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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 



BY 

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 

(c) On arsenic in glass, - 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. 

I 



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 



26 



JENA GLASS 



Run- 
ning 
No? 


Trade 
No. 


Description. 


[ndex for 
D. 


Mean 

Mspersion 
CtoF. 


v 
n-l 
A 


1 


0. 225 


Light Phosphate Crown, 


1-5159 


0-00737 


70-0 


o 


S. 40 


Medium Phosphate Crown, 


1-5590 


0-00835 


66-9 


3 


S. 30 


Dense Barium Phosphate Crown, - 


1-5760 


0-00884 


65-2 


4 


S. 15 


Densest Barium Phosphate Crown, 


1-5906 


0-00922 


64-1 


5 


0. 144 


Boro-Silicate Crown, .... 


1-5100 


0-00797 


64-0 


6 


O. 57 


Light Silicate Crown, .... 


1-5086 


0-00823 


61-8 


7 


0. 40 


Silicate Crown, - 


1-5166 


0-00849 


60-9 


8 


0. 60 


Lime Silicate Crown, - 


1-5179 


0-00860 


60-2 


9 


0. 138 


Silicate Crown of High Index, 


1-5258 


0-00872 


60-2 


10 


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 


13 


O. 203 


Ordinary Silicate Crown, 


1-5175 


0-00877 


59-0 


14 


O. 13 


Potash Silicate Crown, - ... 


1-5228 


0-00901 


58-0 


15 


0. 15 


Zinc Silicate Crown, .... 


1-5308 


0-00915 


58-0 


16 


O. 211 


Dense Barium Silicate Crown, 


1-5726 


0-00995 


57-5 


17 


0. 153 


Silicate Crown, 


1-5160 


0-00904 


57-2 


18 


0. 114 


Soft Silicate Crown, 


1-5151 


0-00910 


56-6 


19 


0. 197 


Boro-Silicate Glass, 


1 -5250 


0-00929 


56-5 


20 


0. 202 


Densest Barium Silicate Crown, 


1-6040 


0-01092 


55-3 


21 


S. 35 


Borate Flint, - 


1-5503 


0-00996 


55-2 


22 


O. 252 


Borate Flint, - 


1-5521 


0-01026 


53-8 


23 


0. 152 


Silicate Glass, 


1-5368 


001049 


51-2 


24 


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 * - 


No 


i and a. 


,and. 


,and y . 






1 


0-00485 


0-00515 


0-00407 


2-58 


Colourless, 




0'658 


0-698 


0-552 






2 


0-00546 


0-00587 


0-00466 


3-07 


Do. 




0-654 


0-702 


0557 






3 


0-00570 


0-00622 


0-00500 


3-35 


Not very hard. 




0-644 


0-703 


0-565 







4 


0-00091 

0-641 


0-00648 
0-703 


0-00521 
0-565 


3-66 


Not hard ; needs protection. 


5 


0-00619 
0-651 


0-00559 
0-701 


0-00446 
0-559 


2-47 


Exceptionally hard. Very colourless. 


6 


0-00530 


040078 


0-00464 


2-46 




0-644 


0-702 


0-564 




7 


0-00545 


0-00596 


0-00479 


2-49 




0-642 


0-702 


0-564 




8 


0-00553 
0-643 


O-oixiu:, 
0-703 


0-00487 
0-566 


2-49 


Exactly corresponds to Chance's Hard 
Crown. 


9 


0-00560 


0-00614 


0-00494 


2-53 






0-642 


0-704 


0-567 






10 


0-00560 


0-00587 


0-00466 


2-24 


Only to be used in protected places. 




0-667 


0-700 


0-555 






11 


0-00543 


0-00592 


0-00478 


2-47 






0-645 


0-703 


0-568 






12 


0-00582 


o-<MMi:i 


0-00514 


2-73 


Very colourless. 




0-640 


0-703 


0-566 






13 


0-00563 


0-00616 


0-00499 


2-54 






0-642 


0-702 


0-568 






14 


0-00572 


0-00637 


0-00515 


2-53 


Has better run of dispersion than ordinary 




ii .;:;:, 


0-707 


0-572 




silicate crown. 


15 


0-00587 


0-00644 


0-00520 


2-74 




0-642 


0-704 


0-568 




16 


O-<N M;;;O 


0-00702 


O-IH >;,;* 


3-21 


Ooloulsm 




0-633 


0-706 


0-571 




17 


0*00976 


0-00637 


o-m.-,n; 


*a 




04H 


0-700 


0-571 




18 


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. 


01 


ii-m it" 1 


n > H H ' c i 


n irti'ii'. 1 




J 


(I IMMi.i | 

0-656 


( iMid.ri 


(1 1 N 1. ill 1 

0-563 




22 


0- ;r,7 


0407SI 


040001 


2-67 To be used to protected places. 




0400 


0-703 


0-567 






23 


040000 


n-m::t 


040010 


2-76 






04B8 




04H 






24 




0-00795 


0406M 


41 












0-571 







28 



JENA GLASS. 



Run- 
ning 
No. 


Tr.ule 
No. 


Description. 


Index for 
D. 


Mean 
Mspersion 
C to /'. 


V 

n-1 
A 


25 


O. 164 




1 '5503 


0-01114 


49'4 


.26 


0. 214 


Silicate Glass, 


1-5366 


0-01102 


48-7 


27 


0. 161 


Boro-Silicate Flint, 


1-5676 


0-01216 


46-7 


28 


S. 7 


Borate Flint, - 


1-6086 


0-01375 


44-3 


29 


0. 154 


Light Silicate Flint, 


1-5710 


0-01327 


43-0 


30 


0. 230 


Silicate Flint of comparatively high 
index, 


1-6014 


0-01415 


42-5 


31 


0. 184 


Light Silicate Flint, 


1-5900 


0-01438 


41-0 


32 


S. 17 


Dense Borate Flint, 


1 -6467 


0-01591 


40-6 


33 


S. 10 


Dense Borate Flint, 


1-6797 


0-01787 


38-0 


34 


0. 118 


Ordinary Silicate Flint, 


1-6129 


0-01660 


36-9 


35 


0. 167 


Ordinary Silicate Flint, 


1-6169 


0-01691 


36-5 


36 


O. 103 


Ordinary Silicate Flint, 


1-6202 


0-01709 


36-2 


37 


0. 93 


Ordinary Silicate Flint, 


1-6245 


0-01743 


35-8 


38 


0. 102 


Dense Silicate Flint, - 


1-6489 


0-01919 


33-8 


39 


0. 192 


Dense Silicate Flint, 


1-6734 


0-02104 


32-0 


40 


0. 41 


Dense Silicate Flint, 


1-7174 


0-02434 


29-5 


41 


O. 113 


Dense Silicate Flint, - 


1-7371 


0-02600 


28-4 


42 


O. 165 


Dense Silicate Flint, .... 


1-7541 


0-02743 


27-5 


43 


0. 198 


Very Dense Silicate Flint, 


1-7782 


0-02941 


26-5 


44 


S. 57 


Densest Silicate Flint, - 


1-9626 


0-04882 


19-7 


4.-, 


0. 599 


Boro-Silicate Crown, 


1 -5069 


0-00813 


62-3 


46 


O. 337 


Silicate Crown, 


1-5144 


0-00847 


60-7 


47 


0. 374 


Silicate Crown, 


1-5109 


0-00844 


60-5 


48 


0. 546 


Zinc Crown, 


1-5170 


0-00859 


60-2 


49 


O. 567 


Silicate Crown, 


1-5134 


0-00859 


59-7 


50 


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 . 


25 


0-00710 
0-637 


0*00786 
0-706 


0-00644 
0-578 


2-81 




26 


0-00690 
0-626 


0-00781 
0-709 


000644 
0-584 


2-73 




27 


0-00762 
0*687 


<i-ms.;o 
0-707 


0-00709 
0-583 


2-97 




28 


040864 

0-628 


0-00974 
0-708 


0-00802 
0-583 


3-17 


To be used under protection. 


29 


0-00819 
0-617 


0-00943 
0-710 


0-00791 
0-596 


3-16 


. 


30 


o-iM.sr.s 
0-613 


0-01009 
0-713 


0-00843 
0-595 


3-40 




31 


0-00882 
0-613 


0-01022 
0-711 


0-00861 
0-599 


3-28 




32 


040060 
0-622 


0-01128 
0-700 


0-00937 
0-589 


3-51 


To be used under protection. 


33 


0-01097 
0-614 


0-01271 
0711 


0-01062 
0-594 


3-81 


To be used under protection. 


34 


001006 
0-606 


0-01184 
0-713 


0-01008 
0409 


3-58 




35 


0-01026 
0-606 


0-01206 
0-713 


0-01029 
0-608 


3-60 




36 


0-01034 
0-605 


0-01220 
0-714 


0-01041 
0-609 


3-63 


Exactly corresponds to Chance's Dense 
Flint. 


37 


0-01053 
0-604 


0-01243 
0-713 


0-01063 
0-609 


3-68 




38 


ooll.VJ 
0-600 


0-01372 
0-715 


0-01180 
0410 


3-87 


Optically identical with Chance's Extra 
Dense Flint. 


39 


0-01255 
0-597 


0-01507 
0-717 


0-01302 
0-619 


4-10 




40 


0414IO 

0-591 


0-01749 

n-Tis 


o-ol.vjl 
0-625 


4-49 


Corresponds to Chance's Double Extra 
Dense Flint 


41 


0-01526 
0-587 


0-01870 
0-719 


0-nir,3-J 
0-627 


4-64 




42 


0-01607 
0*585 


OO1974 
0-720 


001730 
0*630 


4-78 




II 


0-01719 
0*584 


0-02120 
0-721 


0-01868 
0-635 


4-99 




44 


0*9767 
0467 


046641 
0-726 


046661 

0-666 


641 




45 


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. 



30 



JENA GLASS. 



Run- 

ninsr 

No? 


Trade 


Description. 


ndex for 
D. 


Mean 
)ispersion 
C to F. 


V- 

n-1 
A 


51 


0. 598 




1-5152 


3-00879 


58 "6 


52 


0. 512 


Silicate Crown, 


1-5195 


0-00886 


58-6 


53 


O. 463 


Baryta Light Flint, 


1-5646 


0-01020 


55-4 


KA 


OOAQ 






ft.AAQjQ 


K A .ft 


O4 


. OUo 






u uuy4o 


O4 


55 


0. 602 


Baryta Light Flint, 


1-5676 


0-01072 


53-0 


56 


0. 381 


Dispersive Crown, - 


1-5262 


0-01026 


51-3 


57 


0. 583 


Baryta Light Flint, 


1-5688 


0-01110 


51-2 


58 


0. 543 


Baryta Light Flint, 


1-5637 


0-01115 


50-6 


60 


0. 527 


Baryta Light Flint, 


1-5718 


0-01133 


50-4 


60 


0. 575 


Baryta Light Flint, 


1-5682 


0-01151 


49-3 


61 


O. 522 


Baryta Light Flint, 


1-5554 


0-01153 


48"2 


62 


0. 578 


Baryta Light Flint, 


1-5825 


0-01255 


46-4 


63 


0. 376 


Ordinary Light Flint, - 


1-5660 


0-01319 


42-9 


64 


O. 340 


Ordinary Light Flint, - 


1-5774 


001396 


41-4 


65 


0. 569 


Ordinary Light Flint, - 


1-5738 


0-01385 


41-4 


66 


O. 318 


Ordinary Light Flint, - 


1-6031 


0-01575 


38-3 


67 


0. 266 


Ordinary Light Flint, - 


1-6287 


0-01775 


35-4 


68 


0. 335 


Dense Silicate Flint, - 


1-6372 


0-10831 


34-8 


69 


O. 802 


Boro-Silicate Crown, 


1-4967 


0-00765 


64-9 


70 


0. 709 


Zinc Soda Crown, - ... 


1-5128 


0-00894 


57-3 


71 


O. 1209 


Densest Baryta Crown, - 


1-6112 


0-01068 


57-2 


72 


0. 722 


Baryta Light Flint, 


1-5797 


0-01078 


53-8 


73 


O. 846 


Baryta Light Flint, 


1-5525 


0-01042 


53-0 


74 


0. 726 


Extra Light Flint, 


1-5398 


0-01142 


47-3 


75 


0. 378 


Extra Light Flint, 


1 -5473 


0-01193 


45-9 


76 


0. 748 


Baryta Flint, 


1-6235 


0-01599 


39-1 



OPTICAL PROPERTIES OF GLASS. 



