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  1. A stressed glass plate is sometimes employed as a substitute for the Brace mica strip and some exceptional claims made in regard to its sensibility. The mechanical difficulties attendant upon the production of a uniform field and vanishing dividing line are, relative to the mica strip, insuperable, so that it is difficult to conceive that the stressed plate should be preferred by any observer who has had experience with a Brace half-shade of variable azimuth.
  2. A. Q. Tool, Phys. Rev.,  31, p. 1; 1910.
  3. Instrument makers will be furnished, on application to the Bureau of Standards, with blueprints giving details of construction. The drawings were made by Mr. F. A. Case of the Bureau, and the instrument constructed in the instrument shop by Mr. H. C. Wunder.
  4. C. G. Stokes, Phil. Mag. (4),  2, p. 420, (1851).
  5. A quartz plate, of known rotatory dispersion, which can be inserted in the compensator tube, is a convenient adjunct for determining the wave length of the light used.
  6. This focus leaves, at best, much to be desired. It needs therefore the most careful adjustment laterally and alignment of the nicol partition, as provided. A minimum length of nicol is also of importance.
  7. R designates the “retarded” and A the “accelerated” component.
  8. L. B. Tuckerman, “Doubly Refracting Plates and Elliptic Analyzers,” Univ. of Neb. StudiesIX; April1909.
  9. Coll. Sci. Papers I p 68.
  10. Loc. cit.

1910 (1)

A. Q. Tool, Phys. Rev.,  31, p. 1; 1910.

1851 (1)

C. G. Stokes, Phil. Mag. (4),  2, p. 420, (1851).

Stokes, C. G.

C. G. Stokes, Phil. Mag. (4),  2, p. 420, (1851).

Tool, A. Q.

A. Q. Tool, Phys. Rev.,  31, p. 1; 1910.

Tuckerman, L. B.

L. B. Tuckerman, “Doubly Refracting Plates and Elliptic Analyzers,” Univ. of Neb. StudiesIX; April1909.

Coll. Sci. Papers (1)

Coll. Sci. Papers I p 68.

Loc. cit. (1)

Loc. cit.

Phil. Mag. (1)

C. G. Stokes, Phil. Mag. (4),  2, p. 420, (1851).

Phys. Rev. (1)

A. Q. Tool, Phys. Rev.,  31, p. 1; 1910.

Other (6)

Instrument makers will be furnished, on application to the Bureau of Standards, with blueprints giving details of construction. The drawings were made by Mr. F. A. Case of the Bureau, and the instrument constructed in the instrument shop by Mr. H. C. Wunder.

A quartz plate, of known rotatory dispersion, which can be inserted in the compensator tube, is a convenient adjunct for determining the wave length of the light used.

This focus leaves, at best, much to be desired. It needs therefore the most careful adjustment laterally and alignment of the nicol partition, as provided. A minimum length of nicol is also of importance.

R designates the “retarded” and A the “accelerated” component.

L. B. Tuckerman, “Doubly Refracting Plates and Elliptic Analyzers,” Univ. of Neb. StudiesIX; April1909.

A stressed glass plate is sometimes employed as a substitute for the Brace mica strip and some exceptional claims made in regard to its sensibility. The mechanical difficulties attendant upon the production of a uniform field and vanishing dividing line are, relative to the mica strip, insuperable, so that it is difficult to conceive that the stressed plate should be preferred by any observer who has had experience with a Brace half-shade of variable azimuth.

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Figures (18)

F. 1
F. 1

Lippich half-shade polarizer. Field brightness, as seen through the analyzing nicol, is increased by rotating whole nicol to a larger azimuth relative to the half nicol. (Used as analyzer the direction of the light is reversed).

F. 2
F. 2

Cornu-Jellett half-shade nicol showing section removed after which the parts are closed together giving slightly different azimuths of vibration in the two parts of the field.

F. 3
F. 3

Soleil-Babinet variable order compensator.

