arranged as a
single series, in which, from the lightest crown to the densest
flint (with some trifling exceptions) the dispersion steadily in-
creased with the index.

" A theoretical discussion of optical problems places it beyond
doubt that the construction of instruments to fulfil simultaneously
several given conditions would be greatly facilitated, if the optician
had at his disposal glasses of the same mean index and very
various dispersions, and glasses of the same mean dispersion with
very various indices. It is therefore an important step in
advance, that the systematic use of a larger number of chemical
elements in the composition of glass has rendered such gradations
possible, and that, in several instances, the choice between avail-
able glasses, instead of being substantially of a linear character as
heretofore, has become two-dimensional. The practical realisation
of these advantages must be expected to take place gradually,
being dependent on further progress in the theoretical calculation
of optical constructions.

INTRODUCTION. 7

"To what extent our efforts in the two directions indicated
have led to tangible results, may be seen from the accompanying
catalogue of optical glasses, which have been made and can be
reproduced to order.

\Ve propose hereafter to publish a connected account of the
scientific results of these investigations, which contain the chemico-
optical foundations for the production of the different kinds of
glass. We will now only remark that these results were in the
main established before the autumn of 1883, and that the whole
investigation, as a scientific preparation for the rational manu-
facture of optical glass, would then have been brought to a
conclusion, had we not received at this time, from several eminent
ists, the suggestion that we should ourselves take in hand
the introduction of our results into practice, and follow up our
laboratory work by undertaking the commercial production of
optical glass.

\Ve accordingly, in conjunction with Drs. Carl and Roderich
Zeiss, who had materially supported our labours from the
beginning, established a glass factory at Jena, with all the
appliances for regular manufacture. By the autumn of 1884 we
were in a position to commence the wholesale production of optical
glass, both of the old and new varieties.

" We have to express our sincere thanks to the Prussian Bureau
ucation and to the Diet of the Kingdom for the very liberal
subsidies by which we were enabled to carry out the costly
experiments on a manufacturing seal*-.

After overcoming the many and great difficulties which
nvinm a branch of technology hitherto untrodden, where every
step has to be won by individual effort, this factor}* ha>
been in operation for nearly a year, ami tin- experience which
has been obtained in our dealings with most of tli- < iei m.m
factories enables us to enter confidently into public competition."

4. Tin- optical business was then a rising one in Germany, and
the immediate success of the new undertaking was due to the fact
that it met a home want Hitherto German opticians had been
dependent upon import for tli.

Meanwhile other problems confronted the promoters. Tin-

annoyance caused by the deterioration to which thermometers of

in make were subject, caused many appeals to be made to

8 JENA GLASS.

the Jena works to take in hand the improvement of thermometer
glass ; and, after some hesitation, it was decided to do so. In
March, 1883, Schott made his first trial-melting for the purpose,
and by the autumn of 1884 the firm were able to place their first
improved thermometer tubes upon the market, though experi-
ments to test the thermometric properties of different meltings
were continued for many years longer.

Under the circumstances, it will be readily understood that the
intended publication of the results of the chemico-optical researches
was long deferred, and indeed never carried out with the fulness
originally intended. Schott, however, gave some of the main
points in a paper read at Berlin in 1888. 1

When Abbe and Schott began their experiments, there were
only five glass-forming oxides whose optical effects were well
known, viz. : silicic acid, potash, soda, lead-oxide, and lime. In
the case of optical glasses, the necessary requirements placed
difficulties in the way of introducing new elements.

The flux must not act upon the material of the crucible, and so
absorb impurities.

Elements which evaporate during the process tend to produce
veins, and should not be used.

Cloudiness, crystallisation, and bubbles, must be avoided in the
operations of melting, cooling, and subsequent reheating to the
verge of melting ; this last being necessary for shaping irregular
pieces to the desired form.

It must be possible to bring the glass from the plastic to the
solid state without producing stress.

The glass must not be tarnishable ; that is, must not be at-
tacked by the moisture of the air.

The glass must be colourless ; and lastly,

It must be strong enough to bear the manipulation necessary
in grinding and polishing.

5. Besides silicic acid, the only glass-making acid oxides known
are boric acid, phosphoric acid, and perhaps arsenic acid. There
was a tradition that they only gave tarnishable glasses ; but as
this seemed to require proof, the experimenters determined to
start by testing the optical values of phosphoric and boric acid,

Glasschmelzerei fiir opt. und andere wissensch. Zwecke," Verein zur
Beforderung dea Gewerbefleisses, 4th June, 1888.

INTRODUCTION. 9

in combination with as many metallic oxides as possible. The
meltings were made in tiny crucibles of only 20-30 c.c. capacity,
with an ordinary laboratory gas-blast. But, though the mixture
was kept thoroughly stirred, it was found impossible, in most
cases, to obtain pieces of glass of sufficient size and homogeneity
to admit of complete spectroscopic measurement.

The next step was to try somewhat larger quantities. At this
stage Fletcher's gas furnace was found very useful. First, on a
small scale, and driven by bellows, it gave lumps of glass weigh-
ing up to 150 g. Then, when it was enlarged, and fitted with a
motor- blower, masses of 10 kg., and at a later stage, of 25 kg.,
were obtained with it. The melting pots were made of porcelain
or fire-clay.

In addition to the six usual elements, silicon, potassium,
sodium, lead, calcium, and oxygen, the following 28 new ones
wne introduced by degrees, in quantities of at least 10 per cent. :
boron, phosphorus, lithium, magnesium, zinc, cadmium, Uirium,
strontium, aluminium, beryllium, iron, manganese, cerium,
<li<lymium, erbium, silver, mercury, thallium, bismuth, anti-
mony, arsenic, molybdenum, niobium, tungsten, tin. titanium,
uranium, fluorine.

6. It was soon seen that, by the introduction of new elements,

desired object could be attained, namely, variation of tin'

hitherto fixed relation between refraction and dispersion. Hut.

nn tin- nther hand, very few of the elements afforded means of

i.-iini: tin- dispersions of crown and Hint more similar, and so

rtening the secondary spectrum.

Boric arid is peculiar in lengthen in;.: the red end <>f the spec-
trum relatively to the blue. Fluarinc, potassium, and sodium
have the opposite effect.

It is a characteristic of the old. silicate glasses that flint
glass has a higher index and l.ii'jn dispersion than crown, and
hens the blue more than the red.

Hence it was obviously desirable t<> introduce into flint glass
as large a percentage as possible of boric acid. In fad. b.,n.
acid has become the essential iW .ill tlmt Classes intended
slmrtening the secondary spectrum <>,-,- AJ.JM-H-.

The corresponding problem of lenuthrnin- the blue relatively
tn the red in crown glasses is not so easy. Sodium, one of the

18 JENA GLASS.

three available elements, has only very slight influence. Potassium
must only be used in moderate quantities, about 25-30 per cent.,,
in a silicate glass, as it tends to make the glass tarnishable. It
was also found, by repeated experiment, to cause an increase of
total dispersion, an undesirable attribute in crown glass. " Pro-
bably Fraunhofer's lost * Crown Lit. M.,' with an improved
secondary spectrum, was laid aside on account of being tarnish -
able, and became gradually disintegrated by exposure to the
air." l

Fluorine would be by far the most advantageous element to
introduce; since, besides lengthening the blue end of the
spectrum, as desired, it lessens the dispersion throughout the
middle portion of the spectrum, which is a useful quality for the
part played by a crown glass.

" A great number of experiments in this direction have shown
us the possibility of producing colourless glasses, containing a
large percentage of fluorine, in combination with lithium, barium,
aluminium with phosphoric acid, and calcium. But crucibles of
silicious material must not be used, as decomposition of the
fluoride ensues, with generation of silicic-fluoride gas. For our
experiments we used platinum crucibles and stirrers. But even
with these, owing to the action of the oxygen and aqueous vapour
present in the air, pungent fumes containing fluorine were given
off, which were a perpetual source of variation in the homogeneity
of the mass during the cooling process.

" Before finally renouncing the use of an element so pre-
eminently valuable in its optical qualities, further experiments
ought to be tried on a larger scale. The use of platinum vessels
will necessarily make the attempts costly."

A remark must be added on the optical effect of phosphoric
acid. On comparing a phosphate glass with a silicate of the
same total dispersion, the r,un of dispersion is found to be nearly
the same for both, but the phosphate has larger indices, and is,,
therefore, better adapted than the silicate for achromatising borate
flint glasses.

Stokes and Harcourt duly recognised the effect of boric acid,
but they attributed to titanic acid the effect which was really due
to phosphoric acid, their titanium glass having always contained a

1 Czapski supposes Fraunhofer's "Flint No. 13" to have been a borosilicate,.
likewise perishable. Zeitschr. f. Instrumentenk. 6. 358 (1886).

INTRODUCTION. 11

large proportion of phosphoric acid. This explains why a titanium-
silicate glass made by Hopkinson, at Chance's works, disappointed
expectation. 1

7. The above information given by Schott as to the refractive
properties of chemical elements in glass fluxes is restricted to a
brief summary of positive results. But full particulars of his
\ I terhnents on one metal lithium are given in a paper 2 on
lithium glass, which he published while still at Witten in 1882.
It gives an interesting glimpse into the progress of the work, ami
the fact that the result was in the main negative may serve to give
some idea of the amount of labour involved in the undertaking.

On melting down lithium carbonate with silicic acid, it was
found that lithium silicate does not harden amorphously, like the
silicates of potassium and sodium, but by crystallisation, like tin-
silicates of most metals. Two trial glasses, obtained by the addi-
tion of boric acid in different proportions, proved too fragile to be
of any use.

The next step was to try meltings containing only sodium,
lithium, and silicic acid. From preliminary trials, to test the
proper proportions of acid and base, a mixture according to the
formula RO . 2Si0 2 was found to work best; any considerable
increase of silicic acid raising the melting point so high that it
was difficult to completely liquefy the mass, and impossible to
refine it. Next, it was found that with equivalent proportions of
lithium and sodium, there was no danger of devitrification ; and
the percentage of lithium was then considerably increased in order
to give prominence to the action of the metal.

After many experimental meltings, the limiting c<>mlitins for
obtaining clear glass were at last determined. A start was then
made with the following working formula:

lUdpe. Calculated Composition of Resulting OlftM.

Sin, l:'.L"Og. SiO, 78-10% Formula.

Na.CO, 42-4 Na,0 1 AN^Ol

Li,CO, 37-0 LijO 1826 fVL^OJ"

211-4 g.

1 < V, M . Ai. ,-'.,-/ ::.-.'.'. * VtrhawU. d. I'rmM r. ItytaJ. rf. 0wtrtyr. 18

li' JENA GLASS.

A spectroscopic examination by Abbe gave 71=1*507 for the
index of the D line. This is only a little less than the index
of ordinary silicate crown, and there was therefore nothing
remarkable about the glass in this respect. A reliable deter-
mination of the dispersion was impossible owing to the numerous
veins present.

Two other lithium glasses made by Schott had the following
compositions :

II.

Recipe. Calculated Composition of Resulting Glass.

Si0 2 120-0 g. Si0 2 73-71% Formula.

Na 2 C0 3 42-4 Na 2 15-23 ANam

Li 2 C0 3 44-4 Li 2 11-06 ALi 2 bj^

206-8 g.

III.

Recipe. Calculated Composition of Resulting Glass.

Si0 2 240-0 g. Si0 2 73-04% Formula.

Na 2 C0 3 85-0 Xa 2 15> 09 ^-Na 2 0\

Li 2 C0 3 100-0 Li 2 11-86 if Li 2 J *"

425-0 g.

Both these glasses had a somewhat greenish tint, but seemed
otherwise clear and good. During melting, the mixture, while at
white heat, was stirred four or five times, at intervals of 15 to 30
minutes, with a tube of unglazed clay, the quality of the glass
being thereby much improved.

Information as to the optical results is contained in the
following extract from a letter of Abbe's to Schott relating
to preliminary testing:

'' Though the material is still far from being entirely homo-
geneous, as you will see on inspecting the polished pieces, it is a
great improvement on previous specimens. Among the frag-
ments of No. III., I even found a prism from which I was able,
with a little trouble, to get an accurate determination of the
dispersion in various parts of the spectrum. I found for the
absolute index of the D line

n D = 1-5181,

INTRODUCTION. 13

anil for the differences between the lines B, D, E, F, G:

n D -n B = 0-00358) n-OOfiS7

-- 0-00329 *-*- 87 '

n-n =0-00280 -0-00793

The differences are reliable to 1 or 2 units of the last decimal
place.

" As regards No. II., I have not yet been able to find a piece
from which such a complete determination could be made. Hence
I have only got for II. the index of the D line,

*- 1-5133,

and the dispersion for the interval B to F, which is approximately
7^-7^= 0*00962.

" I think we may therefore assume that the dispersions agree
pretty closely with those of No. III.

" To give you an idea of the behaviour of your lithium glass as
compared with the ordinary known glasses, I have tabulated,
several of them, my measures of the absolute index, and the
dispersion, for the intervals B to E, and E to G, and also the
ratio of the two partial dispersions for these intervals."

Abbe's table included, besides Schott's lithium er<wn, five

Classes by Feil, Chance, and Daguet, and six flints 1>\ .
and Chance. We will quote only the data for two <>f the i
crowns and a Daguet magnesia cro\\n.

U D n s H B n o n s

Crown ordinaire 1*514 0*00680 0*00792 M65

1-511 687 so:, l

Lithium crown 1'518 687 793 1

Magnesia crown 1*517 753 898 1

The quantity k in the last column is the ratio of the diaper-
is in the two preceding columns.

u will see from this that the lithium crown is much like
"Piiii.ir\ rn,wn glasses both in index and total dispersion. It
<nly differs from them as regards the ratio of the dispersions f<r
the two halves of the spectrum, which is 1*154 for the lithium as
against 1*172 for the Feil glass preceding. Now, this difference

14 JENA GLASS.

unfortunately lies in the wrong direction. For k being above 1*2
in all flint glass, and increasing rapidly with the dispersion, a
crown glass will be the less fitted for an achromatic combination
the smaller is the value of its k. Since it is just to the want of
similarity in run of dispersions between crown and flint that
secondary chromatic aberration is due, this aberration will be
greater as k differs more for the two glasses used. It is there-
fore one of the most important problems in glass-making to
produce either flint glass with small k and large enough total
dispersion, or crown glass with large k and small enough total
dispersion. The magnesia crown in the table, which for a long
time has not been commercially obtainable, and since Daguet's
death is no longer made, must therefore be regarded as the best
crown glass hitherto manufactured for large telescope objectives.

" I regard it as a great achievement that you have succeeded in
producing, from meltings in tiny crucibles, specimens good enough
to admit of perfect optical investigation. Feil, though an eminent
and experienced glass-maker, has never sent me any such which
would allow of anything like an approximate estimate of the
mean dispersion, much less a reliable determination of the partial
dispersions. The most important condition for improvement in
the manufacture of optical glass seems to me to be the practica-
bility of making good (i.e. spectroscopically measurable) trial
meltings, since in this way only is a course of methodical
investigation possible. So long as one must make every trial
with a quantity of 60 to 80 Ibs. in order to get one small prism
to examine, any systematic testing of new combinations will be
out of the question. Hence, in spite of the negative result, I
regard these researches as of more value than if they had led by
& lucky chance to the discovery of a useful new glass."

8. To return to Schott's paper. He next goes on to describe
experiments in connection with the subsidiary requirements
mentioned above, which must be satisfied if a glass is to be
practically serviceable as well as optically advantageous. This
work, being necessarily of a purely empirical nature, was very
ledious.

In phosphate and borate glasses, alkalis had to be used very
sparingly, if at all, or tarnishing of the polished surface by damp-
mess in the air was inevitable. However, by adding alumina,

INTRODUCTION. 15

/inc oxide, and barium oxide, the sensitiveness could be sufficiently
overcome to render the resulting glasses serviceable. Many
elements, it was found, could be advantageously replaced by
others without change of optical effect. A number of elements
had to be excluded on account of their colouring influence, and
others from their rarity.

At last a series of phosphates, borates, and borosilicates were
successfully produced in small quantities.

For thoroughly mixing the contents of the crucible, a porcelain
agitator was used, which was rapidly revolved, and at the same
time raised and lowered 5-10 cm. automatically. The crucibles
were also of porcelain. But in spite of active stirring, it was
found impossible to obtain large pieces free from veins.

In the hope of better success, it was decided to go to the cost
of employing a platinum crucible of 3 litres capacity, with a
platinum stirrer weighing li kilogrammes. The result was an
unpleasant surprise. Numerous bubbles appeared at the common
surface of the glass and platinum; and the crucible disintegrated
so rapidly that it only held out for four meltings. Later attempts
with a smaller, very thick crucible, showed that platinum could
be used for borates ; but phosphates dissolve the metal and exude
it again in gray masses during cooling.

9. It is very difficult, but at the same time indispensable
especially in making large objectives to produce optical glasses
free from stress acquired in solidification. The attention of the
Icmi makers was called to this difficulty by painful experience.
A number of telescope objectives were ground by C. Bambeiy

!iii. from discs of tin- new Classes, which had been cooled in
I he usual way and were apparently perfect In spite
care in workmanship, it was found impossible, when t he telescopes
were turned on stars, to obtain the \\ell-kno\vn diffraction pattrin
of concentric circles; and the test by polarised li-ht showed the
presence of stresses, which were the cause of the failure.

This led to attempts at imj>ro\ed methods of annealing, \vhi< h
resulted in the adoption of the process designated " fine anneal-
icans of a VIM I MI m.. regulator, which automati-

cally controls the source of heat, the temperature can lie kept steady
my length of time, at any point tetween 350 and 477, or
allowed to fall with any desired slowness. The glass is contained

16 JENA GLASS.

in a very thick cylindrical copper vessel, on which a large gas
flame plays. The temperature of the interior is measured, on
the basis of Regnault's observations, by the pressure of mercury
vapour, which is balanced by a column of mercury in an open
tube; and the height of this column regulates the flame. By
this fine-annealing method with the thermoregulator, even those
glasses for which old methods had entirely failed were successfully
freed from stress.

" The highest temperature to which we have ever found it
necessary to raise a glass to make stress vanish, that is, to cause
softening to begin, 1 was 465. The lowest temperature ever
required to ensure complete hardening was about 370. Thus the
temperatures of solidification all lie between 370 and 465. We
now spread this fall of 95 over an interval of four weeks, instead
of a few days as formerly, with results far surpassing the best
ever attained in the past."

At the time these words were written, a specimen of the fine-
annealing process an objective of 6 J in. aperture, with shortened
secondary spectrum had already been tried at Berlin Observa-
tory, and proved its superiority to the older objectives. 2 It was
shaped by Bamberg, who had not been disheartened by the
previous failures, and whose unselfish devotion to the advance-
ment of his art is warmly acknowledged by Schott.

10. The introduction of fine-annealing also enabled the Jena
firm to practice a method of shaping lenses which had been tried
at Paris many years before. The glass, while red hot, is pressed
between metal cups having as nearly as possible the desired
curvatures. If the ordinary annealing process be employed,

x The so-called softening point, i.e. the lowest permanent temperature at which
a glass gradually loses the stresses caused in cooling, was determined by exposing
a highly stressed short glass cylinder, with plane ends, to a fixed temperature for
20-24 hours, in the thermoregulator, and comparing the appearance in polarised
light before and after the process. Zeitschr. f. Instrumentenk. xi. 330. 1891.

Pulfrich has since remarked that, in highly stressed glasses kept at constant
temperature, measurable displacements, doubtless indicating partial loss of stress,
are noticeable even at 100, after an hour and a half. (See paper by Schott,
Ver. z. Beford d. Gewerbefl., Vortr. 1892, Apr. 4.)

2 As further proofs of the success of the method, may be instanced the large discs
for objectives afterwards made at Jena, which were 1 metres in diameter, and
weighed 7-9 cwt.

INTRODUCTION. 17

lenses of this sort are quite unfit for use in the better class of
instruments. Their internal stress is sometimes so great that
they fly in pieces as soon as grinding is begun. It is only by
tine -annealing that they can be produced free from stress. The
prevailing idea, that the pressure exerted on the glass while in a
semi-liquid condition causes the internal stress, is, however, quite
neons. 1 The production of pressed lenses has since been
MII tinned, as the method was unsuited for large objectives, and
did not pay in the case of small ones. [For later information, see
Appendix.]

11. In conclusion, Schott gives an account of the appliances
and processes for the manufacture of ordinary optical silicate
glasses, as employed at Jena in 1888. 2 The following is a sketch
of the progress of a melting :

The melting pot, which must first be well dried, is very
gradually raised in temperature for four or the da\s until r
red hot, when it is put in the melting furnace. Here it is fun
heated for five or six hoilrs up to the melting temperature of
glass, and then pieces of glass remaining over fmm former meltings
(known in the trade as cutlet) are put in. As soon as these
melted, the inside of the crucible is glazed \vith a great iron
ladle. Tl icii some of the glass mixture (technically called batch)
\- int induced, a little at a time, a fresh layer being added as soon
as the previous layer is melted, till the erueihle is full.

Then comes the second stage of the melting (called plaining or

tig), the mixture bein^ kept at a high temperature for six or
it hours as a rule. Great care and experience are required
to maintain the ri^ht temi>erature during this period. If it is
kept too low the hubbies are not removed ; if it is raised too h
tli* erueihle is attacked, and clay is absorbed ly the glass. At
the conclusion of this stage, th<> tninj is moderated for a tim.-
tti* Hirface scum cnntainin particles is removed, and a

red of fire-flax, in the f.-im <>f a hoi! .del

10-1 J on in diameter, is placed in the glass and 1* n

d.hh-H fnrmm- "ii it rise to the surface. Then begins

1 ' Influence of Cooling on the Optical Behaviour of (JU, and Production
11-annealed Prated Lenaee." Communication from It* Jrmn Otmm Iforb,

I .-,-. Isv.i.

Paper of 4 June, 1888, above quoted.

18 JENA GLASS.

the process of stirring to produce complete incorporation, the
handle of the stirrer being a long iron tube kept cool by a
current of water. By blowing small flasks with a glass-blower's
pipe it is seen when the glass is sufficiently clear ; and the
stirring is completed from three to four hours later, the mass in
the meantime having been gradually cooling.

When the cooling is so far advanced that the stirrer can only
be moved with difficulty, it is taken out, and the crucible, which
with its contents weighs 15-20 cwt., is lifted out of the furnace,
placed on a fire-brick platform, and left there to cool freely for
half-an-hour or three-quarters.

It is then brought to the annealing furnace, in which the
empty crucible to be used at the next melting has meanwhile
been warming. Here, during the next three days, the mass cools
completely down, generally flying into many pieces, large and
small. These are carefully looked over, and faulty portions
hammered off.

The remaining pieces are subjected to the moulding process
(Ramollieren), by which the irregular lumps are made into
rectangular or circular plates. To this end the glass is reheated
in fire-brick moulds till it almost melts. A long tunnel-shaped
oven is heated fully red hot at one end, while the other is just
cool enough to admit of the moulds being pushed in.

The moulded glass is then put in the cooling kiln, where it is
cooled in 10 or 12 days. This kiln is capable of containing
20-30 cwt. of glass in moulds.

When cool, the plates are polished on both sides so as to allow
of clear vision through, and carefully examined for any remaining
defects. If the plates fit for use amount to a fifth of the whole
melting, the result is considered satisfactory.

12. The first price-list of the Jena Glass Works, issued in
1886, contains altogether 44 optical glasses, of which 19 are of
essentially, new composition. In the glasses of the silicate series,
the index for crown could be vouched for to about 2 units of the
third decimal place, for flint to about 3, and for very heavy flint
to 6 or 8 units. To obtain greater exactness, special meltings
were necessary in most cases.

In the case of several glasses, a caution is given that they
" must be protected in use." This is explained as meaning that

INTRODUCTION. 19

though they are quite durable in ordinary air, there is danger in
prolonged contact with damp in any form. Any deposit of
moisture such as might be left by the touch of damp fingers,
should be \\iped off carefully before putting away.

Among glasses for special purposes are mentioned didymium-
phosphate, cerium-phosphate, and uranium-phosphate.

Tin* lively interest excited by the undertaking both at home
and abroad was followed by a steady inflow of orders, which led
to an enlargement of the list of glasses. In 1888 a Supplement
was issued containing '24 additional glasses. Of these, 13 were
new, including 8 baryta light Hints, remarkable for smallness of
dispersion compared to index, and intended chiefly for improving
photographic objectives. So little lead oxide was required in
their manufacture that the absorption usual in Hints was reduced
to quite a small amount.

Since, in the meantime, the composition of most of the crown
glasses had been so improved as to render them almost perfectly
colourless, objectives could now be constructed having greater
transparency for the chemical rays than had previously been
attainable.

l-'urther, the extension of the choice of glasses gave means of
ting photographic objectives for astigmatism.

It was stated in the Supplement that the glasses O.I 9 7, 8
s. 17. S. 10 \\ere no longer regularly manufactured, on account
of special difficulties attending their production, and of small
demand.

In a seei.nd Supplement, issued in .January. 1 S'.iJ. S more
glasses, 6 of them new. \\.-re described, mainly intruded for the
same purposes as those of the tirst supplement. A caution was
given respecting tin- tw> silicates, O. 20 and O. 1 .".<>!' the tirst list.
as being susceptible to damp. It was furl her stated that tin- cr.\\n
glasses <Ui10, 0.608, an. I < 1.381, foRDttlj n--t '| M1I<> *&&* t"i.v
in this respect, had now Uvn made more durable. The use of
< >. 1 I'M 9 iii place of the baryta crown ;is recommended.

Most of the glasses which are important for the improvement

.liMtograplm- uhjectives are extremely diflicult to obtain free

11 small hubbies. The optical requirements leave too little

room for the melier'* choice, and it is impossible to produce large

uni: uning small isolated bubbles. Thenpti-al

results in the camera are, however, practically unaffected, the

20 JENA GLASS.

resulting loss of light, even in unfavourable cases, being barely

13. The introduction of Jena glass into practical optics was
initiated by Abbe, who was now enabled, with the help of the
technical resources of Zeiss' optical works, to realise his louu-
cherished plans for the improvement of the microscope. A series
of objectives and eye-pieces calculated by him were shown at the
Naturforscher Versammlung in Berlin in 1886.

On the same occasion several astronomical objectives of 105-175
mm. aperture, made of Jena glass by Bamberg from Czapski's
calculations, were also exhibited. Investigations with a view to
perfecting astronomical objectives have been carried on at the
Jena works until quite recently. Meanwhile, the practical appli-
cation has been taken up by Zeiss, whose telescopic objectives
and astronomical instruments were first advertised in 1899.

In the domain of photographic optics, the new glasses have
given rise to a multitude of constructions.

14. On 2nd March, 1883, Schott made his first trial melting
for thermometer glass. This was followed on 13th April by the
melting designated No. IV., a pure lime-potash glass, and about
15th October by the melting No. VIII., a pure lime-soda glass. 2
Weber's observation, that pure potash glasses and pure soda glasses
exhibit less thermal afterworking than those containing both
alkalis, was fully confirmed. The further discovery that potash
and soda produce equal amounts of afterworking was of consider-
able practical importance ; for though it is easy to obtain soda free
from potash, it is very difficult to obtain potash free from soda.

The introduction of new elements led to no immediate result, so
far as the lessening of the total depression effect in the thermometer
was concerned. One trial melting, 18 IH , a potash glass with a
considerable percentage of boric acid and zinc oxide, was marked
by the good agreement of a thermometer made of it with the air
thermometer at medium temperatures. But the making and
working of this glass presented difficulties.

It was sought to obtain the high power of endurance so essential
for the best thermometer glass by using a large amount of lime

1 Mitteil. aus d. glastechn. Lalorat. in Jena, April, 1893.

2 Schott's Paper of 4 June, 1888.

INTRODUCTION. 21

ombination with a moderate percentage of alumina. Trial
meltings were made on a large scale with 16/ of lime and 14/
of soda. The resulting glass, though it certainly had small

thermal afterworkin^ did not lend itself to manipulation \vitli
the blowing-pipe. It began to devitrify while the tube was liein-j
drawn out, unless it was kept at a high temperature during the
process, which seemed scarcely possible It also attacked the

ihle. besides exhibiting a green tint difficult to get rid of.
These difficulties were overcome by employing additional in-

lients. It was found, after a few experiments, that a com-
position containing 7% f z i nc oxide, 7% lu&*, 14% M!;I.
alumina, and 2/ boric acid, gave a good thermometer glass
with great resisting power against all external influences. The
addition of the 2/ boric acid lowered the melting point without
affecting the endurance.

With this glass, which was numbered 16 111 and designated
normal thermometer glass, a definite advance was attained, and
its permanent manufacture was comment -ed in 1885. It found a

tl afterwards in the borosilicate 59 IU , and Sdmtt has been

-tantly experimenting with a view to further improvements.

is scarcely necessary to remark that these researches are
of purely scientific interest, having no commercial imjortance.

15 In the course of the thermometer glass investigatioi
became important to know what causes contribute*! to facility of
iroridng. 1

The glass made at the works in the Thurinirwn Forest Ft
repeated meltinu r Mowing and fuMii- without change: \\hile
\- glass, such as is used for windows, becomes rough and
dull of surface, after even short exposure to the flame.

iiiie, elicited the ini m glass owed

its H|x*'ial quality to a certain sand us-d in the making, which

was only found in the n.-i-jhUurh.'^! ..f the village of Martinsroda,

- had long been regarded as the one wind fm thr purpos,. ., n d

all ntber |uart/ -and- \\rn- In-Iii-M-il unsuiublr, e.s|Mvially the

B sand ..f r.i.mdrnl'i;'

of the MaitniHroda sand showed that it contained
3'66 c 'o of "luiniiia. and it was natural t" infi-r th.it thin wan the
cause of its excellence. This inference was verified by analysis
hatdl. <U* I'er. tmr B^9nL d. OtiMr6^ 1887, D). 4. PbfMr by Scbott.

22 JENA GLASS.

of Thuringian glass, and by experimental meltings in which pure
quart/ sand was used with and without the addition of alumina.

Schott suggests that the presence of the alumina hinders the
volatilisation of the alkalis at the surface of the glass.

It is also possible that the dulling of the glass indicates in-
cipient crystallisation, and that the alumina tends t<> prevent
this.

16. As the Jena works have gradually developed, other new
branches of manufacture have been taken up ; the most notable
being the production of glasses characterised by special powers of
withstanding heat and chemical attack, which have rendered them
very important both for scientific and commercial applications.

But, apart from these special problems, the establishment
discharges important functions in the domain of pure science.

The long list of compositions employed by Schott which
already numbered over 1000 in 1886 and has since been continu-
ally increasing shows how varied are the substances which we
comprise under the name glass. The diversity in optical
properties, which was the object originally sought, has brought
with it an equally great diversity in all other physical and
chemical properties. This opens up a rich field of investigation
for which there was formerly little opportunity, owing to paucity
of material for experiment.

Faithful to its original purpose, the Jena factory has carried
on its work hand in hand with scientific research. The manage-
ment has always shown readiness to assist the scientific investi-
gations which have been undertaken in very various directions ;
and, by so doing, has obtained for itself the advantage of greater
security against mere empirical working.

Though the results thus obtained are already considerable, a
large number of questions still remain to be solved.

Attempts to establish a connection between the properties of
glasses and their composition have hitherto been purely empirical.
A more thorough treatment of this question must start with
definite assumptions respecting the molecular constitution of glass
a subject at present obscure.

CHAPTER II.
OPTICAL PROPERTIES OF GLASS.

17. Index and Dispersion. For spe< -ifyin- the refractive
properties of a glass, Abbe uses five bright spectral lines which
can always be easily obtained from artificial sources, namely, the
red potassium line, the yellow sodium line, and the lines H. H^
H Y of hydrogen. 1 The second, third, and fourth are identical
with the Fraunhofer lines C D F in the solar spectrum ; the first
lies near A, the fifth near G, and the five lines are denoted by
the letters A' C D F G'. Their wave lengths are :

A' C D F O'

< > 7U77 n 0-6563 M 0'5S93 /x 0-4802 M 0-4341 M

M denoting a micron or *001 mm. In the case of A' and D,

\vhich are double lines, the moan is taken.

Kor each glass five characteristic |uantitie8 are spectroi Metri-
cally determined by Abie's method;-' in which a ray is made to
! -'nice its path. 8 These quantities are: the index n D for the

1 l'i i.-.- list of the Jena glass-works for optical and other scientific purposes,
third edition, p. 6.

* A short description of tin- method, with a literature list, is given by Pulfrich
in NVinkrlmann's Handbuch der /Vn/ .'W7.

'Abbe's spectrometer, with which the observations are made, is described and
tikrui.-.l .it pp. ii of x.-iss' Catalogue of Spectromittn and ffe/roetoiiMfffv, 2nd
edition, 1899. The principle ! th- InttnUMAl in that, when the ray rvt
upon itself (the back of the prism being silvered) the angle of incidence on the
prism i8 the same as for minimum d<-vmti<>n with a prism of double the angle.
.1. I-

24 JENA GLASS.

D line ; the mean dispersion A, that is, the difference between the
indices for and F; and the three partial dispersions, S l S z S 3 ,
that is, the differences of index between A' and D, between D
and F, and between F and G'. The accuracy of the measure-
ments is sufficient for giving the index to four and the differences
of index to five decimal places. As aids to comparison, four
other quantities are deduced from these data, viz. :

n D -l S 2 <$

' A-' a = A' ^A' ^ = A-

The first is the reciprocal of what is commonly called the
"dispersive power," and may therefore be called the dispersive
reciprocal, or the dispersive weakness ; the last three may be
called the partial dispersive ratios. 1

The following list gives these characteristics, and also the
density, for 76 typical Jena glasses, arranged in descending order
of the values of v. Every glass has, besides the running number,
a trade number with the letter O. or S. prefixed ; 0. (for Ordinary),
signifying that the melting is performed in the ordinary way in a
large crucible, and S. (for Special), that it is performed with
special precautions in a small crucible. Glasses of essentially
new composition are distinguished by heavy type.

The first part of the list, containing Nos. 1-44, was drawn up
in 1886; and the accompanying explanation states that " for
ordinary optical uses (opera-glasses, hand telescopes, small photo-
graphic instruments, telescopic and microscopic objectives not
intended for very high-class work, small magnifiers, and eye-
pieces of every sort) the crown glasses 5, 8, 13, 18, 23, and the
fiint glasses 29, 35, 36, 37, 38, 40 will suffice." The phosphates
are recommended " where small dispersion and small dispersive
power are desired " ; combinations of phosphates and borates or
borosilicates, " where, as in the better class of astronomical tele-
scopes, the abolition or diminution of the secondary spectrum is
important. In systems of lenses, such as microscopic objectives,
which, for the best performance, require not only the closest
agreement in run of dispersion between crown and flint, but
also the best possible correction of spherical aberration and its

1 The translators are alone responsible for these suggested designations. The
original reads "The first is the reciprocal of the relative mean dispersion ; the
three last may (in a somewhat different sense) be called relative partial dispersions."

OPTICAL PROPERTIES OF GLASS. 26

chromatic difference, the theoretical or practical optician must
exercise his judgment in making the best selection from the full
list." 1

The second portion of the list, containing numbers 45-68, was
issued as a supplement in 1888. The new baryta flints here
introduced are designed for photographic requirements. Numbers
69-70, which were contained in a second supplement issued in
1892, are mainly intended for the same purpose.

1 Price List, 3rd edition, i>. 17.

[A revised list of glasses, issued in 1902, will be found in
the Appendix,]

I ; . I ' : ' i

JENA GLASS

Run-
ning
No?

Trade
No.

Description.

[ndex for
D.

Mean

Mspersion
CtoF.

v
n-l
A

0. 225

Light Phosphate Crown,

1-5159

0-00737

70-0

S. 40

Medium Phosphate Crown,

1-5590

0-00835

66-9

S. 30

Dense Barium Phosphate Crown, -

1-5760

0-00884

65-2

S. 15

Densest Barium Phosphate Crown,

1-5906

0-00922

64-1

0. 144

Boro-Silicate Crown, ....

1-5100

0-00797

64-0

O. 57

Light Silicate Crown, ....

1-5086

0-00823

61-8

0. 40

Silicate Crown, -

1-5166

0-00849

60-9

0. 60

Lime Silicate Crown, -

1-5179

0-00860

60-2

0. 138

Silicate Crown of High Index,

1-5258

0-00872

60-2

S. 52

Light Borate Crown,

1-5047

0-00840

60-0

11
12

0. 20
0. 227

Silicate Crown of Low Index,

1-5019
1 -5399

0-00842
0-00909

59-6
59-4

O. 203

Ordinary Silicate Crown,

1-5175

0-00877

59-0

O. 13

Potash Silicate Crown, - ...

1-5228

0-00901

58-0

0. 15

Zinc Silicate Crown, ....

1-5308

0-00915

58-0

O. 211

Dense Barium Silicate Crown,

1-5726

0-00995

57-5

0. 153

Silicate Crown,

1-5160

0-00904

57-2

0. 114

Soft Silicate Crown,

1-5151

0-00910

56-6

0. 197

Boro-Silicate Glass,

1 -5250

0-00929

56-5

0. 202

Densest Barium Silicate Crown,

1-6040

0-01092

55-3

S. 35

Borate Flint, -

1-5503

0-00996

55-2

O. 252

Borate Flint, -

1-5521

0-01026

53-8

0. 152

Silicate Glass,

1-5368

001049

51-2

S. 8

Borate Flint, -

1-5736

0-01129

50-8

OPTICAL PROPERTIES OF GLASS.

Partial Dispersions,

Run-

and ratios to A.

ning

Density

1 ! i i r * -

i and a.

,and.

,and y .

0-00485

0-00515

0-00407

2-58

Colourless,

0'658

0-698

0-552

0-00546

0-00587

0-00466

3-07

Do.

0-654

0-702

0557

0-00570

0-00622

0-00500

3-35

Not very hard.

0-644

0-703

0-565

0-00091

0-641

0-00648
0-703

0-00521
0-565

3-66

Not hard ; needs protection.

0-00619
0-651

0-00559
0-701

0-00446
0-559

2-47

Exceptionally hard. Very colourless.

0-00530

040078

0-00464

2-46

0-644

0-702

0-564

0-00545

0-00596

0-00479

2-49

0-642

0-702

0-564

0-00553
0-643

O-oixiu:,
0-703

0-00487
0-566

2-49

Exactly corresponds to Chance's Hard
Crown.

0-00560

0-00614

0-00494

2-53

0-642

0-704

0-567

0-00560

0-00587

0-00466

2-24

Only to be used in protected places.

0-667

0-700

0-555

0-00543

0-00592

0-00478

2-47

0-645

0-703

0-568

0-00582

o-<MMi:i

0-00514

2-73

Very colourless.

0-640

0-703

0-566

0-00563

0-00616

0-00499

2-54

0-642

0-702

0-568

0-00572

0-00637

0-00515

2-53

Has better run of dispersion than ordinary

ii .;:;:,

0-707

0-572

silicate crown.

0-00587

0-00644

0-00520

2-74

0-642

0-704

0-568

O-<N M;;;O

0-00702

O-IH >;,;*

3-21

Ooloulsm

0-633

0-706

0-571

0*00976

0-00637

o-m.-,n;

04H

0-700

0-571

040077

OlMMil'J

om.V.'l

2-66 Correspond! to Chance's Soft Crown.

0-634

0-706

0-572

l'i

040000

(HMKi.M

040011

2-64

0-645

0-704

0572

040000

0-00771

0400H

3-68 Fragile. Cannot be freed from a few

0-632

0*700

0-573

mall bubbles.

ii-m it" 1

n > H H ' c i

n irti'ii'. 1

(I IMMi.i |

0-656

( iMid.ri

(1 1 N 1. ill 1

0-563

0- ;r,7

0407SI

040001

2-67 To be used to protected places.

0400

0-703

0-567

040000

n-m::t

040010

2-76

04B8

04H

0-00795

0406M

0-571

JENA GLASS.

Run-
ning
No.

Tr.ule
No.

Description.

Index for
D.

Mean
Mspersion
C to /'.

n-1
A

O. 164

1 '5503

0-01114

49'4

.26

0. 214

Silicate Glass,

1-5366

0-01102

48-7

0. 161

Boro-Silicate Flint,

1-5676

0-01216

46-7

S. 7

Borate Flint, -

1-6086

0-01375

44-3

0. 154

Light Silicate Flint,

1-5710

0-01327

43-0

0. 230

Silicate Flint of comparatively high
index,

1-6014

0-01415

42-5

0. 184

Light Silicate Flint,

1-5900

0-01438

41-0

S. 17

Dense Borate Flint,

1 -6467

0-01591

40-6

S. 10

Dense Borate Flint,

1-6797

0-01787

38-0

0. 118

Ordinary Silicate Flint,

1-6129

0-01660

36-9

0. 167

Ordinary Silicate Flint,

1-6169

0-01691

36-5

O. 103

Ordinary Silicate Flint,

1-6202

0-01709

36-2

0. 93

Ordinary Silicate Flint,

1-6245

0-01743

35-8

0. 102

Dense Silicate Flint, -

1-6489

0-01919

33-8

0. 192

Dense Silicate Flint,

1-6734

0-02104

32-0

0. 41

Dense Silicate Flint,

1-7174

0-02434

29-5

O. 113

Dense Silicate Flint, -

1-7371

0-02600

28-4

O. 165

Dense Silicate Flint, ....

1-7541

0-02743

27-5

0. 198

Very Dense Silicate Flint,

1-7782

0-02941

26-5

S. 57

Densest Silicate Flint, -

1-9626

0-04882

19-7

4.-,

0. 599

Boro-Silicate Crown,

1 -5069

0-00813

62-3

O. 337

Silicate Crown,

1-5144

0-00847

60-7

0. 374

Silicate Crown,

1-5109

0-00844

60-5

0. 546

Zinc Crown,

1-5170

0-00859

60-2

O. 567

Silicate Crown,

1-5134

0-00859

59-7

0. 610

Crown of low index, ....

1-5063

0-00858

59-0

OPTICAL PROPERTIES OF GLASS.

Run-
ning
No

Partial Dispersion*,
and ratios to A.

on-ity

Rmark.

Si and a.

,and.

,and Y .

0-00710
0-637

0*00786
0-706

0-00644
0-578

2-81

0-00690
0-626

0-00781
0-709

000644
0-584

2-73

0-00762
0*687

<i-ms.;o
0-707

0-00709
0-583

2-97

040864

0-628

0-00974
0-708

0-00802
0-583

3-17

To be used under protection.

0-00819
0-617

0-00943
0-710

0-00791
0-596

3-16

o-iM.sr.s
0-613

0-01009
0-713

0-00843
0-595

3-40

0-00882
0-613

0-01022
0-711

0-00861
0-599

3-28

040060
0-622

0-01128
0-700

0-00937
0-589

3-51

To be used under protection.

0-01097
0-614

0-01271
0711

0-01062
0-594

3-81

To be used under protection.

001006
0-606

0-01184
0-713

0-01008
0409

3-58

0-01026
0-606

0-01206
0-713

0-01029
0-608

3-60

0-01034
0-605

0-01220
0-714

0-01041
0-609

3-63

Exactly corresponds to Chance's Dense
Flint.

0-01053
0-604

0-01243
0-713

0-01063
0-609

3-68

ooll.VJ
0-600

0-01372
0-715

0-01180
0410

3-87

Optically identical with Chance's Extra
Dense Flint.

0-01255
0-597

0-01507
0-717

0-01302
0-619

4-10

0414IO

0-591

0-01749

n-Tis

o-ol.vjl
0-625

4-49

Corresponds to Chance's Double Extra
Dense Flint

0-01526
0-587

0-01870
0-719

0-nir,3-J
0-627

4-64

0-01607
0*585

OO1974
0-720

001730
0*630

4-78

0-01719
0*584

0-02120
0-721

0-01868
0-635

4-99

0*9767
0467

046641
0-726

046661

0-666

641

OIM..V."..

();.-, )

<)<H >;,(,'.
0-701

040107

0-562

2-48

Ifl

ooor.t:
0646

040006

0-704

omisu

0467

2-60

47
48

(MH,.-,i7
0-648

046660

0-646

046666
0-703

omm.:,
0-704

0-00479
0-568

046166

0-565

2-48
646

Almost absolutely colourless. Optical
properties like English Hard Crown.

48
50

040664

0-645
0-OOOtt

0-643

IK* Mil.:,
0-704

(HHMiirJ
0-702

640461
0466

MH.|s

0-570

201
2-51

Almost absolutely colourless.

JENA GLASS.

Run-

ninsr

No?

Trade

Description.

ndex for
D.

Mean
)ispersion
C to F.

V-

n-1
A

0. 598

1-5152

3-00879

58 "6

0. 512

Silicate Crown,

1-5195

0-00886

58-6

O. 463

Baryta Light Flint,

1-5646

0-01020

55-4

OOAQ

ft.AAQjQ

K A .ft

. OUo

u uuy4o

0. 602

Baryta Light Flint,

1-5676

0-01072

53-0

0. 381

Dispersive Crown, -

1-5262

0-01026

51-3

0. 583

Baryta Light Flint,

1-5688

0-01110

51-2

0. 543

Baryta Light Flint,

1-5637

0-01115

50-6

0. 527

Baryta Light Flint,

1-5718

0-01133

50-4

0. 575

Baryta Light Flint,

1-5682

0-01151

49-3

O. 522

Baryta Light Flint,

1-5554

0-01153

48"2

0. 578

Baryta Light Flint,

1-5825

0-01255

46-4

0. 376

Ordinary Light Flint, -

1-5660

0-01319

42-9

O. 340

Ordinary Light Flint, -

1-5774

001396

41-4

0. 569

Ordinary Light Flint, -

1-5738

0-01385

41-4

O. 318

Ordinary Light Flint, -

1-6031

0-01575

38-3

0. 266

Ordinary Light Flint, -

1-6287

0-01775

35-4

0. 335

Dense Silicate Flint, -

1-6372

0-10831

34-8

O. 802

Boro-Silicate Crown,

1-4967

0-00765

64-9

0. 709

Zinc Soda Crown, - ...

1-5128

0-00894

57-3

O. 1209

Densest Baryta Crown, -

1-6112

0-01068

57-2

0. 722

Baryta Light Flint,

1-5797

0-01078

53-8

O. 846

Baryta Light Flint,

1-5525

0-01042

53-0

0. 726

Extra Light Flint,

1-5398

0-01142

47-3

0. 378

Extra Light Flint,

1 -5473

0-01193

45-9

0. 748

Baryta Flint,

1-6235

0-01599

39-1

OPTICAL PROPERTIES OF GLASS.

Run-
ning
No.

Partial Dispersions,
and ratios to A.

ensity

Remarks,

, and a.

,and.

fcandy.

0-00562
0-640

0-00619
0-704

OO0499
0-568

2-59

Almost absolutely colourleM.

6*00068

0-641

IMMKiLV,

0-705

0-00504
0-568

2-64

Almost absolutely colourless.

0-00648
0-635

0-00720
0-706

0-00586
0-575

3-11

Almost absolutely colourless.

0-00595
0-631

0-00666
0-706

0-00543
0-576

2-60

0-00675
0-630

0-00759
0-708

000618
0-576

8-12

0-00644
0-629

0-00727
0-709

0-00596
0-582

2-70

0-00696
0-627

0-00786
0-708

0-00644
0-580

3-16

000699
0-627

0-00790
0-708

0-00650
0-583

3-11

0-00706
0-623

0-00803
0-709

0-00660
0-582

3-19

0-00718
0-623

0-00817
0-710

0-00672
0-584

3-15

0-00718
0-623

0-00819
0-710

0-00677
0-587

303

OO0777
0-619

0-00891
0-710

0-00739
0-589

3-29

0-00814
0-617

0-00939
0-712

0-00787
0-597

3-12

64
65

0-00857
0-614

0-00853
0-616

0-00994
0-712

0-00987
0-713

0-00837
0-600

0-00831
0-600

3-21
3-22

Exactly corresponds to Chance's Light
Flint.

0-00960
0-609

0-01124
0-714

0-00952
0-605

3-48

0-01072
0-604

0-01270
0-715

O-OlOMi

0-612

3-72

68
68

001099
0-600
040004

0-659

0-01308
0-714

<I-<M).-,:U
0-698

0-01124
0-614

0-00423
0-553

3-77
2-38

Not free from a few minute babbles.

0-m>.-,7.->
0-642

040680

0-636

0-00630
0-704

o-m::,:i
0-706

o-m:,ns
0461
000610
0-571

2-58
146

Not quite free from a few minute bubbles.

040681
0468

0-00761
0-707

040681
0-577

:;-j.;

040607

0-631

0-00736
0-707

040861

0-578

301

0-00711
040

uiM.sln

0*700

040861

0-586

2-87

0*00739
0-620

040047

07H>

om:n;

046

848

040860

0406

0-01142
0-713

040061

0-604

:: .17

JENA GLASS.

18. Achromatism^ one Glass by Another. Let a', c, d, /, cf
be the focal lengths of an achromatic doublet for the colours
A, C, D, F t G'. We have

<f> = k(n-I) + k'(ri-l)', ...................... (1)

denoting the reciprocal of the focal length for any particular
wave-length X ; k the sum of the curvatures of the faces of the
first lens (positive if convex) ; n its index for X ; and k', ri the
corresponding quantities for the second lens.
When X is changed, (1) gives

change of (f> = k (change of n) + k' (change of n') ....... (2)

Using the notation

= n D - n A >
= n F n D

= n - n

= , - n' P

we have, as cases of (2),

i--
j c

-
do.

Let k and k' be so taken that/= c ; then
Also i =

Clf

whence

1
Hence

= j'T7 -- *\
d &(v v)

1 $ 1 1

f t ' \
(y v)

1 a

Thus -

JL11U.O = - -. - -

-. _- .-

= - -. - -, ' 7) n ^j -I ft f a - i / J

d a d v v f d d vv g j d v v

whence

vv a

; = nearly,

, / ,

7^='-Y-f=-r j

.(4)

OPTICAL PROPERTIES OF GLASS.

the approximations being deduced from the consideration that
the ratios of a', d, f, g' to one another are sensibly unity.

Equations (4) give (in terms of the tabulated data for the glasses)
the defect of achromatism for the colours A\ D, G\ relative to C
and F, which are united. The defects for the other colours can
be deduced by interpolation, either graphical or arithmetical

These equations show that two glasses will be the better fitted
for achromatising, the less they differ as regards a, ft, y, and the
more they differ in v. Diminishing a a',ft ft',y y' will, how-
ever, have no effect iiv v' diminishes in like measure at the same
time. Further, from equations (3) we see that the curvatures of
the lenses increase as v v diminishes. Perfect achromatising of
one glass by another would, by equation (2), be attained if all the
partial dispersions of the one were to those of the other in th-

//
fixed ratio -j-. The spectra of the two glasses would then be

rigorously similar from a geometrical point of view. The differ-
ences exhibited by two glasses as regards the quantities a, ft, y
afford a measure of the dissimilarity of their spectra.

19. Secondary and Tertiary Spectrum. A clearer idea of
the nature of this achromatising will be gained from a graphic
representation. In fig. 1 the variation of focal length of a doublet
with wave-length is shown for two combinations: (1) silicate
crown 8 with silicate flint 36; (2) phosphate crown :* with borate
flint 24, wave-length being taken as ordinate, and focal length
as abscissa. Substituting the values of a, a f , v, v\ etc., from the
List, equations (4) give the following values for a' d, etc., in terms
of d as unit (remembering that c =/).

Combination.

a'-d.

C-'/.

f-d.

9-d.

(1) 8 with 36,

+ 00158

+ 00046

+ 00225

(2) 3 with 24,

-00007

+ 00007

+ O0007

+ 00049

On inspecting the curves it will be seen that the scattering of

I confined within much narrower limit** in the combination

(2) than in (1), and, further, that the colour union obtained is

JENA GLASS.

triple instead of double. The parabolic curve (1) is cut by any
ordinate in only two points, so that chromatic foci will only be
united in pairs. But in curve (2), owing to the double bend,
there will be union of three chromatic foci throughout the whole
region extending from near A' to F, so that there only remains a
slight scattering of the rays beyond F.

FIG. 1.

When the achromatism is such that the colours are only united
in pairs, the residual spectrum is called secondary ; when in threes,
tertiary.

Thus combination (1) has a secondary spectrum of considerable
extent, while (2) has only a tertiary spectrum, so short as to be
relatively negligible.

These facts show what an improvement the new glasses have
effected in achromatism. The glasses used in combination (1),
an English hard crown and an English dense flint, are among the
best of the old kind ; and their secondary spectrum may be taken
as representing about the best that can be done with silicate
glasses. It is true that with heavy crown and light silicate flint
doublets can be made in which the deviation from proportionality
of dispersion is less; but this advantage is counterbalanced by
diminution of the difference v v. For example, a combination of
the glasses 17 and 31 gives a curve almost exactly coinciding
with the curve (1) drawn above for glasses 8 and 36. 1 It was
only with the introduction of phosphate and borate glasses that
opticians were first enabled to form combinations which materi-
ally shortened the residual spectrum, and gave only a tertiary

1 See " Mitteilungen aus dem glastechnischen Laboratorium, Jena," Zeitschr.
f. Instrumentenk. , 6, 341 (1886) by Czapski, who points out the fruitlessness of such
attempts.

OPTICAL PROPERTIES OF GLASS. 35

remnant of colour. Besides 3 and 24, the pairs 3 and 28, 2 and
21, 1 and 21, 8 and 25 may be cited as examples.

20. Another method of Achromatising. The following way
of treating the question was first proposed by Scheibner. 1 Let
the lens-curvatures k and k' in equation (1) be so chosen that, for
a particular colour defined by its wave-length \, the focal length
F of the doublet does not change for a small change of X. This
generally makes F a minimum. For visual purposes the selected
colour should be in the brightest part of the spectrum say,
A = '55/x ; for photographic work it should correspond to the place
of strongest chemical action. Let TI O , n' be the two indices for

A ; then, putting for <f> in equation (1), it becomes

and we are to have

tio or j-

whence

1 - dn . t

kF= n - -a?***-

From these two equations k and k' can be computed, if the i.tti"
of dn/d\ to dri/d\ is known. This ratio can be detenu inn 1
with sufficient exactness by employing an empirical dispri
formula carried to three terms. If the formula is expressed in
powers of 1/X 2 , we may employ I/A* as the imlc|KMulfnt variable
in the differentiations, instead of A.

k and k' having thus been found, equation (2) can be employed
for computing the successive changes of I//*, starting from F and
jiving successive increments to X This will show the depart un*
from achromatism in the various parts of the spectrum.

Czapski 2 has carried out this calculation for the three pain

1 Abhmndl. .1. Sachs. Akad. II, 8. 565 (1876).

9 Zeittchr. f. /rrtrumenfe**., 6, 342 (1886). The numerical rwulu and lh three
corves derived from them are abo given in Winkelmann'i Ha*dbwtk d,

II 1, pp. 146, 147.

36 JENA GLASS.

8/36, 3/28, 3/24, starting from X =0'55M, and proceeding by
increments 0'04/x, to \ = 0'77/x in one direction, and A = 0'41/x
in the other. The result is very similar to that obtained by
uniting C and F.

The combinations 8/36 and 3/28 give parabolic curves, that is
to say, secondary spectra, the second having about half the extent
of the first; while, in the combination 3/24, the colour-union is
so close that there is no material difference of focal length
anywhere between A' and F.

21. Diversity of Glasses. If, taking n the index for D
as abscissa, and the " mean dispersion " A as ordinate, we plot
on cross-ruled paper all the glasses given in Art. 17, it will.be
found that the old glasses, except a very few of small index,
group themselves along a straight line, whose equation is
approximately

A = 0-07812?i- 0-10962.

In virtue of this relation, v, which is defined as (ti 1)/A, is
practically a function of only one independent variable instead
of two. This limitation is largely removed by the new glasses,
which, when introduced into the diagram, spread themselves over
a considerable area, lying between the above-mentioned line and
the axis of abscissae. 1

The limitation just mentioned as holding for the older glasses
implies that those which have equal v's have also equal dispersions,
and vice versa, so that large change of A entails correspondingly
large change of v. On consulting the catalogue (which is
arranged in order of v), another inconvenient uniformity in the
older glasses will be found, namely, that similarity in run of
dispersion accompanies equality in v. Here again the new
glasses come to the rescue. Thus, comparing the old glasses 6, 7,
8, 9, with the new borate crown 10, we see that, while the values
of a, /3, y are almost the same for the four former ; in 1 the
red end of the spectrum is considerably lengthened, and the blue
end shortened. Pairs 23/24 and 28/29 offer further illustrations

1 For the first 44 glasses Czapski has plotted a diagram in Zeitschr. f. Instru*
mentenk, 6, 345 (1886).

OPTICAL PROPERTIES OF GLASS. 37

of the fact that, with the help of the new glasses, it is possible,
without appreciably changing i>, to give the different portions of
thr spectrum relatively unequal extents.

22. Hypochromatic and Hyperchromatic Doublets. The
fact that the catalogue includes pairs of glasses exhibiting un-
r.|\ial dispersion for equal or nearly equal index, affords the
possibility of a mode of combination which exaggerates the natural
diversity of the glasses. 1

Equation (1) of Art. 18, applied to a doublet composed of two
lenses L and L' cemented together becomes, when n and n' are
equal,

(1.

k. denoting k+K, that is, the sum of the external curvatures.
We may call k e the total curvature of the doublet.

Let p denote the resultant dispersion, defined, in accordance
\vith equation (2) of Art. 18, by

Then the doublet will be equivalent to a single lens of total
curvature k , index n, and dispersion p.

The dispersion p can, if desired, be made either less than tlu
less, or greater than the greater, of the two quantities , *. In
first case the compound lens is called hypochromatic ; in the
second, hyperchromatic.

Equation (2) may be written in either of the forma :

mi+r-Q ............................ (3)

Now k and k' are always of opposite sign. We shall assume
k always positive, and k' negative.

1 Cf. German patent* Not. 88880 and 92813, Zi.

38 JENA GLASS.

Then we have the following results :

FROM EQUATION (3).

If* +
and 3' > S,
then 8 > p.

FROM EQUATION (3).

FROM EQUATION (4).

If & e -

and ($>(?',

then S'> p.

(Hypochromasy).

FROM EQUATION (4).

p>S'.

(Hypercliromasy).

Tlius the limits of dispersion to which we are confined in deal-
ing with a single glass of given index, may be enlarged by making
use of a combination of two glasses which have this index. The
lower limit may be lowered by giving the weaker dispersion to
the positive component of a positive doublet, or to the negative
component of a negative doublet. The upper limit may be raised
by giving the stronger dispersion to the positive component of a
positive doublet, or to the negative component of a negative
doublet.

Chromatic Difference of Spherical Aberration. The con-
dition n = n, even if strictly fulfilled, can only hold for rays of
one definite wave-length X Q . Since these rays undergo no devia-
tion at the common surface of contact, their spherical aberration
is independent of the curvature of this surface, and is the same
as for a simple lens of index n and curvature k e .

The spherical aberrations of rays of other wave-lengths, though
affected by the curvature of the internal surface, depend mainly
upon the two external surfaces, and the same rule must hold for
differences of spherical aberration resulting from difference of
wave-length. Now, at the external surfaces, it is not the re-
sultant dispersion p, but the individual dispersions S and $', which
actually come into play ; and therefore, in the spectrum formed
by the chromatic foci of the marginal zone, any colour whose
wave-length is different from X will have a somewhat different
situation from what it would have in the case of a simple lens
giving dispersion p. Thus, as regards chromatic differences of

OPTICAL PROPERTIES OF GLASa 3 n

spherical aberration, the compound lens is not exactly equivalent
to the simple one. In the hypochromatic doublet the divergences
will be somewhat greater, and in the hyperchromatic somewhat
less than for the simple lens.

23. Infra-red and Ultra-violet Spectrum. An investigation
of dispersion beyond the limits of the visible spectrum has been
carried out by Rubens 1 and Simon 2 for 13 Jena glasses. As these
glasses are not included in the List of Art 17, they are tabulated
here. Besides the ordinary data, the limits of wave-length to
which the investigation extended in each case are given.

LOt,

10*y

U D

10A

l""a

10^

S. 179. Medium Phosphate Crown,
2-020 /* 0-3261 /i,

1-56207

837

67-2

556
664

587
701

479
572

O. 1092. Light Baryta Crown,
2-200 /* 0-2763 /x,

1-51698

S53

60-6

651

601
705

S. 204. Borate Crown,
1-977 M-0 -2763 M ,

1-51007

868

58-8

581
669

ooo

482

0. 1143. Dense Barium Silicate Crown,
2-1 13 /t 0-2837 /x,

1-57422

1006

57-1

640
636

700

584

581

0. 1151. Silicate Crown of high dis-
persion,
2-120 M 0-2980 M,

1-52002

1003

51-8

632

71S

711

0. 451. Light Silicate Flint,
2-490 /* 0-2980 M,

1-57524

1396

41-1

855

612

991
710

040

0. 469. Dense Silicate Flint,
2-502 /i 0-3261 M,

1-64985

1927

BT7

1105
605

717

0.500. Dense Silicate Flint, yellowish,
2-316 /* 0-3403 M,

1-75130

2723

27-6

LOOO
588

1961

S. 163. Densest Silicate Flint, yellow,
2-368 M 0-4340 M,

1-88995

3997

223

OJH

574

OJOJ

OH
051

0. 1442. Very dense Baryta Crown,
0-768 A* 0-3133 M,

1-60956

57-4

670

OJO

750
700

614
070

0. 1230. Dense Baryta Crown,
0-768 M 0-2837 M,

1*7*01

1006

57-0

OJI

oj|

716

500

O. 1250. Crown of high dispersion,
0-768 M-0-2980 M,

1-52046

1010

51*5

OH
030

IOJ

0. 1398. Baryta Lead Glass, con-
taining Alkali,
0-768 M 0-3081 M,

1244

40-8

774

oji

000
790

1 Uel>er Dispersion ultraroter Strahleo, Aim. d. Pkyt. n. CVw., 40, 810 (1008).
UeUr Dispersion ultraviolcttr StrahUo, 7>MH. BtrKn, 1004; Extract in
.Inn. d. Phy*. u. Chcm., 53, 542 (1804).

40 JENA GLASS

Infra-red Spectrum. llubens determined the dispersion for
the first nine glasses 1 from the G' line down to the limit men-
tioned, using the method of minimum deviation by prisms ; with a
bolometer for the infra-red region ; the bolometer having an iron
or platinum wire according as the dispersion was strong or weak.

A parallel beam of light, formed by placing a lens in the path
of rays from a Linnemann's zircon burner, was thrown at 45 upon
a pair of glass plates pressed together so that the layer of air
between was very thin. The reflected rays were brought, by a
second lens, to a focus on the slit of a spectrometer, the image of
the source filling the entire length of the slit. In the spectrum
formed by the instrument dark vertical bands were seen, due to
interference of rays reflected at the two surfaces bounding the
thin layer of air. The wave-lengths of the extinguished rays
are determined from the equation,

m.\ m = K, (1)

where m is any one of a series of consecutive integers, and K a
constant equal to Id cos a, d denoting the thickness of the layer
of air, and a the angle of incidence on the glass, here 45.

The deviations for the four lines of known wave-length, G', F,
D, and C, were determined from the scale-readings ; and the wave-
length corresponding to any other deviation could then be obtained
by graphic interpolation. The wave-lengths for the interference
bands lying in the visible spectrum were thus found. Now,
supposing the first m bands to lie in the infra-red, the first
band visible in the red will be the (m-j-l)th, the second the
(w+2)th, . . . and so on, and m can easily be found from the
equations.

(m+l)X m+1 ==(m + 2)X w+2 = etc (l)

The products (m + l)X w+ i, (m+2)X OT+2 , etc., gave a series of
values for K whose mean was taken.

The bolometric investigation of the infra-red dispersion followed.
The first minimum of the galvanometer deflection indicated the
position of the first interference band. Its order m and the
constant K being known, the corresponding wave-length was
given by (1). The positions and wave-lengths of the remaining
bands were similarly obtained. The maximum galvanometer

1 Also for water, bisulphide of carbon, xylol, benzol, quartz, rock-salt, and
fluorspar.

OPTICAL PROPERTIES OF GLASS.

deflections were as marked as the minima, and were also utilised
for the determinations. The wave-length corresponding to a
maximum is Kl(n+ ), if n, n+1, be the orders of the two
neighbouring minima. Six minima were found in the infra-red
for each of the eight glasses, except 0. 1092, for which only five
were found.

Rubens gives dispersion curves plotted from his measures, with
wave-length as abscissa, and index as ordinate. The curve for
the glass 0.1151 is reproduced on a reduced scale in fig. 2,
1 mm. representing 30X 10/x in one direction,and lOOOn 1490/u
in the other. The five crown glasses show a point of inflexion in

Flo. 2.

the infra-red region, but the flint glasses do not A later in-
vestigation 1 of the dispersion of the flint glass 0. 508, with more
perfect apparatus, gave, however, a distinct point of inflexion at
about X = r5/z.

Ultra-violet Spectrum. Simon determined the dispersion for
all 13 glasses 2 from the A line down to the lower limits of wave-
length above stated, using prisms of about 30. In the region.
\ tween A and G', the method of minimum deviation was useU
The ultra-violet region was examined photograi>!n< illv by the
normal incidence method, using the zinc and cadmium lines.

Th<3 /inc. ni cadmium, was placed in the crater of the pewit IN

1 AnnaUn d. Phy*ik . Cktmit, A3, 267 (1894V

'Afco for quarto, fluortpar, wtr, bentol, xylol, carbon bisulphide, and

a-monobromonaph thai i n .

42 JENA GLASS.

carbon of an arc lamp, and the bright line spectrum thus pro-
duced was photographed on Schleussner plates, by the help of two
achromatic objectives of quartz and fluorspar, made by Zeiss
from Czapski's calculations. A sharp image of the whole spectral
region from 0'360/x to 0'202/u was formed on one plate. The
wave-lengths of the lines in question were known from Cornu's,
and Kayser and Eunge's investigations. Preliminary trials had
shown that the interference method used by Eubens in the infra-
red was not suited to the ultra-violet, as the interference bands
grew more and more diffuse with the rapidly increasing dispersion.
The indices obtained by Simon may be regarded as accurate to
the fourth decimal.

Simon, also, has plotted dispersion curves from his observations,
with the wave-length as abscissa and index as ordinate. Those
for the first nine glasses join on very well to Eubens', except for
a slight parallel shift. So far as this shift arises from small
errors of observation, Simon claims the greater accuracy for his
own determinations.

A summary of the observations is given in the following table
by Simon. 1 The first column contains the wave-length in
thousandths of a millimetre, the remaining columns 'the indices.
The values for the visible and ultra-violet regions are from Simon's
actual observations ; the values for the infra-red were obtained
from Eubens' determinations, with the aid of graphic interpolation,
which was necessary because the wave-lengths employed were not
the same for different glasses.

24. Absorption. Theory indicates that the dispersion exhi-
bited by a colourless transparent substance is essentially connected
with the absorbing powers of the substance for rays in the infra-
red and ultra-violet.

Assuming the existence of only two effective absorption bands,
one in the infra-red with its centre at \, and the other in the
ultra-violet with its centre at X 2 , the elastic-solid theory leads
to the equation

for the index n at any intermediate wave-length X. Eubens has

1 Ann. d. Phynik n. Chem., 53, 555.

OPTICAL PROPERTIES OF GLASS.

is:

T. \ - n

'!--

-r - r-.

i- i- i~ !- i- i- ,-

S?
<5 w &5 95 cc -a? ^ uS

3C OC CC 3C OO 3C X CC

i Ci ^ CC 1-0

' -- >h cs ?i >": i

i f'^ f^* l^^ go 00 '

i~ i^ >: '- i-

. / ~ -*
r - 5 :j

Illlili

iliili

c i.-: ..^ i': ."

o r oooeeo

44 JENA GLASS.

shown 1 that his later determinations for the dispersion of the
dense silicate-flint 0. 500 from 0'40444yu to 4'06/x are well repre-
sented by equation (1), when the values allotted to its five con-
stants are: a 2 =6'7716, ^=1508-2, .A/ 2 =0-03672, X 1 2 =394-65,
X.r=0'0404. The observations would accordingly be explained
on the assumption of a lower absorption band at about 19'9/x, and
an upper one at about 0'2/u. At any rate, the lower band seems
to be a long way below the visible region, and the upper band
very near it. Indeed, the yellow tinge of the glass shows that
the upper absorption band encroaches on the visible region.

A graphic representation of the dispersion of a glass shows
plainly the influence of both absorption bands, if the observations
extend far enough into the infra-red. The readiest mode of
representation is to plot the curve n=f(\), as has been done in
fig. 2 (p. 43) for the glass 0. 1151.

[The axis of abscissae in the figure runs from right to left for
increasing X, as is shown by A' being to the left of G-'.]

The dispersion is then measured by dn/d\, that is, by the
tangent of the slope of the curve. As will be seen from fig. 2, it
increases rapidly in passing from the red to the blue end of the
visible spectrum ; and in the case of flint glass the increase is
still more rapid. Thus, in all cases, the influence of the upper
absorption band is plainly discernible, as the result of diminishing
X in equation (1) would lead us to expect. On passing from the
red to the infra-red, the dispersion at first goes on decreasing,
then reaches a minimum (as shown by the point of inflection in
the dispersion curve), and then begins to increase again in con-
sequence of the approach to the lower absorption band. It is
difficult to estimate the exact position of the point of inflection,
as a considerable length of the curve in its neighbourhood is
nearly straight. In all the nine curves drawn by Rubens for the
glasses which he examined, the effect of the lower absorption
band is less conspicuous than that of the upper. In the case of
the four flint glasses, the observations would have had to be
carried much further in the infra-red to reach the bend at the
lower end of the dispersion curve. In the five crown glasses the
curve begins to bend just at the last.

On the whole, everything points to the conclusion that the
upper absorption band lie's decidedly nearer the visible region

1 Ann. d. Phys. u. Cliem., 54, 480 (1895).

OPTICAL PROPERTIES OF GLASS.

than the lower band ; and also that in flints the upper band is
still nearer and the lower band still further off than in crowns.
The influence of the infra-red absorption is more distinctly

brought out by drawing the dispersion curve n = f\r^j instead of

n=f(\), as may be seen from fig. 3, which represents the F cujve
for the same glass whose/ curve is shown in fig. 2. The scale of

A' CD

F O'

Fio. 3.

on li nates is 1 mm. for 500?i 740/x, and of abscissae, 1 mm. for
4/X 2 , the unit for X being the thousandth of a mm. as before.
The point of inflection of the new curve falls within the visit >!<>
region, thus leaving room for the dispersive influence of the lower
absorption band to display itself in the infra-red. The different
can be explained by means of the identity

dn .
Mnoe -T7- is negative,

dhi

will vanish and become negative

vanishes and becomes negative, with increasing \.

e the point of inflection of the new curve lies in the visible
spectrum for crown glasses, and never far beyond it for flints, the

46 JENA GLASS.

portion of the curve lying in the visible region will never deviate
much from a straight line. Hence the simplest form of Cauchy's
dispersion formula

................................ (3)

will be approximately satisfied, especially by the crown glasses.

As the curve F shows the dispersion relative to 1/X 2 , and
/ shows it relative to X, their slopes at corresponding points
would be in opposite directions but for the fact that the axis of
abscissae runs from right to left in fig. 2. In the interval
between their respective points of inflection, the slope of /
increases and that of F diminishes. Pulfrich, 1 following Sell-
meier's example, 2 has used the formula n = F(l/X 2 ) in investi-
gating the absorptions in the infra-red and ultra-violet.

25. Measurement of Absorption. The absorptions of a
number of glasses have been directly determined. The measures
relate partly to the visible rays with wave-lengths between
0'677/x and 0'436/x, partly to the more refrangible rays between
0'434/x and 0'375yu, and partly to the infra-red rays.

Absorption in the Visible Spectrum 0*677 0'436/u. The'
following observations were made by Miiller with Vogel's modified
form of Glan's spectrophotometer, 3 and are contained in a paper
of Vogel's. 4 They refer to the five glasses 0. 340, 0. 102, 0. 93,
0. 203, 0. 598 ; having the running numbers 64, 38, 37, 13, 51
in the list of Art. 17.

The investigation was prompted by the circumstance that the
flint O. 340 and crown 0. 203 were the glasses selected for the
objective of the great Potsdam refractor, and that the other glasses
mentioned were to be used in the spectroscope attached to the
instrument.

1 Ann. d. Physik u. Chem., 45, 648 and 664 (1892). See also Winkelmann's
Handbuch d. Phys., II. 1, 326.
*Ann. d. Phys. u. Chem., 143, 272 (1871).

3 JBerichte of the Berlin Academy, March, 1877.

4 Die Lichtabsorption als massgebender Faktor bei der Wahl der Dimension des
Objektivs fur den grossen Refraktor des Potsdamer Observatoriums. Berichte
der Berliner Akademie, Nov. 1896 ; also Mathematische u. naturw. Mitteilungen,
1896, 623.

OPTICAL PROPERTIES OF GLASS.

The thickness /3 (in millimetres) of each of the glass plates
used, and the index for the ^ line X = D'olSyu are here given.

O.|340

O. 102

0.93

0. 203

0. 598

148
1-5835

100
1-657

114-8
1-632

141-5
1-521

102-5
1-519

The loss by reflection was calculated by means of Fresnel's
formula

-MS8T'

denoting the ratio of the reflected to the incident light for
normal incidence on glass of index n. The value of n for the
6 X line was used.

The general law of absorption by a given medium for light of
given wave-length is, that the quantity of transmitted light
diminishes in a constant ratio for successive equal distances
traversed. The ratio of diminution for a variable distance x may
therefore be represented by the expression <;-**, e denoting the
base of natural logarithms (2'718). The constant multiplier k is
called the co-efficient of absorption. We shall write K t for e"**;
and, to deduce the transmission through a standard thickness a
from the observed transmission through a thickness & we have

Mtiller reduced his observations to a standard thickness of
10 cm., and thus obtained the following values of K^ for seven
different wave-lengths:

0-677

o-.Vso

0-535

0-477

(> l.V,

Q-4J6*

Flint 0. 340

0-939

0-878

0-907

()ss()

Ossn

(M-.SU

0. 102

0-794

0-829

USdS

0-782

0-700

<>;.;:<

410

0. 93

0-943

o.M.:t

0-879

0-871

0-tU

oso;

0-714

Crown 0. 203

*ra

0*71

O-MIS

OsT-J

0-800

04H

0-806

0. 698

o-tao

O-sls

0-792

<>::r,

0-771

0-770

0797

48 JENA GLASS.

At X = 0'436yu the observations were difficult, owing to the
faintness in the blue of the petroleum tlame employed as source
of light. They were therefore repeated by Vogel, whose eyes are
very sensitive to blue. He obtained the following values for K a :

\= 0-436/x.

Flint O. 340 -

0. 102 -

Crown 0. 203 -

0. 598 -

0-706

0765
0-655

For 0. 598 there is a striking discrepancy between the two
observers. Vogel gets much larger absorption here than Mliller,
though their observations in the brighter parts of the spectrum
were found to agree well.

Absorption for the more Refrangible Rays 434 375/u.
In the case of the three plates 0. 340, 0. 102, 0. 203, the investi-
gation was carried further up the spectrum by the aid of photo-
graphy. 1 The values of /3 and of the index for h (X = 0'410/x),
which was used in calculating the influence of reflection, are :

0.340. 0.102. 0.203.
P= 148 100 141-5
n h = 1-601 1-682 1-532

It is noteworthy that the absorption does not increase steadily
as the wave-length diminishes, but remains nearly constant over
considerable intervals, and then suddenly increases at certain places.
This leads to abrupt extinctions of light of certain wave-lengths
for certain thicknesses. For example, a plate of light flint 0. 340,
10 to 15 cm. in thickness, stops all rays of wave-length less than
0-370^. With the heavy flint 0. 102 there is a sudden fall in the
intensity of the transmitted light near Fraunhofer's line H.

Further, it was found that a plate about 15 cm. thick of flint
0.340 produced two absorption bands; one faint and diffused,
having its centre at 0437 /UL, the other conspicuous, with sharply
defined edges, at 0'4 1 8 6 /x. The breadth of the latter corresponded
to a difference of wave-length 0'0035/x. The latter band also
l lbid. t pp. 1226 and 630.

OPTICAL PROPERTIES OF GLASS.

showed itself, but not so strongly, with a plate of crown 0. 203
about 14 cm. thick. The heavy flint 0. 102 showed no absorp-
tion band.

In determining the absorption in the upper part of the
spectrum by photographic means, difficulty arises from the fact
that, for a given time of exposure, the darkening of the film does
not increase in proportion to the intensity of the light, but more
slowly. The effect, moreover, varies with the kind of photo-
graphic plate employed. In order to avoid this difficulty, Wilsing,
to whom the following determinations are due, compared only
negatives which had been exposed for equal times to beams of
nearly equal intensities. Thus his measures only depend on the
assumption that lights of equal intensity produce equal darkening
in equal times. By means of Nicol prisms (as in Zollner's photo-
meter), two beams of different intensity were reduced to the same
intensity ; and the ratios of reduction being known, the original
intensities could be compared. Silver bromide gelatine plates
were used. It was found that a difference of 5 per cent, in
intensity was appreciable. The following values were obtained
for K. :

0-434

[0-419]

0-400

0-396

0-390

0-375M

Flint O. 340, -

0-669

[0-411]

0-614

0-466

0-388

0. 102, - -

0-602

0-463

0-167

0-025

Crown O. 203, -

0-667

[0-611]

0-696

0-683

0*583

The numbers in brackets are interpolated values for the
absorption band.

Vogel also endeavoured to determine the absorption of the five
glasses in another way. 1 Strips of chloride of silver paper were
exposed in sunlight for equal times, immediately in front of and
immediately behind the glass plate to be tested. The degrees of
darkening were numerically estimated by comparison with a scale
prepared by gradually iiicrejisin^ exposures. As the paper could
not be fixed and toned, the comparison was made by yellow light
Equal degrees of darkening indicated equal products of intensity
and duration. The action of each glass was determined separately,

/Wd., pp. 1228 and 632.
D

50 JENA GLASS.

and the glasses were also compared one with another. The
following results were derived from a great number of observations :

fr K

Flint 0. 340 148 mm. 0'526

0-102 100 0-282

0. 93 114-8 0-356

Crown 0.203 141-5 0'589

0.598 102-5 0-604

These values of K a are for the portion of the spectrum which
acts most strongly on chloride of silver a portion extending from
G into the ultra-violet ; the strongest action being between h and
H. In calculating the loss by reflection, the values 1"654 for
0. 93 and T529 for 0. 598 were given to n h .

Finally, in view of the above-mentioned use to which the two
glasses 0. 340 and 0. 203 were to be put, Vogel gives mean
values to exhibit the difference between the visual and the
photographic absorptions.

For the visual rays, taking the mean of his own observations
and Mliller's, he deduces :

Flint 0. 340. Crown 0. 203.

JT a =0-84 0*85

For the photographic rays which act upon ordinary bromide of
silver gelatine films (their action beginning at F and extending
far into the ultra-violet, with maximum effect between H y and H & ),
Vogel adopts the following values and means :

VALUES OF K a .

\ Flint 0. 340. Crown 0. 203.

0-455/x 0-83 0-82

0-436 0-69 0-79

0-434 0-57 0-67

0-400 0-61 0-70

h H 0-53 0-59

0-390 0-46 0-58

Mean, 0'615 Mean, 0'692

Calculation of Coefficients of Absorption. From the
definition K x = e~ kx , we have

OPTICAL PROPERTIES OF GLASS.
Again, kx will be unity for a thickness # = !/&; hence

k may therefore be defined as the reciprocal of the distance that
must be traversed in the absorbing medium to reduce the intensity
to l/e of its original amount ; l k is accordingly the reciprocal of
a length. Employing the centimetre as unit of length, k can be
deduced from the foregoing tables by the formula

The following values are thus obtained for k : 2

0-677

0-580

0-535

0-503

0-477

0-455

O-436/i

Flint O. 340,

0-0063

0-0130

0-0098

0-0128

0-0182

0-0386

0. 102,

0-0231

0-0188

0-0213

0-0246

0-0357

0-0411

0-0569

0. 93,

0-0059

0-0102

0-0129

0-0138

0-0106

0-0214

0-0337

Crown O. 203,

0-0102

0-0137

0-0108

0-0137

0-0151

0-0196

00216

0. 598,

0-0151

0-0201

0-0233

(HMM

0-0260

0-0261

0-0227

X =

0-434

[0-419]

0-400

0-390

0-375 M

Flint O. 340,
0. 102,
Crown O. 203,

0-0564
0-0689

0-040.1

[0-0890]
[0-0493]

0-0479
0-0770
0-0364

0-0785
0-3689
0-0540

0-0947

oo.- 10

These figures show that the absorption of the heavy flint
0. 102 exceeds that of the other glasses more and more as the
wave-length diminishes, and also that ita absorption for the longer
waves is not surpassed even by the two crown glasses. It is a
strongly absorbent glass for the whole spectral region investigated.

At the red end of the spectrum the two flints O. 340 and 0. 93
are much less absorbent than the crowns 0. 203 and 0. 598. At
the violet end the case is reversed.

1 Calculation would be facilitated if 10 were put in the place of e in defining the
coefficient of absorption. The logarithms in the formulae of reduction would
then be common logarithms; and the coefficient of absorption would be the
reciprocal of the distance in which the intensity is reduced to ^ of its original
amount. J. D. E.

'The figures in brackets relate to the absorption band.

52 JENA GLASS.

Between the two flints 0. 340 and 0. 93, as far as the com-
parison extends, there is not much to choose.

Of the two crowns, 0. 598 is more strongly absorbent than
0. 203. The coefficient '0227 given for 0. 598 at X = '436/x is
Miiller's value, and is probably too small. Vogel's determination
is -0423.

Measurement of Absorption for the Infra-Red Rays.
Rubens has investigated the transparency to infra-red rays of
the nine glasses for which he determined the dispersion in the
same region. 1 If two plates of thicknesses /3 V /3 2 be placed in
turn in the path of a ray, and I v / 2 be the intensities after
transmission, we easily obtain from equation (2)

The ratio / 2 // x was determined by bolometric observation, and
k deduced by means of the above relation. The results are given
in the following table :

0-7

0-95

1-1

1-4

1-7

2-0

2-3

2-5

2-7

2-9

3-l^t

S. 204

o-oo

o-oi

0-06

O'lO

016

0-21

0-37

0-85

1-25

1-73

S. 179

0-02

0-05

o-io

0-18

0-40

0-71

0-14

1-69

0. 1143

0-02

0'03

0-05

0-07

0-11

0-17

0-34

0-75

1-31

0. 1092

o-oi

0-04

0-05

o-oi

0-01

0-09

0-20

0-34

0-51

073

1-24

0. 1151

0-02

o-oi

0-02

0-06

0-11

0-23

0-29

0-79

1-15

O. 451

o-oo

o-oi

0-02

0-05

0-08

0-18

0-25

0-62

1-09

O. 469

o-oo

0-02

o-oi

0-02

0-03

O'll

0-41

0-69

0. 500

o-oo

o-oi

0-08

0-30

0-63

S. 163

o-oo

0-02

o-oi

0-06

0-25

0-51

Taking into account both the magnitude of k and the distance of
the absorbing region from the visible spectrum, the following
conclusions are easily drawn. In the infra-red, the borate S. 204
and the phosphate S. 179 are the most strongly absorbent, and
the crowns 0. 1143, 0. 1092, 0. 1151, which differ little from
one another, come next. The light flint 0. 45 1 occupies an
intermediate position between these and the heavy flints 0.469,
0. 500, S. 163, which are much less absorbent than the crowns.

1 Ann. d. Physik u. Ohem., 45, 258 (1892).

OPTICAL PROPERTIES OF GLASS. 53

26. Comparison of Glasses Continued. A comparison of
the absorptions of two substances can often be deduced from a
comparison of their dispersions in different parts of the spectrum.
If dispersion depended exclusively on absorption, a knowledge of
the quantities A, a, y defined in Art. 17 would suffice to give a
clue to the position of at least one of the two absorption regions
by the application of the following rule. In comparing two glasses,
if one of them has the greater total dispersion and at the same
time a relatively large dispersion in the upper portion of its
spectrum (especially if accompanied by relatively small dispersion
in the lower portion), then this glass has stronger absorption in
the ultra-violet than the other. Interchanging the words upper
and lower, we obtain the rule for the indication of absorption in
the infra-red.

As a matter of fact, dispersion does not depend exclusively
upon absorption, but is influenced by other properties, especially
ly density; but it is usually permissible to regard absorption as
the main influence. There is, however, one exceptional case
which requires a modification of the above rule. If the larger
total dispersion is due to greater density, a larger relative upper
dispersion may be an indication of smaller absorption in the
infra-red ; and in like manner a larger relative dispersion in the
lower part of the spectrum may be an indication of less absorption
in the ultra-violet. We shall apply these remarks to the prin-
cipal glasses in the list of Art. 17.

The list contains eight heavy silicate flints. Arranged in order
of increasing A, they form the following series: 68, 38, 39, 40,
41, 42, 43, 44, in which the value of y increases from term to
term, and there can be no doubt that this indicates a progressive
increase of the upper absorption. It is worthy of note that the
mean dispersion increases more rapidly than the simultaneously
increasing density. The same remarks apply to the five ordinary
silicate flints: 34, 35, 36, 37, 67. But in the nine light flints,
75, 63, 29, 65, 64, 30, 31, 66, we find that the exclusive
influence of the upper absorption is no longer discernible ; No. 30
h its small y is a well-marked instance. It probably owes
its high place in the series to its great density. Of the seventeen
crown glasses*, 11,47, 46, 7, 50,49, 9, 13, 51, 52, 17, 18,54,
56, 23, 26, the last six form a group in which a-rain the upper
absorption increases from term to term. In passing from 1 7 to 1 8,

JENA GLASS.

there is perhaps also a diminution of the lower absorption. In
the first eleven crown glasses, the dispersion increases very
slowly, and the dispersion-ratios and y progress irregularly,
so that we can only compare individual members of the series.
In passing, for instance, from 11 to 47, and from 50 to 49, there
are signs of increase of the lower absorption. Thus it is only
in the crowns that infra-red absorption makes its presence
evident.

Among the fifteen barium silicates, 12, 16, 53, 73, 71, 55, 72,
20, 57, 58, 59, 60, 61, 62, 76, there are four crowns, 12, 16, 71,
20. Density plays an important part in the case of these glasses.
The strange fact of two crown glasses, 71 and 20, appearing in
the midst of a series of flints would at once suggest this. They
evidently owe their place tq their great density. The relation of
the barium glasses to the silicates may be seen by comparing
12 with 18, 53 with 56, 73 with 23, 20 with 26, 59 with 74.
A glance at the accompanying table, in which the density is given
under " s" shows that the barium glasses absorb the ultra-violet

K^A

10 3 a

lO'/S

10*7

12. 0. 227. Barium Silicate Crown, -

909

640

703

566

2-73

18. O. 114. Soft Silicate Crown,

910

634

705

572

2-55

53. 0. 463. Baryta Light Flint,

1020

635

706

575

3-11

56. 0. 381. Crown of high dispersion,

1026

629

709

582

2-70

73. O. 846. Baryta Light Flint,

1042

631

707

578

3-01

23. 0. 152. Silicate Glass, -

1049

628

708

582

2-76

20. O. 202. Densest Barium Silicate Crown,

1092

632

706

573

3-58

26. 0. 214. Silicate Glass, -

1102

626

709

584

2-73

59. O. 527. Baryta Light Flint,

1133

623

709

582

3-19

74. O. 726. Extra Light Flint, -

1142

623

709

586

2-87

rays much less than silicates of only slightly greater dispersion.
The fall in dispersion which would cceteris paribus accompany
diminished ultra-violet absorption is, in this case, largely balanced
by the effect of increased density. It is true that a comparison
of the partial dispersions of 1 2 and 1 8 or of 5 3 and 5 6 might lead
one to conclude that barium glasses absorb the infra-red rays
more strongly than ordinary silicates, inasmuch as their dispersion

OPTICAL PROPERTIES OF GLASS.

at the lower end of the spectrum is greater; and a similar
instance is furnished by the comparison of 0. 1143 and 0. 1151 :

0. 1143. Dense barium silicate crown, 640
0. 1 151. Silicate crown of high dispersion, 634

704
713

584
597

But neither Rubens' direct observations on absorption in the
infra-red, nor our knowledge of the run of dispersion in that
region, indicate any strong infra-red absorption in barium glasses.
Hence the facts must be interpreted as showing that in barium
glasses the ultra-violet absorption is exceptionally small. This
smallness of absorption tends to make the dispersion small,
especially at the violet end, while the high density tends to
make it large.

Of the six borosilicates, 69, 5, 45, 19, 25, 27, only the last
two are flints. A comparison of 19 with 12, or of 27 with 61,
leaves no doubt that in this group the influence of lower absorp-
tion is stronger than in the barium glasses. This is also easily
seen by comparing the partial dispersions of 25 and 58 :

25. 0. 164. Borosilicate flint,
58. 0. 543. Baryta light flint,

710
699

786
790

644
650

2'81
3'11

The infra-red absorption of the borosilicates is also greater
than that of the ordinary silicates. Hence we should expect
their ultra-violet absorption to be less, and a comparison of 45
with 6, or of 25 with 74, justifies this inference.

