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Патент USA US2403731

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Seamh R00
July 9, 1946-
s. M. MacNEILLE
2,403,731
BEAM SPLITTER
.Filed April 1, 1943
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STEPHEN M. mcNEILLE
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BY
INVENTOR
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WW
July 9, 1946-
s‘ M. MacNEllLLE
2,403,731
BEAM SPLITTER
Filed April 1, 1943'
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STEPHENM.M401\EILLE
INVENTOR
BY W!“
ATT'Y & AG'T
w
2.1."!"l9?
Search K0
Patented July 9, 1946
v
UNITED STATES PATENT OFFICE.
2,403,731
BEAM SPLITTER
Stephen M. MacNeille, Rochester, N. Y., assignor
to Eastman Kodak Company, Rochester, N. Y.,
a corporation of New Jersey
Application April 1, 1943, Serial No. 481,391
12 Claims.
(Cl. 88-65)
-
1
2
This invention relates to beam splitters, particularly those of the type used in range ?nders.
vention. Since the visible spectrum lies well
within a range of wavelengths equivalent to one
It is an object of the invention to provide a
octave, a beam splitter made according to the
beam splitter in which thehre?ewgngms-
present inventionto be exact for a wavelength
in ted rays are polarized at ri u angle to each 5 of about 550 millimicrons will be highly ef?cient
'
2 tially complete.‘
usta -
s,
throughout the visible spectrum.
- ' - erred emi-
For use in range ?nders and similar instru
ment of the invention results in two rays each
of which is at least 95% polarized.
ments, such a beam splitter can be made up in
the form of a compound prism with the inter
According to the invention, suchabeam splitter 10 fering layers between two components of the
includes a multilayer material whose thicknesses
are such that optical interference is used to control the ratio of the re?ected to transmitted light
prism. The angle at which the light passes
through each of the interfering layers is, as
pointed out above, determined according to
and whose orientation is such with respectto the
Brewster's angle. Hence, the angle at which the
incident light that the light strikes the interfaces 15 light passes through the glass or other material
of the layers approximately at Brewster’s angle
of which the prism components are made is ?xed
to control the polarization of the beams. It is
according to Snell’s law. A preferred form of
well known that at Brewster’s angle the re?ected
prism has the entrance and exit faces of the prism
light is 100% polarized. Therefore, if the total
perpendicular to the light beams. In a simple
re?ection is made to equal 50% of the incident 20 beam splitter there is one entrance face and two
light, all of the light vibrating perpendicular to
the plane of re?ection will be re?ected, and
hence, all of the transmitted light will also be
polarized, but at right angles to the polarization
7
/
J
0
of the re?ected beam.
exit faces to a prism. Each of these faces should
be at an angle to the interfering layers equal to
the required angle of incidence at the layers. The
manner in which this angle may be varied will
This 50% re?ection is 25 be apparent from the various examples described
approximately provided by the present invention,
below in connection with the accompanying
by including layers of alternately high and low
index, with at least one of the layers having an
,_ drawings, in which:
_
Fig. 1 is a greatly magni?ed cross-section of an
optical thickness equivalent to a quarter-waveinterfering layer according to the invention;
length of the incident light. The effect is greatly 30 Figs. 2 and 3 show two forms of compound
enhanced by having several layers of alternating
prisms using Such a layer;
high and low index, with each layer having this
Fig. 4 shows a simple ?lter employing the in
effective quarter wavelength thickness. The act-
ing thickness depends on the index of the material
and on Brewster's angle within the material as
will be pointed out in detail below. Another characteristic of Brewster’s angle is that the reflected
ray and refracted ray are at any angle of exactly 90°.
Using seven layers of alternating high and
low index, I have found that the beams will be
about 99.5% polarized for light of the exact wavelength and the exact angle of incidence speci?ed.
However, there is some tolerance allowed and, of
course, some tolerance is necessary both in the
angle of incidence and in the wavelength of the
light. Even a collimated beam of light may have
rays striking a beam splitter from angles differing
as much as 5° from the axis of the beam but one
would still get a useful amount of polarization
from a beam splitter made according to the
present invention. Similarly, the wavelength of
the light may vary from 1/2 to % the value for
which the layer thicknesses are exactly correct,
' vention;
Fig. 5 shows an arrangement alternative to
35 Fig. 1;
Fig. 6 shows a sheet material in cross section;
Fig. 7 shows a beam splitter made up frOm
sections of the material showninFig. 6,v
Fig. 8 shows the trigonometry within one layer,
40 and
Figs. 9 and 10 form Part Of a mathematical
analysis of the phenomenon which occurs in the
invention.