F. 4
F. 4

Bravais bi-plate—an elliptic half-shade in which the two parts are of equal and opposite order (quarter-wave). Working azimuth with respect to the nicol should be small to avoid excessive brightness levels.

F. 5
F. 5

The Stokes’ elliptic analyzer. A. Compensator and nicol are adjusted for extinction and their azimuths recorded.B. Setting is repeated with compensator at a complementary azimuth.

F. 6
F. 6

Assembled view of universal polarimeter.

F. 6a
F. 6a

Disassembled view of same reversed.

F. 7
F. 7

The Brace half-shade elliptic analyzer. A. Plane polarized entrant light; compensator in neutral position; mica half-shade strip produces positive ellipticity; viewed through nicol lower half of field the brighter.B. Compensator produces positive ellipticity; mica half-shade strip augments it; lower half of field the brighter.C. Compensator produces negative ellipticity; half-shade strip restores it; upper half of field the brighter.D. Half-shade strip converts light received from compensator into an equal and opposite ellipticity of unchanged azimuth—the condition for a match.

F. 8
F. 8

Tool’s general polarimeter. Replaces simple nicol of Stokes’ method with a Cornu-Jellett split nicol and attaches thereto a Brace elliptic half-shade. As in Stokes’ method, complementary settings A and B are made in which the four-part field is matched.

F. 9
F. 9

Definition of ω.

F. 10
F. 10

Component amplitudes A and R of an elliptic vibration.

F. 11
F. 11

An elliptic vibration represented by locus of a point on the surface of a sphere; shows the effect of a birefringent plate of order ϕ. This shifts M to H; M′, having same ellipticity, to H′; and in general u to υ.

F. 12
F. 12

Geometrical derivation of Stokes’ formulas. The given vibration M (at longitude H) is restored by the compensator, of order ϕ,set at an azimuth θc′ (longitude, 2θc′), to a rectilinear vibration at H1.

F. 13
F. 13

Trace of Fig. 12 on equatorial plane showing also the complementary settings, Q″ and H2 respectively of compensator and analyzing nicol, obtained by shifting the compensator so that M′ on its circle QMM′ falls at M on the sphere and consequently rotates the given vibration through the same angle ϕ to the position H2 on the equator.

F. 14
F. 14

Analysis of method of isochromatic lines used in photoelastic analyses. All parts of the stressed plate which impress the same phase lead ϕ, irrespective of azimuth, convert the entrant circular polarized vibration, located on north pole S, to points on the latitude circle MM′. A second quarter-wave plate at longitude Qc rotates this circle, about OQc through a right angle, so that its axis falls in the equatorial plane and coincident in longitude Qn with the analyzing nicol. This is the criterion for equal brightness of field as seen through the nicol.

F. 15
F. 15

Analysis of Brace method. The figure represents a projection in part of Fig. 12 on a plane perpendicular to Of0. The line Qhf0g0 represents the equator. M,f and h represent points on the surface of the sphere; the angle marked ϕh is therefore the projected order of the half-shade, not the true order. Qh represents the longitude of the half-shade, similar to that, Qc, of the compensator in Fig. 12.

F. 16
F. 16

Analysis of Tool’s method—similar to Fig. 15.

F. 17
F. 17

Geometrical diagram for deriving formulas used in Tool’s method.

Equations (73)