The seven borates, 10, 21, 22, 24, 28, 32, 33 are all flints
except the first Their infra-red absorption is still greater th in
that of the borosilicates, as will be seen on comparing 10 with
45, 21 with 19, 24 with 25:

10A

10a

10*0

10S

10 S. 52. Light Borate Crown.

840

700

555

46. O. 599. Borosilicate Crown,

051

701

J4S

-'1 S. 35. Borate Flint, ....

702

:*i:<

*-56

19. O. 197. Borosilicate GUn,

045

704

9-04

24. S. 8. Borate Flint,

1129

045

571

2 s-J

25. O. 164. Borosilicate Flint,

1114

706

578

56 JENA GLASS.

A fortiori the infra-red absorption of this group exceeds that
of the ordinary and barium silicates. The following are examples:

10 5 <S 2 10 5 <$ 3 s

22. 0. 252. Borate flint, 667 722 582 2*57

56. 0. 381. Crown of high dispersion, 644 729 596 2'70

53. 0. 463. Baryta light flint, 648 720 586 3'11

32. S. 17. Dense borate flint, - 990 1128 937 3'51

66. 0. 318. Ordinary light flint, 960 1124 952 3*48

76. 0. 748. Baryta flint, 965 1142 965 3'67

The same thing is shown by comparing 10 with 11, 47, 46,
7, 50, 49; 21 with 56; 22 with 23; 24 with 74; 28 with
65 ; also 21 with 16, and 24 with 57, 58, 59, 60, 61, etc. It
may further be remarked that, in comparing successive terms of
the above series of borates, the influence of ultra-violet absorption
becomes more and more evident ; and that there is no decided
indication of infra-red absorption.

The four phosphate crown glasses, 1, 2, 3, 4, having but
weak dispersion, do not afford good comparisons. The influence
of infra-red absorption is weaker in the first two than in the
borates :

10 5 A 10 3 a 10 3 /? 10 3 y s
10. S. 52. Light borate crown, 840 667 700 555 2'24

1. 0. 225. Light phosphate crown, 737 658 698 552 2'58

2. S. 40. Med. phosphate crown, 835 654 702 557 3'07

The same remark applies to the phosphate S. 1 7 9 when compared
with the borate S. 204. In this case the inference is confirmed
by the run of their dispersions in the infra-red.

Dispersion from : 2'0/x 1'4/x l'4yx 0'8/x

S. 204. Borate crown, - 0'0105 0'0094

112

S. 179. Medium phosphate crown, 0'0086 0'0079

1-09

The numbers 1-12 and TO 9 written underneath are the ratios of
the first dispersion to the second. These show that the influence
of absorption is not much greater in the borate ; a result con-
firmed by Eubens' values of the coefficients of absorption.

OPTICAL PROPERTIES OF GLASS. 57

In the very dense barium phosphates, 3 and 4, we again find
the small ultra-violet absorption characteristic of barium. Their
int'ru-ivd absorption is somewhat less than that of the boro-
silicates.

IC^A l&a lO 3 ^ 10*y S
19.O. 197. Borosilicate glass, - 929 645 704 572 2'64

3. S. 30. Dense barium phos-

phate crown,- 884 644 703 565 3'35

4. S. 1 5. Densest barium phos-

phate crown, 922 641 703 565 3*66

The two barium phosphates would thus seem to be the most
transparent of all glasses for the ultra-violet rays.

The five glasses still remaining, namely, the three zinc glasses
70, 15, 48, the lime silicate 8, and the potash silicate 14, do not
furnish very definite conclusions. Perhaps, however, from the
comparison of 14 with 17, we may infer that the influence of
the lower absorption band is even weaker in potash glass than in
ordinary silicate crown.

( "inparisons of this kind do not lead to clear inferences when
the substance of larger A has the smaller a and y, and there
is little difference of density. Such an example is furnished by
the two silicate glasses 49 and 9.

10 6 A 10*a 10*0 Wy s

49. 0.567. Silicate crown, - 859 645 704 569 2'51
9. 0.138. Silicate crown, 872 642 704 567 2'53

27. Influence of Temperature on the Refraction of Glass.
The index of any substance for a ray <f Lrivrn wave-length alters
with the temperature of the substitute. In order to estimate
the variations correctly, it is necessary to compute the indices
relative to air at constant temperature, or to vacuum. Pu If rich 1
investigated the influence of temperature on 12 glasses (as well as
on rock-salt, sylvin, quartz, and fluorspar), and showed that the
observed temperature-coefficients, which. liko those of most 8<>li<l
bodies, present an appearance of great irregularity, had a definite
physical significance.

By means of prisms made from the 12 glasses, their indices

> Annal. d. Pkytik H. Chem., 45, 009 (1892).

JENA GLASS.

for the D line, and dispersions for the three intervals CD, DF,
FG\ relative to air at the same temperature, were measured (by
Abbe's method of a ray returning upon itself). In the first
instance the measures were made at the temperature of the room.
The values obtained are given in the following table. As the A'

n D

100A

IWCD

KWa

lO 5 ^

1. O. 225. Light Phosphate Crown,

1-5160

734

70-3

219

lO^

10',

515
701

402

548

2. S. 40. MediumPhosphate Crown,

1-5619

845

66-5

253

592
701

469
555

0. 627. Borosilicate Crown,

1-5128

806

63-7

241

564
700

449
557

St 205. Light Borate Crown,

1-5075

838

60-6

255

583
696

459
548

0. 1022. Silicate Crown,

1-5173

860

60-2

254

606
705

475
552

16.0. 211. Dense Barium Silicate
Crown,

1-5727

988

58-0

295

693
701

560
567

59.0. 527. Baryta Light Flint,

1-5718

1130

50-6

329

801
709

658

582

0. 658. Light Borosilicate Flint,

1-5452

1084

50-3

320

764
705

622
574

29. O. 154. Light Silicate Flint,

1-5710

1324

43-1

382

942
711

789
596

O. 544. Ordinary Silicate Flint, -

1-6130

1652

37-1

472

1180
714

1004
608

42.0. 165. Dense Silicate Flint,

1-7545

2738

27-6

768

1970
720

1720
628

44. S. 57. Densest Silicate Flint, -

1-9625

4877

19-7

1336

3541

726

3235
663

line, on account of its faintness, was not observed, the dispersion
3 from A to D, and the corresponding ratio a, are absent from
the table, the dispersion from C to D being given instead. With
this exception, the notation is the same as in the catalogue of
Art. 17. Those of the glasses which belong to the catalogue
have their catalogue numbers prefixed. It may be remarked that
the silicate crown O. 1022 is distinguished, by its small 7 = 0'552,
from all the silicates in the general list, none of which have 7
less than 0*564.

A second set of measures were then made at higher temperature,
the prism under examination being enclosed in a steam-heated

OPTICAL PROPERTIES OF GLASS.

chamber. The results gave the amounts by which the indices for
the lines C t D, F y G f were changed owing to the joint elevation
of temperature of the glass and surrounding air. A view of the
interior of the chamber was obtained through a glass plate, which
was perpendicular to the rays, and therefore produced no deviation.
The change of index so found, divided by the corresponding differ-
ence of temperature, gives the average change of relative index
per degree Centigrade, the air being at the same temperature as
the glass. The values thus obtained are reduced to vacuum by
multiplying the observed relative index by the absolute index
of air at the actual temperature, it being assumed that the
absolute index of dry air at C. and 760 mm. is I'OOO 294 for
all colours, and that for other temperatures and pressures n 1
is proportional to the density. 1

Pulfrich's results are contained in the following table. The

Temperature

0. 225. Phosph. Cr.,

16'6 99-7
58-1

-0-202
-0-093

-0-190
-0-080

-0-168
-0-057

-0-142
-0-031

S. 40. Phosph. Cr.,

21-0 99-6
60-3

-0-314
-0-204

-0-305
-0-194

-0-246
-0-134

-0-237
-0-124

O. 027. Bor. Sil. Cr.,

5-899-9
52-8

0-119
0-233

0-137
0-251

0-178
0-293

0-213
0-329

S. 205. Bor. Cr., -

20599-5
600

-0-066
0*040

-0-074
0-033

-0-033
0-075

-0-003
0-106

O. 1022. Sil. Cr.,

19-0-99-7
59*3

-0-129
-0-020

-0-105
0-004

-0-060
0-050

-o-oio

0-101

0. 211. Bar. Sil. Cr.,

16-6 99-1
57-8

0-021
0-132

0-040
0-151

0-103
0-216

0-142
0-255

O. 527. Bar. FL,

17-5-992
58-3

-0-008
-0-103

0-014
0-125

0-080
0-192

0-137
0-250

0. 658. Bor. SiL Fl.,

19-3-99 -2
59-2

0-267
0-376

0-299
0-408

0-356

o K;J

0-410
MM

0. 154. SU. FL,

17-999-2
58-5

0*225
0-336

0-261

0-446

0-407
0-520

0. 544. SiL FL,

11-1-99-1
55-1

0-244
0-360

O'JSl

0397

0*606

0-603
MU

0. 165. Sil. Fl.,

13-899-6
56-7

0-700
0829

0-775
0-906

1-051
1-182

1-311
1-443

8. 57. Sil. Fl.,

18-5-9912
58*8

1-204

1 -.W,

1-449
1-688

ftt

2-810
2-064

1 The theory of the experiment is given by Pulfrich in Winkelmann'i JfandbutA
d. Phynk, II. 1. 308.

JENA GLASS.

column headed " Temperature " contains the temperatures of the
two observations and their mean. The columns headed C, D, F, G'
give the average change of absolute index per degree. This is
adopted as the true rate of change at the mean temperature. The
numbers are given in units of the fifth decimal place, and indicate
an increase or decrease (with increasing temperature) according as
they are positive or negative. Since the corresponding change of
relative index is of practical importance, it is also given, under-
neath the change of absolute index.

Comparison of the values in the above table shows that the
dispersions CD, DF, FG' always increase with the temperature,
whether the indices increase or decrease. The single exception
furnished by the interval CD for the glass S. 205 we shall
disregard, as due either to some exceptional cause or to a mistake
in the observations.

Change of temperature also affects the run of dispersion, as is
shown by the following figures, which express the rate of increase
(per degree) of the absolute dispersion in millionths of its original
amount :

FG'

225,

40,

100

627,

205,

-31

1022,

105

211,

527,

658,

100

154,

544,

113

165,

140

151

57,

183

181

223

The inequality of the three numbers for any individual glass
indicates that the run of its dispersion has been changed.

Diminution of Index arising from Diminution of Density
with Rise of Temperature. In attempting a satisfactory
explanation of the observed data, the fact must be taken into

OPTICAL PROPERTIES OF GLASS. 61

account that thermal expansion causes diminution of density, and
thus tends to diminish the index. Nevertheless, the indices of
many glasses, especially Hints, increase with temperature; hence
some other cause must be at work which overpowers the influ-
ence of density. The following considerations may throw some
light on the subject.

The true law of relation between index and density is
unknown, but attempts have been made to represent it by
empirical formulae, based on the assumption that a certain
quantity called the constant of refraction does not vary with
changes in density due to temperature. This constant is
variously defined by the three following expressions :

n*-l n'-l 1

n denoting the index and d the density.

Employing each of these expressions in turn for calculating
the change of index due to mere change of density in heating,
and using the observed coefficients of expansion for the glasses
in question, Pulfrich found that in no single instance was
there an actual diminution of index as large as the cal-
culation gave. Hence it seems probable that, even in the case
of those glasses whose indices diminish as the temperature in-
creases, there is some counteracting cause at work tending to
increase the index.

This conclusion is confirmed and rendered more definite by the
following considerations. According to the first of the thivr
expressions for the constant of refraction, the run of dispersion is
not affected by change of density. [w c 1, n D l, n p l t and
their differences n D n Ct n f n p would all diminish in the same
ratio as d.] All three expressions agree in making both index
and dispersion diminish with increasing, temperature. As a
matter of fact, however, the dispersion increases. [n c 1.
etc. increase instead of diminishing, and the dispersions n D n c ,
n f n D increase.] Thus the additional cause which we
have supposed to be at work tending to increase the index,
also increases the dispersion, and further, this cause be-
comes more operative as the blue end of the spectrum is
approached.

62 JENA GLASS.

Strengthening of Upper Absorption Band with Increase of
Temperature. The above reasoning points to the probability
that the upper absorption band grows stronger as the tempera-
ture increases, in all glasses, and especially in Hints. This
would account for the kind of increase that is observed, and
would explain the fact that the dispersion always increases,
though the change of index is sometimes positive and sometimes
negative.

Pulfrich, in fact, drew this conclusion and confirmed it by direct
observation. He found that glasses which had only a slight
yellow tinge at ordinary temperatures acquired a continually
deeper tint when they were heated in porcelain vessels to 200,
300, and upwards, up to the melting point (about 400). The
effect, as might be expected, was especially strong in silicate Hints ;
in S. 57 the boiling point of water was sufficient to produce it,
and, on the other hand, a cooling mixture of solid carbonic acid
dissolved in ether produced marked weakening of the yellow tinge
of this glass. When pieces of the glass were strongly heated,
they " gradually assumed the colour of dark amber ; and when the
temperature was reached at which the glass began to soften, it
appeared dark red or brown." Spectroscopic examination showed
that " even a small thickness of the hot glass stopped all rays of
the visible spectrum except a small portion in the red. The
original yellow tinge was restored by re-cooling. The experiment
could be repeated on the same piece of glass any number of times
with the same result, showing that the action was not chemical
but purely physical." These experiments at the same time
furnished an independent explanation of the fact, observed by
F. Vogel, that the index of flint glass changes more rapidly at high
than at low temperatures ; l for the deepening of tint, which
occurred on heating the glass S. 57, was much more rapid
at the higher temperatures. These results are borne out by
phenomena often witnessed at the Jena Glass Works. It may
be added that similar phenomena are exhibited by some other
substances.

28. Continuation. Extension of the Observations to Higher
Temperatures. At the suggestion of Pulfrich, the study of the

l Annal. d. Phys. it. Chem., 25, 87 (1885).

OPTICAL PROPERTIES OF GL.\.

above-mentioned phenomenon was taken up by J. O. Reed, 1 and
extended to temperatures as high as the conditions permitted.
Seven glasses were examined (and also the minerals calc-spar,
quartz, and fluor-spar). Pulfrich's method was closely followed,
but instead of the Gr line, a stronger line ffg y was used, and
denoted by G".

The optical characteristics of the glasses experimented on are
;jiven in the following table. The values under the headings
a' t y are analogous to a and y of the catalogue in Art 17.

n D

10"A

4NS.-,

10*CD

itft*

10W

44. S. 57. Densest Sil. Flint, -

1-96249

19-7

10V

ISM

_'7l

10/3

10V

:<:4<i
726

633

S. 163. Densest Sil. Flint, -

1-89035

3994

1106

277

2888
723

-J4S4

42, 0. 165. Dense Sil. Flint, -

1-75453

2743

I' t

768

2SM

1975
720

1646
600

29. O. 154. Light Sil. Flint,

1-57090

1326

43-0

382 '.n
288 71-J

7.V.
:>7<>

59. O. 527. Bar. Light Flint,

1-57171

1136

60-4

332 804

292 7"'.'

855

16. 0. 211. Dense Bar. Sil. Cr.,

1-57270

9Q|

57-6

295
297

IM
703

.-,:,-_'
556

O.1299, (Like 71. 0.1209), -

l'tHK7

1056

57-4

m
m

747
797

:,::,
544

The five glasses containeil in the catalogue have their current
numbers prefixed. The values of n D are reduced to tempera-
ture 20.

The arrangements for observing at high temperatures are
described in detail in Reed's article. 2 The results are calculated
in the same way as Pulfrich's, but smaller intervals of temperature
are employed ; and the result for each interval is assigned to the
mean temperature of the interval.

These results are tabulated below. The IIUMH temperatures
t referred to are given under t m \ the remaining columns contain
the corresponding changes of absolute m<lc\ p< r degree in units of
i In- fifth decimal place.

*Annal. d. Phy. M. Chtm., 66, 707 (1896).
., 711.

JENA GLASS.

t m

62 -6

1-218

1-472

2-110

2-800

S. 57.

156-2

1-579

1-809

2-536

Dense Sil. Flint.

233-0

1-928

2-251

3-212

281-0

1-591

1-911

2-918

60-5

1-119

1-278

1-752

2-161

S 163

125-5

1.275

1-442

1-959

2-477

Dense Sil. Flint.

177-5
250-5

1-379
1-577

1-594
1-783

2-098
2-396

2-617
2-992

330-0

1-808

2-027

2-753

57-7

0-703

0-778

1-058

1-294

126-0

0-916

1-051

302

1-668

O-\fiK

176-5

0-960

1-092

430

1-714

Dense Sil. Flint.

231-0

280-5

1-127
1-277

1-237
1-396

632
790

1-993
2-140

325-0

1-382

1-544

960

2-405

379-0

1-758

1-904

2-263

2-893

58-0

0-226

0-250

0-307

0-360

O 154

149-6

0-324

0-362

0-456

0-548

Light Sil. Flint.

251-5
351-5

0-509
0-577

0-568
0-639

0-666
0-751

0-768

0-870

436-5

-1-861

-1-720

-1-504

-1-329

56-5

0-014

0-045

0-107

0-150

0.527.

157-1

0-094

0-111

0-179

0-246

Bar. Light Flint.

261-5

0-144

0-167

0-249

0-355

357-0

0-217

0-249

0-350

0-461

61-2

0-024

0-035

0-092

0-099

0. 211.

154-0

0-096

0-113

0-152

0-186

Dense Bar. Sil. Cr.

259-0

0-156

0-174

0-223

0-258

358-0

0-221

0-247

0-297

0-340

55-9

0-394

0-410

0-504

0-528

0. 1299.

148-0
251-0

0-419
0-455

0-444
0-489

0-543
0-603

0-577
0-629

356-5

0-509

0-555

0-648

0-682

Further data to assist in drawing conclusions are given in the
following summary :

n D

n' D

n D n D

S. 57

250 300

299

1-96243

96162

81 . 10- 6

S. 163

250300 ?

364

1-89033

89016

O. 165

300330

408

75448

75434

O. 154

380400

452

1-57089

56996

0. 527

410450

406

57170

0. 211

470490

406

57270

0. 1299

490500

404

1-60983

60983

-1

OPTICAL PROPERTIES OF GLASS. 65

The second column, headed t ty indicates (somewhat roughly)
the range of temperature within which softening occurs. In the
cases of O. 211 and 0.1299 the temperatures given are those
at which any stress present in the glass quickly disappears,
and are not softening points in the usual sense ; true softening
not commencing till a much higher temperature is attained.
/' denotes the highest temperature at which observations were
made, n D the relative index before, n' D after heating. The differ-
ence of the two is given in the last column.

The observed changes of index, in every case, without
exception, tended to increase the three dispersions CD, DF,
FG".

The flint S. 57 shows the greatest increase both in index and
in dispersion ; and the heating of it produced such a large increase
in the upper absorption band that the line G" vanished completely,
even at 100 120. There is, accordingly, only one observation
for this line in the table of experimental results. The rate of
i IK Tease of index, however, reaches a maximum between 200
and 250; and is decidedly lower at 281 than at 233.
Reed suggests, as the explanation, the proximity of the melting
point.

For S. 163 the G" line vanished at a little above 300. No
maximum was observed in the rate of increase of index. The
highest temperature to which the glass was exposed was 364;
and as no sign of softening was here observed, the melting point
must have been considerably higher.

The flint 0. 165 ranks third as regards index and dispersion,
and also as regards increase of absorption. As this glass with-
stood a temperature of 408 without showing any change of
form, its melting point must be much hi^lin

In the case of the light flint O. 154, the rise of index attain-
a maximum lietween tin 1 mean temperatures 250 and 355.
indices begin to decrease during the last observation -interval,
tin- decrease UMML: much more rapid than the previous increase.
Tins suggests that, in the case of S. 57, the maximum met with

the rate of increase of index wius the premonitory sign of a
reversal, such as has actually taken place in 0. L54. Th.- t h.-rmal
ition of index must be zero for Home temperature Itetween

1 and 400. The increase of <! u gives no sign

,, n ; i.ut. nn the contrary, as is shown l.y the accompanying

66 JENA GLASS.

figures, grows more and more rapid, and is very large for the final
interval.

CD DF FG"

24 57 53

38 94 92

59 98 102

62 112 119

141 216 175

There can be little doubt that at the last the glass was
not far from its true softening point; and we have thus
evidence in favour of the explanation put forward in the case of
s. r>7.

The three remaining glasses, 0. 527, 0. 211, 0. 1299, exhibit
only a slow rise of index, nearly proportional to the rise of
temperature. The increase of dispersion is also small, a fact
consistent with the weak absorption of these glasses. The
spectrum lines remain bright and sharp even at high tempera-
tures. The highest temperatures of observation are still far from
the melting point.

The agreement with Pulfrich's previous observations of the
five glasses, S. 57, S. 165, 0. 154, 0. 527, 0. 211, is very satis-
factory.

The values of n D n' D show that, in the case of the glasses
which were not heated to near the softening point, there was no
appreciable change of index. In those which were further heated,
the index was diminished, especially in the case of S. 57 and
0. 154. It may be mentioned, in explanation, that when optical
glasses are freed from stress by " fine-cooling " the index is
somewhat raised. When, however, the same glasses are heated
anew to the softening point, and then cooled without special
precaution, the index is again lowered, and becomes nearly the
same as if the glass had been merely cooled in the ordinary
way.

29. Optical Properties of quickly cooled Glasses. When a
lump of glass passes, by rapid cooling, from the plastic to the
solid state, the outer portions solidify while the interior is still
soft. As the cooling and its attendant shrinkage proceed, the
outer layers are brought into a state of thrust and the central

OPTICAL PROPERTIES OF GLASS. 67

portions into a state of tension. The glass, when it has cooled
down, is thus neither optically homogeneous nor optically isotropic;
and accordingly produces both curvature of rays and double
refraction.

The former action was studied in glass cylinders obtained by
]'< Hiring melted glass into iron tubes. The double refraction was
observed in glass plates, obtained by putting a fragment of clear
glass into a fire-clay mould, gradually heating it till it first
-oftened and then ran in the mould, and afterwards cooling it
ratlin- .juickly.

Cylindrical Glass Plates acting like Diverging Lenses.
Some < quickly cooled cylinders were made by Schott (1886) at
the request of S. Exner, who, like others before him, had been
led, from study of the eyes of animals, to investigate the dioptric
properties of cylindrically stratified media. 1 From the mode of
preparation of such a glass cylinder, it is natural to suppose that
its geometric axis will also be its approximate optical axis of
M mmetry, and that it will be doubly refracting after the manner

f uniaxal crystals, while at the same time showing an increase

index from the axis outwards. Suppose the end of such a
<y Under to be ground to a flat surface perpendicular to the
A ray of ordinary light incident on this surface will
be split into two rays polarised in and perpendicular to
tin- plane through the axis, like the ordinary and extraordinary
ray in a uniaxal crystal. This double refraction will be

iily slightly noticeable if the incident ray is nearly parallel
to the axis and the cylinder so short as to be merely a disc.
I >ut, in all cases, that ray at least which is polarised in the
plane of the axis will follow the same law as a ray of
ordinary light in a singly refracting medium stratified cylin-

Jly.
\<>\v it will easily be seen that, according i. II principle,

irallel pencil falling on the whole end surface of the cylinder
in the direction of will, owing to In-nding of the rays

within the glass, be rendered divergent or convergent a-
an the velocity of the light in the outer layers is less or greater

i in the inner layers, i.c., according as the in .-ases or

decreases from the axis outwards. For .my ray in a plane

1 Uebr Cylinder welche optbche Bilder entwerfen, PjlAfftrt Archir /. d. 99$.
. 38, p. 274 (1886), and 39, p. 244 (1886V

68 JENA GLASa

through the axis, the curvature at any point is given by the
equation

dn
where n = , :

p being the radius of curvature, n the index at the point, x its
distance from the axis, and (p the angle which the tangent to the
ray makes with the direction of the axis. If the index increases
outwards, the curved ray is convex to the axis, and p is negative;
the opposite is the case if it decreases outwards. A ray incident
normally on the end surface of the cylinder will (at least near
the point of entrance), be more curved than one obliquely incident
at the same point, as is seen from equation (1).

The law of curvature expressed by (1) was first given by
Bravais, 1 who deduced it from Huygens' principle, for the case
of a medium stratified in parallel planes. An argument against
Monge's theory of mirage was removed by it. Bravais' paper
being but little known, the law was rediscovered [by James
Thomson, who published it at the British Association meeting
in 1872 ; and numerous consequences were shortly afterwards
deduced from it by Everett, 2 who discussed its application to
cylindrical stratification.] 3

If, from a glass cylinder in which index is a function of
distance from the axis, a plate be cut having its faces per-
pendicular to the axis, this plate will act as a dispersive or
collective lens, according as the index increases or diminishes
outwards. When a pencil of parallel rays is incident normally,
the curvature impressed on the rays within the plate takes the
place of the deviation due to the prism-like action of an ordinary
lens. As shown by Exner, 4 the analogy between lens and plate
is complete when the index satisfies the relation

n = n + M*, ............. . ................ (2)

where n is the value of n at the axis, and c is a constant. In

1 Annales de Chim. et de Phys., 46, 492 (1856).

2 [See two papers in Phil. Mag., 1873, and Deschanel, Part. IV.]

3 [The original cites continental rediscoveries of much later date.]

4 Compare conclusion of paper quoted above, and another " Linsenwirkung
nicht hoinogener Korper," Ann. d. Phyx. u. Chem., 28, 111 (1886).

OPTICAL PROPERTIES OF GLASS. 69

this case the image formed by the plate of a bright point mi its
axis will have the same degree of sharpness as in the case of a
1. MIS. and the well known lens formula, connecting the distance of
object and image with the focal length, will hold unchanged for
the disc. In the case of the disc, the focal length will depend
nn the thickness e of the plate and the constant c, the law 1 being

/=-

,(3)

Quickly cooled glass cylinders only give dispersive plates, as in
them c is always positive. Fig. 4 illustrates K\m-r's proof of
the formula for collective plates.

OC is the plate, AB the axis, AC the incident, CB the
The thickness of the plate is neglected. We have

It <, /8 are small angles, and AO a, OB=b, we may put

xx ,

+ = en.
a b

Krom (1) 8= -en',

and h'-nn-

Nnw if relation (_!) Imlds, i = L'r/-, and therefore

a + I = ~ 2<>/ '

1 [This can be proved as follows. For rays of small inclination to axis, (1 ) gives

n , which by (2) is - 2ex/n. Angle between initial and final directions in
f "
glass =/p= - 2rw/w. Angle between incident and emergent rays in air -

must be equal to jc/f if / is focal length of equivalent
\lf= - '! . \

70 JENA GLASS.

Counting distances measured in the direction in which light
travels as positive, and those in the opposite direction as negative.
and substituting from (3), we obtain finally

111

b a ~ f

Double Refraction of quickly cooled Glass Plates. Glass
cylinders, such as these we have just been describing, when
placed between crossed nicols in parallel light, give concentric
coloured rings like those which a uniaxal crystal plate cut
perpendicular to the axis shows with divergent light. The
appearance is, however, less regular, and is disturbed by the
veins which are always present in the cylinders, especially if
the thickness is considerable. Czapski therefore chose quickly
cooled glass plates instead of cylinders for investigating double
refraction. 1

The plates were prepared in the manner described above.
Using only very simple apparatus, consisting of a collimator, a
telescope, and two nicols, he arrived at practically the same
results as were previously obtained by Kerr 2 in a similar
investigation with more elaborate appliances.

The collimator and telescope, each of 36 mm. aperture, arid
380 mm. focal length, are placed horizontal and directly pointing
at one another. The glass plate to be examined is laid between
them in a horizontal position, with two opposite edges at right
angles to the common axis of telescope and collimator. These
edges are ground and polished so as to form parallel vertical
planes. In the focal plane of the collimator is a horizontal slit,
before which the polariser is placed with the plane of polarisation
inclined to the horizon. The telescope, adjusted for infinity, is
directed upon the slit, which is illuminated by a lamp. The eye-
piece of the telescope is then removed, the analyser inserted in
its stead, and the draw tube pushed in to enable the eye to be
placed at the focus of the objective. With crossed nicols, a series
of approximately straight and horizontal interference bands will
then be seen, showing vivid colouring with white light. In each
half (upper and lower) of the field there is one dark uncoloured
band, and the coloured ones are symmetrical with regard to it.

l Annal. d. Phy*. u. Chem., 42, 319 (1891).
2 Phil. Mag., 26, 321 (1888).

OPTICAL PROPERTIES OF GLASS. 71

AVith monochromatic (sodium) light the bands seen are alternately
bright and dark. In both cases they are broadest at the centre.
This experiment teaches that a quickly cooled glass plate is
made up of a number of optically dissimilar layers approximately
parallel to its faces. A ray of light on entering any layer is
>plit int< twu, polarised parallel and perpendicular to the plate.
Let Tip and n 9 be the indices of the two polarised rays. In the
middle layer of the plate w p <w, and as we travel outwards
inwards the surface n p increases faster than n^ In the layer
giving rise to the dark band with white light n p = n,, and it mu\
therefore be called the neutral zone. In the layers outside it
n p >ng> If be the number of dark bands in either half of tin-
plate with monochromatic light, we have

(4)

where n is the index of the external layer, n of the central la\
X the wave-length in air, D the breadth of the plate between its
polished edges, and the subscripts^ and s denote that the light ia
polarised parallel and at right angles to the plate respectively.

Each of the two neutral zones behaves like a singly refracting
medium between crossed nicols, a fact which explains the preseiu
of the corresponding dark kind.

The next dark hand on the outer side is given by

and mi the inner side by

Aj,, X, denoting in either case the wave-lengths of the < nnj.mi. MM>
polarised parallel and at right angles to the plate in the 1
bordering the neutral zone. For, when the difference of phase of
t \\o perpendicularly polarised rays amounts to a whole wave-
:h. they will e<>ml>iiie in the same way as if the phaw di:
were zero; and the same is true for a difference of phase
amounting to any whole number of wave-lengths. The complete
series of dark hands is tlieielnie ,.htain<-d hy sukstitutin- thr
number .. I'M, 1 in e<|nali N \, be

the wave-length of a ray of monochromatic light in air. the wave-
X in a medium whose index is n is given h\ ;iX X^

72 JENA GLASS.

Substituting for \ p , X,, in equations (5) and (6) by means of this
relation, equation (4) is easily obtained.

The optical results just described correspond to what we should
expect on considering the manner in which such a glass plate
passes from the soft to the rigid state. The internal layers must
be in a state of tension, the outer of compression (or thrust) ;
hence between the two there must be an intermediate layer free
from stress.

The differences (n n Q ) p and (n n Q ) 8 on the left-hand side of
equation (4) may also be determined independently by a dioptric
method. Suppose the eyepiece replaced in the telescope, the
analyser having been withdrawn, and let the polariser be placed
with its principal section parallel to the glass plate, i.e. horizontal.
On adjusting the telescope for infinity it will be found that the
image of the slit is not in focus ; for a parallel incident pencil
becomes divergent on traversing the plate. Let e p be the distance
the eyepiece must be pulled out in order to get a sharp image,
and let e g be the corresponding distance when the principal section
of the polariser is at right angles to the plate, i.e. vertical. If
e p and e s be measured, the two required differences can then be
calculated from the formulae :

2r being the thickness of the plate, and / the focal length of the
telescope objective.

The following is the proof. Putting r for x in equation (2),
and D for e in equation (3), we have

V 2cD 2D(n-n o y

The distances F p , F g of the centres from which the rays diverge
after transmission through the plate are therefore

F = - F = - (8

P O 7") / \ ' ' ) 71 / \ " '

OPTICAL PROPERTIES OF GLASS.

Since both F t s are (on account of the smallness of n n ) large
compared to the distance of the glass plate from the objective,
they may also be regarded as the distances from the objective.
Hence we have

1 1 l l + 4 = i <>

If we eliminate F p and F t from equations (8) and (9), we
arrive at equations (7). The process which has here been
employed differs somewhat from Czapski's, which does not lend
itself to a short summary ; the numerical results, however, are

n-ely affected by the change.

The following table contains three sets of observations and the
values deduced for A p = (n n ) py A 4 = (n n ) t , and A p A r
A relate to a circular disc of crown glass ; set B to the same
disc, with the outer layers as far as the two neutral zones screened
off, so that here n n denotes the difference of indices of the
neutral zone and the mid-layer. Set C relate to a rhomb of Hint

-s. The quantities given are the means of numerous observa-
tions made at different times. Lengths are given in millimetres,
and for the wave-length of the sodium light employed the value
\,= .")893 x 10~ 7 mm. is assumed.

e p

UFA,

in' A.

lo-(A,-,X)

1"'U,-A.)

From jMs. (7).

Fro MUM jn. (4).

110

18-0

9-0

914

41 W

14;

110

Ifi

18-0

156

148

161

156

il-a

17-0

1463

1170

:;:<.

Tin- values obtained by the two independent methyls are in
i-Creement, and afford useful information with regard to the
refracting properties of quickly cooled glass. It will le noticed
that for the crown glass \ is alx>ut twice as great as A r

Disappearance of Double Refraction on heating the Glass.
If -jla.-ss in a state of stress is kept I'm Mum- tnnr at a hiirh
teni|MMature, the stresses gradually disapjx Although this

process involves pennanent di>pl,t -niH-nt .f .lementary ixirti"n<.

1 This result was calculated from the stated number 7 = 9. Apparently Ciapaki
has used the value 7 = 8 instead, which gives 802.

74 JENA GLASS.

it begins at temperatures much below those at which softening,
in the usual sense of the word, takes place. In studying tlu>
conditions for cooling optical glasses without the production of
stress, Schott endeavoured to determine for each glass the lowest
temperature at which relief of stress began to show itself by
diminution of double refraction. 1

He employed glass cylinders 10-15 mm. in diameter and 20-40
mm. in length, with their ends plane polished to admit of clear
vision through. The number of coloured rings shown by such a
cylinder between crossed nicols increases with the amount of
stress. Thus, if a glass cylinder on being heated shows fewer
rings than before, a diminution of stress may be inferred. In
Schott's experiments the heating was carried on in a thermo-
regulator which permitted temperatures of 350 477 to !>
maintained.

Five glasses were examined, namely, ordinary crown 682,
ordinary flint 672, borosilicate crown 792, Jena normal thermo-
meter glass 16 IH , and the borosilicate thermometer glass 59 111 .
The lowest temperatures at which there was an undoubted
diminution in the number of rings were :

Crown 682, - - 400 410

Flint 672, 350 360

Borosilicate crown 792, - 400 410

Thermometer glass 1 6 ] ll , 400 4 1

Thermometer glass 59 in , 430 440

The time of exposure to the given temperatures was 20 24
hours. Exposure to lower temperatures for the same time had
no effect, while higher temperatures made more rings vanish,
i.e. acted more quickly. Schott remarks that lower temperatures
might possibly have produced an effect if allowed sufficient time.

The temperature at which the effect becomes noticeable is
higher or lower according to the melting point of the glass in
question. As there are glasses more fusible than flint 672, and
others less fusible than borosilicate 59 m , it is to be assumed that
diminution of double refraction may begin below 350 or above
440.

In the case of optical glasses, these observations are of import-
ance, as indicating the temperature in the neighbourhood of which

l Zeitwhr.f. Instrumentcnk., 11, 330(1891).

OPTICAL PROPERTIES OF GLASS.

cooling must be most cautiously regulated for the complete
removal of stress. The application of the results to thermometer
will be discussed later.

30. Testing Lenses and Plates by Polarised Light. A
positive lens can easily be tested for the presence and character
of stress in the manner illustrated in tiir. -V

A is the source of light (a parallin lamp), C the lens, and E
the eye, A and E lieing conjugate foci. B and D are t\v<> Ni( >! V
prisms set parallel to start with. The distances beiiu; adjusted
so that the lens appears filled with li^ r ht, tin- Nimls are then
crossed. If the lens is free from stress the field will now appear
dark : hut if not, there will still be illumination. If the stress
is of a symmetrical kind a black cross will be seen on tin- bright
ti'ld: if irregularities are present, the cross will he distorted.
To examine the cross in all positions, the Nicols should l>e rotated
and not the lens, as the warmth <>t' the hand mi^ht cause loral
disturbance.

In testing plane discs for objectives, a slightly different
arrangement is employed, which is represented in tijj. u'. II
S is a concave mirror, and A and E are on opposite* sidr> of it>
ei-ntn- "f ennatnre.

PR ,

A moderate amount ..f Mimnetiieal leans a sl..u

increase of md-\ fr.im UOI t- OUtmmfmnoe, It ha iu> injurious

1 Communication from the OlMtechniachM Laboratorium, Jena, Die., 1888.

76 JENA GLASS.

effect. Irregular stress, on the contrary, produces capricious
variations of refracting power.

(l lasses with irregular stresses are not suitable for objectives
of any considerable size. If the defect is very slight it can be
partially compensated by tentative deviations from the spherical
form in polishing.

The fine-annealing process renders it possible to obtain objective
discs of diameters up to 35 cm. almost entirely free from stress.
With the ordinary cooling process, discs of 12 cm. diameter
generally show the black cross indicative of stress.

31. Elliptic Polarisation of Light reflected from Glass
Mirrors. According to Fresnel's theory a plane polarised ray
after reflection at the surface of a transparent body is again
plane polarised ; and as the angle of incidence (for a ray of
constant azimuth) increases from to 90, the plane of polarisa-
tion approaches the plane of incidence, coincides with it at the
polarising angle, and then passes beyond it. If we suppose the
reflected ray to be resolved into two components P and S,
polarised parallel and perpendicular to the plane of incidence,
R p and R s being the corresponding amplitudes, then, according to
the theory, R 8 continually diminishes as the angle of incidence
increases, vanishes at the polarising angle, and afterwards becomes
negative. If the amplitudes be regarded as essentially positive,
R 8 attains a minimum value zero, and at the same time S under-
goes a change of half a period in phase. No other phase-
difference between P and S is recognised by the theory.

It has been known since the observations of Airy and Jamin
that Fresnel's theory is not in exact agreement with facts. The
component R s reaches at the polarising angle a minimum value
different from zero, and the difference of phase introduced between
P and $ varies with the angle of incidence, increasing from to
a J period as the angle increases from to 90. For the
polarising angle the difference is a J period. Thus the light is
generally elliptically polarised, and the polarising angle is merely
the angle at which the axes of the ellipse are parallel and
perpendicular to the plane of incidence.

Jamin, in discussing surface reflection, calls surfaces positive
or negative according as P is earlier or later in phase than S.
In this sense glasses are generally positive.

OPTICAL PROPERTIES OF GLASS. 77

Cauchy has advanced a theory regarding this elliptic polar Na-
tion which starts from the assumption that at reflection (and
refraction) longitudinal vibrations are also set up, which, however,
are quickly extinguished. In his formula connecting the diHerence
of phase between P and S with the angle of incidence, the only
constants which enter are the index and the so-called coefficient
of ellipticity of the reflecting substance. Thus the whole pheno-
menon is made to depend upon the optical natures of the two
media at whose boundary reflection occurs.

It has since been shown by various authorities that the
phenomena in question might be explained as effects of a very
thin layer clinging to the reflecting surface. In the case of glass
mirrors especially, the presence of a film due to the polishing
has been suggested. As a matter of fact it is found that the pheno-
mena vary with the mode of preparation of the surface. Some
difficulties in Cauchy 's theory are avoided by this supposition. 1

K. E. F. Schmidt, without committing himself to any th-
has described experiments by which he attempted to actually
determine whether the surface layer originates the elliptic
polarisation, or merely modifies it. 2 His reflecting surfaces were
the faces of .SO prisms made of calcspar, light silicate flint

0. 154 (29), dense silicate flint O. 604, silicate crown < >. L'O (11).
and dense barium silicate crown < ). 1 267.

The image of an electric arc was thrown, by means nf the con-
denser and two projection lenses, nn a slit at the focutt of a
collimating lens of 25 cm. focus. The rays emeru r iu^ from the
lens as a parallel beam traversed the polariser, and then fell on
the reflecting surface. After reflection they passed through a
quart/ plate it- JSS7 mm. thick, set at right angles to their path.
The plate was cut parallel to the optic axis, and was set \\ith thi>

is at right angles to the plane of reflection The light m-xi
passed through the analyser, t hen through a direct \i>i..n train of
prisms, and finally through .1 leu- of 40 cm. focus by which it
thrown on a plmtn-jraphie plate.

In this arrangement the S component of the reflected liu'ht
forms the ordinary and the P Component the extranrdinat

1 Compare the paragraph " Modification of Reflection Phenomena by Surface

Film* "by P. Drude in Winkelmann'. Handb. d. /'/..,. Ill, 761.
* Ueber die ellipt. Polar, im rcflekticreuden Lichte. Annal. d, Phy. H. CAem.,

1. Teil : 51, 417 ; II. Teil : 52, 75 (1894).

> JENA GLASS.

the 411111 -tz plate. Hence in passage through the plate S gains on
]> I'.v (n p -n.).d

vibrations. // y) and /i, being the indices of the two components,
<l the thickness of the plate, and X the wave-length in air. If
now, by the act of reflection, a gain e of P over S is introduced,
we shall have for the whole gain of S over P

(n p -n g ).d

~X~

in
wave-lengths. Putting this equal to we get

(n p -n s ).d
m

2 +

Light of the wave-length obtained from this equation by assigning
any integral value to m will again be linearly polarised after
reflection. If its plane of polarisation be perpendicular to that
<f the analyser it will be extinguished by the latter, and a
<lark band will appear in the spectrum at wave-length X.
Schmidt denotes this band by its order m printed in Eoman
numerals. If the reflecting substance be removed, the bands of
even order will be seen when the nicols are crossed, those of odd
order when they are parallel. The reflection causes a rotation of
the plane of polarisation, and hence if the analyser be fixed
permanently at 45 to the plane of incidence, the interference
bands will appear for a certain azimuth of the polariser depending
on the angle of incidence.

If we take as reference point, for an interference band of given
order m, the position it occupies in the spectrum when e= 0, we
see from equation (1) that a positive e shifts the band towards
the violet, and a negative e towards the red. The greater the
absolute value of e the difference of phase, the greater the dis-
placement. For measuring the displacements of the bands on the
photograph, Schmidt used the cyanogen lines to set by; his
measures refer to the bands of orders xvii., xix., and xxi.

Many different ways of polishing the glass reflector were tried,
and the consequent changes in the position of the interference
bands recorded photographically. With the flint glasses O. ] .1 4
and 0. 604, the experimenter succeeded on several occasions in

OPTICAL PROPERTIES OF GLASS.

bringing the same bands repeatedly to the same places in the
spectrum, by stripping off gelatine from the surface. (A layer
f liquid gelatine is poured on the glass surface, allowed to
dry, and then pulled off. The process is due to Wernicke. 1 )
s< hiui.lt infers that e, the gain in phase of P over S corresponding
to this permanent position of the interference bands, does not
originate in a foreign surface film, and supports this conclusion by
further arguments and practical tests. The fact that the gelatine
process had not always the desired effect may be explained by
chemical action, to which the crown glasses, for example, would
be specially liable. The conclusion is thus arrived at that the
elliptic polarisation of light reflected from a polished glass surface
is due to an inherent property of the glass, though modified by
the introduction of foreign matter in polishing,

Variation of the Difference in Phase between P and S
with Angle of Incidence. After these preliminary experiments,
Schmidt measured for 11 glasses the gain in phase of P over S
in the reflected light for various angles of incidence. He used
the method described above, the reflecting surfaces being first
repolished and cleaned by stripping off gelatine. With a view to
determining the phase difference e from the corresponding position
of the interference bands in each case, the displacement of the
hands was calibrated by means of a Soleil's* compensator.

The following data are given for the glasses examined, n p
denoting the index for the F line, A the mean dispersion from C
t<> F, and <f) p the polarising angle for li^ht from the F line:

n f

10A

11. O. 20. Silicate Crown, -

1-5078

56-3

O. 671. Silicate Crown, ....

1 -:.224

r.t; ;

0. 1243. Soft Silicate Crown,

1-5278

1012

56-8

29. O. 154. Light Silicate Crown, -

1 :.S04

1327

57-5

O. 1020. Ordinary Light Flint,

1-6227

1647

58-tt

O. 524. Ordinary Silicate Flint, -

1-6330

1710

:,s;,

0. 604. Dense Silicate Flint,

1-6860

ji'U

O. 1288. Dense Barium Silicate Crown,

1-6796

'.>:>

57-7

O. 1267. Densest Barium Silicate Crown,

1-6202

w-i

59. ( ' J-'T liaryta Light Flint,

1-5798

11*

57-7

169. Phosphate Crown, -

1-5261

717

56-8

Annal. d. /%. u. CAem., 30, 461 (1887).

JENA GLASS.

The measures were for the bands xix. and xxi. Since xix. is
near F, and xxi. near 6r, the differences of phase are for green
and blue light. The precise wave-lengths, which vary from one
observation to the next, are given by equation (1).

The values obtained for the four silicate tiints at band xxi.,
that is, for blue light, are shown in the following table :

O. 154

O. 1020

O. 524

0.604

50-3

53-3

53-7

105

55-7 I

124

165

56-7

188

121

155

112

130

The angle of incidence is given in the first column; the remain-
ing columns give the deviations of the glasses from Fresnel's
theory, according to which c is zero for angles of incidence less
than the polarising angle, and half a wave-length for angles of
incidence greater than the polarising angle. The quantity given
in the table is lOOOe, or 1000( e), according as the angle of

OPTICAL PROPERTIES OF GLASS. 81

incidence is less, or greater, than the polarising angle. Taking.
for example, O.I 5 4, at incidence 50 the gain of P upon S is
0-03 IX, and at 60 is 0'5 - 0*072 = 0'428\.

Schmidt gives the name region of ellipticity to the region
(extending on both sides of the polarising angle), within which
the deviations from Fresnel's law are large enough to be measur-
able; and he finds that the greater the extent of this region the
larger are the deviations which it comprises. The extent of the
region, and the average magnitude of the deviations within it,
jointly determine the ellipticity of the glass in question. Thus,
of the four Hint glasses, the light flint 0. 154 has the least
ellipticity for blue light, and the heavy flint 0. 604 the greatest.
The results for green light are nearly the same. The ellipticity
of the three silicate crowns is much less than that of the flints,
deviations being only observed close to the polarising angle, and
then amounting only to a few thousandths of a wave-length.
a .ling to observations not quoted here, 0.20 is positive, in
l.tmin's sense, for blue and green light below the polarising an-l*
but negative above it; 0.671 is almost neutral for blue light,
and negative for green ; O. 1243 is negative for green light bel<>\\
the polarising angle, positive above. The three baryta glasses

mined are positive; the baryta light flint O. 527 shows less
llipticity than the light silicate flint 0. 154 and also than the
baryta crown 0.1267, while crown 0.1288 again shows very
little ellipticity. Phosphate crown S. 169 also is only slightly
elliptic.

CHAPTER III.

PERFECTING OF OPTICAL SYSTEMS BY THE NEW
GLASSES. THE MICROSCOPE.

32. Numerical Aperture and Limits of Performance of the
Microscope. Let u be the semivertical angle of the cone of rays
which the objective is able to admit from a point of the object,
and n the index of refraction of the intervening medium. Then
if we put

a = ?i sin u, ............................... (1)

a is called by Abbe the numerical aperture of the objective. The
vertical angle 2u of the cone of rays is sometimes called the
angular aperture, or simply the aperture; but the numerical
aperture (abbreviated into N.A.) is much more important in the
theory of the microscope. In order that it may be possible to
represent distinctly in the microscopic image the structure of the
object, the fineness of the structure must not exceed a certain
limit. This limit, which was pointed out almost simultaneously
by Abbe J and von Helmholtz, 2 depends only on the numerical
aperture of the objective and the wave-length of the light
employed. For a regular structure, such as a fine grating, the
limit can easily be stated. If the common distance of the
lines from centre to centre is

(2 >

1 Archivfur mikroskop. Anatomic, 9 (1874).
2 AnncU. d. Phys. u. Chem. Jubdband, 557 (1874).

PERFECTING OF OPTICAL SYSTEMS. 83

X being the wave-length in air, it is just possible to make the
structure visible in the microscope by oblique illumination. If
tin* ilistance be less than this the grating will not be resolved.

Since the angular aperture 2u is necessarily less than 180,
B, the numerical aperture, is less than the index of the intervening
medium, and thus, in a dry system, is less than 1. The greatest
aperture hitherto attained in an immersion system is 1'6 0. If
for X we substitute 0'55/u, which is the wave-length of the
brightest rays, we find that the limiting fineness of resolvable
>tnicture for a dry system is given by rf=0'275/x, and that
d=0'l72fji is the utmost limit of microscopic resolvability.

33. Useful Magnification. When the microscope is adjusted
for the "nearest distance of distinct vision" /, the distance d
between lines which are barely resolved is seen under the angle

(= i '

leimtin^ the magnification. If we substitute for d fr- m
equation (i_M, and solve for m, we find

2k
m= a.

For microscopic observation e must le at least J . and e = 4' is
ample for comfortable vision. Inserting these values in turn,
and putting l='2~*vm., X = 0'55/x, the following values are
obtained for m :

mj= 529a,

w,= 1058a.

Magnifications much less than m l do not utilize the full

capabilities <>\ tin- aperture; those exceeding 974 are futile as

revealing no further detail. Thus the useful powers are those
veen m l and m t .

34 Magnification by Objective and Amplification by Eye-
piece. Let /j l>e the upper focal length of the objective [tin-
ft urn the upper |.im<-ipal point to the Upper principal

us], /, the upper focal length of the eyepiece, / the visual
distance [least distance of distinct vision], and t the optical

84 JENA GLASS.

length, that is, the distance from the upper principal focus of the
objective to the lower principal focus of the eyepiece. Then
the magnification m of the microscope can be shown to be
expressible as

I t

m== 7'7'

J\ /2

The first factor - is the magnification which the objective would

/i
give if used as a simple magnifier, and is called the magnification

Try the objective. The second factor - - is called the amplification by

the eyepiece. The so-called finder eyepiece has amplification unity.

35. Aberration-Constant of Objective. The image formed
by the objective is limited in fineness of detail by the numerical
aperture, as above stated. It also has defects due partly to
imperfections of workmanship in the shaping and mounting of the
lenses, and partly to chromatic and spherical aberration, which
increase with the aperture. As a result of these imperfections,.
the image of a point, instead of being a point, is a round spot
called a circle of aberration. If k be the angular diameter of this
circle for a point on the axis as it would be seen from the
distance /, and the angular diameter to which it is amplified
by the eyepiece, we have

k is called the aberration-constant of the objective.

36. The Critical Amplification. The smallness of the
aberration-constant measures the goodness of performance of the
objective ; but in practice it is more convenient to use another
quantity, which is inversely proportional to the aberration-
constant and can be more easily observed, namely, the critical
amplification, that is to say, the highest amplification that the
image formed by the objective can bear without perceptible loss
of sharpness. As amplification is increased, the angular
diameter of the circles of aberration is increased ; and when
this diameter has become larger than the smallest magnitude
distinguishable by the eye, sharpness begins to diminish.

PERFECTING OF OPTICAL SYSTEM- 85

37. Older Achromatic Objectives. According to Abbe's
> rvations, 1 in even the best objectives of the old kinds the

critical amplification for large apertures is only from 4 to 6.
The optical qualities of the silicate glasses employed made it
impossible to exceed this limit. On the one hand, the difference
in the runs of dispersion of crown and Hint gives a secondary
spectrum after achromatising ; and on the other, the depend*
of dispersion on index makes it impossible to correct spherical

i ration for more than one colour. Thus, for rays of shorter
wave-length the system is generally spherically over-corrected
(the focus for the central rays being shorter than for the border
i. and for rays of longer wave-length, under-corrected.

Hence it follows that, if the foci of the C and F rays are
united for the central zone, the focal length will l)e greater for
/' than for C in all the other zones; thus the marginal zones
will be chromatically over-corrected by amounts increasing
towards the rim.

Practically spherical aberration is always corrected for the

-t intense rays. In the secondary spectrum of the central
these have approximately the shortest focus; and the
remaining rays are united in pairs, each more refrangible ray
with one less refrangible. In these circumstances the change io
the secondary spectrum in the outer zones is easily observable,
the umn; refrangible colours being displaced in the positive, the
less refrangible in the negative direction. Thus the uncom-

. sated portion at the blue end of the spectrum ^rows 1m
as we proceed from centre t< rim. This defect may he lessened
chromatically under-correcting the central zone, so as to
produce union of C and F for one of the intermediate /.ones.

38. Apochromatic Objectives. It has IKHJU shown above
'. 1!) that with the new glasses it is poxvjM,. to aclmunatise

so that only a td't'mry spectrum is left. This result is essentially
ndcnt on the fact that the relation which exists in the silicate
es Let ween total dispersion and run of dispersion is ^ot rid
<>!' hv the introduction of borates and phosphates.

ther, the total dispersion is rendered largely independent of
Hence it is possible to correct axial .-ph. rra-

1 "On the Relation of Aperture and Power, etc./' Jtmrn. oj the ft. After. Soc.,
8er. 2, V.,1. III. p. 803(1883).

86 JENA GLASS.

tion for two colours. This result is most perfectly attained by
(( mil tilling the new glasses with fluorspar.

The name apochromatic has been given, at Abbe's suggestion,
to objectives in which the secondary spectrum is abolished, and
the spherical aberration corrected for two colours. Their superi-
ority to the old achromatic objectives may be gathered from the
fact that, even for the largest apertures, their critical magnification
amounts to at least 12 15. For medium and small apertures
it is considerably greater.

Relieving the Objective. This improvement in quality
lessens the necessity for high power in the objective ; for a
given total magnification can be obtained with a lower magni-
fication by the objective when higher amplification is available.
Thus the very short focal lengths hitherto regarded as essential
are now superfluous, since even large apertures can be fully
exhausted with objectives of moderate focal length.

With an ordinary achromatic, the sinallness of the critical
amplification prevents the full utilisation of large apertures.
An apochromatic shows as much detail as an achromatic of
larger aperture and shorter focal length.

Increased Range of Magnification. The range of serviceability
of an objective extends from its own intrinsic magnification to
the multiple of this determined by the critical amplification. A
single apochromatic can therefore be used for both lower and
higher powers than a single achromatic of the ordinary kind.

Correction of the Chromatic Difference of Magnification. In
apochromatic objectives, as in others, the magnification is unequal
for different colours ; the blue and violet images being larger
than the red and yellow. This difference of size could only be
corrected by introducing other more serious defects. But apo-
chromatics have a great advantage in this respect. For while
in achromatics the difference varies from centre to circumference,
in apochrornatics it can be made approximately equal for all
zones of the aperture, and can therefore be corrected by a suitable
eyepiece.

For this purpose, it is only necessary to assign to the eyepiece
an equal difference but of opposite sign. As it is convenient to
be able to use the same ocular with various objectives, objectives
should all be made with the same chromatic difference, even

PERFECTING OF OPTICAL SYSTEMS. 87

including those of small apertures, in which the difference could
easily be made non-existent.

Order of Ray-Union. In dioptric language the ray union
effected by a simple lens is said to be only of the l rt order, since
two rays proceeding from a point on the axis will not exactly
meet again on the axis, if they have different refrangibilities or
different inclinations to the axis. In apochromatic object i
the achromatism attained raises the ray union to the 3 rd order.
It is further raised by the spherical correction employed with
larger apertures, to the 10 th order, and finally, by equalisation of
chromatic differences of magnification for different zones, to the
1 I th order. The diameter of the clear aperture of the object he
is thus raised to li'S times the focal length.

Bearing on Microphotography. The most intense visual image
of an object is produced by rays from near the red end of the
spectrum, and the most intense photographic image by ray> tiiu
near the violet end. An imperfect achromatism which leaves a
noticeable difference of focal length between these two classes of
rays makes the two images fall in different planes. Hence the
focussing of the photographic image is uncertain, and cannot be
verified by eye observation. Again, if the spherical correction
only extends to the brightest part of the spectrum, the photo-
graphic ima^e will Ix? lacking in sharpness as compared with the
il one. Apochromatic objectives have in these respects an
immense advantage for niicrophotography. By their aid alone
can we secure that the photographic and visual pictures shall be
in the same plane, and both equally sharp.

With tli introduction of apochromatics, the theoretical ad-
itage of niicrophoto^iaphy over eye observation was first
realised in practice. As the wave-length of the rays which are
most active. < hrmically is only J of the wave-length of those
which most affect the eye, the resolving power of an object i\v
when u>ed photographically should <hy equation (-). Art. ."ilM, le
I of its resolving power for direct vision. The advantage of
niitTophoti;jr;iphy ovet dirert vision should therefore be eqni
. multiplying the aperture of the objective by J.

Tl -nti.il point* to be kept in view in |MM fectin;.; the

roscope were explicitly laid down 1'V AbU- as far back as the
year 1878; and he concluded with the following statement of
aims that nn.M l>e realised.

JENA GLASS.

" Theory may, by going deeper into the dioptric problem,
devise in course of time new methods, more effectual than those
now employed for getting rid of chromatic and spherical aberra-
tion ; optical workmanship may, by the introduction of improved
methods and appliances, render possible a closer approximation
to the mathematically exact forms theoretically required ; and
the allied industry of glass-making may possibly in the future
produce, in place of the glasses now employed, new materials
which will furnish, by their optical properties, more favourable
conditions for the production of perfect systems of lenses than
our present crown and Hint." x

Eight years later, in July, 1886, Abbe was able to announce
that these aims had been completely realised. 2 A set of
apochromatic objectives and compensating eyepieces had been
completed, in accordance with his calculations, in the optical
factory of C. Zeiss, from new glasses made at the Jena Works.

39. Use of Fluorspar for Apochromatic Objectives. On

this subject briefly mentioned above Abbe has published
detailed information of great interest. 3 The chief results are
embodied in the following table, which includes three glasses for
comparison. The symbols have the same meaning as in preceding
tables. (See Art. 17.)

10 8 3

n D

KPA

l&y

Fluorspar, ....

1-4338

455

95-4

255
561

Lime Silicate Cr. 0. 60,

1-5170

860

60-2

487
566

Light Phosphate Cr. O. 225, -

1-5159

737

70-0

407
552

Borate Flint O. 252,

1-5521

1026

53-8

582
567

] "Die optischen Hilfsmittel der Mikroskopie." Bericht iiber die Wi&tensch..
Apparate auf der Londoner Internat. Ausstelluny in 1876, I. 420 (Brunswick,

1878).

2 "Ueber Verbesscrungen d. Mikroskops." Sitzungsber. d. med.-natur. Get.
Jena, 1886.

3 Zeit8chr.f. Inatrumentenk, 10, 1 (1890).

PERFECTING OF OPTICAL SYSTEMS. 89

It will l)e seen that the index of fluorite is very small com-
pared to that of the glasses. Now the conditions for the correc-
tion of spherical aberration in a compound objective require that
two media which have a common surface of contact should have

onsiderable difference of index. Suppose that an ordinary
crown of index 1*52 is to form one component of a cemented
doublet, and that the difference of index required for removal of
spherical aberration is 0'20 ; then for the other component a
Hint of index 1'72 must be used. />. a glass of excessive density
and dispersion. But if fluorite is substituted for the crown glass,
then a Hint of index 1'63 will suffice, and this is in many ways
a great advantage. The advantage is especially great for the
< on >t ruction of microscope objectives of large aperture.

Further, the dispersive properties of fluorspar are remarkably
favourable for achromatism. 1 Its v is 95*4, whereas the highest
v for any glass is 70'0 for light phosphate crown. Its y is,
itheless, considerably greater than that of the phosphate.
Hence the secondary spectrum can be got rid of by the aid of
fluorite, and, for combination with a u r i\en Hint glass, less
curvature in the surfaces will l>e required \\ith tluorite than
with crown.

- ;ar as achromatism alone is concerned, spherical aberration
Ix'ing left out of account, a combination of fluorite with crown O. 60
would ;zi\e an almost perfect colour-union, in consequence of the

large difference in v and the very slight difference in y.
These considerations naturally suggested the attempt to obtain

n; of these benefits by employing fluorspar as an ingredient
in -jlass. Indeed. Schott had already, 2 at an early stage of his
researches, succeeded in producing Basses containing lluor. which
>ho\ved small index and greatly diminished dispersion. I'.ut this
nly on a very small scale; and the experiments sho\\ed
that the ditliculties in the way of obtaining homogeneous melting
were exceedingly L'leat.

A.bbe therefore introduced lenses of llnorspar itself into micro-

pe objectives, h, 1H84, at Zeiss* v .n-ious objectives

:._' on.-, two. oi three fluorspar lenses instead of crown

made from his calculations. When ap<* -hiomatic lenses
were introduced, the mineral was brought into regular use at Jena

"ii junction with the new glasses, and the example was soon
1 8eeArt. It See Art. 8.

JENA GLASS.

followed by other opticians. The result is a lessening of labour
both in calculation and practice ; for without fluor it would have
been necessary to make the lens systems even more complicated
and difficult to construct than they are at present.

Abbe has published interesting information respecting the
difficulty of obtaining a suitable supply of the mineral a subject
to which it is desirable to direct attention. 1 The only place (on
the Schwarzhornstock in the Bernese Oberland,) which in the past
has furnished large clear pieces, is quite worked out. At present
it is necessary to be content with comparatively small pieces, and
even these can only be obtained by laborious selection.

40. Zeiss' Sets of Apochromatic Objectives and Compensat-
ing Eyepieces 2 have the properties described in Art. 38. The
following is a list of the objectives :

Numerical
Aperture

Focal
Length

Magnification

Dry
System,

0-30

24-0 mm.
16-0

10-5
15-5

0-60

12-0
8-0

21
31

0-95

6-0
4-0

Water Immersion,

1-25

2-5

100

Homogeneous
Immersion,

1-30

3-0
2-0

83
125

1-40

3-0
2-0

83
12.5

They are constructed to suit either the short (Continental) tube
of 180 mm. or the long (English) of 270 mm. optical length,
except those of focal lengths 24, 12, and 6 mm., which are not
suitable for the short tube. The 2 mm. objectives for homo-
geneous immersion are supplied " in compliance with desires for
the highest possible magnifying power of objective," although the
l lbid., 5-6.

2 New Microscope Objectives and Eyepieces by Zeiw, made of special glasses from
the Jena Laboratory. Jena, 1887.

PERFECTING OF OPTICAL SYSTEMS.

apertures are fully utilised by the 3 mm. objectives. Every
detail of the construction is carried out in strict accordance with
previous calculation, all empirical modifications being excluded.
The magnifications specified in the last column are for unit
amplification.

The following is a list of the Compensating Eyepieces,
showing their focal lengths, and the amplifications which they
give when used with the indicated tube lengths :

Tube

For finding

For working

Amplification,

4 8

Focus in mm.,

Short,

180

45 22-5

Do.,

Long,

135

67 :

22-5

These eyepieces embody an essentially new optical construc-
tion. The high amplifications here specified could not be obtained
with the Huygenian or other older constructions, without makin-
the eye lens too small, and the eye point too close to it.

Trials on Test Objects were undertaken by Dippel 1 and
Schulze. 2 Dippel, using a short tube, observed the following:
With the 16 mm. objective: Sections of Echinoinetra, sections
of wood stained in two colours, the starch grains of potato- l>ern< >
laminated and spirally streaked cell walls, splitting up of nuclei,
and transversely striated muscular fibre. With the 4 mm.
objective: Nitzschia sigma, Grammatophora oceanica, Surirella
< lemma, I'leurosigma angulatum, Nitzschia vermicularis (the
transverse striation l>eing distinctly visible with nhliqm* illuminn-
ti"ii), layers of thickening in cell walls of plants, tuKerde Ku-illi.
With water immersion : Nitzschia Sigmoidea, Amphiptaara
pellucida (the finest transverse striation UMH^J plainly visible
with oblique illumination). With homogeneous immersion:
Navicula rhomltfrides, the markings on the scales of Suiiivll ,
Gemma, the strings of pearls on the scales of Amphipleura
pellucida (with ol.liqur illumination). In every inManee the
actual resolving power reached the theoretical standard, and the
rpness of the images and their purity <>t tint were remarkable.
The strongest dry system gave as good results as can be obtained

1 Z,

* Phil. Soc. oj

Mikr. v. mikr. Terhn., 3, 808 (1886).
, 17, Nor. 1885.

Ml JENA GLASS.

water immersion with the old achromatics ; and water
immersion uave as good as the old homogeneous immersion.

Schul/e, who tested the objectives of 16, 4, 2-5, and '2 mm.
focus, gave the following verdict: "They surpass by far any
objective I have previously examined. Their definition is
exquisite, their resolving power is very great, and the pictures
yielded by them are most brilliant and free from colour; they
possess, further, a very notable increase of illuminating power
and give great flatness of field."

41. Monobromonaphthalin Immersion. Equation (1) of
Art. 32 shows that, in an immersion system, the index of the
intervening medium must be greater than the required numerical
aperture. The same rule applies to the indices of the front lens
and of the cover-glass. N.A. 1*40 is attained with a fluid of
index 1*52 (cedar oil). Monobromonaphthalin, with index 1*66,
therefore suggested itself as a suitable medium for an attempt at
a higher result ; and by its aid the limit of N.A. was increased
to 1'GO. 1 For cover-glass and front lens, a flint glass of index
1*72, a special melting, was employed. Abbe's calculations
showed that, in the new objective, spherical and chromatic
aberration could be corrected almost as completely as in the
apochromatics. The focal length given it was 2 '5 mm., which
makes the intrinsic magnification 100. Special cover-glasses
must be ground and polished to correspond.

If it be intended to observe with very oblique illumination, or
with an illuminating beam of very wide angle, the front lens of
the condenser, and the object holder, must also be of strongly
refracting flint glass, and the space between them must be filled
with mono] >romonaphthalin.

The necessary test objects were prepared by van Heurck (of
Antwerp), who obtained the first specimen of the new objective
and employed it for the study of diatoms.' 2

No immersion fluid suitable for further increase of aperture is
at present known.

42. Projection Eyepieces. Abbe has introduced a new
construction, by which the advantages of apochromatic objectives

1 S. Czapski, Zeitschr. f. wiwensch. Mikr. u. f. mikr. Technik., 6, p. 417 (1889).

2 La, nouvelle combinainon optique de M. M. Zeiss et la structure de la valve des
diatomees. Dr. H. van Heurck, Anvers, 1890.

PERFECTING OF OPTICAL SYSTEMS. 93

are rendered available for purposes of projection. 1 The objective
forms its image in the same way, and at the same point of the
tube, as for eye observation, and a special combination of lenses
throws a projection of this image on the photographic plate or on
a screen. As this combination has the appearance of an eyejti
and is inserted in the tule in the same way, it is called a
projection eyepiece. It is exactly corrected for spherical and
chromatic aberration, and is arranged to compensate like an
ordinary eyepiece for the chromatic difference of magnification.

The linear magnification of the projected image is easily
calculated. When the projection eyepiece is used with tin*
microscope, the upper focus of the whole system is shifted into
coincidence with the end plane of the eyepiece. By the general
law of lens systems, the magnification is equal to the distant
F'Q of the image from this plane divided by the focal length /'
of the system. Let < denote the focal length of the object i
then the magnification ra may Ije expressed as

F'Q d>

m *r

F'Q is to be directly measured, <f> is assumed to be known, and
the value of ^ (called the amplification in the case of projection

eyepieces,) is got from the numlier of the projection eyepiece.

Zeiss' projection eyepieces Nos. 2 and 4 are intend'd t'r tho
short tu!>e, Nos. 3 and 6 for the long tube. The two lo\
powers are meant for giving objective demonstrations of mi<
scopic objects, and for photographing on a small scale or with the
plate at a considerable distance; the two higher po\\
photographing with a short camera. 1

43. Projection Objectives of 7."., 70. and :::, mm. f.cus. to u
used directly, without the aid of a projection eyepiece, have IMMMI

true ted by Zeiss for drj.ie ting large objects. They ha
low magnification and as large a field of view as possil

1 For an account of the older methods and their drawbacks see Z
Catalog** of Apparatus for Microphotoyrapky, Jena, 1888, p. 88.

* Directions for using the projection eyepieces, together with specimens of their
performance, are given in the Special Catalogue.

94 JENA GLASS.

44. Semi-apochromatics. We apply this name to the objec-
tives constructed by various makers from Jena glasses without
the use of fluorite. They far surpass ordinary achromatics
without attaining the full excellence of apochromatics.

The following series of semi-apochromatics are made by
Eeichert of Vienna 1 from phosphate and silicate glasses :

Homogeneous
Immersion

Aperture Focus

1-20 i-2r *' 8 mm '

1-40 1-43 1-8

One of these objectives, with aperture 1'24 and focus 1/8 mm.,
was tested by Nelson, 2 who reports, " This lens is the finest oil-
innnersion I have ever seen excepting only the apochromatics."

The " pantachromatic " objectives by Leitz of Wetzlar, 3 with
which Huygenian eyepieces can be used, are graded as follows :

Aperture Focus

10-12 34 mm.

0-32 15
0-75 7

0-87 3-5

Homogeneous Immersion, 1/30 2 '5

The semi-apochromatic made by Korista* of Milan is an
oil-immersion objective of N.A. 1'30 and focus 1*7 mm.

Under the designation, " Apochromatic Objectives without
Fluorspar," Meyer & Co. 5 of Zurich have introduced the following

set:

N.A. Focus.

1 15 mm,

Dry System
Homogeneous Immersion 1*30 2'3

1 Price list, xvii. (1890).

2 Journ. of the It, Microscop. Soc., London, Feb. 1900.
3 Price list, No. 34 (1891). Catalogue, 1892.
8 Price List, 1893-94.

CHAPTER IV.

CONTINUATION OF THE SAME SUBJECT. PHOTO-
GKAPHIC OBJECTIVES.

45. The introduction of new kinds of glass into photographic
objectives has rendered improvement possible in several directions.

In the first place, the use of glasses very free from colour has
increased the luminous power of the objective, an advantage
which speaks for itself.

Secondly, similarity of run of dispersion in the two components
of a doublet has brought about shortening of the secondary
spectrum, or even the attainment of a tertiary.

It should here be remarked that the correction of chromatic
aberration on the axis of a photographic objective ought to be
planned with a view to the coincidence of a sharp photographic
with a sharp visual image a purpose which requires the shorten-
ing of the secondary spectrum. On the other hand, the sharp
focussing of red rays which is peculiar to the tertiary spectrum. 1

ough important for visual purposes, is of no value for photo-
graphy, and does not affect the sharpness of the photograph i<
image, so long as the chemical action is practically confined to
rays of short wave-length. This consideration suffices to show
that tlm apochromatic correction has not the importance for
j'h.tu.jra]>hi< objectives which it has for microscopic.

"A third improvement, more important than either of the fore-

:i& is that it has been found possible, by means of the new
'mi glasses, to obtain photographic images free from astigmatism

1 See Art 19.

96 . JENA GLASS.

and at the same time free from curvature. This matter requires
a somewhat elaborate explanation.

46. Astigmatism and Curvature of Image. Let us take as
object a plane in front of the objective cutting the optic axis at
right angles in a point A. Let B be the image-point correspond-
ing to A. Then the plane at right angles to the axis through B
is the ideal image-plane. But in general the objective forms,
instead of a plane image, two curved image-surfaces, which touch
the ideal image-plane at their common vertex B. In each of
these two surfaces, all points of the object-plane are represented
by short lines, the directions of these lines being different in the
two surfaces. In one surface the lines point to the axis, and may
be called radial ; in the other they have the perpendicular direc-
tion, and may be called tangential. The surface with the
tangential lines is called the primary image surface ; that with
the radial lines, the secondary. The primary surface contains
sharp images of tangential lines only, the secondary of radial
lines only.

Images of points of the object away from the axis are formed
by means of obliquely incident pencils, whose vertical angles
depend on the position and size of the opening in the diaphragm.
The ray which goes through the centre of the opening is called
the principal ray of the pencil. The plane through the principal
ray and the axis of the objective is called the meridional section ;
and the plane perpendicular to this (through the principal ray)
the sagittal section.

Kays of such a pencil, originally proceeding from a point, will
not as a rule meet again in a point after refraction ; thus the
refracted pencil is astigmatic. This is due to the fact that
rays in meridional and rays in sagittal planes converge with
unequal rapidity. If the sagittal convergence is stronger than
the meridional, the rays will first form a short radial focal line,
and then, further on in their course, a tangential one.

Testing an Objective for Astigmatism. The most obviously
suitable test object for this purpose is a target carrying a system
of concentric circles with their radii. It should be so placed t,hat
the common axis of the circles coincides with the axis of the
objective. If the objective is astigmatic, it will be impossible to
adjust the receiving screen so that the circles and the radii are

PERFECTING OF OPTICAL SYSTEMS. 97

simultaneously depicted sharp at parts of the field distant from
thr axis; for the circles are only pictured sharply in the primary
image surface, and the radii only in the secondary. (A cross-ruled
pattern of straight lines is also a suitable test.) The distance
between the two positions of the screen, one of which makes the
radial and the other the tangential lines sharp, at the outer edge
of the field, is called the astigmatic difference.

Curves of Field Curvature and of Astigmatic Difference.

_ivt> a clear representation of the behaviour of a given objec-
tive as regards the defects in question, two curves may be drawn,
taking as abscissa the angular distance of any part of the image
from the axis, and as ordinates the distances of the primary and
secondary images from the ideal image plane. If a third curve
be drawn, having as its ordinates the differences of the ordinates
of these two, it will represent the variation of astigmatic differ-
ence. Such curves have been plotted by P. Eudolph, for various
objectives. 1

Defective Definition at Edge of Field. The images forum I
by photographic objectives are, in practice, always thrown on
plane plates perpendicular to the optic axis. If the object be
also a plane perpendicular to the axis, the curvature of both
images causes loss of definition at the edu<\ when the focus is
adjusted for the centre. Even if the curvature of one image is
got rid of, astigmatism will still cause difference in sharpness
between tangential and radial lines. Equality of definition over
the whole field can only be obtained by correcting both I'm-
astigmatism and curvature. This is called anastigmatic flattening
!' the image.

Since a fiat object gives a curved image, conversely a fiat
iiuau'e will l>e given by a certain curved object-surface, which \M
shall call the conjugate surface. Thus a sharp image can some-
tinies be obtained when the objective is onlv pornvU'd f. .1
astigmatism, and not for curvature.

Penetration or Focal Depth. Suppose the object not to be
1 nit to have considerable depth from front to back. Thru

-o points of the object whose images lie in a plane will lie on
the conjugate surface, which may either be curved or plane
JUM >rding to the nature of the objective. If the marginal portion
of the lens is sufficiently stopped out by a diaphragm, points of

m Jnhrb. f. Photographie, 1891, 233, 230 ; 1883, 223, 224.
O

98 JENA GLASS.

the object within certain limits of distance from the conjugate
surface, on both sides, will also he in god focus. It is easily
shown that, for a given objective, this focal depth increases with
the distance of the object, and also (unless the conjugate surface
is plane) varies with the distance from the centre of the field.

Distortion of Image. A large astigmatic difference may
sometimes destroy the resemblance of the image to the original. 1
If, in the first test object mentioned above, one part, near the
edge of the field of view, has its radial and tangential lines so
close together as to form a fine network with square meshes, the
network, if there is much astigmatic difference, will not be clearly
visible in the image ; the radial lines being invisible in the
primary image-surface, and the tangential in the secondary ; so
that with one adjustment we shall see only tangential, and with
another, only radial lines. A midway adjustment will usually
show the network with both sets of lines blurred ; and the
blurring may be so great as to cause them to be invisible except
where they overlap. The intersections will, in this case, be
represented as squares with narrow spaces between them, sug-
gesting a reversal of light and dark in the pattern.

If the object is rotated through 45, so that the diagonals of
the square meshes are radial and tangential, the squares of the
original pattern are changed, in either image-surface, into narrow
hexagons, having their length tangential in the primary surface
and radial in the secondary. With increasing astigmatic differ-
ence the appearance more and more resembles a simple alternation
of light and dark stripes.

47. The Introduction of Phosphate Crown and Borate
Flint into Photographic Objectives has been confined to a few
trials, some of them directed to anastigmatic flattening and others
to the perfecting of achromatism.

The Anastigmatic Aplanat. Normal and Anomalous
Doublets. The problem of the simultaneous removal of astig-
matism and curvature in other words, of simultaneously flatten-
ing the primary and secondary image-surfaces was first solved,
in an imperfect way, by Miethe's use of phosphate crown and
1 -orate flint.

Of previous attempts in this direction, one of the most success-

a See Rudolph, Die Zeiss-Anastigmate. Phot. Wochenblatt, 1892. Nr. 18-21.

PERFECTING OF OPTICAL SYSTEMS. 99

t'ul was SteinheiTs aplanat. It consisted of two identical achrom-
doublets, placed symmetrically on opposite sides of a dia-
phragm. When the two doublets were moved nearer together
or further apart, the primary image-surface was more affected
than the secondary. Increase of distance between the doublets
rendered the primary surface flatter, and diminution of their
distance diminished the astigmatic difference. Both advantages
could not be attained simultaneously. This impossibility had
its root in the uniform relation which connected the optical
constants of all the available glasses.

An achromatic doublet is always made of two glasses which
have very different values of v. 1 If the focal distance is to be
positive, the glass with greater v is the positive component of the
doublet. 2 For the old silicate glasses, the rule held that the glass

.ireater v had the smaller index of refraction n. An achromatic
n>n verging doublet therefore always consisted of a converging lens

rown and a diverging lens of flint, the flint having the larger
i in lex. But in order to obtain anastigmatic flattening, in con-
junction with achromatism, it is necessary that the converging
lens should have the greater index. This requires that the glass
of greater v should also have the greater n. Rudolph has given
the name anomalous to doublets constructed on this principle,
those constructed on the old principle being called normal. 3 The
names are also applied to pairs of glasses suitable for the forma-
tion of such doublets. Lummer, instead of anomalous and normal,
uses the names new and old achromatic. 4

With the glasses formerly available, it was impossible to select

a pair of glasses which would form an anomalous doublet with

considerable difference between their values of v or of n.

Tin introduction of highly refracting phosphate crown, however,

lered such a selection possible ; and for this glass, combined

with weakly refracting flint, Miethe calculated an objective, to

which he gave the name of Anastigmat:' It < "iisisted of a com-

I'inatinn of two identical anomalous <loul>lt>ts corrected as far as

1 f is the reciprocal of " dispersive power " defined in a definite w ay. See Art. 1 7 .
Art. 18, equation (3).
Brit. Jour, of Phot., 33, 443 (1890).

' Mull, , I'nuillet, 9th ed., II., 1, 782. Also S. P. Thompson's translation of
Lummer** Photographic Optic*
Vogeln Phot. Mitt., 25, 123 and 173 (1888).

100 JENA GLASS.

possible for spherical aberration. Samples having a focal length
of about 9*75 cm. were made 1>\ Hartnack at Potsdam in 1888,
and showed, as regards nearness of the two image-surfaces to each
and to the ideal image plane, as much superiority over the
best previously known objectives as he had expected from theory.
The objection to the practical introduction of this first anastigmatie
objective lay in the insufficient durability of the phosphate crown
empl<

The Wide-Angled Apochromat constructed by Fritsch 1 of
Vienna in 1889 has been classed among aplanats. It was a
normal doublet of phosphate crown and borate flint, designed not
for getting rid of astigmatism, but for sharpening the chemical
image, and bringing it nearer to the visual image, by shortening
the ><(< mdary sjieetruni.

An Apochromatic Triplet, calculated by Eudolph on a plan
suggested by Abbe, was made by Zeiss 2 in 1890, and for a
i'-\v years after. Its construction is fundamentally the same as
one recommended by H. Schroder for astrophotography, 8 and
is chiefly intended for increasing the available aperture by more
complete correction for spherical aberration. There are two-
simple convex lenses, and between them, but not touching them r
is a compound lens of relatively long focus, consisting of two or
three lenses cemented together, intended to correct the spherical
and chromatic aberration. In the apochromatic objectives of this.
construction, the two concave components of the correcting lens
were of borate flint, and the convex lens between them, as well
as the two separate lenses, were made from one and the same
uen of crown. The two kinds of glass form a normal pair.
The primary image-surface is flattened, and the astigmatic differ-
ence is of the same order of magnitude as in the aplanatic type.

These objectives are no longer made, as the apochromatic
correction is of no great advantage, and there was special
difficulty in making the glasses free from defects.

48. Light Baryta Flints have come into extensive use, and
possess properties which are of great advantage for photographic

1 Phot. Korrtspondenz von L. Schrank, 26, 12 (1889).

'See German Patent, No. 66313, and Zeisa' Catalogue for 1891, pp. 9, 18.

*A*t. Naehr., No. 2682.

PERFECTING OF OPTICAL SYSTEMS.

101

objectives. The two leading types landscape lenses and aplanats
were introduced by Voigtlander as long ago as 1888. 1

The baryta glasses differ from the silicate glasses in having
smaller absorption of the highly refrangible rays, and as a result
of this difference smaller increase of dispersion with decrease of
wave-length. By combining the lighter crowns with the baryta
light flints, doublets can be constructed which are very trans-
parent for both visual and chemical rays, and sufficient amounts
of difference in v and n can be obtained without the high dis-
persion which was previously unavoidable. These favourable
conditions have given an increase of light ; and the better
flattening of the primary image has permitted an enlargement of
the field of view. 2

49. Baryta Crown and Silicate Crown. With the help of
highly refractive baryta crown and highly dispersive silicate
crown, the problem of anastigmatic flattening was attacked afresh,
an<l finally received several satisfactory solutions.

Concentric Lens. Ross of London in 1888 made an anastig-
matic objective, calculated by Schroder, 3 which, like Miethe's
nearly contemporaneous anastigmat, belonged to the aplanatic
type of construction. Each of the two achromatic doublets

Fio. 7.

-iste, as in ti^. 7, of a plano-convex baryta crown and
I |.la!i..-( -..IK -avc silicate crown lens. The objective takes its

1 VogtU Phot. Mitt., 25, 185 (1888); Eders Jahrb. f. Phot., 1889, 100; Phot.
Mitt., 25, 196 (1888). This last reference gives the information that baryta flint
had taken the place of borate flint in / -ins* apochromatic triplet.

2 For further particulars see " U nay m metrical AnastigmaU " in the next An.
8 English Patent, No. 5194 of 1888, published 1889. Phot. New*, :w. 1 . "it

102 JENA GLASS.

name from the fact that the two outer spherical surfaces are
concentric. The index of the baryta crown lies between 1*50
and 1*53. The baryta has the smaller dispersion, as well aa
the greater index, and has consequently the greater v\ thus
the two glasses form an " anomalous doublet." The objective
consists, like Miethe's, of two doublets precisely alike.

Calling the two radii r x and r 2 , as indicated in the figure, we
have, in the notation of Art. 18, k = l/r lt k' = l/r 2 , and equa-
tions (3) of that Art. become

the accented letters referring to the plano-concave lens, and the
unaccented to the plano-convex. For the focal length d of the
combination, we have

^-AoX-TAxXr

and as v is greater than v, the focal length is positive. For a
normal doublet of the same form the focal length would be
negative.

The objective was not placed on the market till 1892, as up
to that time the glasses required were not produced with sufficient
uniformity. 1 The construction was not in all respects an advance.
It gave weak illumination ; and while the margin of the image
was improved by better anastigmatic correction, the centre of the
field lost definition by increased spherical aberration.

Zeiss* Unsymmetrical Anastigmats (D.R.P. 56109). As
already explained, anomalous combinations of two glasses furnish
the means of constructing achromatic systems by which both
image-surfaces are brought near to the ideal image plane. But
this arrangement does not, like the normal arrangement, easily
lend itself to the removal of spherical aberration. The first
anastigmatic objectives did not meet this difficulty ; although in
Miethe's anastigmat the spherical aberration was inconsiderable,
owing to the favourable qualities of phosphate crown.

Rudolph was the first to overcome the mutual incompatibility
of these two corrections. He gave up the symmetrical construc-
tion characteristic of aplanats, and adopted an unsymmetrical

1 British Jour, of Phot., 39, 273 (1892) and Edera Jahrb. f. Phot., 1893, 13 and
348.

PERFECTING OF OPTICAL SYSTEMS. 103

arrangement, 1 as Steinheil had previously done with less success,
in his " antiplanetic." The objective which he designed has two
members, each independently achromatised, one of them being a
normal pair of silicate crown and baryta light flint, and the
other an anomalous pair of baryta crown and silicate crown.
This plan makes it possible to compensate the spherical aberration
of the second member by means of the first, and the astigmatism
of the first by means of the second. 2 The first anastigmat of
this construction was brought out in 1890 in three series ;| to
which, in the course of the next year, four others were added,
the "relative apertures" 4 of the seven series being 1/4*5, 1/6*3,
1/8, 1/7*2, 1/9, 1/12*5, i/18. 6 The first member is always a
doublet ; the second is a triplet in the first three, and a doublet
in the last four. Fig. 8 shows an anastigmat of the first series, of
1 "-II mm. focal length, in f actual size. It has an angle of about
75 and gives a very bright image. Fig. 9 is an objective of the
seventh series, of (j^ mm. focus, shown actual size.

Fio. 8. Km. P.

Tin- advantages of this combination of an old achromat with a
IH-W achromat, over all former objectives, have been fully discussed
by Kinlnlpli." They result chiefly from the previous impossibility
of avoiding astigmatic curvature of images in objectives well
corrected for spherical aberration (see Art. 46). Other advan-
tages are: the favourable pnsiii..n of the images formed by
ctions at the boundaries of air and glass, the resulting flare

1 Knglish Patent, No. 6028. Brit. Jour, of Phot., 33, 443 (1890).

/'Hot., 1891, 226, and 1893, 222.
Vogel* Phot. AfiU., 27, 84 (1890).

4 Relative aperture is diameter of objective divided by focal length.
' Zeiss' list of photo-objective*, 1894.
* Kder* Jahrl: I.e. and Phot. Wochenblatt, 1892, No*. IS Jl

104 JENA GLASS.

being thus redm-ed to a minimum; the increase in light due to
freedom of the glass from colour ; and the short distance between
the two members of the objective, which, together with the
anastigmatic flattening, tends to prevent rapid falling off in
brightness at the margin.

Anastigmatic Compound Lens. The principle of mutual
correction of two doublets adopted in the unsymmetrical anas-
tigmats has also been employed by Rudolph in the construction
of anastigmatic single objectives composed of three lenses A, B, C
cemented together, the two outer ones A, C being positive, and
the inner one B negative. 1 If the spherical correction is assigned
to the pair A, B and the astigmatic correction to the pair B, C\
while the chromatic correction is shared by all three, then the
indices must increase in the order A, B, C, and B must have the
smallest v. B and C must be an anomalous pair. The conditions
can be satisfied by making A a silicate crown, B a light baryta
flint, and C a heavy baryta crown.

The earliest of these anastigmatic triplets were made by Zeiss 2
in 1891, but the completion of the series was delayed, and the
series was first issued in 1893. It includes 9 different focal
lengths, the relative aperture being I/ 14' 5.

Compound Anastigmats. Any two anastigmatic lenses* sym-
metrically placed so as to form a double objective, form what is
called a compound anastigmat. 3 The useful relative aperture of
such an objective lies between 1/8-5 and l/6'9.

Fio. 10.

Fig. 10 represents, about J; natural size, a compound anastig-
mat with front lens of 385 mm. focus and back lens of 250 mm.

1 English Patent, No. 4692, British Jour. Phot., 40, 331 (1893).

2 Price List of Photogr. Objectives, 2nd supplement, 1893, and List, 1894.

3 Zeiss' Catalogue, 1893, p. 8, and 1894, p. 24.

PERFECTING OF OPTICAL SYSTEMS. 105

The applications of Zeiss' various anastigmatic objectives to
photographic purposes of various kinds have been described by
Rudolph. 1

Goerz' Double Anastigmat. K. von Hoegh, independently
of Eudolph, hit upon the principle on which anastigmatic lenses
are based, and made a symmetric combination of two exactly
similar triple lenses, each having one negative and two posi-
tive components. 2 It was accordingly designated a double-
anastiLiinat. The first objective of this kind was made at
Goerz' works in Berlin in 1892; and two series, with effective
apertures 1/7 '7 and 1/11, were issued in 1893. An account
of the performance of these objectives has been published by the
inventor. 1

Voigtlander's Collinear. The manifold adaptability of the
new glasses in photographic optics is illustrated by the fact that
Kaempfer succeeded in attaining anastigmatic flattening by a
different method. 4 The objective designed by him also consists
of two similar members symmetrically placed. Each memljer

sists of three lenses cemented together, two of them being
positive and one negative ; but the negative lens, instead of being
in the middle, is next the diaphragm. The principle of mutual
"irection of a normal and anomalous pair is not employed. In
each member the middle lens has the smallest index and is
concavo-convex. Convergence is accordingly produced at one of
the two cemented surfaces, and divergence at the other. Anastig-
mat ie flattening is thus rendered possible, just as, in the systems
"t li'ndnlph and vOn Hoegh, astigmatic compensation l>etween an
old and a new achromatic is attained by giving the former
a di verging, and the latter a converging surface of junetiuii.

Objectives of this kind, with effective aperture 1/6*3, were
made in 1X94 by Yoi^tlander of I'.ninswiek. who gave them the
name of collinear, because " the imam's which they give agree vei \
exactly with the nhji-et itself, and thus fulfil the conditions of
ideal <] linear representation." 5 By a happy accident the
en] linear objective also gives achromatic nni<n of three colours,

1 /'hot. Knrr,-*i*H t ,l. wn L. Sfhrn,. fa 398, p. 512.