31 



Run- 
ning 
No. 


Partial Dispersions, 
and ratios to A. 


ensity 


Remarks, 


, and a. 


,and. 


fcandy. 


51 


0-00562 
0-640 


0-00619 
0-704 


OO0499 
0-568 


2-59 


Almost absolutely colourleM. 


52 


6*00068 

0-641 


IMMKiLV, 

0-705 


0-00504 
0-568 


2-64 


Almost absolutely colourless. 


53 


0-00648 
0-635 


0-00720 
0-706 


0-00586 
0-575 


3-11 


Almost absolutely colourless. 


54 


0-00595 
0-631 


0-00666 
0-706 


0-00543 
0-576 


2-60 




55 


0-00675 
0-630 


0-00759 
0-708 


000618 
0-576 


8-12 




56 


0-00644 
0-629 


0-00727 
0-709 


0-00596 
0-582 


2-70 




57 


0-00696 
0-627 


0-00786 
0-708 


0-00644 
0-580 


3-16 




58 


000699 
0-627 


0-00790 
0-708 


0-00650 
0-583 


3-11 




59 


0-00706 
0-623 


0-00803 
0-709 


0-00660 
0-582 


3-19 




60 


0-00718 
0-623 


0-00817 
0-710 


0-00672 
0-584 


3-15 




61 


0-00718 
0-623 


0-00819 
0-710 


0-00677 
0-587 


303 




62 


OO0777 
0-619 


0-00891 
0-710 


0-00739 
0-589 


3-29 




63 


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. 


66 


0-00960 
0-609 


0-01124 
0-714 


0-00952 
0-605 


3-48 




67 


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. 


70 

71 


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. 


72 


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 




75 


0*00739 
0-620 


040047 

07H> 


om:n; 

046 


848 




76 


040860 

0406 


0-01142 
0-713 


040061 

0-604 


:: .17 





32 



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 


+ 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 





34 



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, 


M* 


10*y 


U D 


10A 


9 


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 


OH 

on 


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


1-51007 


868 


58-8 


581 
669 


ooo 


482 

m 


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


1-57422 


1006 


57-1 


640 
636 


IN 

700 


584 

581 


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


1-52002 


1003 


51-8 


m 

632 


71S 

711 


HI 


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


1-57524 


1396 


41-1 


855 

612 


991 
710 


040 

Hi 


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 

no 


OH 


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


1-88995 


3997 


223 


OJH 

574 


OJOJ 

m 


OH 
051 


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


1-60956 


MM 


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 


n 

500 


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


1-52046 


1010 


51*5 


OH 
030 


IOJ 


M 


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


,~ 


1244 


40-8 


774 

oji 


000 
790 


m 

m 



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. 



il 



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 

o 

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

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



OPTICAL PROPERTIES OF GLASS. 



43 



is: 



T. \ - n 

'!-- 






1! 

d 






-r - r-. 



.~ 



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






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

3C OC CC 3C OO 3C X CC 

03 



X 












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. 



47 



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 


p- 


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: 



x= 


0-677 


o-.Vso 


0-535 


HM 


0-477 


(> l.V, 


Q-4J6* 


Flint 0. 340 


0-939 


0-878 


0-907 


()ss() 


Ossn 


MM 


(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. : 



x= 


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 



51 



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 



x= 


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 


0-0128 


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 


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 


0-02 


0-03 


O'll 


0-41 


0-69 


0. 500 


o-oo 





o-oo 





o-oo 





o-oo 


o-oi 


0-08 


0-30 


0-63 


S. 163 


o-oo 





0-02 





o-oi 





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, 



54 



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 


s 


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. 



55 



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 



8 

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 


I 


10 S. 52. Light Borate Crown. 


840 


m 


700 


555 


Ml 


46. O. 599. Borosilicate Crown, 


m 


051 


701 


m 


J4S 


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


M 


m 


702 


:*i:< 


*-56 


19. O. 197. Borosilicate GUn, 


M 


045 


704 


in 


9-04 


24. S. 8. Borate Flint, 


1129 


045 


m 


571 


2 s-J 


25. O. 164. Borosilicate Flint, 


1114 


m 


706 


578 


Hi 



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). 



58 



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 


V 


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. 



59 



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 


C 


D 


F 


O' 


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 


MM 

0-446 


0-407 
0-520 


0. 544. SiL FL, 


11-1-99-1 
55-1 


0-244 
0-360 


O'JSl 

0397 


MM 

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 


MM 

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 : 





CD 


DF 


FG' 


0. 


225, 


55 


43 


65 


S. 


40, 


36 


100 


19 


0. 


627, 


75 


69 


78 


S. 


205, 


-31 


70 


65 


0. 


1022, 


94 


74 


105 


0. 


211, 


64 


91 


70 


0. 


527, 


67 


82 


87 


0. 


658, 


100 


75 


87 


0. 


154, 


94 


77 


93 


0. 


544, 


78 


92 


113 


0. 


165, 


98 


140 


151 


S. 


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.-, 


V 


10*CD 


itft* 


10W 


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


1-96249 


19-7 


10V 

ISM 

_'7l 


10/3 


10V 


:<:4<i 
726 


MW 

633 


S. 163. Densest Sil. Flint, - 


1-89035 


3994 


B4 


1106 

277 


2888 
723 


-J4S4 

M 


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"'.' 


m 

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. 



64 



JENA GLASS. 





t m 





D 


F 


O" 




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 : 





4 


T 


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 


17 


O. 165 


300330 


408 


75448 


75434 


14 


O. 154 


380400 


452 


1-57089 


56996 


93 


0. 527 


410450 


406 


57170 


57170 





0. 211 


470490 


406 


57270 


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 

x 



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 



H 



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 : 



e, 



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. 



73 



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. 





D 


2r 


? 


e p 


, 


UFA, 


in' A. 


lo-(A,-,X) 


1"'U,-A.) 














From jMs. (7). 


Fro MUM jn. (4). 


A 


110 


26 


8 


18-0 


9-0 


914 


41 W 


14; 


m 


B 


110 


Ifi 


3 


18-0 


90 


M 


156 


148 


161 


C 


156 


M 


9 


il-a 


17-0 


1463 


1170 


M 


:;:<. 



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. 



79 



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 


BM 


56-3 


O. 671. Silicate Crown, .... 


1 -:.224 


MM 


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 


UM 


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). 



80 



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 


20 







3 


5 


30 





5 


6 


10 


35 





9 





15 


40 


8 





15 


20 


45 


12 


20 


17 





47 


19 











50 


31 


45 


23 





50-3 











58 


53 








56 





53-3 











98 


53-7 





71 








55 


105 











55-7 I 


124 








56 








165 





56-7 





188 








60 


72 


121 





155 


61 


63 


112 


58 


130 


62 








43 





63 





60 





99 


64 








36 





65 


32 


45 





72 


68 


23 





20 


49 


70 


19 


27 


17 


37 


72 











30 


73 











24 


75 











23 


80 


6 












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 

md 

(= i ' 

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

2k 
m= a. 

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 

/2 

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. 



88 



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 


V 


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. 



90 



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 


42 

63 


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. 



91 



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, 


__ 


1 


2 


4 8 


12 


18 


27 


Focus in mm., 


Short, 


180 


90 


45 22-5 


15 


10 





Do., 


Long, 





135 


67 : 


22-5 


u 


10 



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 

k 

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. 

H 



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 

X 



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. 



ft 


100 ^ 


100 Q 


cm. 


Visual. 


Photographic. 


Visual. 


Photographic. 


4 


93 


84 


77 


69 


6 


90 


77 


75 


63 


8 


87 


71 


72 


58 


10 


84 


65 


70 


53 


12 


82 


60 


67 


49 


14 


79 


55 


65 


45 


16 


76 


50 


63 


41 


18 


74 


46 


61 


38 


20 


71 


43 


59 


35 


22 


69 


39 


57 


32 


24 


67 


36 


55 


29 


26 


65 


33 


53 


27 


28 


62 


30 


52 


25 


30 


60 


28 


50 


23 


32 


58 


25 


48 


21 


34 


56 


23 


47 


19 


36 


55 


21 


45 


18 


38 


53 


20 


44 


16 


40 


51 


18 


42 


15 



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, 

fj 

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. 


B 


6867 M 


0-0 mm. 


G 


6563 


- 6-1 


D 


5893 


-11-4 


F 


4862 


o-o 


0' 


4341 


+ 36-8 


h 


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 


000 


OOO 


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. 

I 



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. 


X. 


Pulling Out. 


Per Metre 
Focal Length. 




0-690 A* 


- 0-8 mm. 


-0-19 mm. 


C 


656 


- 1-3 


-0-30 


D 


590 


- 2-8 


-0-65 


b 


517 


- 1-2 


-0-28 


F 


486 










459 


+ 1-8 


+ 0-42 


0' 


434 


+ 4-0 


+ 0-92 


h 


410 


+ 8-5 


+ 1-96 


H 


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. 



X 


I. 


II. 


Fraunhofer. 


0-710 M 


- 0-05 mm. 


-0-02 mm. 


+ 0'67 mm. 


650 


+ 0-05 


+ 0-05 


+ 0-23 


590 


o-oo 


o-oo 


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. 



X 


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 


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 *}>. 



v 



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" 


5 

A 


A' + A" 


CF 


01115 


00844 


1 


1 


A'C 


00374 


00296 


3420 


3425 


DF 


00790 


00593 


7059 


7052 


EF 


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'. 





A 


C 


D 


F 


G 




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. 





c 


,/ 


/ 


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: 





C 


D 


F 


G 


n 


1-55284 


1 -55531 


1-56113 


1-56576 


n' 


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. 


c 


d 


/ 


ff 


mm. 


460-556 mm. 


460 -235 Him. 


460 <>;>:* nun. 


460-53:* nun. 


194 


*to 


w 


or,:? 


M 


17 -(is 


577 


247 


072 


-Ml 


Jl -or. 


*M 


_>;:< 


ns:< 


557 


25 


621 


276 


O'.M 


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 




G 



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 



W. 


Trade No. 


W. 


Trade No. 


W. 


Trade No. 


1 


S. 185 


25 


O. 709 


59 


63'" 


2 


S. 205 


26 


0. 1571 


60 


O. 1022 


3 


172"i 


33 


O. 500 


61 


81"' 


4 


164'" 


36 


59"' 


62 


73111 


5 


802 


42 


0. 428 


63 


93" 1 


6 


16'" 


43 


458 


64 


90 m 


7 


165'" 


46 


O. 479 


65 


82'" 


8 


1419 


47 


O.2154 


66 


87 m 


9 


S. 201 


48 


O. 885 


67 


83 m 


10 


290 


49 


0. 627 


68 


102 1 " 


11 


665 


50 


O. 165 


69 


8. 226 


12 


121"i 


51 


16"' 


83 


0. 137 


13 


8.206 


52 


O. 55 






14 


8. 95 


53 


S. 41 






15 


144i> 


54 


0. 527 






16 


8.120 


55 


O. 1168 






17 


O.3:n 


56 


O. 662 






18 


8.163 


57 


S I.T.I 






21 


O.658 


58 


8. 57 







W. 


W. 


19 


5 


22 


2 


29 


8 


30 


10 


31 


13 


35 


7 


37 


12 


38 


6 


39 


11 


40 


12 


41 


21 


44 


36 


45 


2 


51 


6 


53 


13 


58 


20 


71 


27 


75 


_:; 


so 


5 



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). 

K 



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. 



w. 


n 


1 



i 




K 


a 

s 


: 

3 




0? 

< 


1 


1 


a 

W 


1 


! 


