The production of elliptic interferences in relation to interferometry 2.

104 Pages·1913·5.457 MB·English

by  Carl Barus

UNIVERSITY OF CALIFORNIA
AT LOS ANGELES

THE
PRODUCTION OF ELLIPTIC INTERFERENCES
IN RELATION TO INTERFEROMETRY
PART
II
BY CARL BARUS
HazardProfessorofPhysics andDean of the GraduateDepartment
in Brown University
WASHINGTON, D. C.
Published by the Carnegie Institution of Washington
1912
CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 149, PART II
PRESS OFJ. B. LIPPINCOTT COMPANY
PHILADELPHIA, PA.
2
1
^r.
PREFACE.
The present report is, in the main, an extension of my work on the
displacementinterferometerdescribedintheprecedinginvestigation (Pub-
lication No. 149 of the Carnegie Institution of Washington); but beyond
this, itis a contributionto the theoryofcoronas andtheirpractical appli-
cation for the measurement of sizes of fog-particles in cloudy condensa-
tion. Inotherwords, ifthe source oflight isnot simple, but a doublet of
two interfering beams as in chapter VI, indistinguishable from a simple
source in case of white light, the coronas must show concentric dark
interference rings, for the same reason that the spectra in case of the
gratingshowellipticloci ofinterference. Itistherefore fromrings ofthis
general character that measurements of precision with coronas may be
obtained. In its practical aspects chapter VI deals with the production
ofellipticinterferenceswithplanereflectinggratingsinsteadoftransparent
glass gratings, as the former are much easier to rule. Again, the special
type of linear fringes, produced by identical halves of a reflectinggrating
withtheirrulingsparalleltotheslitandnearlyinthesameplane,probably
has a direct bearing on the theory of coronas, as in both cases an inter-
ference phenomenonis superimposed on the diffractions.
In chaptersVII,VIII,and IX I haveincludedcertainincidental experi-
ments onfog-particlesmadebyaidofthe coronasofcloudy condensation.
The first investigation showsthat the angularaperture of coronas isinde-
pendent of the thickness of the layer of fog, single and triple layers, each
about 6 inches thick, giving the same (continuous) corona. The next
investigation adduces the curious result that when the diameter and size
of the fog-chamber diminishindefinitely relative to the size oftheexhaust
pipe, its efficiency does not uniformly increase, but that it is rather more
efficient for the (virtually) larger nuclei and less efficient for the smaller
groups. Certain allied results on the rate of decay of nuclei of different
sizes produced bymild X-radiationin dust-free wet air are added. These
showtheremarkable result that the coefficient of decayincreasesfromless
thanone-tenth ofthe usual value forions in dry air, to even 50 times the
normal value, as the nuclei range in dimensions from very large to very
small sizes. Hence if these nuclei be regarded as water-drops, they evap-
orate more and more rapidly to a persistent limiting small diameter, in
proportion as they are larger. In the last investigation (chapter IX),
I have returned to the moot subject of the regular persistent nuclei pro-
duced by strong X-rays, through earthed metallic aluminum screens and
a fog-chamber of wood, with the endeavor to find the lower limit of the
densityofionizationwhichmust be reached before thesetypical persistent
nuclei (i.e., those requiring little or no supersaturation to precipitate con-
iii
IV PREFACE.
densation) are formed. This chapter deals with large persistent nuclei
produced by X-rays and is thus in a measure supplementary to the pre-
ceding. From both I conclude that the decay ofions as such beyond the
scope of easy determination by the electrometer with the production of
neutralpairsandmultiplesfindsitscounterpartinthegrowthofpersistent
nuclei, as the result of such coalescence. These nuclei now fall specially
within the scope of detection by the fog-chamber. The number of per-
sistent nuclei produced by the X-rays (caet. par.} will increase with the
time of exposure at an accelerated rate, inasmuch as the nuclei or ions
present themselves take part in the production, and these are present in
continuallygreaternumber, asthelowerlimitofsize decreases.
X
In chapter the equation derived in the preceding report (No. 149,
chapterV) for the displacement of the centerofellipses produced by the
opaque mirror on the micrometer is tested throughout the spectrum and
for all angles of incidence. This requires a knowledge of the indices of