* English Patent, No. 23878; Brit. Jour. Phot., 40, 485 (1893).

/.//i Phot. Afiffril., 30, 485 (1893-94).
/ <>*, 31,455(1894).

Phot. Mitttil., 31. 215 (1894

106

JENA GLASS.

and thus has no secondary spectrum. A patent for substantially
the same construction was applied for by Steinheil of Munich in
189::.

Zeiss' Anastigmatic Lenses. The principle of correction
used in unsymmetrical anastigmats has also been applied 1>\
Rudolph to single objectives composed of four lenses cemented
together. Two doublets, each consisting of a positive and ;i
negative lens, are united. In one doublet the greater index is
assigned to the positive, and in the other to the negative lens,
thus rendering anastigmatic and spherical correction compatible.
As regards chromatic aberration, the two doublets can either In-
corrected independently or by mutual compensation. 1

Since 1895 objectives of this design, with aperture 1/12*5,
have been made by Zeiss under the name of " Anastigmatic
Lenses." ~ As there are a larger number of disposable elements
than in triplet objectives, a more complete correction of the
various errors can be attained.

An anastigmatic lens of 350 mm. focus is shown in fig. 11, on
about scale. It gives a bright image, and the angle of field is
more than 85.

Fro. 11.

FIG. 12.

By combining anastigmatic lenses in pairs separated by an
interval, as in fig. 12, a series of double objectives (compound
anastigmats) is formed of effective aperture up to 1/6 '3. They
give bright images, and the anastigmatic flattening of the field
extends to wide angles. 3

English Patent, No. 19509; Brit. Jour. Phot., 41, 829 (1894).

2 Price List of Photog. Obj. Suppl., Feb. 1895.

3 For the practical applications of this series of objectives, see Catalogue ; also
Vogel* Phot. Mitteil., 31, 355 (1894-95).

PERFECTING OF OPTICAL SYSTEMS. 107

Orthostigmatics. The objectives recently issued by ('. A
SttMiiheil v^c Sons under this name belong to the same type as
Voigtliinder's collinear. They are objectives with two members,
each member being a triplet in which the middle lens has the
smallest index. 1

50. Zeiss' Spherically and Chromatically Corrected Objec-
tive." The simultaneous correction of chromatic and spherical
aberration presents no difficulty in a cemented doublet composed
of a positive crown lens L and a negative flint lens Z', so long as
the relative aperture does not exceed a certain moderate amount,
about 1/6. If, however, a considerably larger aperture is
required, serious difficulty is encountered, arising from the con-
nection between index and dispersion a connection which,
though rendered less stringent by the introduction of the nrw
glasses, is not altogether abolished.

When two chromatic foci are united, let the increments of
the indices n, ri from the first colour to the second be S, $'.
Then, by equations (1), (2) of Art. 18, we have

= *<n- !) + *'(*'- 1): ................................... (1)

=** + *'# .................................................... (2)

These give

whence

k + k' t in the case of a <Tinriitr<l 1ms. is the sum <>f the twnrxtmial

'See Brit. Jour. Phot., 1896, 489. An outline, from the theoretical point of
view, of the gradual development of the photographic objective is given by Lum
mer in an article entitled "Contributions to Photograph i<- Optics," Ztfachr. /.
17, 208 (1897). See also Mttller-Pouillet, Lf.hr. <L /%,*, ninth edition,
II. 1, 745-786, and S. P. Thompson's Translation of Lummer'*
-, Macmillan, 1900.

1 German Patent, No. 88889 (1896).

108 JENA GLASS.

c-urvatures, regarded as positive when convex ; and the last
expression for it shows what relations, between the constants of
the two glasses, tend to keep it small, and so to diminish the
positive aberration which will arise from the refractions at the
two external surfaces. The external curvature will be diminished
by diminishing ri n and by increasing $' S.

For the case n' n = the external curvature is a minimum,
and has the same value as for a single lens of the same focal
length. In this case, the positive aberration at the external
surfaces could not be compensated by a negative aberration at
the surface of junction ; for the rays would pass through this
surface without deviation.

From these considerations, it follows that glasses would be
required in which the dispersion of the flint was considerably
greater than that of the crown, but its refractive power only so
much greater as is sufficient for permitting compensation between
the external and internal spherical aberration.

In the old optical glasses, a large value of the dispersion ratio
$'/ is always associated with a relatively large value of n n.
Hence, in achromatic doublets of large aperture, the external
curvature is always unfavourable for the correction of spherical
aberration.

Introduction of Hyperchromatic Diverging Lens. There
are two ways of overcoming this difficulty. The convex element
of the objective may be replaced by a hypochromatic converging
lens (Art. 22), or the concave element by a hyperchromatic
diverging lens. In the former case, instead of <^, we shall have a
resultant dispersion which we can make as small as we please;
in the latter, instead of S', we shall have increased resultant
dispersion. In both cases we can avoid undesirably large values
of ri n.

In the " spherically and chromatically corrected objective," the
second course is adopted, the simple lens L f being replaced by a
hyperchromatic diverging lens; with the resulting advantage that
the chromatic difference of spherical aberration is less than for a
simple lens of the same dispersion. This lens being cemented to
the simple convex lens L, we have a triple achromatic system,
which not only, by its small external curvature, renders the
correction of spherical aberration easy, but also gives less over-
correction in the upper portion of the spectrum than an ordinary

PERFECTING OF OPTICAL SYSTEMS. 10&

two-lens system, equivalent to it as regards focal length ami
secondary spectrum.

The hyperchroinatic diverging lens can, if desired, have two
convex single lenses cemented to it instead of only one.

The construction above described involves an additional lens,
but this disadvantage is accompanied by several advantages. At
the cemented surface inside the hyperchroniatic lens there is only
very slight bending of the rays. The curvature of this surface
can therefore be made large without injurious consequences.
Again, imperfections in the shaping of the two lens-faces which
are united at this surface are almost harmless, if a cement be
used having nearly the same index as the glasses a condition
easily fulfilled.

Pairs of glasses suitable for the hyperchroniatic lens are
available, in sufficient variety to give a good choice, for values of
n ranging from about 1*54 to about 1*61.

In the specification of the patent for this construction, the
following numerical data are given for two objectives actually
constructed, in which the relative aperture amounts to 1/3.

The first consists of three lenses L v L 2 , Z 3 ; the second of four,
Z p Z 2 , Z s , Z 4 . In both combinations L^ and Z 2 compose the
hyperchroinatic diverging lens, its external curvature taing
denoted by k et and that of its convex component L^ by A-. The
resultant dispersion is denoted by p, and the unit of length
employed is the focal length of the combination. The convention
as to sign, for the radii of curvature r r r,, ... of the successor
faces, is that r is positive for surfaces convex towards the incident
light.

TRIPLE OBJECTIVE

A L t Z 8

7^=1-60844 1-60SH 1-55540

w = 1-62217 1 <ii>967 1-57036

n ff -n D = -01373 -02126

r t = + 0-4745

r,= oo f= -0-85

r s = + 0-2175

r 4 = + 9-8865 p = 0*02763

110 JENA GLASS.

QUADRUPLE OBJECTIVE.
Zj and Z 4 Z >2 Z 3

/i,, = 1-60844 1-60284 1-51914

*0.= 1-62217 1-62060 1-53020
n& -n D = -01373 "01776

r 1= +0-492

/-.,= -0-795 ^= -1-65

r 3 = +0-248

r 4 = +0-475 ,0=0-02441

r 6 = +5-634

51. Zeiss' Spherically and Chromatically Corrected Ana-
stigmat. 1 An objective giving strong illumination and combining
u x )d anastigniatic flattening over a large field with specially good
spherical and chromatic correction, has been constructed on the
following principles.

An objective composed of two lenses, L convex and L r concave,
not in contact, has four disposable radii of curvature, whence it is
possible as in Gauss' telescopic objective to correct spherical
aberration for two colours, and thus abolish chromatic difference
of spherical aberration. In applying this construction to photo-
graphic objectives, the achromatising must extend to the rays
most active in photography, and the anastigniatic flattening must
be much more complete than is necessary in the case of
astronomical objectives.

To satisfy these conditions as regards achromatism, for a large
aperture, without unduly increasing the thickness of the lenses
or their distance apart, it would be necessary, if our choice were
confined to the old glasses, to use a very heavy flint glass for the
concave lens L', and this (see Art. 47) would be altogether
incompatible with anastigniatic flattening.

The difficulty can be avoided by using a hypochromatic con-
verging lens in place of L, or a hyperchromatic diverging lens in
place of L', or both at once. 2 It is not necessary that the glasses
used should have exactly the same index. A difference of a few
units in the third decimal place may even be advantageous,
by affording opportunity for diminishing spberical aberration.

1 German Patent, No. 92313 (1897).

2 See Art. 22.

PERFECTING OF OPTICAL SYSTEMS. Ill

The patent specification gives the following particulars of two
objectives, the first consisting of three lenses with a diaphragm
in front, and the second being a double objective, with its two
members symmetrically placed before and behind a diaphragm in
the middle. The second objective has the advantage of beiim
free from coma and from orthoscopic distortion.

Of the three lenses L v L v Z 3 which compose the first, Z x is a
simple diverging lens, and Z 2 , Z s form a hypochromatic doublet,
L. t leing concave and Z 3 convex.

Of the three lenses L v Z 2 , Z 3 which compose either member of
the second objective, Z 3 , which is furthest from the diaphragm, is
a simple convex lens, and L v Z 2 form a hyperchromatic diverging
doublet, Zj being concave and Z 2 convex.

To assist the memory, the single lens is in each case dis-
tinguished by square brackets. The notation is the same as in
the specification of the previous article.

FIRST OBJECTIVE. RELATIVE APERTURE 1/9.

L lJ * 3

71^=1-57210 1-51 i:.s 1-51111

71^ = 1-58997 1-52:144 L-62127

n(/ -n D = -01787 -01186 '01016
r 1= -0-1164

r.,= -0-2215 k = +1-85

/-.,= -1-0097

r 4 = -fO-2708 /o = 0-00871

r 5 = -0-1760

QUID OBJECTIVE (DOUBLE). KKI.ATIVK AI-KIMI-RE 1/4.

L\ LI and [ZJ

n D = 1-576:; 1 1-5724 I

71^ = 1-59227 l-r>8:.12

ft, -n D = -01596 -01268
/-,= -0-in.M

r = 4-0-4370 ^'= -2-17

r 8 = -0-3599

r 4 = -1-54L' 1 p = 0-02:500

r 6 = -0-3147

CHAPTER V.
CONTINUATION OF THE SAME SUBJECT.

52. Achromatic Diverging Lenses. Optical systems of the
type of the Galilean telescope and the telephotographic objective
consist of two members, one positive and the other negative.
Each is separately achromatised and is usually separately corrected
for spherical aberration.

In the case of the second or negative member, the simplest
construction is to make it consist of two single lenses cemented
together, the negative lens having the larger v and the smaller n.
The achromatising depends on the differences of i/, and the
spherical correction on the differences of n. The old silicate
glasses were capable of satisfying to some extent the requirement*
of this construction, inasmuch as v decreased when n increased.

This mode of constructing diverging lenses had, however, the
inconvenience of giving too large curvatures to the outer surfaces.
To show this, we have, by equations (3) of Art. 18,

d v-v

Let R denote 7-(-r v/K or ~ ? ( ~t r~~i )>

v v \A A/ r/ v \n l n I/

so that we have

For doublets of the old glasses, the smallest value that R can

PERFECTING OF OPTICAL SYSTEMS. 113

have is about 2 '4, and this makes the external curvature k + //
considerable when the focal length d is small. The conditions
are therefore unfavourable for the removal of spherical aterration.

53. Compound Diverging Lenses with Diminished External
Curvature. If spherical aberration is to be treated as un-
important, the constant R can be diminished by diminishing the

difference ri n. For if we identify with <p in the equations

of Art. 50, we have

fc+tf-Jfy,

and -o

showing that \JR is increased by diminishing ri n. By

the new optical glasses, it is easy to obtain in this way values of

R less than 2. By using anomalous doublets 1 in which v and n

are greater than v and ri, and -^ -* is negative, it is possible to

reduce R below the value 1. The external curvature of the
doublet diminishes with R in direct proportion.

If ri is & little greater than n, a little positive aberration will
ivinain at the interior cemented surface. When n and ri are
equal, this internal aberration vanishes completely, and the
external curvature of the doublet becomes equal to that of a
-imple lens of the same focal length. Finally, when n is a little
greater than ri, the internal aberration is negative, like that of a
single diverging lens. In all three cases, taking the action at
the external surfaces into account, the achromatic diverging lens
will exhibit some small degree of negative aberration. This can
be easily compensated by leaving in the objective a small
remnant of positive aberration.

These considerations led Rudolph to a new construction for
achromatic diverging lenses. 1 Equal or nearly equal indices are
assigned to the two components of the cemented system, and the
system is not spherically corrected. This gives smaller external
curvature, for a specified focal length, than would be required b\
previous methods.

1 See Art. 47.

* English patent, No. 10000. Brit. Jour. Phot., 40, 659 (1898). D.R.P. 71473.

114 JENA GLASS.

;." Another advantage is. that the internal aberration (at the
cmii'iiU'd surface) is diminished : and if it is rendered negative,
this facilitates correction outside the axis.

The foregoing discussion shows that baryta crown of lii^h
iinU-x is pre-eminently suitable for the negative lens of the
diverging doublet, and strongly dispersive silicate crown for the
positive lens. Several other pairs can, however, be selected
which are sufficient for the end proposed.

Zeiss makes these achromatic diverging lenses for teleobjecthvs,
with the four focal lengths 30, 40, 58, and 75 mm. 1

1 Price List of Phot. Obj., 1894, p. 30.

CHAPTER VI.

CONTINUATION OF THE SAME SUBJK' I.
TELESCOPES.

54. Hand Telescopes with Inverting Prisms. Of the two
r<linary constructions for erect-image telescopes, known as the
Galilean and the Terrestrial, the former is suitable for magnifications
n>t exceeding 4 diameters, is simple in construction, is short, and
gives a bright field. For higher magnifications it is not \\vll
adapted, owing to the smallness of its field and the falling off of
liiiht towards the margin. The terrestrial telescope, on the other
hand, has a larger field with uniform illumination, but is of
complicated construction, and disproportionately long. It is
seldom made with lower magnification than 12, and is usually
fitted on a firm stand.

Powers of from 5 to 8, which are the most useful for many
purposes, are not well provided for by either construction.

This want has been supplied by intmdurinu r . U'twrcn tln

live and ocular of the ordinary astrono-
mical telescope, glass prisms which, l.y tour
successive total reflections, re-invert the in-
verted image formed by the objective.

different arrangements of prisms can
be used f<>r this purpose. The first is repre-
sented in its simplest form in tiir. 1 .".. It

be regarded as built up of four eqn.d no. is.

right-angled isosceles prisms, the two faces which contain the
right angle being square. Th. n\ armwa show the course of a
ray which undergoes four reflections, one at each of the hypotenusal

11.; JENA GLASS.

faces, and finally emerges parallel to its original direction. Tins
'in of prisms, if used alone, gives aii inverted image of an
object seen thnmgh it: and, when used in conjunction with an
objective which of itself would give an inverted image, changes
this image into an erect one.

To convert the first arrangement into the second, No. 4. prism
in the figure is to be moved parallel to itself from its present
ition to the top of No. 3, so that its left-hand face fits against
the first face of No. 1. Its two arrows are to be carried with
it, and will represent the incident ray and first reflected ray, the
order of succession of the prisms being now 4, 1, 2, 3, and the
incident light being at right angles to its former direction.

In the first arrangement Nos. 1 and 2 may consist of a single
piece of glass, and Nos. 3, 4 of another, the two pieces being
cemented together at the shaded area shown in the figure. In
like manner, in the second arrangement, Nos. 1 and 4 can be
made in one piece, and Nos. 2, 3 in another, and the two may
be cemented together.

Instead of having the four component prisms all close together,,
any two of them may be shifted apart, provided that the shifting
is effected along the course of the ray. The prisms can also be
made to do duty as lenses by giving spherical curvature to some
of their faces.

55. Collateral Advantages. By either system of prisms, the
central ray is bent four times at right angles ; and as the total
length of path from objective to eyepiece is a fixed quantity, the
length of the telescope is thus shortened, especially if there is
wide separation between the prisms. This shortening may or
may not be accompanied by lateral shift of the emergent ray
relative to the incident ray.

With the first system, the maximum shortening for a given
amount of lateral shift will be obtained by placing prisms 1 and 2
at the eye-end of the tube, and prisms 3, 4 at the end next the
object. Rays will thus have to travel over the length of the tube
three times in succession.

By this combination of reflecting prisms with the lenses of the
astronomical telescope, we obtain a construction which, as regards
handiness, field of view, and illumination, leaves nothing to be
desired. The two arrangements of prisms above described were

PERFECTING OF OPTICAL SYSTEMS 117

invriitnl many years ago by Porro, an Italian engineer, but
attracted little attention. 1

Lateral Shifting can be increased by separating No. 1 prism
in the first arrangement, or No. 4 in the second, from the three
remaining prisms. This shortens the telescope, but adds to its
width. The separated single prism can conveniently be mounted
in the holder of the objective, and the remaining group of three
in the holder of the ocular.

Two other advantages (not contemplated by Porro) are also
obtained.

In the first place, by reason of the crookedness of the course
of the rays, the observer can see without exposing himself.

In the second place what is of more practical importance
a binocular can be employed in which the two objectives are at a
much greater lateral distance than the two eyes, thus giving
increased stereoscopic effect; a result which Helmholtz endeav-
oured to obtain in his telestereoscope 2 by employing two
terrestrial telescopes with a principal plane mirror and a reflect-
ing prism.

56. Zeiss' Field-Glasses and Relief Binoculars. 1'orro'stwo

(instructions were so completely forgotten that they were several

times reinvented, especially the form represented in fig. 18. It

through the Jena Optical Factory that prism telescopes first

<M me into general use. 3 The long delay in utilising so old an

1 The first is described in the French magazine CoimvH, edited by Moigno,
vol. _', p. *_' (is.~>3) ; the second, with spherical prism-faces, in the same journal,

P. 401 (1856).

ffimcft, d. Phys. Opt., Isted. p. 681 ; 2nd ed. p. BSL

3 Some historical information respecting prism telescopes will he found in
Czapski's book, On Xew Kind* of TelesfOfw, e*j*c\ally for Hand U*< . Brrlin, 1^.~>.
ml., il r. n i.^Llnit 'I. / /s.-//. dfA.f. Mech. n. Opt. (1896), p. 2) gives the
following testimony :

MI u' n number of old models left by my grandfather, C. A. Steinheil,
I found a few days ago a small metal case of peculiar shape, with two round
.inKH on opposite sides of the case but not directly opposite, which, on closer
examination, turned out to be an inverting assemblage of prisms. [It was a
compact form of the second arrangement.] One of the two openings in the case
had a crew thread, obviously for receiving the objective, and the other was
ol.vi.Mi.lv intended for receiving the sliding ocular tube." The date is believed to
be "about 1830, as at that time C. A. .Steinheil was much occupied with apparatus
in which prisms played a leading ]>a:

118 JENA GLASS.

idea may partly be explained by the difficulty arising from the
length of path in glass and consequent large absorption in
traversing the system of prisms ; this length being much greater
in the prism telescope than even in the ordinary terrestrial
telescope. The Jena Glass Works furnished for the first time
the means of overcoming this difficulty. Indeed, of all the
glasses in the Jena list, there are only two which are suffici-
ently transparent for telescope prisms, and only one of the
two is really available, as the other cannot be obtained free from
bubbles.

The starting point of this new line of work may be found in
the fact that some of the scientific advisers of the firm quite
unaware of what Porro had done were impressed with the
advantage that might be derived from the lateral shift obtainable
by successive reflections.

Two types of prism telescope are made by the firm of Zeiss. 1
For field-glasses, they employ the arrangement described (in the
first half of article 55) as giving maximum shortening. For
relief binoculars, which are the practical realisation of Helmholtz'
conception of a stereoscopic telescope, they employ one of the
methods of giving large lateral shift described in the beginning
of the second half of the article.

The widening-ratio, that is, the ratio of distance between
objectives to distance between oculars (both measured from centre
to centre) ranges from 1*75 to 2 in field-glasses, and from 5 to 7
in relief binoculars. A relief telescope with stand was exhibited
at the Munich International Congress of Psychologists in 180(>,
in which the distance between the objectives was 152 cm., so
that, taking the distance between the eyes as 6 '2 cm., the
widening-ratio was between 24 and 25. According to the report
by G. Hirth, the performance of the instrument corresponded
to these figures.

57. Increase of Resolving Power and Illumination in
Telescopic Objectives. The resolving power of a telescope is
determined by the linear aperture of its objective. Let S denote
the angle between two fine lines or points, for example, two stars,
which are just separable, b the linear aperture (i.e. the clear

Prospectus of Binoculars, 1897.

PERFECTING OF OPTICAL SYSTEMS. 119

diameter of the objective), and X the mean wave-length of the

liirht, then we have 1

The brightness of the image of a body subtending a sensible
un;_rle is proportional to Qb 2 , if we denote by Q the ratio of the
transmitted to the incident light. "VVe shall use a symbol H
. If lined by

H=Qb* ................................ (1)

It is desirable, even for small objectives, that Q should be as near
to unity as possible; but this element comes much more into
consideration in the case of large objectives ; as will appear, if
\v- examine the connection l>etween increase of diameter of the
objective and increase of brightness of the image.
Equation (1) gives

1 dff_2 1 dQ
NWb + Qdb'

Q depends partly on loss by reflection and partly on loss 1>\
absorption.

The ratio of the light transmitted through one of the surfaces
to the light incident on the surface, is, for normal incidence,
according to Fresnel,

n denoting the mean index of refraction.

Again, if K a denote the ratio of the transmitted to the enter-
ing light for thickness a, and K ft the corresponding ratio t'r
thickness ft, we have

(4)

Now consider an objective compos. <l f two lenses whose indices
rtcd in (.",) jL rivc values A t ami /.',. >u|ijM>in^ A',, to ! kn\\u
I'.v experiment for a certain thickness a, and to have the same
\ aluc for both lenses; the total thickness l>eing ft.

In computing th. ivsultant effect, each of the factors J? r 72 2

P See Everett'H WH*I ration* ofC.O.S. Unit*, 1902 edition, Art. 148.]

120 JENA GLASS.

will occur twice, because each lens has two surfaces. The ratio
of the transmitted to the incident light for the complete objective
will therefore be

p = R l z R 2 *K a V* ....................... (5)

The thickness /3 may be taken at from 1/6 to 1/7 of the
diameter b. Taking then /3 = /6'5, we find

The first term 2/b is positive, and diminishes as b increases.
The second term is independent of b, and is negative, since the
fraction K a is less than unity. For small values of b, the positive
term is large compared with the negative, and absorption does
not much influence the change of brightness with change of size ;
but the case is different when b is large. It is theoretically
possible for b to be so large that the positive and negative terms
cancel each other, indicating that the brightness has reached a
maximum and further increase of size will involve loss of light.
This limit is never reached in practice, but there is a limit
beyond which the advantage gained by enlargement would be too
small to justify the additional outlay ; and this limit depends, as
equation (6) shows, on the value of K a , the limit being carried
further as K a approaches unity.

Practical Example. Transparence is specially important in
telescopes' intended for photography. Hence the data found by
H. G. Vogel 1 for the objective designed for the great refractor
recently erected at Potsdam will serve as a very appropriate
illustration. Having regard to the purpose for which it was
intended, and to the results of preliminary experiments, it was
decided to achromatise the objective for chemical rays only, and
to attach to the instrument a guiding telescope of the same
focal length. 2 Steinheil, the maker, proposed as suitable glasses,
the light flint 0. 340 and the crown 0. 203, which could be had
in large pieces without faults ; hence an examination of the
absorbing properties of these two glasses was undertaken. 3 The
results, so far as they concern us, are here summarised.

1 Math. u. natter 10. Mitttil der Berlin. Akad., 1896, vol. 9, p. 623.

2 See Art. 60.
:{ See Art. 25.

PERFECTING OF OPTICAL SYSTEMS. 121

Values of K m for a = 10 cm.

o. :

0. -J03.

Visual rays, -
Photographic rays,

0-84
0-615

0-85

()<>_>

Substituting accordingly for a and K a in equation (6), we obtain

for visual rays }, '"! = 'j - "0027, . . . .(7a)

H do b

for photographic rays -^ jr = 7 '0066, ............... (76)

the unit of length being the centimetre.

The right-hand member of (7a) vanishes for about 6=7">0,
and that of (7ft) for about 5 = .SOO. The maximum <>f visual
brightness would accordingly be reached with an objective of
metres diameter, and that of photographic intensity with one
of ." metres. The diameter actually decided on was 80 cm.,
which is greater than that of any other objective in Europe. 1

I "i the guiding telescope an aperture of alxmt 50 cm. was
adapted, the focal length l>eing in both cases 1U m. The ratios
of aperture to focal length were accordingly 1 1 ." and 1 26,

Putting b = 80 in equation 76, we get

This is the ratio of dH t<> // for an increase of 1 em. in b.
\ IK Teasing the aperture from 80 cm. to 81 cm. would accordingly
increase the photographic intensity 1 '84 per cent. The increase
in area would be - " |-i cent. Increasing the diameter to
100 em. would increase the intensity by less than 40 per cent.,
and \\onld nut repay the additional outlay.

Table for calculating Intensity of Illumination for Ob
jectives of Different Sizes 840 and <> . I'ti:;, or

<>ther> \\ith nearly the same properties are likely to be frequently
employed t'.r a similar purp' 1 has calculated the follow in-

tal-le aj.plieable to them :

[' The ol.jcrtive m*d about the Mune time for the Mention observatory ii *
t n tie larger.]

122

JENA GLASS.

100 ^

100 Q

cm.

Visual.

Photographic.

Visual.

Photographic.

In computing the table, 7T a for a = 10 cm. was taken as '845
for visual, and '653 for photographic rays. The value of Q
depends partly on E^ and 7? 2 , which were computed by equation
(3); the values assigned to n in computing E l being 1*583 for
visual and 1'601 for photographic, and in computing E. 2 , 1*5 "21
and 1*532, these being the indices for the line b l (wave-length
*518/x) and the line h (wave-length *410/x).

In using the table to find the value of H or Qb 2 , ft may be
taken as from % to f of b.

The two glasses above discussed are Nos. 13 and 64 of the
list in Art. 17, and are described as "ordinary silicate crown ' r
and " ordinary light flint." The baryta light flints are even more
free from colour. The improved method of annealing large discs-
introduced at the Jena Works is another important contribution
to astronomical requirements.

58. Cemented Doublets for Objectives. In an objective
consisting of two lenses not in contact, there are four radii of

PERFECTING OF OPTICAL SYSTEMS. 123

curvature disposable. ]\y means of these, it is possible to give
a prescril>ed focal length, to achromatise, to correct for spherical
aberration on the axis, and to satisfy the sine-condition. The
marginal aberration will, as a consequence, be practically annulled,
if the ratio of focal length to aperture is not too small. 1 These
are the general requirements for all good telescopic objectives.
Expressions for the four radii, deduced from the four above-
mentioned conditions, are uivm at the end of a paper by Moser
"ii astronomical objectiv.

If, for small objectives, say, of less than 50 mm. aperture, the
further condition lie imposed that the two lenses shall be in
contact over one surface of each, there will be only three radii
disposable : and the question arises what glasses must l>e used in
order that the requirements may still be satisfied.

H. Harting's investigation of this question by calculation 3
leads to the conclusion that, with the glasses available down to
1884, it is impossible to produce cemented doublets which, in
addition to being achromatic and free from axial aberration, will
also rigorously satisfy the sine condition. In all pairs of cro\\n
and Hint, the dispersion of the crown is too high, and that of the
Hint too low, in comparison with the index. Hence in pencils
ohlique to the axis more or less al>erration remains.

It is true that, in some of the old pairs of glasses, th>
outstanding al>erration did not practically matter, for the simple
reason that they had other worse faults, compared to which it
was unimportant. This is the case, for example, in the following
objective (cmwn in fmnt) which belongs to a type formerly
common:

It*

Crown 0. 40, 1 ' I
Flint O. 167, L-61

, i== 4-0-4117: /,= -0'415. r >; r 3 = + 47'ui.>;

L_I = 2 H

r l 'a

The valm- of the three radii of cur\alure air expressed in

l 8eeCiki, Winkelmmnn'. /////.. </. /'A/,-.. II I. '270.
ZeifecAr./. /**>., 7, 225 (1887).
*Zeit*chr.f. /nVntm., 18, 357 (1898).

1-4 JENA GLASS.

I the focal length taken as unity. The difference given in the
last line is the external curvature.

< >H the other hand, the new Jena glasses permit a strict or
'. ly strict fulfilment of the sine condition, and that in two

Wa\

First, by combining ;i silicate Hint of index 1'64 to 1'65, with
a 1>< implicate crown of index 1/5 to 1*51, and of smaller disper-
sinn than the old crowns; for example,

n D

Flint (in front) 0.102, 1/6485

Borosilicate crown 0. 144, I'olOO

r 1= +0-4234: r,= +0'2446; r s = -14'7l;

i-i-2-43.

r i r s

Here the sine condition is strictly fulfilled. The external curva-
ture, however, is somewhat greater than in the preceding objective,
and this is disadvantageous for avoiding axial spherical aberration,
ndly, by combining a barium-silicate crown of index 1'57
to 1'59, with a flint whose index need only be slightly greater;
for example,

IJaiyta crown (in front), 1'5899
Baryta flint, Hi229

/ - i = U-047: > >: r 2 -0-3059; r s = -3-175:

i -1=1-80.
r i r z

In this objective, the sine condition is very nearly fulfilled, and
the external curvature is considerably lessened. Hence, with this
objective, the aperture may he made decidedly larger, 1 compared
with the focal length, than would lie permissible with crown and
Hint having larue difference of index.

The solution of this special problem in the optics of the
telescope is thus considerably furthered by the new Jena glasses.

59. Astigmatism and Curvature of Image in Astronomical
Objectives. The question whether the astigmatic curvature of
the image formed by an astronomical objective can be materially

1 See Czapski, foe. cit., 271.

PERFECTING OF OPTICAL SYSTEMS. 125

diminished by proper choice of glasses, has been examined by
H. Harting by means of approximate algebraic formulae. 1 These
formulae are based on the three assumptions:

That the thicknesses of the lenses composing the objective are
negligible ;

That the axes of oblique pencils from infinitely distant points
pass through the centre of the objective ;

That the inclinations of these axes to the optic axis do not
exceed about 5.

From these assumptions it is immediately deduced, that the
astigmatic difference (distance between primary and secondary
focus, divided by focal length) 2 is equal to the square of the
inclination. Thus, for an inclination of 5, the distance is about
| per cent, of the focal length.

Since this amount on the assumed hypothesis is invariable, it
remains to be seen whether it is possible to make the two
astigmatic image-surfaces symmetrical with respect to the plane
through the focus at right angles to the optic axis. If this be
also impossible, the only way left of effecting an improvement is
to bring the two image-surfaces nearer to the focal plane.

Beginning with an objective consisting of two lenses, it is
tumid that, other things being equal, it makes no difference in
the two astigmatic image-surfaces whether crown or Hint be in
t'runt. It also makes no difference in this respect whether only
two lenses are used or a larger number, so long as only two kinds
of glass are employed. It is only by introducing more than two
kinds of glass that the curvature is changed.

After this preliminary discussion, Harting confines himself to
objectives made of only two kinds of glass. Let n, v refer to the
crown, and n\ v to the Hint, with the assumption v > v'. Then,
if p, and p t be the curvatures of the secondary and primary
image-enrfaoef (the focal length of the objective being taken as
the unit of length), we have

(1)

/> = 1 + <r]
[
ft-S+OJ

'-'

. /frtrumtnfe**., 19, 138, (1899).
'See Art. 46.

126

JENA GLASS.

p t and p t are regarded as positive when the eorreeponding
surfaces are concave towards the objective.

In all the glasses under consideration, <r is positive. Hence it
is not possible to attain symmetry as regards the two image-
surfaces ; for this would require p a + p t 0, whence or= 2.

Further, any considerable flattening of the image-surfaces 1>\
diminution of a- could only be attained by an " anomalous " pair
(see Art. 47) in which n > ri and v > v. The first term in the
expression for 0- then becomes negative, and can be increased
numerically by diminishing the difference v v. A limit is,
however, set to this diminution by the requirements of spherical
and chromatic correction.

Thus no marked diminution of astigmatism or of curvature of
image can be effected by selection of glasses.

60. Chromatic Aberration in Objectives of Great Focal
Length. The length of the secondary spectrum may become
very considerable with increased focal length. We have a good
example of this in the great instrument of the Lick Observatory.
The following table gives the relative positions of its chromatic
foci, from Keeler's measurements:

Ray.

Wave Length.

Position
of Focus.

6867 M

0-0 mm.

6563

- 6-1

5893

-11-4

4862

o-o

4341

+ 36-8

4102

+ 70-1

The objective, as the table shows, is achromatised for the visual
rays by uniting B with F. The positions of the other foci are
specified with reference to this point of union, the plus sign
indicating greater distance from the objective. The focal length
of the objective is about 17*4 m.

The shortest chromatic focal length belongs to a green ray,
and corresponds to 11*9 in the notation of the table. The
length of the spectrum within the limits of the table is therefore
-82 mm. The focal curve plotted (as in Art. 19), from the data

PERFECTING OF OPTICAL SYSTEMS.

187

n in the table has the form characteristic of the old optical
glasses.

The visual focus of the objective lies at the point of union of
the complementary red and green, at o'l. The greater portion
<>i the remaining rays are not helpful for the visual image, but
tend to blur it.

The photographic rays have an ill-den' ned focus at about
+ 41*9 from the assumed zero point. Thus the distance between
tlu* visual and photographic foci is about 47 mm. The imperfect
achromatism of the objective for chemically active rays becomes
unpleasantly evident when the telescope is used for photography, or
for spectrographic observation of the more refrangible rays. A
< "irecting lens placed before the objective brings about a better
union of the actinic rays, and at the same time shortens the focal
Irmrth considerably. 1

The secondary spectra of the Potsdam 29'8 cm. refractor, and
the Vienna 67'5 cm. refractor, have been investigated by H. <
1. from whose papers the following data are taken: 2

Potsdam Refractor.

Vienna Refractor.

Wave Length.

Position
of Focus.

Wave Length.

Position
of Focus.

690 /x

+ 4-2 mm.

690 M

+ 2'1 mm.

610

+ 0-3

610

- 6-7

530

1-7

570

- 7'8

-tsti

o-o

-486

o-o

470

+ 1-6

470

+ 4-4

4:iO

+ 9-2

430

+ 20-7

410

+ 16-7

410

4-81-1

Tin* Potsdam instrument is achromatised by uniting F with a
line near D\ the Vienna one by uniting F with a line near C.

In \icw of the above results it was decided that the objective
of the great refractor, of 80 cm. aperture and 1 li m. tWii^ (><<
Ail. .~>7), to be erected at Potsdam for photo^raphir purposes,

1 The reference for these particulars is D. Taylor, Improvement* in Compound
Object glares for Telecopt* (1893).

*Monat*ber. d. Berlin. Akad. t 1880, 438, and Publ. d. cutrophy*. Ob*, zu
Potodam, IV. 1. 4. Also Ber. d. Berl. Ak. t 1896, 1221 ; and Mathem. u. Naturw.
Milt., 1896, 625.

128 JENA GLASS.

should be achromatised for the most powerfully actinic rays. It
was at first intended to equip the large telescope with an
appliance for introducing or removing at will a system of lenses
for bringing about a better union of the visual and chemical rays.
This, however, would have required a triple lens, which, in order
to give a fairly large field, must have had a diameter not less
than oO-40 cm. On account of the expense involved, and I'm-
other reasons, the plan was given up, and the only means of
correction provided was Christie's arrangement of a small doublet
near the focus largeness of field being sacrificed. This correcting
lens is used when spectrum observations are to be made in the
less refrangible part of the spectrum.

The auxiliary eye telescope of 50 cm. aperture and I '2 in.
focus is itself a powerful instrument more powerful than any
telescope previously constructed in Germany.

The foregoing data clearly show that the removal of the
secondary spectrum is a pressing problem in telescopic optics.

If the chromatic remnant of spherical aberration could be
removed, this also would have a beneficial effect on the image.
We shall deal in the next article with the attempts hitherto-
made to solve these two problems.

61. Removal of Secondary Spectrum in a Double Objective
by Phosphate Crown and Borate Flint. The two glasses S..'->0
and S.8 (Nos. 3 and 24 in the list of Art. 17) are specially
suitable for mutual achromatisation in a double objective. If
the foci for the C and F rays are united on the axis, and the
focus for D be taken as origin, the residual aberrations are
found, by calculation, to have the following values in mm. per
metre of focal length :

A' CDF G'

-0-07 +0-07 0-00 +0-07 +0'49

The dispersion is thus almost entirely abolished from A' to F,
becoming appreciable only beyond F, and quite small even there.
The character of a tertiary spectrum, such as this, is easily
gathered from a glance at the focal curve (2) of Art. 19.

Czapski has calculated the outstanding chromatic aberrations
for the same pair of glasses when so combined that the focal
length is a minimum for X = '55yu (which is about the brightest

PERFECTING OF OPTICAL SYSTEMS.

129

place in the solar spectrum), according to the method described
in Art. 20. The following are the results, expressed in the same
units as before : l

X=|o-77/i

0-73

0-69

0-65

0-61

0-57

0-55

0-53

0-49

0-45

0-41 M

-0-04

-002

-001

000

OOO

+ OO1

+OO4

+ 0-21

+0-79

The aberrations from X = 4 77/x to X = "49^, that is, from A to F,
are here even more completely corrected, the general character of
the focal curve remaining unchangcil.

Testing of Objectives of S. 30 and S. 8. Two objectives, each
composed of the two glasses in question (a phosphate crown and
a borate flint) made by Bamberg of Berlin from Czapski's calcula-
ting, were tested by H. C. Vogel for their actual achromatism
by a method of his own, distinguished by the sharpness of its
indications. 2

If the image of a bright star, formed by a powerful astro-
nomical telescope, is viewed through a direct-vision train of
prisms, the image of the star is drawn out into a spectrum ; and
this spectrum cannot, by any adjustment of focus, be reduced to
a sharp line. It may rather be described as a diffuse band
constricted in one or two places and widening out at the violet
end. This is due to incomplete achromatism of the objectiva

Suppose, for example, that the objective is composed of the

vn 0. 60 and the flint 0. 103, which, when combined, give the

focal curve (1) of Art. 19. When the eyepiece is focussed for

the part of the spectrum where the focal length is least, which,

as the figure of Art. 19 shows, is a little above />, the spectrum

Fio. 14.

will l>e narrowed down near D, and will broaden out towards
both ends, because the spectrum is increasingly out of focus. It
will therefore have the form roughly sketched in tig. 14, a.

1 Winkelmann, Handb. d. Phyrik, II. 1, 146.
*MonaUbcr. d. Berlin. Akad., 1880, 488.

130

JENA GLASS.

As the eyepiece is pulled further out, the constriction will
break up into two, which will travel in opposite directions ; and
when one has reached F, the other will be at C, as shown in tig. 14,6.
In like manner all the lines seen in the spectrum of the star can
l.)e brought one at a time into focus ; and the positions of the
eyepiece will show the relative positions of the different chromatic
foci. By plotting these observations, with the wave-lengths as
abscissae, empirical focal curves are obtained which can be com-
pared with the theoretical curves, and will show to what extent
theoretical expectations have been fulfilled.

Vogel began by applying this method to four objectives by
Schroder, Grubb, Fraunhofer, and Steinheil, using the star Sinus ;
and secondary spectra of large range were exhibited. The pairs of
coincident foci are different for the different objectives ; but the
distribution of the foci for the most important visual rays say
from C to F is nevertheless practically the same for all. If
the distance from the focus of F to that of G f is also taken into
consideration, the Fraunhofer objective is distinctly superior to
the others. Since it, therefore, is the most suitable for com-
parison with more completely achromatised objectives, we subjoin
a list of its chromatic aberrations.

FRAUNHOFER TELESCOPE AT BERLIN OBSERVATORY.
Aperture 2 4' 3 cm.; Focal Length 43 3'1 cm.

Ray.

Pulling Out.

Per Metre
Focal Length.

0-690 A*

- 0-8 mm.

-0-19 mm.

656

- 1-3

-0-30

590

- 2-8

-0-65

517

- 1-2

-0-28

486

459

+ 1-8

+ 0-42

434

+ 4-0

+ 0-92

410

+ 8-5

+ 1-96

397

+ 15-7

+ 3-62

The minimum focal length comes almost exactly at D. The
red ray C is united to a green ray of about A = "525^, beyond E.
The focus for F is taken as the zero of the measurements.

PERFECTING OF OPTICAL SYSTEMS.

131

The same method was afterwards 1 applied by Vogel to the two
objectives mentioned at the beginning of this Article, which were
< < instructed with a view to preliminary trials of the new glasses
and S. 8. The results are given in the following table,
together with the aterrations of the Fraunhofer objective for the
same wave-lengths. Of the Fraunhofer values, some are directly
WrvtMl. and the rest are derived by interpolation from the
observed values given in the preceding table.

Objective I. Aperture 13-4 cm.; Focal Length 197*3 cm.
Objective II. 17'6 cm.; 250*0 cm.

Chromat. Aberr. per metre of Focal Length.

II.

Fraunhofer.

0-710 M

- 0-05 mm.

-0-02 mm.

+ 0'67 mm.

650

+ 0-05

+ 0-23

590

o-oo

530

-0-06

-o-io

+ 0-24

470 +0-15

+ 0-05

+ 0-86

410 4-1-10

+ 0-40

+ 2-60

Czapski has pointed out 2 that, in testing extremely well-
aichromatised small objectives, the results may be seriously affected
by the chromatic errors of the ocular and of the eye. He
.accordingly suggests that the image of the sun formed in a
globule of mercury should be viewed through the ocular and
prisms, and the errors thus observed subtracted from those
observed in the principal test. Vogel took this suggestion into
-account in his deduction of the above results. 8

In discussing the above comparisons Vogel remarks on the
extraordinary advance in achromatisation which they exhibit, ami
its importance for spectrographic work, in \itnv of the fact that
with the great telescopes of the present day, it is impossible to

1 Vierteljahrtchr. d. Attron. Gc*., 22, 142 (1K88). Referat : Zeit*rhr. f. Inrtru-
menten*., 8,248(1888).

*Zeit*chr.f. /w<rnm., 8, 247 (1888).

'Czapeki in Ztitvhr. /. ln*trum. t 9, 250 (1889) criticise* a method published
by Ch. S. Hastings for calculating the secondary spectra of telescopic objectires,
and the employment of an objective (of 8. SO and S. 8) of only 67 cm. aperture as
.a test of the method.

13:2 JENA GLASS.

obtain a general view of the whole spectrum at once, owing to
the wide separation of the foci of the different colours.

On comparing the tertiary spectrum actually obtained with
that deduced from theory, 1 satisfactory agreement is found, both
as regards the main features of the focal curves, and the order of
magnitude of the residual aberration.

62. Difficulties attending the use of Phosphate and Borate
Glasses. In the attempt to utilise, for the improvement of
telescopic objectives, new glasses of favourable optical qualities,
such as phosphate and borate glasses, various difficulties are
encountered. 2

For an astronomical objective, discs of large diameter are
required, and this may preclude the use of a glass which can lie
employed without difficulty for other optical purposes.

Again, glasses of essentially new composition have their own
peculiar mechanical properties, which, as a rule, render them
unfit to be worked by the ordinary methods of an optical factory.

Further, the customary methods of cooling do not suit the new
glasses. Stresses which would be of no consequence in ordinary
silicate glasses become serious defects in phosphates and borates,
and unfortunately the tendency to acquire these stresses during
solidification is greater in phosphates and borates than in silicates..
It is obvious that this greatly increases the difficulty of making
large objectives.

These difficulties, formidable as they appear, have all been
overcome. There remains, however, another difficulty, which is.
inseparably connected with the chemical composition of the glass*
namely, its liability to be attacked by moisture. Among the
phosphate and borate glasses there are several which cannot
safely be exposed to damp air for any length of time. 3

63. Successful Employment of Newer Glasses. Under the-
circumstances just mentioned, it is not surprising that further
attempts are continually being made to discover new glasses
which are chemically and mechanically durable, besides possessing
the requisite refracting properties.

1 See early part of this Article.

2 See Czapski in The Observatory, June, 1889.

3 See Appendix.

PERFECTING OF OPTICAL SYSTEMS.

133

That these efforts have been crowned with success appears
probable, from an article published by M. Wolf 1 relating to an
objective constructed by Zeiss from calculations by M. Pauly,
which was tested at the Astrophysical Observatory of Heidelberg.
It was composed of two lenses, but particulars of the two glasses
employed are not given ; the article deals only with results.

The objective had a clear aperture of 21*2 cm., and a focal
length of 445 cm.; so that its relative aperture was 1/21. It
showed very little absorption for visual rays.

The chromatic aberrations on the axis were determined by
Vogel's method, described in Art. 61, the stars employed being
< Herculis, a Aquilae, and a Lyrae. The aberrations (per metre
of focal length) are given in the column headed " Pauly " in the
following table, the focus of F )>eing taken as the zero-point.

Chrom. Aberr. per metre
Focal Length.

Pauly.

Fraunhofer.

0-690 /t

+ 0-02 mm.

-0*19 mm.

0-690 M

-i- 0-02 mm.

-0*19 mm.

660

it (.-_'

-0-30

590

<N)|

-0-65

4BQ

o-oo

-0-28

486

o-oo

434

+ 0-53

+ 0-92

410

+ 1-16

+ 1-96

The corresponding aU'rrations I'm- tin- llrrlin l-'raunhofer
ctive are given for comparison. The chromatic aKrrrations
of the eyo were (on principle) not subtracted.

Tli. above values, either taken as tlu-v stand, or plotted with

wa\.- 1. MIJ! h as abscissa, show that the secondary spectrum, from

the red to a little beyond F, is practically aliolJHhed. As AY. .If

remarks, the new objective is HO much U'ttvr than tin- old ones,

that "comparison is out <>f the .jiir-ii.ui. It practically focuses

all thr \isual rays in onr plan. An\ remnant of chromatic

i ration for visual rays "can only l>e measured by careful

nation with lii^h p.\

, 19, 1 (1899).

134 JENA GLASS.

And the advantage is not confined to spectrographic work.
" Surprisingly l>eautiful were the perfectly colourless images of
moon-craters and sun-spots; which possessed a quite unique
charm, and, under a power of 825, showed unusual details."

"On four evenings, in spite of rather stormy weather and
unsteady air, the separating power of the new objective for close
double-stars was tried. The following pairs were well separated: 1

rj Coronae, distance 0"'4 magnitudes 5 and (>

// 2 Bootis, 0"-9 7 S

1 Coronae, 0"'8 (> 7 '

7 Coronae, 0"'4 4 7

A Cassiopeiae, 0"*G 6 6

M Cygni, 2"- 9 4 ."

^ Herculis, O"'.") 3 7

OS 338, 0"-7 6J 6i

2 2695, 0"-9 6 8

the only one that gave any trouble being Herculis. The pairs
^ Bootis and 52 Arietis could not be separated.

" The diffraction rings were beautifully shown. The discs
were absolute circles, and I found, with Dr. Schwassman's assist-
ance, from numerous estimates aided by known distances of
double stars," the following diameters of star discs :

Stars of 6 th magnitude. Diameter 0"'24.
6 0"-24.

These tests establish " the great superiority of the ne\s
objective, which combines the steadiness of the refractor with
the colourlessness of the reflector."

The surface of the glass showed itself to be " fully resisting
and durable."

64. Suppression of Residual Spectrum in Triple Objective.

In the triple objective constructed from H. 1). Taylor's calculations
by Cooke of York, achromatism is effected in the following way.-

[ l Dawes' rule for the limit of separability gives <f'55 as the limit for an aperture
of 21 -2 cm.]

2 Improvements in compound object-glasses for telescopes, English Patent,
No. 17994(1893).

PERFECTING OF OPTICAL SYSTEMS. 136

Let the thicknesses and distances of the three single lenses be
small enough to permit the use of the equation

^(n-iH^n'-iH^w"--!, ............... U)

which is an extension of equation (1) of Art. 18 from two lenses
to three, k, k', k" denoting the total curvatures of the three lenses,
n, n', n" their indices for any one value of X, and <f> the reciprocal
of the focal length of the system for this wave-length.

AN' hen X changes from one given value to another, let the
corresponding changes of n, n, n" be ^, $', $": then we have

Change of = fc&+Atf + *V ................... (2)

Now introduce the condition k" = k'\ then we have

Change of = *<&+&'(* + O ' ................ (2)

(la) applied to the D line gives

/A"); ..................... (16)

and if <f> is to l>e the same for C as for F, (2a) gives

(26)

the notation being that of Art. 18.
I rom (Ib) and (2b) we obtain

, = _ 1 A'+ A" 1_

d A (i/-i>)A'+(/

Substituting these values in the general equation (2a), we find.
for change from one arbitrary value of X to another,

dx change of ^,-^- *^, A J --Jf *}>.

shows that <f) is iii'lrpnulriit of X if, for all changes of X,
-, has the constant value - : in otlur wnnls, if '

has any constant value for all parts of the spectrum (since
A A . A" are particular values of J, $', ").

136

JENA GLASS.

( 'ailing the three lenses Z, Z', Z", the expressions for k and k'
show that, if v is the least of the three v a/ /, k is negative and
k' positive ; that is, L is concave and L' and L" are convex, the
total curvatures of the two latter being equal.

Choice of Glasses. The three following glasses were chosen
by Taylor as suited to his purpose :

For Z, Borosilicate flint 0.658; A ='01089; v = 50'2.
Z', Baryta light flint 0. 543 ; X = -01115 ; v = 50-6.
Z", Silicate crown 0. 374 ; A" = '00844 ; v" = 60'5.

0. 658 is a glass replacing 0. 164, No. 25 in the list of Art. 17
O. 543 is No. 58, and 0. 374 is No. 47.

How far the combination of these three glasses satisfies the
theoretical condition of complete achromatism found above may
be judged from a comparison of the last two columns of the
following table :

Interval.

- '
0.543

<5"

0.374

d' + d"

A' + A"

01115

00844

A'C

00374

00296

3420

3425

00790

00593

7059

7052

00369

00274 -3282

3278

FO'

00650

00479 -5763

5767

FH,

01320

00976 1-1730

1-1745

The dispersions EF and FH l have been calculated from Cauchy's
dispersion formula, and are subject to some uncertainty.

The positions of the chromatic foci as calculated from the
data are:

mm. per metre focal length.

A -'107

C 000

D +'150

E +-086

F -000

& +'086

ff 1 + '322

PERFECTING OF OPTICAL SYSTEMS. 137

The resulting curve of focal lengths has, like the curve (2) of
Art. 19, the double bend characteristic of a tertiary spectrum ;
but the bends are moved higher up the spectrum, so that the
triple union, instead of extending from A to F, extends from C
to a little beyond G'.

An Objective of 152 cm. Aperture and 274 cm. Focal
Length is described by Taylor in detail. It is composed as
follow- :

L' L L"

r^ = + 102-7 cm. i\ = - 34'8 cm. r/' = 23'9 cm.
r 2 '=- :U-8 r t =+23-9 r 2 " = 44-7

Thickness 1'5 Thickness 0'3 Thickness 1*5

Distances, - L'L = 0*0 mm. LL' = 0*2 mm.

Thus the negative lens is between the two positive ones, the
baryta flint being in front. The thicknesses given are for the
centres. There are only 4 different radii of curvature.

Among the special advantages of this construction, Taylor
mentions particularly the getting rid of the chromatic remnant
of spherical aberration.

The aperture ratio is 1/18. In smaller objectives it may be
1/15.

Taylor also expounded the advantages of his objective at a
meeting of the Royal Astronomical Society, 1 and was able to
announce that its actual performance corresponded to theoretical
expectation. The misgivings expressed at the meeting by Grubb
and Kanyard, as to the durability of the borosilicate glass
employed, were probably due to their confounding it with borate
Hint, which is not fitted to bear exposure.

65. Two-part Gaussian Objective. The actual range of

distribution of the elm -untie foci along the axis of an objective

iot the same thing as the length of the secondary spectrum of

that particular zone of the objective which has been iohzomatind ;

t"i if spherical al>erration is, as usual, corrected for only one

'"luiir, the chromatic difference of spherical aterration will

materially increase the length. In the objective which I>ear8

-s name, spherical al>erration is theoretically annulled for

two colours. By this means the displacement .if tln> < limmatic

1 rhf. 0fc*erm/ory, 17, 132 (1894).

138

JENA GLASS.

foci in passing t'roiu the centre to the edge of the objective can
be practically abolished. Gauss' condition for obtaining this-
result ran le fulfilled, besides the three conditions of given focal
length, achromatism, and spherical correction on the axis, when
four refracting surfaces are disposable. The objective can
accordingly be made of two uncemented or three cement rd
lenses.

Objectives of the Gaussian construction have been calculated
both by S. Czapski and by 0. Lummer, consisting, in each case,
of a positive lens of phosphate crown and a negative of silicate
Hint. The Hint is placed in front, as the opposite arrangement
would require excessively large external curvatures.

Czapski's Objective. Two objectives, made by Bamberg of
Berlin from ( '/apski's calculations, were exhibited on the occasion
of the Xaturforscher meeting in Berlin (1886), and have been
described by Kriiss l from data furnished by Czapski. In his-
paper, from which all the details below are taken, the following-
indices are given for the crown lens L and the flint L'.

1-57036
1-60682

1-57342
1-61153

1-61558

1-58226
1-62540

1-58725
1-6335M

The values for the crown glass agree with those given for the-
heavy barium phosphate No. 3 of Art. 17.
The dimensions of the objective are :

Flint i\
r 2

Crown /

r =

- 226*0 mm.
_ 400

- 1256-0

- 278-7

Thickness, flint 7'~> mm.

crown 12'0
Interval, 2'0

Aperture, 134

In the achromatising, C and F were united. The spherical
aberration was corrected for D.

The headings c, d,fin the following table denote the distances-
of the chromatic foci for C, D, F from the last face of the
objective. They are given for three different narrow zones,.

'See page 60 of "A comparative investigation of a number of objectives in
which Gauss' condition is fulfilled"; Zeitorhr. f. Inxf,rum., 8. 7, 53, 83 (1888).

PERFECTING OF OPTICAL SYSTEMS.

namely, the central zone, the marginal zone, and a zone | of the-
way from centre to margin.

Central zone
Intermediate zone
Marginal zone

2085-99 mm.
2085-96
2086-04

2085*51 mm.

2085-38
2085-46

Jiis.ViM mm.
2085-82
2085-72

1 ." >lin\v8 the curves of focal length plotted I'mm
values, the curve a beini: t"i the central /mie. l> I'm- the inter-
mciliate, and c for the marginal /"iir. Tin- Imri/Miital disUnees
in lli<- tiui.K* are 100 times tin- arttial distances indicated l.y the
tahle. The curves ln-in^ ,, u t the t'lln\\ing facts.

For all colours hetween C and D the central and mat
spectra practicallx ( ..in id.v Th-\ IM --m to separate to a notice-

140 JENA GLASS.

able extent, a little beyoml I>, ami the separation increases as the
wave-length diminishes, but only amounts to Q"2'2 mm. even
at F.

The union of the spectrum of the intermediate zone with the
central l>etween C and D is not so close. The separation in this
case is greatest near D, but does not exceed about 0*13 mm.
Beyond this, the spectrum of tbe intermediate zone approaches
nearer to the central, and in doing so coincides at one point with
the spectrum of the marginal zone.

Assuming that the intermediate zone here chosen is that which
diverges most widely from the central,- we arrive at the result
that the length of the secondary spectrum for the rays between
C and F, which for the central zone would be about 0'50 mm.,
is increased to about 0'7 (that is, by about 40 per cent.) by
chromatic difference of spherical aberration. As the focal length
is about 2 m., the length of the spectrum per metre of focal
length may be taken as 0'35 mm.

It would be interesting to compare with these results the
distances between the chromatic foci of a double objective, not
fulfilling the Gauss condition, but having a short tertiary
spectrum. Data for an exact comparison are wanting ; but some
light is thrown on the matter by Wolf's report on the objective
discussed in Art. 63,

With the view of testing for spherical aberration, Fraunhofer's
old method was employed of blocking out alternately the circum-
ferential and the central part of the objective ; focussing on the
moon in each case, and measuring the shift of the ocular by
means of a microscope. From 24 readings so taken, a difference
of '0006 of the focal length was deduced. As we may assume
that the focussing in both cases was governed by rays between
C and F, it may be inferred that the length of the spectrum
composed of these colours exceeded 0*6 mm. per metre of focal
length, or was about double of the length computed for Czapski's
objective. But as the determination was by practical trial in
the one case, and by theoretical calculation in the other, the
comparison is not entitled to much weight.

Lummer's Objective. Lummer has remarked 1 that objectives
in which chromatic aberration is corrected by Gauss' method are

1 Muller-Pouillet, Lehrb. d. Physik. , 9th ed. , II. 1 , 230 ( 1897). The aberrations of
the objectives here discussed are calculated by Lummer at p. 573 et seq.

PERFECTING OF OPTICAL SYSTEMS.

141

suitable for the colliniators and observing telescopes of high-class
spectrometers; 1 as it is desirable that the image of the slit
should be sharp for all colours simultaneously. A spectrometer
of precision, constructed by Wanschaff for the Reichsanstalt,.
has accordingly l>eeii fitted with objectives of the Gauss type,,
calculated by Lummer and made by Bamberg. Their Hint lens
L' is of silicate 0. 102, and their crown lens L of the glass S.41,.
which replaces the phosphate crown S.40. They have the
following indices:

1-55284

1 -55531

1-56113

1-56576

1 -64373

1-64920

1-66294

1-67475

The dimensions are :

Radii of curvature.

r^= - 93-27
7- 2 = - 140-24
7- 3 = +1212-69
r 4 = - 141-42

mm. Thickness Flint, 3'6129 mm.

Crown, 5-4193
Interval, - 0'9032

Aperture, - - 50

In the achromutisation C and G are united, and spherical
aberration is annulled for the same two colours.

The distances c, d, / g of the foci for (7, D, F, G from the back
.f the last lens are given in the following table, for five zones of
the objective, from direct trigonometrical calculation. The zones
(infinitely narrow) are at the distances 0, 12*5, 17*68, 2T65,
_' 5 mm. from the axis :

Distance
from axis.

mm.

460-556 mm.

460 -235 Him.

460 <>;>:* nun.

460-53:* nun.

194

*to

or,:?

17 -(is

577

247

072

-Ml

Jl -or.

_>;:<

ns:<

557

621

276

O'.M

'The spectroscope is iml.-l-t.-.l t unproved glaM-making, not only for well
corrected achromatic objectives, but also for prisms of high index and dispersion
with relatively high transparency for visual and chemical rays.

142

JENA GLASS.

In each column the numbers increase, but only very slightly, as
we pass from the centre to the circumferential zone ; the spherical

i rat ion is therefore slightly overcorrected for all colours from
C to G. This practically means that spherical aberration is
jinnulU'd for the visual rays.

In tig. 16, which is drawn on the same scale as tig. 15, the
focal curve for the central zone is marked a, and that for the

RIO. I''..

circumferential zone c ; the curves for the intermediate zones
lie between these two. The length of the secondary spectrum
for the central zone is 0'503 mm. : and spherical aberration

PERFECTING OF OPTICAL SYSTEMS. 143

increases the length by 0'065 min. (or 13 per cent.), making
it 0'568: which is at the rate of 1*23 mm. per metre of focal
length.

66. Objectives by Zeiss. Our quotation from Wolf's report
(Art. 63) may be supplemented by the following information
taken from Zeiss' 1899 catalogue of astronomical objectives.

The astronomical department, which is under M. Pauly, has
regarded the abolition of the secondary spectrum as its most
important problem. For this purpose, new silicate glasses of
proved durability have been produced. The similarity attained
in run of dispersion between crown and flint, for the region
C to F, has been such as to reduce the secondary spectrum to
a minute remnant, so far as the visual range is concerned.

A second aim has been, to select, from the existing types of
glass, such as would permit an increase of aperture ratio.

The following items from the catalogue originated at the Jena
works ; that is, were either invented there, or first made there in
their present shape.

Doublet Apochromatic Objectives, without secondary spec-
trum, from new glasses of recent years. The crown employed
cannot always be produced quite free from streakiness ; but the
little that remains has no influence on the sharpness of images.
The aperture ratio is from 1/17 to 1/20.

The objectives are generally made with clear aperture
50-450 mm. and focal length 85-900 cm.

Three-part Apochromatic Objectives (Konig's) of one Mint
and two crowns; giving no secondary spectrum.

Aperture ratio, 1/10 to 1/15.
Clear aperture, 40-180 mm.

K.Krai Im-jili. 40-270 cm.

Two-part Telescopic Objectives, with sm.mlary spectrum.

Aperture ratio, to 1/7.
Clear aperture, 60-200 mm.
Focal length, 42-200 cm.

144 JENA GLASS.

Three-part Telescopic Objectives, with secondary spectrum.

Aperture ratio, 1/4 to 1/6.
Clear aperture, 20-150 mm.
Focal length, 8-90 cm.

Apochromatic Aplanats (Har ting's) for astrophotography,
without secondary spectrum; field about 15; of newly introduced
glasses.

Aperture ratio, to 1/8.

Clear aperture, 60-180 mm.

Focal length, 54-304 cm.

CHAPTER VII.

MECHANICAL PROPERTIES OF GLASS.

67. The Density, Strength, and Elasticity of glass have
been investigated by Winkelmann and Schott. 1 Their experi-
ments were performed upon 72 different kinds of glass; but in
the system of numbering which they employ, 13 glasses are
doubly and 3 glasses triply numbered, making 91 numbers in
all. In the following table these numbers are given in the
columns headed W. The left-hand portion of the table shows

Trade No.

S. 185

O. 709

63'"

S. 205

0. 1571

O. 1022

172"i

O. 500

81"'

164'"

59"'

73111

802

0. 428

93" 1

16'"

458

90 m

165'"

O. 479

82'"

1419

O.2154

87 m

S. 201

O. 885

83 m

290

0. 627

102 1 "

665

O. 165

8. 226

121"i

16"'

0. 137

8.206

O. 55

8. 95

S. 41

144i>

0. 527

8.120

O. 1168

O.3:n

O. 662

8.163

S I.T.I

O.658

8. 57

_:;

1 See the four following Papers, which we shall quote as W., I. ; W. and S., I. ;
W. amis., II.; W., II.

1. A. Winkelmann. On the specific heats of glasses of various composition;..
Ann. d. Phyt. und Chem., 49, 401 (1893).

2. A. Winkelmann and O. Schott. On the elasticity and the tensional and
compressive strength of various new glasses, in their relation to chemical
composition ; I.e. 51, 697 (1894).

Winkelmann and 0. Schott. On thermal resistance-coefficients of
various glasses in their relation to chemical composition ; Lc. 51, 790 (1894).

4. A. Winkelmann. On the coefficients of elasticity of glasses of various
compositions, and their dependence on temperature ; I.e. 61, 105 (1897).

146

JENA GLASS.

the corresponding trade numbers of 50 of the glasses ; and the
right-hand portion is a list of duplicate numbers (including the
triplicates 2, 5, and 13).

For convenience of reference, we subjoin a complete table of
the compositions of the 72 glasses.

71-8

22-4

5-8

69-1

18-0

0-2

4-7

8-0

64-4

12-0

11-0

4-5

8-0

o-i

55-0

17-0

14-0

71-0

14-0

5-0

10-0

67-3

2-0

7-0

2-5

14-0

7-0

0-2

73-8

5-0

3-5

10-5

7-0

0-2

67-9

5-8

8-1

1-0

0-3

16-8

o-i

3-0

4-0

10-0

0-5

12-0

70-5

58-7

0-3

33-0

8-0

41 -0

59 -0

51-3

14-0

5-0

4-5

0-2

25-0

3-0

8-0

1-5

28-0

59-5

3-0

1-5

56-0

34-2

10-2

7-8

5-0

0-7

42-1

42-8

52-0

5-0

0-2

45-22

46-0

0-2

1-0

7'5

0-08

22-0

78-0

20-0

80-0

32-75

31-0

25-0

7-0

0-25

1-0

3-0

34-5

10-1

7-8

5-0

0-5

42-0

o-i

44-2

47-0

0-2

0-5

8-0

o-i

70-6

12-0

0-4

17-0

41-0

51-7

0-2

7-0

o-i

3-0

4-0

10-0

1-5

12-0

69-5

64-6

2-7

2-0

0-4

10-2

5-0

15-0

o-i

54-8

17-0

0-2

28-0

29-3

67-5

0-2

3-0

70-2

12-0

3-0

4-5

10-3

72-0

12-0

5-0

11-0

56-0

32-0

12-0

64-0

30-0

6-0

45-2

46-4

0-5

0-2

7-5

54-3

1-5

33-0

0-2

3-0

8-0

48-8

3-0

10-3

0-4

29-0

1-0

7'5

68-3

10-0

2-0

0-2

10-0

9-5

28-4

69-0

0-1

2-5

69-1

2-5

0-4

4-0

16-0

8-0

51-7

7-0

10-0

0-3

20-0

1-5

9-5

68-2

2-0

13-1

0-2

16-5

68-1

3-5

7-0

0-4

5-0

16-0

3-0

4-0

10-0

0-5

12-0

70-5

73-2

0-3

18-5

8-0

65-5

2-5

2-0

0-4

9-6

5-0

15-0

64-3

1-5

0-2

3-0

20-0

11-0

71-7

2-0

0-3

10-0

13-0

3-0

54-8

25-0

2-5

0-2

6-0

11-5

MECHANICAL l'R >PKRTI KS <>F CLASS.

147

\v.

0~
7.

69-7

0-3

25-0

5-0

14-1

2-5

<_>

15-0

9^)

58-8

6-0

4-0

0-2

10-0

14-0

u-o

34-0

4-0

8-0

11-0

57-0

12-0

13-0

21-0

79-0

51-0

12-0

3-J-n

45-1

46-4

0-5

0-8

::;

68-8

18-0

5-0

4-0

54-5

12-0

11-5

14-0

29-0

34-0

9-0

0-5

1-0

65-9

_':.

2-0

9-6

5-0

150

674

3-6

13-0

16-0

71-0

12-0

17-0

67-9

5-8

8-0

1-0

0-3

16-8

61-6

15-0

0-3

23-0

o-i

70-6

0-3

16O

11-0

o-i

67-7

8-0

9-0

5-0

0-3

10-0

8.-,

48-1

4-5

10-1

0-4

28-3

1-0

7'5

o-i

54 "J

1-5

33-0

0-2

3-0

8-0

o-i

68-2

10-0

2-0

0-2

100

9-5

70-4

7-5

0-2

5-3

14-5

2-0

O'l

HIM.

2-5

0-5

4-0

16-0

8-0

m>&

2-0

2-5

0-4

7-0

16-0

74-6

0-3

9-0

11-0

5-0

o-i

68. Density of Glass as dependent on Chemical Com-
position. Let a v a v a s . . . denote the percentages of the several
<\i(les of which a glass is composed, and z v z 2 , z s

densities to be attributed to them in the glass.
ih- partial volumes, we have

the
Then, by adding

(1)

S denoting the actual density of the glass. As might have been
expected A priori, the quantities z r z v 8 . . . are by no means
identical with the densities of the separate oxides before
<-. mbination. If these latter are put in place of z v z v z s ...,
they will give too small a value of 'S. The total volume is
therefore diminished by the act of combination. 1

The question arises whether one and the same oxide h.is
always one and the same value of z in whatever mixture it
occurs. If so, the values of z for the different oxides can e.i
be deduced from observations on ]>m].erly sel<-< -t.-d glasses, and
enable us to compute the densities of other glasses, old or

W. an.lS., II. 741.

JENA GLASS.

new. This supposition is not rigorously fulfilled. Winkeliuaim
and Schntt have, however, shown 1 that the subjoined values for
t \\vlve of the oxides fulfil it approximately. When these
values are employed to compute the densities of the 20 glasses
numbered 19 to 38, neglecting the small amount of Mn 2 3 which
some of them contain, the difference between computed and
observed values is, on the average, only 1 J per cent., and amounts
in only one case to 4 per cent.

Oxide z

SiO 2 =2-3
B,O, = l-9
ZnO =5-9

PbO =9-6
MgO =3-8
AL,O 3 = 4-1

As 2 5 = 4'l
BaO -7-0
Na. 2 0=2-6

KjO =2-8
CaO=3-3
P 2 5 = 2 '55

When we go outside these 20 glasses which were employed
in determining the values of z, we find, in most cases, a fair
agreement. The following list of observed and computed values
includes, along with these 20 glasses, nine others whose densities
are given in an earlier paper by Winkelmann. 2 Two of the latter

Density.

Obs.

Comp.

Obs. Comp.

2=22

2-243

2-24

+ 0-1%

2-424

2-42

+ 0-2

2-480

2-60

- 4-8

5 = 19

2-370

2-31

+ 2-5

6 = 38

2-585

2-52

+ 2-5

7 = 35

2-479

2-50

- 0-8

8=29

2-629

2-62

+ 0-3

2-588

2-69

- 3-9

10=30

2-518

2-51

- 0-3

3-527

3-17

+ 10-1

12 = 37

2-848

2-84

+ 0-3

13 = 31

3-070

3-20

- 4-2

8-288

3-37

- 4-1

3-532

3-47

+ 1-8

3-691

3-42

+ 7'3

3-578

3-63

- 1-5

5-831

5-65

+ 3-1

Density.

Obs.

Comp.

Obs. Comp.

5-944

5-87

+ 1-2%

2-758

2-75

+ 0-3

3-532

3-45

+ 2-3

3-578

3-66

-2-2

2-572

2-54

+ 1-2

3-879

3-88

-o-o

2-588

2-52

+ 2-6

2-580

2-57

+ 0-4

2-668

2-75

-3-1

4-731

4-78

-1-0

2-378

2-34

+ 1-6

2-370

2-32

+ 2-1

l l.c. 739.

2 W.,L 418.

MECHANICAL PROPERTIES OF GLASS. 149

the zinc borate No. 11 and the lead borate No. 16 exhibit

large discrepancies. Water at 4 is taken as the unit of density.

As the values of z for the glass-forming oxides are thus

approximately constant over a wide range of composition, it is

natural to compare them with the densities of the oxides before

ibination. The quotient of the former by the latter is given

under the heading " Condensation " in the following list :

Density. Condensation.

BaO 5-00 1-400

B 2 3 1-46 1-301

MgO 3-40 1-118

P 2 O 6 2-38 1-071

3-85 1-065

Si0 2 2-17 1-060

K 2 2-66 1-053

CaO 3-15 1-048

ZnO 5-65 1-044

PbO 9-32 1-030

Na 2 O 2-55 1-020

As 2 6 4-09 1-002

Barium-oxide shows the largest increase of density (40 per cent.),
and arsenic pentoxide the smallest (0'2 per cent).

69. The Tenacity (tensile strength) was determined by Winkel-
ii Kin n and Schott for 17 glasses, numbered 19 to 35 in
Winkrliiiann's series ; the specimens being square rods, of cross-
sections ranging from 11*55 to 19*27 mm. The apparatus
employed was modelled on that used by W. Voigt and A. Sella

observations on rock salt \ l but the load (which often exceeded
100 kg.) was applied, not by means of flowing mercury, but by
weights, and it was necessary to employ an " arrester," by the

ring or raising of which the load could be put on or off.
The distance fallen through when rupture occurred was only

Mini. Half way up the rod, a shallow depression running
all round it was produced by means of a grinding tool of
cylindrical form, and was afterwards polished. As a result of
tins arrangement, combined with precautions for ensuring a
central pull, surfaces of rupture were obtained, which showed,

1 Gottinger Nachrichten, No. 14, p. 494 (1892).

150

JENA GLASS.

over nearly their whole area, the dull fibrous appearance
indicative of tearing. The load was kept on for not more than
40 seconds. If rupture did not occur, the arrester was raised
till it took off the load ; and the load was then increased by
from 1 to 3 kg., and the arrester slowly lowered. This process
was repeated till rupture occurred. The following table gives
for each kind of glass the number of observations, the minimum,.
the mean, and the maximum.

No.
of
Obs.

Tenacity in kg/mm 2

Observed.

Calculated.

Obs. Calc.

Min.

Mean

Max.

19 = 5
20

5
4

6-51
2-90

6-76
3-28

6-95
3-53

7-75
3-80

-11%
- 8

5-18

5-66

6-12

5-99

+ 2

22=2

4-58

4-93

5-76

5-79

- 1

6-78

7'21

7-52

7'30

+ 3

5-95

6-01

6-07

5-26

+ 13

7-00

7'84

8-51

4-25

4-67

5-39

5-06

+ 6

5-36

5-46

5-56

6-11

-10

5-60

6-09

6-76

7-07

- 5

29 = 8

6-00

6-42

6-79

7-59

-12

30=10

7-02

7-52

7'82

7-22

+ 8

31 = 13

7-06

7-42

7-63

6-50

+ 15

7-87

8-09

8-32

7-75

+ 7

4-65

4-97

5-32

4-36

+ 18

7-66

7-92

8-16

7-56

+ 7

35 = 7

6-62

7-46

8-35

9-19

-10

The errors in these observations arise partly from imperfect
centring of the rods, and partly from superficial inequalities of
condition, causing rupture to begin at a place of small resistance.
Both sources of error make the result too small. We shall
therefore adopt the maximum value as probably nearest to the
truth. In two instances (26 and 35), the minimum is smaller
by 2 1 per cent. ; and if we leave out of the calculation glasses
24 and 27, for each of which there are only two observations,
the difference is always, except in the case of 32, much more
than 5 per cent.

MECHANICAL PROPERTIES OF GLASS. 151

Relation between Tenacity and Chemical Composition.
The attempt was made to express the tenacity P by the formula

a i> a 2 a y ' denoting the percentages of the several oxides in
the total composition. The values adopted for y were :

y y y y

Si0 2 = 0-09 PbO = 0-025 As 2 6 = 0*03 K 2 O = O'Ol
B 2 3 = 0-065 MgO=0'01 BaO = 0'05 CaO = 0'20
XnO = 0-15 A1 2 3 = 0-05 Xa 2 O = 0'02 P 2 5 = 0'075

ami by employing these, the values in the column headed
"Calculated" were obtained. The differences between these
calculated values and the observed maxima are, on the average,
8 per cent. The order of the oxides, when arranged according
to the values of y, beginning with the largest, is : CaO, ZnO,
Si0 2 , P 2 5 , B 2 8 , BaO, A1 2 3 , As 2 6 , PbO, Na 2 0, K 2 0, MgO.
Those which stand first exert a favourable, those which stand last
an unfavourable influence on tenacity. Some uncertainty attaches
to the positions of CaO, As 2 5 , and MgO in the list, owing to the
small proportions of these oxides contained in the glasses in
question. The quantity of Mn 2 3 is so minute that no value of y
has been assigned to it.

70. Resistance to Crushing. As a sequel to the observations
on tenacity, Winkelmann and Schott have investigated the
resistance to crushing for the same 17 glasses, 19-35. 1 The
force was applied by means of a press filled with oil, in which the
pressure could be gradually increased by screwing in a screw-
plunger. The attached manometer indicated forces up to 50 kg.
The specimens of glass tested were approximately cubes of 6 mm.
edge, and were squeezed between two metal plates with gradually
increasing pressure, till they flew into powder. The rupture
occurred suddenly, with a.lmul report, and a flash of light clearly
seen in the dark I'lvlimiiiary trials showed that the greater
! less hardness of the metal plates largely influenced the results.
Mass 19 between tin plates showed, in three experiments, a
mean resistance of 39*2 kg. per sq. mm. Between copper plates,
it showed, in four experiments, a mean of 65'8. The tin

'W. U.S., I. 720.

152

JENA GLASS.

plates, when examined, showed deep depressions, in which linear
elevations were noticeable. The metal had evidently been forced
into small cracks produced in the glass by the pressure. The
copper plates also showed the small elevations in the deep
depressions, but not so distinctly as the tin plates.

After this experience, hard steel plates 5 cm. square and
1'5 cm. thick were employed. They were carefully ground
smooth, and the glass was crushed between them. Even in these
plates depressions were produced by the strongest glasses,
necessitating frequent regrinding. Experiments made for the
purpose showed that damaged surfaces gave too low values of
resisting power. The following table shows for each glass the
number of observations and their mean.

No.
of
Obs.

Resistance to Crushing
in kg/mm 2

Obs.-Calc.

Ratio to Tenacity.

Obs.

Calculated

19=5

126-4

110-9

+ 12%

18-7

18-2

60-6

63-0

- 4

18-5

17-2

105-7

88-2

+ 17

18-7

17-3

22=2

81-2

88-1

- 8

16-5

14-1

84-0

87-8

11-7

11-2

77-5

77-9

- 1

12-9

12-8

97-8

104-6

- 7

12-5

11-5

84-3

75-8

+ 10

18-1

15-6

71-7

72-0

13-1

12-9

91-6

93-7

- 2

15-0 13-6

29 = 8

99-0

102-3

- 3

15-4 14-6

30=10

68-3

75-7

-11

9-1

8-7

31 = 13

75-0

74-8

10-1

9-8

73-9

79-2

- 7

9-1

8-9

67-3

68-8

- 2

13-5

12-7

99-3

111-1

-12

12-5

12-2

35=7

112-9

105-2

+ 7

15-1

13-5

The results for one and the same glass often exhibited large
differences. In the cases of 23 and 29, the minimum was about
26 per cent, below the maximum.

Glass 19 was also tried in smaller cubes of 4-5 mm. in the
edge, and gave a mean resistance of 115*3 kg. per sq. mm. It
would therefore seem that the resistance per sq. mm. increases

MECHANICAL PROPERTIES OF GLASS. 153

somewhat as the section increases. The observations in the
table nearly all relate to sections not very different from 36
sq. mm. For glass 35 it was, however, 45 sq. mm., and for
glass 34 it was 50 sq. mm. The comparability of the results is
thus sufficiently exact.

Five other substances were tested in the same way, for the
sake of comparison with the glasses, and gave the following
resistances to crushing :

Black Belgian marble, - 25*4 kg. per mm 2 .
White Italian marble, 7*1

Saxon granite, - 19'1

Brazilian agate, - - 13 1'7

, , (pressure parallel to axis, - 181/6
Rock crystal J ,. .

[ perpendicular,, - 160'0

Cast iron, similarly treated, did not go to pieces. When the
pressure per sq. mm. exceeded 94*1, its sectional area was
increased, and this prevented increase of intensity of pressure.

Relation between Resistance to Crushing and Chemical
Composition. The values in the column headed " Calculated "
were obtained by employing a linear formula (as in the case of
tenacity), with the following values of y :

Si0 2

= 1

PbO

As 2 6

= 1

K 2

0-05

MgO

= 1

r.ao

CaO

0-2

ZnO

A1A

= 1

Na 2

0-76

The next column gives the differences between the calculated
and observed values, as percentages of the observed. The average
difference is 6 '4, and the greatest 17 per cent. The arrangement
in descending order of y is : Si0 2> MgO, A1 2 8 , As 2 v 1" I 'A,
BaO, ZnO, Na t O, PbO, CaO, K 2 0.

The Ratio to Tenacity is given by two different modes of

comparison. Column a shows the ratio of the mean values of

the two kinds of resistance; column 1> the ratio of the mean

10 of resistance to crushing to the maximum value of tenacity.

Glasses of different composition exhibit very different ratios.

71. The few Earlier Observations on the Strength of
Glass which are available are not accompanied by any informa-

K>4 JENA GLASS.

lion as to the chemical composition of the glasses to which they
relate. 1 For the sake of comparison, we will adduce the observa-
tions of J. v. Kowalski.- They were made on thin glass rods,
" drawn from a melting which was free from bubbles, and then
slowly and carefully cooled." Their section was found to be
approximately an ellipse, with very small difference between its
two axes. In a series of 30 experiments on tenacity, the
maximum obtained was 8*981 kg. per sq. mm., the minimum
8*628, and the mean 8*767. In 14 experiments on resistance
to crushing, the maximum did not exceed 42'063, and the mean
was only 37*700. The circumstance "that v. Kowalski, in
investigating resistance to crushing, placed the glass rods between
two copper plates, does not seem sufficient to explain the small-
ness of his values. The explanation is rather to be found in the
fact that he appears to have only carried his pressure to the
point at which the first fracture parallel to the direction of
pressure occurred ; this being far below the pressure which would
have produced complete disintegration." 3

Observations were also made by v. Kowalski on the resistance
of glass rods to flexure and torsion. From 29 observations on
flexure, it was inferred that the tension on the convex side of the
bent rod had the mean value 8*794 kg. per sq. mm. Strength
to resist torsion was tested by 33 experiments. The greatest
tension occurs at the ends of the axis minor of the elliptic
section, and is inclined at 45 to the length of the rod. The
mean value found for this greatest tension was 10*142. Finally,
for each kind of test the greatest linear extension was calculated.
In the experiments on direct pull, this was in the direction of
the length. When the rod is supported on two knife-edges and
loaded in the middle, the greatest extension is at the lowest
point, and is parallel to the length. In torsion it has the
direction and position indicated above. Lastly, in end pressure,
it is perpendicular to the pressure. The values found were :

In simple pull,- 0*00131

In bending, - '00132

In torsion, -00183

In end pressure, -00129

1 W. and Sch., I. 697 zt seq. 2 Ann. d. Phyx. u. Chem., 36, 307 (1887).

3 W. and Sch., I. 727.

MECHANICAL PROPERTIES OF GLASS. 155

Hence it would appear that glass can bear a considerably greater
extension by torsion than by pull or bending or end pressure. 1

Falling off of Strength at Higher Temperature. A later
communication by v. Kowalski contains observations on the
tlexural and torsional strength of glass at higher temperatures. 2
The material was the same as in the previous experiments. The
tlexural experiments gave the following means, each derived from

1 8 observations :

Temp. Greatest tension. Greatest extension.

12 8794 kg./mnr. 0-00132

100 8-701 -00145

150 8-639 -00156

200 8-604 -00162

The torsional experiments gave the following means, each
derived from 1 1 observations :

Tump. Greatest tension. Greatest extension.

li' 10-142 kg/mm 2 . 0-001837

78 9-182 -00187^

100 9-006 -001901

72. Young's Modulus of Elasticity. The first systematic
investigation of the elasticity of glass was made by Winkelmann
and Schott, 3 who determined the values of this coefficient for

19 different kinds of glass, 19-29 and 31-38. In the case of
the first 16 glasses, 19-29 and 31-35, the values were deduced
from observations of flexure.

"When a rod of rectangular section is supported on two fixed
knife-edges and loaded in the middle, its two ends turn in
opposite directions through the same angle <f>. If this angle is
observed, the coeHirn-ut of elasticity E (Young's modulus) is given
by the formula 3 p p

A = 4a^> taiT0 **'

/ denoting distance between knife-edges, a depth of section.
b breadth of section, and P the load. For the determination

1 The change in a small superficial element of a rod under torsion is a simple
shear, which is made up of an extension in one direction and a compression in a
perpendicular direction, each of these directions being inclined at 45* to the axis
of the rod, and parallel to the tangent plane. The compression tends to prevent
the rupture due to the extension. J. D. I

Mnn. <itr Phy. u. Chern., 39, 155 (1890). 'W. u. Sch., I. 700.

156

JENA GLASS.

of <f>, the following method has been indicated by A. Konig.*
The two ends of the rod carry two mirrors B, C, whose planes are
nearly vertical, but face slightly upwards. A ray from a point E

of a distant scale is reflected from C to B, and thence into an
observing telescope. When the rod is bent by putting on the
load, a displacement of the point E on the scale is observed in
the telescope. Calling this displacement v, it can be shown that
(putting D for AC and d for BC)

v = Dtana-ZHan(a-40) + dtan20, .............. (2)

a denoting the inclination of CE to the horizontal line CBA.
Since 4< is small, (2) can be written

which, when a is small, gives

v = 40(Z)+Jd); ........................... (3)

and this, combined with (1), gives

E=3(D+$d)^ ........................... (4)

This method of Konig's required a greater length of rod than
was available for some of the glasses. It was accordingly
modified on the plan sketched in fig. 18 ; the course of the twice

PIG. 18.

reflected ray being in a horizontal or nearly horizontal plane
instead of in a vertical plane as in fig. 17. The effective rays

l Ann. Phys. Chem., 28, 108 (1886); also Kohlrausch, Prakt. Physik, 35, II. ;
and Winkelmann, Handb. d. Phys., I. 263.

MECHANICAL PROPEETIES OF GLASS. 157

from the point A of the scale passed just clear of the mirror B on
their way to C. The two mirrors were approximately parallel,
and their normals were inclined at about 4 to the incident and
reflected rays. The angle marked ft was therefore about 86;
and this obliquity was allowed for by employing, in equation (3),
the corrected value v/sin ft instead of the observed deflection v.
Equation (4) was thus reduced to the modified form

*** ..................... < 5 >

The most important source of error is inexact measurement of
the depth a of the cross section of the rod ; for this factor occurs
in the third power. It was measured, for each rod, in 15 places
uniformly distributed over the surface, with the help of Abbe's
callipers. In calculating the mean, double weight was assigned
to the three measurements made at the middle of the rod. If
we assume that, in cases in which the single measurements have
differences of 0*1 mm., the calculated mean value of a is affected
with an error of 0'2 mm., this will involve an error of 2 per cent.
in the coefficient of elasticity, seeing that a is about 3 mm.

Of the three remaining glasses, 36, 37, 38, the first two could
not be obtained in the form of rods, and were examined by
Kundt's method for determining the velocity of sound. 1 The third
(normal thermometer glass) was examined both by this method
and by observations of flexure.

A second investigation was carried out by Winkelmann at a
later date, its chief object being to ascertain how the elasticity
alters with rising temperature. The first series of observations 2
were taken at ordinary temperatures, and are comparable with
those mentioned above. They included 23 kinds of glass, namely
19-38, omitting 20, 24, 27, 36, 37 ; and in addition, 84-91. In
the observations at higher temperatures, a different arrangement

19.

was adopted, the two mirrors being replaced by two isosceles
vL f lit-aui:li'l prisms, C and B (fig. 19) having their edges vertical.
The ray I'IMI the scale at A is four times totally reflected in a

1 Kohlrausch, Prakt. Phy$. t 37. \V , 1 1 1 1 ' '

158

JENA GLASS.

horizontal plane, and the last part of its course is nearly parallel
to the first. In the calculation of the elasticity, equation (4) is
applicable, for a in (2) is zero.

The results of the two investigations are combined in the
following table, under the headings J r E 2 respectively :

E 2

E l

19 = 5

7296 kg/mm 2

7563 kg/ram 2

5512 kg/mm 2

5477 kg/mm 2

5088

7001

7180

5474

5468 *

35 = 7

7077

7314

-22 = 2

4699

4906

7260

7952

7992

37 = 12

7232

5389

38 = 6

7340

7465

6498

6766

7401

5467

5461

7416

6780

6097

6626

6599

7971

29 = 8

6514

6638

7461

30=10

6014

7186

31 = 13

6296

6373

6338

5862

5843

6572

The dimensions of the rods are not stated in the table. For the
columns headed E l the depth a of the cross section was between
2-695 and 4'335 mm., and the breadth b between 9'269 and
16'384 mm. The means were (in round numbers) a=3 mm.,
b = 1 5 mm. For the rods to which the columns E z relate, a was
between 3'176 and 4*044 mm., b between 8'484 and 16'091mm.
The means in round numbers were a 3 '5 and 6=15 mm.

In several instances, the values under E l and E 2 for one and
the same glass differ considerably. These differences are explained
by the following considerations :

It is not improbable that the uncertainty in the value of a
may produce a maximum error of 2 per cent.

The glass 19 was from two different meltings in the two cases,
and it is possible that its actual composition was slightly different,
especially as regards boric acid. The glass 22 was also from two
different meltings. Glasses 34 and 35 showed the presence of
stresses, and these have a considerable influence on elasticity.
Glass 38 contained layers of bubbles, and therefore was not
completely homogeneous.

MECHANICAL PROPERTIES OF GLASS.

159

Dependence of Elasticity on Chemical Composition. The
attempt was made, as in the case of other properties previously
mentioned, to express the elasticity (Young's modulus) by the
formula H = v o_ n v _u x + e fc^

Si0 2
B,0,
ZnO

As 2 5 =

BaO =100
Na 2 =100

K 2
CaO

100

a r a v a 3 ... being the percentages of the several ingredients of
the glass. It was found that the 19 values given under the
heading E l were represented in a satisfactory way by giving x
the following values : 1

x x

65 PbO = 47

20 MgO=600

15 A1 2 3 =160

The attempt to calculate the elasticities of the additional
glasses included in the second series, by the use of these numbers,
was not very successful.

In order to obtain satisfactory agreement between formulae
and observed elasticities for all the glasses examined, Winkelmann 2
divides them into three groups: A, B, C. Group A comprises
the pure silicate glasses, which contain neither boric acid nor
phosphoric acid, and are also free from baryta and magnesia.
Group B contains the lead-free borosilicates ; they are also free
from phosphoric acid. Group C is composed of the remaining
glasses, comprising borates, lead borosilicates, and phosphate.
The corresponding values of x are given in the following table :

Values of x for the group.