S 


o" 

91 

fl 


1 


_ 


71-8 


_ 


_ 


_ 


22-4 






_ 


__ 


5-8 






_ 


2 





69-1 











18-0 


0-2 


4-7 


8-0 

















3 


64-4 


12-0 








11-0 


4-5 








8-0 














o-i 


4 


55-0 














17-0 








14-0 


14-0 














5 


71-0 


14-0 











5-0 








10-0 

















6 


67-3 


2-0 


7-0 








2-5 








14-0 








7-0 





0-2 


7 


73-8 





5-0 








3-5 








10-5 








7-0 





0-2 


8 


67-9 





5-8 


8-1 





1-0 


0-3 





16-8 














o-i 


9 





3-0 








4-0 


10-0 


0-5 








12-0 








70-5 





10 


58-7 

















0-3 








33-0 





8-0 








11 




41 -0 


59 -0 
























12 


51-3 


14-0 


5-0 








4-5 


0-2 


25-0 





_ 





_ 


_ 





13 





3-0 











8-0 


1-5 


28-0 














59-5 





14 





3-0 











1-5 


1-5 


38 














56-0 





15 


34-2 


10-2 


7-8 








5-0 


0-7 


42-1 




















16 





42-8 





52-0 





5-0 


0-2 














__ 








17 


45-22 








46-0 








0-2 





1-0 


7'5 











0-08 


18 


22-0 








78-0 






















__ 








20 


20-0 








80-0 
































21 


32-75 


31-0 





25-0 





7-0 


0-25 





1-0 


3-0 














23 


34-5 


10-1 


7-8 








5-0 


0-5 


42-0 

















o-i 


24 


44-2 








47-0 








0-2 





0-5 


8-0 











o-i 


25 


70-6 





12-0 











0-4 





17-0 

















26 


41-0 








51-7 








0-2 








7-0 











o-i 


27 





3-0 








4-0 


10-0 


1-5 








12-0 








69-5 





28 


64-6 


2-7 


2-0 











0-4 


10-2 


5-0 


15-0 











o-i 


32 


54-8 





17-0 











0-2 








28-0 














33 


29-3 








67-5 








0-2 








3-0 














34 


70-2 


12-0 








3-0 


4-5 








10-3 

















36 


72-0 


12-0 











5-0 








11-0 

















42 





56-0 





32-0 





12-0 


























43 





64-0 











30-0 














6-0 











46 


45-2 








46-4 





0-5 


0-2 





0-2 


7-5 














47 


54-3 


1-5 





33-0 








0-2 





3-0 


8-0 














48 


48-8 


3-0 


10-3 











0-4 


29-0 


1-0 


7'5 














49 


68-3 


10-0 


2-0 











0-2 





10-0 


9-5 














50 


28-4 








69-0 








0-1 








2-5 














52 


69-1 


2-5 














0-4 





4-0 


16-0 





8-0 








54 


51-7 





7-0 


10-0 








0-3 


20-0 


1-5 


9-5 














55 


68-2 





2-0 


13-1 








0-2 





16-5 








__ 








56 


68-1 


3-5 


7-0 











0-4 





5-0 


16-0 














57 





3-0 








4-0 


10-0 


0-5 








12-0 








70-5 





59 


73-2 

















0-3 





18-5 








8-0 








60 


65-5 


2-5 


2-0 











0-4 


9-6 


5-0 


15-0 













61 


64-3 














1-5 


0-2 





3-0 


20-0 





11-0 








62 


71-7 














2-0 


0-3 





10-0 


13-0 





3-0 








63 


54-8 








25-0 





2-5 


0-2 





6-0 


11-5 















MECHANICAL l'R >PKRTI KS <>F CLASS. 



147 



\v. 


0~ 
7. 


* 


I 


1 


1 


< 

< 


$ 

< 


I 


J 


fc 


1 





$ 


! 


64 


69-7 


_ 


_ 


_ 


_ 


_ 


0-3 


_ 




25-0 


_ 


5-0 


_ 


_ 


65 


14-1 














2-5 


<_> 





90 


15-0 





9^) 








66 


58-8 





8O 


6-0 





4-0 


0-2 





10-0 


14-0 
















u-o 








34-0 





4-0 








8-0 


11-0 














68 


57-0 





50 








12-0 








13-0 


13-0 
















21-0 








79-0 
































70 


51-0 





12-0 














5D 





3-J-n 














72 


45-1 








46-4 














0-5 


0-8 














::; 





68-8 











18-0 





5-0 


80 

















74 


4-0 


54-5 


12-0 


11-5 





14-0 











4O 














76 


M4 


29-0 





34-0 





9-0 








0-5 


1-0 














77 


65-9 


_':. 


2-0 














9-6 


5-0 


150 














78 


674 





3-6 


13-0 














16-0 



















71-0 





12-0 

















17-0 

















Si 


67-9 





5-8 


8-0 





1-0 


0-3 





16-8 

















82 


61-6 














15-0 


0-3 





23-0 














o-i 


83 


70-6 


_ 














0-3 





2O 


16O 





11-0 





o-i 


84 


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 


86 


54 "J 


1-5 





33-0 








0-2 





3-0 


8-0 











o-i 


87 


68-2 


10-0 


2-0 











0-2 





100 


9-5 














88 


70-4 


7-5 














0-2 





5-3 


14-5 





2-0 





O'l 


N 


HIM. 


2-5 














0-5 





4-0 


16-0 





8-0 








90 


m>& 


2-0 





2-5 





2-5 


0-4 





7-0 


16-0 














M 


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 



S 



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 


Oxide z 


Oxide z 


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. 


w. 


Obs. 


Comp. 


Obs. Comp. 


2=22 


2-243 


2-24 


+ 0-1% 


3 


2-424 


2-42 


+ 0-2 


4 


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 


9 


2-588 


2-69 


- 3-9 


10=30 


2-518 


2-51 


- 0-3 


11 


3-527 


3-17 


+ 10-1 


12 = 37 


2-848 


2-84 


+ 0-3 


13 = 31 


3-070 


3-20 


- 4-2 


14 


8-288 


3-37 


- 4-1 


15 


3-532 


3-47 


+ 1-8 


16 


3-691 


3-42 


+ 7'3 


17 


3-578 


3-63 


- 1-5 


18 


5-831 


5-65 


+ 3-1 





Density. 


W. 


Obs. 


Comp. 


Obs. Comp. 


20 


5-944 


5-87 


+ 1-2% 


21 


2-758 


2-75 


+ 0-3 


23 


3-532 


3-45 


+ 2-3 


24 


3-578 


3-66 


-2-2 


25 


2-572 


2-54 


+ 1-2 


26 


3-879 


3-88 


-o-o 


27 


2-588 


2-52 


+ 2-6 


28 


2-580 


2-57 


+ 0-4 


32 


2-668 


2-75 


-3-1 


33 


4-731 


4-78 


-1-0 


34 


2-378 


2-34 


+ 1-6 


36 


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. 



w. 


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 


21 


9 


5-18 


5-66 


6-12 


5-99 


+ 2 


22=2 


5 


4-58 


4-93 


5-76 


5-79 


- 1 


23 


6 


6-78 


7'21 


7-52 


7'30 


+ 3 


24 


2 


5-95 


6-01 


6-07 


5-26 


+ 13 


25 


5 


7-00 


7'84 


8-51 


8-51 





26 


5 


4-25 


4-67 


5-39 


5-06 


+ 6 


27 


2 


5-36 


5-46 


5-56 


6-11 


-10 


28 


3 


5-60 


6-09 


6-76 


7-07 


- 5 


29 = 8 


4 


6-00 


6-42 


6-79 


7-59 


-12 


30=10 


3 


7-02 


7-52 


7'82 


7-22 


+ 8 


31 = 13 


5 


7-06 


7-42 


7-63 


6-50 


+ 15 


32 


3 


7-87 


8-09 


8-32 


7-75 


+ 7 


33 


4 


4-65 


4-97 


5-32 


4-36 


+ 18 


34 


3 


7-66 


7-92 


8-16 


7-56 


+ 7 


35 = 7 


4 


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. 



w. 


No. 
of 
Obs. 


Resistance to Crushing 
in kg/mm 2 


Obs.-Calc. 


Ratio to Tenacity. 


Obs. 


Calculated 


a 


b 


19=5 


4 


126-4 


110-9 


+ 12% 


18-7 


18-2 


20 


4 


60-6 


63-0 


- 4 


18-5 


17-2 


21 


4 


105-7 


88-2 


+ 17 


18-7 


17-3 


22=2 


5 


81-2 


88-1 


- 8 


16-5 


14-1 


23 


9 


84-0 


87-8 


o 


11-7 


11-2 


24 


5 


77-5 


77-9 


- 1 


12-9 


12-8 


25 


4 


97-8 


104-6 


- 7 


12-5 


11-5 


26 


4 


84-3 


75-8 


+ 10 


18-1 


15-6 


27 


4 


71-7 


72-0 


- 


13-1 


12-9 


28 


3 


91-6 


93-7 


- 2 


15-0 13-6 


29 = 8 


5 


99-0 


102-3 


- 3 


15-4 14-6 


30=10 


4 


68-3 


75-7 


-11 


9-1 


8-7 


31 = 13 


3 


75-0 


74-8 


+ 


10-1 


9-8 


32 


6 


73-9 


79-2 


- 7 


9-1 


8-9 


33 


4 


67-3 


68-8 


- 2 


13-5 


12-7 


34 


5 


99-3 


111-1 


-12 


12-5 


12-2 


35=7 


4 


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 : 







y 






y 






y 






y 


Si0 2 


= 1 


23 


PbO 


= 


48 


As 2 6 


= 1 


o 


K 2 


m 


0-05 


BA 


= 


9 


MgO 


= 1 


1 


r.ao 


= 


05 


CaO 


m 


0-2 


ZnO 


= 


6 


A1A 


= 1 


o 


Na 2 


= 


02 


TA 


= 


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 



B 



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 : 



w. 


*i 


E 2 


W. 


E l 


E, 


19 = 5 


7296 kg/mm 2 


7563 kg/ram 2 


33 


5512 kg/mm 2 


5477 kg/mm 2 


20 


5088 





34 


7001 


7180 


21 


5474 


5468 * 


35 = 7 


7077 


7314 


-22 = 2 


4699 


4906 


36 


7260 





23 


7952 


7992 


37 = 12 


7232 





24 


5389 





38 = 6 


7340 


7465 


25 


6498 


6766 


84 





7401 


26 


5467 


5461 


85 





7416 


27 


6780 





86 





6097 


28 


6626 


6599 


87 





7971 


29 = 8 


6514 


6638 


88 





7461 


30=10 





6014 


89 





7186 


31 = 13 


6296 


6373 


90 





6338 


32 


5862 


5843 


91 





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 = 



x 

40 

BaO =100 
Na 2 =100 



K 2 
CaO 



x 

71 

100 

38 



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. 


A 


B 


C 




70 


70 


70 


BA 





60 


25 


ZnO 


:,-_> 


100 





PbO 


46 





65 


MgO 





40 


90 


AL,0, 


LM 


i:,o 


130 


AA 


40 


40 


40 


BtO 





70 


n 


N.,0 


61 


100 


70 


K,0 


40 


70 


90 


CaO 


70 


70 





PA 








70 



>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 








20 


5088 


5080 


+ 0% 


24 


5389 


5614 


-4 


25 


6632 


6619 


+ 


26 


5464 


5536 


_ j 


29 = 8 


6576 


6644 


-1 


30=10 


6014 


6001 


+ 


32 


5852 


5848 


+ 


33 


5494 


5284 


+ 4 


35=7 


7195 


7186 


+ 


91 


6572 


6573 


-0 


Group B 








19 = 5 


7563 


7560 


+ 


23 


7972 


7511 


+ 6 


28 


6613 


7164 


-8 


34 


7090 


7459 


-5 


36 


7260 


7610 


-5 


37 = 12 


7232 


7364 


-2 


38=6 


7402 


7796 


-4 


84 


7401 


7331 


+ 1 


85 


7416 


7269 


+ 2 


87 


7971 


7247 


+ 9 


88 


7461 


7071 


+ 5 


89 


7186 


7080 


+ 1 


Group C 








21 


5471 


5521 


- 1 


22=2 


4802 


4776 


+ 1 


27 


6780 


6780 





31 = 13 


6334 


6180 


+ 2 


86 


6097 


6104 


-0 


90 


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- 

L 



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. 



w. 


* 


log a 


log/3 


Highest 
Temperature. 


19=5 


7672 kg/mm 3 


0-01760-9 


0-42810 


482 


21 


5606 


0-45239 - 15 


0-70586 


383 


22=2 


5023 


0-44871 - 4 





281 


23 


8146 


0-32998 - 5 


0-09364 


486 


J4 


5433 


0-89662-13 


0-64253 


413 


_'.-, 


6983 


0-91177-5 


0-06481 


409 


26 


601 1.-, 


0-49224-24 


0-94544 


340 


m 


<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 


32 


IW0 


0-19312-4 





417 


:<:{ 


5494 


0*63418-8 


0-40114 


857 


34 


7349 


0-11394-5 





482 


36 = 7 


7524 


0-54267 - 5 


0*08213 


460 


38 = 6 


7649 


0-43533 - 6 


'23175 


426 


84 


:r,r,4 


o-119160-ll 


0-55261 


407 


85 


70M 


0-92267-6 


o-ltt.V>0 


427 


86 


2IK 


0-97275-10 


0-49890 


374 


87 




044797-4 





447 


88 


T.V.I 


n-.-t.V218- 4 





47.-, 


89 


7234 


0-36922 - 4 





433 


90 





-I! I.V.I.-, 4 





434 


n 


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 


w. 