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x 2 a 2 + y 2 b 2 = 1
tan ω = b a = e
sin 2 ω = 2 e 1 + e 2
y = R sin 2 π t T x = A sin ( 2 π T + ϕ )
A = x 1 cos θ y 1 sin θ
x 1 2 a 2 + y 1 2 b 2 = 1 ,
A 2 = a 2 cos 2 θ + b 2 sin 2 θ
R 2 = a 2 sin 2 θ + b 2 cos 2 θ
A 2 + R 2 = a 2 + b 2
A 2 R 2 = ( a 2 b 2 ) ( cos 2 θ sin 2 θ ) = ( a 2 b 2 ) cos 2 θ
p = A sin ϕ
x 2 = p cos θ = A sin ϕ cos θ y 2 = p sin θ = A sin ϕ sin θ
A 2 sin 2 ϕ = a 2 b 2 a 2 sin 2 θ + b 2 cos 2 θ
A R sin ϕ = a b
cos 2 ϕ = 1 sin 2 ϕ = 1 a 2 b 2 ( a 2 cos 2 θ + b 2 sin 2 θ ) ( a 2 sin 2 θ + b 2 cos 2 θ )
cos 2 ϕ = 1 a 2 b 2 [ a 2 ( a 2 b 2 ) sin 2 θ ] [ a 2 ( a 2 b 2 ) cos 2 θ ] = ( a 2 b 2 ) 2 sin 2 θ cos 2 θ A 2 R 2
A R = cos ϕ = a 2 b 2 2 sin 2 θ .
P A 2 + R 2 2 = a 2 + b 2 2 ( a ) Q A 2 R 2 2 = a 2 b 2 2 cos 2 θ ( b ) K A R cos ϕ = a 2 b 2 2 sin 2 θ ( c ) S A R sin ϕ = a b ( d ) } I
Q 2 + K 2 + S 2 = P 2
t g 2 θ = K Q
S P = 2 a b a 2 + b 2 = 2 e 1 + e 2
= sin 2 ω
e = tan ω
tan ϕ = S K
P 0 = a 0 2 + b 0 2 2 ( a ) Q 0 = a 0 2 b 0 2 2 cos 2 θ 0 ( b ) K 0 = a 0 2 b 0 2 2 sin 2 θ 0 ( c ) S 0 = a 0 b 0 ( d ) } I 0
P 0 = P 0 = a 0 2 + b 0 2 2 ( a ) Q 0 = Q 0 cos 2 θ + K 0 sin 2 θ = a 0 2 b 0 2 2 ( cos 2 θ 0 cos 2 θ + sin 2 θ 0 sin 2 θ ) = a 0 2 b 0 2 2 cos 2 ( θ 0 θ ) ( b ) K 0 = Q 0 sin 2 θ + K 0 cos 2 θ = a 0 2 b 0 2 2 sin 2 ( θ 0 θ ) ( c ) S 0 = S 0 = a 0 b 0 ( d ) } I 0
Q 0 2 + K 0 2 + S 0 2 = Q 0 2 + K 0 2 + S 0 2 = a 0 2 + b 0 2 2
Q = Q K = A R cos ( ϕ 0 + ϕ ) = A R ( cos ϕ 0 cos ϕ sin ϕ 0 sin ϕ ) = K cos ϕ S sin ϕ
S = K sin ϕ + S cos ϕ
P 1 = P 0 = a 0 2 + b 0 2 2 ( a ) Q 1 = Q 0 = a 0 2 b 0 2 2 cos 2 ( θ 0 θ ) ( b ) K 1 = K 0 cos ϕ S 0 sin ϕ = a 0 2 b 0 2 2 sin 2 ( θ 0 θ ) cos ϕ a 0 b 0 sin ϕ ( c ) S 1 = K 0 sin ϕ + S 0 cos ϕ = a 0 2 b 0 2 2 sin 2 ( θ 0 θ ) sin ϕ + a 0 b 0 cos ϕ ( d ) } I 1
Q 1 2 + K 1 2 + S 1 2 = Q 0 2 + K 0 2 + S 0 2 = P 0 2 = P 0 2
S 1 = S 1 = a 0 2 b 0 2 2 sin 2 ( θ 0 θ ) sin ϕ + a 0 b 0 cos ϕ I 1 ( d )