ZnO

:,-_>

100

PbO

MgO

AL,0,

i:,o

130

BtO

N.,0

100

K,0

CaO

>W. u. Sch., I. Til W.,IL 122.

160

JENA GLASS.

The values of Young's modulus, calculated by the help of these
numbers, are given side by side with the observed values in the

following table :

Elasticity in kg per mm 2

Observed.

Calculated.

Obs.-Calc.

Group A

5088

5080

+ 0%

5389

5614

-4

6632

6619

5464

5536

_ j

29 = 8

6576

6644

-1

30=10

6014

6001

5852

5848

5494

5284

+ 4

35=7

7195

7186

6572

6573

-0

Group B

19 = 5

7563

7560

7972

7511

+ 6

6613

7164

-8

7090

7459

-5

7260

7610

-5

37 = 12

7232

7364

-2

38=6

7402

7796

-4

7401

7331

+ 1

7416

7269

+ 2

7971

7247

+ 9

7461

7071

+ 5

7186

7080

+ 1

Group C

5471

5521

- 1

22=2

4802

4776

+ 1

6780

31 = 13

6334

6180

+ 2

6097

6104

-0

6338

6363

-0

73. Elasticity of Glass at Higher Temperatures. As

already stated, Winkelmann extended his observations on glass
rods to higher temperatures. 1 Of the 28 glasses mentioned in

MECHANICAL PROPERTIES OF GLASS. 161

the preceding article, 24 were subjected to this further test, the
four omitted being 20, 27, 36, 37. The determinations were
carried as far as the temperatures at which the glasses began
to be plastic, that is, in the case of the least fusible, to nearly
500.

For these new observations, the apparatus previously used was
enclosed in a metal case, consisting of several boxes one within
another, and covered externally with asbestos. Two brass tubes,
closed at the ends by glass plates, were screwed into the walls so
as to give a view through the centre. The case was heated by
a ring of eight Bunsen burners, and the gases from the flames
streamed through the interspace between the walls. The
temperatures were indicated by two thermometers going through
the top walls of the case. They were of borosilicate glass 59 111 ,
and had been tested at the Reichsanstalt. The lower parts of
their tubes were graduated from 10 to + 10. Then followed
a widening, and then a graduation from 180 to 550. The
portion from 200 downwards was within the case, and an
auxiliary thermometer gave the temperature of the external
portion of the mercurial column.

The ordinary silver-covered mirrors soon gave hazy images, in
consequence of the heat to which they were exposed, and after
a little while became quite useless. Their place was therefore
supplied by two right-angled isosceles prisms, arranged as in
fig. 19. Very few kinds of glass were suitable either for the
prisms or the window plates ; most kinds becoming dull and
softening at the high temperatures which were employed. The
heavy baryta glass No. 23 proved the best, and was generally
employed.

When the apparatus is set up as above described, and the
observing telescope focussed on the scale, the scale is seen out of
focus after the temperature has risen ; and sharpness can be
restored 1>\ moving the scale further away. Winkdniann traced
tins effect to the action of the heat on the window plates
which closed the ends of the two metal tubes. The tubes,
becoming heated by the flame-gases, communicated heat to the
glass plates, which thus became hotter at the circumferences
tliitu at the centres. This difference of temperature acts in
two ways. In the first place, it makes the plates thicker at
the circumferences than at the centres, so thai th.-v are double-

162 JENA GLASS.

concave instead of plane. In the second place, the index, being
greater for hot glass than for cold, increases from the centre
outwards. 1 Both actions make the plates act as diverging
lenses (see Art. 29). Winkelmann shows, by calculation, that the
differences of temperature which would be required, according to
this explanation, to produce the effect actually observed, are not
greater than it is reasonable to assume. The correctness of the
explanation was also confirmed by experiments separately per-
formed on one of the view-tubes.

If the flexure experiments at ordinary temperatures are first
performed, no important after-effects are observed during their
continuance or after their cessation. At high temperatures it is
quite otherwise ; the scale continues to move across the field of
the telescope for some minutes after putting on or taking off
the load. This made it necessary to employ an assistant, witli
a lever arrangement by which he could put the weight on or off
in a fraction of a second, the observer remaining all the time at
the telescope.

It was also necessary to attend to therino-elastic after-effects.
If a glass is first tested for elasticity at ordinary temperatures,
and then raised to a high temperature, it exhibits, on its return
to ordinary temperature, greater resistance to bending than before
heating. If it only undergoes one such heating, the new and
larger elasticity observed at ordinary temperatures changes in
course of time. Several successive heatings and intervals of
cooling are required before the elasticity becomes constant. In
comparing elasticities at lower and higher temperatures, the
heatings and coolings were continued to this point, and the
constant results thus obtained were adopted.

Statement of Results. Out of the 24 glasses which were
tested in the manner above described, only nine showed a linear
relation between elasticity and temperature ; in the rest elasticity
diminished more quickly as the temperature rose. Winkelmann
adopted, for the expression of his results, the formula

(1)
E t denoting the elasticity at t. Equation (4) of Art. 72 gives

'For glass 23, according to Reed's observations, n n is 1-60982 at 10 and
J -61194 at 404. Cf. Art. 28.

E t E w = v

MECHANICAL PROPERTIES OF GLASS.

hence we have

163

(2)

Substituting, in this equation, the values of the displacement v
for 20 and for two suitably selected higher values of t, two
equations are obtained, from which a and ft can be determined.
The following table contains the results for the 24 glasses; the
first column containing Winkelmann's numerical designations of
the glasses, and the last column the highest temperatures
to which the glasses were heated ; these being the temperatures
employed in calculating the two constants.

log a

log/3

Highest
Temperature.

19=5

7672 kg/mm 3

0-01760-9

0-42810

482

5606

0-45239 - 15

0-70586

383

22=2

5023

0-44871 - 4

281

8146

0-32998 - 5

0-09364

486

5433

0-89662-13

0-64253

413

_'.-,

6983

0-91177-5

0-06481

409

601 1.-,

0-49224-24

0-94544

340

<i;ii

0-57519-4

394

29 = 8

6650

0-40100 -1.)

0-71706

433

30=10

6159

0-69552-5

0*11280

455

31 = 13

6441

0-22967-6

0-25523

412

IW0

0-19312-4

417

:<:{

5494

0*63418-8

0-40114

857

7349

0-11394-5

482

36 = 7

7524

0-54267 - 5

0*08213

460

38 = 6

7649

0-43533 - 6

'23175

426

:r,r,4

o-119160-ll

0-55261

407

70M

0-92267-6

o-ltt.V>0

427

2IK

0-97275-10

0-49890

374

044797-4

447

T.V.I

n-.-t.V218- 4

47.-,

7234

0-36922 - 4

433

-I! I.V.I.-, 4

434

M87

0*0180

448

lnm these values of log a and log/3, WinkalmaiUD deduced

164

JENA GLASS.

the values of 1 E t /E^ for certain values of t, as shown in the
following table :

(i-jtyjyioo

100

2(M>

300

4m"

500

19=5

o-oi

0-11

0-38

0-85

1-95

o-oo

0-08

0-76

3-61

22=2

2-25

5-06

7-87

0-49

1-34

2-32

3-39

4-53

0-02

0-63

4-37

16-60

1-32

, 3-38

5-66

8'07

o-oo

0-02

1-18

3*01

6-77

10-53

14-29

29 = 8

o-oo

0-14

1-44

7-05

30=10

1-45

4-16

7'39

10-97

14-86

31 = 13

0-45

1-94

4-31

7-46

1-25

2-81

4-37

5-93

0-27

2-06

6-27

o-io

0-23

0-36

0-49

0-62

35=7

0-69

1-85

3-16

4-57

6O6

38 = 6

0-50

1-91

4-17

6-82

o-oi

0-14

0-67

2-00

0-51

1-67

3-20

5-01

0-09

1-22

4-92

1-42

3-19

4-96

6-73

1-80

4-05

6-30

8-55

10-80

1-87

4-21

6-55

8-89

3-30

7-43

11-56

15-69

3-32

7-47

11-62

15-76

For glass 22 containing 69'1 per cent, of boric acid, and for
glasses 26, 33, 86 containing large proportions of lead oxide, no-
values are given at 400, because this temperature was too high
for them. At 500 results are given for only the six glasses
19, 23, 30, 34, 35, 88. Most glasses soften or are on the point
of softening at this temperature.

Remarks on the Results. Write Q as an abbreviation for
mt so that equation (1) may be written

MECHANICAL PROPERTIES OF GLASS. 165

For nine of the glasses 8 is unity, so that at all temperatures
above 20 the glass of greater a has also the greater Q. These
glasses, arranged in ascending order of a, are: 22, 28, 32, 34,
7, 88, 89, 90, 91.

As regards the influence of ft, let two glasses have the same
value of Q at a particular temperature 0. Then, using the
subscripts 1 and 2 to distinguish values for the two glasses, we
find, from (3),

But (3) gives, by differentiation,

,///-()*'

hence, at the temperature at which Q is the same for both, the
glass which has the greater ft has the greater dQ/dt. At higher
temperatures this glass will have the greater Q, and at lower
temperatures the smaller Q.

Influence of Chemical Composition. No satisfactory results
have been obtained in the attempt to express a and ft as linear
functions of the percentages of the several constituents. Taking,
first, the glasses for which ft is unity, so that greater a means
more rapid diminution of elasticity with rise of temperature ; if
we exclude the borate glass 22 and arrange the others in order
of ascending a, the last six of the series are borosilicates in which
potash and soda are both present, namely, 87, 88, 89, 28, 90, 91.
Taking account of their varying percentages of boric acid,
Winkelmann suggests that the simultaneous presence of large
amounts of soda and potash favours the change of elasticity with
temperature, but that the presence of boric acid along with them
tends in the opposite direction. 1

If the 15 glasses for which ,tf i> not unity are arranged in
ascending order of ft, the series is: 25, 35, 23, 30, 85, 38, ." 1 .
33, 19, 86, 84, 24, 21, 29, 1M 1 1 arranged in descending order
of a, the order is the same, except that glass 30 is second instead
of fourth. This order of succession does not correspond to any
regular order of chemical composition: for example, the only
phosphate is number 31. The glasses which contain l, a d have

W. II., 131.

166 JENA GLASS.

certainly the largest values of /3, but not in the order of their
amounts of lead; for this would give the order: 29, 21, 86, 24,
26, 33. Glass 90 is exceptional, for its /3 is unity; but it only
contains 2 '5 per cent, of lead.

74. Correction to be made for Thermal Expansion. Thus
far the linear measurements a, I, I in the expression (4) for the
elasticity (Art. 72) have been treated as constant; but they in
fact change with temperature. Writing E' '. for corrected and
E as before for uncorrected values, we have

-w-jt j-i To 07

E t E t I? a a \

> ~j * i~z' ~a*bt ""W

The supporting knife-edges, whose distance is I, were portions of
a massive apparatus of brass ; a and I are the depth and width
of the glass rod. If a denote the coefficient of linear expansion
for brass, and /3 for glass, equation (1) gives, to the first order of
small quantities,

(2)

According to the observations of Le Chatelier, 1 the mean value
of a between and 40 is 0'0000186, and between and 700
0-0000225.

Assuming that the mean value of a from to f is of the
form A -f Bt, we deduce :

Mean x 10 7 .

to 100, 190
200, 195
300, 201
400, 207
500, 213

For glass (kind not specified), Dulong and Petit 2 found, for
the coefficient of cubic expansion 3/3, from to t, the mean value

0-0000251 + 10- U 6* 2 :

l Com. Hen., 108, 1096 (1889); Beiblatter, 13, 644.
2 Winkelm., Handbuch, II. 2, 48.

MECHANICAL PROPEKTIES OF GLASS.

167

the experiments going up to 300. This would give, for the
cubical coefficient,

Mean x 10 7 .

O p to 100, 257

200, 275

300, 305

400, 347

500, 401

These values of a and /3 would give, at the temperature t,

the vali:

(2a-4/3)<xl0 5

100

+ 37

200

+ 46

300

- 14

400

-196

500

-545

This would make the correction vanish at some temperature
between 200 and 300; at lower temperatures it would be
positive, and at higher negative.

From equation (2) we easily deduce

'I' his equation would serve for correcting the values given in
the table of p. 164, if the coefficients of expansion of the different
glasses were known. The correction has most interest in the case
of those glasses which show the smallest diminution of elasticity
with rise of temperature. Glass 34 is the most marked example,
and a rou.u'h calculation for it has been made by Winkelmann in
th- following wav :

From the chemical eomp,,>iti,,ii of the glass, its coefficient of
lin.Mi expansion between and 100 has been computed to be
il x 10' 7 . Adopting this value for ft and 186 X 10' 7 for a.
the value of 2a-4/3 is 128 X 10" 7 . \vhirh. multiplied by 20.
gives 256x10"'. We have, accordingly,

- 40)* -256x10-'].

1C8 JENA GLASS.

Hence the following corrected values are found :
GLASS No. 34.

(l-JBr/JSaoMOO

(1 -#/#). 100

100

0-10

-o-oi

200

0-23

- 0-04

300

0-36

-0-09

400

0-49

-0-16

500

0-62

-0-26

The minus signs indicate that the elasticity increases with rise
of temperature, but the calculation assumes /3 to have the
constant value 61 X 10~ 7 . If the mean value of ft from to
500 is greater than this by about 25 per cent, the elasticity at
500 will be about equal to that at 20.

It therefore seems probable that for glass 34 the change of
elasticity with temperature is scarcely sensible. The same remark
applies to glass 19. For the other glasses, further knowledge of
their expansions at high temperatures would be required before
the correction could be made.

75. Investigations on the Hardness of Glass, and on
properties associated with hardness, have been published by
F. Auerbach. 1 His observations extend to 14 glasses, and to
various other substances, ranging over the whole of Mohs' scale
with the exception of diamond and talc. The chemical com-
positions of these glasses, except No. 11, are given in the
following table :

1 See the following papers :

I. Absolute measurement of hardness. Getting. Nac.hr., 6 Dec. 1890.
II. Same title, Ann. d. Phy. u. Chem., 43, 61 (1891).

III. Hardness, brittleness, and plasticity. Vtrhandl. d. Ges. dentxrk.

Naturf. u. Aerzte. 1891.

IV. On the measurement of hardness, especially' in plastic bodies. Ann.

d. Phy*. u. Chem., 45, 262 (1892).

V. Plasticity and brittleness. Idem, 45, 277 (1892).

VI. Hardness and elastic qualities of glass. Id., 53, 1000 (1894).
VII. Absolute scale of hardness. Id., 58, 357 (1896).

MECHANICAL PROPERTIES OF GLASS.

169

Auerb.

69-0

2-5

0-4

4-0

16-0

8-0

o-i

29-3

67-5

0-2

3-0

III

70-25

10-0

0-2

10-0

9-5

0-05

20-0

80-0

.-.

71-0

14D

5-0

10-0

70-6

12-0

0-4

17-0

34-5

10-1

7'8

,vo

0-5

12*0

o-i

69-1

18-0

0-2

4-7

8K)

32-7

31-0

25-0

7-0

0-3

1-0

3-0

10
11
12

41-0

51-7

0-2

7-0

o-i
o-i

67-3

7-0

2-5

14-0

7-0

58-7

0-3

33-0

8-0

3-0

8-0

1-5

28-0

59-o

The first column contains Auerbach's numbering of the glasses ;
the second his previous numbering of the first four; the third
the corresponding numbers in Winkelmann's list (Art. 67). As
regards Auherlmch's 4 and 8, they were of the same composition
as Winkrlmann's 20 and 2, but were not from the same nu'ltin^s.
No. 1 1 is the so-called " Geriiteglas " (flask or laboratory glass).
N". 1 2 is thermometer glass (Jenaer Xormalglas).

The most important outcome of Auerbach's work is its
experimental confirmation and < umpletion of a theoretical investi-
gation by H. Hertz 1 "on the contact of elastic solids. The
following is a sketch of the results of this theory, so far as
required for our pin-pose.

76. Contact of a Plane Glass Plate with a Glass Lens
under Pressure. Hrrt/, discusses tin- -vnrral case ..!' i\\<> <>laMir
isotropic bodies exerting mutual normal pressure over a small
area common to both. An absence of tangential force is assumed.
The investigations relate to the form of the surface of contact,
tin' fonn and magnitude of its Ixmnding curve, and the distribu-
tion of tin- pressure.

1 Jonrn.f. d. reitie n. angewandte MathfmtUik, 92, I5 (1882).

170 JENA GLASS.

The results are very simple for two bodies of exactly the
same material, if the surface of one previous to contact is plane
and that of the other spherical ; conditions which are practically
fulfilled when a lens is pressed against a plate of the same glass.
The surface of contact in this case is a portion of a sphere, its
radius of curvature />' being double that of the given sphere,
that is,

p denoting the radius of curvature of the lens.

The boundary of the surface of contact is, of course, a circle.
Let d denote its diameter, p the amount of the mutual pressure
of the lens and plate, /m the value of " Poisson's ratio " (see
Art. 85) and E that of Young's modulus. Then d is determined

(2)

and the intensity of pressure at the middle point is

- .................................. <

77. Confirmation of the Theory, and Calculation of
Indentation-Modulus. In the apparatus designed by Auerbach
and made by Zeiss, 1 a lens is pressed up by levers against
a plate fixed in a horizontal position, and the surface of pres-
sure is observed from above by means of a microscope with a
micrometer eyepiece. The commencement of contact, before the
pressure becomes sensible, is recognised by the first appearance
of blackness in the centre of the interference rings. When
pressure is applied, the surface of contact is seen as a round
black spot of size depending on the pressure. Simultaneous
values of p and d can accordingly be observed.

Equation (2) can be written in the form

which implies that pp/d s is constant for a given material when
p, p, and d vary. This theoretical deduction obtained by Hertz

1 The full description of the apparatus and observations is contained in papers-
I. and II.

MECHANICAL PROPERTIES OF GLASS. 171

is abundantly continued by Auerbach's experiments. The
quotient p/d 3 was found to be in general constant for the same p
and to vary inversely as p.

The following is a specimen 1 of the results for glass 1 , which
is described as of medium hardness. The radius of curvature p
of the lens was 10 mm.

p. d. p/d?.

2-2 kg. 0'33 nun. 62'1 kg/mm 3 .

3-5 -39 59-0

5-4 -45 60-3

7'4 -50 59-1

9-8 -54 59-1

13-3 -62 59-2

15-2 -63 59-9

16-4 -67 55-5

18-9 -69 56-8

31-1 -82 56-8

31*6 -82 56-9

36-5 -87 56-1

44-6 -91 58-9

The mean of the values of p/d? is 58*4 kg. per square millimetre.
With varying values of p the following results were obtained
for glass 1 :

PP
d*'

3 mm. 195-4 kg/mnr. 586 kg/mm 2 .

5 114-9 575

10 58-3 583

15 38-:i 575

The numbers in the last column agree fairly well, and their
mean 580 in accordingly to be regarded ftfl a r..nstant I'dun^ing
to this kind of glass. 2

E
A.uerbaoh adopts as the measure of resistance to indent-

1 1. 632 and II. 86 ; all results being reduced to the kg. and nun.
'Auerbach, I. f>:u un.l II. 88. A subsequent recalculation gave a somewhat
larger value see VI. 1003.

172

JENA GLASS.

ation, and calls it the indetriation-modulus (Eindringimgsmodul).
He denotes it by the symbol E f . We have, accordingly,

(2)

The values of this modulus for 14 glasses, as determined by
Auerbach (VI. 1028), are given in the following table, together
with the values of E and /u.. The values assigned to E are the

E' E

E'-E

7107 kg/mm 2

kg/mm'-

5871

5494

6-4

0-25

7869

7461

5-2

0-23

5588

5088

8-9

0'30

7599

7296

4-0

0-20

6796

6632

2-4

0-16

8192

7972

2-7

0-16

4975

4802

3-5

0-19

5677

5471

3-6

0-19

5953

5464

8-2

0-29

7532

7792

7402

5-0

0-22

6197 6014

3-0

0-17

6811 6334

7-0

0-26

means of E l and JE 2 (in the notation of Art. 72), except that, in
the case of glass 5, E^ is adopted, because E^ was for a different
melting. For glass 3, no determination of E was made; the
value 7461 given in the table was obtained by Winkelmann for
a glass of nearly but not exactly similar composition.

The differences between E' and E are given as percentages of
E ', in the column headed E' E.

Calculation of Poisson's Ratio. The numbers in the last
column are the values of Poisson's ratio yu, calculated from E' and
E by means of equation (2).

The probable errors in the values of E' average \ per cent.,
and never quite reach 1 per cent. Assuming the probable error
of E to be \ per cent, Auerbach deduces 7 per cent, as the
probable limit of error for /u. (see Art. 85 for Straubel's deter-
mination).

MECHANICAL PROPERTIES OF GLASS. 17

These results establish the fact that M the ratio of lateral
contraction to longitudinal extension under longitudinal pull is
very different for different glasses. The view that it has the
constant value J for all homogeneous isotropic bodies is therefore
clearly untenable. 1

78. Law of Limiting Pressure. If the pressure of the lens-
against the plate, as described in the foregoing article, is gradually
and slowly increased to a sufficient degree, the plate suddenly
cracks ; the crack being of circular form and concentric with the
area of contact. Its diameter exceeds that of the circle of
contact by on the average about 1 9 per cent., for glasses of all
kinds.

We shall denote by P the value of the total pressure p at
which this result occurs ; we may call it the limiting amount of
pressure. Auerbach determined its value for the glasses 1-14,
and arrived at the simple law that, for a given material, the-
limiting amount of pressure P is proportional to the radius of
curvature p, so that

P '

F' being a constant depending only on the material. Thi>
constant, which measures the resistance of the material to
fracture by indentation, has not yet received a name. It may
be provisionally called the fracture-modulus. The degree of
accuracy with which this law is fulfilled in the case of glass 1
is shown in the following table :

3 mm. 4'93 kg/mm.

5 478

10 :>04

15 4-80
The mean is /" = 4'89 k<j nun

79. Absolute Measurement of Hardness. Auerbach under-
took his investigations 2 for the express purpose of obtaining

t > See Art. 86.

* A review of previous measurements of ha nines* is given in Auerbach, II. 64.

174 JENA GLASS.

absolute measurements of hardness. His method of experiment
<loes not involve the properties of any material other than that
whose hardness is in question.

The direct data given by his experiments are : the indentation-
modulus E' y and the fracture-modulus F'. The question arises :
in what relation do these two constants stand to the property
expressed by the name " hardness " ? The first experiment, made
on the glasses 1, 2, 3, and rock crystal, sufficed to show that F'
was not identical with hardness ; for glass 2, described by the
makers as " soft," has a decidedly larger value of F' than
1 and 3, of which the former was described as " of medium
hardness," and the latter as " tolerably hard." 1

If a less hard body is able, with equal p, to bear a greater
amount of pressure P, the explanation which first suggests itself
is that it spreads the pressure over a wider surface, and that the
limiting value P l of the intensity of pressure p l is the essential
consideration. In fact, for equal p, the soft glass 2 bore the
smallest P I} and the hard glass 3 the greatest.

Hertz assumed & priori that the limiting intensity P l at the
centre of the pressure-area, when the limit of elasticity is reached,
is a constant for the material, independent of p ; and he accord-
ingly adopted this limiting value P l as the measure of the hardness
of the material. 2 The passing of the limit of elasticity is easily
recognised, in brittle bodies, by the formation of a crack, as in
Auerbach's experiments. In plastic bodies it would be necessary
to determine the pressure at which permanent deformation begins.

If Hertz's assumption were correct, P l would be a definite
function of E' and F'. Introducing, in equations (2) and (3) of
Art. 76, the limiting values P, P v D of p, p v d, and employing
the law of limiting pressure, we obtain the three equations :

1 Compare Auerbach's concluding remarks, I. 541 and II. 100.

2 Verh. d. Berl. phys. Gen. 1882, 67 ; Verh. d. Ver. z. Forder. d. Gewerbfetsses,
1882, 441 ; Gesamm. Werke, 1, 174.

MECHANICAL PROPERTIES OF GLASS. 175

from which the three following are deducible :

(i)

(2)

.(3)

I\ is therefore not a definite function of E' and F', and is not
the sole determining element of hardness.

The problem of obtaining, by further development uf Hertz's
theory, a useful definition of hardness is as yet unsolved.

Proceeding empirically, and accepting P l as one determining
element of hardness, equations (1), (2), (3) offer a choice between

as measures of hardness. Applying these to the three glasses
1, 2, 3, and observing that they depend respectively on E'F' t
(E'F'J, and E'W, we find that the hardest glass 3 has the
largest E'F', but the glass of intermediate hardness 1 has the
smallest. On the other hand, the largest value of E'*F' belongs
to the hardest glass 3, and the smallest value to the softest
glass 2.

It would therefore appear that the hardness H is best defined
by the equation

and can be experimentally determined by the help of the equation

(5)

The following table contains (in the last column) the values of
// deduced by Auerbach from his observations. 1 The glasses are
here arranged in ascending order of hardness, and the values of

1 Auerbach, VI. 1014.

176

JENA GLASS.

E' and F' from which H is derived are also given. 1 The radii of
curvature p of the lenses employed are also given.

No.

p
in mm.

in^i,
mm-

inJ*
mm

fc-NL

mm 8/s

2,5,7

5953

3-0

173

1,2,4

5588

4-1

183

1, 4, 12

5871

5-6

210

2,5

6811

4-6

217

1,3,5

4975

8'8

219

3, 5, 10, 15

7107

4-5

223

3,5

5677

9-3 ! 244

4, 12, 30

7869

5-0

246

2,5

7792

6-4

266

2,5

7532

6'9

267

1,3,9

6796

9-0

272

1,5

7599

7'4

274

2,5

6197

11-6

278

1,3,5

8192

316

In connection with the definitions of hardness, it may be of
interest to state that the arrangement of the glasses in ascending
order of the product E'F' is: 10, 4, 14, 1, 2, 3, 8, 12, 11, 9, 5,
6, 13, 7.

The ratio of 173 to 316 is 1 to 1 '8 3. The greatest hardness
is accordingly not so much as double of the least.

80. Experiments on Scratching. The comparative hardness
of different bodies has hitherto been decided almost exclusively
by the test of scratching. It was therefore important to ascertain
how far this test agreed with the foregoing determinations.
Auerbach accordingly carried out a series of experiments on the
14 glasses in question in the following manner. 2

Broken pieces of all the 14 glasses were provided, each having
at least one point which appeared to be neither too blunt nor too
fragile. The mode of experimenting was to make one of these
points rest upon the plane surface of another kind of glass at an

1 Auerbach does not state the values of F' ; they are deducible from H and E'
by equation (5).

2 Auerbach, VI. 1015.

MECHANICAL PEOPERTIES OF GLASS. 177

inclination of about 60, and then to move it under strong
pressure. This was done with every glass upon every other, the
whole number of combinations being 14 X 13 = 18 2.

It turned out that every glass was scratched by every other,
even the hardest by the softest. In order to decide between
two glasses, it was therefore necessary to find which of them
exhibited the greater scratching power upon the other. With
this view the scratches were examined under the microscope.
This showed not only quantitative but qualitative distinctions.
There were scratches with lateral chipping, with lateral cracking,
with lateral splintering, with longitudinal cracking, with longi-
tudinal splintering, with cavities leaf-shaped or shell-shaped or
irregular.

When no decided superiority in scratching-power was detected
in the comparison of two glasses, they were adjudged to be
equally hard.

Out of the whole 91 comparisons of the glasses, two and two,
(this being the number of combinations of 14 things, two together),
there were 18 departures from the order of relative hardness
found above. They are exhibited in the following list, in which
the numliers are those of the list in Art. 79.

10>4; 2 = 8; 1><J; 1 = 11;

9 = 13; 3 = 11; 3>6; 3 = 5;

12>11; 12>6; 12 = 13;

ll>6; 11 = 5; 11>13; 11>7;

6 = 5; 5>13; 5>7.

Th- largest discrepancy is 11 > 7; for 7 is 49 units hard, i
than 11 according to the values of H in Art. 79.

It we attempt to arrange these glasses in the order of their
scratching powers, 4 is the softest, and 10 comes next. But
there are inconsistencies which render a continuous arrangement
impossible. Thus we have

2<14<8, with 2 = 8,
9< 1<13, with 9 = 13,
11 = 5; 6 = 5, with 11>6;
and still worse,

7<11<12, with 7> li'.

178

JENA GLASS.

Active and Passive Scratching Hardness. With the help
of microscopic examination, Auerbach distinguished 10 degrees of
_th in the scratches. Numbering these from 1 to 10,
1 being the weakest and 10 the strongest, he obtained a
numerical value for the scratching power of each glass by adding
dues of the scratches made by it upon the other 13. In
like manner he obtained a numerical value for susceptibility to
scratching by adding the values of the scratches made upon any
one glass by the other 13. The results are shown in the
following table, in which the top row contains the numbers of
tin- glasses when arranged in order of their values of H, beginning
with the softest ; the second row contains their scratching powers,
and the third row their susceptibility to scratching:

100

There is no regular law of connection either between the first row
and the other two, or between the last two rows themselves.

81. The Absolute Hardness of Glass and its Chemical
Composition. Auerbach made the attempt to express the
" absolute hardness " of glass in terms of the percentages of its.
constituent oxides, in the same way in which other properties,
have been expressed (for example in Art. 69).

Neglecting the small percentages of As 2 5 and Mn 2 3 contained
in some of the glasses, he assigned to the 10 remaining oxides,
-1 low ing coefficients :

Si0 2 =
B 2 3 =
ZnO =
PbO =
A1 2 8 =

3-32
0-75
7-1
1-45

BaO =1-95
Na 2 0= -2-65
K 9 =3-9
CaO = - 6-3
P 2 5 = 1-32

Multiplying the percentages given in Art. 75 by these coefficients,.

tain the values headed "Calculated" in the following table.

The differences between these and the " Observed " values are so

MECHANICAL PROPERTIES OF GLASS.

179

large, especially in the case of the lead silicate glass 10, that the
representation fails.

Absolute Hardness in kg mm" 878

Observed.

Calculated.

Obs.-Calc.

223

232

- 4%

210

207*

+ 1

246

251

- 2

183

182

+ 1

274

270

+ 1

272

275

- 1

316

310

+ 2

219

222

- 1

244

248

- 2

173

238

-38

267

266

219

+ 18

J7S

273

+ 2

217

216

82. Unequal Brittleness of different Glasses. If the experi-
mental method described in Art. 77 is applied to plastic bodies,
for example, to rock salt or fluorspar, the result of overstepping
the elastic limit is not a crack, but a permanent deformation a
depression in the plate and a flattening of the lenses. These
permanent effects increase gradually with increasing pressure ;
and it is impossible to determine the exact pressure which
corresponds to the elastic limit. The limiting intensity of
pressure is therefore not a suitable criterion for the deter-
mination of hardness in such bodies.

When the increase of pressure is carried beyond the elastic
limit, equation (2) of Art. 76 no longer holds; thus Auerbach
I- iind, for rock salt and fluorspar, that in a series of experiments
with given p the quotient p/d? did not remain constant, but
rapidly decreased as the pressure increased beyond a certain
a mi Mint. If, however, the intensity of pressure in the centre of
tin- pressure-area is calculated by equation (3), this is found to
reach a maximum I\ which remains constant as the pressure is
fui ther increased. In this case, then, we have

180 JENA GLASS

The following values were found for fluorspar : l

P A

3 mm 737 kg/mm 2
5 61-4

10 49-1

I-W Itrittle as well as for plastic bodies, P l can accordingly be
ik'tiiu'd as the limiting pressure-intensity in the centre of the
pressure-area.

This limiting value follows the same laws in the case of plastic
as of brittle bodies, and the product P-^^/p is constant. Thus
the above values give

P P \Z/P

3 mm 106 kgmm" 5/3

5 105

10 106

Auerbach accordingly defines the hardness H of plastic bodies
(as well as of brittle bodies) by the equation

and derives it from observations by the equation 2

(2)

It is worthy of mention that the quantitative laws found by
Auerbach for plastic minerals have been confirmed by observa-
tions made by A. Foppl on a series of metals. The specimens
had one side ground to a cylindrical form, and two of these
cylindrical faces, laid across each other at right angles, were
pressed together. In order to permit of subsequent measurement
of the area of contact, one of the cylindrical surfaces was covered
with a fine layer of soot. The pressure-area was found to vary

1 Auerbach, IV. 268.

2 Equation (2) of course holds also for brittle bodies. For these we have

but the limiting value D cannot be directly observed with certainty. On the
other hand, for plastic bodies the indentation-modulus can only be determined by
observations within the elastic limit.

MECHANICAL PROPERTIES OF GLASS. 181

directly as the total pressure ; the average intensity remained
therefore unchanged, that is, it attained its limiting magnitude
at an early stage. The product of this intensity and the cube
root of the radius of the cylinder was found to be constant for a
jive n metal. 1

Plasticity and brittleness may be regarded as two extreme
conditions between which there is a continuous transition ; and
calcspar seems to occupy an intermediate position. 2

These properties may serve to throw light on some peculiar
effects exhibited by certain kinds of glass.

Glasses 1, 8, 9, 12, 13, 14 gave constant values of p/d? in all
series of experiments ; and so did glasses 6, 7, 11, except that in
one series this quotient diminished with increasing pressure.

On the other hand, glasses 2, 4, 10 exhibited numerous and
sometimes quite large departures from this rule. Take, for
instance, the following data given 3 by Auerbach for glass 2, and
obtained with a lens of radius of curvature p = 1 mm. :

?> Q * 19

P - v P . 51

3-43 kg

488 kg mm- 2

179 kgmm- 5/2

4-41

475

191

5-39

426

190

7-35

405

203

9-31

417

224

11-27

365

219

17-15

299

220

19-11

283

220

As the pressure increases, the quotient p/d? shows large
diminution. At the same time the total pressure increases far
beyond the normal limit P= 5*6 kg., so that the law of limiting
pressure is not fulfilled. These anomalies become intelligible, if
we assume that the glass in question is less brittle than those
which exhibit normal behaviour. This view is borne out by the
n umbers in the last column. These are the values of the
whose limit, as the pressure increases, is equal, by

-/. Phy*. u. CAm.,50, 101 (1
Compare Auerbach, III. and V.

'The actual numbers given in Auerbach, VI. 1032, are here reduced to the
kg. and mm.

182 JENA GLASS.

equation (2), to the hardness H y in the case of a plastic body.
This limit -20 is 5 per cent, greater than the value of H for
glass 2 in the table of Art. 79.

Specially noteworthy appearances were exhibited by glass 4,
a lead-silicate containing 80 per cent, of lead oxide, and distin-
guished by its deep yellow colour. The crack did not, in most
cases, occur suddenly in this glass, but was formed gradually in
the same manner as in calcspar ; appearing first as a short line,
which, as the pressure was increased, extended further, and finally
formed a closed curve. In some cases it was not a decided crack
that was seen, but what might rather be called fine furrows ; and
in these cases the series of observations did not follow the
ordinary law, but resembled those above described for glass 2
The overstepping of the ordinary limit of pressure was the more
easily obtained the more gradually the pressure was increased.
The crack which at last occurred was then abnormally large,
accompanied, however, by a concentric crack of normal size. In
some cases it was found possible by means of a blow to produce
three concentric cracks, the smallest of the three being of the
normal size. 1 These appearances may also be regarded as indica-
tions of imperfect brittleness.

83. Position of Glass in the General Scale of Hardness.

Auerbach has extended his method of determination of absolute
hardness to the minerals of Mohs' scale of hardness, with the
exception of its two extreme members, talc and diamond. 2 The
results are collected in the following table, and as the materials
are not isotropic, the direction of the pressure in the plate and
lens is stated in each case.

Direction. Hardness.

Gypsum, - - Perpendicular to cleavage, - - 14 kg mm~ 5/3 .

Rock salt, - - face of cube, - 20

Calcspar, cleavage, - - 92

Fluorspar, - octahedral face, 110

Apatite, - - Along axis, 237

Felspar (adular), Perpendicular to base, - - - 253

Quartz, - - Along axis, - 308

Topaz, - Perpendicular to base, - - - 525

Corundum, - Along axis, 1150

1 Auerbach, IV. 272 ; V. 290. 2 Auerbach, VII.

MECHANICAL PROPERTIES OF GLASS. 183

Of these minerals, corundum, topaz, quartz, and felspar are
brittle ; gypsum, rock salt, and fluorspar plastic ; calcspar and
apatite imperfectly brittle.

According to these numbers, the borosilicate crown glass 7 is
harder than quartz, and even the soft lead flint glasses are con-
siderably harder than fluorspar. Auerbach has suggested filling
the large gaps in the middle part of Mohs' scale by inserting
the crown of hardness 274 between quartz and felspar, and two
flints of hardness 210 and 170 between apatite and fluorspar.

In his attempt (Art. 81) to give a formula for calculating the
hardness of glass from its chemical composition, Auerbach assigned
the coefficient 3'32 to Si0 2 and lO'l to A1 2 3 . He calls
attention to the agreement of these numbers when multiplied by
100 with the hardness of quartz and corundum as given in the
above list, 1 especially in view of the fact that the maximum
hardness of corundum is for pressure in the direction of the axis,
its mean hardness being somewhere about 100 units less.

84. Relations between Hardness and other Properties of
Glass. Comparisons of the hardness of glass with its tenacity,
its resistance to crushing, and its modulus of elasticity have not
led to any distinct conclusions. 2 Auerbach remarks that for the
most part hardness increases with resistance to crushing and with
Young's modulus. The mean value of resistance to crushing is
74 for the five soft glasses 10, 4, 2, 14, 8, and is 95 for the five
hard glasses 9, 6, 5, 13, 7. The mean value of Young's modulus
is 6051 for the six soft glasses 10, 4, 2, 14, 8, 1, and is 7196
for the eight hard glasses 9, 3, 12, 11, 6, 5, 13, 7.

Auerbach suspects a close relation between hardness and
Poisson's ratio. He gives the following list of the values of the
hardness H, the Poisson ratio M, and their product

No. H. n.

10 173 -29 50

4 183 -30 55

2 210 -25 35

14 217 -27 57

8 219 -24 53

9 244 -19 46

1 Auerbach, VII. 364 and 369. "Auerbach, VI. 1022, 1031.

184 JENA GLASS.

No. H. M.
3 246 -23 57

12 266 -21 54

6 272 -21 57
5 274 -20 55

13 278 -17 48

7 316 -17 54

The last column shows that the product of yu and H for glass is
approximately constant. 1

Hertz has calculated, 2 for the general case of two spheres
pressed together, the diminution of distance between their
u n distorted portions. For the case of a lens pressed against a
plate, the general formula reduces to

<'>

g denoting the amount of approach in question. 3 Eliminating the
diameter d by equation (2) of Art. 76, we have

To compute the maximum value G of g (which is attained
immediately before cracking), we must give p the value P, and
by employing the equation P/p = F' of Art. 78, we obtain

Instead of the modulus of limiting pressure F' t we may
introduce the hardness H, by means of equation (5), Art. 79.
This gives

H\*

f \* i

-1*4) P" ( 4 >

The depth of the depression in the glass plate, at any time
during the application of the pressure, can be shown to be almost
exactly \g y or, at the instant of cracking, \G.

1 [This conclusion is overturned in the last article of this chapter.]
*Jour.f. d. reine u. angew. Math., 92, 166.

'From equation (1) it is easy to deduce g = J , which is a convenient formula
for the direct calculation of g from observations.

MECHANICAL PROPERTIES OF GLASS. 185

G ia the greatest amount of linear compression of the system
composed of lens and plate, before cracking. It varies as the cube
root of the radius of curvature p of the lens ; and the quotient

is a constant of the material. It may be called " the limit of
linear compressibility of a brittle substance in experiments on
absolute hardness." Its values for the 14 glasses are given in
the following list :

No. H

10 173 0-0083 mm 2/3
4 183 -0106

2 210 126

14 217 100

8 219 191
1 223 97

9 244 182
3 246 96
12 266 115

11 267 124

6 272 158
274 128

l:: 278 199

7 316 147

The second column contains the hardness in asceiulinu order.
Comparison of the two columns shows that for the most part
(with some marked exceptions) increase of hardness gives increase
of limiting compressibility. The mean value for the first six
glasses is '0117, and for the last eight glasses '0144.

85. Poisson's Ratio. [The name elasticity mnnlr (Elastic! tut--
zahl) is given in (iennanv to the ratio denoted by yu in the
foregoing articles. In Kn^laml it is usually called Poisson's ratio,
because Poisson maintained that it had the constant value \ for
all isotropic Ixxlies. It is usually defined as " the ratio of lateral
contraction to longitudinal extension (or of lateral bulging to

186 JENA GLASS.

longitudinal compression) when a cylindrical portion of the
substance is subjected to longitudinal pull (or thrust)." More
precisely, let L and D be the length and diameter of the cylinder
before, and L + l, D + d after, the application of the pull or
thrust ; then the ratio in question is

d L

The value of this ratio for the different kinds of glass has
recently been investigated by R Straubel. 1 He begins with a brief
account of the previous investigations of Everett, Cornu, Voigt,
Can tone, Kowalski, and Amagat, and gives the preference to
Cornu's method.

Cornu employed glass plates or strips, of rectangular section,
and of various thicknesses, supported horizontally on two parallel
knife-edges; and subjected them to flexure by hanging on weights
at their ends. The upper surface of the glass thus acquires a
peculiar deformation, which can be observed by means of inter-
ference fringes, and made the basis of calculation for Poisson's
ratio. Straubel produces the same deformation in nearly the
same way, but employs a different method of observing the
interference fringes a method indicated (though not employed)
by Cornu.

When the longitudinal axis of the strip is bent into an arc
convex upwards, the transverse axis is at the same time bent into
an arc convex downwards. The surface of the strip, originally
plane, acquires anticlastic curvature (or becomes saddle shaped),
and the curvature in the transverse section is /m times the
curvature in the longitudinal section. 2

If the lower (plane) face of a circular cover-plate, parallel to
the tangent plane at the centre of the upper surface of the strip,
is brought into close proximity with this surface, and illuminated
by normally incident monochromatic light, an interference pattern,
consisting of two conjugate systems of hyperbolas, will be pro-
duced, as represented in fig. 20. Let a be the angle at which
each asymptote is inclined to the transverse section ; 3 then tan 2 a

Mnn. d. Phy*. u. Client., 68, 369 (1899).

2 Thomson and Tait, II. 250; also Wiukelmann, Handb. d. Phyx., I. 263.

3 [In the figure, the transverse section is nearly vertical.]

MECHANICAL PROPERTIES OF GLASS.

187

is the ratio 1 of the transverse to the longitudinal curvature
(neglecting sign), and we have

x = tan 2 a.

Flo. 20.

The glass strip, resting on a pair of knife-edges, was pressed
up against a second pair of knife-edges, further apart, and
symmetrically placed. 2 As a rule, the distance between the first
pair was 7 cm., and between the second pair 10 cm. To prevent
undesirable reflections, the cover-plate was slightly wedge-shaped,
the angle of the wedge being 20', and the under side of the glass
strip was roughened. The under siN >t the cover-plate was
etched with cross rulings.

The source of light employed was a hydrogen vacuum tube
worked by a coil. For eye observation, a red glass (colour*. 1

1 Knoblauch, Theor. d. krummtn Fldchen (1888) p. 126. Hoppe, Principle* d.
utheorie (1890) p. 40.

3 [This mode of producing flexure has the advantage, over that described in
Ait. 72, of giving a uniform bending torque in the portion of the strip between
the inner knife-edge*.]

188 JENA GLASS.

with oxide of copper) served to suppress all the light except that
belonging to the red hydrogen-line C. For photographing the
pattern, the light was decomposed by two flint glass prisms, and
the F component alone employed. In both cases, the light, after
lieing made parallel, fell perpendicularly on the surfaces to l>o
examined, and, on its return after reflection, entered either the
camera or the observing telescope, passing on its way through an
arrangement for measuring the wedge-angle a.

In the subsequent measurement of angles on the photographic
plate, a graduated revolving table was employed, belonging to a
mineralogical microscope. The plate was laid on this table and
centred, and the table was then turned till the two asymptotes in
the pattern had been successively brought into parallelism with &
fixed thread in the ocular. For measuring the details of the
pattern, Pulfrich's apparatus l for interference measurements was
found suitable, after its Dove prism had been fitted with a
divided circle and vernier. Here again, by revolving the Dove
prism, the directions of the asymptotes were made parallel to a
fixed thread in the ocular, the angle between them being given
by the difference of readings.

It was necessary to contend with the difficulty, or impossibility,
of obtaining strips of so small a thickness as 2'5 mm. with
sufficiently plane surfaces. In consequence of this defect, the
strips almost always showed either a regular increase or a regular
decrease of the angle a, as the flexure was increased. Straubel
therefore made, with each strip, a series of observations, with
different amounts of flexure; and, from comparison of their
differences, deduced the value of a which would have been
observed, if the surface of the strip had been originally plane.
The calculation 2 was made by the method of least squares ;
account being taken of the fact that, as the flexure becomes
greater, the observations become more trustworthy.

A complete testing of the method would involve a determina-
tion of the influence of the width and thickness of the glass plate,
and of the distances between the knife-edges. Such tests were
only partially made. The most important influence detected
was that of the width of the plate. As the widtli increases,

1 Zeitschr.j. Instrument, 18, 261 (1898).
2 Straubel, I.e. p. 385-390.

MECHANICAL PROPERTIES OF GLASS. 189

the theoretical assumptions on which the method rests are less
strictly fulfilled, and the form of the surface is modified. By
inserting thin slips of indiarubber between the glass and the
knife-edges, the cross-bending was facilitated; and experiments.
with glass plates 3 cm. wide and 3 mm. thick, showed the
reality of the above-indicated sources of error, by a notable
diminution in the value obtained for JUL.

For one particular glass the tests were very complete,
and are fully described. Its trade number was 1991, and'
its composition

Si0 2 B 2 3 ZnO As 2 6 BaO Na 2 K 2 Mn 2 3
J2 2-7 1-5 0-5 10 5 15 0*08%

All the specimens of this glass were cut from a single plate,
which was free from veins, stresses, and bubbles. Their widths
were I'O, 1'75, 2'0, 2'5, 3'0 cm., and their thicknesses 2'0, 2'5,
3'0 mm.

The distance between the inner knife-edges was sometimes 3*4
and sometimes 5*7 cm. ; the distance between the outer ones
was always 10 cm. The values found for yu ranged from '215
to '233.

On the whole, Straubel concludes that he has obtained
sufficiently constant determinations for the several kinds of
glass which he examined. The question whether the constant
values thus obtained are correct, can only be answered after
comparison with results obtained by various methods, and must
for the present be left open ; though the answer is likely to be
in the atlinnative. If they are not correct as absolute valuo.
they may be accepted as relative values, from which the absolute
values can be inferred as soon as a few certain determinations are
available.

Straubel has taken no account "t the temperatures at which
his observations were made. He states however that, judging
in >m observations by Kowalski, the corrections for differences of
temperature in different determinations may amount to '003.

List of the Glasses. Straubel has given results for 29
different Jena glasses, and also for pure boric acid. Out of the
29, there are 20 which are included in Winkelmann's list
(Art 67), with the following differences in numbering:

190

JENA GLASS.

Str.

1450

S. 219

680

S. 208

2158

1973

658

290

2154

S. 196

270

627

1299

370

709

500

714

1571

16 111

The widths of the plates or strips lay between 2 and 2 '5 3 cm.,
and their thicknesses between 2*42 and 2'58 mm. The inner
knife-edges were 7 cm. and the outer 10 cm. apart. These data
apply to all the glasses except S. 95 and 665. For these, and
for boric acid, the data were

S. 95

665

Boric acid

Breadth.

1-40 cm.

1-65

1-78

Thickness.

2-36 nun.

1-56

3-34

F< a- all three, the inner knife-edges were 5 and the outer 7 cm.
apart. With the boric acid the regular series of observations
was only partially carried out.

Eight of the nine glasses not included in Winkelmann's list
had the following chemical compositions. For the remaining
glass 278 m the composition is not given.

No.

2175

68-7

1-5

5-3

14-5

0-03

1893

53-.">

6-5

2106

44-6

46-6

0-3

0'5

2122

37-.-,

1-5

1933

39-64

9-2

2-5

0-5

42-1

0-06

S. 95

1-5

s. L8fi

71-8

22-4

S. 120

42-8

0-2

No. 1893 contained also 20 per cent, of Sb 2 3 .
S. 185 contained also 5 '8 per cent, of Li. 2 0.

MECHANICAL PROPERTIES OF GLASS.

191

Straubel endeavoured to express the value of /x as a linear
function of the percentages of the constituent oxides, and made
out five different sets of coefficients, of which we shall only
reproduce one. To calculate /x, the percentages are to be multi-
plied by these coefficients, and the sum divided by 100.

Si0 2 ,

ZnO,
PbO,
A1 2 3 ,
BaO,

1533
2840
3460
2760
1750
3560
4310

CaO,

Sb 2 3 ,

3969
4163
2147
2772
2500
2500
2500

MgO,

As 2 5 ,

Mn 2 3 ,

In the following table /u. denotes the observed and /x' the
calculated value. The difference M M', as compared with /x,
amounts on the average to 1*7 per cent., and in the worst case
to 5 per cent. No coefficient is assigned to Li 2 0, and the single
glass S. 185 which contains it is omitted from the calculation.

No.

/* M-A*'

No.

At -A*'

1450

197

-003

658

250

+ 014

278" 1

208

+ 001

1973

252

-006

8178

210

-010

290

408

-002

627

213

-008

270

253

1K93

219 -'001

2122

256

-003

714

221

+ 002

370

261

+ 006

221

+ 003

S. 208

261

+ 010

2154

222

-002

1933

266

2106

222

-009

1299

271

+ 003

1571

224

-Oil

S. 95

272

+ 002

226

+ 002

S. 185

273

16'"

S. 196

274

(Mi:,

2158

231

-002

S. 120

279

- (HH

8. 219

_>:r,

-002

_>s;<

-001

m-,

<;<;.-,

319

-001

Comparison with Auerbach. The indirect determinations of
tin' same element made by Auerbach (Art. 77) in connection with
his experiments on hardness, when compared with Straubel's
determinations for the same glasses, exhibit large discrepancies, as
shown by the fnll.miiiLi tal.h-. Auerbach's estimate of 7 per

192

JENA GLASS.

cent, as a probable limit of error, and 14 per cent, as the
greatest possible error, in his values of /x, seems to be much
too favourable.

No.

Straub.

Auerb.

Diff.

No.

Straub.

Auerb.

Diff.

1450

0-197

0-20

- 1-5 %

290

0-253

0-17

+ 32-8%

1571

o-_>-_>4

0-29

-29-5

270

0-253

0-27

- 6-7

709

0"226

0-21

+ 7-1

S. 208

0-261

0-30

-14-9

16'"

U--J2S

0-21

+ 7-9

1299

0-271

0-17 ,

+ 37-3

500

0-239

0-25

- 4-6

S. 196

0-274

0-24

+ 12-4

658

0-250

0-19

+ 24-0

If we multiply Auerbach's values of the hardness H by
Straubel's values of /x, the products, instead of being nearly
constant as in Art. 84, range from 38*8 to 12 0*3. The supposed
connection between hardness and Poisson's ratio thus falls to the
ground.

Resistances to Compression and Shearing. Let C denote
the " volume-elasticity " or " resistance to compression," and
T the " simple rigidity " or " resistance to shearing " usually
measured by experiments on the torsion of cylinders. Then,
writing E for " Young's modulus," and fj. for " Poisson's ratio,"
.as in the preceding articles, the two following relations are known
.to hold for isotropic bodies : x

T-

3(1-2,*)'

Straubel, by employing these two formulae, has deduced the
values given in the last two columns of the following table.
The values of E were taken from the results of Winkelmann
and Schott (see Art. 72). In the case of the two glasses
278 111 and 1893, the values were personally communicated by
Winkelmann. The values of E for 2175 and 2106 have not
been directly determined ; and Straubel adopted for them the
values actually found for two other glasses (88 and 24 in
Winkelmann's list) which closely resemble them in composition.
For 665 there was also no direct determination of E. Straubel

1 Thomson and Tait, 694 ; Winkelmann, ffandb. d. Phys., I. 224.

MECHANICAL PEOPERTIES OF GLASS.

193

computed it from Auerbach's values 9094 and 377 for indenta-
tion-modulus and hardness, combined with his own detenu i nation
of /x. (See formulae of Art. 77.)

No.

1450

197

7300

4020

278'"

_>os

6640

3790

9700

2170

210

7460

4290

3oxo

627

213

7970

4630

3-290

1893

219

5170

3070

2120

714

221

6570

3920

2690

221

6340

3790

2600

2154

-222

6100

3660

2500

2106

222

5390

3230

2210

1571

294

5460

3300

2230

709

226

6630

4030

2700

16'"

7400

4530

.SOlo

2158

231

6610

4100

9080

S. 219

235

6780

4260

9700

500

239

5490

3510

2220

658

250

5470

3650

2190

1973

252

7420

4990

2960

290

253

6010

4060

2400

970

253

6330

4270

2530

370

261

5X50

40x0

2320

S. 208

261

5090

3550

2020

1299

271

7<>7"

5800

3140

S. 196

274

4700

3470

ISJH

665

319

8170

7520

3100

Straubel points out that glass 665 is distinguished by its
extreme properties; 1 that it shows the greatest hardness, and
the largest coefficients of elasticity (including Young's modulus,
indentation-modulus, and volume-elasticity), as well as the
largest Poisson's ratio; that it has also the smallest thermal
expansion ; also that it probably has great tenacity and resist-
ance to crushing, great power of withstanding heat, and small
electric conductivity.

'[No. 665, M the above Hat shows, is \Vinkelmunn'* No. 39. The list of
iluplicatcs in Art. 67 shows that No. 39 is identical with No. 11, which is
composed of 41 per cent. B./) 3 and 59 per cent. ZnO.]

CHAPTER VIII.
THEKMAL PKOPERTIES OF GLASS.

86. In this Section, the order of treatment will be : Specific
Heat, Conductivity, Expansion, and Power of Withstanding Heat.
The experiments which we shall have to describe were performed
almost exclusively on the glasses enumerated in Art. 67, where
their chemical compositions are described ; and we shall designate
them by Winkelmann's numbers, there given.

87. Specific Heats. The first systematic investigation of the
specific heats of glasses of different compositions has been made
by Winkelmann, using Kegnault's method. 1 Pieces of glass, of
an aggregate weight of from 100 to 250 gm., were heated by
steam, in a small brass-wire basket, to a temperature T near
100; and then immersed, with the basket, in a water calorimeter,
containing a thermometer and stirrer, and having an initial tem-
perature tfj , not differing much from 14. The final temperature
of equilibrium t was not far from 18. This temperature t 2 has
been lowered by an amount, which we will call A 2 , by the
escape of heat during the time occupied in attaining equilibrium.
Let

p be the mass of the glass (in gm.),

c the specific heat of the glass,

P the mass of the water in the calorimeter (in gm.),

A the water-equivalent of the calorimeter, stirrer, and

thermometer.
B the water-equivalent of the brass-wire basket.

1 Ann. d. Phya. u. Chem., 49, 401 (1893).

THERMAL PROPERTIES OF GLASS. 195

Then we have

From this equation c is to be found, the other quantities having
first been determined by observation.

The heating apparatus consisted of three coaxal vertical
cylinders, the innermost being provided at both ends with sliding
metal plates for opening and closing.

Into it the wire-basket was lowered half-way down, suspended
by a silk thread, and having in its centre the bulb of a ther-
mometer graduated to tenths of a degree. Steam was passed
through the two intervening spaces between the three cylinders ;
and after 2J hours the indications of the thermometer were
sufficiently constant.

The calorimeter was pushed into its place beneath the heating
apparatus a long time before the experiment ; and with the help
of a stirrer, and a thermometer divided to tenths of a degree, its
temperature was observed at regular intervals. It thus attained
almost exactly the temperature of its surroundings. The weight
of the water was determined immediately before the experiment.

The wire-basket with its contents having then been lowered
into the calorimeter, observations of temperature were made
every 20 seconds, -the basket itself being used as stirrer. The
temperature of equilibrium 2 thus found, combined with
the observations taken before immersion, gave the means of
determining A/ 2 , which was about '023. 1

The water-equivalent A of the brass calorimeter with stirrer
and thermometer, was estimated by calculation at 15' 13 gm.

Two different baskets were used. One weighed 24*23 gm.
Three experiments made with it when empty gave 2'184 as its
water-equivalent. The resulting value of the specific heat of
brass was '09014, the actual specific heat of brass being *093.
The difference is due to loss of heat from the basket on its way
to the calorimeter. This error is allowed for by using the
observed value 2*184 for the water-equivalent; a conclusion
verified by two experiments, with about 336 gm. of brass in the
basket, which, when worked out, gave the correct value of the
specific heat of the metal.

1 8ee Winkelniann, //</>,//.. II., _>, 328.

196 JENA GLASS.

The second basket wei- he. 1 :J 1'77 gm., and its water-equivalent
is accordingly to l>e taken as

2-184x3176
24-23

The weight P of water in the calorimeter was about 500 gm.

In this way determinations were made for 11 glasses, by ">
experiments for each ; and then for 7 glasses, by 2 experiments
for each. The difference between different determinations for
the same glass never reached 1 per cent. The column headed c
in the table of the next article contains the means of these
determinations. Winkelmann estimates their uncertainty due to
constant sources of error at 0*6 per cent, as a maximum.

88. Calculation of specific heats from chemical composition.
If the thermal capacity of a glass were the sum of the thermal
capacities of its constituent oxides, its specific heat c could be
calculated by the formula

2 denoting " the sum of such terms as," p t the percentage of
any oxide, and c t its specific heat.

For the first seven oxides of the list in Art. 67, the specific
heats were determined by Kegnault, for intervals of temperature
roughly identical with those employed by Winkelmann. The
values published by Eegnault 1 are,

Sp. heat. Interval.

Si0 2 '1913 13 99

B 2 3 -2374 16 98

ZnO '1248 17 98

PbO -05118 22 98

MgO -2439 24 100

A1 2 3 -2074 8 98

As 2 5 -1276 13 97

The value given for A1 2 3 is the mean of Kegnault's values
for corundum and sapphire, '1976 and '2173.

l Ann. de Chim. et de Phya. (3), 1, 129 (1841).

THERMAL PROPERTIES OF GLASS. 197

No direct detenu inations are known for the other seven
oxides. Winkelmann calculates their specific heats on the basis
of Wostyn's law that one and the same chemical atom, in its
various solid combinations, has always the same atomic heat,
and arrives at the following values:

Sp. heat.

BaO -06728

Na 2 O L ) o74

K,0 'I860

Li 2 O -5497

Cab -1903

P 2 O 5 -1902

M~ii 2 3 -1661

The atomic weight of oxygen is taken as 16, and its atomic
heat in solid combinations as 4'2 (Wiillner's value). For chlorine
3 5 '5 and 6 '2 6 are taken. The following data are also employed :

The atomic weight of barium is 136*8, and the sp. heat of
barium chloride, as determined for the interval 14 to 98 by
Eegnault, is '08957.

The atomic weight of sodium is 23 ; the specific heat of
sodium chloride between 14 and 99 is '2140 according to
KeL r nault. The specific heat of sodium has only been determined
between - 28 and +6.

The atomic weight of potassium is 39 ; the sp. heat of
potassium chloride between 14 and 99 is '1729 according to
Kegnault. The sp. heat of potassium has only been determined
between - 78 and 0.

The atomic weight of lithium is 7, and its sp. heat between 27
and 99 is "9408 according to Kegnault.

The atomic weight of calcium is :'.'.)-9. Its sp. heat between
and 100 is -1804 by Bunsen's determination. Hence '2039
i- deduced as the sp. heat of calcium oxide. On the other hand.
Kegnault found '1(>42 as the sp. heat of calcium chloride In 'tween
23 and 99; whence the value *1767 is deduced for the oxidr.
The in- an "t the two values is 1 90S,

'l'li- ntnniir Wright of phosphorus is :U. For the sp. heat of

tin* salt \\l\0 7 between 11 and 98, Regnault found '08208 ;

that of the oxide 1*1)0 is given above; hence follows -1789 for

oxide I' 2 6 . On the other hand, Kegnault found -L'L's.'l as

198 JENA GLASS.

the sp. heat of the salt N a ,I'.,<> 7 between 17 and 98; whence,
with the help of the above value for Na 2 O, the value '1941 is
deduced for P 2 6 . Lastly, Regnault found '1910 as the sp. heat
of K 4 P 2 7 between 17 and 98, which, with the above value for
K 2 0, gives "1975 for P 2 O 5 . The mean of the three values is
1902.

The atomic weight of manganese is 54'8. For its sp. heat
between 14 and 97, Eegnault found '1217; this leads to -1G46
for Mn 2 O 3 . Again, Regnault found '1570 for MnO between
1 3 ami" 98; this leads to '1676 for Mn 2 3 . The mean of the
twu is -1661.

AN' hen Winkelmann compared his observed values for the
glasses with the values calculated by the formula at the
beginning of this article, from the values of c { above adopted for
the constituent oxides, he found differences of more than 2 per
cent, in the case of the glasses 1, 2, 9, 11, 16. Four of these
(1, 2, 11, 16) are distinguished by large percentages of boric
acid. Hence he suspected that the sp. heat assigned to B 2 3
in the calculations was too large. To decide the point, a new
determination of the sp. heat of boric acid was made, and
this confirmed Eegnault's result.

But Regnault determined also the specific heats of four salts
of boric acid ; and Winkelmann deduced from each of these a
determination for the acid, with the following results, including
the one previously employed :

2374 from direct observation on boric acid.
2158 from the value '09046 for PbB 2 4 .
2153 -1141 PbB 4 7 .

2421 -2197 K 2 B 4 7 .

2252 -2382 Na 2 B 4 O r

The mean of the five is -2272.

Employing this value instead of '2374, without changing the
values for the other constituents, he obtained the values given in
the column headed c' of the following table. The differences
between the observed values c and the calculated values c are
given in the next column, expressed as percentages of c; they
amount on the average to about 1 per cent. The much larger differ-
ence for the first glass is probably due to the content of lithium in

THERMAL PROPERTIES OF GLASS.

199

the glass being overestimated, as the lithium oxide appears not
to have been dry when weighed. The last column contains the

c-c'

s. c

231 S

2415

-4-2%

2-238

5188

2182

2192

-0-5

2-243

4894

-jnsti

20SO

+ 0-3

2-424

5056

2044

2040

+ 0-2

2-480

_>>:is

2049

-0-5

2-370

4830

1988

1983

+ 0-3

2-585

5139

1958

1964

-0-3

2-479

4854

1907

1888

+ 1-0

2-629

5013

1901

1944

-2-3

2-588

4920

1887

1893

-0-3

2-518

4751

1644

1668

-1-5

3-527

5798

1617

1626

-0-6

2-848

4605

1589

1573

+ 0-9

3-070

4878

1464

1439

+ 1-0

3-238

4740

1398

1379

+ 1-4

3-532

4938

1359

1344

+ 1-1

3-691

5016

1257

1272

-1-2

3-578

4498

08174

08201

-0-3

5-831

4766

products of the specific heats by the densities (from his own
determinations). They represent the thermal capacities per unit-
volume, and show only a rough approach to constancy.

89. Observations on the conductivity of glasses of various
compositions were made by 0. Paalhorn in the Physical Institute
of the University of Jena. 1 The investigation included the
15 glasses numbered 69 to 83 in Winkelmann's list (Art. 67).

The observations were taken with the aid of an apparatus
introduced by C. Christiansen 2 under the name of " conducting
column," arranged in the form in which Winkelmann used it for
his researches on the variability of the conductivity of gases with
tempera! i

[Conductivity is usually determined by measurement of the
temperature-gradient in the conducting body, and of the heat

1 Dictation, Jena, 1894.

Man. d. Phy*. u. Ckrm., 14, 23 (1881).

Mnn. d. Phy*. u. Chem., 29, 68 (1886).

200 JENA GLASS.

transmitted through it in a given time. The conductivity is
tluMi dedm-ed by means of the relation:

tlux of heat = gradient x conductivity.

Thf chief peculiarity of Paalhorn's method was that, instead of
directly measuring the transmitted heat, he inferred its amount
t'mm previous knowledge of the laws of transmission of heat
across a layer of air separating two plates at different tempera-
tmvs. Our account of these experiments and their reduction is
very much condensed from the German.]

The conducting column consisted of three copper plates, with
two other substances filling the two gaps between them ; one of
these substances being air and the other the glass to be tested.
The copper plates were circular, each of them being 11 cm. in
diameter and 1'503 cm. thick, and were gilded. They were
placed horizontally one above another; and each of them had a
hole bored horizontally in the middle of its thickness for the
insertion of a thermometer; these holes being 5 '2 cm. deep and
0'6 cm. in diameter. The thermometer for the lowest plate was
divided to fifths of a degree from - 3 to +35; that for the
middle plate, to tenths of a degree from 9 to 42. For the top
plate there were tw r o thermometers, one divided to fifths from
33 to 75 and the other to tenths from 69 to 100. All four
were of Jena glass, were of suitable shape, and were compared
with a standard thermometer. They all projected from the
copper plates on the same side of the column, so that their stems
were one above. the other.

Between the topmost copper plate and the middle one there
was a layer of air of the thickness of either "023458 cm. or
048088 cm., the plates being kept apart by the insertion of
three tiny plates of glass about 1 sq. mm. in area, having either
the former or the latter thickness.

Between the middle and lowest plate was the glass disc to be
tested. It had the same diameter as the copper discs, and was
about half a centimetre thick. The transfer of heat between the
glass disc and the copper discs, which were pressed against it, was
found to be facilitated by covering the plate with a thin layer of
glycerine.

The " conducting column " was contained within a sheet-iron
box of square section. The central portion of the base of the

THERMAL PROPERTIES OF GLASS. 201

box consisted of a brass plate of 16 cm. diameter soldered in.
The column stood on this brass plate in such a position that
the stems of the thermometers in the three copper plates
\\vre in a diagonal plane of the box. The under-side of the
brass plate could be kept cool by allowing a jet of water to play
against it In the sides of the box there were glass discs
inserted, serving as windows ; and in the top there was a round
hole filled by a cylindrical brass vessel, whose bottom (made
truly plane) rested on the top of the first copper plate, which it
exactly fitted. Into this brass vessel steam iould be brought
from a generator at a sufficient distance.

In addition to the thermometers above mentioned, there were
three horizontally placed thermometers inside the iron box, at the
level of the middle copper plate, their purpose l)eing to determine
the temperature of its surroundings. One had its reservoir close
to the column, one midway between the column and a side of the
1 MIX, and the third in a corner near one of the glass windows.
They were divided to whole degrees.

Each experiment began by letting in steam to the brass vessel
at the top of the column. As soon as increase of temperature in
the middle copper plate appeared, the water jet was allowed to
play against the bottom of the brass plate on which the lowest
copper plate rested. The highest and lowest copper plates soon
acquired their permanent temperatures. The middle plate
changed its temperature, first quickly, and then more and
more slowly. When it ceased to change, regular readings
were begun.

90. Reduction of the Observations. Since the temperatures
are steady, the middle copper plate receives just as much heat as
it gives out. This fact is expressed by the equation

L denoting the heat which it receives by conduction.

S liy radiation.

/ the heat conducted from it to the lower plate.

o> its loss by air-contact and radiation to the surroundings

of the c>limm.
cr the loss by air-contact and radiation from tin- -lass plate.

*>:> JENA GLASS.

91. In one experiment, which may be taken as a sample, the
following permanent temperatures were observed :

^ = temp, of top plate = 96'13 ( !,

* 2 mi.l 58-29.

t s lowest,, 13-75.

t 4 air around column = 20 '3.

Thickness of glass plate, 1-075 cm.

air layer, -048088 cm.

From these were derived by calculation :

L 4*8 1 therms per second.

S= -02318

= -29329

<r= -13944

Hence I is found by (1) ; and by the help of formulae for the
transmission of heat across a layer of air, the value 20'156 was
obtained for the relative conductivity k at the temperature
J(^ + *.,)= 36-02. This is to be multiplied by the absolute
conductivity of air at the temperature of the air layer, which is
about "00006, giving '00121 as the absolute conductivity at 36.

The value finally adopted for the absolute conductivity K of
the glass in question (the lead silicate glass 69) at 25 C. was
001083.

Experiments conducted in the same way gave for glass 79
(a silicate containing soda and zinc oxide) at the same tempera-
ture, JT= -001931.

92. Several comparative observations were made by inserting
one of two glasses between the first and second copper plates,
and the other between the second and third ; the formula
employed being

L = l + w , (3)

which reduces to

ij <*!-<>- (,-,)+-oooi64j( 1 -< 4 r' 1 ; (*>

JTj and d l being the conductivity and thickness of the upper glass
plate ; K, d of the lower ; I) the thickness of the middle copper
plate ; R the common radius of the plates. For results, see the
next article.

THERMAL PROPERTIES OF GLASS.

93. Relation to Chemical Composition. Paalhorn's values
for the absolute conductivities (in C.G.S. units) of the glasses which
he tested (namely the 15 glasses 69-83 in Winkelmann's list,
Art. 67), are given in the following table, under the heading
" observed." They are for temperatures not differing much from
25 C.

K in gm. cm" 1 , sec' 1

Ob8.-Calc.

Observed.

Calculated.

401063

001094

- 1%

001304

001324

- 2

71=27

001409

001406

7-j

001433

001379

+ 4

001445

001572

- 9

001470

001401

+ 5

7.-, = 23

001610

001511

+ 6

001650

001479

+ 10

001832

001661

+ 9

001861

001879

- 1

001931

001954

- 1

80=5

002267

002092

+ 8

001938

001905

+ 2

ooi !:_'

002024

- 3

001952

001954

Paalhorn adopted, on the basis of these results, a set of
coefficients for expressing the absolute conductivity of a glass as
a linear function of the percentages of its constituent oxides ;
and Winkelmann subsequently suggested changes in the co-
efficients for B 2 S , ZnO, MgO, BaO, which brought the results
into closer agreement with observation. The following are the
coefficients as thus altered :

SiO,

ZnO
PbO
ligO

A1A

0000220

150

100

200

As 2 6

BaO

Na 2 O

CaO

- -0000020
100
160
10
320
160

These are the coefficients employed in deduein^ the above values
headed "-Calculated."

-J. ' i

JENA GLASS.

94. Relative determinations by Isothermals. W. Voigt,
improving on de Srimrmont's plan of exhibiting the unequal
conductivity in different directions of crystalline plates, has
shown that isothermal lines on the surface of a plate can be
made self-recording by covering the plate with a thin coating of
puiv elaidinic acid to which certain proportions of wax and
turpentine have been .added. The elaidinic acid has a definite
melting pnint of about 45 C., and, in solidifying from the melted
state, is deposited in minute crystals, which form a remarkably
tine and clear line of demarcation. 1 After employing the method
for comparing the principal conductivities of a crystal, he adapted
it in the following way to the comparison of the conductivities of
two isotropic solids, and thus obtained comparisons between three
.Jena glasses, nearly identical 2 with Winkelmann's 19, 20, 21.

Two equal plates ABC, CD A (fig. 21), of different glasses,
each having the form of a right-angled triangle, are cemented

Fi.i. I'l.

together along their hypotenuses, so as to compose a rectangular
plate of uniform thickness. The ratio of the length and breadth
may with advantage be about the ratio of the conductivities.

The rectangular plate, with a very thin uniform coating of the
mixture, is set upright with one end AB (belonging to the better

1 Winkelmann, Handb., II. 1, 301.

* Ann. d. Phys. u. Chem., 04, 95 (1898).

THERMAL PROPERTIES OF GLASS.

205

conductor) resting on an amalgamated block of copper heated to
something between 70 and 90 C. The line of melting EFG
will gradually advance ; and when it has attained its permanent
position, the angles CFG = <f> v and AFE=<p are to be
measured. If the experiment has been skilfully performed, the
two lines EF, FG will be very straight and clear, permitting of
determination of the angles to a fraction of a degree. As an
uncertainty of J of a degree in the angles entails an uncertainty
of about 2 per cent, in the ratio of the conductivities, the method
makes a reasonable approach to accuracy.

The line of melting is an isothermal line (having the uniform
temperature of the melting point) ; and the lines of flow of heat
are perpendicular to it ; hence <j>j_ and <f> 2 are the inclinations of
the lines of flow in the two plates to the normal to the surface

Km. I"-'

of junction (that is to the line marked n in fig. 22); and, by the
general law 1 for change of direction of lines of flow in passing
from one isotropic body to another of different conductivity, we
have

tan

,(5)

|_Let F denote the flux of heat at any point of a solid conductor, and the
angle which it makes with the normal to the surface of junction with another
conductor. The component flux along the normal is Fcos^and the component
flux parallel to the surface of junction /*sin0. The former has the same value

-jot;

JENA GLASS.

The three glasses were combined two together in each of the
three possible ways, the triangles being isosceles, so that the plates
were square. Each plate furnished two observations ; heat being
iipplitnl first to the one side and then to the other of the better-
conduetini: triangle. Fig. 23 represents one of the square plates

Fio. 23.

magnified about three times. The lower side and the right side
are those to which heat has been applied. The cooling was
effected very slowly, and the crystals formed were consequently
large. The lines of melting were remarkably fine and sharp ; an
inadequate idea of their sharpness is given by the representation.
The following were the angles (fa and < 2 ) observed in these
six determinations :

44.40

49-1

257
31-6

44-8 ; 36-0
45-1 37-0

45-6

34-8

47-0

37-1

on both sides of the junction (otherwise the temperature of the junction would
not remain steady) ; and the latter varies directly as the conductivities (since
the temperature-gradient along the junction is common to the two bodies). We
have thus the two equations

which, by division, give

THERMAL PROPERTIES OF GLASS.

907

The values of the ratio K^K* resulting from these determina-
tions, according to equation (5), are given in the following table ;
the values headed a being derived from the upper, and those
headed b from the lower line of the above table.

Observed.

i *

*( + *)

19:20

2-035 | 1-877

1-956

1-947

19:21

1-367

1-332

1-349

1-355

21:20

1-469

1-418

1-443

1-450

J (a + b) is the mean of the two directly observed values of the
same ratio. The values headed " Calculated " are the values of
each ratio as computed from the other two. The agreement is
very close.

Using Paalhorn's determination "002267 of the value of K for
the glass 19 = 5, we derive from the above values of ^

001159
001680

It is, however, to be remembered that the glasses employed by
Voigt (from which the ratios were derived) were not quite
identical with Winkelmann's 19, 20, 21.

95. Isothermal Method extended to 25 Glasses. More
recently Th. M. Focke, 1 on the suggestion and with the assistance
of Voigt, has applied the method of isotherms to the 25 Jena
glasses numbered (by Winkelmann) 19-33, 38, 86-94. To
deduce their absolute conductivities, he determined, by a method
which had been suggested by Voigt and employed by 0. Venske 2
for some preliminary measurements, the absolute conductivity
(which we shall call J5f ) of a specimen of plate glass, and found
it to be

# A = -002454.

' Ann. d. Phy*. v. Chem., 67, 192 (1899).
'GottingerNachrichren, 1892, 121.

Inaug. Dissert. (Jottingen.

.IKNA GLASS.

Comparisons weiv made, by the method of isotherms, between
this glass (of relatively high conductivity) and each of the 25 ;
also (as a duvk) between each of the 25 and one of the others.

The double plates were square, and of from 2 to 4 sq. cm. area.
They \\ere wunneJ on i water bath, coated very thinly with
shellac, and then with the melted mixture of elaidinic acid and
wax. The shellac caused the acid mixture to adhere better. As
soon as a plate was coated, it was cooled on a metal stand ; the
being effected quickly in order that the crystals formed
be small. The plate after cooling was pressed at one of
its edges against a block of copper at 60 or 80 C. When the
melting had advanced about 4 mm., the plate was removed from
the heater and cooled slowly. As the crystals formed during
-low cooling were large, there was a well-marked distinction
between the part that had melted and the part that had not.

For measuring the two angles <f> lt <p 2 (fig. 24) made by the
two isothermals with the diagonal, a Norremberg polarisation

;. -24.

apparatus was used, the analyser being replaced by a small
telescope with well centred crosswires. The plate was laid on
the stage of the apparatus, and illuminated by reflection from a
small mirror below. When the flow of heat was from the better
conducting half to the worse, the isotherms were nearly straight
and the measurement was easy. When it was from the worse to
the better conductor, the isotherms were curved and the measure-
ment was more difficult. After some practice, however, it was
fnund possible to make fairly accurate measurements, even in
this case.

Reduction of the Experiments. Fig. 24 shows the two
cases. In case a, which we shall call " the first arrangement,"
the flow of heat across the diagonal has been from the better
to the worse conductor. In case b, which we shall call " the

THERMAL PROPERTIES OF GLASS. 209

second arrangement," its flow across the diagonal has been from
the worse to the better conductor.

The first measurements were all made with the first arrange-
ment. In some cases, in which the difference of conductivity
was small, both arrangements were employed, and it was found
that the second arrangement gave a ratio of greater inequality
than the first, the discrepancy averaging about 10 per cent.
Also, when two glasses were compared with the standard glass
and with each other, the results were generally inconsistent.
' For example, glasses 2 1 and 9 1 gave

K 2l /K = -802, K Ql /K = '903,
giving, by division,

whereas direct comparison gave '798.

Attempts to explain and remove these discrepancies 1 were not
very successful ; and a compromise was made by adopting, instead
of tan 0j/tan <f>. 2 given by the first arrangement, or tan c^'/tan^'
given by the second arrangement, the intermediate value

K 2 tan 2 + tan 2 ' '

The Results are collected in the following table. The first
column gives the designations of the two glasses which compose
a double-plate. The second column, headed " Observed," gives
the mean values calculated by equation (6). Each set of three
consecutive comparisons consists of comparisons of two glasses
with the standard, followed by their direct comparison with each
other. The discrepancies, if examined, will be found to be small ;

[' If K denote the conductivity of the intervening shellac ; a, /3 and a', ' the
angles made by the isotherm in the shellac with the surfaces of the plates
in the two cases ; theory gives

whence = tan tan^ten

A , tan 0, tan a tan 0., tan a

It is suggested that, owing to irregularity in the shellac (which showed numerous
bubbles), the alternate angles were not equal, but a</9, and a'>/3'. The two
values obtained for KJK 9 would then be unequal. We have omitted fig. 25,
which illustrates this point.]

210

JENA GLASS.

and Focke has smoothed his results by ascribing equal errors to
each of the three comparisons. The smoothed values thus
obtained are given in the column headed " Calculated." This

PUte

Ob..

Calc.

HIOOA*

M.O

0-831

o*a

2-041

25.0

1-001

1-000

2-458

23.25

0-831

0-832

31.0

0-737

0-741

1-819

s: . o

1-062

1-056

2-591

31.87

0-846

0-837

21.0

0-850

u-857

2-103

91.0

0-986

0-978

2-399

21.91

0-884

0-877

27 .

0-807

0-805

1-974

89.0

0-971

0-973

2-387

27.89

0-825

0-827

20.0

0-649

0-650

1-595

90.0

0-968

0-967

2-372

20.90

0-673

0-672

22.0

0-780

0-785

1-927

93.0

0:898

0-904

2-222

22.93

0-886

0-880

24.0

0-835

0-833

2-044

Plate

Obs.

Calc.

1000 K

94.0

1-015

1-017

2-495

24.94

0-818

0-819

26.0

0-816

2-003

29.0

0-982

0-981

2-407

26.29

0-833

0-832

30.0

0-860

0-867

2-128

88.0

1-027

1-019

2-499

30.88

0-859

0-852

32.0

0-811

0-822

2-016

38.0

1-008

0-995

2-442

32.38

0-836

0-826

33.0

0-698

0-699

1-715

92.0

1-005

1-002

2-462

33.92

0-698

0-697

19.0

1-111

1-105

2-712

28.0

0-915

Of 25

2-269

28.19

0-846

0-837

86.0

0-896

0-892

2-189

86. 19

0-804

0-807

description does not apply to the last five comparisons in the
table, which relate to the last three glasses and have been
smoothed by the method of least squares.

The entries in the last column, when divided by 1000, are the
absolute conductivities (of the first named glass in the first
column). They are found by multiplying the smoothed values by
2*454, which is 1000 times the conductivity of the standard glass.

Influence of Chemical Composition. In continuation of
Winkelmann's list (Art. 67), the following table is added for
the three glasses 92-94 :

SiO,

B 2 S

ZnO

Al a 3

AsA

Na-jO

K 2

sbA

65-9

23-5

0-8

6-3

3-5

53-5

20-0

6-5

20-0

63-37

11-0

12-0

4-0

0-6

9-0

THERMAL PROPERTIES OF GLASS.

211

Focke, in deducing from his results a linear formula for the
conductivity of a glass in terms of the percentages of its
constituents, obtained the coefficients given in the last column
of the following table. The coefficients obtained by Paalhorn
and by Winkelmann (see Art. 93), are prefixed for comparison :

Oxide.

Paalhorn.

Winkelmann.

Focke.

SiO a

22.10- 6

22. 10- 6

31-56. 10'

20-02

ZnO

12-05

PbO

12-40

MgO

8-2

8-4

37-13

A1A

25-89

-131-7

BaO

12-59

NajO

7-03

K 3

5-98

CaO

9-46

SbA

2-82

Focke's coefficients give fair agreement with observation for each
of the 25 glasses, as is seen by comparing the column headed
" Calculated " in the following table with the preceding column,
which contains the observed values. The last column contains
the differences (observed calculated) expressed as percentages.

No.

1000 JT

Calc.

Diff.

J7I

_':_'

-o%

1-60

1-62'

-1

2-10

J !.{

-1

1-93

1-94

-1

2-04

1 <>x

+ 3

2-04

2-00

+ 2

2-46

_' U

+ 1

2-00

1-95

+ 3

1-97

2-27

2-32

-a

j Jl

2-42

-0

_' i::

2-09

+ 2

1 s-j

1-82

No.

1000 K

Calc.

Diff.

2-02

2-08

-3%

1-72

1-75

-2

2-44

_' is

-2

2-19

J-f><

J is

_>:,<>

2-49

-HO

148

2-36

+ 1

849

_'!_'

-2

2-40

i-48

-4

2-46

B-00

-2

2-22

2-18

+ 2

250

+ 2

21-2 JENA GLASS.

Comparison with Paalhorn's Values. In the case of the
three glasses 19 (also called 5 and 80, see Art. 67), 23, and 27>
dirert nunparison is possible between Fucke's values and Paal-
horn's, and is given in the following table. The last column
contains their differences expressed as percentages of Paalhorn's.
values, Focke's values being the larger in every case.

Glass. Paalhorn. Focke. Diff.

19 -002267 -002712 20
23 1610 2041 27
27 1409 1974 40

Besides the large average excess of Focke's values over Paal-
horn's (about 30 per cent.), there are large differences in their
ratios; for instance, K^jK^ is T61 according to Paalhorn, and
1*37 according to Focke. Winkelmann has shown 1 that it is.
not easy to decide which of the two sets of results is the more
correct ; and that there may be genuine differences, depending
on differences in the temperatures of observation.

Conductivity and Index of Refraction. Finally Focke
determined for 22 of the glasses the index of refraction for
sodium light, and compared them with the conductivities to see
if any connection could be found between them. The results
were in the main negative, though, on the whole, the worst
conductors had the highest indices.

96. Another way of Computing Conductivity from Chemical
Composition. In place of the mode of computation employed
in Art. 93, Winkelmann has recently adopted another with better
success. Instead of the percentages by weight a lt a 2) ..., lie
introduces the percentages by volume b lt Z> 2 , ..., and determines.
the coefficients a^, x 2 , ..., in the formula

for the reciprocal of the conductivity.

Let v lt v z , ... denote the volumes, and z lt z 2 , ... the specific
gravities of the constituent oxides in the condition in which they

1 Ann. d. Phy*ik u. Chem., 67, 794 (1899).

THERMAL PROPERTIES OF GLASS.

213

exist in the glass (see Art. 68), w lt w. 2 , ... being their weights;
then we have v l = wj^, v 2 = w 2 /z 2 , etc., and

Too

(2)

Hence b ly 6. 2 , ... can be calculated from the values of a in
Art. 67, combined with the values of z in Art. 68.

The following values of x have been deduced by Winkelmann
from Paalhorn's observations (Art. 93):

Si0 2 = 3-4
B 2 3 = 6-6
ZnO =15-0
PbO =16-0

MgO = 5-0
Al,0 3 = 2-5
As 2 5 = 3-0
BaO =13-0

Na,0=10'5
K 2 6 =13-3
CaO =6-0
PA = 6-7

The values of K obtained by employing these coefficients in
the formula (1) for \JK are given in the following table, under
the heading "Calculated"; and they do not show any large
departure from the observed values :

A' in cm" 1 . 7 sec' 1

Difference.
Obs.-Calc.

Observed.

Calculated.

0-001083

0-001067

+ 1%

1304

1361

-4

71=27

1409

14MS

:-'

1433

1495

-4

1445

1524

-5

1470

1416

+ 4

75 = 23

1610

1637

-2

1650

i:.s-_>

+ 4

1832

1764

+ 4

isiil

1919

-3

1932

-0

80=5

2267

Jl's

+ 3

1940

L9M

+ 1

1972

-3

1 <.-,_>

1946

Derivation of Formula (1). Winki'lmaim was led to
formula (1) by considerations which may be put in the following
shape : let there 1>e any number n of successive parallel layers

214

JENA GLASS.

A, B, etc. (fig. 26) with steady flow of heat perpendicularly
through them. Let their thicknesses be d lt d 2 ... d n ; their

Fio. 2U.

conductivities K ly K^ ... K n ; the temperatures of their junctions
t lt t 2 ... t n _ lt and of the first and last surfaces T, t.

The flux of heat F per unit area will be the same for all the
layers, and is given by

Tt t t

(3)

Hence we have

Tt=^ l F' tt= 2 F ' t t = - n F-
and by addition,

If the layers were replaced by a single uniform layer of the
same total thickness D, and of such conductivity K as to give
the same flux of heat F, we should have

T-t-^-F
~K*

T t

Equating the two values of - , we have

d n

THERMAL PROPERTIES OF GLASS. 215

which is equivalent to (1), since ^100 is the volume percentage
of the first layer, ^100 that of the second layer, and so on.
These being the values of b lt &>, ..., we must have

and so on.

97. Coefficient of Cubical Expansion of Glass ; and its
Dependence on Chemical Composition. The cubical expansi-
bilities of the glasses 39-68 in Winkelmann's list have been
determined by Winkelmann, Straubel, Pulfrich, and Weidmann ;
and the results have been published by Schott 1 together with the
chemical compositions of the glasses. The following table contains
the coefficients thus determined. The first column, headed W y
contains Winkelmann's numbers for the glasses ; the second
column, headed B, the observer's name abbreviated ; the third
column, headed M, indicates the method of observation, A
denoting the Abbe-Fizeau method, 2 and D, Dulong and Petit's
method, by filling a glass vessel with mercury. 3 The letters in
the next column, headed K, indicate the mode of cooling of the
glass from the red-hot condition, denoting the cooling-oven,
L open-air cooling, R fine-cooling in the thermo-regulator. The
column headed " Interval " gives the initial and final tempera-
tures ; and it will be noticed that their mean is, in every case,
not far from 50 C. The coefficient of linear expansion being
denoted by a, the coefficient of cubical expansion is 3 a, and its
values multiplied by 10 7 are given in the next column, headed
" Observed," the order of arrangement being from the least to the
greatest. Schott remarks that the differences are much larger
than in the case of ordinary glasses.

There are not many bodies with such small expansibility as
tin- zinc borate glass No. 39; on the other hand the alumina glass
No. 68 is nearly as expansible as iron and nickel.

1 Vorlray im Verein zur Btf&rd. d. Gcwtrb/bi9es t Berlin,
\\inkelm., Handb. 11.2,54.

Wink.-lin.. llnn.n,. II. '2,48.

216

JENA GLASS.

Schott has also investigated the dependence of expansibility on
chemical composition ; and has pointed out the influence of the

Interval.

3a x 10 7

Diff.

Obs.

Calc.

39=11

10 J '35-92-88

110

+ 0%

40=12

> i

12-67-89-78

137

149

- 9

41=21

7-16-91-8

157

175

-11

Wd.

0-100

161

162

- 1

168

44 = 36

177

194

-10

45 = 2

14-4 -94-4

202

191

+ 5

15-7 -92-2

236

244

- 3

12-9 -97-6

238

241

- 1

18-9 -93-1

238

220

+ 8

17-5 -94-9

239

240

19-8 -94-5

241

251

- 4

51=6

14-6 -92-2

241

254

- 5

18-7 -90-5

265

272

- 3

53=13

20-3 -92-2

261

246

+ 6

9-95-93-3

270

240

+ 11

1 5

15-65-94-2

271

263

+ 3

17-9 -97-2

275

254

+ 8

17-7 -92-7

279

295

- 6

58=20

24-5 -84-0

280

256

+ 9

0-100

290

284

+ 2

17'0 -95-5

289

263

+ 9

0-100

292

314

- 8

300

294

+ 2

f 9

806

289 +5

> J

305

294 + 4

314

327 - 4

j i

324

319 + 2

.328

330

- 1

17-8 -9<i-.->

337

355 - 5

alkalis in promoting expansibility. He remarks, in connection
therewith, that sodium and potassium are highly expansible
metals.