100 


2(M> 


300 


4m" 


500 


19=5 


o-oi 


0-11 


0-38 


0-85 


1-95 


21 


o-oo 


0-08 


0-76 


3-61 





22=2 


2-25 


5-06 


7-87 








23 


0-49 


1-34 


2-32 


3-39 


4-53 


24 


0-02 


0-63 


4-37 


16-60 





25 


1-32 


, 3-38 


5-66 


8'07 





26 


o-oo 


0-02 


1-18 








28 


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 





32 


1-25 


2-81 


4-37 


5-93 





33 


0-27 


2-06 


6-27 








34 


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 





84 


o-oi 


0-14 


0-67 


2-00 





85 


0-51 


1-67 


3-20 


5-01 





86 


0-09 


1-22 


4-92 








87 


1-42 


3-19 


4-96 


6-73 





88 


1-80 


4-05 


6-30 


8-55 


10-80 


89 


1-87 


4-21 


6-55 


8-89 





90 


3-30 


7-43 


11-56 


15-69 





91 


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: 



t 


(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. 



t 


(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. 


w. 


$ 


* 




8 


1 


| 


I 


1 


J 



M 


6 


* 


| 


1 


II 


_ 


69-0 


2-5 


_ 


__ 





0-4 





4-0 


16-0 


8-0 





o-i 


2 


I 


33 


29-3 








67-5 





0-2 








3-0 













III 





70-25 


10-0 











0-2 





10-0 


9-5 








0-05 


4 


IV 


20 


20-0 








80-0 


























.-. 





D 


71-0 


14D 








5-0 








10-0 














6 





25 


70-6 





12-0 








0-4 





17-0 














- 





23 


34-5 


10-1 


7'8 





,vo 


0-5 


12*0 














o-i 


- 





_' 





69-1 








18-0 


0-2 


4-7 


8K) 



















Jl 


32-7 


31-0 





25-0 


7-0 


0-3 





1-0 


3-0 











10 
11 
12 


= 


26 


41-0 








51-7 





0-2 








7-0 








o-i 
o-i 


6 


67-3 


20 


7-0 





2-5 








14-0 





7-0 





13 





10 


58-7 














0-3 








33-0 


8-0 








14 





u 





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, 

E 



E' 



(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 



A. 


W. 


E' E 


E'-E 


/* 


1 





7107 kg/mm 2 


kg/mm'- 


-% 





2 


33 


5871 


5494 


6-4 


0-25 


3 





7869 


7461 


5-2 


0-23 


4 


20 


5588 


5088 


8-9 


0'30 


5 


5 


7599 


7296 


4-0 


0-20 


6 


25 


6796 


6632 


2-4 


0-16 


7 


23 


8192 


7972 


2-7 


0-16 


8 


2 


4975 


4802 


3-5 


0-19 


9 


21 


5677 


5471 


3-6 


0-19 


10 


26 


5953 


5464 


8-2 


0-29 


11 





7532 











12 


6 


7792 


7402 


5-0 


0-22 


13 


10 


6197 6014 


3-0 


0-17 


14 


13 


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 : 



p- 

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. 


E' 

in^i, 
mm- 


r 

inJ* 
mm 


H 

fc-NL 

mm 8/s 


10 


2,5,7 


5953 


3-0 


173 


4 


1,2,4 


5588 


4-1 


183 


2 


1, 4, 12 


5871 


5-6 


210 


14 


2,5 


6811 


4-6 


217 


8 


1,3,5 


4975 


8'8 


219 


1 


3, 5, 10, 15 


7107 


4-5 


223 


9 


3,5 


5677 


9-3 ! 244 


3 


4, 12, 30 


7869 


5-0 


246 


12 


2,5 


7792 


6-4 


266 


11 


2,5 


7532 


6'9 


267 


6 


1,3,9 


6796 


9-0 


272 


5 


1,5 


7599 


7'4 


274 


13 


2,5 


6197 


11-6 


278 


7 


1,3,5 


8192 


97 


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: 



10 


4 


2 


14 


8 


1 


9 


3 


12 


11 


6 


5 


13 


7 


17 


31 


36 


41 


45 


55 


53 


68 


64 


78 


63 


75 


66 


68 


82 


100 


79 


71 


60 


46 


51 


33 


32 


46 


45 


42 


48 


27 



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. 


1 


223 


232 


- 4% 


2 


210 


207* 


+ 1 


3 


246 


251 


- 2 


4 


183 


182 


+ 1 


5 


274 


270 


+ 1 


6 


272 


275 


- 1 


7 


316 


310 


+ 2 


8 


219 


222 


- 1 


9 


244 


248 


- 2 


10 


173 


238 


-38 


11 


267 








12 


266 


219 


+ 18 


13 


J7S 


273 


+ 2 


14 


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\* 

E 



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. 



w. 


Str. 


W. 


Str. 


W. 


Str. 


19 


1450 


27 


S. 219 


39 


680 


ao 


S. 208 


28 


2158 


85 


1973 


21 


658 


30 


290 


86 


2154 


28 


S. 196 


31 


270 


87 


627 


23 


1299 


32 


370 


90 


20 


25 


709 


33 


500 


91 


714 


26 


1571 


38 


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. 


1 


1 


I 


1 


| 

< 


I 


O 

A 


3 




& 


S 


$ 


1 


2175 


68-7 


8 





_ 


_ 


1-5 


_ 


5-3 


14-5 


2 


_ 


0-03 


1893 


53-."> 


20 




















6-5 











2106 


44-6 








46-6 





0-3 





0'5 


8 











2122 


37-.-, 


15 








5 


1-5 


41 

















1933 


39-64 


6 


9-2 





2-5 


0-5 


42-1 














0-06 


S. 95 





3 








1-5 


1-5 


38 











56 





s. L8fi 





71-8 








22-4 








' 











_ 


S. 120 





42-8 





52 


5 


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. 


A* 


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 


20 


221 


+ 003 


S. 208 


261 


+ 010 


2154 


222 


-002 


1933 


266 





2106 


222 


-009 


1299 


271 


+ 003 


1571 


224 


-Oil 


S. 95 


272 


+ 002 


HQ 


226 


+ 002 


S. 185 


273 





16'" 


s 





S. 196 


274 


(Mi:, 


2158 


231 


-002 


S. 120 


279 


- (HH 


8. 219 


_>:r, 


-002 


BA 


_>s;< 


-001 


no 


M 


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 



E 



T- 



E 



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. 


W. 


/* 


E 


C 


T 


1450 


19 


197 


7300 


4020 




278'" 





_>os 


6640 


3790 


9700 


2170 





210 


7460 


4290 


3oxo 


627 


87 


213 


7970 


4630 


3-290 


1893 





219 


5170 


3070 


2120 


714 


91 


221 


6570 


3920 


2690 


20 


90 


221 


6340 


3790 


2600 


2154 


86 


-222 


6100 


3660 


2500 


2106 





222 


5390 


3230 


2210 


1571 


26 


294 


5460 


3300 


2230 


709 


25 


226 


6630 


4030 


2700 


16'" 


38 


>s 


7400 


4530 


.SOlo 


2158 


28 


231 


6610 


4100 


9080 


S. 219 


27 


235 


6780 


4260 


9700 


500 


33 


239 


5490 


3510 


2220 


658 


21 


250 


5470 


3650 


2190 


1973 


85 


252 


7420 


4990 


2960 


290 


30 


253 


6010 


4060 


2400 


970 


31 


253 


6330 


4270 


2530 


370 


32 


261 


5X50 


40x0 


2320 


S. 208 


20 


261 


5090 


3550 


2020 


1299 


23 


271 


7<>7" 


5800 


3140 


S. 196 


22 


274 


4700 


3470 


ISJH 


665 


39 


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 



w. 


c 


c' 


c-c' 


1 


s. c 


1 


231 S 


2415 


-4-2% 


2-238 


5188 


2 


2182 


2192 


-0-5 


2-243 


4894 


3 


-jnsti 


20SO 


+ 0-3 


2-424 


5056 


4 


2044 


2040 


+ 0-2 


2-480 


mi 


B 


_>>:is 


2049 


-0-5 


2-370 


4830 


6 


1988 


1983 


+ 0-3 


2-585 


5139 


7 


1958 


1964 


-0-3 


2-479 


4854 


8 


1907 


1888 


+ 1-0 


2-629 


5013 


9 


1901 


1944 


-2-3 


2-588 


4920 


10 


1887 


1893 


-0-3 


2-518 


4751 


11 


1644 


1668 


-1-5 


3-527 


5798 


12 


1617 


1626 


-0-6 


2-848 


4605 


13 


1589 


1573 


+ 0-9 


3-070 


4878 


14 


1464 


1439 


+ 1-0 


3-238 


4740 


15 


1398 


1379 


+ 1-4 


3-532 


4938 


16 


1359 


1344 


+ 1-1 


3-691 


5016 


17 


1257 


1272 


-1-2 


3-578 


4498 


18 


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 



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. 



w. 


K in gm. cm" 1 , sec' 1 


Ob8.-Calc. 


Observed. 


Calculated. 


69 


401063 


001094 


- 1% 


70 


001304 


001324 


- 2 


71=27 


001409 


001406 


+ 


7-j 


001433 


001379 


+ 4 


73 


001445 


001572 


- 9 


74 


001470 


001401 


+ 5 


7.-, = 23 


001610 


001511 


+ 6 


76 


001650 


001479 


+ 10 


77 


001832 


001661 


+ 9 


78 


001861 


001879 


- 1 


79 


001931 


001954 


- 1 


80=5 


002267 


002092 


+ 8 


81 


001938 


001905 


+ 2 


82 


ooi !:_' 


002024 


- 3 


u 


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, 

BA 

ZnO 
PbO 
ligO 

A1A 



0000220 

150 

100 

80 

84 

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 



D 



E 




Q 



n 



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 : 



19 



44.40 

49-1 



20 



19 



21 



257 
31-6 



44-8 ; 36-0 
45-1 37-0 



21 


20 


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 * 


a 


* 


*( + *) 




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 ^ 



w. 



20 

21 



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.] 

O 



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 


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 


92 


65-9 


23-5 


_ 


_ 


0-8 


6-3 


_ 


3-5 


93 


53-5 


20-0 














6-5 


20-0 


94 


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' 


BA 


16 


15 


20-02 


ZnO 


11 


10 


12-05 


PbO 


8 


8 


12-40 


MgO 


8-2 


8-4 


37-13 


A1A 


20 


20 


25-89 


AA 


2 


2 


-131-7 


BaO 


11 


10 


12-59 


NajO 


16 


16 


7-03 


K 3 


1 


1 


5-98 


CaO 


32 


32 


9-46 


PA 


16 


16 





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. 


19 


J7I 


_':_' 


-o% 


20 


1-60 


1-62' 


-1 


21 


2-10 


J !.{ 


-1 


22 


1-93 


1-94 


-1 


23 


2-04 


1 <>x 


+ 3 


24 


2-04 


2-00 


+ 2 


25 


2-46 


_' U 


+ 1 


26 


2-00 


1-95 


+ 3 


27 


1-97 


1-97 





28 


2-27 


2-32 


-a 


20 


j Jl 


2-42 


-0 


30 


_' i:: 


2-09 


+ 2 


31 


1 s-j 


1-82 






No. 


1000 K 


Calc. 


Diff. 


32 


2-02 


2-08 


-3% 


33 


1-72 


1-75 


-2 


38 


2-44 


_' is 


-2 


86 


2-19 


2-19 





s; 


J-f>< 


J is 


+4 


88 


_>:,<> 


2-49 


-HO 


89 


148 


2-36 


+ 1 


90 


849 


_'!_' 


-2 


91 


2-40 


i-48 


-4 


92 


2-46 


B-00 


-2 




2-22 


2-18 


+ 2 


94 


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 : 



w. 


A' in cm" 1 . 7 sec' 1 


Difference. 
Obs.-Calc. 


Observed. 


Calculated. 


