This book is DUE on the last date stamped below
UNIVERSITY OF CALIFORNIA
DISPLACEMENT INTERFEROMETRY BY THE AID
OF THE ACHROMATIC FRINGES
BY CARL BARUS
Hazard Professor of Physics and Dean of the Graduate Department
in Brown University
PUBLISHED BY THE CARNEGIE INSTITUTION OF WASHINGTON
CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 249, PART IV
PRINTED BY J. B. LIPPINCOTT COMPANY
AT THE WASHINGTON SQUARE PRESS
PHILADELPHIA, U. S. A.
The anomalous behavior observed in the last report, in treating the elastic
deformations of small bodies on the interferometer, induced me to endeavor
to devise a different method for the same purpose. This led to the construc-
tion of the contact lever, using achromatic fringes described in the first
chapter. The instrument at once functioned admirably, when employed
either as a surface tester or as a spherometer.
The contact lever is then modified (Chapter II) for the interpretation of
the elastic discrepancy specified, and it is shown that both the new and the
old methods lead to trustworthy results, even for material as rigid as brass,
if the rods examined are sufficiently slender.
A different kind of application of the contact lever is made in Chapter III.
The very small elongations with subsequent contractions experienced by iron
in magnetic fields are peculiarly interesting, because these phenomena are at
their maximum variation after the metal has become magnetically saturated;
so that something persists here, of which the magnetic moment gives but an
inadequate account. Hence particular attention is given to the occurrences
in strong magnetic fields, though the behavior in very weak fields is also
explored. With metals other than iron no effect was observed.
An instrument which lends itself with equal facility to the measurement of
thermal expansion and to the determination of elastic moduli is in a measure
self-contained for the solution of many thermodynamic problems. A project
of this kind, bearing on the specific heat of liquids under pressure and tempera-
ture, is discussed, with the requisite experimental data, in Chapter IV.
Chapters V and VI contain contributions to the electro-dynamometry of
very weak (telephonic) alternating currents. No available effect is obtained
unless the vibrator of the measuring-instrument is sharply in resonance with
the alternation of current. When it is so, the response is astonishingly large
and very definite in amount. In Chapter V the measurement is made by
means of the vibrating telescope, the vibrator of the telephonic system carry-
ing the objective. This chapter is merely introductory to the next, and the
sensitiveness is not beyond a few micro- amperes per ocular scale-part of reason-
able value (o.oi cm.) . Within these limits, however, it may be very serviceable
for instance, in determining the number of turns in each of a variety of
secondary coils successively slid over the same long solenoidal primary.
The sensitiveness may be increased upwards a hundred-fold, however (so
that io~ 8 ampere per fringe is measurable), by placing an instrument similar
to the last on the displacement interferometer adjusted for achromatic fringes.
The reading in such a case must be made 'with a vibration telescope, syn-
chronized with the alternating current in the primary and with the objective
vibrating normally to the displacement of fringes. The measurement is thus
somewhat awkward, and consists in determining the range of fringe ellipses
parallel to the direction of the vibration of fringes. To make amends for this,
however, both the amplitude and the phase of the induced current are given
by the form of the vibration ellipses obtained, whether modified by resistance,
inductance, or capacity. So sensitive an apparatus naturally catches all the
quivering stray magnetic fields in the room; but here again any such effect,
which might at first sight seem to be fatal, may be compensated by the
primary solenoid (for instance) almost as easily as the needle of an astatic
galvanometer. Indeed, in the absence of current (secondary), the needle may
be given any reasonable amplitude or phase. It is shown, furthermore, that
the persistence of the symmetrical ellipse, with its axes respectively parallel
to the directions of vibration, is a strikingly accurate criterion of resonance.
Chapter VII shows that a slight but essential modification of a form of
interferometer used by Michelson and Morley, makes this apparatus virtually
self-adjusting, while satisfying many of the requirements of displacement
interferometry. This is a very great convenience when many separate adapta-
tions of apparatus to the interferometer have to be made successively; for
the wearisome search for fringes is thus reduced to a minimum. It is even
possible to put a part of one of the mirrors of the interferometer on a microm-
eter screw for direct measurement, though the instrument is then no longer
quite self-adjusting. The endeavor to use this device for finding the refrac-
tion of solid media apart from form did not, however, furnish results of prac-
tical value. On the other hand, a possible design of this kind for measuring
the Fresnel coefficient is tested with a promising outcome in Chapter VIII.