Winkelmann and Schott have since published l the following
coefficients by which the percentages of the constituent oxides

l Ann. d. Phys. u. Chem., 51, 735 (1894).

THERMAL PROPERTIES OF GLASS. 217

are to be multiplied, in order to obtain, by addition, the value of
1 7 times the cubic expansibility 3a :

Si0 2 =0-8 BaO = 3'0

B 2 3 =0-1 Na 2 =10-0

ZnO =1-8 K 2 6 = 8-5

PbO =3-0 CaO = 5-0

MgO =0-1 P,0 5 = 2-0

A1 2 8 = 5-0 LU) = 2-0
As 2 6 = 2-0

The arrangement in order of magnitude, beginning with the
largest, is N^O, K 2 0, CaO, A1 2 O 3 , BaO, PbO, As 2 5 , Li 2 0, P 2 5 ,
ZnO, Si0 2 , MgO, B 2 O 8 .

The column headed " Calculated " contains the results of
employing the above coefficients in conjunction with the list
of percentages in Art. 67, which is taken from the first of the
two papers by Winkelmann and Schott mentioned at the be-
ginning of the article. An earlier list published by Schott, in
the paper mentioned in Art. 4, shows some slight differences ;
Mn._,O s in small quantities not exceeding 0'2 per cent, being given
as an ingredient of several of the glasses. Again, in the second
of the two papers by Winkelmann and Schott, there is a difference
in the case of glass 61, which, instead of 1/5 per cent, of A1 2 O 3 ,
is stated to contain 1'5 per cent, of B 2 3 . The calculated value
.'14 for this glass will be changed to 307 by this substitution.

The last column gives the difference (obs. calc.) expressed as
a percentage of the observed value.

98. Influence of Stress on Expansibility. Three of the
glasses, Nos. 44, .". 1 . r>6, were also tested for expansibility in
varying conditions of stress. The quicker a glass is cooled, the
greater is the stress left in it after cooling. In his paper,
mentioned in Art. 4, Schott expressed the view that, with
increasing stress, the coefficient of expansion probably increased
also; and adduced the following observations on these three
glasses in HU]I|M.M .,1' the view.

The largeness of the difference, in the case of glass 5(i ifl
attributed by Schott to the circumstance, that the solid glass
cylinders, employed in the AM'<> -Ki/.ruu observations, lui.l stronger
stresses in them than the thin-walled vessels, employed in the

-21$

JENA GLASS. .

l)ulon;_!-lViit nit'tlioil. The rapidly cooled cylinder which gave
the value is cut from a glass rod 20 nun. in diameter,

Observer. Method.

Cooling.

3a x 10'

Winkelmann

Dulong-Petit

Thermoregulator

171

Free air

177

Pulfrich

Abbe-Fizeau

Cooling oven

\Vinkelmann

Dulong-Petit

Free air

244

Pulfrich

Abbe-Fizeau

Thermoregulator

275

(See below)

289

which, after being drawn in the plastic state, was allowed to cool
in air. The following is a fuller account of its behaviour, as
observed by Pulfrich and quoted by Schott.

Its ends were originally ground perfectly flat, but, after the
cylinder had been kept for some time at 96 C., were found to
le distinctly concave, showing that the thermal expansion parallel
to the axis increased from the axis to the circumference.
Measurements made at different distances from the axis gave

Distance, i 3a x Id 7

mm
7'5
10

302
327

AY hen the cylinder had cooled down, the ends were still concave.
After being again ground flat, they remained flat after three-
hours 1 immersion in boiling water; and a determination made in
the usual way gave 3 ax 10 7 =289.

The cylinder, with its ends still plane, being then immersed in
oil at 200 C., again showed concavity at the ends. The concavity
was sensible after five minutes, and after an hour became constant.
Similar results were obtained with other glass cylinders.

These experiments show, as Schott remarks, that a permanent
small deformation of the elementary portions of the glass is
possible at temperatures far below the softening point. Much
depends on the composition of the glass. A cylinder of the baryta-

THEKMAL PKOPERTIES OF GLASS. 219

borosilicate (free from alkali) numbered 12 =40 by Winkehnann,
and having the trade number 121 111 , preserved perfectly the
planeness of its ends after heating, although it was in a highly
stressed condition.

Schott suggests that phenomena of this kind play a part
in the change of zero of mercury thermometers, and that they
also explain the frequent failure of attempts to make truly
spherical vessels of stressed glass.

In previous investigations of the thermal expansibility of glass,
no precise information as to chemical composition has usually
been given. Regnault, however, in his research on mercury
thermometers, 1 gives the percentage composition 2 of the eleven
glasses whose expansions he determined. Four of the eleven,
though having the same origin and only slight differences in
composition, showed considerable differences in expansion. This,
as Schott remarks, can be explained by supposing that they had
been cooled under different conditions.

99. Change of Coefficient of Expansion with Temperature.
For one of the glasses included in Schott's list of Art. 97, namely
No. 52, Pulf rich's observations had shown a distinct increase of
the coefficient with temperature. He found

Interval.

SaxlO 7

4'8o to 18-7
18-7 to90-5

Fuller observations on the course of thermal expansion in
glasses from to 100 have been carried out by M. Thiesen
and K. Scheel, and at higher inn] .natures by E. Keimerdes.

Course of Expansion from to 100. Thiesen and Scheel's
observations 8 were taken at the KViehsanstalt, and relate to three
glasses used for the construction of high-class thermometers ;
namely, the French hard jjjlass known as rcrre dur, of which

1 Mtm. (UrAcad4mi>, Jl

'The particulars are given in full in Winkelinunn'a Handb. d. Phy*., II. 2. 62 ;
also in Schott's paper.
> Ztittchr. /. iMtnimentf id-wide, 1892. L"

-2i'.> JENA GLASS.

Tonnelot's thermometers are made, and the two Jena thermometer-
glasses numbered 44 and 51 in the list of Art. 67.
The vcrre dur had the following composition : 1

SiOj. MgO. AU0 3 . Na.,O. K,0. CaO.
70-96 0-40 1-44 12'02 0*56 14'40

The number given for A1 2 8 includes oxide of iron as well as
alumina. The glass is not very different in composition from
ordinary window-glass.

The specimens employed were capillary tubes a little more
than 1 m. long and about 5 mm. in external diameter, such tubes
as are used in making thermometers. A portion about 1 cm.
long at each end was reduced from the cylindrical to the heini-
cylindrical form by grinding away half of it ; and the flat surface
thus obtained was etched with five divisions half a mm. apart,
the central division being about 1 m. distant from the correspond-
ing division at the other end of the tube.

Three series of comparisons were made. In each series one of
the tubes was kept at a nearly constant temperature of about
25, and another tube, at the successive temperatures 0, 25, 50 C ,
75, 100, was compared with it. The tubes were kept at these
temperatures by floating them in mercury-troughs, each tube
being (by means of two corks) held down in immediate proximity
to the thermometer which indicated the temperature of the
mercury. The actual data of observation are given at length in
the published memoir.

For expressing the results, the formula

was employed. The mean coefficient of expansion from to f
is a + bt, and the true coefficient of expansion at t is a + 2bt.

The first calculations of the values of a and b were affected by
the circumstance that the periodic errors of the micrometer
screws had not been determined. A recalculation, after this
want had been supplied, led to the following values, which are
taken from a communication bearing the names of Thiesen,
Scheel, and Sell. 2 The first table is applicable when t is

1 Ber. d. Berliner Akad., 12 Nov., 1885 ; see Art. 111.

2 Witseiixck. Abkandl. der Keichsamtcdt, 2. 73 (1895); also Zeitschr. /.
Intrum., 16. 54 (1896).

THERMAL PROPERTIES OF GLASS.

221

expressed in degrees of the mercury thermometer of Jena normal
glass 16 111 . The second table is applicable when t is in degrees*
of the hydrogen thermometer.

MERCURY THERMOMETER OF GLASS 16 111 .

Mark

10*a

10" 6

591"

5655

0-272

16'"

708-9

387

Verre dur

738-fi

390

HYDROGEN Ti i K i ; M >.M ETER.

Mark

IWa

1086

59"'

r>6S-o

0-245

16"'

772-3

350

Verre dur

741-7

355

For the cubic expansions of the three glasses, there results

with A = 3a and =3(a? + b), giving, for the mercury-thermo-
meter scale,

Mark

10M

HfB

59"'

1696-4

0-82S

16'"

2306-6

1-181

Verre dur

2215-4

1-189

and for the hydrogen scale,

Mark

lo".-!

10"

1703-9

0-746

16 1 "

2316-7

1-071

Vfrrt dur

2225-2

l-os:i

It may be assumed that these values of expansibility include the-
thermal after-effect [Nachwirkung], as the rods were maintained

2-2-2

JENA GLASS.

for a considerable time at the temp* matures of observation before
the temperatures were taken

Normal Expansion and Principal Expansion. In the

nomenelature adopted l.y Thiesen, Selieel, and Sell, 1 the whole
expansion from to t is made up of two parts : the principal

ansion and the after-effect ; so that if At + Bt 2 is the full
nin<unt >t' expansion when sufficient time is allowed for the
after-effect to be completed (called the normal expansion), and it
A't + BP is the after-effect, then (A -A)t + (B- B f )t- is the
principal expansion [Hauptausdehmmg]. The constants A A'
and BB' are to be employed instead of A and B for computing
the expansions which accompany sudden changes of temperature.

Km ploying for the three thermometer-glasses the values of
A 1 and B\ given in next chapter (Art. 114), we obtain, for the
interval 100,

FOR HYDROGEN THERMOMETER SCALE.

Mark

IW(A-A')

IW(B-B')

59'"

1695-8

0-770

16 111

2306-5

1-022

Verre dur

2209-3

1-068

We may so far anticipate as to say that the determination is
made by comparing the volume after cooling to with the
original volume at 0.

Expansion of Glass from 40 to 220. The investigation
carried out by Keimerdes 2 related to the three glasses with the
trade names, O. 802, 0. 627, 0. 1552. Their chemical composi-
tions, which are here given, differ little, if at all, from those of
the glasses 5, 49, 28 of Winkelmann's list (Art. 67); so they
may also be designated by these numbers.

Mark

Si0 2

B 2 3

ZnO

A1A

AsA

BaO

NaaO

K,0

MnA

O. 802

70-83

14-0

5-0

o-i

10-0

0-07

0. 627

68-24

10-0

2-0

0-2

10-0

9-5

0-06

0. 1552

64-72

2-7

2-0

0-5

10-0

5-0

15-0

0-08

l Zeit*chr.f. In.-itrum., 16. 50 (1896).

2 Aufidehnunf/ des Quai*ze*. Dissertation, Jena, 1896.

THERMAL PROPERTIES OF GLASS.

The Abbe-Fizeau method was employed ; but instead of the
usual table with screw feet, which was found unsuitable, a quartz
ring was used as the comparison body. It was therefore necessary,
as a preliminary to the principal measurements, to determine the
course of expansion for the quartz ring. The determination of
this, from the temperature of the room up to 230, forms there-
fore the first part of the record. The mean linear coefficient a
for each glass was then determined for four (in the case of glass
49 for five) partial intervals of temperature, lying between the
extremes 40 and 220 or thereabouts.

Constancy of temperature was maintained by means of a
thermostat of the d'Arsonval construction filled with linseed oil,
its indiarubber membrane being replaced by a steel diaphragm.
Its performance was at first very good, but was gradually impaired
by repeated and long-continued heating to above 200; and in
the later observations on the glasses it did not afford sufficient
security for the desired constancy. An element of uncertainty
was thus introduced into the measurements. From the values of
a obtained directly from the observations, the values of a and b
in the formula

were deduced. The results are contained in the following table :

\v.

lO 8 **

102b

108a

Diff.

Obo.

Calc.

O. 802

510-4

0-482

34 -81

527

:>_>:_>

- 0-2

92-33

552

554-9

- 2-9

148-95

586

SttTl

+ 3-8

212-09

612

612-6

- 0-6

O. 627

724-9

I -010

88-99

764

764*8

- 0'8

55-10

782

780-6

+ 1-4

94-91

826

820*7

+ 5-3

151-25

879

877-7

+ 1-3

217-45

937

!44(i

- 7'6

O. 1552

ss7-i

1*101

87*16

!>_'

929-2

- 9-2

-._> in

1004

<l<)0 1

+ 13-6

151-12

KNil

1064*6

+ 6-4

212-34

111! 1 12-2-1

111

Each tempera tun- in the column headed / is the mean inn-

224 JENA GLASS.

perature of the interval to which the number standing opposite
to it in the next column (headed " Observed ") belongs. The
iiumlters under the heading "Calculated" are derived from the
formula a + 2bt.

100. Compensation Vessels. Schott has pointed out that it
is possible, by suitably combining an outer containing vessel of
hiirh expansibility with an inner displacing vessel of low ex-
pansibility, to obtain compensation of expansions, so that the
remaining volume is independent of temperature.

Let v l be the capacity of the containing vessel,

>-._, the volume of the displacer,
a p a 2 their coefficients of linear expansion.

Then the simultaneous increments of v l and v. 2 for a small rise
of temperature will be as a^ to a 2 v 2 ; and if these increments
are equal, the remaining volume will be unchanged. The
condition to be fulfilled may be written

the constant volume being v l v z .

By reversing this arrangement that is, by making a 1 greater
than a 2 , the changes in the remaining volume v 1 v 2 can be
exaggerated, and may even be made so great as to compensate
the expansion of a contained liquid. The condition for this, if
y denote the coefficient of expansion of the liquid, is

_
tj 3a 2

A suitable combination for either of these purposes would be
102 111 with 59 m or 121 111 , or, in Winkelmann's numbering,
68 with 44 or 40.

101. Compound Glass [Verbundglas]. In discussing the
unequal expansions of different glasses, Schott, in his paper of
1892, 1 gave some information respecting compound glass.
Experiments were made to ascertain how two glasses of different

1 Vortrag im Verein z. Befvrd des Gewerbfl., 4 April, 1892, p. 11.

THERMAL PROPERTIES OF GLASS. 225

expansibilities behave when one is superposed upon the other in
the blowing, so as to give a glass composed of two dissimilar layers.
The results showed that certain received views are only true
with a qualification.

"It has been an accepted rule with glass makers that, when
an article is built up of portions of material taken separately
out of the melting pots, all the portions must be of similar
composition, and if possible from the same pot. In the
cases in which it is necessary to unite two glasses of different
composition for instance, in making glasses with coloured
coatings, or glass tubes with streaks of white enamel, care is
taken to employ two kinds which have as nearly as possible the
same expansibility, in order to prevent the product from flying
to pieces in cooling."

" Some trials which I made for the purpose of deciding whether
two glasses of different expansions, if joined by laying one over
the other at the pipe, will always fly to pieces in cooling, showed
that the view hitherto prevalent is not altogether correct. It
was soon demonstrated that, by fulfilling certain conditions, it was
possible to unite even glasses with considerable differences of
expansibility. The main condition concerns the relative thick-
nesses of the two glasses."

Let A and B be two kinds of glass, with linear coefficients of
expansion a and ft, a being the greater. If they are welded
together when hot, so as to form two layers of a single plate,
then, when the plate has cooled, A will be in tension, and B in
thrust. If the double layer is drawn out into a thread, the
thread, as it cools, curls up, with A on the inside.

In general, the intensities of the stresses in a compound glass
are difficult to specify. They depend, not only on the coefficients
a and ft, but also on the moduli of elasticity and Poisson's ratios
of the two glasses, on the thicknesses of the two layers, and on
the form and dimensions of the vessel composed of them. The
vessel will fly to pieces if the tension in A exceeds the tensile
strength of A, or if the thrust in B exceeds the power of B to
resist crushing. As power to resist crushing is much greater
than power to resist pull, the layer A is generally the one that
breaks down; and to prevent this, it should be made thicker
thin the layer B. For example, if A is the "normal ther-
mometer glass" 16 ni , and B the thermometer glass 59 in , so that

-'.; JENA GLASS.

:*u = i>41 x 10' 7 , 3/3= 177 x 10" 7 , a tube or hollow vessel made
of the compound glass, with A outside and B inside, should have
the layer A from 10 to 15 times as thick as the layer B, to be
secure against flying to pieces in cooling.

If a lump of glass is heated till it is soft, and then quickly
cooled, the outside solidifies while the interior is still soft. The
subsequent complete cooling will produce thrust in the outer
layer, just as cooling produces thrust in the layer B of the
compound glass. Every layer in a state of thrust, no matter
how produced, will necessarily exhibit an enhanced power of
resisting pull; as well as greater power of resistance both to
scratching and to sudden cooling. The well-known properties
of the so-called toughened glass [Hartglas] fulfil this anticipation.
A layer in thrust in whichever way produced may therefore
be called a toughened layer.

When a lump of glass, by quick cooling, has covered itself
with a toughened layer, the interior of the mass must be in a
state of extension. Experience shows that, in quickly cooled
hollow vessels, the inner surface is in tension. Such a vessel
behaves as if it were of compound glass with A inside and B
outside.

A layer in tension, however produced, behaves in the opposite
way to a toughened layer. Its power of sustaining pull is
diminished, and a slight scratch or sudden chill suffices to make
it give way and to shatter the whole vessel. The so-called
Bologna phial is the most familiar instance. A glass layer in
this condition of permanent tension may very well be called a
sensitive layer [Sprengschicht].

Adopting these designations, we may say that the resisting
power of glass vessels against mechanical and thermal disturb-
ances is increased by covering them with toughened layers, and
diminished by covering them with sensitive layers.

In accordance with the above principles, there are two different
ways- of completely toughening glass vessels. One way is, to
employ a compound glass A . B, putting the less expansive layer
B inside, and to toughen the outside by rapid cooling in air. In
carrying .out this plan, uniform cooling of the whole surface is
essential ; any considerable inequality of stress in the surface
being an element of danger. The second plan is, instead of
toughening the outer layer A by quick cooling, to cover it with

THERMAL PROPERTIES OF GLASS. 227

a layer of smaller expansibility. The difficulty here is to make
this outer layer thin enough.

Schott has shown that both methods can be carried out, and
has applied the first to the making of boiling-flasks, beakers, lamp
chimneys, and water-gauge tubes for steam boilers. He states
that the boiling-flasks, when heated till aniline boils violently in
them (boiling point 184 G.), may be safely sprinkled with a fine
jet of cold water ; that the beakers can, without any protection,
be heated over a Bunsen flame without cracking; and that the
lamp chimneys, while doing duty over an Argand burner, can be
sprinkled inside with water without breaking.

It may seem strange that a toughened glass is able to bear
abrupt heating on one surface, seeing that such heating increases
the thrust already existing in the toughened outer layer. To
understand the reason, it must be borne in mind that, when
a glass originally free from stress is suddenly heated on one
surface, the effect is twofold: a toughened layer is formed on
the surface to which heat is applied, and a sensitive layer
on the other; and it is this other surface that gives way,
because power to resist compression is many times greater than
power to resist extension.

Compound Glass Tubes. Of the applications of compound
glass which have been introduced subsequently to this first
announcement, the most important is the construction of water-
gauge tubes for steam boilers. Glass tubes which have been
so slowly cooled as to be free from stresses cannot be used for
this purpose ; for the heating of their inner surfaces by the water
of the boiler converts their outer surfaces into sensitive layers,
which would give way on the contact of a drop of cold water
and would be even endangered by a draft of air. On the other
hand, tubes merely toughened externally by quick cooling, if not
excessively thin, have an extremely sensitive layer at their inner
surfaces. The compound glasses with both surfaces toughened,
introduced by Schott, 1 satisfy in a high degree the requirements
of practice. Their power of withstanding changes of temperature
is so great that they may be heated in oil to 200 or 230, and
immediately plunged upright into cold water, without flying.
According to tests made at the Reichstanstalt, they may be
sprinkled with drops of cold water when their internal tempera-

1 German patent 61573.

22S JENA GLASS.

ture is 200. Another good quality is, that they are only in
the very slightest degree liable to be chemically attacked by hot
water, as the inner layer consists of the thermometer glass 59 m ,
wliirli has very great power of resisting the action of water.

Compound tubes of this kind are also found serviceable for
combustion tubes ; as they can stand great pressure, and may,
without preliminary heating, be played upon by the flame of a
blast furnace.

102. Power of Withstanding Inequality of Temperature.
Coefficient of Thermal Endurance. If a homogeneous piece
of glass, free from stress, is suddenly subjected to changes of
temperature which do not extend to its whole substance, stresses
are produced which are liable to become so great as to cause
fracture. Experience has shown that different glasses have very
unequal powers of withstanding such changes.

Winkelmann and Schott have investigated, both theoretically
and experimentally, a practically important case. 1

Let a massive lump of glass be raised throughout to a tempera-
ture lf and then immersed in a liquid whose temperature is
or at least is taken as the zero of reckoning. The temperature
0j is taken higher and higher till the glass cracks on immersion.
It is required to find the relation of this critical value of X to
other properties of the glass. The following investigation may
guide us in the inquiry.

Suppose a very thick plate of glass, bounded by an infinitely
extended plane face, and having the uniform temperature P to
have this plane face suddenly reduced to the temperature at
the time t = 0, and permanently maintained at this lower tempera-
ture. Let denote the temperature in the glass at distance x
from the surface at any subsequent time t. Then [according to
Lord Kelvin's integral of Fourier's differential equation, Thomson
and Tait, II. p. 474] the value of is given by

e-e =(e 1 -e )-

m denoting

1 Ann. d. Phyn. u. Chem., 51, 7.30 (1894).

THERMAL PROPERTIES OF GLASS. 229

K being the conductivity, s the density, and c the specific heat
of the glass. /3 is a mere numeric which disappears on putting
in the limiting values.

For our purpose, only small values of t and of x come into
consideration, and it is possible, for any assigned value of t, to
choose x so small that ra is small. Expanding e~^ and integrat-
ing between the limits, we see that, for small values of m, the
integral is sensibly equal to m. Writing m for it, equation (1)
V>ecome8

(2)

We shall assume that the tension produced in the surface is
proportional to

and therefore to aEm (Oj ),

that is, to aE-j- t ^ . (0 1 - ),

E denoting Young's modulus and a the coefficient of linear
expansion for the glass.

In comparing two glasses, if we take x and t the same for
both, the tensions in their surfaces will be the values of

B being a constant, the same for both. Fracture will occur if
the difference of temperature 9j 9 is sufficiently great to make
this tension exceed the tenacity P of the glass in question. The
limiting difference of temperature is therefore

and Schott accordingly adopt
P IK

ad the measure of power to withstand inequality of temperature,
and call it the thermal coefficient of endurance [thermischer
Widerstandskoefficient].

If the coefficient of cubic expansion were written in the
denominator instead of the coefficient of linear expansion, F

JENA GLASS.

would be divided by 3. The following list of calculated values of
$F for the 20 glasses numbered 19 to 38 in Winkelmann's list
(Art. 67) has been published by Winkelmann and Schott. The
values of the elements employed in the calculation are also given.

10 7 3a

\&K

19 = 5

G !.->

1S-5*

7296

2-267

2-370

0-204

3-56

3-53

280

6068

1-080*

5-944

0-079*

1-17

6-12

157

5474

1-544*

2-758

0-169*

4-10

= 2

5-76

202

4699

1-572*

2-243

0-218

3-45

7'52

195*

7952

1-610

3-532

0-138*

2-79

6-07

250*

5389

1-365*

3-578

0-125*

2-49

8-51

249*

6498

1-946*

2-572

0-201*

3-23

5-39

248*

5467

1-323*

3-879

0-118*

2-14

5-56

295*

6780

1-409

2-588

0-189*

1-49

6-76

265*

6626

1-689*

2-580

0-179*

2-32

29 = 8

6-79

263*

6514

1-905*

2-629

0-191

2-45

30 = 10

7-82

368*

6014

1-605*

2-518

0-189*

2-05

31 = 13

7'63

261 ; 6296

1-440*

3-070

0-159

2-51

8-32

313*

5862

1-404*

2-668

0-178*

2-47

5-32

252*

5512

1-188*

4-731

0-096*

1-96

8-16

183*

7001

2-004*

2-378

0-206*

4-06

35 = 7

8-35

226*

7077

2-157

2-479

0-196*

3-48

7'73*

177

7260

2-040*

2-370

0-205*

3-90

37 = 12

7-75*

137

7232

1-729*

2-848

0-162*

4-84

38 = 6

9-06*

241

7543

2-100

2-585 0-199*

3-18

Those marked with an asterisk were not directly observed, but
computed from the chemical composition of the glasses in accord-
ance with formulae which we have given in previous articles.
The column headed E contains the values denoted by E l in
Art. 72, except in the case of glass 30, for which E 2 is given.
The column headed P gives the maximum observed values of
tenacity of Art. 69. The last column contains the values of %F t
computed from the six elements P, 3a, E, K, s, c. Eeference to
the units employed in the articles from which these elements are
quoted will show that the unit for J F is cm. sec. " *.

103. Experimental Tests of Thermal Endurance. Winkel-
mann and Schott made experimental tests of withstanding power
for inequality of temperature in the case of 13 different glasses.

THERMAL PROPERTIES OF GLASS.

231

Polished cubes of the glasses were heated in water, or (when
temperatures above 100 were required) in glycerine, and then
suddenly immersed in cold water, to ascertain the greatest differ-
ence of temperature they could bear without cracking. The
trials showed that the more the difference of temperature
exceeded that which could just be borne, the greater was the
number of cracks produced.

For 5 cubes of 2 cm. edge of glass 21, the following results
were obtained. With a difference of temperature of 94'8, three
of the five were uninjured, and the other two showed a few
cracks. The three then bore a difference of 96*8 ; but one of
them when tested with a difference of 111 showed a very few
cracks. The other two bore a difference of 103*5, and then
of 108. One of them bore 110'5, but the other when subjected
to the same difference showed a few cracks. The difference 1 1 0*5
was therefore adopted as the maximum for this kind of glass.
Difficulties presented themselves very similar to those which
were encountered in the determination of tenacity ; slight defects
in the surface of a glass being found to produce very considerable
diminution of its withstanding power.

The following table shows the results thus obtained for the
13 glasses; the values of %F (from the table of Art. 102) being
reproduced for comparison. They are arranged in descending
order of F.

6j for Cube whose edge is

2cm.

1 cm.

4-10

110-5

148-0

4-06

148-0

19 = 5

3-56

95-5

22 = 2

3-45

84-7

103-5

3-23

78-5

103-5

279

70-9

90-5

31 = 13

2-51

32-0

-,<:,

2-49

<;<;_>

2-32

77-8

88*4

2-14

69*8

88-5

1-96

65-8

87-0

1-49

62-7

1-17

52-8

61-9

M2 JENA GLASS.

As stated in the early part of Art. 102, Q l denotes the
difference hetween the temperature of the cold water in which
the glass was immersed, and the temperature of the glass
i iatcly l>efore immersion. It is to be presumed that the
temperature of the cold water was the same within 1 or 2 in
all the experiments : and assuming this to have been the case,
the order of arrangement for F should also be the order of
arrangement for 6 r A glance shows that the order is on the
whole the same ; but there are some irregularities near the
middle of the list, especially as regards glass 31, whose large
departure from regularity the observers were not able to explain.
It is, however, to be remembered that many of the elements
employed in calculating the values of ^F were not furnished by
direct observation (see the asterisks in the table of Art. 102),
and very precise agreement could therefore scarcely be expected.

It will be noted that in every case the cube of 1 cm. edge was
able to bear a greater difference of temperature than the cube of
'2 cm. edge. This, as Winkelmann and Schott remark, is in
accordance with the familiar fact that the thinner a glass is,
the better is it able to bear exposure to sudden changes of
temperature.

104. In connection with the question of the greatest differ-
ence of temperature between itself and a liquid in which it is to
be immersed that a body can bear without cracking, it is
pertinent to inquire what difference of temperature it can bear
between the surface layer and its interior.

If a body, raised to temperature 1 , has its surface so rapidly
cooled to temperature that only a relatively very thin layer
has changed its temperature at the time when cracking occurs,
we may assume that the tension at the surface is a function of
the difference of temperature O l O . When the body is a
sphere, this tension and its maximum value can be easily
calculated.

105. The surface layer of the sphere, being at temperature 9 ,
and surrounding an internal sphere of temperature p is in the
same conditions of stress as a thin spherical shell whose internal
volume has undergone the expansion 3a(9 1 ) in consequence

THERMAL PROPERTIES OF GLASS.

233

of internal pressure against the shell. The ordinary formulae 1
for the case give, when the shell is indefinitely thin,

-(1)

p denoting the tension produced in the shell, E Young's modulus,
and fi Poisson's ratio.

If we assume that the shell will be ruptured when p exceeds
the tenacity P ; then, for the maximum difference of temperature,
we have,

(2)

It is, however, to be noticed that the pull applied to an
element of the surface layer is not, like the pull on a prismatic
rod in determinations of tenacity, a pull in one direction only,
but in all tangential directions equally. It can be resolved into
two pulls in directions perpendicular to one another. As each of
these two pulls has the intensity p, the tenacity as measured by
the maximum value of p will be considerably smaller than the
tenacity as usually understood.

In the following table for the 13 glasses of Art. 103, the

10 7 3a

ei-e

0-250

5-66

157

5471

148

0201*

7-92

183*

7090

146

19 = 5

0-197

6-76

160

7296

140

22 = 2

0-274

4-93

202

4S(,'_>

111

0-226

7-84

249*

6632

110

0-232*

6-01

250*

5389

103

0-271

7-21

195*

7972

102

31 = 13

0-253

7-42

261

6334

101

0-239

4-97

209*

5494

0-224

4-67

L>4S*

5464

0-231

6-09

283

6613

0*286

5-46

295*

6780

o-Jiii

3-28

0Q68

values of the maximum difference Gj 9 , as calculated from
equation (2), are given in the last column, arranged in order of

1 Von Lang, Thtortt. Phyrik (1891), S. 615.

i>34 JENA GLASS.

magnitude. The other columns contain the elements used in the
calculation. The values of yu are taken, with two exceptions >
from Straubel's determinations (Art. 85). For P the mean
values given in Art. 69 are selected (not the maximum values
as in some previous tables), and even these are too large, for the
reason above stated. The values of a are the same as in
Art. 102, except that Keimerdes' determinations are adopted
for 19 and 28. The values of E are the means of E l and E 2
of Art. 72, except that for glass 19 E l is given. All numbers
marked with asterisks are values which have not been directly
observed, but computed from the chemical composition of the
glasses. The errors in these may have slightly deranged the
order of succession of the values of Q l 9 .

106. Effects of Surface Conduction. Fourier's equation

x= Q

which expresses that the heat communicated from the surface of
the body to the surrounding medium is equal to that conducted
through the surface layer, suggests that steepness of the

temperature-gradient -j- is promoted by large values of the

surface conductivity H. As steepness of gradient is one of
the factors tending to produce rupture, it is possible that
the low withstanding power of glass 31 (Art. 103), which
appeared to conflict with theory, may be due to exceptionally
good surface conduction in this glass. It is also possible that
there may have been in some cases unequal surface conduction
at different parts of the surface of one and the same cube. Such
inequality would obviously tend to promote fracture, and it is
more likely to occur in the case of large cubes than of small
ones.

107. Endurance of Sudden Heating. When a massive
piece of glass, initially at atmospheric temperature, is suddenly
immersed in a hot bath, its surface is thrown into a state of
thrust, and its inner portion into a state of tension. It is to be
expected that the difference of temperature which can be borne
in these circumstances will far exceed that which can be borne

THERMAL PROPERTIES OF GLASS. 235

when the difference is in the opposite direction ; for the stress at
the surface is in both cases far more intense than the opposite
stress of the inner portion, and strength to resist thrust is far
greater than strength to resist pull.

\\ inkelmann and Schott, after giving expression to these
views, confirmed them by a striking experiment. 1 No. 20, the
last glass in the list of Art. 103, is conspicuous for the smallness
of its power to withstand sudden cooling; its 2 cm. cubes could
only bear a difference of 52*8. A cube of this glass of the same
size, when tested by immersion in melted tin, showed itself able
to bear a sudden elevation of temperature of 465 without
cracking.

108. Application to Laboratory Uses and Lamp Chimneys.
In the Jena Works, certain glasses, distinguished by their power
of withstanding sudden changes of temperature, are employed for
the construction of vessels for use in chemical and physical
laboratories, and also for chimneys to protect incandescent gas
lights.

Laboratory Glass [Gerateglas]. The glass used for flasks,
beakers, retorts, and evaporating dishes, is thoroughly tested for
its behaviour under sudden cooling and heating. Flasks of
moderate size will usually bear dipping in cold water when they
contain boiling toluidin, which has a temperature of 200 C.

Winkelmann and Schott 2 have published a detailed account of
results obtained in the use of these vessels ; the following are
some of the items :

Beakers, without the protection of wire-gauze, could be heated
by a Bunsen burner, or by several such burners, for raising cold
water to the boiling point, and keeping it boiling.

A much severer test is furnished by the Fletcher blast-flame.
To this intensive source of heat 68 different vessels were exposed.
13 of them were boiling-flasks of 3'3 to 0*5 litre capacity.
24 were Erlenmeyer conical flasks of 1*1 to 0*2 lit.
31 were beakers of 3*6 to 0'2 lit.

In all these vessels, without wire-gauze or other protection,
cold water was heated; and only two of the 68 cracked, these

1 Ann. d. Phy*. n. Chem., 51. 746 (1894).
1 Zeittchr.f. Inttrwntntrnknnde, 14. 6 (1894).

236 JENA GLASS.

two being beakers of about 1 lit. capacity. By a Fletcher
blast-flame a litre of water was raised in 3*3 minutes from 12 to
1 'Ailing. The same operation occupied 11 minutes with a simple
Bunseu bunuT : no wire-gauze being employed in either case.
A much longer time is occupied when wire-gauze is used. The
following observations relate to a beaker of 10 cm. diameter
containing 1 litre of water.

Without wire-gauze.

Minutes. Temperature.

o ir-o

6 61

11-3 boil.

With wire-gauze.

Minutes. Temperature

10-5

6 36-5

12 59-2

18 78-9

24 92-5

28-6 boil.

With the saving of time there is a corresponding saving of
gas. To raise a litre of water from 13 to boiling in a beaker
of 10 cm. diam. required 74*0 litres of gas when wire-gauze was
used, and only 30'5 when it was dispensed with. To maintain
a litre of water in ebullition in a beaker of 10 cm. diam.
required a consumption of 2*6 litres of gas per minute with, and
1*1 litre without wire-gauze. Dispensing with wire-gauze thus
effects a saving of 60 per cent, in time and 58 per cent, in gas.

Chimneys for Incandescent Gaslight. Several accounts
have been published of the properties of Jena glass chimneys.
We may refer especially to three papers in Schilling's Journal
for Gas Lighting and Water Supply, 1895, from which the
following are extracts. We may premise that the Jena chimneys
are of two kinds of glass, designated " Green-stamp " and " Gold-
stamp."

Miiller says : " Having heated the cylinder by using it with
an Auer burner, I touched its hottest zone with a stick of ice,
and it did not crack. I then repeated the experiment over a
Siemens-Kranz burner, with the same result.

" To test its ability to withstand draughts, I then blew cold
air from a pump against the hottest zone, without injury. I then
repeated the experiment with air compressed, first to two and
then to three atmospheres, with the same negative result.

" I next dipped the cylinder in water and placed it, dripping

THEKMAL PROPERTIES OF GLASS. 237

wet, over an Auer burner, which I immediately lighted. The
water went off in steam, but the cylinder remained unbroken.
When all the water had evaporated, and the cylinder had become
hot, I sprinkled water upon it with a brush. Eleven cylinders
of different kinds of glass, including the Bacharat glasses, gave
way immediately under this treatment, but all the gold-stamp
cylinders remained uninjured. A green-stamp cylinder broke in
two after being five times sprinkled with cold water. The
experiment was repeated several times, both with the same
cylinders over again, and with other Jena cylinders taken
promiscuously out of stock.

" To see how far the endurance of the gold-stamp cylinders,
could be carried, they were then taken hot from the burner and
immersed in cold water. This was done in three different ways.
First, they were entirely submerged quickly, then slowly, and
thirdly they were slowly immersed for half their height. Every
specimen stood these tests, though some were tested three or
five times in succession.

" I then inclined the burner and chimney from the vertical at.
angles of 30, 40, 50, 60, and 80, and in each case sprinkled
the chimney abundantly with cold water. All the Jena cylinders
stood this test, except one specimen of " green-stamp," which at
an inclination of 30 gave way at the fourth sprinkling.

" Further, the same experiments were repeated with a dam-
aged incandescent mantle. It had a hole 1 4 mm. wide at the
top, and also a slit 12 mm. wide running from top to bottom.
The cylinders stood this test also."

Further trials with a damaged mantle, however, showed, as-
was anticipated, that the cylinders were not able to bear a
pointed flame playing for a long time on one place. 1 The
intimation issued by the makers relates to the endurance of the
cylinders in the normal use of incandescent gas lights, and not to-
abnormally severe experiments.

Finally, Muchall tested the relative merits of glass and mica
cylinders for incandescent lights, 538 burners being fitted with
mica cylinders instead of glass. The result showed a small
saving in mantles, but a loss of light, besides a great inferiority
from the aesthetic point of view.

1 " Laboratory glass" also U nnable to bear a pointed flame directed for a.
length of time on one spot.

jas JENA GLASS.

He goes on to say : " In the meantime some trials were made
with various glass cylinders composed of separate pieces joined
together, but no especially satisfactory result was obtained.
Further experiments in this direction would be superfluous; as
for some months past ordinary glass cylinders of really astonishing
endurance have been supplied by the Jena Works. These
cylinders, while in actual use over the burner, can be sprinkled
with cold water without cracking." ..." Here, in Wiesbaden,
out of 22 street lamps (of the candelabrum kind) in one street,
\\hu-h were fitted with these new cylinders on the 22nd of
December 1 as a test, now, after the lapse of four weeks, not
one has yet cracked, though the weather has been unusually
trying with rain, wind, and snow."

1 1894.

CHAPTER IX.
AFTER-WORKING AND THERMOMETRY.

109. After-working in Thermometer Bulbs. If a newly-
made thermometer is left to itself, and merely exposed to
variations of atmospheric temperature, the glass, which acts as
containing vessel for the mercury, gradually contracts. The end
of the mercurial column accordingly gives continually higher
indications for one and the same actual temperature. The
progress of the change can be traced by observing the freezing
point from time to time in an ice bath. It is found that the
slow rise of indication, usually called semdar rise of zero, becomes
continually slower as time goes on.

On the other hand, this creeping-up can at any time be
interrupted by raising the thermometer to a high temperature,
and cooling it quickly, but not suddenly. By this treatment
the capacity of the containing vessel is increased, and the freezing
point is accordingly lowered. This action, which we shall have
frequent occasion to refer to, we shall designate depression of zero.
If the thermometer is then again left to itself, this depression is
gradually cancelled by renewed rising of zero.

The depression of zero which can be produced in a given thermo-
meter by raising it to 100 and cooling it with the proper quickness
is called the depression -constant of the thermometer. It does
not attain its permanent value till the thermometer is old. The
depressibility before this stage is reached is smaller, and its
increase is more and more slow till the permanent maximum
of depressibility is attained.

A new thermometer can be " aged " artificially by keeping it

24" JENA GLASS.

for a long time at a high temperature for example, at 100-
and then cooling it with extreme slowness. This raises the zero,
and at the same time increases the depressibility.

If a themometer is maintained for a long time at a tempera-
ture a little over 250, and then allowed to cool without special
precautions, its zero will be considerably raised and its depres-
sibility will in general be diminished.

110. Weber's Investigation of the Influence of the Com-
position of the Glass on the Depression- Constant. The very
comprehensive observations of R. Weber on this point were
published in 1883. 1 They were performed upon 23 different
thermometers, of which some were made from commercial tubing,
and some from tubing specially provided for the purposes of
experiment. The chemical compositions of all were determined
by analysis. The scales of the thermometers were divided to
tenths of a degree in the neighbourhood of the zero-point, and
the intervals were large enough to admit of subdivision by
estimation.

After careful determination and marking of their zero-points,
with every precaution to ensure accuracy, they were left to
themselves for 1 or 2 months. After the lapse of this time
the new positions of the zeros were noted. The thermometers
were then immersed for 15 minutes in boiling water, and thence
transferred to the ice bath, in which another observation of their
zeros was made. These operations were repeated several times
at intervals of at least some months.

Very conspicuous differences were found between glasses of
different compositions. At the time of these experiments, it was
very usual to make thermometers of soft and easily fusible
glasses, containing no lead, and rich in alkalis. Weber's No. 1
thermometer was of a very light and fusible Thuringian glass ;
and the results which it gave are here reproduced, together with
its percentage composition. The column headed D contains the
values of the depression-constant at each date, the final value
being nearly half a degree. Leaving out of account glasses
which were not old enough to admit of a determination of the
constant with certainty, most of the glasses which Weber tested
showed large depressions.

1 Ber. d. Berlin. Akad., Dec, 13, 1883.

AFTER- WORKING AND THERMOMETRY.

241

THERMOMETER OF THI:I:IN;IAN GLASS.

Made June 5, 1878.

Si0 2 . NajO. K 2 O. CaO. A1 2 3 .

68-30 12-08 8-27 10*41 1-28

Date of
Observation.

Freezing-point.

Before boiling.

After boiling.

1878, Oct. 21

+ 0'497

+ 0'095

0'40-2

79, May 17

507

064

443

81, Jan. 27

81, July 22

82, May 22

83, June 7

83, Oct. 31

A decidedly better result was given by thermometer Xo. 13.
made from " an old tube of uncertain origin."

THEK.MO.METER Xo. 13.

Made June 5, 1878.

Na 2 0. K 2 0. CaO.

0-07 19-51 13-58

Si0 2 .
65-00

A1 2 3 .
2-04

Date of
Observation.

Freezing-point.

Before boiling.

After boiling.

1878, Oct. 23

+ 0-072

-0-015

0-087

79, May 17

069

043

112

81, Jan. 27

+ -01

81, July 22

+ -01

82, May 22

83, June 7

83, Oct. :n

With the view of obtaining a lar^T quantity of glass of this
last kind, experimental meltings were undertaken.
The first melting, with the furnmla

Si(X

XaJ ).

65-73

K,0.

19-15

CaO.
13-26

2-18

j4i> JENA GLASS.

proved disappointing. The thermometer No. 14 made of it had,
at the end of two years, a depression-constant 0*36. Closer
examination showed that the glass was not homogeneous.
Further meltings were therefore made with larger quantities,
but these also were unsuccessful. On analysis it was- found that
the intention to exclude soda had been defeated by the employ-
ment of impure potash.

By using chemically pure potash, two glasses were produced
having the compositions

Si0 2 . Na 2 0. K 2 0. CaO. A1 2 2 .

65-42 19-46 13-67 0-93

69-04 18-52 13-21 0'89

and two thermometers (Nos. 19 and 20) were made of them on
Aug. 18, 1883. On Oct. 31, they both showed a total rise of
zero amounting to 0'll, and a depression-constant 0'09.
Weber sums up the results of his investigations by saying :

" The depression-constant is largely dependent on the composi-
tion of the glass. The very fusible alkali glasses, which on
account of their easy working have been much employed, give
bad results. A good result is given by pure potash glasses with
large proportions of silicic acid and lime."

111. Further Investigations of After- working and its
Relation to Chemical Composition were undertaken jointly by
the Berlin Standards Commission ! and the Jena Glass Laboratory.
An account of the results has been given by H. F. Wiebe. 2

Analysis of Glasses of known Depression-quality. In the
first instance, analyses were made at Jena of the glass of seven
thermometers, belonging to the Standards Commission, for whicli
the depression-constants were very exactly known. Before the
determination, the thermometers had been lying idle for at least
a year ; and in making the determinations, they were kept at the
boiling point for about an hour.

The results of the analysis confirmed and completed Weber's
conclusions. It was clear that largeness of depression depended

1 Normal-Aichungs-Kommission.

2 ID three papers : I. Ber. d. Berlin. Akad., 17 July, 1884 ; II. Ibid., 12 Nov.,
1886; III. Zeitechr. f. Imtrum., 6. 167 (1886). In the following articles these
papers are referred to as I., II., III.

AFTER-WORKING AND THERMOMETRY.

mainly on the proportions of alkalis in the glasses. A glance
at the following extract from Wiebe's table 1 shows that the
depression D is greatest in those glasses which contain soda and
potash in about equal proportions ; that when the proportions
are unequal, no material difference in D results from inter-
changing them ; and that the smallest D is for a potash glass
nearly free from soda. The percentage of lime ranges from 7 to
14 for the glasses in our list.

Designation of Thermometer,
and when made.

Na.,0

KjO

NaoO
K.A)

KoO
Na.,0

Humboldt No. 2 (before 1835)

0-86

20-09

0-06

J. G. Greiner F l (1848) - -

1-48

18-89

J. G. Greiner/^ (1856) -

3-75

17-14

38 s

J. G. Greiner F 3 (1872) -

16-89

3-56

Ch. F. Geissler No. 13 (1875) -

15-35

3-97

G. A. Schultze No. 3 (1875) -

16-15

3-95

Rapps Nachf. F 4 (1878) -

12-72

10-57

-68

The analysis of English standard-thermometer glass (called
crystal) gave 33*90 per cent, of lead-oxide with only 49*49 of
silicic acid, and only 1*20 of lime. The percentages of alkali,
tabulated as above, with the depression, were :

Na 2 0. K 2 0. Na 2 0/K 2 0. D.

l-r>4 12*26 '13 0*15

Wiebe 3 gives a little over 0*2 as the average value of the
depression-constant for the lead-containing crystal glass exten-
sively used in England.

In Fiance, in Kegnault's time, the chief glass for thermometers
was apparently the crystal glass manufactured at Choisy le Hoi,
which was probably nearly the same as the English glass. Some
years previous to the investigation which we are describing,
Tonnelot of Paris began to make thermometers of a tolerably

1 1. 847.

'This number is not quite certain, as the thermometer had a paper scale ; and
it was ascertained later (III. 168) that such scales affect the determination of

'IIL 17".

JENA GLASS.

soda glass (/' r), which does not differ much in <-<>m-

posii m ordinary window ^lass. 1 The figures were:

Na,0. K,0. K,0/Na 2 0. D.

12-02 0-56 '05 0-008

The presence of potash is doubtless due to impurity in the soda
riMploved. Lime runs up to 14'40 per cent.

Results of New Meltings. With the view of attack in-
synthetically the problem of the connection between chemical
rMinjHKsitioii and thermal after-working, about 30 different mix-
tures wciv melted at the Jena Works, and thermometers made
f the glasses so produced were tested by the Standards rum-
mission. The results for 17 of these glasses, divided for con-
nee of description into three groups, are given below :

GROUP A.

No.

13-5

16-5

0'08

VIII

-08

XXII

1 -05

XXXI

11-1

16-9

1 -03

17 m

10-5

1 -06

20"'

7'5

7-5

0-17

GROUP B.

No.

es
K

0-02

VII

1-8

3-7

27-7

6-5

9-3

XIX

XXIII

1 II. 1025 ; see Art. 90.

AFTER-WORKING AND THERMOMETRY.
GROUP C.

245

No.

o r

Pif

14 m

0-05

16 111

67-5

_.->

0-05

IS 1 "

0-05

The thermometers were not all of the same age ; and to make
the determinations of the depression-constant D as nearly com-
parable as possible, the new instruments were artificially " aged "
in the manner described in Art. 109.

Group A illustrates the action of soda, pptash, lime, and
alumina. It establishes, beyond question, the general principle
that good thermometer glass ought only to contain one alkali
either soda free from potash, or potash free from soda. As a
qualification of this principle, it appears, from a comparison of
XXII. with 20 IH , that by the addition of lime it is possible to
prevent large depression, even in the very unfavourable case of
equal quantities of soda and potash. Alumina exercises this
restraining influence to nearly the same extent as lime.

In Group B, besides the five oxides in Group A, five others
are introduced : PbO, ZnO, BaO, Li 2 0, B 2 3 . In none of the
glasses of this group does the depression-constant exceed 0'10 ;
and in the case of the glass II., which contains 53 per cent, of
baryta, it is only 0'02.

Passing from experimental meltings to the requirements for a
practical thermometer glass ; it is necessary to consider not only
smallness of after-working, but other properties, such as facility
of working, durability, and absence of colour. Taking these
properties into account, the practical outcome of the investigation

xhihited in (imup ( ', which contains three glasses 14 111 , 16 nl ,
18 m , suitable for general thermometric requirements, and having
a depression -constant of only 0*05.

The Actual Selection. The only one of these three that has

D practically adopted for thermometers is 16 m ; it has been

made in large quantities for this purpose at the Jena W

since 1885, under the name Normal-tkcrmom<t>r ///". The

glass 18 IH promised \\rll at first, inasmuch as thermometers

Mfl

JENA GLASS.

made of it agreed well with the air-thermometer up to 50; but
it did not Mm\v well in the operations of glass blowing. It
was difficult to make into good tubes ; and when it was subjected
to reheating, fine needle-like pieces crystallised out of it. Its
use was therefore renounced.

Fresh experimental meltings were then undertaken, and they
resulted in the adoption of the borosilicate glass 59 111 .

Schott published a short account of these further researches. 1
He gives the following comparison between 59 m and 63 m :

59"'

0'02

63" 1

73-2

18-5

8-0

0-3

Our figure 72 for Si0 2 includes the small quantity 0'05 of
oxide of manganese, which Schott gives separately.

The two depression-constants given under D were for new
thermometers, and are therefore not to be regarded as final.
AYiebe, who undertook the thermometric testing of these glasses,
estimated the permanent values which the depression-constant
would attain in course of time, at 0'03 to 0'04 for 59 m , and
0-07 to 0-09 for 63 ni .

The borosilicate glass 59 m has thus rather smaller after-
working than the members of Group C. It also possesses (in
common with 18 m ) the advantage of giving mercury thermo-
meters which agree well with the air thermometer up to 50.
It is also distinguished by the smallness of its expansion, its
cubic coefficient being 177 X 10~ 7 . Tubes of this glass, as well
as of the normal-thermometer glass, are accordingly regularly
made at the Jena Works for the construction of thermometers.

Resistance-glass. A glass recently introduced by Greiner
and Friedrichs of Sttitzerbach, and now regularly supplied by
them under the name of resistenzglas distinguished (as its name
indicates) for its power of withstanding chemical attack and
sudden changes of temperature has also come into use as a
thermometer glass. Five thermometers made of it were tested

Zdtschr.f. Inttrum., 11. 334(1891).

AFTER-WORKING AND THERMOMETRY. 247

for depression-constant by Fr. Griitzmacher l at the Reichsanstalt.
The depression observed was from 0'07 to 0'10. A depression
of practically the same amount, namely 0'09, was subsequently
rved in other instruments of the same glass. The thermo-
meters were too new to give certainty as to their permanent
depression-constant. The thermometric qualities of the resistenz-
glas are considered by Grutzmacher to be nearly identical with
those of the verre dur employed by Tonnelot. The makers
describe it as a tolerably pure soda glass.

Baryta-borosilicate 122 m . In the account in Art. 98 of
Pulfrich's experiments on the after-working exhibited by stressed
glass cylinders when subjected to long-continued heating, it was
mentioned that a cylinder of the baryta-borosilicate 12 1 111 ,
although under severe stress, did not exhibit these effects.
Schott, 2 in commenting on these observations, expressed the
opinion that this glass would make mercury thermometers in
which change of zero would be very small. It is No. 12 = 40 of
Winkelmann's list, 3 and the table in Art. 97 shows that, with one
exception (a zinc borate), it had the smallest coefficient of
expansion of all the glasses examined.

Another glass, made at Jena, very similar to it in composition,
was numbered 122 111 . Four thermometers made of tlu's were
tested by Grutzmacher at the Reichsanstalt, 4 and found to have
depression-constants of only 0'01 to 0'02. It must be added
that baryta-borosilicate, being a very hard glass, is very difficult
to work.

112. General Characteristics of Different Thermometer
Glasses. Thus far our comparisons of glasses have been
restricted to one feature the magnitude of the " depression -
constant" (Art. 109). It remains to indicate the connection
between the values of this constant and the general behaviour of
the glasses, as brought out by Wiebe's comparative observations.

Recovery from Depression. The thermometers included in
Group C of last article recovered so quickly from the small

1 Zeittehr. f. lustrum., 15. 261 (1895).

* Vtrh. dc* Terei/w :. ttefOrd. dt* Qewerbft., April 4, Is

See Art. 67.

'Zeittchr.f. ferfntifc, 15.262(1895).

Nfl

JENA GLASS.

depressions there specified, that, after two or three days, they
had regained their original zero readings. The French thermo-
meters tested by Wiebe gave almost as good a result. The
thermometers of English glass took about a month to halve their
depressions. The thermometers of Thuringiaii glass, though
seventy years old, took on the average from four to six months
to regain thfir original zeros. 1

Secular Rise. The observations on the slow rise of zero in

thermometers left to themselves, showed a close connection

.-u this phenomenon and the depression -constant D. The

following table gives the elevation of zero after the lapse of

the stated number of days :

<.u.

Number of Days Elapsed.

4*2 4<>

135

160

175

200 242

285

317

447

570

1450

1600

U III

French Gl.
Kngl. GL
Thur. <;i.
IV.

vin.
gpn

XXII.
XXXI.

or*
46

(HI.-,

0-07
0-18
0-36

i.-Os

0-08
0-17
1-05
1-06
1-03

0-02

0-04

0-03

0-04
O-O")

0-04

0-44

0-02

0-04

(HO

0-12

0-07
O.OPJ

0-15

0-16

0-38

0-43

0-06
0-Ott

0-05
0-24

0-42

0-09
0-22

u-l-2

0-33

0-16

n.^o

0-25

0-43

The list includes 1 2 glasses ; the first three constitute Group
of last article, and the last six Group A. The thermometers of
Thuringian glass were six or seven months old ; the others were
new. The elevations given are, in each case, the means derived
from simultaneous observations of two or more instruments.
The glasses IV., VIII., 20 111 are not included in Wiebe's table;
but he states subsequently 2 that in thermometers made of 20 m
the elevation after 3 months was 0'13, and that thermometers
made of IV. and VIII. showed only half this elevation after the
lapse of a year.

1 II. 1024.

2 II. 1027.

AFTER-WORKING AND THERMOMETRY.

249

It may be added 1 that in thermometers of 63 HI the elevation
after six weeks was 0'03 or 0'04.

Artificially Aged Thermometers. Wiebe gives finally 2 the
results of the artificial ageing described in Art. 109. By keeping
the instruments at 100 for the number of hours stated, and
then cooling them with the greatest possible slowness, the
following elevations of zero were produced :

Glass.

Time at 100

Elevation
of zero.

14"' -

0-05

7 hours.

0-0'2

161" .

18 1 " -

o.->

7 ,,

French Glass

8 ; ,

English Glass

20'" -

In a number of new instruments of Thuringian glass, mainten-
ance for 26 hours at 100 raised the zero by 0'26, and three
days at 100 raised it by 0'40. One thermometer of glass 59 m
had its zero raised 0'06 by maintenance for 12 Jiours at 100.
A second thermometer of the same glass, whose bulb before filling
had been subjected to the " fine-cooling " process, had its zero
raised only 0'01 or 0'02 by keeping it for 12 hours at 100.

First Comparison with Air Thermometer. To complete
his tests of the fitness of various glasses for the construction of
thermometers, Wiebe made preliminary comparisons of various
mercury thermometers with the air thermometer. 3 The following
table of results will give an idea of the relative tahaviour of

Correction for Reducing to Air Thermometer.

1 rill I )fl ill ll If.

14'"

16 1 "

18"'

Thuringian.

French.

English.

o-oo

o -m

o-oo

-o-oi

+ -01

-0 -03

-0-02

+ 0-03

-0-07

i ,;,

-0 -02

-0 -11

-0 <*>

o-oo

-0-08

(1-1.7

-0-02

-0-12

-0-05

+ -02

-0-04

-0-05

+ 0-01

-0 -08

-0-02

+ -09

+ 0-01

+ -14

i Schott, Zeifcc/i .,,.. 1 1. :;:i4 (1H91). MI. 1023. MI. l"-Ji.

i':,.. JENA CLASS.

the glasses named. They were obtained by comparison with a
standard mercurial thermometer whose relation to the air thermo-
meter was kn>\vn. (ilass 18 111 gives the best agreement, and
Thuringian and English the worst. The positive sign in the case
nf the Knirlish glass is a special feature. It is very unusual to
find the mereury thermometer below the air thermometer between
0and 100.

values for Thuringian glass are mean values for the kinds
chiefly used. The chemical characters of the French glass
(Titimelot thermometers) and the English (crystal) are described
in the preceding article.

The following data for thermometers of glasses 59 m and 63 ni
have ht'en published by Schott. 1

CORRECTIONS FOR REDUCING TO AIR THERMOMETER.

59 II[ . 63 1 ".

0-00 0-00

10 -0-01 -0-06

20 -0-02 -0-10

30 -0-01 -0-11

40 -0 -01 -0 -11

50 +0-02 -0-12

As no information is given respecting the mode of determination,
it is not clear whether these results are comparable with those
given above.

113. Depression as a Function of the Higher Temperature.
A closer insight into the phenomenon of depression is obtained
by determining the position of the freezing point on the scale of
the thermometer, as a function of the temperature to which the
thermometer is raised before immersion in the ice bath. For
the Jena normal-thermometer glass, this has been done by
A. Bottcher, 2 in the course of a comparison of new and old
thermometers belonging to the Eeichsanstalt.

The new thermometers were made by R. Fuess from Jena
glass, and bore the numbers 245, 246, 247 ; the old ones
numbered 50 and 20 were of Thuringian glass, and a thermo-
meter of English crystal (No. 1115) was also included. For
several weeks previous to the trials and in the case of Nos.
/. itaeftr. / lu*tnvm., 11. 334 (1891). - Ibid., S. 409 (1888).

AFTER-WOKKING AND THERMOMETRY.

251

50, 1115, for several months, the thermometers had been lying
idle at the temperature of the room.

The comparisons were made at every fifth degree from to
100. The thermometers were kept for about two hours at the
temperature stated when this was below 60, and for about one
hour when it was above 60.

Below 60 the temperature was maintained by immersion in
a water bath. After immersion for a quarter of an hour, a
preliminary observation of the freezing points was made in
an ice bath. The thermometers were then transferred back to
the warm bath, and at the end of the allotted period the decisive
observations of their freezing points were made.

At the temperatures from 60 to 100, the thermometers wnv
immersed in the vapours of suitably selected liquids, and the
freezing points were only observed at the end of the immersion.

The results of these experiments are given in the two following
tables, the zero-point readings denoted by E t being expressed in

VALUES OF JE t FOR THERMOMETERS OF JENA NORMAL-GLASS.

No. 245.

No. 246.

No. -247.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

+ 48

+ 75

+ 57

-1

+ 2

+ 1

-3

+ 2

-1

+ 2

-1

+ 5

Sfl

+ 1

4.3

+ 3

-7

-2

+ 1

-7

-2

-5

+ 1

+ 3

-5

-1

-a

+ 1

-1

-i

-3

_>;{

-5

72-5

-4

-1

-5

-3

IT.

-5

+ 3

-3

91-5

- 1

-1

+ 3

- 4

+ 4

-2

+ 3

MM,

- 6

JENA GLASS.

thousandths of a degree. [To find the depression E Q - E t from
thfsi' tallies, may be taken as ^ + '003 nearly. The values
of E Q are not stated in Bottcher's paper.]

VALUES OF E t FOR THKKMOMKTERS OF THURINGIAX AND
KN<;LISH GLASS.

No. ."iO. Thuring.

No. 20. Thuring.

No. 111,1. English.

Obe.

Calc.

Diff.

Obs.

Calc.

Diff.

Obs.

Calc.

Diff.

+ 526

+ 246

-110

($]

243

245

- 2

]_>:>

112

-13

521

520

+ 1

J4(i

244

- 4

130

11. ->

-13

:.17

515

+ 2

239

243

- 4

186

120

-15

514

508

+ 6

240

135

126

- 9

BQ7

500

+ 7

236

238

- 2

145

133

- 12

501

491

+ 10

236

235

+ 1

150

142

- 8

490

480

+ 10

229

231

- 2

150

152

+ 2

473

468

+ 5

227

225

+ 2

158

163

+ 5

459

454

+ 5

223

220

+ 3

170

176

+ 6

428

439

-11

2Uf

JKi

- 1

195

190

427

419

+ 8

216

209

! + 7

210

209

- 1

407

404

+ 3

210

203

+ 7

213

222

+ 9

72-5

386

375

+ 11

200

193

: + 7

243

246

+ 3

361

351

+ 10

199

184

+ 15

240

271

+ 31

352

332

+ 20

188

177

+ 11

1 265

288

+ 23

01-5

313

285

+ 28

179

160

+ 19

'278

332

+ 54

292

261

+ 31

169

1,'1

+ 18

335

354

+ 19

100

238

143

375

87fi

The values headed " Calculated " in the first table are obtained
by assuming that the differences in the zero reading E t are
proportional to the differences of t, alid by identifying D with
E b E m . These assumptions give

o ) =

, + 9g (100-). (1),(2)

As the errors of observation may amount to 0'005, the
agreement between calculation and observation is satisfactory ;
hence we infer that linear interpolation is permissible in dealing
with the depressions of thermometers of Jena normal -glass
a great convenience in practice.

AFTER-WORKING AND THERMOMETKY. 253

For the three thermometers to which the second table refers,
the difference of E t for an increase of 5 in t is much larger at
high than at low temperatures, so that the linear law is not
applicable. Bottcher applied to them Pernet's assumption 1 (for
temperatures between and 100) that E E t is proportional
to the square of t. Putting D for E E m , this gives

which leads to a value of D or E b l m differing by only J per
cent, from D ; so that we may write

It is by (3) or (4) that the " calculated " values in the second
table have been obtained.

The greatest error of an observation in the case of the two
thermometers 50 and 20 may be estimated at 0*005 ; in the
case of thermometer 1115, which was only divided to half
degrees, it may be taken at 0'020. Comparing these errors
with the three columns of differences, we may say that the
calculation is fairly satisfactory from to 70.

Other Formulae for Depression. Employing the more
general formula 2

t = # 100 +a(100-0+&(100-0 2 ................. (6)

Bottcher finds, for the three thermometers 245, 246, 247,

a = '00055, b = '0000008
The formula gives

which reduces to Pernet's assumption (4) when a +2006 is
negligible, the value of D Q being then D = 100 2 6. It would
seem that these conditions are nearly fulfilled, between and
70", by Thuringian thermometer glass and English and French

l-ad .L'lass.

For Tonnelot's thermometers of vcrre dur, Gu ilia unit' has
found 3 the depression-formula

# -# = -0008886* + -000 001084* 2 ,

1 Carl's Repertorium, 11. 294 (1875).

* Winkelmann, Hnmli,., II. -J. J'.i. .

* Travau et mtmot> au international det paid* <t muure^ tom. \

-:.4 JENA GLASS.

which, by the smallness of the coefficient of t 2 compared with
that of t, shows that linear interpolation is applicable.

The value of the depression-constant D or J2 J? m comes
out -0997, which is sensibly -10, and practically the same as
that of the Tliuringian glass thermometer No. 20. This shows
that the magnitude of the depression-constant is not of itself
A sufficient index of the goodness of a thermometer glass.

Depressions after Long Continuance in Ice Bath. In order
that a thermometer may show its true maximum of depressibility,
it must be sufficiently old. It must also have been for so long
.a time in the ice bath before warming, that the effects of previous
warming have been effaced. Observations in which these con-
ditions appear to have been fulfilled, were made by Thiesen,
Srheel. and Sell, 1 upon thermometers of Jena normal -glass and
of Tonnelot's verre dur (four of each), and afterwards upon
thermometers of normal -glass and of the borosilicate 59 111 (three
of each). All the instruments had been for several weeks in the
ice bath, and were then kept for a considerable time at each of
the temperatures 25, 50, 75, 100. The results were summed
up in the three following formulae :

Normal-glass 16 m : E - E = '06484 + "03104
Borosilicate 59 111 : E, - E t = '04936 ^ - '01 456 -.

1UU \1UU/

Verre dur : E-E t = '10036 + '00928 *.

A second calculation was made, from which the less certain
observations were omitted. It gave .

Normal-glass : E, -E t = "0748 + -0236

Verre dur: #-^

The following tables for 16 HI and 59 111 -were calculated by
Scheel 2 from the first two formulae :

1 Zeitschr. f. In*trum. t 16. 58 (1896).
., 17; Beiblatt, No. 13, 98 (1897).

AFTER. WORKING AND THERMOMETRY.

255

DEPRESSION OF THERMOMETER OP 16 m IN THOUSANDTHS

OF A DEGREE.

Deg.

100

DEPRESSION OF THERMOMETER OF 59 IH IN THOUSANDTHS

OF A DEGREE.

Deg.

100

Collecting together the results for each glass, and using the
notation

we have the following list of values :

NORMAL-GLASS 16 IH . />xio

Bottcher, - - 71

Thiesen, ScheeU 1st formula, 64'84
and Sell, J2ml formula, 74'8

0-08

0-3104

0-236

0-063
0-096
0-098

JENA GLASS.
BOROSILICATK GLASS 59 UI . pxlO 5 gxlO 5 D

Thiesen, Scheel, ami Soil, 49-36 - 0'1456 0*035

VKI:I:K wi:.

(iuillanme. - - - 88'86 0'1084 O'lOO

Thiesen, Scheel,) 1st formula, 100'36 0'0928 O'llO

and Sell, ) 2nd formula, 11 9'9 - 0'052 O'lln

The values Ljiven under the heading D are obtained by putting
f=100 in the formulae. For the normal-glass 16 m they are
considerably larger than the original determinations mentioned
in Art. 111.

114. Coefficients of After -working. Let v be the original
volume of a piece of glass at ; and when it has been main-
tained for some time at t, and is then again brought to 0, let
its volume be

then the ratio of the additional volume v' to the original volume t'
is the measure of the afterworking. This ratio is

To show how this is related to the depression of zero of a
thermometer produced by raising the thermometer to t; let /3
be the mean coefficient of cubic expansion of the glass of the
thermometer between and 100,

y the mean coefficient of expansion of mercury from to 100%

i? the volume of the mercury at 0,

g the original volume of a degree at O c .

Then the volume of the mercury at 100 is v Q (l -f lOOy) and is
equal to (v -f 100#)(1 + 100/3) ; whence we find rigorously

9 =

or approximately g = v Q (y ft).

When the thermometer, after being raised from its original
temperature O 9 to f, is restored to the ice bath, the volume left

AFTER- WORKING AND THERMOMETRY. 257

vacant between the mercury and the original zero-mark will be

and the depression d will be vjg, that is,

A't+B'f 2

(2)

y-p

observed values of depression are expressed by d =pt +
we have

(3)

Taking Thiesen's values of p and q for the three thermometer
glasses, as given in last article, with the values of /3 derived
from the results given in Art. 99 (for the mercury thermometer
scale), and y = -000182, we find for A' and B :

A' x 10 8 ff x IDS

Normal-glass 16 10'2 -049

Borosilicate 59 m 8'1 -'024

Verre dur 15'9 *015

It is of interest to compare the mean coefficient of afterworking
between and t, which is A' + Hi (and which we denote by a-),
with the mean coefficient of cubical expansion from to f
(which we denote by ft). The numbers are

10V lO 8 ^ 100

Normal-glass 16 m 15'1 2424'7 '6228

Borosilicate 59 m 5-7 1779-2 '3204

Verredur 17'4 2334'3 '7454

All the above are from Thiesen and Scheel's determinations.
Bottcher's mode of experiment was more in conformity with the
ordinary use of thermometers. His data for normal thermometer
glass 16 111 , with /3 = 24 x 10' 6 , and 7 as above, lead to

115. Depression of Boiling-point Thermometers. Boiling-
point thermometers afford an easy means of determining tin-
bun mil-trie pressure to within a quarter of a millimetre; they are
therefore well suited for the measurement of altitudes in exploring
expeditions. That their use for this purpose is appreciated, may

-r,s JENA GLASS.

be inferred from Wiebe's statement that 29 boiling-point ther-
mometers were made at the Reichsanstalt during the first eleven
months of its existence.

A necessary condition of their trustworthiness is the per-
manency of their zero points after successive heatings to the
same temperature. This can only be secured by the use of
suitable glass in their construction. From researches described
by Wiebe, in a report of proceedings at the Reichsanstalt, 1 it
appears that, unless this precaution is attended to, their indica-
tions are uncertain to the extent of 0'l, equivalent to more than
three millimetres of pressure.

The investigation was suggested in the following way. Two
thermometers, numbered 42 and 43, of Thuringian glass, when
compared with a standard on Sept. 7, 1888, at temperature 87,
were found to require the corrections

-0-05, -0-24.

They were then kept for 15 minutes at 100, and their zeros
were found to be thereby lowered by the amounts

0-43, 0-45.

Being left till Sept. 10 at the temperature of the room (15 to
20) and then again compared at 87, their corrections were found
to be

+ 0-08, -0-09,

showing depressions 0*13, 0*15 as compared with the observa-
tions of Sept. 7.

This change attracted Wiebe's attention ; and he followed it up
by elaborate tests of two thermometers, No. 125 of Jena glass,
and No. 31 of Thuringian glass.

The thermometers were first compared several times in alcohol
vapour at 78*5 ; they were then kept for half an hour at the
boiling point of water, and then again compared repeatedly at
78*5; several comparisons at being made between these various
observations. The results are given in the two following tables,
the first containing the observations at 0, and the second those
at the higher temperatures. Each result is the mean of four
separate readings made with a small telescope.

1 Zeitschr.f. Instrum., 8. 362 (1888).

AFTER-WORKING AND THERMOMETRY.

259

The first table shows that the thermometers were exposed to
the temperature 78*5 during four successive periods, together
amounting to 134 minutes, the total depressions thus produced

1888

Determination of Zero.

No. 125.

No. 31.

September 17.

After rest at 15

+ 0-071

+ 0-128

,, 7 min. at 78 -5

038

-0 -189

7 78-5

035

207

64 78-5

033

310

56 78-5

031

337

,,32 ,, 100 -2

018

510

22 78-5

028

411

September 18.

rest at 13"

060

267

48 min. at 87'7

383

l>eing '040 and "465. The first of these heatings lasted
7 minutes, and produced depressions '033 and "317. The
further heating for periods amounting to 127 mins. produced

1888.

Time.

No. 125.

No. 31.

1888.

Time.

No. 125.

No. 31.

Sept. 17.

11 h. 33m.

In alcohol vapour.

Sept. 17.

1 A. 34m.

78 -492

78-491

78 '466

78 -648

491

483

646

Changing to 79 '5

In alcohol vapour.

4SD-

460

493

592

2 A. 4m.

492

466

12 A. 9m.

In alcohol vapour.

492

466

486

571

494

460

492

571

Comparison at 100-2

491

562

3 h. 26 m.

In alcohol vapour.

> t

495

546

469

334

495

539

481

347

492

546

484

356

496

538

480

488

492

534

4SS

174

493

*sa

487

385

480

488

Sept, 18,

1 _>/,. 59m.

In alcohol vapour.

4<i:i

080

1 A. 6m.

78-703

78-476

Ik. 1m.

481

516

706

500

480

-000

704

506

In alcohol vapour.

7<M

519

MO JENA GLASS.

further depressions '007 and '148. The further exposure to
the temperature of boiling water for 32 mins. made the total
depressions amount to *053 and *638.

second table throws further light on the behaviour of the
t\\t> thermometers.

After the comparison at Ih. 36m., Sept. 17, the temperature of

.ipour rose to 79*5, owing to an increase in the pressure;

and the observations were not resumed till the pressure had again

become normal. The barometer remained nearly constant on

Sept 17, and was 3 mm. higher on Sept. 18.

If we leave out of account the early observations taken before
the instruments had quite attained the temperature of the bath,
the readings of the Jena thermometer are all in good agreement,
f\vn including those taken after exposure to the temperature of
boiling water. On the other hand, the thermometer of Thur-
ingian glass shows a continually increasing depression during' the
whole time of its exposure even to the alcohol vapour. The
depression comes into evidence even at the beginning; the
thermometer reading lower although its temperature wa.s really
rising. Before exposure to the temperature of boiling water, the
depression had attained the value 0'19, and after this exposure
it was about 0'30. Wiebe calls attention to this circumstance
as showing that the use of Thuringian glass for boiling-point
thermometers is out of the question.

Since the introduction of boiling-point thermometers of Jena
normal-glass, it has been frequently pointed out 1 that these
instruments are fully competent to take the place of barometers,.
0ven in travels of great extent; and the same may be said
a fortiori of thermometers of the borosilicate glass 59 m . In the
case of this latter, the depression of zero resulting from such
heatings as are required in the use of the instrument, would be
quite immaterial. Moreover the instruments would be much less
perishable than mercurial barometers, being able to bear jolts, as
well as sudden changes of temperature. If made of glass that
has been skilfully cooled/and subjected to artificial ageing, there
will l>e no necessity to test them at 0, and several centimetres
can thus be saved in their length.

116. Secular Rise in Unused Thermometers. Some

'See Griitzmacher, Zeitschr. /. lustrum., 17. 200 (1897).

AFTER-WORKING AND THERMOMETRY.

261

information on the secular rise of zero in thermometers of Jena
normal-glass is given by the observations of F. Allihn published
in the Zeitschrift fur Analyt. Chcmie, 28, 435, and 29, 381
(1889-1890), which are reproduced in the following table. The
twelve instruments on whicli they were made were by Warm-
brunn, Quilitz and Co., and were divided to tenths of a degree.

No.

Freezing-Points Observed.

Total
Rise.

Shortly after Making.

Feb., 1889.

Mar., 1890.

106

March, 1886

o-oo

+ 0'03

+ 004

0-04

108

+ -01

665

August, 1886

667

668

669

670

September, 1886

671

August, 1886

672

673

8,">0

February, 1888

853

May, 1888

The first set of readings were taken a few weeks after the
making of the instruments, which then remained unused till Feb.
1889, when their zeros were again tested; and in March 1890
those of them which still remained unused were again tested.
The total rise, in about 4 years, varies from 0'03 to 0'04.

117. Effects of Higher Temperatures. The creeping up of
zero with lun^r exposure to high temperatures has been a frequent
subject of investigation for the last fifty years or more. We
shall deal only with researches which include comparisons of
Jena-glass thermometers with other thermometers. 1

1 The papers cited as Wiebe I., Wiebe II., Allihn, Schott, are the following :

I. H. F. Wiebe. On changes of mercurial thermometers at high tem-

peratures. Zeitwh.f. liMtnnn.. s. 373 (1SSS).

II. II. I'. Wiebe. On the employment of mercurial thermometers at high
temperatures. Zeitch. f. Inxt., 10. 207 (1890).

III. I'. Allihn. On rise of zero in mercurial thermometers of Jena normal -
glass. Ztitch. /. AnalytMche Chemie, 28. 435 (1890).

IN*. O. Schott. Study of some physical properties of glasses, and on a
valuable new glass for thermometry. Zeitechr. f. lustrum., 11. 330
(1891).

.IKNA GLASS.

The older observations showed that, when a thermometer is
maintained for a long time at a high constant temperature,
its zero rises, first quickly, and then more and more slowly,
tending probably to a limit dependent on the temperature;
further, that the thermometer is thereby rendered less susceptible
to change of zero at more moderate temperatures.

NViebe brought together (I. 374) the observations of Person,
K"j}>, and Crafts, and confirmed and extended them by his own.
Alii tin's researches are in good agreement with Wiebe's. Schott's
paper includes the recently produced borosilicate glass, and also
describes researches calculated to throw light on the causes of
rise of zero when thermometers are heated.

Amount and Progress of Rise of Zero for Various Glasses.
Wiebe published (I. 375) a short account of his experiments,
performed in the years 1877-1881, on thermometers all of
wh it-li were of Thuringian glass. One of his results may here be
quoted. Two thermometers about 9 months old, were exposed to
temperatures which increased by steps up to 300, each exposure
lasting a few minutes, and being succeeded by immersion in the
ice bath. In this experiment, the depression increased with each
step up to 250; but when the two thermometers were raised to
300 for five minutes, their depressions, which had gradually
advanced to 0'5 and 0*6, were diminished by 0'l. Extended
experiments on the temperatures at which such reversals occur
seem never to have been made.

Wiebe also made a series of comparative observations on the
elevations of zero for thermometer glasses of different compositions.

Position of Zero.

Date.

Aggregate
Exposure.

18 m

I 4 m

16 m

20 ni

Eng.
Glass.

17111

1885 November 11.

:H hours

0'14

0-30

0'29

0-34

0'38

0-60

> 13.

0-31

-61

-63

-57

1 -04

1 -57

14.

10i

0-66

-94

1 -07

1 -88

2 -33

3 -07

19.

13*

'80

1 -09

1 -24

273

3 -60

20.

19i

1 -11

1 -40

1 -57

3 -63

Mean ratio to 18"',

1 -0

1 -6

1 '7

2-4

3 -2

4-8

Thermometers of the Jena glasses 14, 16 m , I7 lir , 18 m , 20 m , as
well as of English crystal (see Art. Ill), all of them several

AFTER- WORKING AND THERMOMETRY.

263

months' old, and up to that time only exposed to moderate
temperatures, were simultaneously raised several times to the
temperature 300, for periods of a few hours' duration. The
positions of their zeros after each heating are exhibited in the
foregoing table. 1 For the sake of clearer comparison, Wiebe
computed, for each period of exposure, the ratios of the readings
to the reading of 1 8 m , and then took the means, which are given
at the foot of the table.

The following are the results of some comparisons which he
made 2 between the Jena normal-glass 16 m and Thuringian glass.
The values for 16 m are the means of the results given by two
iir\v thermometers in July 1888. The values for Thuringian
glass are derived, with the aid of interpolation, from observations
also made on new thermometers. The temperatures were in all
cases between 360 and 370. The elevations of zero were more
than three times as great for the Thuringian as for the Jena glass.

Duration
of Heating.

Elevation of Zero.

Ratio.

16 ni

Thuringian.

8 hours

1-51

4-62

1:3-1

1 '89

6 '56

1:3-5

2-21

7 '30

1:3-3

Wiebe concludes with a detailed account of the behaviour of
three thermometers, which have been mentioned in Art. Ill
under the designations F v F y F y F l was of the German potash
glass used in the middle of the nineteenth century for the
construction of thermometers; F 3 and F^ were of Thuringian
glass. According to Wiebe's table, the elevations of zero pro-
duced were :

F^ after 38 hours at 260 = 0'73,

=2-15.

Allihn, in his researches, heated the thermometers in a
sand-bath, in order to avoid the chemical attack of the hot water
on the glass, which might possibly occur in the usual liquid bath.
The arrangements were such that the temperature could be kept

Wiebe, I. :;::.

//*., 378.

JENA GLASS.

in the neighbourhood of 300, with fluctuations not exceeding
10. Tlif mean temperature is taken by Allihn as 290.
Three thermometers were selected for the tests; two of them by
Warmbruiin, <Juilitz and Co., of Jena normal-glass, and one of
jjlnss. The t\v.. former were unused thermometers,
a week old, with nitrogen above the mercury, divided to
whole 1 degrees from to 360. The third (also unused), was
about five weeks old, and was similarly divided,' but without
nitrogen. The observations of zero were in most cases made
i!4 hours subsequent to the exposures to high temperature. The
ivMilts are contained in the following table. Before the com-
ment of the first heating, all three instruments read 0'0
in the ice-bath.

Duration
of
Exposure.

Position of Zero.

Jena Normal-Glass,

Thuringian.

."> hours

+ i-o

+ 2'l

1 -3

1 -5

2 -7

1 -5

1 -7

3 -1

5 ,,

1 -6

1 -8

3 -4

1 "7

1 -9

3 -6

5 ,,

1 -8

2 -0

3 -7

25 ,,

2 -0

2 -2

4 -2

In Wiebe's researches above-mentioned, a thermometer of
16 m showed a rise of zero 1'57, after 19 J hours continuous
exposure to 300. Allihn here finds, after four exposures of five
hours each, a rise 1'6 to 1*8 ; the agreement is therefore pretty
close. All through Allilm's observations, the Thuringian glass
slmws nearly double the elevation of the Jena normal-glass.

Wiebe afterwards extended his researches to higher tempera-
tures, up to 500 . 2 Mercurial thermometers are generally used
"iily iij) to 300, because at higher temperatures the mercury
(in vacuum thermometers) begins to boil. Boiling can be pre-
vented by filling the space above the mercury with nitrogen or
some other gas indifferent to mercury. 3

1 [Dr. Hovestadt suggests in a footnote that this may be a misprint for tenths of
a degree.]

- Wiebe, II. 3 Carbonic acid is now commonly employed.

AFTER- WORKING AND THERMOMETRY.

265

If the gas is introduced at atmospheric pressure at 20 C , and
there is a space equal to r degrees above the 71 th degree of the
scale, then, when the mercury stands at n degrees, the volume of
the gas has been reduced from r + n 2 to r, so that even if

its temperature were not raised, its pressure would be 1H
atmospheres.

Wiebe used five thermometers of Jena normal-glass, numbered
279, 281, 282, 283, 284. They were " Einschluss " thermo-
meters, 1 with an enlargement at the top of the capillary tube, and
were filled with nitrogen intended to prevent boiling at 450.

If we put 7i = 450, and equate 1-f - to 4J, which is the

pressure (in atmospheres) of mercurial vapour at 450, we get
r= 123 as the volume of nitrogen required.

The scale of No. 281 reached down to 0; those of the other
four began a little below 100.

The investigation was begun by exposing the two thermometers
numbered 281 and 282, for successive intervals of a few minutes,
to temperatures rising by successive steps up to 475 ; and the
following results were obtained :

No. 281.
Position of freezing.

No. 282.

Position of boiling.

Before heating

o-o

100 -0

After 5 min. at 100 -

5 200 -

o -o

,,5 300 -

-o-i

.. r, ,, 400 -

+ 0-9

100 :>

.. -I ,, 450 -

103 "2

15 475 -

+ 9 -0

109-5

In explanation of these results, it is to be noted that No. 281
had on the previous day been heated to 211 an operation which

'The EiH*rhlu*Hthtrmometer [enclosure-thermometer] has ita stem enclosed
within an outer glass tube sealed on to the stem at both ends, leaving the bulb
exposed. The divisions are not on the stem, but on a thin glass plate held close
to the stem by glass seals attached to the outer tube. The pattern is common in
Germany, but is not made in England. The ordinary pattern is called, for
distinction, StaJlithtrmomtter [rod thermometer]. J. D. E.

JENA GLASS.

had already depressed its zero. It accordingly showed no change
till heated above this temperature. Its first change is a further
depression of 0*1 by heating to 300. The depression is changed
to an elevation by heating to 400. In Thuringian glass (as
stated on p. 262), Wiebe found a similar change from depression
to elevation, not at 400 but at 300.

I'.y further heating at 420 and 460, further elevations of
freezing point and boiling point were produced, but at a slower
rate, as the following record shows :

Successive Exposures.

No. 281.
Position of freezing.

No. 282.
Position of boiling.

1 hour at 420

11-1

112-0

f 460

15 -8

116 -2

U >. 460

19-9

120 "2

li 420

20-3

120 -8

It 420

20-7

121 -1

The other three thermometers were subjected to the same
treatment as these two, and showed finally the boiling points :

No. 279.
122-0

No. 283.
123-2

No. 284.
120-4

These three instruments were then subjected for four hours
to a temperature of about 500 in fused lead chloride. This
produced a considerable lowering of the boiling points, which
persisted after subsequent heating at 450, and must therefore
be regarded as indicating yielding of the glass bulb to the strong
internal pressure when softened by heat. The depressed boiling
points were

104-6 106-2

In preliminary tests, Wiebe subjected two thermometers of the
borosilicate 59 IH to the temperature 300 for 30 hours. 1 One
was treated in the ordinary way ; and the bulb of the other, before
tilling with mercury, had undergone the " fine-cooling " process.
The zero of the first was raised 3'9 ; that of the second only
0-1 or 0-2.

1 Schott, 334.

AFTER. WORKING AND THERMOMETRY. 267

Schott himself undertook further experiments with this glass. 1
The thermometers which he tested had at the upper end of the
tube a bulb about as large as that at the lower end, so that rise
of the mercury in the tube could not much affect the pressure of
the gas above it. This gas was nitrogen at an initial pressure
of 10 atmospheres. Two of the thermometers were kept from
two to three days without intermission at from 470 to 477,
then for nine days in a thermoregulator at 360, and then cooled
down to ordinary temperature. The mercury finally stood from
13 to 15 too high. The pressure of the gas must have reached
between 27 and 28 atmospheres.

Finally Schott heated a thermometer of this kind up to the
softening point of the glass. The temperature was measured by
a Jolly's gas-thermometer, the gas being hydrogen, and the glass
59 m . The gas-thermometer and the thermometer to be tested
were heated together in a jacketed sheet-iron cylinder, from
which only the enlargement at the end and a small portion
of the tube of the mercurial thermometer projected. The
heating was continued until, in spite of the gradual elevation
of temperature which was going on, the mercurial column in
the gas thermometer began to fall, indicating softening of the
glass. The temperature attained was estimated at 667, after
making allowance for the distension of the softened bulb under
the internal pressure. Without this allowance the calculation
gave 596.

Hence it appears that for a period of half an hour a tempera-
ture averaging 640 was maintained. The bulb of the mercurial
thermometer must therefore have withstood an internal pressure
of from 10 to 15 atmospheres. Its capacity had increased about
10 per cent

We may mention finally some tests applied by Griitzmacher 2
to two high-temperature thermometers of the glass 122 111 , which
is a baryta borosilicate free from alkali. The instruments were
maintained at temperatures lying between 300 and 350, with
the following results :

After 18 hours, elevation i' 1

44 0-41

60 0-:.l

1 Schott, * Zeit*chr. f. Iiutntm. , 1 5. 282 ( 1 895).

-,,s JENA GLASS.

These are even better than the results obtained with the
borosilicate 59 m .

Permanence of Raised Zero. One of the six thermometers
which Wiebe tested for five days, in November, 1885, 1 by 19J
hours' aggregate exposure to the temperature 300, was of Jena
1 6 111 . On this instrument some subsequent observa-
tions were made. 2 On Nov. 10, before the experiments already
quoted, its zero reading was 0'll. On Nov. 24, when they
were just completed, it was 1'68 a rise of 1*57, as stated
in the table already given.

The thermometer was left to itself till Feb. 23, 1886, and its
zero reading was then found to be 1'73. After another rest of
nearly irs, its reading was 1-.75. It was then subjected

to several long- con tinned heatings at 260, with the following
results, which show a small increase to a definite limit practically
attained in the last observation.

1888, July 14, after 4 hours at 260, reading 1-80

18, 5 1-83

19, 4 1-85
Sept. 4, 4 ,,1'86

It is thus seen that 19 hours of heating at 300 prevent the
production of any considerable further rise under subsequent
exposure to 260. "For chemical thermometers of Jena normal-
glass, a 24-hour heating at 300 before graduation will suffice, in
most cases, to ensure that any elevations of zero in subsequent
use shall be inconsiderable."

Further experiments on the constancy of the raised zero were
made 3 at still higher temperatures with the three thermometers
numbered 279, 283, 284 already mentioned. 4

The softening of the glass at 500 had left the boiling-points
at the positions 101-0, 104-6, 106-2, as already stated. Sub-
sequent heatings between 40J) and 450 were found to produce
rise of boiling-point readings, but on a much smaller scale than
before heating at 500. After a time, heating at 400 or 450
produced no further change of boiling-point reading. 5 The

1 See page 262. - Wiebe, I. 377. ; Wiebe, II. 209. 4 See page 265.

5 A mixture of equal parts of potassic and sodic nitrates, fused in an enamelled
vessel, was the heating medium employed.

AFTER- WORKING AND THERMOMETRY.

269

observations are given in the following table, which commences
with the heating at 500, already mentioned:

Date.

Boiling- Point Readings.

No. 279.

No. 283.

No. 284.

July 12

After 4 hours at 500

101-0

104-6

106 -2

9 450

103 -2

105 '.'

108 -1

,,18 ,, 450

104 -4

106 -7

108 -9

.. 22

,,5 ,,450

104 -4

106 -6

109-1

4 400

104 -5

109 -1

12 420

104 -4

109-0

Sept. 4

41 days' rest

104-4

108 -9

8 hours at 450

104 -4

109 -1

From these results, Wiebe concludes that mercury thermo-
meters of Jena normal-glass, with nitrogen above the mercury, can
be used with confidence for measuring temperatures up to 450,
if they have been previously fortified by long-continued heating.

Thermometers of the borosilicate glass 59 ni can be used for
still higher temperatures, as its temperature of softening is
higher.

Schott states, 1 on Czapski's authority, that Baudin of Paris
seasons his high-temperature thermometers by keeping them
for eight days in boiling sulphur, which has a temperature of
about 445.

Instead of heating and cooling without special precautions^
Schott recommends that, before filling with mercury, the thermo-
meter bulb should be subjected to the " fine-cooling " process, the
benefit of which has been clearly proved 2 in the case of a thermo-
meter of 59 m .

^Yhen thermometers, after elevation of zero by heating, are
left to themselves, they sometimes show further elevation,
sometimes depression, and sometimes constancy. The normal-
glass thermometer first mentioned in this section showed, after
three months' rest, a rise of 0*05 ; No. 279, after 41 days' rest,
showed no change; while No. 284, after the same rest, showed
a depression of 0*1.