69 


0-001083 


0-001067 


+ 1% 


70 


1304 


1361 


-4 


71=27 


1409 


14MS 


+ 


:-' 


1433 


1495 


-4 


73 


1445 


1524 


-5 


74 


1470 


1416 


+ 4 


75 = 23 


1610 


1637 


-2 


76 


1650 


i:.s-_> 


+ 4 


77 


1832 


1764 


+ 4 


78 


isiil 


1919 


-3 


79 


1932 


MM 


-0 


80=5 


2267 


Jl's 


+ 3 


81 


1940 


L9M 


+ 1 


82 


1972 




-3 


83 


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 

F 



D 



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 



w. 


B. 


M. 


K. 


Interval. 


3a x 10 7 


Diff. 


Obs. 


Calc. 


39=11 


P. 


A. 


R. 


10 J '35-92-88 


110 


110 


+ 0% 


40=12 


M 


> i 


L. 


12-67-89-78 


137 


149 


- 9 


41=21 


M 


M 


0. 


7-16-91-8 


157 


175 


-11 




Wd. 


M 


9 


0-100 


161 


162 


- 1 


43 


ii 


,, 


R. 


,, 


168 


168 


+ 


44 = 36 


W. 


D. 


L. 


,, 


177 


194 


-10 


45 = 2 


p. 


A. 


R. 


14-4 -94-4 


202 


191 


+ 5 


46 


II 


ii 


0. 


15-7 -92-2 


236 


244 


- 3 


47 


II 


,, 


ii 


12-9 -97-6 


238 


241 


- 1 


48 


II 


., 


R. 


18-9 -93-1 


238 


220 


+ 8 


49 


II 


,, 


,, 


17-5 -94-9 


239 


240 


- 


50 


II 


,, 


0. 


19-8 -94-5 


241 


251 


- 4 


51=6 


H 


,, 


,, 


14-6 -92-2 


241 


254 


- 5 


a 


M 


M 


M 


18-7 -90-5 


265 


272 


- 3 


53=13 


J} 


|f 


R. 


20-3 -92-2 


261 


246 


+ 6 


54 


II 


,, 


0. 


9-95-93-3 


270 


240 


+ 11 


55 


1 5 


ii 


,, 


15-65-94-2 


271 


263 


+ 3 


56 


,, 


,, 


R. 


17-9 -97-2 


275 


254 


+ 8 


57 


M 


,, 


,, 


17-7 -92-7 


279 


295 


- 6 


58=20 


M 


,, 


0. 


24-5 -84-0 


280 


256 


+ 9 


59 


W. 


D. 


L. 


0-100 


290 


284 


+ 2 


60 


p. 


A. 


0. 


17'0 -95-5 


289 


263 


+ 9 


61 


s. 


D. 


L. 


0-100 


292 


314 


- 8 


62 


}> 


M 


>} 


,, 


300 


294 


+ 2 


63 


M 


f 9 


it 


,, 


806 


289 +5 


64 


> J 


,, 


,, 


,, 


305 


294 + 4 


65 


J} 


M 


,, 


,, 


314 


327 - 4 


66 


J 


,, 


j i 


it 


324 


319 + 2 


67 


p. 


,, 


,, 


,, 


.328 


330 


- 1 


68 





A. 


0. 


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, 



w. 


Observer. Method. 


Cooling. 


3a x 10' 


M 


Winkelmann 


Dulong-Petit 


Thermoregulator 


171 


> 


M 


ii 


Free air 


177 


51 


Pulfrich 


Abbe-Fizeau 


Cooling oven 


Ml 


> 


\Vinkelmann 


Dulong-Petit 


Free air 


244 


H 


Pulfrich 


Abbe-Fizeau 


Thermoregulator 


275 


M 


ii 


i 


(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 


W. 


10*a 


10" 6 


591" 


44 


5655 


0-272 


16'" 


51 


708-9 


387 


Verre dur 





738-fi 


390 



HYDROGEN Ti i K i ; M >.M ETER. 



Mark 


W. 


IWa 


1086 


59"' 


44 


r>6S-o 


0-245 


16"' 


51 


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" 


58 


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 


W. 


IW(A-A') 


IW(B-B') 


59'" 


44 


1695-8 


0-770 


16 111 


51 


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 


W. 


Si0 2 


B 2 3 


ZnO 


A1A 


AsA 


BaO 


NaaO 


K,0 


MnA 


O. 802 


5 


70-83 


14-0 


_ 


5-0 


o-i 


_ 


10-0 





0-07 


0. 627 


49 


68-24 


10-0 


2-0 





0-2 





10-0 


9-5 


0-06 


0. 1552 


28 


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 


t 


108a 


Diff. 


Obo. 


Calc. 


O. 802 


5 


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 


49 


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 


28 


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 

p 



-'.; 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 

m 

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 



uE 



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. 



w. 


P 


10 7 3a 


E 


\&K 


8 


c 


*r 


19 = 5 


G !.-> 


1S-5* 


7296 


2-267 


2-370 


0-204 


3-56 


20 


3-53 


280 


6068 


1-080* 


5-944 


0-079* 


1-17 


11 


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 


23 


7'52 


195* 


7952 


1-610 


3-532 


0-138* 


2-79 


24 


6-07 


250* 


5389 


1-365* 


3-578 


0-125* 


2-49 


25 


8-51 


249* 


6498 


1-946* 


2-572 


0-201* 


3-23 


26 


5-39 


248* 


5467 


1-323* 


3-879 


0-118* 


2-14 


27 


5-56 


295* 


6780 


1-409 


2-588 


0-189* 


1-49 


28 


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 


32 


8-32 


313* 


5862 


1-404* 


2-668 


0-178* 


2-47 


33 


5-32 


252* 


5512 


1-188* 


4-731 


0-096* 


1-96 


34 


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 


36 


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. 



w. 


W 


6j for Cube whose edge is 


2cm. 


1 cm. 


21 


4-10 


110-5 


148-0 


34 


4-06 





148-0 


19 = 5 


3-56 


95-5 





22 = 2 


3-45 


84-7 


103-5 


25 


3-23 


78-5 


103-5 


23 


279 


70-9 


90-5 


31 = 13 


2-51 


32-0 


-,<:, 


24 


2-49 


<;<;_> 


M* 


28 


2-32 


77-8 


88*4 


26 


2-14 


69*8 


88-5 


33 


1-96 


65-8 


87-0 


27 


1-49 





62-7 


20 


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 



w. 


n 


P 


10 7 3a 


E 


ei-e 


21 


0-250 


5-66 


157 


5471 


148 


34 


0201* 


7-92 


183* 


7090 


146 


19 = 5 


0-197 


6-76 


160 


7296 


140 


22 = 2 


0-274 


4-93 


202 


4S(,'_> 


111 


26 


0-226 


7-84 


249* 


6632 


110 


24 


0-232* 


6-01 


250* 


5389 


103 


23 


0-271 


7-21 


195* 


7972 


102 


31 = 13 


0-253 


7-42 


261 


6334 


101 


n 


0-239 


4-97 


209* 


5494 


82 


26 


0-224 


4-67 


L>4S* 


5464 


80 


28 


0-231 


6-09 


283 


6613 


75 


27 


0*286 


5-46 


295* 


6780 


63 


20 


o-Jiii 


3-28 


no 


0Q68 


51 



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. 


D 


Before boiling. 


After boiling. 


1878, Oct. 21 


+ 0'497 


+ 0'095 


0'40-2 


79, May 17 


507 


064 


443 


81, Jan. 27 


65 


20 


45 


81, July 22 


60 


27 


33 


82, May 22 


66 








83, June 7 


65 








83, Oct. 31 


68 


20 


48 



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. 


D 


Before boiling. 


After boiling. 


1878, Oct. 23 


+ 0-072 


-0-015 


0-087 


79, May 17 


069 


043 


112 


81, Jan. 27 


11 


+ -01 


10 


81, July 22 


10 


+ -01 


09 


82, May 22 


10 








83, June 7 


10 








83, Oct. :n 


10 


00 


10 



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 

Q 



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 


D 


Humboldt No. 2 (before 1835) 


0-86 


20-09 


04 





0-06 


J. G. Greiner F l (1848) - - 


1-48 


18-89 


08 





15 


J. G. Greiner/^ (1856) - 


3-75 


17-14 


22 





38 s 


J. G. Greiner F 3 (1872) - 


16-89 


3-56 





21 


38 


Ch. F. Geissler No. 13 (1875) - 


15-35 


3-97 





26 


40 


G. A. Schultze No. 3 (1875) - 


16-15 


3-95 





24 


44 


Rapps Nachf. F 4 (1878) - 


12-72 


10-57 





83 


-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". 



M4 



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. 


1 


1 


& 





S 

< 


D 


IV 


70 


_ 


13-5 


16-5 


_ 


0'08 


VIII 


70 


15 





15 





-08 


XXII 


66 


14 


14 


6 





1 -05 


XXXI 


66 


11-1 


16-9 


6 





1 -03 


17 m 


69 


15 


10-5 


' 


5 


1 -06 


20"' 


70 


7'5 


7-5 


15 





0-17 



GROUP B. 



No. 


* 


Q, 

es 
K 


e, 







$ 

<J 


1 


o 

a 

NJ 


I 


1 


3 


D 


II 


24 


7 


_ 


_ 


16 






53 






0-02 


V 


54 





16 











30 











09 


VII 


51 











1-8 


3-7 


27-7 





6-5 


9-3 


10 


IX 


63 


15 





8 





10 











4 


08 


X 


46 


8 

















40 





6 


09 


XI 


65 





18 





5 














12 


09 


XIX 


50 


15 














20 


15 








07 


XXIII 


57 


8 





20 


10 














5 


10 



1 II. 1025 ; see Art. 90. 



AFTER-WORKING AND THERMOMETRY. 
GROUP C. 



245 



No. 








o r 


o 


: 


9 


0" 


/> 




GC 


* 


'* 


'O 


< 


N3 


Pif 




14 m 


69 


14 





7 


i 


7 


2 


0-05 


16 111 


67-5 


14 





7 


_.-> 


7 


2 


0-05 


IS 1 " 


52 





9 








30 


9 


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 : 



. 


1 


| 


& 


1 


d> 

< 


2 


J 


D 


59"' 


72 


11 








5 


12 





0'02 


63" 1 


73-2 


18-5 





8-0 








0-3 


05 












1 





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. 


D 


Number of Days Elapsed. 


4 


21 


4*2 4<> 


66 


88 


135 


160 


175 


200 242 


285 


317 


447 


570 


1450 


1600 


U III 

16 

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 











0-04 


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- 


10 


















0-05 
0-24 


0-42 


0-09 
0-22 


u-l-2 


0-33 


0-16 


n.^o 


0-25 


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. 


D 


Time at 100 


Elevation 
of zero. 


14"' - 


0-05 


7 hours. 


0-0'2 


161" . 


05 


7 


01 


18 1 " - 


o.-> 


7 ,, 


01 


French Glass 


07 


8 ; , 


05 


English Glass 


18 


9 


16 


20'" - 


17 


8 


15 



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-oo 


o-oo 


o-oo 


10 


-o-oi 


-o-oi 


+ -01 


-0 -03 


-0-02 


+ 0-03 


20 


-0-07 


i ,;, 


-0 -02 


-0 -11 


-0 <*> 


o-oo 


30 


-0-08 


(1-1.7 


-0-02 


-0-12 


-0-05 


+ -02 


40 


-0-04 


-0-05 


+ 0-01 


-0 -08 


-0-02 


+ -09 


60 


+ 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. 


t 


Obs. 


Calc. 


Diff. 


Obs. 


Calc. 


Diff. 


Obs. 


Calc. 


Diff. 


5 


+ 48 


+ 48 





+ 75 


+ 75 





+ 57 


+ 57 





10 


44 


45 


-1 


73 


71 


+ 2 


55 


54 


+ 1 


15 


42 


42 





65 


68 


-3 


53 


51 


+ 2 


20 


39 


40 


-1 


64 


64 





51 


49 


+ 2 


25 


36 


37 


-1 


60 


60 





51 


46 


+ 5 


30 


Sfl 


34 


+ 1 


58 


57 


+ 1 


46 


4.3 


+ 3 


35 


34 


31 


+ 3 


53 


53 





43 


40 


+ 3 


40 


21 


28 


-7 


48 


50 


-2 


38 


37 


+ 1 


45 


18 


25 


-7 


46 


46 





32 


34 


-2 


50 


17 


22 


-5 


43 


42 


+ 1 


34 


31 


+ 3 


55 


15 


20 


-5 


38 


39 


-1 


26 


29 


-a 


61 


17 


16 


+ 1 


33 


34 


-1 


24 


96 


-i 


65 


11 


14 


-3 


26 


31 


5 


18 


_>;{ 


-5 


72-5 


10 


10 





22 


26 


-4 


18 


19 


-1 


78 


1 


6 


-5 


19 


22 


-3 


10 


IT. 