An interesting class of interferences obtained by superposing the fringes
resulting from dispersion on identical fringes resulting from the inclination of
rays, is discussed in Chapter IX. It is possible in this way to obtain sharp
spectrum fringes in the very luminous spectrum of an indefinitely wide slit and
to specify the angular orientation of the spectro-telescope on its axis ; for the
fringes, if small, jump out of an unbroken spectrum band suddenly, when
a definite angle is reached. Both of these possibilities are of practical value.
A number of results incidental to the preceding work are collected in
Chapter X. Evidences of continuous micrometric convection currents within
liquids, obtained from the shadows of motes in a highly dispersed spectrum,
the satellites of the achromatic fringes already referred to in the preceding
report, peculiarly brilliant phenomena obtainable in connection with Her-
schel's fringes, and other subjects are here treated.
Finally, in Chapters XI and XII, I have returned to certain gravitational
experiments begun in the last report. The former, in which the deviations
of the horizontal pendulum are read off by the displacement of achromatic
fringes, is very definite in its evidence of the effect of temperature distributions
within the supporting pier. Chapter XII is a continuation of the endeavor
to follow the actual motion of a gravitation needle, under periodic gravita-
tional attraction, with a view to deducing conclusions from that motion.
The apparatus ultimately met with serious accident in the endeavor to exhaust
it; but though the experiments have not been concluded, the progress made
BROWN UNIVERSITY, July, 1919.
*CH AFTER I. An Interferential Contact Lever with Achromatic Fringes.
1. Apparatus. Figs. I, 2, 3 7
2. Equations. Fig. 4 8
3. Observations. Figs. 5, 6 , 10
CHAPTER II. Elastic Deformations of Small Bodies Measured by the Preceding
4. Introductory 13
5. Apparatus. Figs. 7,8 13
6. Observations. Hard rubber. Figs. 9, 10. Table I 14
7. The same, continued. Fig. n. Table 2 16
8. The same, Brass. Figs. 12, 13, 14 17
9. The same, continued. Figs. 15, 16, 17 19
10. The same, continued. Figs. 18, 19, 20 21
11. Glass. Figs. 21, 22, 23, 24, 25, 26, 27, 28 21
12. Conclusion 24
CHAPTER III. The Elongation Due to Magnetization, Measured -with the
Interferential Contact Lever.
13. Introductory 25
14. Apparatus. Fig. 29 25
15. Observations. Figs. 30, 31 27
16. Vibration telescope. _ Fig. 32 29
17. Theoretical observations 30
18. Further observations. Figs. 33, 34. Table 3 31
19. Magnetic elongations in a free-end coil. Figs. 35, 36 33
20. Coefficient of expansion. Figs. 37, 38, 39 34
CHAPTER IV. On the Pressure Variation of Specific Heat in Liquids.
2 1 . Introductory 37
22. Equations. Fig. 40 37
23. Measurement of the pressure coefficient /? 38
24. Measurement of the thermal expansion a 38
25. Available liquids 39
CHAPTER V. An Electrodynamometer Using the Vibration Telescope.
26. Introductory 41
27. Apparatus. Figs. 41, 42, 43 41
28. Observations. Figs. 44, 45 44
29. Further observations. Fig. 46. Table 4 45
30. Effect of frequency. Figs. 47, 48, 49, 50, 51 46
31 . Steel wires 47
32. Adjustable telephone 48
33. Coil tester. Figs. 52, 53, 54 4&
34. Heavier armature and less damping. Fig. 55 51
35. Further magnification. Fig. 56. Table 5 52-
36. Organ-pipe. Fig. 57 x . 53
37. Equations 54
CHAPTER VI. The Rapid Telephonic Vibrator on the Interferometer.
38 . Introductory 55
39. Apparatus. Figs. 58, 59. 55
40. Observations with the slit-image 56
41. Observations with the interferometer. Fig. 60 57
42. Decreased bifilar distances. Fig. 61 58
43. Observations with the new apparatus. Figs. 62, 63 59
44. Capacity and self-induction in the secondary. Figs. 64, 65, 66, 67 61
45. Self-induction in the primary. Figs. 68, 69 62
46. Direct telephonic induction. Figs . 70, 71, 72, 73, 74 64
47. Narrow bifilar 67
48. The vibratory stray magnetic fields
49. Resistance, capacity inductance in case of the compensated vibrator. Figs. 75
50. Ring transformer
5 1 . Magnetic screens
52. Amplitude of the interrupter
53. Telephones in parallel 73
CHAPTER VII. Self-adjusting Interferometer in Relation to the Achromatic
Fringes and Refraction.