\\ inkelmann, in his experiments on tin- variation of elasticity

1 See page 236.

170

JENA GLASS.

with temperature, 1 used two high- temperature thermometers of
borosilicate glass, numbered 4142 and 4144, which showed the
following changes of zero. 2

Position of Zero.

No. 4142. No. 4144.

0-3
3-6
4-6

4-0

1-2

5-0.
4-4

1893, August 18,

1895, May 16,

Dec. 20, -

1896, Oct. 22,

In the interval from Dec. 20, 1895 (or, rather, from Jan. 24,
1896, when the heating ceased) to Oct. 22, 1896, the elevations
of both thermometers were diminished by 0*6.

Rise of Zero Compared with Depression-constant. From
his observed values of the elevations of zero produced in six
thermometers of different glasses by continued heating, Wiebe
deduces (as above stated) 3 " mean ratios," which he adopts as
representing the relative susceptibilities of the six glasses to this
influence. They are reproduced in the subjoined table, under the
heading A ; and the depression-constants (as defined in Art. 109)
for the same glasses are given under the heading D, It will be
seen that the order of arrangement is the same for both. 4

18 -
14 m -
16 m -
20 m -
English crystal
17 111 -

1-0
1-6
1-7
2-4
3-2
4-8

0-04
0-06
0-06
0-20
0-27
1-05

The following table 5 shows that the same rule holds for the
three thermometers F v F y F# which have been previously
mentioned : 6

Elevation.

After 38 hours at 260

0-73

0-15

F 3

32 ,

260

1 -37

-38

38 ,

260

2 -15

-65

1 See page 161. 2 Ann. d. Phys. u. Chem., 61. 141 (1897).

3 See page 262. Wiebe, I. 377. 6 Ibid. , 378. 6 See page 263.

AFTER-WORKING AND THERMOMETRY.

271

Temporary Diminution of Depressibility. These three
thermometers (F l being of old German potash glass, and F y F 4 of
Thuringian glass) were subjected by Wiebe, between March 21,
1881, and Sept. 24, 1888, to numerous heatings at 260, and
numerous determinations of zero. The following extract from
the record of these observations 1 contains the history of the
thermometer F^ from March 21, 1881, to Aug. 31, 1888. In
M;iy, 1883, all three thermometers were opened, and, after
cutting off a sample of the capillary tube for chemical analysis,
heated till the mercury boiled, and sealed up again.

Date.

Zero- Point.

1881 March 21.

After several months' rest,

+ 0-21

,, half-an-hour at 100,

-0 -44

0-65

1883 May.

Opened, boiled, resealed, -

Sept. 19.

After two months' rest,

+ 5 -22

,, half-an-hour at 100,

+ 4 -66

0-56

1884 Feb. 26.

,, 5 months' rest, - -

+ 5 -34

half-an-hour at 100,

+ 4-74

0-60

,, 27.

6^ hours at 250, -

,, 29.

After 2 days' rest,

+ 6 -29

1885-^July 21.

,, 17 months' rest, - -

+ 6 -61

22.

half-an-hour at 100,

+ 6 -00

0-61

1888 July 13.

After 3 years' rest, - - -

+ 6 74

half-an-hour at 100,

+ 6 -08

0-66

3 hours at 260, -

14.

3 hours at 260, - - - -

17.

After 3 days' rest,

+ 6 -58

.. 17-20.

23 hours at 260, - - -

21.

After 1 day's rest, - - -

+ 7 '13

Aug. 31.

,, 1 month's rest, - -

+ 7 '49

half-an-hour at 100,

+ 7 -07

0-42

The last column gives the depression-constant as observed after
each half-hour of heating at 100. The influence of previous
heating on the depression-constant is here distinctly perceptible.
On Sept. 19, 1883, shortly after the boiling and resealing, and
again on Aug. 31, 1888, shortly after long heating at 260, the
depression-constant is considerably diminished. The other two

1 Wiebe, I. 379.

JENA GLASS.

tan l-\ and /'.. behaved in the same way. "One sees,

from these results, that observations of depression, taken soon

after the making of a thermometer, furnish a very dubious

criterion of the suitability of the glass for thermometric use,

.nub as tlie high temperatures employed in the making cause

these depressions to be too small. To determine the full amount

. T-effect characteristic of any glass, the thermometer must

either be kept for many months or be artificially seasoned."

Rise of Zero as a Consequence of Relief of Stress. Schott
nggested that the rise of zero of a thermometer, produced by
continued exposure to a high temperature, may be due to the
removal of stress previously existing in the glass of the bulb.
In his account of his observations on the diminution of double
refraction by continued heating, in the case of strongly stressed
glass cylinders, 1 he remarks that the gradual disappearance of
the stresses which are present in all specimens of glass not
cooled with extreme care, " is accompanied by a diminution of
volume (involving increase of density), and, in thermometers, by
diminished capacity of the bulb," which will of course produce
advance of the mercurial column. 2 He goes on a little later to
describe an arrangement which he employed for giving optical
evidence of the existence of stress in the glass of a thermometer. 3

A cylindrical thermometer is placed within a tall rectangular
cistern, made of glass plates cemented together at the edges.
When the vessel is filled with a transparent liquid having the
same index as the glass of the thermometer, light passes through
the tube without undergoing refraction, and the appearance
presented is that of a vertical section through the axis of the
thermometer. The usual test by polarised light (with crossed
Nicols and a concave mirror) showed the characteristic bright
and dark bands.

In strongly stressed cylinders of normal-glass, Schott observed,
after heating to 400-410, a diminution of double refraction,
indicative of diminished stress. With cylinders of borosilicate
thermometer -glass, a similar diminution was found after heating
140. Acting on the knowledge 4 that Baudin had
employed boiling sulphur for the seasoning of high-temperature
thermometers, he subjected the borosilicate glass 59 m to a further

1 See Art. 29. 2 Schott, 332. 3 Ibid., 335. 4 See page 269.

AFTER-WORKING AND THERMOMETRY. 273

test. 1 A short cylindrical piece of this glass with plane
polished ends, which when first tested between two Nicols
showed " more rings than could be counted," was kept in
1 toiling sulphur for four days, and afterwards showed only
three rings.

The diminution of stress shown by these optical tests is
obtained without softening in the ordinary sense of the word.
Thermometers of the glass 59 m at temperatures between 470
and 477, when subjected to internal pressures of 27 to 28
atmospheres, were not distended, but, on the contrary, had their
zeros considerably raised, 2 and thermometers of 16 m with
nitrogen above the mercury also showed elevation of zero after
heating at 475 . 3

The possibility of producing, in strongly stressed glass cylinders,
by exposure to even such a moderate temperature as 100, and
for a comparatively short time, permanent molecular displace-
ments tending to relieve the stresses, is shown by Pulfrich's
observations on cylinders of the silicate crown 0. 662, which we
have mentioned in page 218.

Taking these facts into account, and also the consideration
that stress is more easily removed from the walls of a hollow
vessel than from the substance of a solid cylinder, Schott's
^estion as to the cause of the rise of zero produced by heating
mercury thermometers seems to be a satisfactory explanation of all
the known facts.

In particular, these observations of Pulfrich's show that, after
the displacement produced by maintenance at a given temperature
has reached its limit, exposure to a higher temperature can make
the displacement begin anew and rapidly advance. After a
cylinder of 0.662 had remained immersed in boiling water for
three hours, without distortion of its polished plane ends, five
minutes' immersion in oil at 200 caused them to exhibit
concavity. This is precisely analogous to the fact, established by
all researches, that a thermometer whose zero has been raised
by long-continual heating at a given temperature, until it has at
length become stationary, will begin to exhibit further rise of
zero when maintained at a higher temperature.

Indubitable proof that the rise of zero produced by maintaining
a thermometer at 100, is due to relief of stress existing in the

1 Schott, 336. s, , ,,,-!-,. _',;;. igee page 266.

-7-1 JENA GLASS.

bulb before filling with mercury, is furnished by Wiebe's experi-
ment (mentioned on p. 249) in connection with artificial ageing.
Two thermometers of borosilicate glass, one of which had been
subjected to the " fine-cooling " process before filling, were both
maintained for 12 hours at 100 and slowly cooled. Under this
identical treatment, the fine-cooled thermometer had its zero
raised only one-third as much as the other thermometer, which
had not undergone special preparation.

The temperature of 400 at which, according to Schott's
observations, the falling off of stress in cylinders of normal-glass
is optically perceptible, shows itself as a critical temperature in
experiments on change of zero. When Wiebe heated the ther-
mometer No. 281 [p. 265] at successively higher temperatures up
to 475, for periods of a few minutes, depression was produced
by heating at 300; but heating at 400 changed this into a
much larger elevation. It has been already mentioned, in our
account of these experiments, that a similar transition from
depression to elevation occurred at 300 in the case of ther-
mometers of Thuringian glass ; the lower temperature of transition
being a natural consequence of the lower melting point.

Increase of the Fundamental Interval [that is of the
difference between the reading at the true temperature and
the reading at the true temperature 100]. The rise of zero
produced by heating a thermometer is accompanied by increase
of the fundamental interval. This fact was first detected by
Crafts, and has been abundantly confirmed. It is attributed, by
general consent, to diminution in the expansibility of the glass,
and furnishes another argument in support of the view that the
rise of zero is due to the relief of pre-existing stress ; for we
have seen, in Art. 98, that the expansibility of stressed glass
may be greater by several per cent, than that of the same glass
when freed from stress.

An observation by Wiebe on the thermometer No. 2 8 1 of Jena
normal-glass will serve as an illustration. By continued strong
heating, the zero point was finally raised to +20 0<t 7, and the
" fundamental interval " was at the same time changed from the
initial value 99'9 to the final value 100'4.

Let v be the volume of the mercury in the thermometer at 0,
7 the mean coefficient of expansion of mercury between and
100, ft the mean coefficient of cubic expansion of the glass before

AFTER-WORKING AND THERMOMETRY. 275

heating. Then the volume (at 100) of the space between the
freezing and boiling points is I00v (y /3).

Let /3 r be the diminished value of /3 after the heating. Then
the volume between the new freezing and boiling points is
100i? (7 ft'). If n and n f are the values of the fundamental
interval before and after the heating, we have l

n' - ri-n -

_ _ _ ^ - - _ ,--

n ~y ft ' n yfi

Putting ?i=99-9, n'=10(K, 7=182xlQ- 6 , and 0=244

x 10~ 7 , which is the observed value for Jena normal-glass cooled

in the ordinary way (see Art. 98), we deduce P p = 7'9 x 10~ 7 ,

showing a diminution of more than 3 per cent, in the expansibility

of the glass.

118. Comparison of Normal-glass Thermometers with one
another and with other Mercurial Thermometers. Wiebe
compared, over the interval D to 100, the indications of various
mercurial thermometers, of Jena normal-glass and of other
glasses. 2 Thiesen, Scheel, and Sell have since made com-
parisons, over the same interval, between normal-glass 16 m ,
borosilicate glass 59 m , and the verre dur used by Tonnelot. 3
For the interval 100 to 300, Wiebe and Bottcher 4 have
furnished data for comparison between several thermometers
of 16 IH , in the course of their comparisons of mercury thermo-
meters with the air thermometer.

Comparisons between and 100. Wiebe's comparisons
were carried out at the Reichsanstalt in 1888 and 1889, on
three normal-glass thermometers, numbered 245, 246, 247.
The instruments were divided to tenths of a degree, and their
errors of calibration were known. They had also been several
times tested as regards their errors of "fundamental interval" for
different positions of the zero point.

I ' In this calculation, the volume between two given marks on the stem ia
treated as unchanged, in comparing initial an 1 final states, at the same tempera-
ture. Its values at the boiling point are in fact as 1 + 100/3 to 1 + 100/3', and
the ratio of these two is 1 + 100(/3-/9 / ) or l+8x 10'*, which may be treated as

unity.]

<ch.f. /nrfrum., 10. 436(1890). Ibid., 16. 433(1895).

4 /W<*., 10.233(1890).

270 JENA GLASS.

Between 5 and i>r> c the comparisons were made in a water-bath,
whole of the mercurial column being always below the surface
of tin- water. For higher temperatures up to 96, the vapours of
various liquids were used as immersing media, the boiling-point
apparatus employed for the purpose being essentially a Rudberg
boiling- tube with back-flow cooler. 1

Four series of observations were made ; the first in April 1888,
on Nos. 246 and 247, from 5 to 97; the second in August
1888, on the same, from 5 to 35 ; the third in September 1888,
on all three thermometers, from 5 to 92; and the fourth in
April 1889, on all three, from 5 to 96. Wiebe gives the
results in four tables, one for each series.

In the first series, the difference between the reading of one
thermometer and the mean of the two, averages 0'002, and
amounts in only one instance to 0'005.

In the second, it averages 0'003, and once reaches 0'006.

The third series includes readings of all three thermometers at
17 temperatures of comparison. The average difference from the
mean is 0-004, and the largest 0'009.

In the fourth series, which consists of readings of all three
instruments at 16 temperatures, the average difference from the
mean is 0'005 ; the difference being, in three instances, greater
than 0'01, and amounting in one instance to 0'019.

The differences did not follow any well-defined law. The
outcome of the observations is, that thermometers of Jena
normal-glass, after being corrected for errors of calibration, of
zero, and of value of a degree, show complete agreement within
the limit 0'01.

Wiebe further compared, between and 100, the above-
mentioned three thermometers with a thermometer, No. 20, of
Thuringian glass, another, No. 115, of English crystal, and a
Tonnelot thermometer, No. 246.

The Thuringian thermometer, which was 70 years old, and
had the relatively small depression -constant 0'14, gave, at
temperatures below 82, higher readings than the normal-
glass thermometers, the difference amounting, at two points,
to 0-05.

The English thermometer read lower than the Jena glass,
thermometers, the difference often amounting to 0- 17.

1 It is figured and minutely described in Zeitsch. f. Inatrum., 10. 27 (1890).

AFTER-WORKING AND THERMOMETPxV. 277

The Tonnelot thermometer was difficult to compare, as it had
not the usual strip of white enamel. It was only tested up to
30, and so far it agreed perfectly with the corrected reading of
No. 246 ; that is to say, the differences noted never exceeded the
possible errors of observation.

The observations of Thiesen, Scheel and Sell were (like those
of Wiebe), conducted at the Reichsanstalt. The instruments,
after the most exact determination of their errors (of calibra-
tion, zero point, and distance between fixed points), were
compared in several series of observations. In some series
the thermometers were in the usual upright position, in others
they were horizontal. All the comparisons were made in a
water-bath, the higher temperatures being maintained by a
worm traversed by steam.

Three series of observations (the thermometers being vertical
in one of them, and horizontal in the other two,) agreed in
showing a systematic difference between normal-glass and verre
dur thermometers, three instruments of each kind being obsei^ed.

Let t 1Q denote the mean reading of the three thermometers of
the normal-glass 16 m ; t T the mean reading of the three Tonnelot
thermometers of verre dur\ and t without suffix the mean

K<W-Mr>

Then, assuming that the difference between t lQ and t T is

proportional to the product of the two intervals t and
100 t, we have (x being a constant),

(100-0
100 2

100*

The value of x deduced from the observations was 0*0259.

Again, the mean reading of three thermometers of the boro-
silicate glass 59 HI being denoted by rf 69 , it was found that the
observations agreed with the equation

t t -

100 s

the value of y being 0-.3336.

By means of these formulae, the folio \vin_r table of differences
between the three kinds of thermometers was calculated :

278

JENA GLASS.
0-0001.

Tempera tun-.

<i-<

<-<

t T -t

<16-<W

<r-'ie

t T -t m

5 and 95

1-J

-158

-12

+ 171

- 25

+ 146

I" 90

300

323

277

15 86

425

458

392

., 80

534

575

492

U .. 7:.

626

674

577

30 7"

701

755

109

646

35 65

759

818

118

700

40 60

801

863

124

738

45 55

826

890

128

761

834

899

129

769

The temperatures in the first column may be taken indifferently

, t T , or

The comparisons between 100 and 300, which we have now
to describe, were carried out by Wiebe and Bottcher during
Ma*-September 1889, with seven normal-glass thermometers,
numbered 253, 254, 255, 257, 258, 259, 271, which were
made for the Keichsanstalt in Nov. 1887. All of them had
enlargements (in their capillary tubes) whose capacities were
known multiples of the volume of a degree (on a plan employed
by Fernet in 1879).

Nos. 254 and 255 were graduated up to 160, in fifths of
a degree, and had two enlargements, one between and 50, the-
other between 50 and 100.

Nos. 253 and 257 were graduated up to about 220, in fifths-
of a degree, and had only one enlargement, which was between
and 100.

Nos. 258, 259, and 271 were graduated up to about 350, in
half degrees, and had two enlargements, one between and
100, the other between 100 and 200.

The calibration was effected by Pernet's apparatus, according
to the method of Neumann and Thiesen. The correction for
calibre in Nos. 253, 255, and 257 nowhere exceeded 0'3. In
the others it amounted, in some places, to more than a degree,
but did not exceed half a degree at any point which entered
into the measurements. Nos. 257 and 259, besides being
calibrated soon after making, were recalibrated after they had
been several times exposed to high temperatures. The second

AFTER- WORKING AND THERMOMETRY. 279

calibration showed that the heating had made a difference, the
lower portion of the tube having shrunk. In 257 the change
amounted to 0'05 at the point 200, and in 259 to 0'04 at the
point 300. The progress of the change was taken into account
in the reductions. The calibration of the other thermometers
was not carried out till they had been several times employed at
high temperatures, and is not likely to have been much affected
by their subsequent heatings. The interval between the two
fixed points was checked several times in the case of each of the
thermometers.

The correction for internal pressure amounted to 0'02 or 0'03
for Nos. 254, 255, 253, 257, and to 0'04 for Nos. 258, 259,
279.

Each observation of temperature was immediately followed by
an observation of freezing point.

The corrections for the non-immersed portions of the stems
were determined with great care by means of small auxiliary
thermometers, at proper heights, close beside the principal
thermometers.

Corrections were fully applied for every known source of error.

The immersion-media were the vapours of 18 different liquids,
having boiling-points spread over the interval from 100 to 300.
The first on the list was isobutylalcohol, boiling at 105*7 at
760 mm., and the last diphenylamin, which at 751 mm. boils
at 301'5. Two different forms of the already mentioned boiler
with back-flow cooler were employed. One of them, pf thin
brass soft-soldered, was used up to 160; the other, of stout
copper hard-soldered, for the higher temperatures. 1

A complete list of the readings of the seven thermometers in
these various vapours and the corrections applied is given by
Wiebe and Bottcher in tabular form. 2 It brings out an unex-
pected closeness of agreement between the instruments. The
difference of an individual thermometer from the mean of all
in the same bath with it, usually amounts to only a few
hundredths of a degree; its average is 0*022. Only once (in
amylbenzoat vapour) did the difference of one thermometer from

tin- mean reach 0*1.

'The exact details of all the arrangements here summarised are given in ;i
paper devoted to the subject. Zeitschr.f. Instrum,, 10. 10 (1890).
*Ztitchr.f. Inttrum., 10. 238-243.

180

JENA GLASS.

The following short extract will serve as a specimen of these
results. I simultaneous corrected readings of the four

lometers 254, 255, 253, 257 in isobutylalcohol vapour
(105-7); of the four thermometers 257, 258, 2&9, L'71 in
ethylbenzoat vapour (212'2); and of the three thermometers
258, 259, -71 in amylU'ii/oat vapour (I'SO^S). The means of
the simultaneous readings are given in the last column.

CORRECTED HEADINGS OF THE SEVEN THERMOMETERS.

254

2,">

253

257

258

259

271

Mean.

105-72

105 -71

105 -73

Kir, -::i

Kir, -71

105 -70

105 -72

in:, -74

105 -73

105 -72

105 -71

105 -73

.j,._, .._,,,

2 12 -24

212 -24

2 12 -25

212 -24

212 -32

212 -33

212 -36

212 -35

212 -34

212 -37

212 -38

212 -40

212 -38

212 -40

212 -43

212 -42

212 -44

212 -4-2

259 -74

259 -65

259 -52

_v><> -r.4

260 -23

260 '15

260 -12

260 -17

260 -53

260 -41

260 -35

2150 -43

260 -62

260 '47

260 "49

260 -53

260 -66

260 -53

260 -57

119. Comparison with the Air Thermometer. The above
comparison of seven thermometers formed part of an elaborate
investigation by Wiebe and Bottcher of the relation between
temperature by mercurial thermometers and temperature by the
air thermometer. The investigation included three series of
researches. The first series (which were merely preliminary)
were conducted in 1888; the second in January-March 1889;
and the third in May-September of the same year.

Two different air thermometers were employed, one of them in
the first, and the other in the second and third series. In both
of them the temperature was measured by the pressure of air at
nearly constant volume. For details of construction and reduc-
tion, we must refer to the original papers. 1

The observations of the third series are given in full by
Wiebe, 2 together with the following table of corrected results.

l Zetischr.f. lustrum., 10. 17 and 10. 233 (1890).

a //><V/., 10. 238-243.

AFTER-WORKING AND THERMOMETRY.

281

T q is corrected temperature by mercury thermometer, and T l by
air thermometer. 1 In each case, simultaneous readings of different
mercury thermometers are not given separately, but are combined
into a single mean.

DIFFERENCES BETWEEN NORMAL-GLASS THERMOMETER AND
AIR THERMOMETER.

First Series.

Second Series.

Third Series.

T t -T,

T t -r q

T t -T 9

106

+o-oi

105-7

+o-oi

109 -3

+ 0-03

113-7

+ 0-06

114 -1

+ -04

124 -6

+ -07

120

+ 0-09

127 -6

+ 0-07

129 -5

+ -09

138

-f-0-02

138 -2

+ 0-07

139 -1

+ -12

139 7

+ 0-11

148 -3

-00

148 -6

+ 0-08

159

-0 -15

158 -7

-0 -03

159-9

+ -11

184

+ -12

184 -4

+ 0-07

184 -1

+ -08

193-7

-00

196

+ 0-04

199 -4

+ 0-02

199-2

-0-05

21]

-0 -30

211 -9

-0-39

_M2 -3

-0-13

j::7

-0 -99

236 -6

-0-92

236-3

-0-48

261 -0

- 1 -41

260 -3

-0 ".i:,

289-5

-' 'IT

291 -5

-1 -64

:m -9

-2-47

The three series agree fairly well with each other. There are,
however, considerable discrepancies in the temperatures near
159, which were observed in vapour of turpentine. In the first
and second series, it was not found possible to make this vapour
give a constant temperature ; probably the liquid was not homo-
geneous. Above 200 the first and second series agree together,
but differ by from 0'2 to 0'5 from the third. The formula

was selected for expressing the differences in I.TMIS of T q \ and

'The subscript q stands for Queckstfber (quicksilver), and the subscript / for
L\ift (air).

JENA GLASS.

the method of least squares, when applied to each series
separately, gave the following values of a and b :

First series,
Second series, -
Third series, -

-iMO x 10~ 7
-284x 10~ 7
-280xlO- 7

-311 x 10-
-370x 10~*
-299 x 10~ 9

The values of T t T q calculated by employing these values of
the coefficients a and b differ from the observed values by the
following amounts (observed calculated), expressed in hundredths-
of a degreee :

First Series.

Second Series.

Third Series.

+ 2

- 1

+ 5

- 3

- 1

-18

- 8

+ 1

+20

+ 2

+ 21

+ 11

+ 3

+ 2

- 8

+ 2

-29

-44

- 2

-11

+ 1

+ 12

+ 4

+ 45

+ 5

- 2

- 7

-12

- 1

Practical Conclusion. In adopting a formula for practical
use, Wiebe and Bottcher decided to rely upon the third series
alone. It was the most complete ; it gave the best agreement
between calculation and observation ; and it was the only series
during which the zero point of the air thermometer remained
steady. They accordingly adopted the values

-280 x 10- 7 , 6= -299 x 10" 9 ,

for the coefficients in the general formula already given. They
have thus computed the following practical table, 1 for reducing

1 Zeittchr. f. Instrum., 10. 245.

AFTER- WORKING AND THERMOMETRY.

the corrected readings of a thermometer of the Jena normal-glass
16 111 to the corresponding temperatures by air thermometer.

Ti-T,

T t -T 9

100

o-oo

170

+ 0-08

240

-0-46

110

+ 0-03

180

+ -06

250

- -63

120

+ 0-05

190

+ -02

260

-0-82

130

+ 0-07

200

-0 -04

270

-1 -05

140

+ 0-09

210

-O'll

280

-1 -30

l.-,o

+ 0-10

220

-0-21

290

-1 -58

160

+ 0-10

230

-0 -32

300

-1 -91

Finally, Wiebe computed, with these coefficients, the corrections
T t T q for normal-glass thermometers at temperatures below 100,
and compared them with the corrections found by Chappuis for
reducing Tonnelot thermometers of verre dur to the nitrogen
thermometer. In the following table, these two sets of corrections
are given, in the columns headed " normal -glass " and " Verre dur"

Normal-Glass.

Verre. dur.

Diff.

<r-*i

-20

+0-153

+ 0-159

-10

+ 0-067

o-ooo

-000

o-ooo

+ 10

-0-049

-0-046

-0 -003

-0 -005

-0 -083

-0 -075

-0-008

-o -008

-0 -103

- -091

-0-012

-0-011

-0 -110

-0 -097

-0-013

-OO12

-0-107

-0-094

-0-013

-0 -013

-0-096

-0-085

-0-011

-0 -012

-0-078

-0-071

-0 -007

-0 -Oil

-0-O.V4

-0-O.VJ -0-002

-0 -008

-0-028

-0-029 +0-001

-0-005

100

o-ooo o-ooo o-ooo

-o-ooo

The next column, headed " Diff." gives the excess of the normal-
glass correction above the Tonnelot correction, which, if we
identify the air thermometer with the nitrogen thermometer,
should be the excess of the Tonnelot reading above the normal -
glass reading, and should therefore agree with the values of
f r 'ie b serve d by Thiesen, Scheel and Sell, which are reproduce.!

isi JENA GLASS.

in the last column (they were given to four decimals in Art. 118).
The maximum discrepancy is 0'006.

Application of Wiebe and Bbttcher's Reductions to

subsequent Observations. In using vapour baths for the

comparison of thermometers, if the boiling takes place at

procure, the observer is restricted to particular

:{>eratures, which may be very unevenly distributed over the
range of the comparisons. Further complications are introduced,

the decomposition which many liquids undergo from contact
with the hot walls of the boiler, and by the impurities which in
many liquids can scarcely be avoided. Wiebe and Bottcher
pointed out these difficulties, and remarked that, if suitable
arrangements were employed for increasing and diminishing
th' pressure, so as to raise and lower the boiling points, a few
liquids would suffice, and those which give trouble could be
excluded. 1

The plan thus indicated was afterwards carried out by
W. Pomplun, at the lleichsanstalt. 2 His boiling point apparatus
consisted essentially of a boiler, and an air-reservoir in connection
with a closed manometer having a large air-bulb.

It was first used for comparisons of normal-glass thermometers
above 50, and proved very effective. The liquids employed were
methyl-alcohol, distilled water, and amyl-acetate. The instru-
ments compared were Nos. 244, 246, 253, 254, 270. The first
was divided to fifths, and the second to tenths ; the others have
been described already. All were corrected in the usual way for
calibre, distance between fixed points, zero, and internal pressure ;
and special attention was paid to the influence of external pres-
sure. The corrected readings were then, by means of Wiebe and
Unttcher's corrections, reduced to air-thermometer temperatures.
The results showed very close consistency over the whole range
of the comparisons, 48 to 141.

120. Mediate Reduction to Air Thermometer. Griitz-
macher 3 carried out comparisons of 1 5 thermometers of three
other kinds of glass, with thermometers of Jena normal-glass
16 MI ; and thus, by using Wiebe and Bottcher 's reductions given
above, compared his 15 thermometers with the air thermometer.

l Zeit*ch.f. Instrum., 10. 28 (1890). 2 /6id., 11. 1 (1891).

9 Ibid., 15. 250 (1895). Communication from the Reichsanstalt.

AFTER. WORKING AND THERMOMETRY. 285

Among them were six " inclosed thermometers " of borosilicate
glass 59 Iir . Two of these were divided to tenths from to 100;
two others to fifths from 100 to 200, with auxiliary graduation
at 0; and the remaining two to half-degrees from 200 to 300,
with auxiliary graduation at and 100. The divisions
were in each case equidistant, and the calibre corrections were
determined by the Neumann-Thiesen method. The distance
between the fixed points was determined in the usual way ;
and also the coefficients for internal pressure, which, on account
of the widenings, were required for the high-temperature thermo-
meters.

Another group consisted of four thermometers, of the baryta
borosilicate without alkali No. 122 m . There had been insufficient
experience in the manipulation of this glass, and the instruments
were not so perfect in construction as could be desired for such
an investigation. Two were divided to fifths from to 100
The other two were divided to half-degrees from 100 to 300.
Their corrections were determined in the same way as for the
thermometers of 59 m .

Lastly five thermometers of " Eesistance-glass " by Greiner and
Friedrichs of Stutzerbach were tested, their graduations being
to tenths from to 100. They were calibrated by a thread
of mercury 50 long for the steps from to 50 and from 50 to
100; and also by a thread 10 long for each step of 10.
Only one of these thermometers was subjected to a complete
calibration. The distance between its fixed points was deter-
mined in the usual way. Up to 50 the comparisons were made
in the water bath; above this temperature, in the vapours of
liquids boiling in the thermostat under ordinary atmospheric
pressure.

Denoting by T q the corrected mean reading of the thermometers
of any one kind of glass the corrections including zero-point,
distance between fixed points, calibration, and, as far as necessary,
internal pressure, and by T the temperature by air thermometer,
deduced from the normal-glass thermometers by Wiebe and
Bottcher's table, the formula

T-T q = aT q (l()Q-T q )+bT q (WO-q)*

was assumed, and the values of a and b were then deduced from
the observations by the method of least squares.

186 JENA GLASS.

The following were the results :

(ilassoO 111 to 100 + 48-70 - 263'8

; <s 59'" 100 to 300 - 72-33 -425*9

^ I2'2 in to 100 + 93-48 - 82-45

Jass to 100 -316-9 -373-76

glass 59 1 ", to 100, the calculated and observed values
agree well, only 7 determinations out of 44 showing a difference
exceeding 0-01. The largest differences going up to 0-015 as
a maximum occurred where the boiling liquids had lost some-
thing of their purity. The "probable error" is 0'003.

For the same glass from 100 to 300, the probable error is 0-09,
even after the exclusion of the last three observations as uncertain.
At the higher temperatures, the mercury was so near its boiling
point (the space above it being nearly free of air) that the column
was apt to break ; and distillation of mercury, which frequently
occurred at the end of the column, added to the uncertainty.

The coefficients a and b for the interval to 100 can be used
without much error between 100 and 200; the values thus
obtained agreeing within 0*08 with those obtained by using the
coefficients for 100 to 300. Above 200 this approximate
agreement does not continue; and at 300 the difference amounts
to 1"2. But the observations above 200 cannot be regarded as
very accurate, and need confirmation.

For 1 2 2 111 between O c and 100, the calculated reduction to
air thermometer has a probable error of 0"005. The observations
on this glass, like Wiebe's observations on English thermometer
glass (Art. 112), indicate that, between and 100, the mercury
thermometer reads lower than the air thermometer. The com-
parisons of the two high temperature thermometers of this glass
showed considerable differences from the air thermometer; but
these were due, at least in part, to defects in calibration and in
evaluation of distance between fixed points.

For "resistance glass," between and 100, the probable
error is 0-006. The largest difference from the air thermometer
was found between 60 and 61 in chloroform vapour. Observa-
tions were not taken above 100.

The tables given below have been calculated by using the four sets
of values of a and b above given. They show that thermometers of
the borosilicate 59 m agree more closely with the air thermometer

AFTER-WORKING AND THERMOMETRY.

than thermometers of normal-glass. They have also, as has been
already stated, less liability to depression of zero by heating. The
baryta borosilicate 122 m surpasses even 59 m in these respects.

'T,

T-T 9

T-T,

59'"

,._>-_>,;;

Resi8t.-Gl.

59"i

122" 1

Resist.-Gl,

o-ooo

-0-02l

+0-013

-0'lL>6

-0 '009

+ 0-001

-0 -032

- -017

+ -014

-0-120

-0 -017

+ -002

-0-059

-0 -014

+ -015

-0 -112

- -022

+ 0-003

-0 -081

- -010

+ -015

-0 -102

-0 -026

+ 0-004

-0-098

-0 -006

+ -014

-0 -090

-0 -028

+ 0-006

-0 -112

-0-003

+ -014

-0-077

-0 -029

+ 0-008

-0-121

-o-ooi

+ -012

-0-063

-0-028

+ -009

-0 -127

+ 0-001

+ -010

-0 -048

-0-026

+ -Oil

-0 -130

+ -002

+ -008

-0-032

-0-024

+ -012

-0 -129

+ -002

+ -004

- -016

-0-021

+ -013

-0-126

100

-000

FOR THERMOMETERS OF 59 m .

T-T q

T-T,

100

o-oo

135

-0-04

170

-0-27

105

o-oo

140

-0-06

175

-0 -32

110

o-oo

145

-0 -08

180

-0 -39

115

o-oo

150

-0 -11

185

-0 -46

120

-00

155

-0-14

190

-0-53

125

-0 -01

160

-0-18

195

-0-62

130

-0 -02

165

-0-22

200

-0-71

(initzmacher applies the following check to the correctness of
his determinations. Let T L T w denote the excess of the air
thermometer over the normal-glass thermometer as determined
by Wiebe and Bottcher ; 1 T bg T the excess of the borosilicate
thermometer above the air thermometer according to Grutzmacher ;
and t u t M the excess of normal-glass over borosilicate, as directly
observed by Thiesen, Scheel, and Sell. 2 The sum of the three
excesses is

which ought to vanish, since each pair of bracketed terms is the
1 See Art. 119. See Art. Us.

JENA GLASS.

AO things which ought to be identical. Grtitzmadier
has applied this test to the temperatures between and 100,
and finds that the sum never exeeds 0< 004.

H. Leinke l has since compared five other thermometers of

(through the medium of normal-glass thermometers) with

the air thermometer, and represented the resulting corrections by

i formula, for the range 100 to 200. His corrections

(litler en the average from Griitzmacher's by not more than 1 02.

The difference increases towards the top of the scale, becoming

at 195, and 0'04 at 200.

KKITCTION OF THERMOMETERS OF THE BOROSILICATE GLASS
59 IH TO THE AlR-THERMOMETER.

T-T,

'1\

T-T q

T q

T-T q

100

o-oo

!'_V,

-0-03

150

-0-13

175

-0-33

101

-00

126

-0 -03

151

-0 -13

176

-0 -34

10-2

-00

127

-0 -03

152

-0 -14

177

-0 -35

103

-00

128

-0 MI4

153

-0 -15

178

-0 -37

104

-00

129

-0-04

154

-0 -16

179

-0 -38

105

-00

130

-0-04

155.

-0 -16

180

-0 -39

106

o-oo

131

-0-04

156

-0 -16

181

-0-40

107

-00

132

-0 -05

157

-0 -17

182

-0 -41

108

-00

183

-0 -05

158

-0 -18

183

-0 -43

109

-00

134

-0 -06

159

-0 -19

184

-0 -44

110

o-oo

135

-0-06

160

-0 -19

185

-0 -45

111

o-oo

136

-0-06

161

-0 -20

186

-0 -46

112

o-oo

137

-0 -07

162

-0 -21

187

-0 -48

113

-o-oi

138

-0 -07

163

-0 -21

188

-0 -49

114

-o-oi

139

-0 -08

164

-0 -22

189

-0 -51

115

-o -01

140

-0 -08

165

-0 -23

190

-0 '52

116

-0 -01

141

-0 -08

166

-0-24

191

-0 "53

117

-0 -01

142

-0 -09

167

-0 -25

192

-0 -55

118

-0-02

143

-0 -09

168

-0 -26

193

- -56

.11!)

-0-02

144

-o-io

169

-0 -27

194

-0 -57

120

-0 -<n>

145

-0 -10

170

-0 -28

195

-0 -59

121

-0-02

146

-0 -11

171

-0 -29

196

-0 -60

122

-0 -02

147

-0 -11

172

-0 -30

197

-0 -62

123

-0-02

148

-0 '12

173

-0 -31

198

-0 -64

124

-0 -03

149

-0 -12

174

-0 -32

199

-0 (>

125

-0-03

150

-0 -13

175

-0 -33

200

-0 -67

l Zeitschr.f. lustrum., 19. 33 (1899).

AFTER-WORKING AND THERMOMETRY. 289

Finally, Lenike has deduced from his own observations con-
sidered jointly with Grutzmacher's, having regard to their relative
weights, the foregoing table of reductions for each degree from
100 to 200.

121. Relative Expansions of Liquid and Envelope. In

this article we suppose temperatures to be expressed in the scale
of the air thermometer.

Let y be the mean coefficient of expansion of mercury from
to t ; /3 the mean coefficient of expansion of the glass from to
f ; V Q the common volume at of the mercury and of the
interior space bounded by the zero mark, which we suppose to be
correctly placed.

Then, at temperature t , this space has increased from V Q to
v (l+/&), and the volume of the mercury has increased from
V Q to v o(l +70' The difference v (y /3)t is the volume at t of
the column of mercury which has passed the zero mark, and
therefore of the portion of the tube between this mark and the

mark which indicates t by air thermometer. Hence -^2 Jill
is the volume of the tube between these marks, measured at O c ;
and ' - is the volume that the mercury which has passed
the zero mark would occupy, if reduced to 0.

Thiesen 1 calls - -^- the " expansion of the mercury relative
to the glass " from- to t t and denotes it by p t .

In like manner he calls the negative quantity zL.LL the

l + yt

pansion of the glass relative to the mercury " from to t\
and denotes it by p\ . From the two equations

~ ................. (1

we have

1 Zeitochr. /. Instrum., 16. 50 (1896).
T

JENA GLASS.

giving

.(3)

-pi

.(4)

In an overflow thermometer which is just full at 0, p\ is
the ratio of the overflow to the total quantity of mercury which
filled the instrument at 0.

122. Thiesen's Experimental Results for Relative Expanr
sion. Overflow thermometers of small size are usually called
weight thermometers. When very large, and constructed with a
view to great accuracy, they are called dilatometers.

Thiesen, Scheel and Sell 1 made elaborate determinations of
p' t at the Reichsanstalt, with five dilatometers, two of which were
of normal -glass 16 m , two of Tonnelot's verre dur, and one of
borosilicate glass 59 m . The values headed p and p in the
subjoined table were for =100. The dilatometer under exami-
nation was kept full of mercury at the temperatures and 100

Dilatometer.

-p'

1007

No. 1 of 16 111

0-01552494

0-01576976

0-0182327

No. 2

0-01550211

0-01574620

0-0182091

No. 1 of verre dur

0-01557575

0-01582220

0-0181934

No. 2

0-01557674

0-01582321

0-0181944

of 59 In

0-01618236

0-01644854

0-0182570

alternately, and the quantity of mercury which flowed alternately
out and in was determined by weighing the small glass cup which
received the overflow, the weight of mercury which filled the
dilatometer at being also known with sufficient exactness.
The ratio of these two weights is p ; and jO was deduced by
the equation

Different determinations with the same dilatometer agreed within

l Zeitschr.f. Instrum., 16. 55 (1896).

AFTER-WORKING AND THERMOMETRY. 291

one unit of the sixth decimal place ; but the values of p for the
two dilatometers of 16 in differ by 22 of these units. This must
be ascribed to the fact that the two instruments were not made
from portions of the same melting. The two dilatometers of
verre dur were made from parts of one and the same glass tube,
and they agree to one unit of the sixth place.

The values of lOOy that is the absolute expansion of mercury
from to 100 given in the last column, were obtained by
combining the values of p or of p' with the absolute expansions of
the three glasses, as previously determined by Thiesen and Scheel
{see Art 99). We have, in fact, by putting t= 100 in the first
of equations (1),

(5)

The security for identity of the dilatometer glass with the glass
of the tubes whose expansion was observed, was greater for No. 1
dilatometer of 16 m , and for the dilatometer of 59 m , than for the
three others. Adopting the mean of these two, to five significant
figures, we have

100y = 0-018245.

This is in good agreement with Bosscha's and Wiillner's reduc-
tions of Regnault's observations.

As the internal volume of a thermometer tube between the
marks and 100, measured at 0, is v p, and the thermometer
is graduated by dividing this volume into 100 equal parts; the

T
volume from to the mark T, measured at 0, is iy> - ; but

it is also (by Art. 121) v Q p t -, we have therefore

In the investigation of Art. 121, t was the air thermometer
temperature equivalent to T '; but the investigation and its result
are equally applicable when t is the corresponding temperature
I'y hydrogen thermometer. Hence if p (which stands for /o 100 ,
And is the same for all scales that have the two usual fixed
points) is known for a particular glass, and also the differences
between T for thermometers of this glass and t for the hydrogen
scale, over a given range, equation (6) enables us to compute />,
over this range.

_>:.j JENA GLASS.

Chappuis* differences between Tonnelot thermometers and
the hydrogen scale give, in combination with the above tabulated
value of p for verre dur, the values of p t for thermometers of
verrc dur between and 100 . The comparisons 1 by Thiesen
and Scheel of thermometers of 16 m and 59 HI with Tonnelot
thermometers, and so mediately with the hydrogen scale, give,.
with the above tabulated values of p for 16 111 and 59 m , the
values of p t for thermometers of these two glasses over the saim-
range. Auin, since the definition of p t is

where y and ft are the mean coefficients of expansion of volume-
of mercury and glass from to tf, the values of p t for the three
-ses, in conjunction with the values of /3 over the range to
100 , which were previously found for these glasses by Thiesen
and Scheel, 2 give for each glass a separate determination of 7
over the range to 100. The 'calculation has been carried out
by these authors, 3 and the resulting mean coefficient from to f
of the hydrogen scale is

y t = '000 18161 + -000 000 0078*.

Observations above 100. The relative expansion p t of
mercury for the borosilicate glass 59 m , which is specially
suited for high-temperature thermometers, was investigated by
Mahlke at the Eeichsanstalt, up to 500, by means of dilato-
meters of this glass. 4 Five dilatometers were used, and each of
them had a graduated neck, of sufficient length to include a
range of 100. The plan of procedure was, to introduce, in the
first instance, such a quantity of mercury that the graduated
portion included the range to 100; then to expel so much
mercury that the range was 100 to 200; then to expel more,
so as to make it 200 to M00, and so on. The arrangements-
for this purpose are fully described and figured in Mahlke's
paper.

Three dilatometers on this plan were employed ; they are
designated I, II, and III. Each of them had its tube divided

1 Page 277. 2 See page 221. * Zeitschr. /. Instrum. , 16. 58 ( 1896).

4 Ann. d. Phy. u. Chem., 53. 965 (1894). Extracts are given in Zeitschr. /.
Inttrum., 15. 171 (1895).

AFTER- WORKING AND THERMOMETRY. 293

into millimetres for a length of 20 cm. All three were main-
tained for three hours at a temperature between 530 and 540
before the mercury was introduced. The quantity introduced
was such that, in the ice-bath, the end of the column stood at the
zero of the divisions. The rest of the tube was exhausted of air
to permit of calibration. When the calibration had been effected,
the first measurement of distance between the two fixed points
(0 to 100) was made. Then, having regard to the temperatures
to which they were to be exposed, the tube of I was filled up with
carbonic acid at 16 atmospheres, and II and III with the same
gas at 8 and 24 atmospheres. 1 A cooling arrangement was
employed to keep the gas at its initial pressure in the observa-
tion of- high temperatures.

When the distance between the two fixed points was remeas-
ured after the filling with gas, it was found to have undergone no
material change ; whence it was inferred that the expansion of
mercury from to 100 is practically the same at 24 atmos-
pheres as at 1 atmosphere.

The next operation was to separate a thread of mercury of
such length that the boiling point should retreat from the end
of the scale to its beginning. The instrument was then immersed
in methyl-benzoat vapour, and the rise of the mercury to 200
was observed. Another separation of a thread of mercury
brought the 200 point to the beginning of the scale, and an
observation was made in a nitre bath at 290. These intervals
of approximately 100 to 200 and 200 to 290 were succeeded
by the intervals 290 to :550', 350 to 400, 400 to 450,
450 to 500. In each of the three last an intermediate
point was also observed. Xo. II dilatometer was the only
one that underwent all these operations without sustaining

thilii;:

The exact temperatures were read off on mercury thermo-
meters, and reduced to the air thermometer by a table of known
corrections.

Reduction of the Observations above 100 . Let V Q be the
volume at of the original quantity of mercury, and c the volume
at 100 of one of the equal parts into which the tube is divided
liv the millimetre scale. Also let n be the number of these

1 At a later stage the pressure in I was changed to 8, and in II to 16 atmos-
pheres. Ann. i.e., t>77.

j:n JENA GLASS.

parts between the two fixed points, and M the ratio defined by
v = Me. Then we have

Let the first portion of mercury removed have at O u the
volume /x, leaving the remaining volume at 0, (M^e.

The dilatometer, with this mercury in it, is heated first to a
temperature ^ near 100, and then to a temperature t z near 200,
temperatures being reckoned by air thermometer. Let e x and e z
denote the volumes of a scale division at these temperatures.
Then we have

11& = (M- M ) e ( 7l - ft)^ ,
n 2 e 2 = (M- p) e (y 2 - /3 2 )Z 2 ,

y l} /3 l being the mean coefficients between O 9 and t^, and %,, /3 2
between and t 2 .

Dividing the first equation by e lt the second by e 9 , and using
the values

6 = ^(1 + 1000),

we find n 2 -n 1 = (M- / m)(l + lOO/3)(p 2 - Pl ), ............. (8)

and from the directly observed magnitudes n lt n 2 , the difference
Pz~ Pi can ^ e computed.

As regards /u, we have defined it by making /me denote the
volume at of the separated column, whose volume at 100 we
will call me. This makes

If we modify the definition by making jme denote the volume
at of a separated column which at the temperature t l (not
differing much from 100) occupies m divisions, then, since the

volume of this mercury at ^ is - ^ , its volume at is

me(l+/3t,) me

(i + ioo/8)( 1 + 7 y that ls ' (i + ioo/S)(i+ ft ) ' by equatlon (2

of Art. 121, p : denoting the value of p t for t = t r This gives

m ,

(

AFTER-WORKING AND THERMOMETRY.

290

In like manner, from the observed number of divisions occupied
by the column of mercury which is detached at the temperature
t 2 , we can calculate p 3 p 2 , and so proceed step by step.

In the numerical calculation, Mahlke employs the values

1 + 100/3 = 1-0017783,
l + 100y = 1-0182161,

the former being Thiesen and Scheel's determination for the glass
in question, and the latter Broch's deduction from Regnault's
observations. These give

P = -01 6 409.
Mahlke deduces the following values of the expression

100)8)

^
**
equation (8) ).

for the successive intervals t k t i . (See

From tt to t k .

Values of the expression.

From to 100

0-00016438

99-43,, 199 -69

16493

201 -43

289 -44

17044

288 -39

349 -80

17698

353 -9

373 -9

17691

373 -9

397 -7

17936

353 -9

397 -7

17820

396-7

424 -0

18318

424-0

452-2

19114

396-7

452-2

18735

456 -0

475 -2

19304

475 -2

495 -0

19358

456 -0 495 -0

19217

As regards the first value, t t is ; t k is 100 ; p t is ; and

To deduce a numerical formula for /> t in terras of tf, assume, for
temperatures between and 290,

(1 + 100/3) ' =

which gives
(1 + 100)

ttfl

JENA GLASS.

Substituting the observed values of the left-hand member,
we have numerical equations in , I, c, from which Mahlke
deduces

10a = 165-873, 10 6 6 = - '0478, 10 6 c = '0002669,
giving, for temperatures between and 290,

10(1 + 1000)^ = 165-873* - -0239* 2 + "000 088 97 3 .

For temperatures between 290 and 500, a four-term formula
is assumed, and the result deduced by the method of least
squares is,

(l + 100)p t = -032931 + 10- 6 x 161-544(^-200)
+ 10- 8 xl2-89(*-20<)) 2
+ 10- 10 x4-858(-200) 3
+ 10 - 12 x 0-8489 (Z-200) 4 .

The following table of values of (1 + 100/3)^ and of p t is
computed by these two formulae :

(1 + 100/3) pt

100

0-016437

0-016408

200

0-032931

0-032873

300

0-049974

0-049885

325

0-054397

0-054300

350

0-058853

0-058749

375

0-063342

0-063230

400

0-067868

0-067748

,425

0-072446

0-072317

450

0-077098

0-076961

475

0-081857

0-081712

500

0-086754

0-086600

Reduction of the Borosilicate Glass High-Temperature
Thermometer to the Air Thermometer. Equation (6), which
may be written

JL = .fiL

100- Pm'

.(6)

enables us to compute the borosilicate thermometer temperatures
T which correspond to the air-temperatures t in the above table.

AFTER- WORKING AND THERMOMETRY.

Mahlke deduces

897

325

330 -9

425

440 -7

100

350

*358 -1

450

469 -1

200

200-4

375

385-4

475

498 -0

300

304 -1

400

412-3

500

527 8

This gives 04 as the correction at 200 for reducing the
borosilicate thermometer to the air thermometer. Griitzmacher
and Lenike (Art. 120), by direct comparison with the air
thermometer, found 0*7. In view of this discrepancy, it is
worth while to examine the separate results given for the
interval ^ to t 2 by the three dilatometers I., II., and III. As a
preliminary step, we shall first deduce a convenient expression
for T 9 T l in terms of the data of observation. We have, by (6),

2 2~

But by (8), .

~~ \P ~~ Pi)'

/>2

where

Hence

and

M =

,-Pi =

l + 100y 100(y-)'

lOO(y-/3)_

.(10)

7i 2 7i]
n+mp

T 2 was calculated by adding the value of this expression to T r
which, from its closeness to the fixed point 100, was readily
-determined with sufficient exactness. The following are the
values of the elements in tin- formula for the three dilatometere :

II.

III.

.-*

I.-.1-3B

159-89

160-46

l.V'

161-35

162-lfi

MS-09

155-28

886

JENA GLASS.

Muhlke adopts

182 161,
= 000017783;

which

T l may be identified with t v their difference being certainly
Less than 0'001. We thus obtain

II.

III.

199 -9

199 -6

199-5

T. 2

200 -2

200 -1

199-8

T 3 -< 2

-3

-5

0-3

The employment of Thiesen and Scheel's value of p' in place
of Mahlke's will not make enough difference to alter any of the
three differences 0'3, 0'5, 0'3, each of which is decidedly smaller
than the value 0'7 found by Griitzmacher and Lemke.

123. Tables for Reducing Mercury Thermometers of 16 m ,
59 m , and Verre Dur, to the Hydrogen Thermometer. Let

t H denote temperature on the hydrogen scale, t lQ , 59 , t T tempera-
tures on the scales of thermometers of 16 m , of 59 111 , and of
Tonnelot's vcrre dur.

Chappuis l adopts, for the reduction of the Tonnelot thermo-
meter to the international hydrogen scale, the formula

W-*(t H -t T )= -0-10921037(100-*)*

+ 5-8928597(100 2 - 2 )aO- 4
-ri5773247(100 3 - 3 )10- 6 .

K. Scheel 2 gives, as an equivalent formula,

- 0-000011577 1 2 ), ................... (1)

and deduces similar formulae for the Jena glass thermometers.
The comparisons carried out by Thiesen, Scheel and Sell (Art. 118)
gave the formulae of reduction

(100-*)*

-L K =-0'0518

100 2

1 Trav. et mtm. du bur. internal , 6. 116 (1888).
9 Ann. d. Phy. u. Chem., 58. 168 (1896).

AFTER- WORKING AND THERMOMETRY. 299

in which t in the second member can, without sensible error, be
taken as denoting the temperature in any one of the three scales.
These equations, combined with equation (1) by addition, give

-0-000011 577 1*\ (2)

(_ 0-31089 + 0-0047351*
-0-000011577* 2 ) (3)

From these formulae (1), (2), (3), the following tables have been
calculated :

VALUES OF t T -t H IN THOUSANDTHS OF A DEGREE.

100

101

102

103

104

105

106

107

106

105

104

103

102

101

100

Y.u.rEs OF t lQ t H IN THOUSANDTHS OF A DEGREE.

100

103

!(>--.

107

109

110

112

IKS

114

115

116

117

118

119

120

119

118

117

116

115

114

lit

111

110

109

107

106

104

103

101

:><;

:,:<

100

300 .IKNA GLASS.

VAI.I'KS >F t. t H IN TiiorsANimis OF A DEGKKK.

_>t

:>7

-'7

_'.-.

1 l

-1

_ o

-2

-1

100

Formulae (1), (2), (3) were deduced from observations between
and 100. Applied to temperatures below 0, they give the
following values, which are liable to the uncertainty attending
extrapolation :

tg-tr

tM-*H

*//-59

- 5

0-03

0*-04

0'02

-10

-15

-20

-25

-30

-35

124. Compensated After-working. Two glasses of unequal
after- working can be so combined, in the construction of a mercury
thermometer, that the after-working of the one is compensated by
that of the other. To attain this end, the bulb must be made
of the glass of smaller after- working, and a properly calculated
volume of the glass of greater after-working must be placed inside
it. Compensation thermometers on this plan were first intro-
duced by Schott. W. Hoffmann published observations taken
with such instruments, and at the same time deduced the relation
which connects their change of zero with the after-working of the

AFTER- WORKING AND THERMOMETRY. 301

two glasses. 1 G. Miiller of Ilmenau has since published some
researches on compensation-thermometers, and prepared the way
for introducing them into practice. 2

Calculation of Depression. 3 Let v l denote the internal
volume of the first or outer glass, measured up to the zero mark,
and at the temperature zero ; v 2 the volume at zero of the second
glass ; and therefore v^ v, the volume of the space originally
occupied by the mercury at zero. Let both glasses have the
same mean coefficient of cubic expansion /3 from to t. Also

let k stand for , y being the mean coefficient of

1 4- lOOp

expansion of mercury from to t. Then, if d l be the depression
of zero which would be produced in a thermometer of the first
glass by heating to t, the volume of this depression, in a
thermometer containing volume v l of mercury at zero, is kv^ ;
since ki\ is the volume of a degree at zero (Art. 121). Similarly,
the volume of the depression d 2 in a thermometer of the second
glass, containing v 9 of mercury at zero, is kv 2 d 9 . In the com-
pensation thermometer, the volume up to the zero mark, which
was initially v l v 2 , is increased by kv^ kv z d 2 ; also the volume
of a degree at zero is k(v l v 2 ). Therefore, the depression,
reckoned as usual in degrees, is

, _ v^ r

(Jf/

The depression vanishes if

= 0, or = -i 2 ; ..................... (4)

and when it does not vanish, its sign is the same as that of

A-*A-

From what is known of the properties of glasses suited for this
purpose, it may be expected that djd l will increase with t. As
v il v t * 8 constan fc> it follows that, if the compensation is exact at
a temperature t, the depression will be negative for higher
temperatures, and positive for lower temperatures ; in other
words the thermometer will be under-compensated for lower and.
over-compensated for higher temperatures.

l Zeil*chr.f. Instrum., 17. 267 (1897).
*Zctt*chr.f. angewandte Chemie, 1898, Heft 2.
'[Shortened and simplified.]

302 JENA GLASS.

Actual Construction. In the compensation thermometers
hitherto made, the outer glass has been the normal-thermometer
glass 16 HI . For the inner, a glass has been specially prepared,
called 335 111 . It has the percentage composition

Si0 2 B 2 3 MgO A1 2 3 As 2 5 Na 2 K 2 Mn 2 3
67-1 7-0 5-0 3-0 0-3 8-5 9-0 O'l

Its expansion is nearly the same as that of 16 IH , and its
proportions of potash and soda ensure large after- working.

If the inner glass were left free to move about in the bulb, it
would give rise, at any place where it touched the outer glass, to
sharp angles in the intervening space surrounding the point of
contact, and the mercury would be drawn out of these
angles by surface tension, thus diminishing the effective
volume of the bulb, and causing the mercury to stand
too high in the stem. The construction which has
been adopted is shown in tig. 27. 1 Hoffmann states
that the attachment of the glass pillar, in the position
indicated, presents no difficulty to the glassworker,
and that it is not difficult to give the volumes the
prescribed ratio. Miiller on the other hand remarks
that special precautions are necessary for obtaining
the desired ratio of volumes.

Observations. Hoffmann observed, in an enclosure-
thermometer, constructed in the ordinary way of glass
335 m , a depression 0> 22 to 0'23, after half-an-hour's
heating at the boiling point of water. Comparing
this with the corresponding depression in normal glass
thermometers, which is 0> 05, we obtain, for the volume-ratio
in a compensation-thermometer of these two glasses,

^__^25_

This conclusion has not yet been tested by the construction
of a compensation thermometer with this volume-ratio ; but
Hoffmann tested nine instruments which had the following
volume-ratios :

No. of thermometer 64 66 62 71 73 61 65 67 68
vjv z 7 7 9 9 9 11 11 11 11

1 Hoffmann, I.e. 258.

AFTER- WORKING AND THERMOMETRY. 303

These ratios are much larger than that above deduced; it
would therefore appear (see page 301) that the temperatures
for which they were truly compensated were much higher than
100. To permit of their exposure to these temperatures, they
were provided with vacuous enlargements at the upper end of
their tubes. Previous to the observations, the instruments were
kept at over 300 for several days; a treatment which produced
considerable elevations of their zeros.

The observations began with a determination of zero, followed
by maintenance for about half-an-hour at about 300. Then
came another determination of zero, succeeded by another on the
same day, and another the next day.

In the heating at 300, some mercury distilled over into the
enlargement at the top of the tube, and had to be subsequently
brought back to the bulb. This circumstance vitiated the
determination of the depression immediately produced by the
heating ; but good observations were made of the gradual change
of zero during several days of rest which followed. The time of
rest varied from 7 to 25 days, and was too short, in comparison
with the intensity of the heating, to give full information. The
observations included, in each case, one at the beginning and one
at the end, of the time of rest. 1

Seven experiments of this kind were made with thermometers
64 and 66. In one experiment there was no change of zero in
1 1 days ; in the other six experiments, the zero fell, by from
0'0l to 0*05, in from 7 to 18 days. This shows that the
volume-ratio v l /v 2 = 7 gave over-compensation for heating to 300.

Better results should therefore be expected from numbers 62,
71, and 73, which had v l /v 2 = 9. No. 62 in fact showed a rise
of 0'01 in its zero after 1 day of rest ; but this rise had dis-
appeared after 18 days' rest. It would seem that after- working
ceases sooner in glass 16"' than in 335'". In four experiments
with these three thermometers, 7 to 25 days of rest showed no
change of zero ; in four others 7 to 18 days of rest showed a fall
of 0-02.

Very similar results were exhibited by Nos. 61, 65, 67, and 68,
which had v l /v t = 11 ; there was no distinct evidence that they
were under-compensated. The exactness of the assumed volume-
ratios does not appear to have been submitted to any after tests.

1 i.e. 259.

304 JENA GLASS.

Adopting the supposition that a volume-ratio v l /v 2 = 10 would
compensate the after-working due to heating at 300, it follows,
from equation (4), that for this temperature, the ratio of the
after- work ings of the two glasses is ^ 2 /^i =10. This is between
two and three times the value of d^d l for 100. It is, however,,
not improbable that the final maximum of the depression-constant
of 335 111 is larger than the value which was adopted, from
experiments of comparatively brief duration.

125. Elastic After- working. Gustav Weidmann 1 undertook
an investigation of the relations between elastic after-working in
glass and its chemical composition. His observations include 13
different glasses. Twelve of them are Jena glasses, which have
been already mentioned (p. 244) among thennometric glasses,
under the designations II., IV, V., VIL, VI II., X, XL, XIX.,
XXII, 16 m , 17 m , IS 111 . The 13th is a Thuringian glass, having
the composition

Si0 2 Na 2 K 2 CaO A1 2 3

68-69 5-87 7'32 15-72 2 2-11

The meaning to be attached to the phrase elastic after-working is
an extension, suggested by Abbe, of the meaning of the term
after-working in thermometry. An antecedent deformation leaver
behind it a residue, which only gradually subsides when the body
is left to itself. The ratio of this residue, after given time, to the
antecedent deformation, is the measure of the elastic after -working.

Flexure Experiments. The first measurements of this
after-working were made by bending glass rods (strictly speaking,
stout capillary tubes).

The following was the mode of procedure. The rod was firmly
clamped near one end, and was at the same time supported on a
knife-edge about 58 mm. from the clamp. Near the other end,
a weight was hung on by a thread. In the later experiments,
thie loading lasted 10 minutes. The free end of the rod
carried a fine scale 1 cm. long, which, when the rod bent, moved
across the field of view of a horizontal microscope. The dis-
placement of the end could thus be measured in thousandths of a
millimetre, with an error not exceeding 2J thousandths. The

l Dixxert, Jena, 1886.

2 Weidmann gives 5 '72, which appears to be a misprint.

AFTER-WORKING AND THERMOMETRY.

305

readings were taken at 10, 20, 40, 60, 90 ... seconds after
loading.

Preliminary trials showed that after- working, as above defined, was
independent of the amount of bending, and also independent of the
dimensions of the rod. It accordingly depends only on the nature
of the glass, and the duration of the loading. Results are there-
fore comparable, provided that the durations of loading are equal.

If a light loading was immediately succeeded by a heavy loading,
the after- working showed an increase. If, however, several succes-
sive observations were made with this heavy loading, the after-
working diminished again, and, after about three observations, re-
sumed and retained its original value. Transition from heavy to light
loading gave, as was to be expected, precisely the opposite result.

Experiments with one and the same kind of glass, at different
temperatures, kept steady during the continuance of an experi-
ment, showed that glasses resemble caoutchouc in having decrease
of after-working with increase of temperature.

It was therefore necessary to conduct all experiments at the
same temperature, as nearly as circumstances permitted. The
long continuance of the investigation made the rigorous fulfilment
of this requirement impossible.

The disappearance of deformation from the unloaded rod was
hastened by warming, and also by tapping.

Tapping (and probably also warming) the loaded rod increased
the after-working.

Results. The course and magnitude of after-working in the
different glasses, as deduced from the flexure experiments, are
given in the following table :

AFTER-WORKING.

After.

IV.

ii.

18 1 "

XI.

16" 1

20 sees.

0011

0018

0027

40M

0038

0065

<* H

120

180 ,,

Temperature.

JENA GLASS.

AFTER-WORKING.

After.

VIII.

XIX.

VII.

Thuring.

XXII.

17111

20 sees.

0082

0085

0088

0106

0150

0323

138

2:>9

124

221

113

185

120

157

180 ,,

128

Temperature.

In the last five glasses, the decrease of after-effect was followed
still further, with the results shown below.

AFTER-WORKING.

After.

XIX.

VII.

Thuring.

XXII.

17111

3 minutes.

0011

0023

0057

0085

0128

5 ,,

Temperature.

Piezometric Experiments. Two thermometers, one of the
above-mentioned Thuringian glass, and the other of the normal
thermometer glass, 16 m , were tested by internal pressure. They
had spherical bulbs of diameters 36'2 and 32*2 mm., and tubes
of internal diameters 0'27 and 0*45 mm., open at the top. The
open end of the thermometer under experiment was connected,
by a sealing wax junction, with a glass tube bent twice at right
angles, which passed through the cover of the piezometer ; and
there was another opening in the cover through which the
tube of a manometer passed. Pressure applied to the water
which filled the piezometer was thus transmitted to the interior
of the thermometer, producing dilatation of the bulb and tube,
which was indicated by the depression of the mercurial column.
The pressures employed were from 1 to 10 atmospheres, and

AFTER- WORKING AND THERMOMETRY.

307

each pressure was kept on for 10 minutes at a time. The
displacement of the summit of the mercury was observed with
a reading microscope.

The most important precaution to be attended to in such
experiments is that they be executed at a constant temperature.
With this view the thermometer bulb was surrounded with snow
in the caking condition. But as an experiment sometimes lasted
three hours, the influence of the temperature of the surroundings
was not quite excluded. It is probably the chief source of
inaccuracy in the determinations. Another source is the long
time required to take off the pressure, amounting to from 10 to
40 seconds.

In accordance with the definition above given of the numerical
measure of after-working, Weidmann records the ratio of the
remaining dilatation to the original dilatation after the lapse of
stated times. He concludes from his observations that this ratio
is constant for one and the same thermometer ; and gives the
following comparison of elastic after-workings as determined by the
two different methods flexure and dilatation :

Time
iu seconds.

Glass 16 UI .

Thuringian.

Flexure.

Dilat.

Flexure.

Dilat.

0065

0069

0106

0107

120

180

Temperature.

For the Thuringian glass the two methods of deformation give
nearly identical results. Weidmann inclines to the view that the
larger differences in the case of the 16 HI are due to larger errors
of observation.

Torsion Experiments. Lastly, Weidmann tested the after-
\vnrking of two glasses 16 IH and 18 IU , by torsion. He used
glass fibres, which, at the definite temperature, were first subjected
for ten minutes to torsion, and then relieved. The apparatus

806

JENA GLASS.

employed exactly resembled that described by Kohlrausch, and
the readings were taken by telescope and scale. Within certain
limits the experiments confirmed his result that the original and
the remaining torsion are proportional ; their ratio is taken as the
measure of the after-working. The results are given in the
following table, along with those of the other two methods,
which are reproduced for comparison :

Time
in seconds.

16"'.

18'".

Thuring.

Flex.

Dilat.

Tors.

Flex.

Tors.

Flex.

Dilat.

0065

0069

0036

0106

0107

0055

0024

36 .

120

180

Temperature.

The comparison seems to indicate that the magnitude of after-
working is not independent of the nature of the deformation.

Formula for the Progress of After- working. F. Kohlrausch,
in accordance with a theory of after-working developed by Boltz-
mann, represents the falling off of the after-effect by the formula

x = Ce~ atm

x denoting the amount of deformation remaining after time t,
reckoned from the instant when the body is set free, divided by
the original deformation. For a given body, and given kind of
deformation, the constants C, a, and m are independent of the
magnitude of the deformation, if not too great.

Weidmann finds that his flexure observations on glasses
V. and VII. and Thuringian glass are well represented by the
formula, with the following values of the constants :

V. VIL

C 0-005980 0-01604

1 1

- 0-5731 0-5526

m -

Thuringian.

0-01686
0-696 7
0-416 7

On the other hand, his torsion observations cannot easily be
reconciled with the formula.

AFTER- WORKING AND THERMOMETRY. 309

126. Elastic After-working and Chemical Composition.
Of the 1 3 glasses tested for elastic working by Weidmaim,

4 are potash glasses, viz., IV., V., XL, 18 m :

5 are soda glasses, II., VIIL, X, 16 1 ", XIX. ;
1 is a lithia glass, VII. ;

3, viz., 17 m , XXII., and Thuringian, are mixed glasses in
the sense of containing both potash and soda.

The observations in Art. 125 show that the three mixed
glasses are distinguished from the others by the largeness of their
elastic after-working, and the lithia glass comes next to them.
The following figures relate to the three mixed glasses :

Thuring. \ XII. 17 m .

After-effect after 20 s , "0106 -0150 '0323

Soda 5-87 14 15

10> Potesh 7-32 14 TO^

In the initial stage, the lithia glass shows after-working
comparable with (though less than) that of soda glass, but its
falling off is much more rapid.

The following figures show that the order from less to greater
is nearly the same for content of soda as for after-effect :

II. X. 16 1 ". VIIL XIX.

Effect after 20 s , '0018 '0027 '0065 -0082 -0085

Percentage of soda, 7 8 14 15 15

Temperature, 3 4 7 10 4

Taking temperature into account, VIIL ought to be regarded as
having more after-working than XIX. It also shows a slower
fjil ling off.

The after-effect for potash glasses, even in the early stage,
is very much smaller than that of soda glasses in the middle stage.
The order from less to greater in content of potash is not the
same as the order from less to greater in after-effect, and would
not be made the same by correcting for difference of temperature.
This is shown by the following figures :

is".. IV. V. XI.

Percentage of potash, 9 13'5 16 18

Effect after 2 O 8 , -0036 '0011 '0036 '0038

Temperature, 8' 11 1 12

310 JENA GLASS.

127. Comparison between Elastic and Thermal After-
working. Weidmaim's investigations, which we have been
describing, were mainly directed to answering the question
whether any relation can be found between elastic and thermal
after-working.

Taking as an index of thermal after-working the depression-
constant D denned in Art. Ill, and noting its values for the
groups of glasses which we have just been discussing, we have
the following list of values of D, in decimals of a degree :

Thuring. XXII. 17 111 .

Mixed glasses,

1-05

1-06

Lithia glass,

II.

16 m .

VIII.

XIX.

Soda glasses,

18 1 ".

IV.

XI.

Potash glasses,

- -05

These figures bear out the statement (see Art. Ill) that mixed
glasses show larger thermal after-working than glasses with only
one alkali. The same is true, as we have just been showing, for
elastic after- working. Looking upon after- working of either kind
as a thing to be avoided, we may therefore say, with Weidmann,
that " thermally bad " glass is " elastically bad," and that
" elastically bad " glass is " thermally bad." The same conclusion
results from comparing flexure observations with depression.

No exact relations between elastic and thermal after-working
are however to be gathered from these comparisons, and it was
to obtain further indications in this direction, that Weidmann
undertook the piezometric experiments, in accordance with the
following line of thought.

Let V Q be the volume of mercury in a thermometer at 0,
y and ft the mean coefficients of expansion of the mercury and
the glass from to 100, Then the capacity of the bulb is
greater at 100 than at by 100^ , the volume of a degree at
100 is (y /3)v , and hence the increase of volume is equivalent

to ^ degrees. Call this number n ; then internal pressure

y-P

producing an increase of volume measured by n degrees will
afford a fair comparison, in its after-effect, with the depression D

AFTEK- WORKING AND THERMOMETRY. 311

produced by heating from to 100. The piezometric results
were, however, in the meantime only employed for comparison
with the results from flexure.

Weidmann expresses a suspicion that thermal and elastic
after-working cannot be comparable, inasmuch as elastic after-
effects disappear quickly, whereas the vanishing of depression is a
very tedious process. He also contrasts Pernet's law (Art. 113),
that the depression produced by heating from to t is propor-
tional to the square of t y with the fact that elastic after-effects
are simply proportional to the original deformation.

128. On the Theory of the Thermal After-working of
Glass. The phenomenon of depression, which is found in all
mercury thermometers, has not yet received a satisfactory explan-
ation. 1 There can be no doubt that depression indicates an
increase in the capacity of the bulb ; but the cause of the
increase is still an open question.

Under these circumstances we may be permitted, without pre-
tending to offer a complete theory, to give a few indications as to
the nature of the actions whose existence can be inferred from
the observations.

The after-working which is in question includes a series of
phenomena. The first of them is, that when a glass is raised
from O c to t, its volume, while maintained steadily at this
temperature, goes on increasing for a considerable time. A good
example is furnished by Wiebe's observations on the continually
advancing depression of a boiling point thermometer of Thuringian
glass in alcohol vapour (Art. 115). The continual increase depends
(for any given glass) not only on the temperature t to which the
thermometer is raised, but also on the progress of the heating up
to that temperature.

Deformation of the Walls of a Hollow Vessel by Heating.
When an approximately spherical or cylindrical hollow vessel,
with its walls originally free from stress, is rapidly raised in
temperature from to f , it is obvious that, during the rise, the
walls will consist of layers of different temperatures. If we
imagine the connections between the layers to be dissolved, the

'A brief account of attempted explanations is given by R. Weber in the
introduction to his investigation of the influence of the composition of the glass
on depression. Ber. d. Berlin Akad., Nov. 1883.

312 JENA GLASS.

layers would separate from one another, to distances increasing
with the differences of temperature, and with the expansibility
of the material. As soon as all the layers have attained the
common temperature t, they will, for the first time, be all in
contact, and free from stress. The capacity of the vessel when
this condition is attained, may be designated its normal volume.

As the layers are actually united firmly together, it follows
that, during the rise of temperature, they deform each other ; the
outer layers are subjected to thrust, the inner ones to pull, and
between the two there will be a layer free from stress. In
spherical or cylindrical vessels, the deformations thus produced
could be calculated, if the thermal expansibility of the material,
and its coefficients of elasticity, were known, and if a definite
assumption were made as to. the distribution of temperature from
layer to layer.

After-working of this Deformation. It cannot be doubted
that the elastic deformations thus called out in the walls during
the rise of temperature produce after-working. The circumstance
that the deformations are accompanied by rise of temperature
has probably an influence on their magnitude and course, and
renders their estimation more difficult.

Weidmann's observations (Art. 125) furnish a basis of calcu-
lation for the after-working of the dilatation, if we employ the
assumption (which was supported by his flexure observations)
that after-working is increased by warming during the application
of stress.

No data are available for the after- working called out by thrust.
Whether it is influenced and if so in which direction by rise
of temperature during the application of stress, is not known.

The ratio of these two after- workings one to the other is also
not indicated by available observations. Moreover it is quite
possible that the coefficients of expansion of the different layers
are slightly modified by the conditions of tension and thrust.

Influence of After-working on Capacity. It is not & priori
probable that the layers, affected as they are with opposite after-
workings of varying intensities, should, on attaining the per-
manent temperature t, be in permanent equilibrium, and have their
normal volumes. The gradual relief of the stresses in the layers
is not likely to be brought about without changes in the volume
of the vessel. It would not be altogether unreasonable to suppose

AFTER-WORKING AND THERMOMETRY. 313

that there might even be alternate inward and outward move-
ments, as results of the two opposite kinds of stress, which
contend with one another. Lack of experimental evidence forbids
confident statements on these matters, and we can only form
conjectures.

Hypothesis on Thermal After- working. As a working
hypothesis, let us assume that these supposed movements actually
occur, and bring about the observed thermometric depression.
The following will then be the course of events.

Alter the temperature t is reached, the after- working of thrust
in the outer layers first comes into operation, and the vessel
regains its normal capacity. The movement continues beyond
this position, and the after-working of pull in the inner layers
comes into play. The limit of this movement will be determined,
on the one hand by the magnitude of the after-working itself, and
on. the other by the elastic resistance of the outer layers. After
the movement of extension has ceased, there will be a slow recoil,
the after-working of pull vanishes gradually, and finally the
normal volume is attained, but this time without stress in the
walls. 1

From this view of what occurs, it will immediately follow that
the conditions which promote largeness of depression in a glass
are, large thermal expansibility, large after-working from pull,
small conductivity, and small coefficients of elasticity.

Verification of these Conclusions. These conclusions, as to
the physical properties which conduce to largeness of depression
of the zero of a thermometer subjected to rapid heating, can
be tested by comparison with observed depressions.

Fernet has laid down the rule that, in order to obtain agree-
ment between the indications of thermometers which have unequal
depressibilities, the observed muling must be compared with the
zero as determined immediately after. 2

1 [Whether we accept or reject this outline of successive stages, it seems clear that,
taking as independent variables (1) thermal expansibility, (2) thermal diffusivity,
(3) resistance to distortion, (4) liability to imdi.mical after-working which
nearly correspond to /;. A. /.'. .V, the distortion ]>r<><liKl by sudden change of
temperature of the surface will increase with the largeness of (1), and with the
Hnuillness of (2) and (3). The after-working consequent on the distortion will
naturally be proportional jointly to the distortion and to (4). We thus arrive at
the conclusion stated in the text. J. D. K. ]

2 Winkelmann, Handl>. d. 7>Ayi*., II. 2. 84.

JENA GLASS.

Hence we must infer that the depression brought about by
heating from to 100 C is not much changed by the immediately
subsequent cooling from 100 to 0. As regards the physical
qualities above indicated as affecting depressibility, the following
facts may be adduced.

\\.i.lmann found a connection between depression and the
elastic after-working brought about both by bending and by
nal pressure a connection which he expressed by saying that
a thermally bad glass is also elastically bad, and vice versa" The
absence of a definite quantitative relation is only what was to
be expected, if depressibility depends on other qualities as well.

The opinion that smallness of thermal expansibility keeps
down depressibility has been long held, and is borne out by
even a superficial comparison of coefficients of expansion with
after-workings resulting from internal pressure. In giving an
account of the thermal after- workings of 16 m , 17 111 , and 18 m ,
Weidmann calls attention to the great differences in expan-
sibility between these three glasses. 1 In fact, if depressibility
is to be made small, it is absolutely necessary to employ glass
of small expansibility.

Conductivity has also been long regarded as influencing
thermal after- working. In citing old researches by Wild, Weid-
maun expresses the belief that " bodies which conduct heat well
have small thermal after- working." This explains the absence
or extreme smallness of thermal after-effects in metals.

Furthermore, it is not merely internal conductivity that must
be regarded as influential. The difference of temperature between
the external and internal surfaces of a bulb when exposed to
heating, will depend mainly on the ratio of surface conductivity
to internal conductivity. An experiment of Weidmann's seems
to show that different kinds of glass differ largely in surface-
conductivity. When steam was passed through tubes of 16 m ,
17 m , and 18 m for the purpose of heating them, 16 m and IS 111
were quickly bedewed, but not I7 m , although, as he goes on to
remark, 3 it was a hygroscopic glass. Clearly, the surface of the
hygroscopic glass was more quickly heated up than the surfaces
of the others ; which is easily intelligible, as steam was the
:ig substance. In internal conductivity it was intermediate
between the other two.

1 Di*., 18. - /;/.**., 34. a Dis8. t 18.

AFTER-WORKING AND THERMOMETRY.

315

The influence of elasticity upon depressibility seems never to
have been suggested. There is, therefore, special need for
evidence on this point.

The following table will serve for testing the foregoing con-
clusions. The first column gives the names of the eleven glasses.
In the second column, ft is the coefficient of cubic expansion.
In the third, K is the internal conductivity, in C.G.S. units. In
the fourth, Nis the measure of the after-effect 20 s after unloading,
in the flexure experiments. E in the fifth column is Young's
modulus of elasticity ; and D in the last column is the depression

Name.

10 7 /S.

10' A'.

10W.

328

1-490

8490

0-02

IV.

253

2O81

6595

n -i.s

233

1-504

5980

0-09

VIII.

281

2-260

6865

(l -us

237

1-630

7180

0-09

XI.

231

1 V_N

7iN<

-09

16'"

241

2-100

7543

-05

17"'

342

1-869

323

6781

1 -06

18 1 "

162

1-588

7810

-05

XIX.

271

1-690

8000

0-07

XXII.

342

1 -sx-j

150

6454

1 -05

after heating from to 100. All the values of N and of D
are from direct observation. Most of the other values are com-
puted from the chemical composition of the glasses (see Arts. 97,
93, 72); the only observed values being ft for 16 m , 17 HI , 18 m ,
and 1C and E for 16 m . The values of N were all observed at
the same temperature. The values of D are not rigorously
comparable, inasmuch as the thermometers were not all of the
same age. As there are here several elements of uncertainty,
inferences must be drawn with caution, and not based on small
differences.

A conspicuous example of the influence of elasticity is furnished
by* the first two glasses II. and IV., the former a soda and the
latter a potash glass. Both of them show small elastic after-
working; IV. has the smaller coefficient of expansion, and much
the larger conductivity. These are reasons for expecting it to
have the smaller depressibility ; and the fact that its depression-
constant is four times as large as that of II. can only be

316 JENA GLASS.

accounted for by the fact that it has a coefficient of elasticity
rather below the average, while that of II. is the largest in
tlu- list. The comparison of VIII. with XIX. furnishes another
example <f the influence of elasticity.

The influence of conductivity is seen by comparing VIII. with
X. The influence of the coefficient of expansion (as well as of
the coefficient of elasticity) is brought out by the comparison of
IS 111 with the group* V., X., XI. The equality of the depres-
sions for these three glasses is not quite in accordance with
theory we should expect that of V. to be the largest and the
discrepancy is perhaps to be ascribed to errors in the values
deduced from chemical composition.

Comparisons of this kind could easily be multiplied. In the
great majority of cases they are in harmony with the predictions
of the foregoing theory.

129. Thermo-elastic After- working. In Art. 73, in con-
nection with the elasticity of glass at high temperatures, it was
mentioned that Winkelmann found indications of an increase in
the coefficients of elasticity of glasses, after heating and cooling
down again. He illustrates the point l by a series of observations
on glass 23 (in his own numbering). On April 27, 1894, after
a determination of its coefficient of elasticity on the previous
day, it was heated to 380; and, being tested on April 28,
showed a larger value of the coefficient, which, however, had
fallen off a little by April 29; and on May 19 the fall had
reduced it to nearly its original value. Being then heated to
480, it was found on May 30 to have nearly returned to its
original value; but being then again heated to 480, the
increased value which it showed remained steady till June 14.

Several glasses were treated in this way until the increased
coefficient of elasticity became steady ; and these steady values
are given, together with the original values, in the following
table. They are in kg. per sq. mrn., for the temperature 20.
The column headed W. contains Winkelmann's numbers for the
glasses. The differences are given in percentages, and range
from O'l to 4'6 per cent. 2

1 Ann. d. Phys. u. Chem., 61. 114(1897).

2 The value 7563 given in Art. 72 for glass 19 is the mean of observations on
three rods ; 7540 is the value for one of these rods.

AFTER-WORKING AND THERMOMETRY.

317

The table does not furnish exact comparisons between the
glasses ; inasmuch as they were not all heated to the same
temperature. The increased values were not, in a strict sense,

Before.

After.

Diff.

Before.

After.

Diff.

7540

7672

1'8%

5477

5494

0'3%

5468

_':.

7180

7349

2-3

4906

2-4

7314

7524

2-9

7992

8146

1-9

7465

7649

_>:.

.-,4-jc,

5433

O'l

7401

7564

2-2

6766

6983

:; _'

74 16 1

7589

2-3

540]

5600

0-8

6097 1

6218

6599

6669

1-1

7971

8340

4-6

6650

0-2

7461

7551

1-2

6014

6159

J-4

Tls.i

7234

6373

6441

1-1

6572

6687

1-7

5843

5885

0-7

permanent. After the lapse of a long time smaller values were
found, which gradually diminished to the original values. In
glass 19, for example, this complete return occurred after about
16 months ; in glasses 85 and 87 after about 10 months.

Thermoelastic after- working is not, by any means, a property
peculiar to glass. Winkelmann has found very conspicuous
manifestations of it in platinum. 2 A strip of platinum, of the
same thickness as the wall of a thermometer bulb, showed an
initial coefficient of elasticity of 16926 kg. per sq. mm. After
several warmings to 20, this had increased to 18380 ail
increase considerably larger than that observed in glass. After a
rest of 10 months, the coefficient had gone back to 17516 ; and
it showed little further decrease during the next 4 months.

The observed phenomenon cannot be a mere consequence of in-
crease of volume ; for this is too small to account for the observed
difference, as Winkelmann has pointed out, both in the case of
glass and of platinum. A thermometer made by L. Marchis, with
a glass tube melted on to a platinum bulb, 8 showed, after heating

1 These three glasses had been in the heating apparatus before the first
observation.

9 Awn. d. Phy. u. Ghcm., 63. 117 (1897).
Jour, de Phy. (3) 4. 217 (1886).

318 JENA GLASS.

to 100 y , a depression so small that its existence could not be
established with certainty. Still less is it possible to ascribe the
effect to diminution of volume resulting from protracted heating ;
for, as Winkelmann has remarked, this would produce an
apparent diminution of the coefficient of elasticity.

The increase is real, and not merely apparent. Winkelmann
suggests, as the most obvious explanation, the introduction of
stress by the heating and quick cooling ; the glass being supposed
to be previously well annealed. If this is the explanation, the
stresses must, however, be different in kind from those produced
by the rapid cooling of glass heated to softness ; for Winkelmann
and Schott have confirmed Quincke's result, that unannealed
glasses have smaller coefficients of elasticity than well annealed. 1
Furthermore, the circumstance that the glasses were heated to
near their softening points does not seem to be material ; for the
platinum showed similar effects after heating to 400 a
temperature very remote from its melting point.

l Ann. d. Phys. u. Chem., 51. 710 (1894).

CHAPTER X.
CHEMICAL BEHAVIOUR OF GLASS SURFACES.

130. For glasses which are to be used in the construction
of physical instruments or of chemical utensils, immunity from
chemical attack, by any liquids, vapours, or gases which are likely
to come in contact with them, is often a prime consideration.
For instance, glasses possessing valuable optical properties may be
unfit for use in optical instruments by reason of susceptibility to
the action of damp air. Or, to give another illustration, it is well
known that Stas, in his revision of the atomic weights of the
elements, thought it necessary to have the glass vessels which
were to be used in the research expressly made, of glass
characterised by special power of resisting such influences.

The nature and course of the chemical actions produced on
the surface of glass, by contact with various substances and
under various conditions, and the dependence of these actions
on the chemical composition of the glass, have been the subject
of very numerous researches. We must confine our attention
to those which are most closely related to the work of the
Jena glass-making laboratory. They are contained in the
following memoirs, which we give in chronological order,
together with the abbreviated designations by which we shall
refer to them :

M. I. = F. MylhiB, "On I M-nirluices of Spirit Levels." ('<>iiiinuiiiation
from Reictowu^t.ili /

M. II. = F. Mylius, "Testing tl e of Glass by Colour Reaction."

Comm. from Reichs. %,>it*,-I, r . / . 9. 50 (1K^

Sch. =O. Schott, " Soaking of Water into Glass fS> Zcitichr. f.
9. 86 (1889).

320 JENA GLASS.

M. u. F. I. = Mvlius;in,I F. Poenter, "Solubility of Glass in Water." Ber.

l ^89).

M. u. I-'. II. M \ liu> a n.l F.K'rster, " Solubility of Potash- and Soda-glasses iu
\V iiiiuun. from Reichsanstalt. Zeitschr. f. lustrum.,

9. 117(1889).

M. u. F. III. = Mylius aii.l K.H-rster, "Determination of Small Quantities of
Alkali, etc., in Water." Commun. Reichs. Ber. d. deutxch.
. 1 L82 U*91).

M. u. F. IV. = Mylius and Foerster, "Glass Vessels for Chemical Use.
Behaviour of Glass Surfaces to Water." Com. Reid is.
fedtr. / lustrum., 11. 311(1891).

K. I. = F. Kohlruns.-h, " Solubility of Some Glasses in Cold Water." Ann. d.
I'hys. u, Chem., 44. 577 (1891).

K. 1 I. = Kolilrauseh (Same title. Extract from above). Ber. d. deutsch.
\. 3560 (1891).

F. I.= F. Poeroter, k> rli<-iniral Behaviour of Glass. Action of Solutions of
Alkalis and Salts on Glass." Com. Reichs. Ber d. deutsch.
Chem. Ges., 25. 2494 (1892).

F. II. = Foerster, "Further Knowledge of Chemical Behaviour of Glass.
Investigations at Reichsanstalt." Ber. d. deutsch. Chem. Ges.,
26. 2915 (1893).

K. III. = Kohlrausch, " Further Observations on Glass and Water." Ber. d.
deutsch. Chem. Ges., 26. 2998 (1893).

F. III. = Foerster, "Action of Acids on Glass. Investigations at Reichs."
Z,-;t*<'l { r.f. analyt. Chem., 33. 299 (1893).

F. I V. = Foerster, "Glass Vessels for Chemical Use." Commun. from
Reichs. Zeitschr. f. Instrum., 13. 457 (1893).

K. u. H.=Kohlrausch and Heydweiller, "Pure Water." Ann. d. Phys. u.
Chem., 53. 209 (1894).

F. V. = Foerster, "Comparison of Some Glasses in Chemical Behaviour.
Invest. Reichs." Zeitsch. f. analyt. Chem., 34. 381 (1894).

R. = Reinitzer, " Contributions to Quantitative Analysis." Zeitsch. f. ange-
wandte Chem., 1894. Heft. 18 u. 19.

V. I. = P. Volkmann, "Measurement of Surface Tension of Water in
Capillary Tubes of Various Glasses." Ann. d. Phys. u. Chem.,
53. 633 (1894).

V. II. = Volkmann, "Studies on Surface Tension of Water in Fine Capillary
Tubes." Ann. d. Phys. u. Chem., 66. 194 (1898).

131. Decomposition of Surface of Glass by Water. After
attention had, for several years, been directed to the circumstance
that glass levels in course of time became useless, owing to a
rouuh coating which formed upon their inner surfaces, an
investigation was undertaken by the Keichsanstalt into the
cause of this trouble. It disclosed the fact that the phenome-
non occurred in levels in which the ether was not free from
water, and that it arose from chemical decomposition of the

CHEMICAL BEHAVIOUR -OF GLASS SURFACES. 321

surface of the glass by the water. In accordance with many
earlier observations, it was found that the water had extracted
potash and soda from the glass, while only a relatively small
quantity of silicic acid had been dissolved.

The formation of the rough coating being thus traced to the
decomposition of the glass by water, a comparison of the relative
susceptibility of different glasses to this kind of attack was
obviously suggested. Previous publications contained no com-
parisons from which quantitative conclusions could be drawn.
Such a comparison was undertaken by Mylius, for 14 different
glasses, among which were five Jena glasses, including the normal-
thermometer glass 16 111 . 1

The following was the method of procedure. The glass to
be operated on was first pounded in an iron mortar, and, by
the help of two sieves, was obtained in the form of rather coarse
particles of nearly uniform size. A volume of 8*01 c.c. of this
material was weighed, and put into 70 c.c. of distilled water in
a platinum vessel, in which it was heated for five hours in a bath
of boiling water. The platinum vessel carried a small back-flow
condenser cooler, connected with a Liebig's potash apparatus
for excluding atmospheric carbonic acid. The solution, when
it had become cold, was filtered, and a volume of 60 c.c. of the
filtrate was employed for the determination of the constituents.
A defect, as regards comparability, is the absence of security
for equality of the total surface of the glass particles in different
experiments.