-5 


82 


7 


4 


+ 3 


16 


19 


-3 


LJ 


II 





91-5 


2 


- 1 


43 


11 


19 


-1 


11 


s 


+ 3 


96 





- 4 


+ 4 


7 


9 


-2 


8 


5 


+ 3 


MM, 


- 6 


- 6 





6 


6 





3 


3 






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. 


t 


Obe. 


Calc. 


Diff. 


Obs. 


Calc. 


Diff. 


Obs. 


Calc. 


Diff. 


5 


BM 


+ 526 





+ 246 


+ 246 





-110 


-110 





10 


ra 


($] 


(i 


243 


245 


- 2 


]_>:> 


112 


-13 


15 


521 


520 


+ 1 


J4(i 


244 


- 4 


130 


11. -> 


-13 


20 


:.17 


515 


+ 2 


239 


243 


- 4 


186 


120 


-15 


80 


514 


508 


+ 6 


240 


240 





135 


126 


- 9 


30 


BQ7 


500 


+ 7 


236 


238 


- 2 


145 


133 


- 12 


35 


501 


491 


+ 10 


236 


235 


+ 1 


150 


142 


- 8 


40 


490 


480 


+ 10 


229 


231 


- 2 


150 


152 


+ 2 


45 


473 


468 


+ 5 


227 


225 


+ 2 


158 


163 


+ 5 


50 


459 


454 


+ 5 


223 


220 


+ 3 


170 


176 


+ 6 


55 


428 


439 


-11 


2Uf 


JKi 


- 1 


195 


190 


o 


61 


427 


419 


+ 8 


216 


209 


! + 7 


210 


209 


- 1 


65 


407 


404 


+ 3 


210 


203 


+ 7 


213 


222 


+ 9 


72-5 


386 


375 


+ 11 


200 


193 


: + 7 


243 


246 


+ 3 


78 


361 


351 


+ 10 


199 


184 


+ 15 


240 


271 


+ 31 


82 


352 


332 


+ 20 


188 


177 


+ 11 


1 265 


288 


+ 23 


01-5 


313 


285 


+ 28 


179 


160 


+ 19 


'278 


332 


+ 54 


96 


292 


261 


+ 31 


169 


1,'1 


+ 18 


335 


354 


+ 19 


100 


238 


238 





143 


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. 





1 


2 


3 


4 


5 


6 


7 


8 


9 








1 


1 


2 


3 


3 


4 


5 


5 


6 


10 


7 


8 


8 


9 


10 


10 


11 


12 


13 


13 


20 


14 


15 


16 


17 


17 


18 


19 


20 


21 


21 


30 


22 


23 


24 


25 


26 


27 


27 


28 


29 


30 


40 


31 


32 


33 


34 


35 


35 


36 


37 


38 


39 


50 


40 


41 


42 


43 


44 


45 


46 


47 


48 


49 


60 


50 


51 


52 


53 


54 


55 


56 


57 


58 


60 


70 


61 


62 


63 


64 


65 


66 


67 


68 


69 


71 


80 


72 


73 


74 


75 


76 


78 


79 


80 


81 


82 


90 


83 


85 


86 


87 


88 


90 


91 


92 


93 


95 


100 


96 





















DEPRESSION OF THERMOMETER OF 59 IH IN THOUSANDTHS 

OF A DEGREE. 



Deg. 





1 


2 


3 


4 


5 


6 


7 


8 


9 











1 


1 


2 


2 


3 


8 


4 


4 


10 


5 


5 


6 


6 


7 


7 


8 


8 


8 


9 


20 


9 


10 


10 


11 


11 


11 


12 


12 


13 


13 


30 


14 


14 


14 


15 


15 


15 


16 


16 


17 


17 


40 


17 


18 


18 


19 


19 


19 


20 


20 


20 


21 


50 


21 


21 


22 


22 


22 


23 


23 


23 


24 


24 


60 


24 


25 


25 


25 


26 


26 


26 


27 


27 


27 


70 


27 


28 


28 


28 


29 


29 


29 


29 


30 


30 


80 


30 


30 


31 


31 


31 


31 


32 


32 


32 


32 


90 


33 


33 


33 


33 


34 


34 


34 


34 


34 


35 


100 


35 





















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 



D 

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 



-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 


M 


,, 7 min. at 78 -5 


038 


-0 -189 


it 


7 78-5 


035 


207 


> 


64 78-5 


033 


310 





56 78-5 


031 


337 


l 


,,32 ,, 100 -2 


018 


510 


i 


22 78-5 


028 


411 


September 18. 


rest at 13" 


060 


267 


ii 


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 


n 


36 


78 '466 


78 -648 


ii 


36 


491 


491 


it 


39 


483 


646 


ii 




Changing to 79 '5 


M 


52 


In alcohol vapour. 


n 


59 


4SD- 


460 


II 


58 


493 


592 


ii 


2 A. 4m. 


492 


466 


II 


12 A. 9m. 


In alcohol vapour. 





9 


492 


466 


tt 


15 


486 


571 


> 


11 


494 


460 


t 


21 


492 


571 


n 




Comparison at 100-2 





23 


491 


562 


,, 


3 h. 26 m. 


In alcohol vapour. 


> t 


26 


495 


546 


N 


33 


469 


334 


n 


32 


495 


539 





35 


481 


347 


> 


33 


492 


546 


n 


39 


484 


356 


M 


36 


496 


538 





40 


480 


488 


M 


38 


492 


534 


ii 


44 


4SS 


174 


M 


43 


493 


*sa 


tt 


47 


487 


385 


H 


49 


*M 


480 




i 


54 


488 


m 


Sept, 18, 


1 _>/,. 59m. 


In alcohol vapour. 


tt 


66 


4<i:i 


080 


N 


1 A. 6m. 


78-703 


78-476 


tt 


Ik. 1m. 


481 


516 


it 


18 


706 


500 


,, 


4 


480 


-000 


>i 


II 


704 


506 


If 


19 


In alcohol vapour. 


tt 


47 


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 


M 


+ -01 


02 


04 


03 


665 


August, 1886 


01 


03 


05 


04 


667 





02 


04 


05 


03 


668 


> 


02 


05 


06 


04 


669 





03 


06 








670 


September, 1886 


00 


03 


04 


04 


671 


August, 1886 


05 


09 


09 


04 


672 





05 


08 


08 


03 


673 





03 


07 








8,">0 


February, 1888 


00 


03 








853 


May, 1888 


00 


04 









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). 



Mi 



.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. 


6* 


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 


13 


1 '89 


6 '56 


1:3-5 


16 


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, 



F, 



38 



=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 


+ i-o 


+ 2'l 


5 


1 -3 


1 -5 


2 -7 


5 


1 -5 


1 -7 


3 -1 


5 ,, 


1 -6 


1 -8 


3 -4 


5 


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 


15 


9 450 


103 -2 


105 '.' 


108 -1 


20 


,,18 ,, 450 


104 -4 


106 -7 


108 -9 


.. 22 


,,5 ,,450 


104 -4 


106 -6 


109-1 


23 


4 400 


104 -5 





109 -1 


25 


12 420 


104 -4 





109-0 


Sept. 4 


41 days' rest 


104-4 





108 -9 


6 


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 - 



A 

1-0 
1-6 
1-7 
2-4 
3-2 
4-8 



D 

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. 


D 


Fl 


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. 


D 


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. 

8 



-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 


23 


300 


28 


323 


47 


277 


15 86 


33 


425 


33 


458 


66 


392 


., 80 


41 


534 


41 


575 


83 


492 


U .. 7:. 


49 


626 


49 


674 


97 


577 


30 7" 


54 


701 


54 


755 


109 


646 


35 65 


59 


759 


59 


818 


118 


700 


40 60 


62 


801 


62 


863 


124 


738 


45 55 


64 


826 


64 


890 


128 


761 


50 


65 


834 


65 


899 


129 


769 



The temperatures in the first column may be taken indifferently 



as 



, 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 -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 -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 t -r q 


T, 


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 


9 


+ 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. 



T< 


Ti-T, 


T* 


T t -T 9 


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" 



n 


Normal-Glass. 


Verre. dur. 


Diff. 


<r-*i 


-20 


+0-153 


+ 0-159 


. 


_ 


-10 


+ 0-067 


+ 0-067 











o-ooo 


-000 


o-ooo 


o-ooo 


+ 10 


-0-049 


-0-046 


-0 -003 


-0 -005 


20 


-0 -083 


-0 -075 


-0-008 


-o -008 


30 


-0 -103 


- -091 


-0-012 


-0-011 


40 


-0 -110 


-0 -097 


-0-013 


-OO12 


50 


-0-107 


-0-094 


-0-013 


-0 -013 


60 


-0-096 


-0-085 


-0-011 


-0 -012 


70 


-0-078 


-0-071 


-0 -007 


-0 -Oil 


80 


-0-O.V4 


-0-O.VJ -0-002 


-0 -008 


90 


-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 


r. 


T-T, 


59'" 


,._>-_>,;; 


Resi8t.-Gl. 


59"i 


122" 1 


Resist.-Gl, 





o-ooo 


o-ooo 


o-ooo 


50 


-0-02l 


+0-013 


-0'lL>6 


5 


-0 '009 


+ 0-001 


-0 -032 


55 


- -017 


+ -014 


-0-120 


10 


-0 -017 


+ -002 


-0-059 


60 


-0 -014 


+ -015 


-0 -112 


15 


- -022 


+ 0-003 


-0 -081 


65 


- -010 


+ -015 


-0 -102 


20 


-0 -026 


+ 0-004 


-0-098 


70 


-0 -006 


+ -014 


-0 -090 


96 


-0 -028 


+ 0-006 


-0 -112 


75 


-0-003 


+ -014 


-0-077 


30 


-0 -029 


+ 0-008 


-0-121 


BO 


-o-ooi 


+ -012 


-0-063 




-0-028 


+ -009 


-0 -127 


85 


+ 0-001 


+ -010 


-0 -048 


40 


-0-026 


+ -Oil 


-0 -130 


90 


+ -002 


+ -008 


-0-032 


45 


-0-024 


+ -012 


-0 -129 


95 


+ -002 


+ -004 


- -016 


50 


-0-021 


+ -013 


-0-126 


100 


-000 


-000 


-000 



FOR THERMOMETERS OF 59 m . 



T, 


T-T q 


T. 


T-T q 


T< 


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-T, 


'1\ 


T-T q 


T q 


T-T q 


T* 


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' 


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 

T 



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 : 



t 


(1 + 100/3) pt 


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 



t 


T 


t 


T 


t 


T 








325 


330 -9 


425 


440 -7 


100 


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), 



T 

2 2~ 



But by (8), . 



n 

~~ \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 : 





I. 


II. 


III. 


.-* 


I.-.1-3B 


159-89 


160-46 


71 


l.V' 


161-35 


162-lfi 


m 


15 


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 





I. 


II. 


III. 


t* 


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. 








1 


2 


3 


4 


5 


6 


7 


8 


9 








6 


12 


18 


23 


28 


33 


38 


43 


47 


10 


51 


56 


59 


63 


67 


70 


73 


76 


79 


82 


20 


85 


87 


89 


91 


93 


95 


97 


98 


100 


101 


90 


102 


103 


104 


105 


106 


106 


107 


107 


107 


107 


40 


107 


107 


107 


107 


107 


106 


106 


105 


104 


104 


50 


103 


102 


101 


100 


98 


97 


96 


95 


93 


92 


60 


90 


89 


87 


85 


84 


82 


80 


78 


76 


74 


70 


72 


70 


68 


66 


64 


62 


59 


57 


55 


52 


80 


50 


48 


45 


43 


41 


38 


36 


33 


31 


28 


90 


26 


23 


21 


18 


16 


13 


10 


8 


5 


3 


100 
























Y.u.rEs OF t lQ t H IN THOUSANDTHS OF A DEGREE. 








1 


2 


3 


4 


5 


6 


7 


8 


9 








7 


13 


19 


25 


31 


36 


41 


47 


51 


10 


56 


61 


65 


69 


73 


77 


80 


84 


87 


90 


20 


93 


96 


98 


100 


103 


!(>--. 