P 1 = P 1 = = P 0 I 1 ( a )
cos 2 ω 0 cos HOM = O B O M = O B O H 1 = sin O H 1 B sin O B H 1 in Δ O H 1 B = sin ( H 1 B H H 1 O B ) sin H 1 B H
H 1 B H + H 1 B O = H 1 B O + H 1 O B + O H 1 B
cos 2 ω 0 = sin ( c 0 n 0 ) sin c 0
cos ϕ cos H 1 T 1 M = B T 1 M T 1 = B T 1 H 1 T 1 = O T 1 / H 1 T 1 O T 1 / B T 1 = tan O H 1 B tan H 1 B H
cos ϕ = tan ( c 0 n 0 ) tan c 0
H 1 B H 2 = 2 ( θ c θ c )
c 0 H 1 B H = 1 2 H 1 B H 2 = θ c θ c
n 0 = = θ n θ n
P n = A n 2 + R n 2 2 = const Q n = A n 2 R n 2 2
Q n = const
R n 2 = P n Q n
Q n = P n cos ϕ
R n 2 = P n Q n = P n ( 1 cos ϕ )
( S 1 ) f = a 0 2 b 0 2 2 sin 2 ( θ 0 θ ) sin ϕ + a 0 b 0 cos ϕ
sin 2 ω f = ( S 1 ) f P 0 = a 0 2 b 0 2 a 0 2 + b 0 2 sin 2 ( θ 0 θ ) sin ϕ + 2 a 0 b 0 a 0 2 + b 0 2 cos ϕ
sin 2 ω f cos ϕ = 1 e 0 2 1 + e 0 2 sin 2 ( θ 0 θ ) tan ϕ + 2 e 0 1 + e 0 2
sin 2 ω f cos ϕ = sin 2 ( θ 0 θ ) tan ϕ
k 1 = tan ϕ [ sin 2 ( θ 0 θ ) sin 2 ( θ 0 θ ) ] k 2 = tan ϕ [ sin 2 ( θ 0 θ ) + sin 2 ( θ 0 θ ) ] ,
e 0 = 1 k 2 ( 1 ± 1 + k 1 k 2 )
e 0 = k 1 2 ( 1 k 1 k 2 4 + k 1 2 k 2 2 8 )
e 0 = k 1 2 = 1 2 tan ϕ [ sin 2 ( θ 0 θ ) sin 2 ( θ 0 θ ) ] = 1 2 tan ϕ [ sin 2 ( θ θ 0 ) + sin 2 ( θ 0 θ ) ]
sin 2 ( θ 0 θ ) = sin 2 ( θ 0 θ )
2 ( θ 0 θ ) = π + 2 ( θ 0 θ ) ,
θ 0 = θ θ 2 π 4
O H 1 T 1 = c 0 n 0 O b T 1 = c n
sin ( c 0 n 0 ) sin H 1 b O = O b O H 1 = O b O f
sin ( c 0 n 0 ) sin ( c n ) = cos 2 ω f
cos 2 ω 0 = = sin ( c n ) sin c cos 2 ω f
cos ϕ = tan ( c 0 n 0 ) tan c 0 = tan ( c n ) tan c 1 + tan 2 2 ω f cos 2 ( c n )
cos 2 ω f = sin c 1 sin ( c 1 n 1 )
cos 1 2 ϕ k = ( cos 2 ω f ) max
θ 0 = θ n + θ n 2 ± π 2
0 < ( θ c θ 0 ) < π 2 and negative when 0 > ( θ c θ 0 ) > π 2 }
e 0 = 1 2 tan ϕ [ sin 2 ( θ θ 0 ) + sin 2 ( θ 0 θ ) ]
θ 0 = θ θ 2 π 4
cos 2 ω 0 = sin ( c n ) sin c cos 2 ω f e 0 = tan ω 0
cos 2 ω f = sin c 1 sin ( c 1 n 1 )
θ 0 = θ n + θ n 2 ± π 2
positive when 0 < ( θ c θ 0 ) < π 2 negative when 0 > ( θ c θ 0 ) > π 2
cos ϕ = tan ( c n ) tan c 1 + tan 2 2 ω f cos 2 ( c n )