Mylius gives, in a table which we do not reproduce, the quan-
tities (in milligrammes) of silicic acid, soda, and potash in each
60 c.c. of solution; and the quantities of oxygen in the soda and
potash are calculated on the assumption that there are 16 parts
by weight of oxygen in 62 of Na 2 O, or in 94 of K 2 0. The quan-
tities of oxygen thus computed for the two alkalis are added, and
the sum is adopted as the measure of susceptibility to attack by
water. This gives the same order of arrangement as would be
obtained by dividing the weight of soda by 62, the weight of
potash by 94, and adding.

In the list of glasses thus arranged in order of susceptibility to
attack, the first that is, the most susceptible is potash water-
glass, and the second, soda water-glass. The pure silicates of

.M., I. 276.

:i> JENA GLASS.

potash and of soda respectively, were also tested for comparison.
Flint glasses with a large content of lead were found to have
specially high withstanding power. The densest Jena lead silicate,
containing 78'3 per cent, of lead oxide, and 21'7 of silicic acid,
came last in the list, being almost completely exempt from attack
by water. It is known that these flint glasses are only very
slightly hygroscopic, and that they are good insulators for
electricity. On the other hand, they are easily decomposed by
acids and alkalis.

The ratio of the constituents extracted from glass is not the same
when the water is cold as when it is hot. Mylius found, in the
case of soda water-glass, that water at 100 gave a solution
containing 0*36 of a molecule of soda to each molecule of silicic
acid, while water at 20 gave, after nine days' contact with
powdered water-glass, a solution containing 3*1 molecules of soda
to one of silicic acid.

132. Testing of Surface by Colour-Reaction. R Weber has
introduced a method of testing glasses by exposing them for 24
hours to an atmosphere of hydrochloric acid vapour, and after-
wards to air. 1 The glass becomes covered with a rime of chlorides
which is more abundant in proportion as the glass is more suscep-
tible to attack. Weber himself carried out, by this method, a
thorough investigation of the relation between the composition
of glasses and their chemical behaviour under atmospheric
influences. 2 The method requires a trained eye, and cannot
be applied to rough surfaces, because the rime is generally not
recognisable upon them.

Several attempts have been made to bring out the behaviour of
glass by colour-reactions. The usual plan is to expose the surface
to the contact of aqueous solutions of substances which change
colour when acted on by alkalis. As the water draws out
alkali from the glass, red solution of litmus is coloured blue
where it is in contact with the glass ; a colourless solution of
phenol-pthalein or of haematoxylin becomes purple-red. Mylius
endeavoured to utilise the blue colouring produced in a solution
of starch and iodine by a trace of alkali; and he describes
a pretty lecture experiment, in which the action of water on
glass is rendered visible. 3 These reactions are suitable for
'M.,II. *Ann. d. Phys. u. Chem., 6. 431 (1879). 8 M., II. 51. 5.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 323

showing that glass gives up alkaline constituents to water, but
cannot well be employed for comparative testing of different
glasses.

The lod-eosin Test. If a glass surface is brought into contact
with watery ether, it draws water from the solution and gives up
alkali to it. On the other hand, the orange yellow colour of a
solution of iod-eosin (C^Hg^Og) in ether is changed by alkali
into red. Mylius, who had previously used this colour reaction
for another purpose, 1 has applied it to the practical testing
of glasses. Commercial ether is shaken up with water at
ordinary temperature, till it is saturated with water. It is then
poured off from the rest of the water, and iod-eosin is added
in the proportion of O'l gm. to 100 c.c. of the liquid. The
solution is filtered, and can be preserved in well-closed flasks
till wanted.

Glass vessels are tested by pouring in the solution. The first
step is to clean the surface from any products of weathering which
may adhere to it, by carefully rinsing it with water, with alcohol,
and lastly with ether. Immediately after the cleansing with
ether, the eosin solution is poured in, the vessel is carefully closed,
and the solution is allowed some 24 hours to do its work. It is
then emptied out, and the glass rinsed with pure ether. The
surface of the glass is now seen to be coloured red ; and the
strength of the colour furnishes an indication of the susceptibility
of the glass to attack by cold water.

Mylius tested in this way a number of the glasses of commerce,
the vessels employed in the first instance being glass tubes. He
gives a coloured plate showing the appearances presented by
different specimens after the same treatment. The differences in
the colouring are very considerable. They are however not due
solely to differences of composition in the glasses. Inequalities
of weathering, and other differences of condition in one and
the same kind of glass, are also revealed to the eye by this very
sensitive method.

A crystal glass with large content of lead was conspicuous for
the strength of its colouring, although it did not give up much
soluble material to water. The colour was partly produced by the
lead salt of eosin, which remained clinging to the glass when the
alkali salt of eosin was removed by rinsing with water.

>M.,I. 289.

324 JENA GLASS.

Normal-thermometer glass showed about the same colouring
as the least fusible kinds of Thuringian glass. The weakest
colouring was shown by the Bohemian glass from the works
of Kavalier.

The eosin test agreed completely in its results with Weber's
method.

Lastly, Mylius used the eosin test to show the effect of various
modes of treatment, in increasing or diminishing susceptibility to
decomposition. For details of these researches, in which the
utility of the method is conspicuously shown, we must refer to
the original memoir. 1

133. Penetration of Water into the Surface. 2 Some
specimens were handed over to Schott in 1883 by the Standards
Commission, of thermometer tubes which, after being kept for
several days in boiling water, had shown hook-shaped cracks
going right through the walls, and, on the gentlest touch, broke
into large pieces, which clung together. When Schott heated
the pieces in a gas- flame to a temperature higher than that of
boiling water, a thin layer of the outer surface resolved itself into
small amorphous splinters, while the inner walls of the tube
remained unaltered. Previous to the heating in the gas-flame,
no visible changes could be detected in the surface. The
appearances suggested that water, in contact with glass, not only
dissolves components of the glass, but is taken in by the superficial
layers. The water which has penetrated will, on sudden heating,
be converted into steam, which produces the fine splintering.

To put this suspicion to the test, specimens of several kinds of
glass, in the form of tubes and of small discs, were submitted to
the action of hot distilled water, in a digester, on five consecutive
days. They were then carefully cleaned, with water, alcohol, and
ether successively ; then dried for several hours over sulphuric
acid; and then kept at 150 in an air bath. Three weighings
were made, the first before exposure to the hot water ; the second
after the drying ; and the third after the final heating in air. The
losses of weight from the first to the second, and from the second
to the third weighing, are given below, the percentage com-
position being prefixed. The losses of weight are expressed in
mg. per sq. decim. of glass surface.

1 M.,II. 55. 2 Sch.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 325

1. INFERIOR THURINGIAN GLASS.

Si0 2 Na 2 O K 2 CaO Al 2 3 + Fe 2 8 MgO

68-69 15-87 7'32 5-66 2'11 0'24

Losses of weight, 10'7 mg., 4'9 mg.

After the heating in water, the surface showed no change;
after heating in air, at 150, it was quite corroded, and fine scales
came off in abundance. The loss, 4*9, was therefore not all water.

2. SUPERIOR THURINGIAN GLASS.

Si0 2 Na 9 O K 2 CaO A1,0 S Fe 2 3 MgO
69-02 16-01 3-38 7'24 3 : 0'43 0'26

" There was, in addition, a little manganese oxide, and arsenic
acid. The glass was tested under three different conditions;
(a) after keeping for two years in air ; (b) after previous heating
at 100; (c) after heating to the commencement of softening.
The results were

(a) Losses of weight, 3*5 mg., 0'8 mg.

(b) Losses of weight, 2 '5 0'8

In (a), the surface after the heating in water appeared
absolutely unchanged. After the heating in air, it was all
covered with fine scratches, but threw off no scales.

In (b), these scratches were very fine, and barely visible to
the naked eye.

In (c), no scratches were visible, even with a magnifier.

3. JENA GLASS XVIII.

Si0 2 Na 2 PbO ZnO B 2 3

66 13 10 7 3

Losses of weight, 1*2 mg., 0*0 mg.

The surface showed a bluish shimmer, without other change.

4. JENA GLASS XXII.

Si0 2 Na 2 K 2 CaO

66 14 14 6

3*> JENA GLASS.

The glass, after only 36 hours' heating in water, already
showed numerous irregular cracks, and began to go to pieces ;
the surface became rough. When heated to 150, the surface
flaked off, and the glass was marked all over with numberless
scratches.

5. JENA GLASS 3 m .

Si<X Na 2 CaO A1 2 3 B 2 3

62 16 16 2 4

Losses of weight, 5*5 mg., O'O mg.

The surface had assumed a bluish shimmer, without other
change.

6. JENA GLASS 6 in .

Si0 2 Na 2 K 2 O A1 2 3 B 2 3
73 15 5 52

Losses of weight, 0'9 mg., 0'7 mg.

The surface was unchanged.

7. JENA GLASS 15 ln .

Si0 2 Na 2 K 2 CaO A1 2 3 ZnO

67 8 9 7 2 7

Losses of weight, 0'9 mg., 0'06 mg.

8. JENA GLASS 13 111 .

Si0 2 K 2 ZnO B 2 3

58 15 20 7

Losses of weight, 1-6 mg., 0'24 mg.

These researches, as Schott points out, show clearly the
superiority of soda to potash glasses.

If a laboratory utensil of common glass, that has seen much
service involving long-continued contact with water, is brought
into the gas-flame, its surface often becomes marked with fine
scratches. Easily fused glasses containing potash and little or no
lime, are capable of taking in so much water, even from the air,

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 327

that their surface, on heating, becomes full of scratches, as may
be often seen in lamp chimneys that have lain for a long time
unused.

Three Jena potash glasses, numbers 547, 564, 563, containing
percentages 33, 35, 42 of potash, were found, after lying by for
many weeks, to have taken in from the air so much water that,
on heating, they showed extensive splintering. After lying by
still longer, they were covered with a wrinkled skin, which could
be scraped off with a knife. After some years, this skin, in the
case of No. 563, had continually increased in thickness, and gradu-
ally came away from the sound glass beneath it, though it gave
the impression of being solid. The detached coating, so far as
it was not decomposed externally by carbonic acid, preserved
its amorphous character perfectly. With protracted heating
at from 200 to 300, it swelled up and acquired a pumice-like
structure.

Two glasses with large content of soda, namely No. 232,
containing 45 Si0 2 , 20 Na 2 0, 35 Ba0 2 ; and No. 107, a soda
silicate glass, showed as little power of holding together as the
glasses with potash in their composition. They became covered
with a crystalline crust which was easily detached from the glassy
core. Heating produced no change in the surface.

Similar observations have been made in many quarters, and
have been collected by Foerster. 1 They relate to cases in which
considerable quantities of water were taken up by glasses.
According to Foerster, 2 water is always taken up where glass is
acted on either by liquid water or by steam. The water enters
into chemical combination with the glass, forming hydrated
products.

According to this view, the action of water on glass is not a
true process of solution, in which there is direct transition from
the undissolved to the dissolved state ; but rather a process of
soakage, in which the passage, from the original solid substance, to
the final dissolved products, is effected through a series of inter-
mediate transformations. In water-glass, and other glasses
containing very little lime, this process of soakage is especially
conspicuous.

>F., II. 2920, and F., IV. 457, besides observations of his own in I .
I. 2495.
F. t II. 2920, and F., IV. 458.

JENA GLASS.

134. Investigation of the Behaviour of Test-samples of
Potash and Soda Glasses. 1 In order to complete Schott's
observations described in the preceding article, Mylius and
rster carried out a comparative investigation of the action of
water on test-samples, of systematic composition. Their memoir
begins with an account of observations on water-glasses, from
which we extract the following particulars.

The great affinity of potash water-glass for water reveals
itself, under suitable conditions, by distinct generation of heat.
Fifty grammes of pulverized potash water-glass, of composition
K 2 . 3 Si0 2 , were well mixed with enough water to form a thick
)>ulp, which was left to itself at the temperature 18. In a
quarter of an hour it had risen to 32, and it remained at about
this temperature for a long time. When the same glass, mixed
with a little water, was warmed by means of a water bath of
temperature 55, the mixture rose in a few minutes to 80 ; and
in about ten minutes the pulp had solidified into a homogeneous
mass. 2

To this property of potash water-glass Mylius and Foerster
attribute its setting, like hydraulic cement, under water. The
pulp formed by the swelling-up which occurs when it takes in
water, cements together the as yet unhydrated particles of the
powder. In a day or two it becomes a glassy mass, of the
hardness of stone, containing up to 50 per cent, of water. When
heated, it gives out this water with violent tumescence ; and
at a red heat it acquires the character of pumice.

Soda soluble-glass combines with cold water much more
slowly. When reduced to powder, and kept under water, it takes
two or three months to harden.

The Meltings for Producing the Test Specimens were carried
out in a Seger gas furnace. The melting pots were made from
a fireclay compounded by Heinecke. The glass took up less
than 1 per cent, of alumina from them, and this impurity (the
same for all) was neglected. The amount of a melting did not
exceed 500 gm. Those of the glasses thus obtained which were
included in the investigation, had the molecular compositions
shown in the following list; the 6 molecules of Si0 2 being
common to all.

J M. u. F., I. and II. ^M. u. F., I. 10<)8.

CHEMICAL BEHAVIOUR OF GLASS SURFACES.
6 Si0 2

329

I.
III.

V.
VII.
IX.

It
H

U
1

K 2 O
K 2 0,
K 2 0,
K 2 0,
K 2 0,

i
1

CaO
CaO
CaO
CaO

II.
IV.
VI.
VIII.

2
11
li

NajO

Na 2 0,
Na 2 0,
Xa.A
Na 2 0,

1
I

CaO
CaO
CaO
CaO

This gives as their percentage compositions :

SiO 2 .

K 2 0.

Na 2 0.

CaO.

65-7

34-3

II.

74-4

25-6

III.

66-8

30-6

2-6

IV.

74-6

2'2'5

2-9

68*0

26-7

5-3

VI.

74-8

19-4

5-8

VII.

69-3

22-6

8-1

VIII.

75-0

16-2

8-8

IX.

70-6

18-4

11-0

75-3

13-0

11-7

The 1 specimens, in the form of coarse grains, were subjected
to the action of hot water, the investigation being conducted on
the same plan as Mylius' experiments, which we have described
in Art. 131. The quantity operated on in each experiment was
7*74 c.c., this being the volume of 20 gm. of normal thermometer
glass. To keep down the error arising from variations in the
total area of glass-surface in contact with the water, care was
taken, by repeated siftings, to ensure that there should be
approximately the same number of grains to the cubic
centimetre in all cases. The actual numbers ranged from
7300 to 7624 per c.c.

The results are given by Mylius and Foerster in a table, from

which we reproduce an extract. The first column contains the

mctive numbers of the glasses; the second, the number of

molecules of alkali to one molecule of silicic acid in the com-

330

JENA GLASS.

position of the glass; the third, the quantity operated on, in
grammes. The next three columns give the quantities of silicic
acid, potash, and soda, found in the solution ; and the last two
columns are derived from these three by calculation ; one of
them giving the amount of oxygen contained in the dissolved
alkali, and the other the number of molecules of alkali to one
molecule of silicic acid in the solution ; the volume of the solution
being in each case 60 c.c. The number of milligram equivalents
of alkali in the solution can be found by dividing the numbers in
the last column but one by 16.

In 60 c.c. of solution.

Quantity.

1 Si0 2 .

Si0 2 .

KjO.

Na. 2 0.

*-' x y8 en

in alk.

1 Si0 2 .

gm.

mg.

0-33 K 2

18-824

4246-8

2377-2

404-6

0-36 K,O

II.

0-33 Na^O

18-979

2144-7

842-4

217-3

0-38 Na 2

III.

0-29 KjO

18-948

2997-6

1675-8

285-24

0-36 K 2 O

IV.

0-29 Na^O

18-979

303-9

202-8

52-33

0-64 NaO

0-25 KjO

19-002

65-1

158-4

26-92

1-56 K 2 o

VI.

0-25 Na,0

19-118

8-1

34-3

8-86

4-1 Na,o

VII.

0-21 K 2 6

19-072

5-4

26-69

4-54

3-15 K 2

VIII.

0-21 Na-P

19-257

5-9

11-5

2-97

1-9 Na.,0

IX.

0-17 K 2

19-125

3-5

5-99

1-02

1-1 K 2

0-17 Na.,0

19-381

3-2

4-19

1-08

1-27 Na/)

The two water-glasses had only been so far dissolved as is
shown in the table. After cooling, the powdered water-glass
was found to have become a coherent amorphous mass, which,
in the case of the potash glass, appeared homogeneous, but,
in the case of the soda glass, full of grains. Of the other
glasses, the only one that exhibited this coherence was
No. III. ; all the others retained the condition of completely
separated grains.

The table shows, as was to be expected, that the solubility of
both potash and soda glass diminishes rapidly as the content of
lime increases. In the comparison of the potash with the soda
glasses, the most prominent fact is the superior resisting power of
the soda glasses. The superiority however diminishes as the

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

331

content of lime increases. The following are the total amounts
of dissolved matter, including both silicic acid and alkali :

Content of

Dissolved matter in mg.

Lime.

Soda Glass.

Potash Glass.

Ratio.

i Molecule

506-7

4673

1 :9-2

42-4

223-5

1 :5'3

I M

17-4

32-1

1:1-8

7'4

9-5

1 : 1-3

The following is a list of the amounts of oxygen in the dissolved
alkalis, or of 16 times the number of milligram -molecules of
alkali dissolved :

Content of

Alkali-oxygen in mg.

Lime.

Soda Glass.

Potash Glass.

Ratio.

i Molecule

02-91

JS.VJ

1 :5-5

8-86

26-9

1 :3'3

2-97

4-54

1 : 1-5

1-0

1 : 1-0

Lastly, the ratio of alkali to silicic acid in the solution is worthy
of attention. The solution contains, in every case, relatively more
alkali than the glass. In our table of direct results, the second
column gives the ratio of alkali to silicic acid in the glass, and
the last column gives the corresponding ratio in the solution,
which is in every case greater than in the glass. The ratio of
the numbers in the two columns is exhibited in the following
list:

Content of
Lime.

Soda Glasa.

Potash Glass.

None

1 : I'll

: 1-08

i Molecule

1 -2-19

: 1-23

4 M

1 : l. 1

: 1

* ..

1 : 9-12

: l.Vl'_>

1 :

: 6-6

JENA GLASS.

In the case of each of the two kinds of glass, there is a
certain content of lime which gives a maximum of inequality
to the ratio, and this proportion of lime is larger for potash
than for soda glass. Mylius and Foerster arrive at the con-
clusion that, in good glasses, double silicates of lime and
alkali, in mutual connection, promote resisting power against
water.

135. Comparison of Commercial Glasses. 1 The method of
testing described in the preceding article has been applied, in
altered form, by Mylius and Foerster, to 11 different commercial
glasses. The following table gives, in weights per cent., those
components which are important for our purpose:

No.

Description.

Si0 2 .

Na.,0.

K 2 0.

CaO.

PbO.

Yellow alkaline glass -

60-49

15-41

13-25

5-42

Inferior Thuringian -

69-92

16-5

6-6

3-75

Glass of Tittel & Co. -

71-5

14-3

7-1

6-7

Schilling's flask glass -

75-2

11-9

4-2

8-3

Kavalier Bohemian -

78-3

1-4

13-3

6-8

Rhenish window-glass

71-2

13-5

13-4

Lead crystal ; Ehrenfeld -

56-0

0-6

12-1

31-2

Green flask ; Charlottenb. -

63-5

9-5

1-3

14-0

Jena thermometer 16 m

67-5

14-0

7-0

Jena lead glass 483

44-75

0-2

7-3

47-0

Lead silicate

21-7

78-3

No. 1 contained 0'22 per cent, of sulphur, and was coloured
yellow by sulphur-alkali. No. 8 contained 3 '9 per cent, of
magnesia. The normal-thermometer glass contains zinc oxide
7 per cent., and boric acid 2 per cent.

The results are given in the following resume, which is an
extract from Mylius and Foerster's table. 2 They are arranged in
the same form as the direct results given in last article, except
that one column is omitted. The numbers in the last column
now include, of course, both alkalis, when both are present in
the glass. The glasses are arranged in the order of their total
losses by the five hours' immersion in hot water.

M. u. F.,I. and II.

2 M. u. F., I. 1107.

CHEMICAL BEHAVIOUR OF GLASS SL'RFACES.

333

In 60,c.c. of solution.

No.

Quantity

SiO,

K 2 O

Na 2

Oxygen in Alk.

Molec. Alk.

gm.

mg.

to 1 SiO,.

19-451

84-7

59-0

98-5

35-6

1-5

19-125

14-3

18-1

59-0

18-4

4-8

19-304

6-9

6-5

14-4

4-8

2-7

19-079

5-3

1-7

4-8

1-5

1-1

18-468

5-5

5-3

0-8

0-6

18-963

4-3

4-6

1-2

1-0

23543

1-9

7-0

1-2

2-3

20-162

3-2

2-7

0-7

0-9

20-000

2-7

3-2

0-8

1-2

27-814

1-5

1-8

0-3

49-021

0-6

In cold water, the removal of soluble matters from the glasses
is a very slow process, and is found by the iod-eosin colour test 1
to give a somewhat different order of arrangement from the
above. For example, Kavalier's Bohemian glass is less affected
than normal-thermometer glass, although much more affected
by hot water. Mylius and Foerster's explanation is, that the
lime and zinc oxide in the thermometer glass bind the soda,
while in the Bohemian glass the quantity of lime is not
sufficient to do this. They allude to the fact that water-glass
is at first almost unaffected by cold water, but offers little
resistance to hot.

The first action of cold water on glass consists mainly in the
removal of alkali. The alkaline solution thus formed takes up
silicic acid with increasing rapidity, and the more so the higher the
temperature is. Mylius and Foerster infer that the susceptibility
of glasses to attack by cold water can be approximately estimated
by the number of milligram-equivalents of alkalis removed by hot
water, or by the amount of oxygen contained in the alkalis in the
solution. This gives, for the above 11 glasses, the order 1, 2, 3,
4, 6, 7, 9, 5, 8, 10, 11.

The last column in the table of results shows that, in nearly
all cases, the solution contains more molecules of alkali than of
silicic acid.

1 Art 132.

334 JENA GLASS.

Besides silicic acid, potash, and soda, the solution also contained
lime, and zinc or lead, but only in traces too small to admit of an
estimate. The lime certainly goes into solution as hydrate ; and
in like manner baryta glasses give baryta hydrate.

136. Quantitative Analysis of the Material Dissolved from
Glass by Cold Water. The first quantitative determination of
the substances taken out of glass by cold water seems to have
been made by F. Kohlrausch. 1 It applied to two glasses a
chemical glass rich in alkali, and a Bohemian glass rich in silica.
The following are their compositions in equivalents per cent. ;
the molecular weights of the glass-forming oxides being reckoned
as their equivalents :

Si0 2 . Na 2 0. K 2 0. CaO. A1 2 3 .
Chemical glass, 72 20*3 1-3 4'0 2'1

Si0 2 . Alkali. CaO.
Bohemian glass, - 82 10'3 7*9

The ratio of potash to soda in the Bohemian glass was 6 '3 to 1 ;
but an exact separation of the two metals in the solution formed
from it was impracticable. In the calculation of the analysis
they were assumed to have the same ratio as in the glass.

Nine gm. of the chemical glass, reduced to powder, were treated
with 250 gm. of water ; and 220 gm. of the clear solution which
was poured off gave 124 nig. of dry material. The solution
therefore contained 560 mg. per litre.

The analysis was effected with the aid of hydrochloric acid,
ammonia, ammonium oxalate, silver nitrate, and platino-hydro-
-chloric acid ; and gave, in equivalents per cent. :

Si0 2 . Na 2 0. K 2 0. CaO. A1 2 3 .
Chemical glass, 40 57 0'8 0'2 2*0

Thus, for one molecule of silicic acid, the glass contained 0'3
molecule of alkali, and the solution 1'44.

Eight gm. of the Bohemian glass, in the state of powder, were
left for six weeks in contact with 200 gm. of water at 8. The
solution, after two filterings, contained 61*5 mg. of dry material

1 K., III.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 335

in 143 c.c., which is at the rate of 430 mg. per litre. The
analysis gave, in equivalents per cent. :

Si0 2 . Alkali. CaO.
Bohemian glass, 76 18 6

For one molecule of silicic acid, the glass contained 0*13 molecule
of alkali, and the solution 0*24.

It is also to be noted that sensible quantities of alumina from
the chemical glass, and of lime from the Bohemian glass, went
into solution.

137. Titration and Colour Tests with lod-eosin and Ether. 1
As the dissolving of alkalis plays a leading part in the decom-
position of glass by water, Mylius and Foerster proposed that the
susceptibility of glass to the action of water should be determined
by measuring the quantity of alkali in the solution. This pro-
posal led to a search for sensitive methods of measuring small
quantities of alkali ; and by the employment of iod-eosin (which
had previously been used by Mylius in comparative tests), two
suitable methods were worked out.

Titration, with Millinormal Solutions. In the determination
of fairly large quantities of alkali by normal or decinormal
solutions, there is no reason lor departing from the regular
practice. Determinations with centinormal solutions can also
be carried out with some degree of certainty in the ordinary way ;
but this is about the limit.

With the help of iod-eosiu and ether, determinations can how-
ever be made with millinormal solutions of sulphuric acid, and
with increased sharpness. In preparing these solutions, great
attention must be paid to the necessity of employing pure (or at
least neutralised) water, as the alkaline impurities communicated
to distilled water by the glass vessels in which it has been kept,
will produce disturbance. Millinormal solutions may be kept for
some time in vessels of good glass.

The alkaline solution to be tested is put into a stoppered
bottle, and covered with a layer of very dilute eosin solution.
Small quantities of the acid solution are then added, with vigorous
shaking, until the watery layer, which was originally red, just

M. ami P., III. and IV.

336 JENA GLASS.

loses its colour. Each c.c. of acid solution corresponds to *031
mg. of soda (Na 2 0) or '047 rag. of potash (K 2 0).

Measurement of Alkali by Colour Test. This method of
titration suffices for detecting and measuring in 100 c.c. of water
a quantity of alkali equivalent to 0*1 mg. of soda (Na 2 0). For
smaller quantities of alkali than this, the process is not applicable,
and the following colour test is to be preferred.

It a very dilute aqueous solution of alkali is shaken up with
an etheric solution of eosin, containing an excess of iod-eosin
above what is necessary for neutralising the alkaline solution,
eosin-alkali is formed, and the mixture acquires a rose colour, of
intensity proportional to the 'quantity of alkali remaining
unneutralised. In determining the amount of alkali by this colour
test, certain precautions are to be observed, for which, as well as
for a full account of the titration method, we must refer to
M. u. F., III. Iod-eosin is affected by soda, potash, lime, and
any other alkaline components of the glass that may be given off
to the water. The result depends merely on the total number of
equivalents of alkali, without regard to kind, and is usually stated
in terms of the quantity of soda that would be equivalent to all
the alkali given off.

138. Earliest Employment of the Quantitive Test by Iod-
eosin. 1 In working out the methods of testing briefly described
in last article, Mylius and Foerster had immediately in view the
selection of the best glasses for chemical uses from among the
various kinds in the German market. For this purpose, flasks
and bottles by the most eminent makers were obtained from the
authorities at the Eeichsanstalt, who were asked to furnish the
best kinds available, and to state their origin. The capacities of
the vessels were from 250 c.c. to 300 c.c. The flasks were
spherical, and the bottles cylindrical, so that the wetted areas
could be determined with close approximation.

Preliminary Trials. To find out the best way of testing, the
following preliminary experiments were made, upon the action of
water on glass surfaces under various external conditions.

A. The flasks and bottles were freed from adherent products of
weathering by repeated rinsing with water, 2 and then left for

M. u. F.,IV. 315.

3 Here, and in what follows, neutral water is to be understood.

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

337

24 hours in contact with water at 20. The alkalinity of the
water was then determined, either by titration or by colour
estimation. The numerical values in the table below denote the
quantity of alkali given off from each square decimeter of glass
surface to the water, expressed in thousandths of a milligram of
soda, as above explained.

No.

Flasks.

Alkali.

Kahler & Martini,

Schweig & Co., Weisswasser,

Kavalier, Sazava, Bohemia,

Bohemian Hollowglass,

Fettke & Ziegler, Doebern, -

Leybolds Nachf., Cologne, -

Bohemian Glass,

Warmbrunn, Quilitz & Co.,

Schilling, Gehlberg,

10.

Tritschler & Co., Stuttgart,

309

11.

Lambach, Bavarian Forest, -

435

No.

Bottles.

Alkali.

Bohemian Hollowglass,

II.

Warmbrunn, Quilitz & Co.,

III.

Fettke & Ziegler, Doebern, -

IV.

Schilling, Gehlberg,

Kiihler & Martini, - ] 76

VI.

Leonhardi, Schweppnitx,

189

VII.

Stender, Lampspringe, - 201

VIII.

Scweppnitz Works, 339

IX.

Leybolds Nachf., Cologne, -

49S

The initial intensity of action, as measured by these numbers,
depends entirely on the weathering and other changes which the
surface may have previously undergone.

B. The bottles were subjected on the second, third, and
fourth day to the same treatment as on the first. They were then
left, for a week at a time, for three weeks in succession, and the
average amount of alkali taken up per day was deduced. The

338

JENA GLASS.

following were the daily amounts thus found (in the same units
as above).

BottU.

1st day.

Jnc I day.

4th day.

.">th to
llth.
Mean.

12th to
18th.
Mean.

19th to
26th.

Mean.

2-9

3-0

2-0

0-66

11.

6-7

4-5

1-5

0-8

0-25

111.

6-8

4-4

2-6

0-5

IV.

8-0

5-2

2-8

10-9

5-3

VI.

189

6-2

3-1

VII.

202

8-8

4-5

VIII.

340

101

6-9

3-9

IX.

499

111

22-7

12-6

A glance at this table shows that the amount of alkali given to
the water on the first day is much greater than on the following
days ; and the order of the glasses, as regards amount of action,
does not remain the same throughout the trial.

It is not necessary to suppose that the outermost layer of the
surface is specially rich in alkali. The water has direct access to
the first layer, but cannot attack the others without getting
through a very impermeable shield of silica and silicate of lime.

C. Bottles of the same origin as the above were then left for
an hour, with water at 80 in them, and then quickly cooled.
This was done several times in succession, the water being
renewed each time, and the alkali in the previous filling
measured. We do not reproduce the results, as they were
unsatisfactory.

Another trial on the same lines was then made with three
flasks, of glasses differing very widely from one another; and
special attention was paid to the maintenance of one uniform
temperature. The following were the results thus obtained :

Flask.

1st.

2nd.

3rd.

4th.

5th.

6th.

7th.

8th.

9th.

10th.

4-4

4-2

4.4

3-8

2-9

3-8

137

360

129

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 339

The quantity of alkali dissolved in the first hour is here greater
than in 24 hours with cold water. The rate of dissolving attains
its permanent value earlier with good glass than with bad.

D. From the above experiments it would appear that glass
bottles tend to improve with continued use. Specially good
glasses, after some time, cease to give off alkali to any
appreciable extent; but glasses of moderate quality will con-
tinue to render distilled water alkaline even after the lapse
of years.

Warburg and Ihmori have accordingly suggested that glass
vessels should be kept full of boiling water for long periods, in
order to improve them by the removal of alkali from their
surfaces ; and trials have been made to ascertain how far this
mode of improvement is practicable. The upshot of the trials
was, that in glasses of poor quality, intended for holding cold
water, a preliminary treatment with hot water is very beneficial.
The absorption of alkali will not however be thus altogether
stopped. Even 100 hours of contact with boiling water will not
suffice to prevent a bad glass from being decomposed by cold
water.

E. When glass has been strongly attacked by hot water, as
in the experiments above recorded, the contrast between good
and bad glass becomes much less marked. This is shown by
further experiments which were made on the three flasks above
mentioned. After their 10 hours of exposure to water at 80, as
described in (7, they were continuously subjected for 6 hours, in
a bath of boiling water, to the action of pure water obtained by
distillation in an apparatus of platinum. Under this treatment,
the amounts of alkali which they gave up to the water from
each sq. decim. of wetted surface, were (in mg. of Na-jO), 0*89
from No. 2, 1-51 from No. 6, 2'50 from No. 9.

These are as 1:1-8: 2'8,

whereas for the first hour (see table in C) the quantities were as

1:6: 157,
and for the ninth hour as 1 : 4*2 : 13'7.

The total quantities of matter dissolved in the six-hour
experiment were determined, by evaporating the solutions ; and

JENA GLASS.

were not excessively different for the three flasks, the extreme
values being about four and about six mg. per sq. decim.

/'. In order to obtain trustworthy comparisons of the suscepti-
bilities of dilfi'ivnt -lasses to attack by water, great care must be
taken to ensure constancy of temperature. Mylius and Foerster
illustrated this point by operating in identical fashion on four
eijual tlasks (by Greiner & Co.) with water at 0, 18, 40 and
80 respectively. The amounts of alkali dissolved, expressed in
thousandths of a milligram of soda per sq. decim., were :

In 24 hours, at 0, 1'9

18 6-4

In 1 hour, 42 9'1

80 158

Practical Testing of Glass Vessels. The complete testing of
a specimen of glass, as regards its behaviour towardswater, is a
complex business, as the above investigations show. The practical
requirements for a ready and sensitive method of determining the
relative merits of glass vessels from different sources, are fairly
satisfied by exposing the vessels (as yet unused) to the action of
water, and comparing the quantities of alkali dissolved. Any
disproportion which may exist between the silica and alkali
dissolved is left out of account. On these lines, Mylius and
Foerster have carried out the following comparisons.

The vessels were first exposed for three days to the contact of
water at 20, and the solution thus obtained (which of course
included products of weathering) was put aside. The vessels were
then exposed for another three days to contact with a fresh
supply of pure water ; and these second solutions were tested by
iod-eosin and ether, for the quantities of alkali which they
contained. The quantity of alkali per unit of wetted surface,
was taken as the measure of susceptibility to attack by cold
water.

The following results were obtained by carrying out this
programme, except that, during the preliminary three days'
exposure, the water was changed on the second day. Also,
at the conclusion of the test with cold water, which occupied
the second three days, a one-hour test was made with hot water
at 80 :

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

341

Glass.

Kahler & Martini,

Flasks

1-0

6-7

Schweig ft Co., -

1-5

8*9

Kavalier, -

2-1

8*9

Fettke & Ziegler,

3'7

Normal-thermometer 16 m , -

4-0

Bohemian hollowglass,

Bottles

4.S

Bohemian hollowglass,

Flasks

7"2

Warmbrunn, Quilitz & Co.,

Bottles

8-9

Fettke & Ziegler,

107

LeyboldsNachf.,

Flasks

176

Lambach Works,

203

Warmbrunn, Quilitz & Co.,

211

Bohemian glass, -

200

Schilling, -

270

Schilling,

Bottles

341

Stender ....

279

Leonhardi, . - - -

PI
ii

378

Schweppnitz Works, -

331

Kiihler & Martini,

405

Tritschler & Co., -

Flasks

558

Leybolds Nachf.,

Bottles

100

4T'_>

The unit is T^W f a milligram of soda per square decimetre.

The numbers show that most of these glasses are fit for the
ordinary work of chemical laboratories, but that only a few
satisfy the more stringent requirements.

Chemical Composition of Six of the Glasses. Mylius and
Foereter came to the conclusion that, of the flasks, the best are
those of Kiihler & Martini, of Schweig & Co., and of Kavalier ;
and of the bottles those of Bohemian hollowglass. Of these they
give the following analysis, together with those of flasks 6 and 9,
which, together with 2, were subjected to the experiments

No.

Si0 2

Na. 2

CaO

\10 s + FeA

Kahler ft Martini,

7.VI

<K{

)'..

1-0

2. Schweig ft Co. , -

78-8

3-6

7-2

0-3

Kavalier, -

79-1

6*4

6-7

0-2

Bohemian hollowglass,

7ii-f>

9-2

5-5

M,,

Laybolds Nachf., -

Tfrfl

6-6

5-9

0*6

-lulling, -

T:H

i:;-i

5-3

5-8

._,.._,

342

JENA GLASS.

described in E. The values are percentages by weight. The last
glass contained also 0'2 per cent, of MnO.

There is a general opinion among glassmakers that glass con-
taining one molecule of alkali and one of lime for every six of Si0 2 is
specially resisting against chemical attack. Mylius and Foerster
give, as a test of the correctness of this view, the following values
for the first four glasses in the above list, and also for the glass
employed by Stas for the vessels used in his determinations of
atomic weights.

For every 6 molecules of Si0 2 .

Kahl.

Schweig

Kav.

Bohem.

Stas.

Mol. Alkali

046

0-90

0-72

0-99

0-76

Mol. CaO

0-85

0-60

0-57

0-69

0-86

The percentage composition of the Stas glass is 77 Si0 2 , 5 Na 2 0,
77 K 2 0, 10-3 CaO.

139. Later Rules for Times of Exposure. Later researches
have shown that the preliminary three-day treatment with water
at 20 completely suffices to remove all products of weathering
from the surface of the glass. They have shown, at the same
time, that to obtain certain results, great care must be taken to
preserve constancy of temperature ; and further, that to find the
quantities of alkali given up by good glasses, the exposure to
cold water (at 20) must be extended to a week, and the treat-
ment with hot water to three hours.

Foerster (see F., V.) has followed these rules in obtaining further
comparisons of some of the glasses indicated as best in his previous
iod-eosin tests, with one another, and with some additional glasses.

The total number of glasses was 14, and they had the following
compositions.

Glasses 1-11 were known to have great power of resisting attack.

15 and 16 are commercial glasses easily attacked.

17 is a good lead crystal glass.

1, 2, 10 are Jena glasses, 1 being borosilicate, and 10 normal-
thermometer glass.

In addition to the components mentioned in the table, No. 1 had
12 per cent. B 2 3 ; No. 2 had 5 per cent. ZnO ; No. 10 had 7 per

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

343

cent. ZnO, and 2 per cent. B. 2 3 ; No. 17 had 30 per cent. PbO.
There were small quantities of MnO, which are left out of account.

No.

Si0 2

Na,0 K,O

CaO

A1,0 S

Alkali.

1=59"'

71-9

11-0

5-0

10-8

2=165"'

74-4

9-8

7-0

3-5

10-0

75-9

7-6 5-8

10-4

0-3

1 1 _'

76-6

6-7 6-6

9-5

0-6

11-0

76-8

6-4 6-2

100

0-4

10-4

76-3

8-3 7-0

8-1

0-3

12-7

75-1

4-9 11-8

7-6

0-5

12-8

:: ;

10-0 4-3

7-8

0-3

12-6

77-2

10-1 4-6

7-7

0-4

13-0

10=16 m

67-5

14-0

2-5

14-0

70-6

14-3 0-6

11-2

2-9

14-6

74-1

9-0 9-7

6-8

0-4

15-4

68-9

13-7 6-7

7-2

3-2

18-6

57-3

12-7

11-0

The last column gives the number of molecules of alkali to
every 100 molecules of glass-forming oxides.

The tests were applied to flasks made of the glasses. In the
following summary of results, the unit is, as before, the thousandth
of a milligram of soda per sq. decim. The last column gives the
ratio of the numbers in the two preceding columns :

No.

Alkali taken up.

Ratio.

8 days at 20

3 hours at 80

1= >!"'

2-5

->:

2= n>.V

J-l

6-3

:M>

10-7

_>S'4

2-65

8-9

JS-2

:M7

I:M

Jti-x

9-00

II-M

| INI

14*0

4.-,

s-iq

149

17-

:'.:-.

10= Hi'"

16-6

<>s

8-78

<i.->4

8*5

IT:;

:m .M:N.\

The t\ MS at the head of the list show very much greater

ing ]M,\\VI against both cold and hot water than any of the

(tin-is. In the case of the 59 HI Foerster attributes this to the

of acid oxides; silicic and boric acid make up 84

per cent, of its composition.

The following conclusions (to the end of this article) are also
<lrawn by Foerster.

In glasses 3 to 9, and 11, all of them ranking as specimens of
the best commercial glasses for chemical use, the number of mole-
cules of alkali per 100 molecules of glass-forming oxides, is a
material element in their resisting power against water. The
current opinion among glass-makers that the ideal type of a glass
>d resisting power is an approximation to

II I

EO . R 2 . 6 Si0 2

is not supported by the comparison of 8 with 11 ; for 11 comes
much nearer to this so-called normal formula than 8, and yet is
much more attacked.

The view insisted on by R. Weber * some time ago as to the
importance of a proper ratio of lime to alkali and silica finds little
support till we come to the comparison of 11 with 15.

Glasses 7 and 8 furnish a further illustration of the remark
that in good glasses it is immaterial whether potash or soda
predominates.

A comparison of 8 with 9 seems to show that a trilling
increase in the proportion of alkali may produce a large
diminution of resisting power.

The difference between the effects of hot and cold water varies
considerably. In the inferior glasses it increases as we go from
better glasses to worse. In the lead crystal it is rather small,
owing perhaps to the presence of a layer of hydrated lead silicate,
which hinders penetration.

When resistance to cold water only is in question, as in the
finest spirit-levels, one of the first 8 glasses should be employed.

Attention is called to the announcement that, as a consequence
of the stimulus furnished by the labours of the Reichsanstalt,
vessels of the glass used by'Stasare now commercially obtainable. 2

1 Ann. d. Phy. u. Chem., 6. 431 (1879).
-Chem. Repert. Suppl. z. Ghent., 16, 257.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 345

140. Tests with Water Above the Normal Boiling Point.
The action of water heated under high pressure conies into con-
sideration, in the case of gauge tubes for steam boilers, and for
some of the uses of the chemical laboratory.

Researches specially directed to this subject were published by
Foerster in 1892. 1 Glass tubes three-quarters filled with dis-
tilled water, the remainder being occupied by air, were sealed, and
then immersed upright for six hours in boiling aniline (temp. 183).
When the glass came to be examined, the surface was found to be
sharply divided into two parts at the line of demarcation between
water and steam.

The part exposed to the steam had become coated with an
opaque white layer of products of decomposition. This layer
could be rubbed off, and, after drying in air, readily gave off
alkali and silica to cold water.

The part which had been in contact with the water was
covered with a white flocky material, easily removed, portions of
which had become detached and were swimming in the water.
They consisted mainly of silica with a little lime. The quantity
of alkali which had gone into solution was so considerable that,
even in the case of the best tubes in use up to that date, it could
be measured by titration with a decinormal solution. Consider-
able quantities of silica were also dissolved. An analysis, which
was made in one case, showed that the water had soaked in, just
as was previously found with more moderate temperatures.

Four glasses were heated for six hours in water at 183, and
tested for dissolved alkali by titration with decinormal solutions,
very dilute iod-eosin being employed as indicator. The following
results are given by Foerster as the means of several trials. The
;ilkali is reduced as usual to its equivalent in soda, and expressed
in IM& per sq. decim. :

A. Ordinary gauge-tube glass, - 22'4

B. Better quality, - 137
Kavaliers combustion-tube glass, 7*1

I >. Jena compound glass, 1*1

Thr inner surface of the tubes of compound glass (see Art. 101),
is the borosilicate 50'", which, whether alone or as one of the
layers of a compound glass, is more proof against attack by super-

'P., I. 2494-2497.

346

JENA GLASS.

heated water than the other glasses experimented on, one of
which, C, had up to that time been regarded as the most resisting
ut all '_Mii;_ r e-tube glasses. The borosilicate, when subjected to the
test above described, was not corroded either by the water or by
the steam, but remained unlike all the other glasses perfectly
smooth and transparent.

Foerster subsequently l carried out more elaborate and exact
tests with ten glasses, which we designate 1, 4, 7, 9, 10, 11, 12,
1 .">. 14, 16. So far as these numbers agree with those in the
preceding articles, they denote the same glasses. The following
are their compositions, in weights per cent. :

No.

Si0 2 .

NlLA

K 2 0.

CaO.

ALA,

Alkali.

1 --,9"i

Tl-'.i

11 -0

5-0

llfS

76-6

6-7

6-6

9-5

0-6

11-0

7.V1

4-9

11-8

7-6

0-5

l-J-s

77-2

10-1

4-6

7-7

0-4

13-0

10= 16 1 "

<;:.->

14-0

7'0

2-5

14-0

:<><;

14-3

0-6

11-2

2-9

14-6

1-2*

78-9

1-0

14-0

5-8

0-2

1(1-4

13*

73-0

12-9

1-8

11-0

1-3

13-8

14*

68-9

13-7

6-7

7-2

3-2

18-6

In addition to the components here specified, No. 1 contained
B 2 3 , 12 per cent; No. 10, ZnO, 7 per cent., and B 2 3 , 2 per
cent. The composition of No. 14 is not stated. The content of
MnO (which is given in F., Y.) is neglected.

The three numbers with asterisks belong to gauge-tube glasses
in practical use, and the first two were described as specially
good. The column headed " alkali " gives, as before, the number
of molecules of alkali in every 100 molecules of glass-forming
oxides.

The following was the method of testing. Portions of tubes of
the different glasses were dried at 100, and weighed. They were
then enclosed with water in carefully cleaned iron tubes, and
heated for 4 hours at 190. These tubes having been cooled
down and opened, the alkali taken up by the water was determined
in equivalents of soda, by titration with centinormal and deci-

F., v.

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

347

normal solutions ; and at the same time the bits of glass tube, having
been freed from loosely adhering products of decomposition, were
dried at 5 00- 5 50, and then weighed to ascertain their losses.
These losses are given in the second column of the following
table, in mg. per sq. dec. of glass surface. In the case of glass
11, the agreement between single observations was not close
enough to give a trustworthy mean. The quantities of alkali
taken up by the water, expressed by their equivalents in soda,
are given in the fourth column. From these, the actual quanti-
ties of alkali given in the third column are calculated, on the
assumption that the ratio of potash to soda is the same in the
solution as in the original glass, the small quantity of dissolved
lime being neglected. These quantities of alkali, subtracted from
the totals in the second column, leave remainders representing the
amounts of silica dissolved. The last column of the table gives
the number of molecules of Si0 2 to one molecule of alkali, as cal-
culated from these remainders.

No.

Loss in mg. per sq. dec.

Molecules of
SiO.,

Total.

Alkalis.

Equiv. in Na,jO.

1=59"'

_>:;:

3-5

6-0

11-2

5-6

4-6

2-65

51-3

15-4

11-1

3-35

16*4

147

3-57

10=16 m

6-4

6'4

4-4'J

7-3

7-1

12*

Hi"_>

l>-7

\:->

13*

:;:

8-3

:;;

14*

126

The order of the glasses as determined by the amounts of
alkali dissolved at 190 is different from the order at 20, and
from the order at 80. Foerster maintains that the glasses whicli
are rich in lime and zinc, and approximate in their composition
to the so-called normal formula.
ii I.

RO .

6 Si0.

are much more resisting than glasses poor in lime and rich in
silica, which approximate to the composition of water-glass. In

348 .II;NA GLASS.

correspondence with their greater solubility, glasses of the latter
kind take in considerable quantities of water at 190, which
produce flaking oil' when the glass is subsequently heated a
Momenon n.t exhibited by glasses 4, 10, 11, 13, which are
rieh in lime and zinc.

The quantities of silica taken up by the water at 190 are so
.-, in comparison with the dissolved alkali, that they cannot be
left out of account in estimating the goodness of the tubes.

Judged by the quantity of dissolved alkali, the borosilicate
59 m is the most resisting of all the glasses in the table. Judged
i>y the quantity of dissolved silica, it is inferior to No. 4, and to no
other. It has an advantage over all the other gauge-tube glasses
in retaining its transparency when exposed to highly superheated
water. Not till the temperature exceeds 250 is its surface
corroded by water or steam. Of the other glasses, those which are
most strongly resisting, having a large content of lime, are specially
subject to obscuration of surface, owing to a deposit of silicate of
lime. It may also be mentioned that tubes of 59 m have remained
in good preservation when they have been employed for containing
neutral substances, with water at high temperatures.

141. Weathering of Glass Surfaces. The durability of a
glass in moist air depends mainly upon its resisting power
against attack by water. Bunsen has shown l that dry carbonic
acid exerts no action of any kind upon glass quite free from
water.

It must be assumed that hygroscopic glasses begin by taking
water into chemical combination with their surface layer, whence
arises the swelling up of the surface, observed by Foerster (Art.
133). As a result of this absorption of water, alkaline components
of the glass are gradually set free, and these afford the first
opportunity for the action of the carbonic acid of the air.

Experiments on the susceptibility of glass to attack by cold water
give accordingly a measure of its susceptibility to weathering. 2

The carbonic acid of the air combines with these alkalis from
the glass to form the carbonates Na 2 C0 3 and K 2 C0 3 , which, on
drying, are deposited in the form of crystals. They can easily be
removed by rinsing with water. Mylius and Foerster have
shown that the quantity of carbonate thus formed may be very
>1. /%*. u. Chem., 24. 321 (1885). 2 F., II. 2919.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 349

considerable. 1 The experiments which they made with eleven
flasks do not, however, furnish a satisfactory basis for determining
the susceptibilities of the glasses to weathering, as too little was
known respecting their previous history.

142. Testing by Electrical Conductivity of the Solution.
A very simple and comparatively exact measure of the suscepti-
bility of glass to attack by water is furnished by the electric
conductivity of the solution formed by the attack. This test
was first systematically applied by F. Kohlrausch. 2

Observation of the conductivity of the solution establishes, as a
universal proposition, that glass does not, like the majority of
very insoluble substances, pass over unchanged into the solution
but is gradually decomposed. Such bodies as gypsum, calcspar,
fluorspar, heavyspar, and chloride of silver, when left in contact
with water, give a solution which, if its temperature is kept
constant, soon attains a permanent conductivity. With glasses,
on the contrary, no limit to solubility is attained. In observations
extending over weeks or months, the quantity of matter in
solution continues to increase, though at a diminishing rate.
The conductivity test affords great facility for tracing the gradual
progress of chemical action.

The Kinds of Glass Tested. Kohlrausch's first compre-
hensive examination included thirty -one kinds of glass. In
addition to chemical bottle glasses procured by himself, there
were tube glasses, supplied to him by the Reichsanstalt, and a
collection of glasses, chiefly optical, from the Jena works. The
chemical compositions of the Jena glasses were furnished by the
senders. The compositions of the tube glasses were supplied by
the Reichsanstalt. Several of these glasses had already been
tested, by iod-eosin or by direct analysis, for their behaviour
to cold or hot water. The bottle glasses were analysed, some
of them at the Reichsanstalt, and some at the Jena works.

From these data, Kohlrausch calculated the following table of
Mjuivalents per cent, for all the glasses, except Nos. 2 and 3,
which were not analysed. In making the calculations, he
in ployed, as the molecular weights of the several glass-forming
les, the numbers which stand at the head of the table,
immediately under the chemical symbols for these oxides.

M. U. I . l\. Kl, K , I. ; in ,l II.

3. r

JENA GLASS.
COMPOSITION IN EQUIVALENTS PER CENT.

SiO,

Na.,0

K.,0

CaO

ALA

MgO

PbO

ZnO

MnO

BaO

A&A

ioa

228

153

198

142

67-6

16-3

10-0

._,.._>,,

0-17

>_>

0-44

7-J 1

L'31

8-96

-J-11

0-25

11-1

_>{>'.

0-09

u B

7-7J

1-52

5-35

0-18

1-77

78-0

.vtw>

6-61

9-55

0-08

509

49-0

o-oi

0-07

5-1

10-1

9-62

0-09

0-06

1-36

11-6

2-75

9-03

0-40

trace

81-8

1-41

8-87

7-61

0-31

68-2

13-9

4-53

10-9

2-18

0-3

8-28

9-49

7-97

2-36

0-09

o-io

0-91

:::!

14-J

4-O.S

7-33

0-24

0-31

0-18

68-8

Ifl

4-0

11-2

1-7

0-2

70-6

l.V!

3-9

8-1

1*1

0-4

72-1

17-5

3-9

4-9

1-3

0-3

65-6

1-23

6'47

1-03

12-2

0-08

9-97

0-11

3-27

57-3

3-58

12-5

0-16

21-0

0-13

5-42

71-4

3-53

778

4-50

0-05

9-52

0-07

3-13

71-6

6-38

8-40

12-2

0-03

0-07

1-41

74-8

11-3

7-11

0-75

0-06

5-90

_'t

74-9

5-52

10-9

1-69

o-io

4-25

0-14

2-44

61-7

24-9

10-8

0-07

2-38

0-11

65-4

4-68

29-7

0-15

0-11

71-8

0-77

8-08

19-7

0-12

0-09

76-0

1-93

7-39

14-4

0-14

0-11

77-0

0-80

10-6

0-12

11-5

14-8

11-3

11-6

0-72

4-98

56-6

4-12

10-0

6-87

12-6

0-15

66-3

The following descriptions are added :

2
*

9.
10.
11.
12.
13.
14.
15.
16.

Thuringian bottle glass, medium quality, Stiitzerbach.

I Good bottle glass, origin unknown, old, has been long in

j contact with water.

Inferior bottle glass, origin unknown.

Soft crown, Jena, No. 359.

Jena normal-thermometer glass, 16 m .

Extra light flint, Jena 788.

Densest flint, Jena S. 164.

Crown (like English), Jena 283.

Thuringian Glass A, from Gehlberg.

Bohemian potash glass.

Thuringian glass B, from Stiitzerbach.

Crown (like Feil's), Jena 260.

Thuringian glass C.

Thuringian glass D from Stiitzerbach.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 351

17. Inferior Thuringian E.

18. Inferior Thuringian F.

19. Zinc barium crown, Jena 463.

20. Densest barium crown, Jena 634.
Jl. Barium crown, Jena _'_' 7.

_'J. Ordinary zinc crown, Jena 493.

23. Borosilicate crown, Jena 599.

J4. Crown (like English), with baryta, Jena 861.

25. Potash crown, Jena 365.

26. Very dense flint, Jena 303.

27. Ordinary flint, Jena 824.

28. Light flint (like English), Jena 677.

29. Lead crystal glass.

30. Light phosphate crown, Jena, like O. 225.

31. Borate flint, Jena, like S. 8.

The Conductivities are always given by Kohlrausch for a
standard temperature of 18. The measurement was made after
the manner of that of a mercury-in-glass standard resistance.
The glass-holder employed in nearly all the experiments held
20 c.c. of liquid, and, when filled with mercury at 0, gave a
resistance of "0000138 Siemens unit, a value checked by frequent
repetitions. The relative conductivities of the solutions as com-
pared with mercury at were determined ; and Kohlrausch uses
the symbol k to denote 10 10 times this relative conductivity.

The purest water that can readily be procured in large quan-
tities, has on this scale about the conductivity k=l. The water
usually employed by Kohlrausch was kept, after distillation, for a
considerable time, in loosely covered flasks ; and its conductivity
ranged from k = 1 to k = 2. In each case the value of k for the
water was subtracted from the observed value for the solution.

Reduction Factor R. If a glass solution has conductivity
k, and contains Rk milligrams of dissolved material -per litre,

- is a measure of the conducting effect per milligram of dissolved
K

matter. Kohlrausch calls R the reduction-factor, and finds the
following values :

Solution of R

NaOH 0-22

KOH 0-28

NajSiO, 0-50

K 2 SiO, 0-64

JENA GLASS.

The following determinations for eleven different glasses were
obtained by evaporating their solutions :

No. 18 25 5 1 16

Value of R- - - 0'4 0'41 0'48 0'63 0'7

No.
Value of R -

/
0-73

13
0-8

11
0-9

4
1-8

31
5-2

The large values of R for glasses 4, 12, 31 indicate that they con-
tain matters in solution which contribute little to the conductivity:
Kohlrausch suspects silicic and boric acids. There is, however,
another way of accounting for a large value of R in a very dilute
solution, namely this : that while, in a neutral solution, the
conductivity is approximately proportional to the strength, this
is not the case in acid or alkaline solutions till the strength has
attained a certain amount, below which the conductivity increases
more slowly than the strength.

Water in Bottles. Ordinary stoppered bottles of glasses
1, 2, 3, 4, 5 were charged with pure water, and moved several
times a day as long as the experiments lasted. The bottles of
glass 1, being new, were first rinsed quickly with water. The
following table shows the course of the observations. M denotes

After 1 day

0-48

5 days

1-0

1-6

0-09

1-6

2-7

0-15

. 20

5-0

0-27

0-8

0-6

0-20

0-04

1-6

0-7

120

3-6

0-65

4-0

1-7

0-49

0-09

160

1-2

7 hours at 80

800

3-7

2-7

1250

100

5-4

5-2

the number of milligrams of solid matter in solution per sq. decim.
of glass surface. The figures show that the increase of strength
of the solution followed different courses for different glasses.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 353

Heating to 80 quickened the process of solution very much
in the cases of 5, 1, 2, but comparatively little in the case
of 3. In the case of 4, which was the best glass, the value
of k after ten hours at 60 had only increased by about 0*15.
At 90 the increase was 2, and in the neighbourhood of 100
was about 5.

The better glasses showed improved resisting power after
treatment with hot water, and also after prolonged treatment
with acid.

Etched Surfaces. Bottles of glasses 1 and 4 were etched with
fluoric acid, and then again tested for their behaviour with cold
water. Their resisting power showed no material change.

Powdered Glass. Kohlrausch also tested all the thirty-one
glasses, except 2, 3, and 6, in the form of powder. A piece
of the glass was pounded in an agate mortar, and rubbed down
till there was no longer a gritty feeling under the pestle, and the
powder began to cake. It was estimated, from microscopic obser-
vation, that the total surface furnished by a gramme of the powder
was of the order of a square metre.

In the case of each of the glasses 1, 4, 5, 7, 11, 12, the
powder was put, with 100 times its weight of water, into a
closed glass vessel, and frequently shaken up every day for a
week. It was then allowed to settle, the liquid very carefully
poured off, and a second quantity of water added equal to the
first. At the end of another week, there was a second pouring
oil': which was succeeded in like manner by a third. The com-
paratively trifling action of the vessel itself on the water was
known and allowed for.

Hrst supply of water was found, after the first few minutes,
to have already dissolved an appreciable quantity of material;
but the rate of solution decreased rapidly, and generally most
rapidly in the most resist i ML? -lasses. The second supply began
with a slower rate of solution, which, as in the case of the first,
diminished with incn-asin^' rapidity: and the action of the third
supply showed a similar relation to that of the second.

The powder and solution (at 17) were contained, with a
tlu-rmonieter, in a vessel with platinum electrodes; and the
measurements for k were made by Wheatstone's bridge with
telephone. Multiplication by R gave the amount of material
dissolved. Observations were n the; lapse of 2 minutes,

JENA GLASS.

1 hour, 1 day, and 1 week, from the pouring in of each supply
of water.

Kohlrausch gives l a table, showing the total amount of matter
dissolved off each glass, the progress of the dissolving during each
week, and the ratios of the effects of the second and third
waterings to that of the first. We subjoin a brief extract. The
first column contains the numbers of the six glasses ; the second
the sum of the quantities (in nig. per litre) dissolved off the glass
by the three waterings ; the third column the ratio of the effect
of the third watering to that of the first ; the fourth column the
sum of the conductivities k v & 2 , & 3 exhibited by the three solu-
tions, each observed at the end of the week's action.

No.

mg./lit.

III. : I.

&! + * 2 + * 3 .

136

0-15

18.6

189

0-15

210

281

0-11

156

357

0-21

568

405

0-25

184

992

0-40

2070

The other glass powders were somewhat differently treated :
Previous to the three wettings for a week with 100 times their
mass of water, they were wetted for two days with 20 times
their mass of water, and thus gave more concentrated solutions.
With the worst lime silicate glasses the strength of the solution
in mg. per litre was 1200, and with the best 200. With the
limeless glasses, the minimum was still lower, but the maximum
reached 3000, and, in the case of the borate flint, 6000. With
the densest lead silicates, the quantity dissolved was vanishingly
small. As, however, there was a slight increase of conductivity
at first, followed by a decrease, Kohlrausch suspected that matter
had first gone into solution, and then been separated ; a view
which was confirmed by the appearance of a firmly adhering
deposit on the walls of the vessel.

As most of the solutions were not evaporated, it was not
generally possible to make direct comparison of the dissolved
amounts, but only of the conductivities. In the table which we

'K.,!!. 3567.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 355

reproduce below, k denotes the conductivity of the solution
obtained in the first two days, with 20-fold mass of water, and 1C
the sum of the conductivities of the three subsequent solutions,
plus i k (because 20 is \ of 100).

Corrections have been applied, for temperature, and for the
specific gravity of the glass. The small variations of temperature
which occurred during the observations showed a surprisingly
large influence. Kohlrausch estimates it at 10 per cent, increase
of k for 1 3 of rise of temperature, and has corrected accordingly,
in, denoting by s the specific gravity of the glass, the observed
value of K is multiplied by the correcting factor s/2'5, so as to
reduce to a standard specific gravity 2'5. This gives values of K
related to equal volumes of glass.

Glasses 1, 4, 5, 7, 11, 12 are also included in the table; the
observed values of 7^ + /_. + / ;i given for them above being in-
creased by \ k y to make up for the absence of the two days'
preliminary wetting.

To throw further light on a very important quality of glasses
the persistence of their corrosion by water, the glass powders
were exposed for half a year to the attack of water, changed
from four to six times during that period. They were then
exposed for a week to the action of 100 times their mass
of fresh water. The conductivity of the solution obtained by
this last wetting is denoted by k^ t and given in the fourth
column of the table.

In those cases in which the reduction factor R was known, the
total quantity of matter that went into solution during the half-
year was calculated ; and it is given in the last column, as a
percentage of the mass of glass powder from which it
derived.

The table is divided by horizontal lines into three compart-
iin -nts, of which the second contains the lead glasses, and the
third the non-silicious glasses. The order of arrangement in each
compartment is according to the values of K.

The table confirms the result, previously deduced from hot-water
experiments, that solubility is mainly determined by the gross
content of alkali. Potash, however, appeared more conducive to
solubility than soda.

Tlir order of the lead glasses 9 to 29 follows a very simple
law; the solubility increases with the content of alkali, with the

356

JENA GLASS.

exception of 29, which stands out prominently by the largeness
of its AT; perhaps owing to its large content of potash.

Boric acid in combination with silicic acid seems to check
solubility. The borosilicate 23 is a well-marked instance. It is
composed almost entirely of silicic acid, boric acid, and alkali, and
has but slight solubility. The borate flint No. 31, on the other
hand, shows an amazing amount of solubility. The phosphate
shows much the same behaviour as the silicate glasses.

No.

Per cent.
Dissolved.

120

18(1

210

130

270

130

170

f
i

270

180

2-0

380

200

490

220

360

220

2-7

320

230

440

2*)

3-5

420

320

730

420

600

460

680

570

640

1200

860

2600

2200

200

2300

7000

6800

500

300

100

360

130

350

190

800

350

500

320

1000

The solutions, with the exception of those derived from the
phosphate glass, showed more or less alkaline reaction.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 357

The behaviour of the crown glass No. 1 (called English crown,
but made at Jena) is peculiar for the largeness of its k^ compared
with its & and K. At first it ranks among the best glasses ; but
six months' washing improves it so little that at the end it is low
on the list.

Influence of Temperature. In the case of some of the
powdered glasses, after they had been a long time in water,
variations Were made in the temperature ; and it was found that
the rates of dissolving at

10-8 17'2 23-6
were as 1 2 '7 7'4

This large influence of temperature is in conformity with earlier
observations by E. Pfeifer.

Kohlraush, after keeping a number of powdered glasses in cold
water (occasionally renewed) for half a year, warmed them up,
in their last solutions, to 80, and maintained them at this
temperature for seven hours. He then compared the conductivity
of the last solution with the sum of the conductivities of all
the solutions obtained from the same glass during the preceding
half-year. It amounted, on the average, to nearly half this sum ;
the ratio varying greatly for different glasses.

Hygroscopic Behaviour of Powdered Glass. Eleven speci-
mens of glass in the form of very fine freshly ground powders
were placed, in quantities of about 1 gm., on a small platinum
dish, for two days, beside water, under a bell glass, and were then
again weighed, to show the amounts of moisture they had acquired

Xo. Gain per cent. A'. RK.

12 L' 230 506
11 i 220 198

7 -J 180 131

13 4 230 184
i:> 5 420

16 5 4GO 322
1 5 640 403

17 7

18 L'liOO sso
10 _'.',00 1104
18 6800 L'788

368 JENA GLASS.

from the air. These gains of weight, expressed as percentages of
the original weights, are given in the second column of the
foregoing table. By way of comparison with these, the third
column contains the values of K already given for the same
glasses ; and the fourth column, in the case of those glasses for
which the "reduction factor" E is known, contains the product
'. which represents quantity of matter dissolved. It will be

that, with the exception of the Bohemian potash glass 12

!i has 82 per cent, of silica), the order of arrangement is
substantially the same for the fourth column as for the second.
A fair estimate of the solubility of a glass in water can therefore

i de, from its gain of weight, when exposed in the form of
powder to moist air under the above conditions.

Improvement of Surface by Long Contact with Water.

f the difficulties in the way of getting pure water is the in-
fluence of the air in distillation. Kohlrausch has shown that the
electric conductivity of water can be very largely diminished by
distilling in vacuo. The apparatus which he employed (Fig. 28)

FIG.

is of the nature of a water hammer. A glass globe 100 to 200
cm. in diameter serves as the retort, and is connected by a
T--l>'iped tube with a small vessel which serves as the receiver.
This contains a pair of platinum electrodes for measuring the
resistance of the distillate. By the use of a warm bath at 30 to
45, and a cold bath at to - 8, the requisite 6 to 8 c.c. of
water can be distilled over, and its resistance measured.

]'.\ distillation with this apparatus, 1 under a pressure of about
01 mm. of mercury, Kohlrausch succeeded in obtaining water of
so low a conductivity as 7j = *25. 2

1 Ann. '/. /%.s. ii. Chem., 44. 48(1885).

- Tliis is relative to mercury at taken as having Jt = 10 10 (see p. 351 ).

CHEMICAL BEHAVIOUR OF GLASS SURFACES.

359

The vessel used in the experiment was then washed out with
water for 1 years. At the end of that time, the surface of the
glass had so much improved that Kohlrausch and Heydwiller
(1894) were able to obtain water of much greater purity -than
before. 1

The vessel was charged, on 5th January 1894, with water of
conductivity k =0'7 5, and exhausted for 1J hours. The re-
maining air bubble was of the size of a pin's head ; whence the
pressure over the water was estimated at 40 * 00 mm. The value
of k had now fallen to about a quarter of its original amount.
During the next two months, 45 distillations were performed,
which gave continually improving water. The store of water in
the globe, at the same time, as was to be expected, increased in
conductivity, but only very slowly, showing that the long-continued
washing had rendered the surface of the glass very insoluble.

An outline of the course of these experiments, which are very
promising as regards the obtaining of unusually pure water, is
given in the following table. The first column indicates the
order of succession of the distillations whose results are given.

No.

Day.

tin

tort

Receiver.

0-17

0-075

0-18

069

0-35

068

13, 14. 1 ,

0-43

044

20, 21

(I.-,:;

0425

( c.v,

0412

.i-:,7

0409

Mi-i

0409

0-82

ii in:,

u-s-_>

4404

1-06

(HI:

Thus, after about 30 distillations, the conductivity had practically
attained its limit, k = '04 : whereas distillation in air never gives
less than k = 'l.

The kind of glass with which this success was attained is not
stated.

'K. u Ii

360 JENA GLASS.

143. Action of Dissolved Alkali on Glass. The mode of
attack of glass by alkaline solutions under various conditions has
been discussed in general terms by Foerster, mainly on the basis
of his own observations. 1 The following are his inferences.

As the action of water on glass sets alkali free, no sharp line
can be drawn between the action of water and that of dilute
solutions of alkali. The alkali extracted by the water from the
glass, as long as it remains close to the glass and only moderately
diluted, strengthens the attack in two ways : first by producing
swelling up of the surface; and secondly (especially at high
temperatures) by dissolving silica. When the alkali has spread by
diffusion to a distance from the glass surface, it is usually so much
diluted that it is no longer in a position to strengthen the attack.

Very dilute solutions of alkali say millinormal attack glass
no more actively than pure water. If however the dilution is
not so excessive, it strengthens the attack, and this effect
increases somewhat rapidly with increasing concentration.

In lime-alkali glasses, decomposition is effected by taking out
alkali-silicate, while lime-silicate is left. Pure 1 per cent, soda
lye at 100 dissolves so much from ordinary lime glass that the
surface is dulled by the lime silicate which remains. Further
concentration of the alkaline solution causes the lime silicate to
be also attacked. Soda lye of double normal strength dissolves
lime-alkali glass as a whole.

From this point onwards, further concentration produces, in no
case, any material strengthening of the attack. The solubility of
glass in lye of either soda or potash, shows a decided falling off
at ordinary temperatures when the concentration is made very
high, and at 100 remains nearly constant. Highly concentrated
solution of ammonia, whether at ordinary temperatures or at 100,
attacks glass much less than a weaker solution. Hence, for good
keeping of caustic alkalis in glass vessels, the solutions should be
as strong as possible.

As regards strength of attack on glass, the chief alkaline
solutions take the order (from stronger to weaker) soda lye,
potash lye, ammonia water, baryta water.

Glasses do not as a rule differ nearly so much in susceptibility
to attack by alkaline solutions as by water. The differences are
usually in the same direction, for glasses of any one type.

*., IV. 459.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 361

The above general statements are largely based upon an
investigation carried out by Foerster with four lime glasses. 1
These glasses, which were representative of the kinds then chiefly
used commercially, showed considerable uniformity of composition.
Better materials for the comparison of different types of glass
were furnished by his later research. 2 It deals with 12 out of
the 14 glasses enumerated in Art. 139, and the numbers by
which they are there designated are here retained.

As the actions of different alkalis upon glass are qualitatively
alike, it was thought sufficient to make the tests with soda,
which is the most active of them. Flasks of the 12 glasses
were charged with soda lye of double normal strength, free from
silica, and were kept at 100 for three hours in a paraffin bath.
Their loss of weight under this treatment was observed, and is
given in the second column of the subjoined table, in mg. per sq.
deciin. In the third column are reproduced, for comparison, the
quantities of alkali dissolved out of the same glasses in three
hours by water at 80, expressed in thousandths of a mg. of soda
per sq. decim. 3

No. Soda lye at 100. Water at 80.

1 67-3 27

2 39-7 6-3

3 35-4 28-4

4 37-5 28-2

6 39-8 56

7 377

8 38-5 50

9 42-4 66

10 46-5 65

11 31-3 98
Hi 46 654
17 58

find here some marked exceptions to the similarity of
behaviour towards water and towards alkaline solutions. Though,
in the majority of instances, the two sets of values increase

i . \ . :*84.

l-'or glass 5, which resembles that employed by Stan, and is not iiu-hi.l. ! in
the table, the two values are 37 .m-1 -'7. according to int<>i mat ion ^ivm in !'.. II.

:$;:! JENA GLASS.

together, the borosilicate 1 = 59 IH , which is the most resisting of
all against water, is the least resisting of all against soda lye.
Foerster attributes this to its large content of boric acid, and
remarks that, even with decinormal soda lye, it lost 45 mg., as
against 26 mg. lost by lime glass. The two zinc-containing
glasses 2 = 165 ni and 10 = 16 in , especially the former, behave
worse with soda lye than would be expected from their good
behaviour to water. On the other hand, the soda glass 11, which
contains alumina and a large amount of lime, is the best of all
for resisting soda lye, though weak in resistance to water.

It is only in dealing with glasses of one and the same type,
that their relative resistances to alkaline solutions can be inferred,
even roughly, from their resistances to water.

144. Action of Acids on Glass. Earlier experiments on the
action of acids upon glass having led to contradictory conclusions,
Foerster took up the subject anew, and succeeded in arriving at
definite results. Besides the detailed account of his observations, 1
he has published comprehensive summaries. 2

Experiments at 100 were made with round flasks of three
lime glasses A, B, C, identical with Nos. 8, 15, 16 of Art. 139.
No. 17, under the name of H, was included in some later
experiments. After cleaning, drying, and weighing, the flasks
were heated in a paraffin bath at 100, and filled with acid at
100. After six hours at this temperature, the acids were
removed, the glasses cleaned and dried, and their losses of weight
determined.

The acids thus employed were ; sulphuric acid, in 6 different
degrees of dilution, and pure ; nitric acid in 5, hydrochloric in 5,
and acetic in 3 different degrees of concentration. Similar
experiments were also made with pure water, for comparison.

It was found that, for one and the same glass, the loss of
weight was the same, whether the dilute acid was sulphuric, nitric,
hydrochloric, or acetic, and was the same whether the solution
was normal or millinormal or tenfold normal. A considerably
higher degree of concentration gave weaker action. In all cases
the actions were much weaker than that of pure water. With
glass A the action never exceeded yV, and with glass C about i
of the action of pure water.

'F., III. *., II. and F., IV.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 363

Foerster concludes that the acid in the solution exerts no sen-
sible amount of direct action on the glass, but merely modifies the
action of the water on the glass.

Experiments with Superheated Acids were made, in the fol-
lowing manner, on three lime glasses, D, E, F, of which E and F
were described as good, and D as inferior. Cylindrical bits of tube,
of the three glasses, were dried at 100, and weighed, then enclosed
with the acid solutions in larger tubes, heated for four hours in a
glycerine bath, either at 160 3 or 190, and afterwards tested for
loss of weight.

Here also it was found that the strength of attack was the
same with such different acids as sulphuric and acetic, provided
th;it the concentration, reckoned by the number of gram equiva-
lents in a litre of water, was the same. The influence of concen-
tration became more conspicuous at these high temperatures,
and was still in the direction of diminished attack for increased
concentration.

A similar result was obtained, when coarsely pounded linre
glass was exposed, for six hours, to the action of hydrochloric acid
of different strengths, at temperatures between 260 and 270.
Glasses D, E, F, treated in this way, were again much more
strongly attacked by pure water than by the acids.

Explanation of the Behaviour of Lime Glass to Acid
Solutions. To explain these results, Foerster starts from the
assumption that the acids exert no direct action on the glasses, and
that the attack is exclusively due to the water which is present.
This view leads naturally to the conclusion that a larger content
of acid weakens the attack, by diminishing the concentration of
the attacking water.

A further and more important reason for the influence of
acids, is furnished by the following consideration : The first action
on glass consists in taking out alkali. This alkali then aids
further attack, as explained in previous articles. The presence of
an acid neutralises this alkali, and prevents it from aiding attack ;
and the neutralisation is effected more quickly and more com-
pletely in concentrated than in weak solutions. The inllncnc'e of
concentration is greatest when alkali is being most quickly set
free, and it is set free most <|iii< -kly at high temperatures.

The action of water on glass, though inHm-nccd l>y the presence of
an acid, if not thereby altered in character. The whole difference

3t>4 JENA GLASS.

turns upon the tact that the accumulation of free alkali in the solu-
ti >n is checked. But the alkali which is set free in large quantity by
hot water, dissolves a large quantity of silica and brings it into
solution. This action is likewise checked, when acid is present
i.'iitralise the alkali. It is accordingly found that alkali is far
more completely washed out of glass by acid solutions than by
pure water.

It must not be supposed that the above conclusions are
t'/inrrfit.tlli/ applicable to silicates. There are a few silicates of
lime and potash which are directly attacked by acids, especially
]>y hydrochloric acid. It attacks them far more powerfully than
water ; and the strength of attack increases with the concentration.
Foerster was able to establish the existence of this exceptional
behaviour in the case of Wollastonite (CaSi0 3 ) and a Labra-
dorite. The fused metasilicate Na 2 Si0 3 was also more strongly
decomposed by concentrated than by dilute acids, and more
strongly by these than by water. On the other hand, a melting,
of the composition Na 2 . 3Si0 2 , conformed to the rules for
glasses. From a review of all the facts, Foerster concludes that
the ordinary behaviour of glass towards acid solutions is due to
its large content of silica. In fact, glasses with exceptionally
small content of silica are strongly attacked by dilute acids.

Behaviour of Lead Glasses. With three lead glasses G,
H, J, Foerster made experiments at 100 similar to those made
with the lime glasses A, L\ C. The flasks of the glass /, which
contained 3 3 '8 per cent, of lead, were made at Jena. It was
f<und, just as in the case of the lime glasses, that dilute sul-
phuric, hydrochloric, and acetic acids had less action than pure
water, and that the nature and concentration of the acid made
practically no difference. Foerster recalls the fact that the
resisting power of lead crystal glass to acids is increased by
long-continued exposure to acids. Were it otherwise, the use
of this material for wine glasses would long ago have been given
ill). Against pure water these glasses are more resisting than
lime

On the other hand, flint glasses poor in silica and rich in lead
exhibit entirely different behaviour. The Jena flint glass, of
composition

Si0 2 . Na 2 0. K,0. PbO. MnO. As 2 5 .
:50-85 0-5 G : 5 52'8 O'Oo 0'3

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 365

reduced to coarse powder, was introduced, in quantities of 10 gni.,
into 100 c.c. of water, normal solution of acetic acid, and normal
solution of hydrochloric acid ; and gently boiled for six hours,
with backttow cooling. The water acted only very slightly,
but the acids very strongly, and the hydrochloric beyond all
comparison more strongly than the acetic. The powder in the
hydrochloric lost 12 per cent, of its weight, and the silica left
behind gave the surface a porcelain-like appearance.

Behaviour of Glasses 16 IH and 59 in . These two glasses,
which (Art. 139) differ materially in composition from those of
which we have been speaking, were tested by Foerster for their
behaviour with normal, five-fold normal, and ten-fold normal
acids (HC1, H 2 S0 4 , C 2 H 4 0. 2 ) at 190, it having been found that
they were very little attacked by acid solutions at 100. They
were also tested with pure water for comparison.

With water they lost less weight than the good lime gl
E, F\ and with acids less than with water. In the case of 59 IH
the attack by acids diminished as the concentration increased ;
the glass thus resembling the lime glasses in its behaviour. With
sulphuric and acetic acids 1 6 IH also behaved in this way ; but
hydrochloric acid attacked it more powerfully with increasing
concentration, as shown by the comparative figures :

Normal. Five-fold normal. Ten-fold normal.

16 21 24

Foerster infers that this glass was directly attacked by
hydrochloric acid, and finds a confirmation in the circum-
stance that the bits of tube after the experiment showed
dull surfaces.

Action of Pure Sulphuric Acid on Glass. With the lime
glasses B and C, Foerster made the following experiment : Bits of
tube were suspended ly platinum wire in sulphuric acid, which
was gently boiled for six hours in flasks of very good The

resulting loss of weight, in nig. per sq. decim. was 1/5 for B ami
for C. These figures show that boiling sulphuric acid is much
weaker in its attack than boiling water.

Tin- vapour of sulphuric acid also acts on glass, and more
njy as the temperature rises. Foerster remarks, in conn
tion with this fact, that the sulphuric acid contained in the
products of combustion of coal, and of illuminating gas, attacks

366 JENA GLASS.

it a white coating of alkali sulphates, easily
ivmnvable by water.

145. Action of Saline Solutions on Glass. The four lime
glasses mentioned in Art. 143 were also tested for their behaviour
rious solutions of salts. 1 Trials with solutions of carbonates
of alkalis showed that they may, in some cases, attack a glass
more strongly than solutions containing equivalent quantities of
the caustic- alkali <. Carbonate of soda usually acts much more
: fully than carbonate of potash. Special attention is called
by Foerster to the fact that, according to the observations made
with these four glasses, a content of even 3 per cent, of alumina
increases resistance to carbonates of alkalis, in the case

_jlass containing much alkali and little lime. This effect
he ascribes to the circumstance that alumina is insoluble in
carbonates of alkalis. He mentions that, in experiments on the
action of very dilute alkaline solutions on glass, irregularities are
apt to be introduced by the taking up of carbonic acid from the
air during the necessary operations.

Experiments with other salt solutions soon showed that, in
general, the greater or less resistance of a glass to attack by car-
bonates of alkalis, is no criterion of its behaviour towards salts of
other kinds.

A solution of sulphate of soda had but little effect on any of
the four glasses.

They were much more strongly attacked by phosphate of soda ;
and here again the glasses that contained alumina were dis-
tinguished by their greater resistance.

Exact knowledge of the action- of very concentrated salt
solutions on glass is not of much practical importance. The
solutions employed in analytical work are often so dilute that
their action on glass does not sensibly differ from that of water.
The relations become more complicated when we have to do with
solutions which are not neutral, but acid or alkaline.

Whether there is any glass pre-eminent for high resisting power
against the greater number of important chemical reagents, must
at ] in -sent be left an open question.

Attack by Carbonate of Soda. Foerster subsequently 2
experimented on a greater variety of glasses, for their behaviour
J F., I. 2510. 2 F.,V. 384.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 367

to a solution of carbonate of soda. The glasses employed were
11 out of the 14 described in Art. 139, namely Nos. 1, 2, 4, 6,
.7, 8, 9, 10, 11, 16, 17. They are all included among those tested
by soda lye at 100 and by water at 80 (Art. 143).

Globular flasks of these 1 1 glasses were charged with carbonate
of soda solution of double normal strength, heated for three hours
in a paraffin bath at 100, and then tested for loss of weight.
The subjoined table gives, in the second column, these losses
reduced to mg. per sq. decim. of glass surface. The third and
fourth columns are reproduced from Art. 143 for comparison.
The time of exposure was three hours in all three cases, and the
circumstances were similar; but whereas cols. 2 and 3 give total
loss, col. 4 gives only loss of alkali, reduced to equivalents of soda.
The soda lye, like the carbonate of soda solution, was of double
normal strength. 1

v Carb. of soda Soda lye Water

solution at 100. at 100. at 80.

1 23-5 67-3 2-7

17-6 39-7 6-3

4 59-5 37-5 28'2

6 76-9 39-8 56

7 79-2 37-7 45

8 73-0 38-5 r>0

9 79-4 4'2-4 66

10 i'3-O 46-5 65

11 40-7 31-3 98

16 4.". 46 654

17 51 58 :',50

( ' lasses 4, 6, 7, 8, 9, which consist mainly of silica, alkali, and
lime, are very strongly attacked by the carbonate of soda solution;
much more strongly than by the soda lye. The best resisting glasses
against the carbonate of soda are numbers 1, 2, 10. The fact
that they contain alumina is not alone sufficient to account for
this; for 11 and 16 also contain alumina, and yet show only
moderate resistance.

146. Jena Laboratory- Glass (Gerateglas). This is a boric
acid glass with remarkable power of withstanding changes of

No. 5 glass, which was similar to that used by Stas, Foerster elsewhere
1 II 2922) gives 59, 37, 27 as the corresponding three values.

968

JENA GLASS.

temperature (see Art. 108). Foerster makes a passing allusion
to it, with the remark that it is even less attacked by water than
the glass used by Stas. 1 Fuller information has been published
by F. Kohlrausch, 2 who tested this glass along with two varieties
of a Jena melting containing no alkali ; the compositions of these
latter, in equivalents per cent., being

I.
II.

Si0 2
65
68

Al 2 a
3-3
3-7

ZnO
4-6
3-7

BaO

12
12

B 2 3
15
13

The specimens to be tested were rubbed down to quite fine
powders, and then shaken up with a hundred times their weights
of water. The solutions thus gradually formed were tested for
electric conductivity in the manner described in Art. 142. The
results for these three glasses are given in the following table, in
the columns headed I., II., G. (G standing for Gera'te glass, which
in the English catalogues is called "Laboratory glass"). The table
also includes results obtained in the same way for five other glasses
mentioned in Art. 142. The values given denote, as in Art.
142, the electric conductivity k, so defined as to have the value
10 10 for mercury at 0. The values in the line at the foot of
the table apply to the solutions obtained, by pouring away the
first solutions after the lapse of the six days mentioned, giving
second supplies of pure water equal to the first, and observing
after the lapse of another week.

First supply after

II.

2 minutes, - 9

120

1 hour,

260

Iday,

580

104

6 days,

850

111

130

Second supply after 1
1 week, /

570

Judged by these values, glasses I., II., and G. have much greater
resisting power against cold water than any of the rest. But the
conductivities do not truly represent the quantities of dissolved

1 F., V. 396.

2 K., III. 3000.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 369

matter, and are too favourable to the first three glasses ; as
boric acid, which they largely contain, has relatively small
conductivity in solution. But even after correction is made on
this account, they still retain a distinct superiority over the
other glasses. 1

The Good Preservation of Water in Jena Gerateglas was
shown by Kohlrausch in the following way. 2 Two new bottles
of this glass were left in running water for about a quarter of
an hour; and then filled with very pure water of conductivity
/ = 2, and left, slightly covered, at the temperature of the room.
The amounts of increase in k were

Days elapsed 2 7 23 62 200

In 1st bottle '06 '17 '20 '23 -35
In 2nd bottle '02 '04 '06 '14 '30

These figures give, for the matter taken up from each square
decim. of surface, only half the amounts which Kohlrausch
had previously found for the best bottle-glass that he had ever
tested, although that glass had the advantage of having been
seasoned by long use.

Kohlrausch also made experiments on the behaviour of this
glass to hot water. 3 The above-mentioned solution, with the
powdered Gehiteglas in it, was kept for three days at 60. It
then, on being cooled to 18, showed the value = 46. Being
then kept for four hours at 93, it showed k= 108. The solution
was then, after decantation, evaporated, and found to have con-
tained 194 mg. per litre. This gives 1*8 as the value of the
"reduction factor" jR (Art. 142). The residuum was only very
slightly hygroscopic.

A small bottle of the glass, filled with water, and maintained
for 16 hours at between 50 and 60, showed a loss of 0'2 mg.
per sq. decim. of surface ; which was increased to 0*8 by two
hours' further heating at 100. Kohlrausch winds up by saying,
These results are likewise considerably better than for any other
glasses known to me."

Use in Quantitative Analysis. Reinitzer (see reference to

1 Kohlrausch several times remarks that the alkali-free kinds of glass powder,
after long exposure to water, formed a very firm crust on the bottom of the
vessel. It is interesting to compare this behaviour with that of water-glass, aa
described at page 328.

'K., III. 3002.
2A

370 JENA GLASS.

authorities in Art. 130) published in 1894 a memoir entitled
" Contributions to Quantitative Analysis," containing results of
many years' experience in large chemical works. The last section
of the memoir treats of the attack of water and aqueous solutions
upon glass vessels during boiling.

About 300 c.c. of distilled water were mixed with a little lime
water in a boiling flask of ordinary soft glass, and, after boiling
off the carbonic acid, titrated violet with decinormal hydrochloric
acid. The liquid was then boiled for about 15 minutes, and
turned pure blue. When neutrality was restored, the acid con-
sumed was found to have increased from 12*74 to 12*77 c.c.
Two repetitions of the boiling brought the amount up to 12-80
and 12-90 c.c. The influence of the alkali dissolved from the
glass was thus very perceptible.

700 c.c. of distilled water, in a new flask of Bohemian glass
by Kavalier, were boiled for four hours, the water evaporated
being condensed back. To neutralise the alkali dissolved from
the glass, 9'53 c.c. of decinormal acid were required. A
further quarter of an hour of boiling raised the consumption
to 10'22 c.c. ; and another quarter of an hour raised it to
10 '9 2 c.c. "The impurity introduced into large quantities of
liquid by 15 minutes' boiling, is thus so considerable that it
could be distinctly measured with normal solution, and the
employment of decinormal is quite unnecessary."

The experiment was then repeated with a retort of the best
very infusible potash glass of the same maker. After four hours'
boiling, 1*09 c.c. of decinormal acid had to be added to neutralise
the alkali. As the boiling went on, the quantity had to be
increased in 10 minutes to 1'14 c.c., and in a further 7 minutes
to 1*16 c.c. In this glass, then, with 10 minutes' boiling, small
quantities of alkali can be measured by decinormal acid, without
material error.

Reinitzer goes on to say, " It was a matter of great interest to
me, after these results, to test, in a similar way, the new Jena
laboratory-glass, as regards its suitability for the more delicate
work of quantitative analysis, especially for the measurement of
small quantities of alkali in large quantities of liquid. In a new
flask of this glass, 700 c.c. of distilled water were boiled as before
for four hours, and then tested, with decinormal acid and litmus,
for the quantity of dissolved alkali.

CHEMICAL BEHAVIOUR OF GLASS SURFACES. 371

" 0*13 c.c. of acid was consumed. After 18 minutes further
boiling, the whole consumption had reached 0'18 c.c. of deci-
normal acid.