107 


109 


110 


112 


:> 


IKS 


114 


115 


116 


117 


118 


119 


119 


119 


120 


40 


120 


120 


120 


120 


119 


119 


118 


118 


117 


116 


50 


116 


115 


114 


lit 


111 


110 


109 


107 


106 


104 


60 


103 


101 


99 


97 


95 


94 


92 


90 


87 


85 


70 


83 


81 


78 


76 


71 


71 


69 


66 


64 


61 


80 


58 


:><; 


:,:< 


50 


48 


r, 


42 


39 


36 


n 


90 




27 


24 


Jl 


18 


15 


12 


9 


6 


3 


100 


ii 





















300 .IKNA GLASS. 

VAI.I'KS >F t. t H IN TiiorsANimis OF A DEGKKK. 








1 


2 


3 


4 


5 


6 


7 


8 


9 








3 


6 


9 


11 


14 


16 


18 


20 


22 


10 


_>t 


20 


27 


_N 


30 


31 


82 


33 


34 


80 










37 


87 


87 


38 


38 


38 


88 




38 


37 


:>7 


87 


37 


36 


86 


86 


35 


34 


40 


84 




89 


82 


3i 


30 


29 


28 


-'7 


27 






_'.-. 


24 


23 


22 


21 


20 


19 


18 


17 




16 


15 


14 


1 l 


13 


12 


11 


10 


9 


8 


70 


8 


7 


(5 


5 


5 


4 


3 


3 


_' 


1 


80 


1 











-1 


-1 


-1 


-1 


_ o 


> 


90 


_' 


-2 


-2 


-2 


-2 


-1 


-1 


-1 


-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 


07 


08 


04 


-15 


12 


13 


07 


-20 


17 


19 


10 


-25 


23 


25 


14 


-30 


30 


32 


18 


-35 


38 


40 


23 



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. 


X. 


18 1 " 


V. 


XI. 


16" 1 


20 sees. 


0011 


0018 


0027 


40M 


MM 


0038 


0065 


40 


06 


08 


21 


24 


28 


25 


45 


60 


04 


06 


17 


15 


22 


19 


33 


<* H 


03 


03 


14 


11 


18 


13 


25 


120 








10 


08 


14 


09 


19 


180 ,, 








08 


05 


10 


05 


14 


Temperature. 


ir 


1 


4 


8 


4 


12 


r 



JENA GLASS. 

AFTER-WORKING. 



After. 


VIII. 


XIX. 


VII. 


Thuring. 


XXII. 


17111 


20 sees. 


0082 


0085 


0088 


0106 


0150 


0323 


40 


57 


57 


73 


95 


138 


2:>9 


60 


42 


40 


59 


84 


124 


221 


90 


30 


27 


47 


75 


113 


185 


120 


22 


19 


37 


66 


94 


157 


180 ,, 


14 


11 


23 


57 


85 


128 


Temperature. 


10 


4 


3 


1 


16 


3 



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 ,, 


05 


14 


39 


75 


96 


7 














79 


10 








21 


54 


57 


15 











42 


32 


Temperature. 


4 


3 


1 


16 


3 



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. 


20 


0065 


0069 


0106 


0107 


40 


45 


56 


95 


92 


60 


33 


45 


84 


85 


90 


86 


36 


75 


77 


120 


19 


29 


66 


66 


180 


14 


20 


57 


57 


Temperature. 


7 





1 






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. 


20 


0065 


0069 





0036 





0106 


0107 


40 


45 


56 


0055 


24 


0024 


95 


92 


60 


33 


45 


45 


15 


21 


84 


85 


90 


25 


36 . 


36 


11 


18 


75 


77 


120 


19 


29 


31 


08 


14 


66 


66 


180 


13 


20 


24 


05 


12 


57 


57 


Temperature. 


7 








8 





1 






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 



a 



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, 


- 


- 


50 


1-05 


1-06 


Lithia glass, 


- 


- 


10 










II. 


X. 


16 m . 


VIII. 


XIX. 


Soda glasses, 


02 


09 


05 


08 


07 






18 1 ". 


IV. 


V. 


XI. 


Potash glasses, 


- 


- -05 


08 


09 


09 



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. 


E. 


D. 


n. 


328 


1-490 


18 


8490 


0-02 


IV. 


253 


2O81 


11 


6595 


n -i.s 


V. 


233 


1-504 


36 


5980 


0-09 


VIII. 


281 


2-260 


82 


6865 


(l -us 


X. 


237 


1-630 


27 


7180 


0-09 


XI. 


231 


1 V_N 


38 


7iN< 


-09 


16'" 


241 


2-100 


65 


7543 


-05 


17"' 


342 


1-869 


323 


6781 


1 -06 


18 1 " 


162 


1-588 


36 


7810 


-05 


XIX. 


271 


1-690 


85 


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, 



w. 


Before. 


After. 


Diff. 


W. 


Before. 


After. 


Diff. 


19 


7540 


7672 


1'8% 


33 


5477 


5494 


0'3% 


21 


5468 


MM 


_':. 


34 


7180 


7349 


2-3 


22 


4906 


MM 


2-4 


35 


7314 


7524 


2-9 


23 


7992 


8146 


1-9 


38 


7465 


7649 


_>:. 


24 


.-,4-jc, 


5433 


O'l 


84 


7401 


7564 


2-2 


25 


6766 


6983 


:; _' 


85 


74 16 1 


7589 


2-3 


26 


540] 


5600 


0-8 


86 


6097 1 


6218 


20 


28 


6599 


6669 


1-1 


87 


7971 


8340 


4-6 


29 


MM 


6650 


0-2 


ss 


7461 


7551 


1-2 


30 


6014 


6159 


J-4 


89 


Tls.i 


7234 


07 


31 


6373 


6441 


1-1 


91 


6572 


6687 


1-7 


32 


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. 

X 



: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 

(c) Losses of weight, 1-8 0'6 

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. 


2 

It 
H 

U 
1 


K 2 O 
K 2 0, 
K 2 0, 
K 2 0, 
K 2 0, 


i 
1 

i 

1 


CaO 
CaO 
CaO 
CaO 


II. 
IV. 
VI. 
VIII. 

X. 


2 
11 
li 

u 

1 


NajO 

Na 2 0, 
Na 2 0, 
Xa.A 
Na 2 0, 


i 

1 
I 

i 


CaO 
CaO 
CaO 
CaO 



This gives as their percentage compositions : 





SiO 2 . 


K 2 0. 


Na 2 0. 


CaO. 


I. 


65-7 


34-3 








II. 


74-4 





25-6 





III. 


66-8 


30-6 





2-6 


IV. 


74-6 





2'2'5 


2-9 


V. 


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 


X. 


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. 



y 






In 60 c.c. of solution. 


| 


To 


Quantity. 








_ 




1 


1 Si0 2 . 




Si0 2 . 


KjO. 


Na. 2 0. 


*-' x y8 en 

in alk. 


To 


fc 














1 Si0 2 . 






gm. 


mg. 


mg. 


mg. 


mg. 




I. 


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 


V. 


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 


X. 


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 


i 


42-4 


223-5 


1 :5'3 


I M 


17-4 


32-1 


1:1-8 


1 


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 


1 


2-97 


4-54 


1 : 1-5 


1 


1-0 


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 


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. 


1 


Yellow alkaline glass - 


60-49 


15-41 


13-25 


5-42 





_' 


Inferior Thuringian - 


69-92 


16-5 


6-6 


3-75 





3 


Glass of Tittel & Co. - 


71-5 


14-3 


7-1 


6-7 





4 


Schilling's flask glass - 


75-2 


11-9 


4-2 


8-3 





5 


Kavalier Bohemian - 


78-3 


1-4 


13-3 


6-8 





6 


Rhenish window-glass 


71-2 


13-5 





13-4 





7 


Lead crystal ; Ehrenfeld - 


56-0 


0-6 


12-1 





31-2 


8 


Green flask ; Charlottenb. - 


63-5 


9-5 


1-3 


14-0 





9 


Jena thermometer 16 m 


67-5 


14-0 





7-0 





10 


Jena lead glass 483 


44-75 


0-2 


7-3 





47-0 


11 


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. 


mg. 


mg. 


mg. 


to 1 SiO,. 


1 


19-451 


84-7 


59-0 


98-5 


35-6 


1-5 


2 


19-125 


14-3 


18-1 


59-0 


18-4 


4-8 


3 


19-304 


6-9 


6-5 


14-4 


4-8 


2-7 


4 


19-079 


5-3 


1-7 


4-8 


1-5 


1-1 


5 


18-468 


5-5 


5-3 





0-8 


0-6 


6 


18-963 


4-3 





4-6 


1-2 


1-0 


7 


23543 


1-9 


7-0 





1-2 


2-3 


8 


20-162 


3-2 





2-7 


0-7 


0-9 


9 


20-000 


2-7 





3-2 


0-8 


1-2 


10 


27-814 


1-5 


1-8 





0-3 





11 


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. 


1. 


Kahler & Martini, 


5 


2. 


Schweig & Co., Weisswasser, 


10 


3. 


Kavalier, Sazava, Bohemia, 


12 


4. 


Bohemian Hollowglass, 


14 


5. 


Fettke & Ziegler, Doebern, - 


25 


6. 


Leybolds Nachf., Cologne, - 


53 


7. 


Bohemian Glass, 


66 


8. 


Warmbrunn, Quilitz & Co., 


66 


9. 


Schilling, Gehlberg, 


83 


10. 


Tritschler & Co., Stuttgart, 


309 


11. 


Lambach, Bavarian Forest, - 


435 



No. 


Bottles. 


Alkali. 


I. 


Bohemian Hollowglass, 


23 


II. 


Warmbrunn, Quilitz & Co., 


30 


III. 


Fettke & Ziegler, Doebern, - 


31 


IV. 


Schilling, Gehlberg, 


42 


V. 


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 

Y 



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. 



I. 


23 


2-9 


3-0 


2-0 


0-66 





11. 


30 


6-7 


4-5 


1-5 


0-8 


0-25 


111. 


81 


6-8 


4-4 


2-6 


T4 


0-5 


IV. 


42 


16 


11 


8-0 


5-2 


2-8 


V. 


76 


28 


21 


15 


10-9 


5-3 


VI. 


189 


53 


16 


9 


6-2 


3-1 


VII. 


202 


65 


20 


11 


8-8 


4-5 


VIII. 


340 


101 


16 


9 


6-9 


3-9 


IX. 


499 


111 


53 


28 


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. 


2 


23 


4-4 


4-4 


4-4 


4-2 


4.4 


3-8 


2-9 


3-8 


3-8 


6 


137 


52 


31 


25 


19 


18 


17 


15 


16 


16 


9 


360 


129 


94 


75 


69 


60 


55 


54 


52 







I 



















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. 




20 


80 


Kahler & Martini, 


Flasks 


1-0 


6-7 


Schweig ft Co., - 





1-5 


8*9 


Kavalier, - 


u 


2-1 


8*9 


Fettke & Ziegler, 


ii 


3'7 


29 


Normal-thermometer 16 m , - 





4-0 


43 


Bohemian hollowglass, 


Bottles 


10 


4.S 


Bohemian hollowglass, 


Flasks 


7"2 


78 


Warmbrunn, Quilitz & Co., 


Bottles 


8-9 


81 


Fettke & Ziegler, 


u 


: 


107 


LeyboldsNachf., 


Flasks 


13 


176 


Lambach Works, 


ii 


13 


203 


Warmbrunn, Quilitz & Co., 


> 


17 


211 


Bohemian glass, - 


> 


21 


200 


Schilling, - 


ii 


26 


270 


Schilling, 


Bottles 


21 


341 


Stender .... 




41 


279 


Leonhardi, . - - - 


PI 
ii 


41 


378 


Schweppnitz Works, - 


u 


50 


331 


Kiihler & Martini, 


,, 


51 


405 


Tritschler & Co., - 


Flasks 


40 


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 


ku 


CaO 


\10 s + FeA 


L 


Kahler ft Martini, 


7.VI 


<K{ 


M 


)'.. 


1-0 


2. Schweig ft Co. , - 


78-8 


KM 


3-6 


7-2 


0-3 




Kavalier, - 


79-1 


6*4 


6-7 


76 


0-2 


I. 


Bohemian hollowglass, 


7ii-f> 


9-2 


5-5 


M> 


M,, 


;. 