refraction of the glass of the grating for all wave-lengths. A method of
total reflection suitable to the case, where only a flat spicule of glass is at
hand, was therefore developed and applied.
In conclusion, a displacement interferometer is described, combining
the desiderata of rigidity, lightness, and portability, and provided with
long arms ofinvariable length and with sufficientlyhighmirrors to admit
oftheintroductionofbulkyapparatus, likeafog-chamber, betweenthem.
The apparatus is peculiarly adapted for the measurement of the refrac-
tion of gases at high temperatures, and conversely for the measurement
ofhigh temperatures bymeans ofthe refraction of a gas, as well as for
themeasurement ofthe adiabatic transformations of a gas, eitherdry or
wet, and at all temperatures. It is hoped that the researches may de-
velop fruitfully in this direction, and some promising work has already
beencompleted.
Chapter XI, with a special view to an application of the interference
method, endeavors to measure the degree of adiabatic expansionencoun-
tered in fog-chambers of such dimensions as I have used. To actually
measure the ratio of specific heats much more voluminous apparatus will
be necessary, and the present form of the interferometer is not adapted
for air-chambers large in their vertical dimensions. An interesting result
of theinvestigationis themarked differenceoftheheatratio forwet and
dry air, data from which it should be possible to compute the amount of
waterprecipitated percubic centimeter.
My thanks are due to MissAda I. Burton, who assisted me with rare
efficiency bothin the editorial part of the work and in the preparation of
diagrams, aswellasintheexperimentalpartsandintheextendedcompu-
tations which aresearch ofthe present kind demands.
CARL BARUS.
BROWN UNIVERSITY, December 1911.
CONTENTS.
CHAPTER VI. EllipticInterferenceswithReflectingGratings.
PAGE
51. Firstmethod. Fig.34 79
52. Inversionofthemethod 80
53. Secondmethod. Resolutionoftheslitimage 81
54. Thirdmethod. Parallelgratings. Figs.35, 36 81
55. Natureoftheevanescence. Fig.37 83
56. Data. Table 18 85
57. Equations. Fig.38 85
58. Differentialequations. Displacementperfringe, de/dn 87
59. Deviationperfringe,dn/dn,dH/de 88
60. Coloredslitimagesanddiskcolorsofcoronas 89
CHAPTER VII. Independence of Coronas of Thickness of the Fog Layer.
61. Introductory 91
62. Effectofthickness. Apparatus. Fig. 39 91
63. Resultsandsummary 92
CHAPTER VIII. Experimentswith avery SmallFog-Chamber,togetherwith
DataontheDecayofLargeandSmall Nuclei.
64. Smallfog-chamber. Figs. 40, 41,42,43;tables 19,20 93
65. Decayofdifferentsizesofions. Fig.44;tables21, 22,23 96
CHAPTER IX. OnthePersistentNucleiProducedbytheX-rays.
66. Introductory 101
67. Olderseriesofexperiments 103
68. Recentexperiments. Table24 104
69. Initialfogs 107
70. Amountofionizationneededtoproducepersistentnuclei 107
CHAPTER X. The Rectification of the Spectrum by the Aid of Total
Reflection, together with a Computation of the Shift of Ellipses in
EllipticInterferometry.
7721.. AIpnptarroadtuucsto.ryFig. 45 1i1n1
73. Methods 113
74. Examples. Liquids. Figs. 46, 47;tables25, 26 114
75. Examples. Solids. Figs.48,49;tables27,28 116
76. Independentmeasurements 119
77. Prism (liquidCSs) andsubmergedgrating. Fig. 50;table29 119
78. Thedispersionconstantsoftheglassofthegrating. Table30 121
79. Computation of the shift of centers in elliptic interferometry. Fig. 51;
8801.. CCoantsatebilnoeufsed73.1=,93C02a,seneoafrl7y.=o.TabFliegss.3552,,3563; tables33,34 111222286
82. Summary 129
83. Apparatus. Figs. 54, 55, 56 129
84. Otherinterferences. Fig. 57 134
85. Other measurements; high temperature, adiabatic transformations, etc.
Fig. 58;table37 135
VI CONTENTS.
CHAPTER XL TheDegreeofAdiabaticExpansioninGasesRapidly Cooled,
asObservedbyDisplacementInterferometry.
PAGE
86. Introduction. Apparatus. Fig.59 141
87. Equations 143
88. Smallbrassfog-chamber, dryandwet. Fig. 60; tables38, 39,40, 41,42... 148
89. Larger(wood)fog-chamber. Dryair. Fig.61; tables43,44,45,46 151
90. Thesame. Wetair. Tables47,48,49 . 154
91. Copperfog-chamber. Exhaustion. Dryair. Tables50,51 155
92. The same. Compression. One-inchstop-cock. Tables52,53 157
93. The same. Compression. Twoandone-halfinchstop-cock. Tables54,55 157
94. ClementandDesormes'sapparatus. Fig.62;tables56, 57,58, 59,60 158
95. Largewoodfog-chamber. Figs.63,64;tables61,62,63,64,65,66 161
96. Air-chamberofvanishingthickness. Tables67,68 165
97. Conclusion 166