" These figures show clearly that the new Jena laboratory-glass
is far superior, in resisting power against boiling water or dilute
saline solutions, even to the best Bohemian potash glass (which
is never used for boiling flasks and beakers). It is about eight
times as good as the very infusible Bohemian potash glass, and
about eighty times as good as the ordinary Bohemian laboratory-
glass. It is accordingly beyond doubt that, by this new glass,
the resources of the chemist have been enriched to an extra-
ordinary extent. Hitherto the titration of large quantities of
weakly alkaline liquid (for example, the measurement of the
alkalinity of natural water) has been rendered quite erroneous by
the change produced in the water by boiling in glass vessels ;
but it can now be performed with the greatest sharpness. Since,
as I have previously shown, the most careful boiling away of the
carbonic acid is always necessary in order to obtain, with deci-
nonnal solutions, definite and sharp changes of colour in large
quantities of liquid, it is quite clear, having regard to the
demonstrated influence of boiling in glass vessels, that the test
by decinormal acids for alkali has now for the first time, by
the use of vessels of Jena laboratory-glass, really attained the
accuracy which has hitherto been claimed for it" l

1 The passage italicised is leaded in the original memoir. It is followed by a
practical illustration, which Dr. Hovestadt reproduces, but which is couched in
too technical language to be of general interest to our readers.

Art. 147, "On Surface Tension of Water in Capillary Tubes of Different
Classes," describes experiments by Volkmann (see references in Art. 1*)) to
determine whether capillary elevation of water in glass tubes is influenced by the
nature of the glass. The conclusion is in the negative, and the discussion lacks
interest.

CHAPTER XL

ELECTKIC AND MAGNETO-OPTIC PROPERTIES
OF GLASS.

148. Insulating Power of Different Glasses. Differences in
the insulating properties of different glasses depend mainly on
their chemical behaviour towards water. Glasses easily attacked
by water are bad insulators.

F. Kohlrausch has investigated this point by comparative
observations, and sums up his results in the following brief
communication to the German Chemical Society. 1

" That chemically bad glasses insulate badly is a fact which has
been long known. That this is due to the Faraday water- film,
acting in concert with the alkali, has been thoroughly established
by Warburg and Ihmori. 2 I will merely add some information as
to how glasses group themselves from this point of view. I suppose
the glasses in question to have been for some time in water, then
rinsed with distilled water, and dried in the sun, or in an oven, or
in some such way.

" At the outset all will insulate well ; but after some time con-
siderable differences will show themselves.

" Decidedly bad glasses will then be recognizable by their
discharging a gold-leaf electroscope almost instantly when the
percentage of saturation in the air is between 50 and 60, and
in a short time (1 sec. or 2 sec.) when it is between 40 and 50.
With glasses of medium quality, as well as with lead crystal and

*Ber. d. deutsch. chem. Ges., 26. 3002 (1893).
2 Ann. d. Phyx. u. Chem. 27. 481 (1886).

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 373

Jena thermometer glass, the corresponding percentages of satura-
tion will be about 20 higher.

"The Thuringian glass made at Gehlberg 1 insulates perfectly
up to 40 per cent, of saturation, fairly well at 60 per cent., and
discharges in a few seconds at 80 per cent.

" With Bohemian potash-glass, 2 which, at least as regards quan-
tity of alkali dissolved, must be reckoned among good glasses, no
traces of conduction appeared till the percentage was above 50 per
cent. ; and the insulation was still fairly good at 75 per cent.

" At the head of all stood the alkali-free Jena glass, 3 which
insulated perfectly at above 60 per cent., and well even at 80 per
cent, of saturation.

" It would be convenient if this glass were obtainable commer-
cially for some purposes."

149. Transparency for Rbntgen Rays. Rontgen himself
announced that glasses of different composition behave differently
as regards the transmission of the X rays in particular, that lead
glasses show larger absorption than glasses free from lead.

Winkelmann and Straubel 4 carried out an extended investiga-
tion of various properties of the Rontgen rays, which included the
testing of a large number of glasses for facility of transmission.
The rays, before falling on the sensitive photographic film, had
to pass through one or more of the plates to be tested. These
were of 23 different glasses, and their total thickness was 2*9
mm. ; their common area being about 2 sq. cm. Most of them are
included in the list of Winkelmann's glasses, which we have given,
with their compositions, in Art. 67 ; and the identities are
indicated in the following list, which is arranged in order of
transparency, I being the most and 23 the least transparent.

7 = 52W. i:i 19 = 21\Y

2-49 8= 6 14 20 = 47

3 9 = 84 15 = 32W. 21 = '2:\

4 10 = 90 1(1= 8 :>L = 33
5=i'7 11 = 25 17 = 13 23 = 69
6=i'7 12 = 28 18

1 Lik- No. 11, Art. 14-j. No. 12 of Art
'Represented by specimen* I. a.,, 1 II., Art 140.
hem., 59. 324 (1806).

374 JENA GLASS.

No. 3 is described as a uranium glass of unknown composition.
No. 4 is a plate glass having approximately the composition

Si0 2 Na 2 CaO Fe 2 3 + A10 2
75 15 8 2 per cent

No. 13 had the same composition as 12 = 28W, except that
the percentages of Si0 2 and As 2 5 were greater by 0*1, and the
percentage of BaO less by 0*2.

No. 14 was an antimony glass, of composition

Si0 2 B 2 3 K 2 Sb 2 3

53-5 20 6-5 20

No. 18 agreed with 85W, except that, instead of 10*1 ZnO,
it had 10-1 PbO.

The investigation thoroughly confirmed Eontgen's conclusion
that the presence of lead oxide increases absorption. It further
showed that baryta has a similar effect. No. 21 contains no lead,
but 42 per cent, of baryta. The antimony oxide in No. 14, and
the zinc oxide in No. 15, seem also to dimmish transparency.

Influence of the Several Components. To obtain further light
on the action of the most important glass-forming oxides, Winkel-
mann and Straubel experimented directly on the transparency of
these oxides or their salts. The substances were reduced to
powder, and equally thick layers of powder were compared.

A. The most transparent were : boric acid, nitrate of soda,
carbonate of soda (of 97 per cent.), alumina.

B. Of intermediate transparency : nitrate of potash, zinc oxide,
sand, carbonate of potash.

C. The least transparent were : lead oxide, minium, antimony
oxide, barium nitrate.

The difference betweeen B and C was greater than that between
A and B. These results confirmed and extended those deduced
from comparison of the glasses.

Rare Earths. Finally, experiments on the influence of the
oxides known as rare earths became possible ; Schott having
introduced these materials, in quantities of from 5 to 10 per
cent., into a number of new meltings, otherwise agreeing in
composition with glasses previously made. For example, the

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 375

composition of a zircon glass is given by Winkelmann and
Straubel as

Si0 2 B 2 3 As 2 5 Na 2 K 2 CaO ZrO 2
60~ s 0-2 5-3 14*5 2 10

The first point tested was, whether these glasses possessed, like
fluorite, the property of transmuting the X rays. 1 The conclusion
was distinctly in the affirmative as regards zircon. A weaker
action of the same kind was shown by a glass containing didy-
miura, and by one containing erbium. No such effect was shown
by glasses containing beryllium, uranium, cerium, or thorium.

Transparency for the X rays was then tested ; and trustworthy
conclusions were obtained from those pairs of glasses whose
compositions were identical except in content of the rare earths ;
the rare earths in question being cerium, didymium, zircon,
thorium. To intercept the fluorescent rays, a thin sheet of paper
was interposed between the glass under examination and the
sensitive film. The order of transparency (from greatest to least)
thus found for the glasses was :

Cerium, didymium, zircon, thorium.
Without the interposed paper the order was :

Zircon, didymium, cerium, thorium.

150. Special Glass for X Ray Transmission. Soon after
the publication of Rontgen's discovery, Schott 2 devoted his
attention to the preparation of a glass which should be specially
transparent to the new rays. As a preliminary step, he determined
the order of arrangement of the undermentioned oxides and car-
bonates to be

Li 2 CO 3 B 2 O 8 Na 2 C0 3 MgO A1 2 3 Si0 2 K 2 C0 8 CaO
Mn 2 s As 2 6 BaC0 8 PbO

a result which confirms the previously accepted rule that trans-
parency follows the inverse order of the atomic weights. Experi-
ments on this basis led Schott to a glass of composition

Si0 2 B,0 8 A 1,0, As A Na,0
:'.<)<; 30 20 0-4 10

1 See Ann. d. Phy*. . Chfm., 59. 386-343.
*Beiblatt zur Zeitschr. f. Inttrum., Heft 13, 1899.

376 JENA GLASS.

Photographic tests showed this glass to be distinctly more
transparent to the X rays than the Gehlberg glass used by
Gundelach.

Gundelach took in hand the preparation of X ray tubes of the
new glass : but scarcely any difference could be detected between
their effects and those given by ordinary tubes. The glass has
therefore not been put upon the market. The effectiveness of
X ray tubes is, in fact, much more dependent on other properties
than on transparency. 1

151. Dielectric Constants of Different Glasses. The
" dielectric constant," or " permittivity," or " specific inductive
capacity " of glass has been a frequent subject of investigation.
The following are some of the principal determinations for various
kinds: 2

3-0 to 3-24 Gordon, - Phil. Trans., 1879, 1. 417.

6-6 to 9-1 Hopkinson, 1878, 1. 17; 1881,2. 385.

3'3 to 6'34 Schiller, - Pogg. Ann., 152. 555 (1874).

6-46 to 7*57 Winkelmann, - fFted. Jnn., 38. 161 (1889).

6-88 to 7-76 Donle, ,, ,, 40.307(1890).

3-6 to 25-3 - Quincke, - 19. 556 (1883).

6-1 Wiillner, - - Exper. Phys., 4 Aufl., 4. 333 (1886).

7'5 Romich & Nowak, - Weiner Ber. (2), 70. 380 (1874).

The specifications of the glasses tested have not in general been
very definite.

Winkelmann, with the view of determining the influence of
chemical composition, made comparisons between a glass contain-
ing no lead and one containing 45 per cent, of lead.

Winkelmann's Method of Observation. The observations
were made with the help of a telephone.

Two equal and parallel metal plates, P l P 2 , face one another,
and in the space intervening between their central portions there
is a smaller metal plate Q parallel to them.

] The expansibility of the kinds of glass which are transparent to X rays is
considerably less than that of platinum. There is, accordingly, a bad joint
between the sealed-in wires and the glass. To prevent danger of the glass flying,
the course of the wire should be straight, and its surface smooth. The joint can
be made air-tight by a non-volatile oil.

2 Results collected by Lowe, Ann. d. Phys. u. Chem., 66. 401 (1898).

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 377

The glass plate to be tested is larger than Q, and of such
thickness as to tit closely between Q and P r It can be inserted
or removed at pleasure. The other plate, P 2 can be moved
parallel to itself, to or from Q, through a measured distance.

When an observation is to be made, Q is connected with one of
the secondary terminals of a small induction coil, the other
terminal being earthed, and the two terminals of a telephone are
connected with P l and P 2 . The effects in the telephone will be
balanced so as to give a minimum of sound, when the condenser
PiQ (consisting of P lt the side of Q facing it, and the intervening
medium) has the same capacity as the condenser P 2 Q.

Let d be the thickness of the glass plate, and K its permittivity.
Then, before the introduction of the plate, the two distances will
have the same value d when balance is obtained. When the
glass is inserted, it will be necessary to move P 2 nearer, by a
certain amount x, to restore the balance, and K will be given by
the equation

v d

.11 = - ,

Ct X

In this way, Winkelmann investigated the permittivities of four
specimens of glass, besides ebonite and paraffin, also of the
liquids benzol, petroleum, oil of turpentine, and alcohol. The
glass plates, which had thicknesses varying from 3'07 mm. to
26*23 mm., showed the following permittivities :

Plate glass, - G'4G

Plate glass, - 7 '5 7

Lead-free glass, - 7*11

Glass with 45 per cent, lead,- - 7'44

The last two were discs for objectives, from the Jena Glass
Works. In view of the small dittcrence in their permittivities,
with so large a difference in composition, Winkelmann renounced
the idea of extending the test to other kinds of glass.

Later Determinations. H. Starke, by an adaptation of the
method of NVriist, has recently determined the permittivities of
ten different kinds of glass, and of a number of other solids. 1

The alternate currents given by a small induction apparatus

Phy*.

378

JENA GLASS.

are sent through a Wheatstone's bridge, Fig. 29, whose four arms

are liquid resistances

Two condensers, of capacities

FIG. 29.

(7 3 , C, are placed in parallel with the branches ?' 3 , ?* 4 . The
conditions for balance in the telephone T can be shown l to be

!ll = ^ = -i

*2 r 4 <? 3

In order to make the capacities conform to this condition, C 3 is
varied by sliding a glass plate in or out through measured
distances, the two metallic plates of the condenser being fixed.

1 To prove this, let lf i. 2 , i 3 , i 4 be the currents at any instant in r lt r 2 , r 3 , r 4 .

When no current goes through the telephone T, the current into the first
coating of C 3 and out of the second, is \ - i 3 .

For equality of potential at the two terminals of the telephone (or at the
left and right corners of the diagram), we have the conditions

h~h = h~h

Eliminating i' 2 and i 4 from the 3rd equation by substitution from the other
two, we get

In order that the ratio of i 3 to ij may be variable, the second member must
take the form .

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 379

A liquid condenser, consisting of a shallow cylindrical vessel
of nickel (in the first instance empty), with a collecting plate
parallel to its base, is joined* in parallel with the condenser C 4 ;
and C 3 is then adjusted till balance is obtained in the telephone.
The liquid condenser is then filled with purified benzol, which,
according to Fl. Ratz 1 has, at temperature t, the permittivity

K t = 2-2582 - -00164(* - 15).

Let x be the distance through which the slider in 6' 3 must be
moved to restore balance.

Now let the benzol be removed, and replaced by another
liquid say of permittivity K and let the slider be moved
through a further distance y till balance is restored. As equal
movements of the slider produce equal changes of capacity, we
have

K-l

which gives 1C in terms of K t and measured distances. A
liquid thus employed was ethylene-chloride, which, according to
Landolt and Jahn, 2 has at the permittivity 11 '31.

If a glass plate introduced into the liquid of the condenser is
found not to disturb the balance in the telephone, the inference is
that the permittivity of the glass is the same as that of the liquid
which it has displaced. By making a mixture of the two
liquids above named, this result can be approximated to, and
the slider can be adjusted till the balance is exact. Two
mixtures, one of rather higher and the other of rather lower
permittivity than the glass, will thus give the true value by
interpolation.

One advantage of the method is that it can be carried out with
small glass plates say of 3 sq. cm. area. It is also independent
of the shape of the plate and of the character of its surface. The
limits of interpolation are widened, when the plate is a right
cylinder or prism with its ends touching the two bounding
plates of the liquid condenser. 3

The following table gives Starke's results for the ten glasses ;

' Zcittckr.f. Phy* Ckem., 19. 94 (1898). I (1892). i

the source* of error in the method we must refer to tlie original paper.

JENA GLASS.

including permittivity K, specific gravity s, and the index of

j --traction for the /> line :

Mark.

Description.

K/s

n D

- 186

Borate crown, -

5-48

2-24

_>-r>

1-50936

O. 1948

Borosilicute crown,

6-20

2-47

2-48

i-r.1180

S. 169

Phosphate crown, -

6-39

2-58

2-51

1 .V2090

Borate flint, -

7-66

3-17

2-41

1-60305

O. 1610

Baryta crown, -

7-81

3-21

2-45

1 -57519

O. 1777

Baryta flint, -

8-28

3-40

2*44

1 -60284

0. 19-J-J

Densest bar. crown,

8-40

3-55

2 -37

1 -60899

0. 1087

Silicate crown,

7-ao

2-54

2-83

1-51883

0. 1M.T>

Dispersive crown, -

9-13

2-70

3-38

1-52333

0.1469

Half flint, -

7-77

3-58

2-17

1-6129

Upon the whole, the order of arrangement for K is the same
as for density, and also the same as for index of refraction ;
but there are strongly marked exceptions.

152. Electromagnetic Dispersion. In connection with his
investigation of the dielectric behaviour of glass, Winkelmann
gives a list of previous determinations of the changes in K
produced by changes in the frequency of alternation. 1 They all
showed, in the case of glass, that K increases as the frequency
diminishes. Since K corresponds, in Maxwell's theory, to the
square of the index of refraction, this is opposite to the law
of ordinary dispersion in the case of light, and may be regarded
as coming under the head of " anomalous dispersion."

J. J. Thomson 2 found the value of K for a specimen of glass to
be 2 '7 when the oscillation-period was 4 x 10~ 7 of a second, and
to be from 9 to 11 when it was that of an ordinary tuning fork.

Lecher, 3 in experiments on two glasses, obtained an opposite
result. With a period 3 x 10~ 7 sec., the values of K were 7'3
and 6 '5, and with a period of half a second, 47 and 4'6.

Blondlot, 4 by a comparison of glass with sulphur, obtained an
indirect confirmation of the smallness of K for glass at high
frequency. He deduced the value 2 '8, which nearly agrees with
J. J. Thomson's.

1 A nn. d. Phys. .. fJhem., 38. 168 (1889).
' J Ann. d. Phy. it. Chem., 42. 142 (1891).

2 Proc. Roy. Soc., 46. 292 (1889).
4 Com. Hen., 112. 1058(1891).

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 381

K. F. Lowe, 1 in a comprehensive experimental investigation,
determined the magnitude and sense of the dielectric dispersion
for a number of organic compounds, and for 10 different kinds of
glass. He employed Starke's plan of mixing two liquids in such
proportions that displacement of the mixture by a solid body does
not disturb the electrical balance. In dealing with slow oscilla-
tions, he used the same two liquids as Starke, and tested the
lialanci* ly Xernst's method. The glass plates introduced into the
liquid had thicknesses of from *18 to '26 mm.

For rapid oscillations the liquids employed were benzol and
acetone, with Drude's method of observation. 2 The glass plates
were strips 4 mm. wide and 2 mm. thick. This method proved
less exact than the other, and the final values were affected with
an uncertainty of 1J per cent.

In the following table the column headed K' contains Lowe's
results for high frequency. His results for low frequency are
given under the heading K, with Starke's results for nine glasses
in an adjoining column. Lowe states that his glasses were similar
to Starke's, except that he used the borosilicate S. 99 in place of

Mark.

Description.

Starke.

Lowe.

- 196

Berate crown,

5-48

5-25

5-05

0.2238

Borosilicate crown,

6-20

6-15

- 218

Phosphate crown, -

6-39

6-40

6-20

O. 1580

Baryta crown,

7*1

7-83

7'65

0. 13.-.3

Silicate flint,

s-_s

s _>'.

7'30

O. 1993

Densest baryta crown, -

8-40

7-96

7 l-J

0. 1 .-._'

Silicate crown,

7-20

7-00

7-10

O.2074

Dispersive crown, -

9-13

9-14

7-70

O.2051

Silicate flint,

7-77

7 ;_'

S. 99

Borate flint,

S-<Ni

7-63

the borate flint S. 4. The trade numbers of the glasses are
however different in the two lists, and it would therefore seem
that the glasses were not exactly identical in kind. This may
account for the difference in the case of densest baryta crown
With one doubtful exception, the high-frequency value K' is in

1 Ann. d. Phy*. ti. Chtm., 66. 390 (1898).
. Phy*. Chem., 23. 282 (1897).

38:> JENA GLASS.

every case smaller than the low-frequency value K. In the one
exceptional case O. 1542, the difference in the opposite direction
is within the limits of the errors of observation.

153. Absorption of Electromagnetic Radiation. For nine
of the ten glasses, Lowe calculated the " coefficient of electric
absorption " K, defined by the rule that the amplitude of electric
vibration diminishes in the ratio e~ 27r *' for each wave-length of
advance in the dielectric.

Drude l has deduced, for the calculation of /c, the formulae

being an angle found from

n denoting the index of refraction for luminous rays. The values
thus calculated for AC are given in the second column of the following
table. The third column contains the values, for the same glasses,
of the optical characteristic v [which may conveniently be called
the constringence], defined in Art. 17. Lowe calls attention to

Glass.

S. 196

60-4

O. 2238

035

63-4

S. 218

69-9

0. 1580

56-9

0. 1353

145

44-3

0. 1993

56-4

0. 1542

58-5

0. 2074

175

52-0

0.2051

36-8

S. 99

42-5

the fact that the highly dispersive crown 0. 2074 has the largest
" electric absorption " ; which is indicative (see Art. 24) of very
high electric dispersion, A comparison of the values of K and v
brings out no obvious relation, beyond the fact that, for the three
flint glasses, K and v increase together.

l Ann. d, Phy*. u. Chem., 64. 131 (1889).

ELECTRK AM. MAiN KTO-OPTK' PROPERTIES OF GLASS. 383

An attempt to determine by direct experiment the "electric
absorption " of the glass 0. 2074 was unsuccessful, and the above
method of calculating K needs verification.

154. Verdet s Constant for Optical Glasses. In an appendix
to the description of a ring electromagnet, which gave a field of
about 40 000 C.G.S. units of intensity, H. du Bois 1 has given the
values of Verdet's constant for a number of Jena crown and flint

-ses, found by examining them in this field. The glass plates
employed were the identical plates previously used by Rubens in
his measurement of absorption in the ultra red (see Art. 25).
The glasses are the first nine in the list of Art. 23.

Verdet's constant for any substance may be defined as the
amount of rotation of the plane of polarisation produced during
the propagation of light from one point to another of the
substance, when the magnetic potentials of the two points differ
by one C.G.S. unit. If the rays of light are parallel to the lines
of the field, the constant can be calculated by dividing the
amount of rotation by the distance, and by the intensity of the
field. The amount of rotation is usually expressed in minutes.

The last column of the following table, headed w Dt gives the
values of Verdet's constant, in minutes, for sodium light, for the
nine glasses, and also for fluorite. The order of arrangement is

Mark.

Description.

n D

w D

Fluorite

1-4340*

0-0091

8. 204

Borate crown, - ...

1-51007

0-0163

0. 1092

Light baryta crown,

51698

0-0190

O. li:.l

Dispersive silicate crown,

.VJ002

0-0234

S. 179

Medium phosphate crown,

56207

00161

O. 1 1 :;

Dense barium silicate crown, -

57422

0-0220

O. 451

Light silicate flint,

:>7.vj i

0-0317

O. 469

Dense silicate flint, -

-64080

0-04 _'

O. 500

Dense silicate flint,

-70130

0-0608

8. 163

Densest silicate flint.

1-88905

0-0688

according to the magnitude of the index of refraction for sodium
light, whose values n D are given in the preceding column. !>>ili
columns are for ordinary temperatures. Comparison between the

- '/. /%. u. Chfin. t 51. 647 (1894).

3S4 JENA GLASS.

two columns shows that, for the most part, the rotation increases
with the index.

Standard Plates for Measuring Magnetic Fields. The
rotation of the plane of polarisation, by a glass plate whose plane
is perpendicular to the lines of the field, affords a convenient
means of measuring the intensity of the field, especially if the
u f lass be silvered at the back, so as to double the length of path
and thereby double the rotation. The plate can be standardised
beforehand, by observing its effect in a field of known intensity.

Zeiss supplies, for this purpose, standardised plates of the
" densest silicate flint " S. 163. To avoid the confused mixing of
multiple reflections which occurs with parallel plates, they are
made (on the suggestion of H. du Bois) x slightly wedge-shaped,
so that the disturbing images are thrown away from the principal
image, and can be stopped out from the field of view of the
analyser. If the diaphragm of the polariser does not subtend
too large an angle as seen from the analyser, the angle
of the wedge need not exceed 15' to 30'. A standardised
glass about 1 mm. thick is suitable for fields of the order
1000 C.G.S. For weaker fields, thicker plates should be
employed.

155. 2 Another Investigation. An investigation "on the
electromagnetic rotation of the plane of polarisation in glasses,
and its employment for measuring currents " has been recently
published by 0. Junghans (Zurich, 1902). The glasses were
used in the form of cylinders about 5 cm. long and 1*5 cm. in
diameter, with plane parallel ends, and, when under observation,
occupied a definite position in the centre of a cylindrical coil
traversed by a current. The rotation of the plane of polarisation
was measured with a Wild's polaristrobometer. In the following
table of results, the 9 glasses are arranged in descending order of
their indices of refraction n D , which is also the descending order
of their values of Verdet's constant W D . The first 6 are described
as silicate flints, and the remaining 3 as barium silicates. The
numbers I. to IX. are not the trade names, but mere reference
numbers. As regards the other headings, i denotes the current,
in amperes ; R the rotation for sodium light, expressed in cente-
simal " grades " ; R the quotient of R by i ; 21 the length of the

} /.c. 548-549. -Supplied by Dr. Hovestadt for this edition.

ELECTRIC AND MAGNETO-OPTIC PROPERTIES OF GLASS. 385

glass cylinder, Junghans does not carry his reductions beyond
the computation of R ; and the values of u) D given in the last
column have been deduced by Dr. Hovestadt in the following
way. The values of R are in grades per ampere. To reduce to
minutes per ampere, we must multiply by 54. Data given by
Junghans show that the intensity of field for 1 ampere is 375
c.G.s. units. We have, accordingly,

/," 54 .R'.

*"- 2*375" *2T

which is the formula that has been employed. These values of
W D may be compared with those given in Art. 154. Junghans
does not appear to have been acquainted with Du Bois'
investigation.

Glass.

21
cm.

w/>

1-9303

6128

l-827

2-978

5-010

0856

II.

1-7938

6157

1 -439

2 -335

5-005

III.

1-7408

6157

1 -161

1 -910

5-010

0549

IV.

1-6797

6116

959

1 -563

5-010

0449

1-6487

6140

810

1 -317

4-982

0381

VI.

i-i;-ji_>

6110

747

1 "224

4-982

0354

VI!.

1-6109

6108

466

763

4-982

0221

VIII.

1 --.731

6134

462

748

L482 (_> it;

IX.

1-5398

6100

421

683

4-982 -0197

Unsuccessful attempts were made to find a definite relation
between the specific rotatory power of the 6 flint glasses, and
their content of lead oxide. H. Becqueral's suggestion 1 that the
rotatory power is proportional to ri*(n 2 1 ) gave deviations of
4*33 per cent. The supposition that the rotatory power is
proportional to the square of the density, gave deviations of
about 3 per cent.

et de phy., 5 Serie, t. Ml.

APPENDIX.

REVISED LIST OF JENA OPTICAL GLASSES.

THK following list, issued January 1902, supersedes that given on

The phosphate and borate glasses are withdrawn, as they have been
found wanting in durability.

The italics indicate glasses of decidedly new composition, first
introduced at Jena.

The following are mentioned as specimens of ordinary silicate glasses
for objectives :

Crowns O. 144, O. 60, O. 203.

Light flints O. 340, 0. 318, 0. 569.
Flints O. 11*, 0. 167, 0. 103, O. 98.

They can be supplied in all sizes up to 1 m. or more. Attention
is called to the telescopic crown 0. 2388, and the telescopic flint
O. 2001, as almost completely abolishing the secondary spectrum.

Pressed lenses and prisms are supplied in the rough.

Coloured glasses of 18 kinds are specified.

Reference is made to separate catalogues for laboratory glass,
thermometer tubing, water-gauge glasses, and lamp chimneys.

JENA GLASS.

Trull-

Description.

Index for
D.

Mean
Dicpenion

C to F.

n-l
A

0. 82

Borosilicate Crown,

1-4944

00743

66-fi

0, 2188

Borosilicate Crown, .

1-5013

00760

65-9

Crown of Lowest Index, ....

1-4782

00726

65-9

o. MB

Borosilicate Crown,

1-4967

00765

64-9

O. 144

Borosilicate Crown,

1-5100

00797

84*0

0. 599

Borosilicate Crown,

1-5069

00813

B2'3

0. 57

Light Silicate Crown,

1-5086

00823

61-8

O. 2388

Telescope Crown, 1

1-5254

00852

61-7

0. 2122

Heaviest Baryta Crown, ....

1-5899

00970

60-8

0. 337

Silicate Crown,

1 -5144

00847

60-7

0. 546

Zinc Crown,

1-5170

00859

60-2

0. 60

Lime Silicate Crown,

1-5179

00860

80-2

O. 138

Silicate Crown of High Index, -

1-5258

00872

80-2

O. 567

Silicate Crown, -

1-5134

00859

59-7

O. 227

Barium Silicate Crown, ....

1-5399

00909

r>9-4

0. 2118

Crown of Low Index,

1-5095

00858

59-4

0. 203

Ordinary Silicate Crown, -

1-5175,

00877

59-0

0. 2164

Crown of Low Index,

1-5102

00873

58-4

0. 2071

Heaviest Baryta Crown, ....

1-6098

01037

58-8

0. 15

Zinc Silicate Crown,

1-5308

00915

58-0

O. 211

Heavy Barium Silicate Crown,

1-5726

00995

57*5

0. 1200

Heaviest Baryta Crown, ....

1-6112

01068

57-2

0. 114

Soft Silicate Crown, -

1-5151

00910

56-6

0. 1615

Heaviest Baryta Crown, ....

1-6080

01078

56-4

0. 2994

Heaviest Baryta Crown, ....

1-6130

01087

50 '4

0. 463

Baryta Light Flint, ....

1-5646

01020

5.V4

1 Never quite free from bubbles and veins.

APPENDIX.

3SJ)

Trade
No.

Partial Dispersions.

Ratios to A.

K'li.-ny.

A'toD.

DtoF.

Ftoff.

O. 82

00496

00510

00412

667

698

233

,,. Jlss

00498

00533

00424

655

701

557

246

0. 3258

00485

00507

00400

668

699

2-23

O. 802

00504

00534

00423

659

698

553

2-38

O. 144

00519

00559

00446

651

701

2-47

O. 599

00529

00569

00457

-661

701

562

_' is

O. 57

00530

00578

00464

643

TO-J

564

2-46

O. 2388

00549

00602

00484

644

707

568

2-85

< >. -J122

00621

00683

00546

640

704

3-32

O. 337

00547

00596

00480

645

703

567

2-60

O. 546

OQ6M

00605

00485

646

704

565

2-00

0. 60

00553

00605

00487

643

703

566

2-49

O. 138

00560

00614

00494

642

704

566

2-53

00654

00605

00488

646

704

569

J :.!

00582

00639

00514

640

70!

566

0. 2118

00607

00604

00491

649

872

2-54

00563

00616

00499

642

702

568

2-54

O. 2164

00559

00616

00500

640

706

2-54

"71

00665

00730

00590

641

704

569

3-54

i. I.',

00587

00644

00520

tij-j

7"l

068

2-74

0, -Ml

00630

00702

00568

706

:.71

0. 1209

00680

007

00610

636

705

571

3'55

0. Ill

00577

00642

00521

634

705

572

_>:>:,

00685

00761

00817

488

706

:;.v,

0, -"'.' i

00683

00767

00626

<;_><)

708

3-60

00648

00720

00086

688

706

575

; 11

JENA GLASS.

Trade

Description.

Index for
D.

Mean

Dispersion
CtoF.

n-1

0. li(s

n of High Dispersion, .

1-5149

00943

64*6

0. 7-2-2

Bnn/ta Light Flint,

1-5797

01078

53 \S

0. 846

Baryta Light Flint, ....

l -r.r.-j.-,

01042

63-0

0. 602

Baryta Light Flint,

1-5676

01072

53-0

0. 2001

Telescope Flint,

1 .-)_> 1 1

01007

.->]-x

0. 381

Crown of High Dispersion,

1-5262

01026

51-3

0. 583

Baryta Light Flint,

1-5688

OHIO

51 -2

0. 1.V2

Silicate Glass, -

1-5368

01049

51-2

0. 543

Baryta Light Flint, ....

1-5637

01115

50-6

0. 527

Baryta Light Flint, ....

1-5718

01133

50-4

0. 164

Borosilicate Flint,

1-5503

01114

49-4

0. 2015

Heaviest Baryta Crown of High Disper-

1-6041

01-22-2

49-4

sion,

0. 575

Baryta Light Flint, .

1-5682

01151

49-3

0. 522

Bartita Liaht Flint.

1 -5554

01153

4S-2

0. 7-2G

Extra Light Flint,

1-5398

01142

47-3-

0. 161

Borosilicate Flint,

1-5676

01216

46-7

0. 578

Baryta Light Flint,

1-5825

01255

46-4

0. 378

Extra Light Flint,

1-5473

01193

4.VH

0. 364

Borosilicate Flint,

1-5753

01254

46-9

0. 1266

Baryta Light Flint, ....

1-6042

01381

43-8

0. 154

Light Silicate Flint, -

1-5710

01327

43-0

O. 376

Ordinary Light Flint,

1-5660

01319

42-9

0. 276

Ordinary Light Flint, ....

' 1-5800

01373

42-2

0. 569

Ordinary Light Flint,

1-5738

01385

41-4

0. 340

Ordinary Light Flint,

1 -5774

01396

41-4

0. 184

Light Silicate Flint. -

1-5900

01438

41-1

0. 748

Baryta Flint,

1-6235

01599

39-1

APPENDIX.

391

Trade
No.

Partial Dispersions.

Ratios to X

Density.

A'toD.

DtoF.

Ftoff.

0. 608

00595

00666

00543

631

706

576

2-60

0. 722

00681

00761

00621

632

707

577

3-26

0. 846

00657

00736

00602

630

707

577

3-01

0. 602

0067.-.

00759

00618

630

708

576

1*19

0. 2001

00639

00710

00.177

635

705

573

2-50

O. 381

00644

00727

00596

629

709

582

2-70

O. 683

00696

00786

00644

708

580

3-16

0. 152

00659

00743

00610

628

708

582

2-76

O. 643

00699

00790

00650

627

708

583

3-11

0. 527

00706

00803

00660

623

709

582

3-19

O. 164

00710

00786

00644

637

706

578

2-81

O. 2015

00763

00867

00712

624

709

583

3-55

O. 575

00718

00817

00672

623

710

584

3'15

O. 522

00718

00819

00677

623

710

587

3-03

0. 726

00711

00810

00669

623

709

586

2-87

O. 161

00762

00860

00709

-689

707

583

0. 578

00777

00891

00739

619

710

589

3-29

O. 378

00739

00847

00705

620

710

591

2-93

0. 364

007^7

00888

00735

628

708

586

2-90

O. 1266

00861

00982

00821

616

711

594

0. 164

00819

00943

00791

617

710

506

3*16

00814

00939

007v

617

712

096

I-U

O. 276

00646

OOH77

00827

616

712

802

3-22

0. 569
O. 340

00863
00867

00987
00994

00831
00837

614

711

400

top

3-22
1*81

O. 184

00882

01022

00861

613

71-'

697

148

O. 748

00906

01 iu

00966

*:,

71::

3-67

JENA GLASS.

Trade
No.

Description.

Index for
D.

Mean

l>is]U.TSi.>M

CtoF.

V-

n-1

0. 318

Ordinary Light Flint,

1-6031

01575

38-3

0. 118

Ordinary Silicate Flint,

1-6129

01660

36-9

0. 167

Ordinary Silicate Flint,

1-6169

01691

36-5

O. 3269

Heavy Baryta Flint, ....

1-6570

01809

36-3

O. 103

Ordinary Silicate Flint,

1-6202

01709

36'2

O. 93

Ordinary Silicate Flint,

1-6245

01743

35-8

0. 919

Ordinary Silicate Flint,

1-6315

01770

35-7

0. 335

Heavy Silicate Flint,

1-6372

01831

34-8

0. 102

Heavy Silicate Flint,

1-6489

01919

33'8

0. 192

Heavy Silicate Flint,

1-6734

02104

32-0

O: 41

Heavy Silicate Flint,

1-7174

02434

29-5

0. 113
0. 165

Heavy Silicate Flint,
Heavy Silicate Flint, ....

1-7371
T7541

02600
02743

28-4
27'5

0. 198

Very Heavy Silicate Flint,

1-7782

02941

26-5

S. 228

Heaviest Silicate Flint,

1-9044

04174

21-7

APPKNhlX.

393

Trade
No.

Partial Dispersions.

Ratios to A.

Density.

A' to D.

DloF.

Ftoff.

O. 318

00960

011-24

00952

609

711

t Ii 15

3-48

O. 118

o. it;:

01006
01026

01184
01206

01008
01029

606
606

718
711

607
608

3-58
3-60

O. :;

-010

1295

01106

604

71(1

611

3-95

0. ins

01'

.,._,._.,,

01041

605

714

609

3-63

01053

"1243

"1063

'-,.!}

7i:

609

3-68

0. '.U'.i

01063

"1-266

01085

600

71.-.

613

O. 335

01099

01308

011-24

600

714

614

O. 102

01158

01879

01180

600

714

615

3-87

O. 192

01255

01507

01302

597

717

619

4-10

O. 41

01439

01749

01521

69]

718

625

4-49

o. m

(1526

01870

(1632

087

71D

;_':

I HI

0. i;.-.

01607

01974

(1730

585

:_'.'

630

I7s

O. 198

'1719

"2120

01868

fifl I

721

635

4-99

S. 228

02394

02726

573

7--M

653

5-92

JENA GLASS.

%* Sections A to H of the Appendix (together with Art. 155,) have been
"U if prepared bi/ Dr. Hovestadt for this edition.

A. COLOURED GLASSES.

The persevering efforts which have been made at Jena to supply
the long-felt want of ray-filters suited for various applications in
science and art, are described in three communications.

I. " The absorption of light in coloured glasses." By R. Zsigmondy.

Ann. d. Phys. 4. 60 (1901).
II. "Coloured glasses for scientific and technical purposes." By

the same. Zeitschr. f. Instrumen., 21. 97 (1901).
III. "Jena light-filters." By C. Grebe. Zeitschr. f. Instrumen.,

21. (101) 1901.

In the first, Zsigmondy gives a very exact description of the
light-absorption in several coloured glasses of definite composition,
based on measurements made with a large spectro-photometer. The
following types of composition were included :

Na 2 O . 3Si0 2 , K 2 O . 3Si0 2 , Na 2 . CaO . 5SiO 2 ,

K 2 . CaO . 5Si0 2 , Na 2 . PbO . 5Si0 2 , K 2 O . PbO . 5Si0 2 ,
Na 2 . ZnO . 5Si0 2 , Na 2 B 4 O 7 , B 2 3 ,

and finally a lead silicate with 20 per cent. Si0 2 and 80 per cent.
PbO. Observations were also made on a soda borosilicate and a
baryta borosilicate.

The proportions of colouring matter employed were respectively
Chrome oxide 1 per cent., Copper oxide 2 per cent.,

Cobalt oxide O'l per cent., Nickel oxide 0*25 per cent,

Manganese oxide 1 per cent., Iron oxide 2 per cent.,

Uranium oxide 2 per cent.,
of the mass of uncoloured glass.

The glasses were melted down in oxidising flames ; then stirred,
in the liquid condition, to get rid of streaks; then poured into
moulds, and, after gradual cooling, cut into plates. The cut and
polished plates were examined with a Glan spectro-photometer.
The coefficients of extinction thus determined were used for the
construction of representative curves, for which we must refer to
the original memoir.

In his second communication, Zsigmondy describes the practical

APPKNl'IX.

395

results which have been attained at the Jena works. They are set
forth in the following list of coloured glasses.

The last column gives the thicknesses of the plates which were
examined; the examination being made with a Pulfrich comparison-
spectroscope. The original gives also a graphical representation of
each absorption spectrum, as seen in the instrument.

Tra.U-

Designation. Colour.

Spectral rays trans-
mitted.

mm.

27-Js

Copper ruby glass deep red

only red, to X=0-6/i.

1-7

4.->9 m

Gold ruby glass

red

red, yellow ; and in thin
layer, blue and violet.

Uranium glass

bright yellow

red, yellow, green to Et>\
and in thin layer, blue.

465

Uranium glass bright yellow.
strongly fluorescent

440MI

Nickel glass bright yellowish
brov 11

red, yellow, weakened
green, greatly weak-
ened blue.

414"'

Chrome glass

yellowish green

yellowish green, almost
like the Zettnow filter.

433'"

Chrome glass

greenish yellow

red to green, from X =
(MU to \='50fi.

431 1

n copper-glass

green

green, yellow, a little
red and blue.

Chrome glass

yellowish green

yellowish green, a little
red.

2-5

436 1 "

Copper-chrome glass

grass green

green.

4:<7"<

Green filter

dark green

green ; and in thin layer,

blue.

438" 1

Green filter

dark green

green.

; per glass

blue, like <

green, blue, violet.

B 1-J

447'"

Blue violet glass

blue, like cobalt
glass

blue, violet.

Cobalt glass

blue

blue, violet, extreme
red.

4 :.

450"'

\i kelglaw

dark violet

violet O-Jf, extunu'
red.

Violet glass

dark violet

violet O-H slightly
weaktMu-d; withdau-
i Humiliation, ex-
treme red.

444"

Smoke gray glass

gray

whole spectrum weak

rlir.l.

1--8

445111

Smoke gray glass

gray

whole spectrum weak

i n.. 1.

1 :?

396 JENA GLASS.

These glasses can be used for the solution of various colour
problems ; for example :

Bipartite division of the spectrum, or its division into two com-
plementary colours, can be effected in two ways : I. By 2728
(deep red) and 2742 (blue, like copper sulphate). II. By 454 111
(bright yellow) and 447 111 (blue, like cobalt glass). The pair II. can
be replaced by 433 111 (greenish yellow), and 424 m (blue).

For the complementary pair I., the proper thicknesses are about
J728, 1-6-1 -7 mm. ; 2742, 5mm.

For the complementary pair II.

454 m , 16mm.; 447 111 , 1 '5-2 mm.,
or I. 1 -". 111 , 2-5-3-5 mm. ; 424 m , 3mm.

Tripartite division of the spectrum into red, green, and blue
(with violet), can be effected in various ways; for example by

2728, 1-7 mm. ; 41 4 m , 10mm.; 447 m , 1-5 mm.,
or by 2728, 1-7 mm. ; 436 m , 2'6 mm. ; 447 m , 1*8 mm.

Further information on three-colour selection is given below.

A fourfold division can only be imperfectly carried out. Up to the
present, there is a want of a blue filter which will transmit the spectral
blue alone and with sufficient brightness. Possibly 450 m or 45i""
might serve for microphotography, and 447 In for botanical purposes.

There is no glass transmitting only spectral yellow, and no purple
glass absorbing only yellowish green.

Most of the Jena coloured glasses can be supplied to order ; but the
absorption bands vary somewhat in different meltings.

Grebe tested the sample glasses by means of a small spectrograph,
using Cadett plates, sometimes with and sometimes without compen-
sation. The following conclusions respecting glasses suitable for filters
are selected from the results thus obtained.

The three glasses

2745, red; 438 m , green; 447 111 , blue-violet

are specially suitable for the additive methods of three-colour pro-
jection. They correspond, with sufficient closeness, to Young's three
elementary colour-sensations.

The glasses of a second group,

Putzler 1 , reddish orange ; 438 111 , green ; 447 111 , blue-violet

+ complement + complement
are conspicuously fitted for the panchromatic process.

1 A glass easily obtainable, made by Putzler of Dantzig.

APPENDIX. 397

Their transmission curves closely resemble the curves of distribution
of the three elementary sensations in the spectrum.
Lastly, the three glasses

I:.':* 111 , bright blue ; 459 m , purple; 454"', yellow;

taken in order, are very nearly the complements of the three last
named. They represent the ideal colours for three-colour printing, and
for subtract ive synthesis. By means of these three glasses combined
subtractively, Grebe has obtained a nearly perfect reproduction of
the primatic spectrum (the " three-colour-glass spectrum ").

B. OPAL GLASS.

Some data respecting Jena opal glass [milchglas] have been published
by Schott and Herschkowitz. 1

The purpose of the usual external globes, whether of opal glass,
roughened glass, or etched glass, is to produce an advantageous
distribution of the light. The ideal of such a diffusely distributing
glass would be attained if absorption were quite abolished, and all the
light were scattered and transmitted in about equal proportions. The
absorption which actually occurs is due, in the case of opal glasses,
to the fact that the separated particles which scatter the light are
only imperfectly transparent. Theoretically, there is no difficulty
in iina^inin.u' this function to be discharged by perfectly transparent
particles. It would suffice that these particles had a different iiulr\
from tin- material iu which they were embedded. For some time past,
the Jena works have been producing an opal glass which comes much
nearer to this ideal than those hitherto obtainable. A thin section of
this new glass shows, under the microscope, a glassy bodyground
through which numerous closely lying separate transparent spheres
are scattered.

No information is given as to its composition and manufacture.
Photometric comparisons of it with ordinary opal glass have shown
that the absorption of light is reduced, in the most unfavourable cases,
to one half, and in most cases to one fourth, of its ordinary amount.

'"On the distribution of incandescent gaalight in space, and the effective
employment of opal glaas in illumination" Jour.f. GiubeUuchtung iwi Wa
vtrwrgung, 1901, Heft 28.

398 JENA GLASS.

In discussing the best form for a lamp shade, an ordinary incan-
descent gaslight cannot be treated as a point source. If it is centrally
placed within a large globe, the different zones of the globe will receive
unequal illuminations. Schott and Herschkowitz have determined
photometrically the distribution of the light for successive zones, each
of 10, commencing from the equator; and their paper (which is
fully illustrated) shows how this knowledge may be applied (with
the help of the new opal glass) to render the distribution as effective
as possible. The autosit shades made by Schott and Co. are intended
for this purpose.

C. DURAX GLASS FOR GAUGE TUBES.

(Seep. 227.)

A new glass for water-gauge tubes for steam boilers has recently been
made at the Jena Works, and commercially introduced under the
designation Durax Glass. As regards its composition, no information
is given beyond the fact that it is a borosilicate. Recent advances in
the production of iron and steel of high and uniform tenacity have led
to the use of much higher pressures of steam, with a corresponding
gain in efficiency ; and the requirements for strength in gauge-tubes
have accordingly become more severe. An experimental investigation
conducted by 0. Schott and M. Herschkowitsch J has furnished definite
information as to the relative merits of the various kinds of gauge-tube
glass at present in use, as compared with one another, and more
especially as compared with Durax glass. The tubes tested included
French, English or Scotch, Jena compound, melting, combustion, and
Durax tubes. The external diameters were 18-20 mm., and the
thicknesses 2-3'5 mm. The following were the main results.

All kinds, when cold, were able to withstand very high internal
pressure (170 to 333 atmospheres).

The use of hot water and steam, without external chilling, diminished
the resisting power of all tubes by from 35 to 40 atmospheres. The
comparisons up to this point showed no superiority of one glass to
another in any respect.

1 " On water-gauge tubes and their protecting glasses," Zeitschr. d. Vereins
deutscher Ingenieure, 45 (1901). The methods employed could scarcely be made
intelligible without the illustrations which the paper contains.

APPENDIX. 399

Great differences, however, appeared when the tubes, under the
internal pressure of hot water and steam (as in actual use) were
exposed externally for one second to a continuous stream of cold
water drops. For example, in one series of experiments, the following
were the pressures at which the tubes gave way :

French. English. Compound. Combustion. Dnrax.

6 7 15 -J 1 _7 atmospheres.

The Durax tubes here show a distinct superiority to any of the others.
And it is a well-known fact that in practice many breakages occur
from accidental external cooling by drafts of cold air, sprinkling of
water, rain-drops, or snow-flakes.

The corroding action of water and steam, at high temperatures, on
the surface of glass, was much less noticeable in Durax than in the
other glasses, provided that the water did not contain an excessive amount
of free alkali.

D. DEPRESSION OF ZERO OF THERMOMETER BY
HEATING,

(See p. L>.V>.)

\\ . Schloesser, 1 in comparing thermometers belonging to the
" Standards Commission " with thermometers of verre dur whose
errors had been determined at the Bureau International, observed the
depressions produced by heating to temperatures between 10 and
90 for eight thermometers of 16 IH , and ten of verre dur. His
results, when reduced to the form

EO - E t = pt + q? (see p. 255),

give the following values of the two constants p, q, and of the

" depression-constant " D :

\&p 10? D

Normal-Glass 1C 1 " 5-2 0-655 0-071

Verre dur 55-35 0-6875 0-124

Comparing these with the values given at pp ~>6, one is

k with the smallness of p and the largeness of q, which (especially

in the case of 16 m ) deprive the depression-curve of all likeness to a

;-ht line. The working out of the formula between and

100*, with the values assigned by the three different observers, is

ittchr.f. /firfrum.,21. 281 (1<>

400

JENA GLASS.

exhibited in the following table. The discrepancies are not yet
explained.

Normal-glass 16 in .

Verre i/nr.

Temp.

her.

Thiesen.

Schloesser.

( Juillaume.

Thieson.

Schloesser.

-S7

105

100

110

124

E. REDUCTION OF MERCURY THERMOMETERS OF 16 m

AND 59 m TO THE HYDROGEN SCALE.

(See p. 299.)

The introduction of the hydrogen scale into practical thermometry,
has given great importance to the reduction tables of Art. 123. Every
step towards their completion, and every contribution throwing light
on the degree of their exactness, is therefore of interest.

Thermometers of Normal-Glass 16 m . W. Schloesser conducted an
investigation 1 (see D) having for its object to compare a large
number of thermometers belonging to the Standards-Commission,
made of different German glasses, with the hydrogen scale, by
intermediate comparisons with thermometers of verre dur. We will
first give the results obtained for 10 thermometers of 16 111 .

This was the first comparison ever made between thermometers
of these two glasses at 1 temperatures below freezing; and a special
apparatus was employed, of which the author gives a description with
illustrations. The observations extended from 20 to + 90, and
the formula deduced from them was

t r - t lG = 10-9 x 172 ( 100 _t u)tu _ 10-10x606 (100 -* ltf ) 2 * 16 ,
the symbols having the same meanings as in Art. 123 (p. 298).
\Zeit*chr.f. Iwtrum., 21. 281 (1901).

APPENDIX.

401

The values computed by this formula are given under the heading
Iculated " in the third column of the following table, the corre-
sponding observed values being given in the second column. The
fourth column gives, for comparison, the results obtained by Thiesen,
el and Sell (see p. 278); and the differences (Thiesen - Schloesser)
are shown in column ."..

\ AI.IKS oF* r -* 1(J ; UNIT 0-0001.

Temp.

Schloesser.

Thiesen.

Diff.

Obs.

Calc.

-25

+ 265

+ 251

-20

+ 197

+ 185

i:>

- I:,:*

+ 127

-10

+ 110

+ 77

- 5

+ 45

+ 35

+ 10

+ 20

- 50

- 81

+ 30

- 96

- 93

-109

-16

+ 40

- 68

- 90

l-.M

-34

+ 50

- 73

- 78

-129

:.l

+ 60

- 89 - 59

-124

-65

+ 70

- 26 38

-109

-71

+ 80

- 28

- 18

- 83

-65

+ 90

-43

The elal>orate attempts which were made to explain this discrepancy
I'M t<> no dc-finitc result: and the agreement was not improved by

ing out of account Schloesser's observations below 0. A
partial explanation is furnished by the differences which notoriously

t between individual instruments of the same kind of -las>.

milarities arising from this source can only bo eliminated Ky tin-
use of large numbers of thermometers of both kinds; and it is to
be noted that Schloesser used ten thermometers of "normal glass,"
and eight of verre dur ; whereas the other observers used only thnv
of each kind.

By adopting Chappuis' reductions of Tonnelot thermometers to the
hydrogen seal'-. S.-hloe->er finally oUained the results given in the
third enlumn of the following tal.le, which also contains Thie><

lor comparison. (t a denotes temperature by Hydrogen
scale).

402

JENA GLASS.
VALUKS OK V,-/,,; UNIT 0-001.

Temp.

Thiesen.

Schloesser.

DiflF.

:>(j

113

112

-1

1-20

116

-4

116

110

-6

103

-7

-6

In Art. 123 it was necessary to employ extrapolation for reducing
/ 16 to the hydrogen scale at temperatures below freezing. It is of
interest to compare these provisional determinations (p. 300) with the
determinations which can now be derived from direct comparisons
of t l6 with t T at these temperatures.

VALUES OF t a -t lK .

Schloesser.

Extrapolation.

-25 J

0'258

0'25

-20

191

-15

132

-10

081

- 5

037

The difference in no case exceeds 0-01.

Thermometers of the borosilicate 59 IH . No direct comparisons of
thermometers of this glass are available, but indirect comparisons
with the hydrogen scale can be made in the following way.

Griitzmacher l has calculated for each degree from to 300 by
Wiebe and Bottcher's reduction formula (p. 281) the difference
between the air thermometer and the "normal-glass" thermometer.
These differences we shall now denote by t L - t w . By adding these to
the values of t 16 -- t H calculated by Scheel (see p. 298), he obtains the

1 Zeitschr. f. Glasinstrum.- Industrie, 5. 108 (1896).
reproduced by Griitzmacher in Ann. d. Phys. u. Chem.,

The reductions are
68. 769 (1899).

APPENDIX.

403

values l of t L - t a . By adding these to Griitzmacher's determinations
of t& - IL (see table, p. 287), values of t n - t a are obtained, which may
be used to check Scheel's values given on p. 300. We content
-fives with giving the results for every tenth degree.

r.\iT o-ooi.

Temp.

ti - 'is

fc-fc

ft. - t u

<b-x

t n -t*

Schecl.

Diff.

- 83

93 in

i".-; 113

in 29 39 38

40 -110 120

60 -107 i 116 ! 21 30 26

60 - 96 ' 7 14

70 - 78 83

6 11 83

80 - 54 58 4 161 4

90 - 28

30 -2 '2 o -2 2

11). ditlerences have all the same sign, but their maximum amount
U only 0-005.

Other reductions to the hydrogen xro/. Twelve old thermometer glasses,
including seven Jena glasses, were compared with the hydrogen
thrnnometer by Griitzmacher- at the Reichsanstalt. The 12 thermo-
meters were compared with four chief standards of 16"', which had
;idy been compared with the air thermometer, and could thus, by
(irut/ni .. -In T'S values of //.-///, be compared with the hydrogen
thermometer. Inductions to the hydrogen thermometer were thus
computed for the 12 old glasses. Most of these glasses hav<-
superseded, or have never been in practical use.

Srhlot'sser, in tin- investigation quoted above, also gives comparisons
of several old (Jena and other) thermometer glasses with the hydrogen
scale, derived from direct comparisons by himself \\ith Tonnelot
thermometers.

'The values from o to UK)' are given for each degree to furnish the means of
reducing to the hydrogen thermometer the various reductions to the air thermo-
meter published by the Reichsanstalt down to Oct 1896. B date the
Msanstalt has reduced temperatures between and 1<> to tli* hv<lrogen
1 1 IOmeter.
* Di**ertation, Berlin, 1900.

404 JENA GLASS.

F. INFLUENCE OF TEMPERATURE ON THERMAL
CONDUCTIVITY.

The Influence of Temperature on the Conductivity of Glass has beer*
specially examined by J. Kriiger, 1 mainly with the view of testing
the correctness of AVinkelmann's conjecture (see p. 212) as to the
cause of the differences between Paalhorn's and Focke's Results. Kriiger
used the identical apparatus which had been employed by Paalhorn ;
an apparatus containing (as described in Art. 92) a conducting column
composed of three copper and two glass plates; but the two glass
plates were now of the same glass at different temperatures. In the
course of his research, he introduced a modification consisting in
alternate reversals of the direction of the flow of heat through the
conducting column, observations with the flow in opposite directions
being combined in pairs ; and his final results were deduced from
observations so combined.

The reductions were directed to finding the value of the temperature-
coefficient a defined by

and the values found for a were so small that little could be done
beyond determining their signs. No attempt was therefore made
to examine the influence of chemical composition ; and the experi-
ments were limited to three glasses, 0. 137, S. 226, and 0. 709. The
first is identical with No. 83 of AVinkelmann's list (p. 145), the second
is nearly identical with No. 69, and the third with No. 25. The
values found for a were

0. 137 S. 226 O. 709

10 5 a= -(31 15), -(341), -(45 + 13).

The conductivity accordingly (as in the case of most solid bodies)
diminishes slightly as the temperature increases ; the difference per
degree amounting to only about -.03 or '05 per .cent. These coefficients
do not correspond either in magnitude or in sign with the view that
the difference between Paalhorn's and Focke's results is to be
explained by them.

After discussing the circumstances, Kriiger comes to the conclusion
that the differences in question are probably due to small differences
in the chemical composition of nominally identical glasses.

1 Inaugural Dissertation, Jena, 1901.

APPENDIX 405

G. DECOMPOSITION BY AIR AND DUST.

(See Chap. X.)

I \ations on the decomposition of different glasses when exposed to

>een published by E. Zschimmer. 1 They were

made upon about 200 pieces of glass with polished plane surfaces,

which, with the view of testing the dnniliilifi/, in on/iiion/ conditions,

of glasses destined for optical use, had been stored in .lena for several

years in a dry place, and enclosed in a way which only imperfectly

uled air.

A close connection was found (as might have been expected) between
the chemical composition of the glasses and their susceptibility to
decomposition under the influence of air and dust, the following being
the most important conclusions.

The behaviour of Silicates without lead depends almost entirely on
i content of alkali. Even with as little as 10 per cent, they
xhibit, under the microscope, the so-called dusty disintegration ;
that is to say, the minute particles of dust which fall on the surface
become centres of decomposition, the character of the decomposition
being different according to the composition of the glass.

When the proportion of alkali is increased beyond 10 per cent.,
tin- transition is soon made to homogeneous decomposition, which attacks
hole surface uniformly.

With L'<> per cent, of alkali, the deposit on the surface is visible
U> th<- naked c\ : and larger proportions give rise to coarser phe-
nomena the formation of drops, and the crystallisation of carbonates.
Deliquescent carbonate of potash covers the surface with more or less
minute drops; whereas carbonate of soda, being only slightly hygro-
scopic, covers it with assemblages of crystals. Whether lime, and
/.MM- oxide, have a material influence on these phenomena, is not
definitely known. Ilaryta, when present in considerable quantitv,
promotes the dusty disintegration.

I silicate glasses showed dusty decomposition in tin form of what
are known as lead-spots. They were not seen till the lead oxide amounted
to _" per ..-lit. : and with increasing percentages they became more
and more prominent. Lead-spots are a phenomenon well known to
opticians in the case of Hint glasses. The spots were l>ro\\n. or lluc-
black, and showed (under the microscope), in the centre ,,f each, the

406 JENA GLASS.

exriting particle of dust, surrounded by scaly leaf-like products of
decomposition, forming a black or brown mass. A similar appearance
can be produced, in glasses rich in lead, by immersing them in a
concentrated solution of grape sugar. After the lapse of a few days,
thev develop spots with a bluish-brown shimmer, which remain after
washing and gentle wiping. Presumably it is a case of the formation
of lead mirrors by reduction. In lead silicates containing alkali, the
separation of alkali at the surface is promoted by the presence of the
lead, if in sufficient amount.

The borate glasses without lead behave in a manner easily understood,
Pure boric acid, after fusion, and most of its salts, absorb from the air
considerable quantities of water, while continuing to exhibit a dry
surface. Glass rich in boric acid behaves in the same way ; it swells,
while remaining dry ; and no change in the surface is noticeable till
the quantity of moisture absorbed becomes excessive ; when the surface 1
begins to split. The bursting of the surface can be produced at an
earlier stage by heating the glass. In the case of a glass with 60
per cent, of B 2 3 , this action was so strong that the whole surface
broke up into splinters when heated. Another glass, with 50 per cent.
B.,0 3 , began to show microscopic cracks when heated to 150. A
borosilicate with 22 per cent, showed no change in its surface even
after heating. Percentages of from 30 to 40 of B. 2 3 may be regarded-
as consistent with durability.

Lead borates exhibit decomposition of the surface as soon as the
amount of lead oxide reaches 20 per cent. ; the effect showing itself 1 > v
iridescence, the colours changing with the angle of incidence of the
light. Heating deepens the colouring, but there is no flaking off; ancl
polishing the surface increases the brilliancy of the display of colour.
The glass must therefore be affected to a considerable depth.

The pJwsphate glasses are all hygroscopic ; and their changes of
surface resemble those of the alkali silicates ; but are easily distin-
guished from these, under the microscope, by the characteristic
property of the separation of crystals.

H. OPTICAL EFFECTS OF STRESS.

The change of optical properties pi'oduced by elastic deformation has
been investigated for various glasses by F. Pockels. 1 His investiga-

l Ann. d. Phys., Ser. 4, Vol. 7, 745 (1902).

APPENDIX

tions were directed to the determination of the two coefficients p, <j
in the equations

employed by F. Neumann for expressing the influence of elastic
deformation on the propagation of light in isotropic substances ;

, . denoting the three principal dilatations;

o> the velocity of propagation in the absence of stress ;
w * % w t tne three principal velocities of propagation in the stressed
substance. 1

The axes of ', //. . are so chosen as to coincide with the directions
of the three principal dilatations. They will be the principal
of the wave-surface.

Taking E (as in Chap. VII.) to denote Young's modulus, and p.
Poisson's ratio, a thrust Z t in the direction of z will produce the
three principal dilatations, z t = -ZJE, x x = y y = pZJE ; and ;> and q
can be deduced from measurements of o>. - u> and w, - o>, or one of
these quantities and the difference of the two. Their values will be
different for different wave-lengths.

Rectangular plates, about 20 mm. long, 7 mm. wide, and "> nun
thick, of the glasses to be tested, were ground at Zeiss' works, in
pairs or in sets of four. The 20 x 7 faces were ground accurately
plane and parallel, and finely polished. In each experiment, one of
these plates, with its greatest dimension vertical, was subjected to
vertical pressure applied by a steel lever.

Observations were first made with a Jamin's interfemitial refractor,
to determine the absolute retardation, introduced by the compression,
in the wave polarised perpendicular to the direction of pressim- :
and then, second 1\, with a Babinet's compensator, to determine the
iv. retardation of the two waves propagated perpendicular to
the polished faces. These determinations furnish the means of
calculating />/u> and ///.

11 glasses were tested, and particulars respecting them are
i in the following table. The first column contains their trade
numbers; the M-roml column, headed Jf, their numbers in Wirikel-
iV list (pp. 1 r-l 17) ; s is specific gravity /. Young's modulus;

'(PockeU call* them "the velocities of the waves polarised perpendicul..
the x, y, and : axes."

408

JENA GLASS.

/x Poisson's ratio; 3<x the cubic coefficient of expansion; n the index
<>f refraction for sodium light.

The values of E and ^ for the glass 0. 42S were not directly

vctl. but computed from chemical composition.
Glass 0.21.54 is nearly identical in composition with Winkelmann's
md 0.500 with 50.

Trade

X...

ir.

/-;.

/JL.

3a . 10 7 .

S. 205

2 = 22

2-243

4800

0-274

202

1-5075

0. 428

-2 -4,-);

4720

0-268

1-5123

O. 658

2-758

5470

0-250

157

1 -5452

0. 2154

3-115

6100

0-222

1 -5700

0. 1571

3-88

5470

0-224

1 -6440

O. 500

4-731

5500

0-239

241

1-7510

S. 57

6-335

5035

0-261

280

1 )()_'.->

The results of the investigation (for sodium light) are given in
the following table ; in which v denotes na> the velocity in vacuo.

S.205.

O. 428.

0. 658.

0.2154.

0. 1571.

0.600.

S. 57.

274

0908

289

306

335

364

427

166

0228

182

213

264

319

466

182

060

187

195

204

202

218

110

015

118

135

160

182

237

Ky means of the equations

<,-<* _n-n x _q

the values of p/u and g/w serve to determine the changes of the
index of refraction.

The glasses are arranged in ascending order of s and of n. If
we leave out of account O. 428, for which the values of E and /A
were only determined by a doubtful calculation, all the four

quantities , ^, ^, ^, increase with s and n from each column to

w u> v v

APPENDIX
the next, the increase being more rapid for -2 and ^ than for 2- and J> :

(O V Ul V '

lut along with this increase there is a diminution of the difference
between ? and ?., and, therefore, of the difference between p and q.

(0 (II

- greater than y in all light glasses, and also in the heavy
Hint 0.500; the double refraction in these is accordingly negative.
In the heaviest Hint S. 57, q is greater than p ; that is, thrust in
this glass produces positive double refraction. This is a result never
before observed in an amorphous substance.

A < ). .~>00 and S. :7 are both of them lead silicates, Pockels
interred that there must be some intermediate lead silicate for which
p and q are equal, so that it would remain singly refracting un< lei-
thrust in any one direction, and therefore under any distortion
whatever within its elastic limits.

In endeavouring to determine by graphical interpolation the
|K)sition which would give this result, the four glasses S.
'K), O. 1571, O. _'!.") 4 were taken into account, and the composi-
tion indicated \va>

- Si().,, 7.V7 PbO, K K,0.
An experimental melting of about this composition was made at the

Works, and, when tested with sodium light, was found to
positive double refraction having only j\ the magnitude of that
given by S. 57. Pockels concludes that a diminution of 0*6 in the
PbO would make the double refraction vanish.

I '.'-ides sodium light, the glasses were also tried with lithium

lii^ht and thallium light. Observations were fewer than with sodium

li^ht, and therefore the same degree of precision cannot be claimed

for the results. They served, however, to show that the rluomatir

rsion <f the double refraction is mostly very small, and may

have either i^n It is only considerable in the heaviest Hint glasses.

The t' index pro<ln>il In/ compr&tio* or itihit"fiim uniform

can be calculated from the values found for p/u and / <>.
< ailing the cubic dilatation 6, wo have

ibo

whence

,- (o /2j> Y\ </<> ///

** I I I i ** ^3 m -' - I

(0 \W W/J (tf u

410 JENA GLASS.

Wo thus find for the seven glasses

s. 2n:> a 488 0.668 0.2154 O. ir.Tl O..VK) S. 57

/." = -ini; -392 -isr, :>!_> -wiO -865

If \ve assume any one of the three formulae on p. 61 (for the
"constant of refraction") as remaining constant during uniform

compression, the assumption will give s j- as a function of n. Pockels

tested all three formulae in this way, and found that the second (which
makes //- - 1 proportional to the density) gave fair results for some of
the glasses, but bad results for others. The first and third formulae
(especially the third) gave much worse results. In connection with
this question, it is to be noted, as an obvious inference from the above

values of s-r- for the seven glasses, that the change of index with
uniform compression, whether measured by s-r or by ' , increases

rapidly with the original density and index.

By the pure temperature coefficient of index is meant the whole value

of -T. minus the part due to mere change of density. Using the

symbol 3 for partial and d for total differentiation, we have-.
accordingly,

*dn _ dn 'dn ds _dn 15n

'dt == dt~dsdt = ~dt + LS 3s

as the formula for computing the "pure temperature coefficient" 'dnfit.
Pulfrich's observations (partly given at p. 59) led to the values :
S. 205 0. 658 0. 500 S'57

10 5 ^=--07! +'299 + -775 +145
at

10'?" =+-65 +-914 +2-22 + :W

The pure temperature coefficient of index in these glasses, ^., is thus

always positive, and increases very rapidly with the content of lead ;
this increase being probably due to the increase of absorption in the
ultra-violet with increasing temperature (p. 62). As a further test of

the correctness of this explanation, Pockels calculated ~ . for lithium

fjf*1

light and thallium light, using Pulfrich's values of -jj (with the aid of
interpolation) and his own values of $ .

APPENDIX. 411

The following are the results :

ITI

0.658

O.500

-O64

261

685

1-16

u.V,

i-::;

374

411

602

879

339

37C

596

906

2-13

3-62

920

L>-:;I

4-05

-06

014

*43

They bear out the explanation, except in the case of the borate crown
'5, which shows a diminution of the temperature coefficient with
decrease of wave length. This is opposite to what we should expect
from increase of ultra-violet absorption, and suggests rather a displace-
ment of the ultra-red absorption bands in the case of this glass.

41-2 .IKNA <JLASS.

NOTES BY THE SENIOR TRANSLATOR.

)\ THK NAME TO BE GIVEN TO THE QUALITY REPRESENTED
BY ABBE'S SYMBOL v. (See page 24.)

The quality in question is a tendency to hold together the rays of
difl'erent colours, so as to make dispersion small; and I propose that it
be denoted by the name constringence, which literally signifies binifiu;/
t'Hit-tln-i: The adjective constringent already exists, and is given in all
dictionaries.

(J,) ON THE EFFECT OF EMPLOYING SOFT PRESSURE-PLATES
IN EXPERIMENTS ON CRUSHING. (See page 152.)

The cracks observed when soft metal is employed are due to the
tearing of the surface by frictional pull, applied by the soft metal as
it spreads. This action is familiar to modern experimenters on
crushing.

Having learned that the oxide of arsenic used in glass-making is
always the common white arsenic (arsenious acid, As 2 O 3 ), whereas the
higher oxide (arsenic acid, As 2 ) is invariably mentioned in this
work, I wrote to Dr. Hovestadt on the subject. The following is
a translation of his reply :

"I cannot accept your proposal to print As 2 O 3 instead of As 2 5 .
It is true that the substance put into the mixture is As 2 3 ; but in all
the Jena glasses oxidising materials (nitrates) are added a statement
which Dr. Schott has to-day expressly confirmed. These convert the
lower oxide into the higher during the melting ; and in the glass as
finally obtained the As 2 5 is combined with alkali. Dr. Schott adds
that, in many commercial glasses, such as plate and sheet glasses,
As 2 O 3 is employed without the addition of oxidising materials, so that
no As 2 O 5 can be formed; but he adds that, in his opinion, no arsenic
then remains in the glass ; it is driven off in vapour and exercises no
influence."

On the other hand, Mr. Walter Rosenhain, of Chance's Glass Works,
after considering the above view, writes :

" I have very good ground for believing that, so far as arsenic enters
into the composition of glass at all, it is likely to do so as arsenious

AITKNIHX. 41*

acid. The nature of the acids themselves is such as to lead to this

belief. Arsenic acid is easily reduced by heat alone, and, though

inly less volatile than As^g, it is still volatile. Further, it is a

lo acid, and at high temperatures, in the presence of such acids as

boric or silicic, it would hardly be capable of remaining in combination

with alkalies. I believe that arsenic acid or its compounds, when they

are present in glass at all, either form insoluble impurities or cause it t<>

become opaleseent.

.1. D. K.

INDEX.

The references are to the pages.

Abbe's appeal, 2-4, 88.

improvements of microscope, 86-92.

specification of indices, 23-24.

spectrometer, 23.
Abbe to Schott, 12-14.
Aberration-constant of objective, 84.
Absolute hardness, 173.
Absorption, 42-57.

bands and dispersion, 42-46.

coefficient of, 47, 50-51.

influences dispersion, 42, 53-57.

influenced by temperature, 62.
Achromatising, 32-36.
Achromatism in telescopes, 126-131.

- Vogel's test for, 129.
Acids, action of on glass, 362-366.
Afterworking, 239-275.

coefficients relating to, 256.

elastic, 304-311.

elastic and thermal compared, 310.

in terms of time elapsed, 308.

theory of, 311-316.

thermo-elastic, 162, 316.
Ageing a thermometer, 239, 249.

Air thermometer, difference from, 249,

280-288.
Alkali, action of on glass, 360.

colour test for, 336.

expressed as soda, 336.
Alkali-free glasses, 368-369, 373.
Alkalinity of water tested, 370.
Allihn on rise of zero, 261, 264.
Amplification by ocular, 84.
Anastigmatic aplanat, 98.

flattening, 97.

Anastigmats, unsym metrical, 102.
Annealing, 15.

Anomalous doublets, 99.
Antiplanetic, 103.
Aperture, numerical, 82.
Apochromatic objectives, 85-90.

triplet, 100.
Arsenic in glass, 412.

Artificial ageing. 239, 249.
Astigmatism of image, 96.

in astronomical objectives, 124.
Auerbach on hardness, 168-185.

Bamberg, 15, 16, 129, 138, 141.
Baryta borosilicate 122 111 , 247, 267,

286, 287.
Baryta crown, 101.

bearing high temperature, 161.

Baryta light flints, 100.

Batch, 17.

Baudiii and boiling sulphur, 269.

Beakers for rapid heating, 235.

Bending torque, uniform, 187.

Binoculars with prisms, 117.

Boiling-point thermometers, 257-260.

Borate flint, 98.

Borate and phosphate glasses, 132,

387.

Borates, behaviour to water, 406.
Boric acid lengthens red end, 9.
Borosilicate 59 m , 21, 74, 221, 246, 254-

257, 260.

resistance to decomposition, 345,

and air thermometer, 250, 287, 2ss,

297.

and hydrogen thermometer, 402.
Bottcher, depression formulae, 250-

256.

Bottles tested, 338, 341, 352.
Bottles, long tests of, 355-357.
Brass, expansion of, 166.
Bravais on ray-curvature, OS.
Brittleness, 179-181.
Bubbles in glass-making, 17-19.

Capillarity, Volkmann on, 320, 371.
Carbonate of soda, attack by, 366.
Carbonic acid, atmospheric, 348.
Catalogue, 26-31.

revised, 387-393.

preface to, 5.

INDEX.

415

nted doublets, li'J 1_M
i.uis, reduction to nitrogen ther-
inom

to hydrogen scale, 298.

ical behaviour of glass, 31'.'
compared with composite
( 'himneys for mantle burners, -
Choisy le Roi glass, iM :;.
Christiansen, conducting column, 199.
Chromatic aberration in long tele-
scopes, 126- 1 -Jv

difference of magnification, 86.

spherical aberration.

Collimators of spectroscope*, 141.
i'ollinear, Voigt lander's, H>.~>.
Colour problems, 396.

Colour tests for alkali.

< ommercial glasses compared, 332.
Compensated afterworkiu^
Compensating eyepiece, 80, '"1.
Compensation vessels, J_M
.i>ound anastigmats, 104.

ound glass, _'_' l 228,
Compressibility. !<_>.

vity produced by warmiiiL
Concentric lens, 1"1.
Conducting column, 200.

v. thermal, 199-215, 404.

and comjKjbitioii, '2\~2.

an 512.

(electrical) of solution, 34"
Constant of refraction, 61.
Constringence = i', 4IJ.
Convention for signs of radii, 100.
Cooke triple objective.

o.l i'i.r I 'nis son's ratio, 186.
;s, fundamental interval. 'J74.
Creeping up of zero at high tempera

.. 17.

.. H-J.
Culler

ray, 68.

ed rays in stremed glass, 67.
Czapski, :; 129.

ry of telescopes, 117.

objective ((Jaussian), 1

mix i:>i.

Decomposit and dust, 405.

Degree ch ft

Density and compost tin, i 17

I |ression of /

l.ition to compo>
Depression -ronsUnt defined, 239.

compared wiU> other qualitk

Depression in terms of temperature,
25<' 100.

- formula* .

Depressibility changed by heating, 271.

dependence on other qualities, 314-

Dick-ctric constants, 376 -::-
Dilatometer, theory of, 290.
Dippel, microscopic tests, 91.
1 >i>< and rings in star image, 134.
Dispersion, notation for, 24.

and absorption connected. 4-J.
iufluencea by temperatur*

1 M-persion-curve for 1/X 2 , 4".
Distilling water in vacuo, I
Distortion of image, 98.
Diverging lens-combinations, 1 1 _'.
Diversity of Jena glasses, -J-
Double refraction in stressed glass,

70-7(5. 406,

Double-star resolution
Du Bois, Verdet's constant
Durability (see tndnrance, hardness).
Durax glass, 398.
Dusty decomposition, 405.

Kinsrhlu.-s tht-nnometer, 'Jd.').
Elaidinic acid for isotherms
Elastic after work ing, 304.

compared with thermal.
Elasticity, 1 .".'.
"Elasticity-number," 186
Elastic constants compared.
Electric conductivity -f soluti'

dispersion and absorpti< i
Elliptic polarization. 7
F.ndui-.ui.r. tlu-rma!.

of sudden coolinj:.

of sudden heating,

- against chemical attack

406.

English thermometer glass.
Everett, 68, Isr,.
Exner, lens-like
BxMndbility,

influciu-ed by stress, *JI7.

at various temperature*.

Expan . principal,"

of liquid .nid envelope, 289-1?"

it properties' of a zinc borate

Kye and ocular not a. \:\\.

Eye-pieces of high power, '.'1.

i glossen, li

Finder eyepiece, 84.

K.I..- ..i.i.V.-ilu.L:. I- 17. -'". M,

416

JENA GLASS.

Fining, 17.

Flasks tested, 3r

Flexure with uniform torque, I

Flexure and utu-nvorking. ."<M.

for Young's modulus, 155.
Fluor for objectives, 88-90.

plasticity of, 17".
Fluorine, 10.
Focal tlrpth, !>7.

Focke, conductivity, 2U7-212, 404.
Foerster, penetration by water, 327.
Foppl, indentation of metals, 180.
Formula, traditional, 34-2, :U7.
Fracture modulus, 17->.
Fraunhofer, 1, 4, 10.

telescope, 130.

Fritsch, wide-angled apochromat, 1(K).
Fundamental interval, 274.

Gauge-tubes, 227, 345, 398.
Gaussian objectives, 137-142.
Gelatine, cleaning surface by, 79.
Gerateglas, 235, 367-371.
Glasses, list of, 26-31, 387-393.
Glassmaking process, 15-18.

requirements, 8, 14.
Goertz double anastigmat, 105.
Goldstamp and greenstamp cylinders,

236.

Greiner, resistenzglas, 246.

Griitzniacher, thermometer compari-
sons, 284-289.

Guillaume, depression formula, 253.

Guiuand, 1.

Gundelaeh, X-ray tubes, 376.

H- hardness, 175.
Hand telescopes, 115.
Harcourt, 2, 10.
Hardness, 168-185.

absolute (Auerbach's), 175.

and composition, 178.

and other properties, 183, 192.
Hartglas, 226.

Harting, cemented doublets, 123-124.

curvature and astigmatism, 125.
Hartnack, anastigmat, 100.
Heidelberg telescope, 133.

Hertz on hardness, 169, 174, 184.

High temperatures, maintaining, 284.

Higli temperature, rise of zero at, 261-
270.

High temperature thermometer with
nitrogen, 265-269.

Hopkinson's titanium glass, 11.

Hot- water tests of glass, 329, 338-341,
345-348.

Hydrochloric vapour, test by, 322.

Hydrogen scale and mercury ther-
mometer, 298-300, 400-403.

Hygroscopic gain of weight, 357.

Hyper- and hypo-chromatic, 37
Hyperchromatic diverging lens, 109.
Hypsometers, depression in, 257-260.

Illumination, telescopic objectives,.
118-122,

Immersion objectives, 90, !>i2.
Incandescent mantles, 236.
Indentation-modulus, 172.
Index and density, 61.

dispersion, 23-24.

Index and temperature, 57-<i<>.

fine-cooling, 66.
Infra-red dispersion, 39-46.

absorption, 52.
Insulating power, 372.
lod-eosin test, 323.

and ether test, 335.
Isothermals, 204-210.

Jena glassworks, 1-22.
Junghans, rotatory power, 384.

k is 10 10 for mercury, 351.
Kaempfer, collinear, 105.
Kavalier's glass, 324, 333, 341. 345,

370.

Kelvin's equation, 228.
Kohlrausch, conductivity of solution,

349-359.

analysis of solution, 334.

on afterworking, 308.
Konig, telescope objectives, 143.
Korista, semi-apochromatic, 94.
Kowalski, v., strength of glass, 154-

155, 189.
Kriiger, temperature coefficients of

conductivity, 404.
Kriiss, 138.

Laboratory glass, 235, 367-371.
Lamp chimneys, 236.

globes and shades, 397.
Large objectives, 16, 121.
Lead-glasses, and acids, 364.
Leitz pantachromatics, 94.
Lead spots, 405.

Lemke, 59 m and air thermometer, 288.
Length of degree changing, 274.
Lens-like action of quick-cooled discs,

67.

Levels corroded, 320.
Light baryta flints, 100.
Light-gathering power, 118-122.
Lime diminishes solubility, 330.
Lime-glass and acids, 362.
Limit of linear compression, 85.
Limiting pressure, 173.
Liquid and envelope expanding, 289,
Liquids for high temperatures, 284.

INDEX.

417

List and supplements, 18-19, 26-31,

387-393.

Lithium glass, 11-14.
Long telescopes and chromatic foci,

126-128.

Lowe, dielectric dispersion, 381.
Lunnner, 99, 1"7.

objective, Uo-H'J.

/i = Poisson's ratio, 185.
Magnetic field test plates, 384.
Magnification by objective, 84.
Mahlke, dilatometers, 292-298.
Marchis, thermometer with platinum

bulk

Martinsroda sand, _'!.
Materials, 8-10.

Mechanical properties, 145-193.
Mi-ltim: p.
Mercurial and hydrogen thermometers,

298-300, 400-403.
Mercury, expansion of, 292.
Metals, hardness of, 180.
Meyer's apochromatk. 'M
Mica chimneys and glass, -
Microphotography, 87.
Microscope, 82-94.
- Abbe on, 8.
MU t he's anastigmat, 99.
Milky glass, 397.
Milliiiormal solutions, 335.
Mixed alkali glasses, 243, 309, 310.
Modulus (Young's), 155.
M.-lis" scale of hardness, 182.

romonaphthalin immersion, '._'.
Moulding, 18.
Miiller, observations on absorption, 46.

and Foenter.

v = constringence, 4 1 J

New and old achromatics, 99.

Nitrogen in mercury thermometers,

Normal and anomalous doublets, 99.
'Normal thermometer glass" 16 ni ,iil,
_>_' I

at 640 .

Numerical apei

nl.l thermometer gUMea,
Opal glass, 397.

il properties, i>3 -M.
Orthostigmaticu.
Overflow thermometers, 290.

. ated water, tests with, 345-343,

Paalhorn, conductivity, 1"

Pantachromatic, 94.

Pauly telescope, I ', 133, 143

Penetration of water into glass, 324,

4Mi.

Perfecting optical systems, 82-144.
Permanence of raised zero, 268.
Permittivity, 37<i
Pernet, depression formula, 253.

on observation of zero, 313.
Phosphate and borate glasses, 132, 387.
Phosphate crown, 98.

Phosphoric acid, H.
Photographic glasses, 19.

objectives, 95-111.
Piezometric experiments, 306, 310.
Plaining, 17.

Plastic solids, hardness, 1 8
Plasticity and brittleness, 174, IT'.i 1 vS
Plates for testing magnetic field
Platinum bulb to thermometer, :: 1 7.

crucible, lf>.

Pockels, optical effects of stres

411.

Poisson's ratio, 17<, 172, 185-192.
-- and composition, 191.
-- and hardness, !'.'_'.
Polarisation by stressed glass, 7<
Polarised light, testing by, 75.
Pomplnn, 2M,
Porro's prisms, 117.
Potash and soda glass compared .
Potsdam refractor, 4(5, li'n. l-_'7 l_'v
Pounded glass in water, ."
Powdered glass in water, 353-357.
-- hygroscopic eain in air, 357.
Practical tests of glass vessels, 340-353.
Pressed lenses, 16, 387.
Pressure, limiting, 173.
Primary and secondary image-surfaces,

96.

I'riMu-telescopes, 115-118.
Projection -eyepieces, 92.

objectives, 93.
Pulfrich and Srllm. -i.-r, 46.
Pulfrich, temperature and index, 57 -62.
Purity of water, 211,219, 359.

(ilijrctivo .spn-ilicd, 110.
t n.itive analysis a
Quickly cooled discs and cylinders,
6-74.

"f curvature, signs of, 109.
Rare earths in glass, 374.
Ray-union, order of, 87.
K. .1 i : : . t- i ..-..i

Reed, temperature and index, 62-66.
Reflection, loss by, 47.

t lines of flow, 209.
Itert, semi-apochromatics, 94.
K. -itn.-id. H., KMMfctteiflftHt B2l' -.".'I.

/cr's tesU of germtegUa, 369 37 1 .

418

JENA GLASS.

Relief of stress, 218, 272.

lowers index, 66.

raises zero, 272.

Relieving the objective. ^ii.
Resistenzglas, 246, 286.
Resolution, limit, 82-83.
Resolving power of telescope, 119.
Rigidity (simple), 192-193.
Rime of chlorides on surface, 322.
Rings, diffraction, 134.
Rise of zero (see icu/ar), 261-274.

explained by Schott, 272-274.

compared with depression, 270.
Rock salt plastic, 179.

Rontgen ray transmission, 373-376.
Rosenhain, 412.
Ross, concentric lens, 101.
Rubens and Simon, 39-41, 52.
Rudolph, astigmatism, 97.

triplet, 100.

anastigmats, 102-106.

diverging doublet, 113.

Sand, Martinsroda, 21.
Sandbath for zero observations, 263.
Sagittal section of pencil, 96.
Saline solutions and glass, 366.
Scheel (see Thiesen).
Scheibner's achromatisation, 35.
Schloesser, hydrogen scale, 400-403.
Schmidt, polarisation by reflection,

77.
Schott, 3, 5.

paper read 1888, 8-10, 14-15.

early trial meltings, 14.
thermometer glass, 20-22.

and Winkelmann, 145, 217, 228.

compensated afterworking, 300.
Schroeder, concentric lens, 101.
Schulze, performance of microscope,

92.

Scratching-hardness, 176-178, 182.
Seasoning glass vessels, 339.

high - temperature thermometers,

269.

Secondary spectrum, 33-36.
Secular rise of zero, 239, 248, 260.
Sell (see Thiesen).
Sellmeier, 46.
Semi-apochromatics, 94.
Sensitive layer, 226.
Separating power, 82, 119.
Setting under water, 328, 369.
Shearing, resistance to, 192.
Shrinkage in combining, 147.
Simon and Rubens, 39-41, 52.
Skin coming off glass, 327.
Soakage into glass, 327, 406.
Soda carbonate attacking glass, 366.
Soda-equivalent of alkali, 336.
Softening point, 16, 65.

Solution from glasses, 329-335.
Specific heat, 194-199.

and composition, 196-199.
Spectrometer, Abbe's, 23.
Spectrophotometer, 40.
Spherically and chromatically corrected

objectives, 107-111.
Stabthermometer, 265.
Standards-Commission, 24 % 2, :J2-l.
Star images. l.'U.
Star-spectrum test, 129.
Starke, permittivity method, 381.
Stas, glass used by, 319, 344, 361.
Stereoscopic binocular, 118.
Stirring the melting, 17.
Stokes and Harcourt, 2.
Strain (see stress).
Straubel, 186-193, 215.
Strength of glass, 149-155.

affected by temperature, 155.

against pull and thrust, 152-153.

in flexure and torsion, 155.
Stress affects expansibility, 217, 275.

relieved by heating, 272.

in thermometer stem, 272.

optical effects of, 66-76, 406-411.
Stripping off gelatine, 79.
Sulphur, boiling, 269, 273.
Sulphuric acid vapour, 365.
Surface conduction, 314.

Tangent law for flow, 205.

Tapping and elastic afterworking, 305.

Taylor on objectives, 127.

triple objective, 134-137.
Teleobjectives, 114.
Telescopes, 115-144.
Temperature and index, 57-66.

and solubility, 355.

Tenacity and composition, 149-151.
Tensile strength, 149.
Tertiary spectrum, 34.
Test by star spectrum, 129.
Test objects, microscopic, 91.
Thermal endurance, 228-238.

- properties, 194-238.
Thermally bad, elastically bad, 314.
Thermo-elastic afterworking, 162, 316.
Thermometer glass, 20-22, 255-257 (see

normal, borosilicate, baryta borosili-

cate, verre dur).
Thermometer-glass expansions, 220-

221.
Thermometers, comparison of, 275-280.

and air thermometers, 280-288.
hydrogen thermometers, 298-300,

400-403.

Thermoregulator, 16.
Thiesen, relative expansion, 289-290.

- Scheel, and Sell, 220, 275, 290.
Thomson, James, ray curvature, 68.

IXDKX.

419

Thuringian glass, -21, 240, 248, 252, 258,

260-264, 306, 308, H
Titanic acid, 10.
Titration, 335-336.
Tonnelot thermometers, 243.
Torsional afterworking, 307.
Torsion and flexure compared, 154-155.
Toughened layer, 226.

Triple objective specified, 109.
Tubes (water gauge), 227, 345, 398.

Ultra-violet dispersion and absorption,

41-48.

Unannealed discs acting like lenses, 67.
Unsymmethcal anastigmats, 102.
Useful magnification, 83.

t constant, 383-385.
Ferr* <i . 890, '244, 248, 250, 253-256.
Vogel and Miiller, absorption, 4IJ-.VJ.
Vogel, chromatic aberration, 127, 129-

large objectives, 120-122.
Voigt, method of isothermals, 204.
Voigtlander, 101.

collinear, 105.
Volume-elasticity, 192-193.

T, th<* purest, 359.

preservation of pure, 211, 218.
Water-gauge tubes, 227, 345, 398.
Water-glass, 328-330.

setting of, 328.
Weathering of glass, 348.

tested by conductivity.

Weber, depression and composition,
240.

test of susceptibility.

Weidmann, elastic afterworking, 304-
111,

Weight-thermometer, 290.
Wheatstone's bridge, 353, 378.
\\i k>- angled appchromat, 100.
Wiebe, comparison with air thermo-
meter, ->';

depression and composition, 24-J _' r.i.

rise of zero, 261-269.

at high temperature, 2G4-26ii.

and Bottcher, 275-284.
W Using, absorption, 49.

\\ inkelmann's list of glasses, 1 :. 1 ;7
Winkelmann, conductivity, 199, _'".;,

2 11 '-'I.-,.
Winkelmann, expansion, -}'

specific heat, 14 I'.t'.i.
-andSchott, 145. -J IT

and Straubel, 373.
Withstanding heat chang*

chemical attack, 366-371.
Wolf on Pauly telescope, 133-134.

X-rays, transparency to, 373 376.

fluorescence to, 375.

Young's modulus, 155-160.

at high temperature, 160-168.

and composition, 159-160.

Zeiss, 7, 20.

microscopic objectives, 90.

- telescopic, 143-144.

Zero (see rise, dfpre*i<m, secular).

Zinc borate of extreme properties,

193.
Zircon fluorescent to X-rays, 37

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