Laybolds Nachf., - 


Tfrfl 


MH 


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 


1 


75-9 


7-6 5-8 


10-4 


0-3 


1 1 _' 


4 


76-6 


6-7 6-6 


9-5 


0-6 


11-0 


5 


76-8 


6-4 6-2 


100 


0-4 


10-4 


6 


76-3 


8-3 7-0 


8-1 


0-3 


12-7 


7 


75-1 


4-9 11-8 


7-6 


0-5 


12-8 


8 


:: ; 


10-0 4-3 


7-8 


0-3 


12-6 


9 


77-2 


10-1 4-6 


7-7 


0-4 


13-0 


10=16 m 


67-5 


14-0 


70 


2-5 


14-0 


11 


70-6 


14-3 0-6 


11-2 


2-9 


14-6 


15 


74-1 


9-0 9-7 


6-8 


0-4 


15-4 


16 


68-9 


13-7 6-7 


7-2 


3-2 


18-6 


17 


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 


->: 


ri 


2= n>.V 


J-l 


6-3 


:M> 




10-7 


_>S'4 


2-65 


4 


8-9 


JS-2 


:M7 


5 


I:M 


Jti-x 


9-00 


6 


II-M 


56 


| INI 


7 


14*0 


4.-, 


s-iq 


B 


149 


50 


40 


9 


17- 


66 


:'.:-. 


10= Hi'" 


16-6 


65 




11 


27 


<>s 




15 




m 


8-78 


16 


77 


<i.->4 


8*5 


17 


74 




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 


4 


76-6 


6-7 


6-6 


9-5 


0-6 


11-0 


7 


7.V1 


4-9 


11-8 


7-6 


0-5 


l-J-s 


9 


77-2 


10-1 


4-6 


7-7 


0-4 


13-0 


10= 16 1 " 


<;:.-> 


14-0 





7'0 


2-5 


14-0 


11 


:<><; 


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* 














' 





16 


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 


3-5 


6-0 


4 


11-2 


5-6 


4-6 


2-65 


7 


51-3 


15-4 


11-1 


3-35 


9 


67 


16*4 


147 


3-57 


10=16 m 


34 


6-4 


6'4 


4-4'J 


11 





7-3 


7-1 




12* 


63 


Hi"_> 


l>-7 


\:-> 


13* 


:;: 


8-3 


8-3 


:;; 


14* 


87 





29 





16 


126 


61 


52 


14 



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. 



v 


SiO, 


Na.,0 


K.,0 


CaO 


ALA 


MgO 


PbO 


ZnO 


MnO 


BaO 


A&A 


BA 


PA 




60 


62 


94 


56 


ioa 


40 


228 


81 


70 


153 


198 


70 


142 


1 


67-6 


16-3 




10-0 


._,.._>,, 






_ 


0-17 


_ 






_ 


4 


77 






>_> 


0-44 


























5 


7-J 1 




L'31 


8-96 


-J-11 











0-25 














6 






11-1 


_>{>'. 














0-09 














7 


wo 


u B 





7-7J 


1-52 








5-35 


0-18 








1-77 





8 


78-0 


.vtw> 


6-61 











9-55 





0-08 





0-08 








9 


509 

















49-0 





o-oi 





0-07 








10 




5-1 


10-1 


9-62 














0-09 





0-06 


1-36 





11 




11-6 


2-75 


9-03 


0-40 











trace 














18 


81-8 


1-41 


8-87 


7-61 


0-31 


























u 


68-2 


13-9 


4-53 


10-9 


2-18 











0-3 














14 




8-28 


9-49 


7-97 











2-36 


0-09 





o-io 


0-91 





15 


:::! 


14-J 


4-O.S 


7-33 


0-24 


0-31 








0-18 














16 


68-8 


Ifl 


4-0 


11-2 


1-7 











0-2 














17 


70-6 


l.V! 


3-9 


8-1 


1*1 











0-4 














18 


72-1 


17-5 


3-9 


4-9 


1-3 











0-3 














19 


65-6 


1-23 


6'47 











1-03 


12-2 


0-08 


9-97 


0-11 


3-27 





90 


57-3 





3-58 














12-5 


0-16 


21-0 


0-13 


5-42 





81 


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 





0-06 


5-90 





_'t 


74-9 


5-52 


10-9 














1-69 


o-io 


4-25 


0-14 


2-44 





25 


61-7 





24-9 














10-8 


0-07 


2-38 


0-11 








26 


65-4 





4-68 











29-7 





0-15 





0-11 








27 


71-8 


0-77 


8-08 











19-7 





0-12 





0-09 








28 


76-0 


1-93 


7-39 











14-4 





0-14 





0-11 








29 


77-0 


0-80 


10-6 








0-12 


11-5 


















n 








14-8 





11-3 


11-6 














0-72 


4-98 


56-6 


31 


~ 


4-12 


~ 


~~ 


10-0 


2 


6-87 


12-6 








0-15 


66-3 





The following descriptions are added : 



1. 

2 
* 

5. 

6. 

7. 

8. 

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 



12 



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 





5 


1 


2 


3 


4 




k 


M 


k 


M 


k 


k 


k 


M 


After 1 day 


16 


0-48 














__ 





5 days 


33 


1-0 


1-6 


0-09 








. 





10 


54 


1-6 


2-7 


0-15 














. 20 








5-0 


0-27 


0-8 


0-6 


0-20 


0-04 


40 














1-6 


0-7 








80 


120 


3-6 


12 


0-65 


4-0 


1-7 


0-49 


0-09 


160 








22 


1-2 














7 hours at 80 


800 


24 


69 


3-7 


49 


2-7 





_ 


19 


1250 


37 


100 


5-4 


93 


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, 



8M 



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 . 


7 


136 


0-15 


18.6 


11 


189 


0-15 


210 


4 


281 


0-11 


156 


1 


357 


0-21 


568 


12 


405 


0-25 


184 


5 


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. 


to 


K 


* 


Per cent. 
Dissolved. 


19 


120 


50 


8 





20 


18(1 


80 


10 





21 


210 


130 


15 





22 


270 


130 


7 





4 





170 








f 
i 


270 


180 


10 


2-0 


10 


380 


200 


80 





28 


490 


220 


8 





11 


360 


220 


7 


2-7 


12 


320 


230 


7 


7 


13 


440 


2*) 


40 


3-5 


14 


420 


320 


12 





15 


730 


420 


50 





16 


600 


460 


20 


5 


24 


680 


570 


30 





1 





640 








17 


1200 


860 


60 





18 


2600 


2200 


200 


13 


5 





2300 








25 


7000 


6800 


500 


30 


9 


5 


1 








26 


40 


9 








27 


300 


100 


7 





28 


360 


130 


7 





8 


350 


190 


6 





29 


800 


350 


30 





30 


500 


320 


20 


_ 


81 


1000 


1000 


60 


50 



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. 


1 





0-17 


0-075 


3 


1 


0-18 


069 


7 


K> 


0-35 


068 


13, 14. 1 , 


16 


0-43 


044 


20, 21 


22 


(I.-,:; 


0425 


23 


23 


( c.v, 


0412 


J7 


24 


.i-:,7 


0409 


31 


|] 


Mi-i 


0409 


35 


39 


0-82 


ii in:, 


36 


39 


u-s-_> 


4404 


_' 


55 


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 


I. 


II. 


G 


4 


5 


7 


11 


12 


2 minutes, - 9 


6 


22 


35 


120 


46 


55 


33 


1 hour, 


14 


11 


26 


44 


260 


62 


71 


41 


Iday, 


18 


16 


33 


77 


580 


88 


104 


75 


6 days, 


22 


18 


38 


99 


850 


111 


130 


97 


Second supply after 1 
1 week, / 





7 





30 


570 


34 


36 


42 



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 


i 


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 


4 


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. 


A' 


A" 


Starke. 


Lowe. 


. 


- 196 


Berate crown, 


5-48 


5-25 


5-05 


0.2238 


Borosilicate crown, 


6-20 


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. 


K 


V 


S. 196 


11 


60-4 


O. 2238 


035 


63-4 


S. 218 


07 


69-9 


0. 1580 


06 


56-9 


0. 1353 


145 


44-3 


0. 1993 


11 


56-4 


0. 1542 





58-5 


0. 2074 


175 


52-0 


0.2051 


06 


36-8 


S. 99 


09 


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. 


*M 


t 


It 


R' 


21 
cm. 


w/> 


I. 


1-9303 


6128 


l-827 


2-978 


5-010 


0856 


II. 


1-7938 


6157 


1 -439 


2 -335 


5-005 


im 


III. 


1-7408 


6157 


1 -161 


1 -910 


5-010 


0549 


IV. 


1-6797 


6116 


959 


1 -563 


5-010 


0449 


V. 


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. 


V 

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. 


a 


ft 


7 


O. 82 


00496 


00510 


00412 


667 


698 


*M 


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 


7W 


872 


2-54 


O. 


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. 


V 

n-1 

A 


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. 


a 


/5 


7 


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 


n 


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 


ra 


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 


O. 


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:: 


M 


3-67 



JENA GLASS. 



Trade 
No. 


Description. 


Index for 
D. 


Mean 

l>is]U.TSi.>M 

CtoF. 


V- 

n-1 

A 


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. 


a 




7 


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 


o. 


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 


<0 


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. 


16 


465 


Uranium glass bright yellow. 
strongly fluorescent 






440MI 


Nickel glass bright yellowish 
brov 11 


red, yellow, weakened 
green, greatly weak- 
ened blue. 


11 


414"' 


Chrome glass 


yellowish green 


yellowish green, almost 
like the Zettnow filter. 


10 


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. 


5 


4:<7"< 


Green filter 


dark green 


green ; and in thin layer, 

blue. 


5 


438" 1 


Green filter 


dark green 


green. 


5 


; per glass 


blue, like < 


green, blue, violet. 


B 1-J 


447'" 


Blue violet glass 


blue, like cobalt 
glass 


blue, violet. 


5 




Cobalt glass 


blue 


blue, violet, extreme 
red. 


4 :. 


450"' 


\i kelglaw 


dark violet 


violet O-Jf, extunu' 
red. 


fi 




Violet glass 


dark violet 


violet O-H slightly 
weaktMu-d; withdau- 
i Humiliation, ex- 
treme red. 


7 


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. 























10 


7 


7 


1 


9 


10 


6 




14 


14 


4 


18 


20 


14 


30 


21 


22 


7 


28 


31 


23 


40 


27 


31 


13 


-S7 


42 


88 


50 


33 


40 


19 


47 


52 


46 


60 


40 


50 


27 


57 


64 


68 


70 


46 


61 


36 


67 


75 


72 


80 


52 


72 


46 


78 


86 


88 


90 


57 


83 


58 


89 


98 


105 


100 


63 


96 


71 


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 


17 


47 




+ 20 


- 50 


- 81 




a 


+ 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 





4 


17 


-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. 


10 


:>(j 


B7 


1 


20 


93 


93 





30 


113 


112 


-1 


40 


1-20 


116 


-4 


50 


116 


110 


-6 


60 


103 


96 


-7 


70 


83 


76 


-7 


BO 


58 


52 


-6 


90 


30 


26 


4 











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 


19 


-15 


132 


13 


-10 


081 


08 


- 5 


037 


04 



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. 


10 


M 


56 


7 


17 


91 


M 





10 


- 83 


93 in 


26 


1 


30 


i".-; 113 


in 29 39 38 


1 


40 -110 120 


10 


26 


34 


_> 


60 -107 i 116 ! 21 30 26 


4 


60 - 96 ' 7 14 


21 


16 


5 


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. 


8. 


/-;. 


/JL. 


3a . 10 7 . 


n. 


S. 205 


2 = 22 


2-243 


4800 


0-274 


202 


1-5075 


0. 428 


42 


-2 -4,-); 


4720 


0-268 





1-5123 


O. 658 


21 


2-758 


5470 


0-250 


157 


1 -5452 


0. 2154 


47 


3-115 


6100 


0-222 





1 -5700 


0. 1571 


26 


3-88 


5470 


0-224 





1 -6440 


O. 500 


33 


4-731 


5500 


0-239 


241 


1-7510 


S. 57 


20 


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. 


p 

(a 


274 


0908 


289 


306 


335 


364 


427 


2 


166 


0228 


182 


213 


264 


319 


466 


p 

V 


182 


060 


187 


195 


204 


202 


218 


1 

V 


110 


015 


118 


135 


160 


182 


237 



Ky means of the equations 

<,-<* _n-n x _q 



p 



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 

tu 

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 

ct 

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, 


33 


90 


i-::; 


374 


411 


602 


879 


339 


37C 


596 




69 


906 


2-13 


3-62 


63 


920 


L>-:;I 


4-05 


-06 


014 


21 


*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. 

(c) ON ARSENIC IN GLASS. 

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. 

U. 

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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