54. Introductory. Fig. 79 74
55. Character of the achromatic fringes. Fig. 80 75
56. Curvilinear compensators. Fig. 81 77
57. Index of refraction, irrespective of form 78
58. The same. Glass plate. Lenses. Figs. 82, 83, 84 78
59. Adjustable compensators. Fig. 85 79
60. Observations of refraction 80
61 . Equations and data. Table 6 81
62. Micrometer measurements. Table 7 85
63. Summary 86
CHAPTER VIII. An Adjustment in Relation to the Fresnel Coefficient.
64. Apparatus. One internal reflection. Figs. 86, 87, 88 88
65. Apparatus. Two internal reflections. Fig. 89 89
66. Equations. One internal reflection. Figs. 90, 91 90
67. Equations. Two reflections 92
68. Experiments. Figs. 92, 93 93
69. Modification of the experimental design. Rotating, self-adjusting interferometer.
Fig. 94 95
CHAPTER IX. Sharp Spectrum Fringes With an Indefinitely Wide Slit, including
the Superposition of Fringes Due to the Color and to the Obliquity of Rays.
70. Introductory 96
71. Apparatus. Fig. 95 96
72. Equations 97
73. Observations. Figs. 96, 97, 98, 99 98
74. Summary 99
75. Reversed spectra 100
76. The same, continued roc
77. Monochromator. Figs. 100, 101 101
78. Quartz prism. Fig. 102 102
CHAPTER X. Miscellaneous Results of the Preceding Experiments.
79. Spectrum phenomena due to moving motes. Fig. 103 104
80. Separated Jamin plates. Figs. 104, 105, 106, 107 107
81. Interferometry with aid of secondary and tertiary achromatic satellites. Fig. 108. 109
82. The triangular self-adjusting interferometer. Fig. 109 no
83. Herschel's fringes. Fig. no 1 1 1
84. The same, continued. Fig. in 112
85. Measurement of small angles by a half -silver plate. Fig. 112 113
CHAPTER XL Interferometer Observations and Achromatic Fringes in Connection
with the Horizontal Pendulum.
86. Apparatus and data. Fig. 1 13 114
CHAPTER XII. Gravitational Experiments.
87. Introductory 116
88. Apparatus. Fig. 117 116
89. Needle in air. The two methods. Fig. 114. Table 6 117
90. Reversal at symmetrical positions. Figs. 1 15, 116 118
91. Reversal after equal time intervals. Figs. 1 18, 119 119
92. Static elongation. Table 7 120
93. Recent work 122
AN INTERFERENTIAL CONTACT LEVER, WITH ACHROMATIC FRINGES.
1. Apparatus. The method heretofore described for the measurement of
small angles by the aid of the rectangular interferometer, lends itself con-
veniently for the construction of apparatus like the contact lever or the spher-
ometer. Having in view work needing such instruments, I designed the fol-
lowing simple apparatus for the purpose :
Figure i is a plan of the design; figure 2 an elevation of the fork and appur-
tenances; figure 3 finally shows the same apparatus adapted for use as a
spherometer. The interferometer receives the white light from a collimator
at L. After the reflections and transmissions controlled by the mirrors M,
M', N, N', and the auxiliary mirror mm', as indicated in the figure, the light
is conveyed into the telescope at T for observation of the interferences. The
mirror M' is on a micrometer with the screw 5 normal to its face.
It is through the mirror mm' that the small angles are to be measured, and
this is therefore mounted at one end of the lever dc, capable of rotating around
the long vertical axle aa, in the circular fork FF. The latter is rigidly mounted
on the bed of the apparatus by aid of the stem / in the rear. The lever c is bent
upward at right angles at d, and it is here that the mirror mm' is firmly secured
by bolts, etc., as at M. The spring k draws the lever toward the front of the
diagram, so that the blunt metal pin e suitably attached to the end of mm'
may be kept in contact with the glass plate g to be tested.
The plate g, in order to be examined as to its degree of plane parallelism,
must be capable of sliding up and down, or right and left, under standard
conditions. To obtain these the stout bar G (rigidly attached like / to the base
of the apparatus) has been provided, carrying three set -screws h, h, h, the
points of which lie in the same circumference about 120 apart. They there-
fore constitute a kind of tripod against which the plate g is firmly pressed by
the flat spring or clip rr and screw i. This method of mounting may be
8 DISPLACEMENT INTERFEROMETRY BY
appropriately varied in accordance with the tests to be made on the plate g,
its shape, etc. Similarly, the set-screws h, h, h may be placed nearer together
or further apart in appropriate screw-sockets, and finally, the lever c may be
lengthened or shortened at pleasure. The pin e remains in permanent contact
with the plate g in consequence of a wide circular hole in the clip rr; or e may
clear rr, above or below it.
If but one face of the plate g is to be tested, the system Ghrg must slide as a
whole, right and left, nearly parallel to the rays p, q. In such a case every-
thing will depend on the excellence of the slide carrying the system. I did
not attempt to make such arrangements, as I had no need of data of this kind ;
but the parts MM', NN', Fcmm', and Grg were nevertheless mounted on heavy
slides (lathe-bed fashion) for convenience in securing a variety of adjustments.
In figure 3 the bar G has been reversed in position and the contact pin e
now passes through a circular hole in G, to be in contact with a lens g, for
instance, kept pressed to the tripod screws h, h, h in the same way as before.
The latter should in general be much closer together than the figure shows.
The instrument is now a spherometer.
The experiments indicated that the mounting of the contact-pin e to the
extremity of the mirror mm' may be the occasion of annoyances ; for on sliding
g right and left, or even up and down, the mirror mm' is liable to be flexed.
In such a case the achromatic fringes rapidly lose sharpness, not to speak of
the errors involved. I endeavored to avoid this by keeping the pin e out of
contact with the plate g by a special lever (not shown) while g was being dis-
placed and to test a number of successive contacts thereafter; but it is best
(and I eventually did this) to mount e on a separate rigid cross-piece parallel
to mm' and firmly attached to c. In such a case no flexure of mm' can occur
and the contacts may also be repeated at pleasure. Before each reading the
bar G should be gently tapped.
The achromatic fringes can be found only
through the spectrum fringes. This is not usu-
ally difficult, remembering that not only must
the slit-images in the spectrum be in contact
throughout, but the two beams must be locally
in contact on the mirror M'. Moreover, the
mirrors M' and N' must be equally thick and
the silvered faces all turned towards the auxil-
iary mirror mm' .
2. Equations. If the mirrors M, M r , etc., are set at an angle i, if the
deflection of the auxiliary mirror is 0, and if the breadth of the ray parallelo-
gram MM' or NN' is b, we may write
(i) 6A0 = AWcos*
where AW is the displacement at the micrometer at M'.
THE AID OF THE ACHROMATIC FRINGES. 9
If r is the length of the lever c, figure i, and Ax the displacement of the pin e
(2) rA0 = A*
(3) A* = (r cos */6) AW
The apparatus is more sensitive as r is smaller and b is larger. In the
instrument used (adapted from an earlier apparatus),
r=ncm. 6= 10 cm. = 45
(4) Ax = o.778A]V
But the main condition of sensitiveness is contained in the size of the
fringes, and these may be made indefinitely large by suitable rotation of the
mirrors M and M r , for instance, in like direction on a horizontal axis (local
coincidence of rays on M') . Since
in case of the passage of n fringes, equation (3) becomes
so that the limiting sensitiveness (n= i) would be (with the above data)
(6) Ax=nX6oXicT 6 /20 = 33Xio- 6 cm.
for a single fringe, a few tenths of which may be registered with certainty.
When the achromatic fringes are used it is, however, usually more convenient
to standardize the ocular plate micrometer in the telescope directly by aid of
the screw micrometer s, at M', figure i . If the ocular plate is divided in tenth
millimeters along a centimeter of length and the fringes are of moderate size,
one may estimate that about 40 scale-parts correspond to A/V=io~ 3 cm., so
that a single scale-part of displacement of the achromatics is equivalent to
AAT = 2 5 X io~ 6 cm., while a few tenths of a scale-part may here also be estimated.
If the apparatus (fig. 3) is to be used as a spherometer, the ordinary method
of measuring from a plate of glass is at once available. If r is the radius of
the circle of the tripod and Ax the height of the central foot, we obtain, as
usual, for the radius R required
(7) #=r 2 /2A*
This method gives good results for lenses of all curvatures, however strong,
as the tests below indicate. But it is not necessary to use the plate to obtain
a fiducial reading, provided the system Gr carrying the lens g is on good right
and left slides. For in figure 4, let 6 be the angle between the plane of the
tripod and the slides, and let three readings of AJV be taken for three preferably
equidistant points, /, c, v, of the lens, by sliding Gg over equal distances, r.
Let the reading be
(8) y=N y' = N+rtand+AN y"=N+2rtan6
10 DISPLACEMENT INTERFEROMETRY BY
where AW corresponds to A* in figure 4. Hence
and equations (4) and (7) apply as before. This method also gives good
results even for short distances, r.
3. Observations. The use of the apparatus, figure i, with the strip of
glass g to be tested sliding up or down, did not at first give satisfactory results,
because the mirror mm' was too thin (2 mm. thick). It was found however,
that on breaking contact at e during the sliding of g between successive posi-
tions, or by gently tapping the bar or standard G, very fair results were obtain-
able. There would have been no difficulty in using a thick glass mirror mm'
(0.25 inch or more), in which case the annoyance of flexure would have been
negligible. The following is an example of results obtained, the position of the
glass strip g being read off on a parallel vertical millimeter scale :
38.7 40.8 cm.
n. 2 ii. 8 cm.
These data are shown in figure 5 and the direct and return series are con-
sistent. The average slope of the strip, which is not quite uniform, may be
per centimeter of length, so that
per centimeter of length.
Using the ocular micrometer, it was found that one scale-part corresponded
to one-fortieth of AAT= io~ 3 cm. Tests along a single centimeter of the glass
strip gave the results
i.e., a difference of 19.2 ocular scale parts per centimeter of length, so that
a result virtually identical with the preceding, as no refinement was attempted.
THE AID OF THE ACHROMATIC FRINGES. 11
Tests made with another piece of plate glass (the auxiliary mirror provided
with an independent cross-arm and the apparatus gently tapped before obser-
vation), gave the results following:
Position 40.8 35.6 37.7 39.8 40.7 cm.
15.8 40.6 30.7 21. i 16.7 cm.
They are constructed in figure 6. Hence per unit of length of plate
AAT = 0.00239 cm. A# = 0.00186 cm.
As the micrometer read to about io~ 4 cm., a corresponding error in the indi-
vidual data is inevitable.
Tested within 5 mm. by the ocular micrometer (scale-part equivalent to
AAT = 46Xio~ 6 cm.), the mean displacement was about 50 scale parts, so that
per centimeter of length AN = 0.0023 c" 1 - The results for so small a length are
complicated by the difficulty of securing the same lateral position as well as
the same longitudinal position, since the thickness changes in both directions.
Lateral sliding, which is equivalent to lateral flexure of the contact lever is
particularly to be guarded against, but it vanishes on tapping.
Experiments were now made with the design figure 3, except that the mirror
mm' was left free, while a special arm (conical tube) parallel to mm' carried the
stylus e. Although small fringes were used, the behavior of the apparatus as a
spherometer was quite satisfactory. The three set-screws h, h, h were equi-
distant on a circle of radius r= 1.08 cm. Sliding the lens g (about 5 cm. in
diameter) so that its center and the outer parts of four quadrants lay succes-
sively under the pin e, the readings obtained after gentle tapping were
Top. Bottom. Right. Left. Center.
io 8 AAT = 2.oo 2.00 2.05 2.05 2.00 cm.
The screw micrometer was thus not sufficiently sensitive to register
The apparatus used as a spherometer gave for:
Plate. Lens. Plate.
AATXio' = 28.s 23.2 28.4 cm.
so that the height above the plate corresponded to
io'AA^=5.2 cm., or io 8 A# = 4.o4 cm.
If R is the radius of curvature of the lens,
The fringes, however, were here too fine to admit of greater precision. In
another experiment with somewhat larger fringes, the data were
Lens. Plate. Lent.
AA^Xio*=io.48 15.52 10.53
o (J- 08 ) 2
/? = ^- = 149 cm.
The fringes in the former case were not large enough to admit of better
These experiments were made merely for the purpose of showing that there
is no difficulty, so far as the fringes are concerned, in the successive substitu-
tion of plates and lenses. The pin e should be removed from contact by an
auxiliary lever during this exchange and the apparatus gently tapped before
a reading is taken.
The lens tested by the ocular micrometer (here io 3 A/V = o.o37Ae) showed at
the left center and right side readings of i.o, i.o, 0.8 scale-parts, respectively.
Thus the three values of io 6 Ax are 28.9, 28.9, 28.4 cm., respectively. The dif-
ference is but 5 X io~ 6 cm., the positions taken being about a centimeter apart.
A concave lens was next tested, giving the readings
0.00478 cm., r=i.o8 cm., as before, and therefore
The front and reversed sides of the lens calipered did not differ by more than
A# = 3Xio~ 6 cm.
In the case of two magnifying lenses the readings obtained on different
days were (all data in centimeters) .
Mean AxXio 3
No. I ....
No. 2 ....
In case of such large displacement (nearly a centimeter) the fringes are
liable to rotate considerably unless they are vertical. The latter should there-