In Fig. 1 a multilayer material made up of
45 alternate layers II and I2 is between two trans
parent materials In and I3. A ray It strikes the
interface between the layers In and l I at an angle
of incidence A and is refracted at an angle B such
that N: sin A=N1 sin B where N3 is the index of
50 refraction of the layer l0 and N1 is the index of
refraction of the layer IL, The layers l0 and I2
have indices of refraction less than that of layer
H. The ray is refracted at the interface between
the layer I I and I2 50 that N1 sin B=N2 sin 0.
n
without nullifying the utility of the present in- 66
The angle A is selected so that B+C=90°; that
2,403,731
4
3
tween two plano?lms and the incident light H
is, so that the ray passes from the layer H into
the layer l2 at Brewster's angle. As shown in
Fig. 1 this ray continues to strike the successive
interfaces at Brewster’s angle. or course, if
is divided into a re?ected ray 42 and a transmit
ted ray 43.
The theory of these three cases shown in Figs.
N2==N3, the angle A will equal the angle C and GI 2, 3 and 4 will now be outlined brie?y. Accepted
terminology will be used wherein light is said to ‘
will also be at Brewster’s angle, but in general
vibrate in a certain direction, which is its “di
this is not convenient for two reasons which tend
rection” or “azimuth” of polarization and. cor
to con?ict. The ?rst reason is that in order to
get the maximum effect with the least num
ber of layers, the index N2 should be as low as
possible and the index N1 should be as high as
responds to its electric vector. A light ray strik
ing a surface at an angle defines a plane con,
taining the incident ray, the re?ected ray, re
fracted ray, and the normal; this is the “plane
of incidence” or the “plane of re?ection." Azi
possible. If N3 is selected to be approximately
the same as N2, the angle A becomes fairly large
muths s and p are respectively perpendicular
and for many purposes, one would prefer to have
it equal to about 45°‘. On the other hand, one 15 and parallel to this plane and of course trans
verse to the direction the ray is travelling. From
cannot have a material in which Brewster's angle
the Fresnel laws of re?ection it is known that
is 45° and still get a high percentage of re?ection
from an interface, with available materials. Thus
—sin (or-- 6)
the best solution to these con?icting requirements
sin (a-l- 6)
is obtained with components whose index is inter 20
mediate to that of the layers; as in Fig. 1. In Fig.
tan (a—-B)
1, if the index N4 of the layer l3 equals N3, the
R’etan (a+ B)
transmitted ray I1 is parallel to the incidental
ray l4.
Thus the preferred embodiment of the inven 25
tion has the index N3 differ from N: and prefer
=
2 sin (1 cos 6
ably between N1 and N2. Since the angle A is
Tr sin (a+?) cos (oz-I5)
thus slightly different from the Brewster angle
where Ra and R9 are the amplitudes of the re
for N3, the re?ected ray l5 will have a small per
?ected beams vibrating respectively perpendicu
cent of un-polarized light in it. However, this has
lar and parallel to the plane of re?ection and T:
been taken into account in my calculations. The
and Tp are transmitted amplitudes of these
re?ected ray IS, on the other hand, is completely
beams. More exactly, these are the proportions
polarized. As shown in Fig. 1 the successive re- ’
of the incident amplitude. Intensity is of course
?ected rays add up or subtract from the in
obtained by squaring the amplitude. 11 and p
tensity of the re?ected beam in accordance with
are the angles of incidence and; of refraction.
interference laws, when the layers II and I2
are on the order of a wavelength of light.
When a+?=90°, Rp=0 which means that the’
re?ected ray is made up entirely of light vibrat
In order to get the maximum re?ection from
ing perpendicular to the plane of re?ection.‘
each layer and to have these re?ections add (spe
ci?cally the amplitudes are added) the layers II 40
Further, when a+l9=90, it can be shown that
and I2 are each made equivalent to a quarter
(as in Fig. 8)
'
wavelength layer for light passing through at
the angle at which the ray it passes. That is,
the thickness of the layer l I must be
45
4m
N12
times the quarter wavelength of the light and
the layer l2 must have a thickness of
where N1 and N: are the refractive indices of
50 materials at the interface in question. Thus,
the angles a and p are ?xed as soon as materials
tmr
N22
are selected. As applied to Fig. 1, this theory ap-‘
plies to the angles B and C. For example, if Ni.
times this quarter wavelength. - At any interface,
Brewster’s angle depends on both indices of re
fraction and in the present invention, the opti
is 2.40 as for zinc sul?de and N2 is 1.38 as for
55
evaporated magnesium ?uoride, the angle B
mum layer thicknesses are those effective at
is about 30° and the angle C is about 60°. To
Brewster’s angle; hence the layer thicknesses
get an angle equal to about 45° in order to pro
involve both indices in each case as indicated by
vide a prism of the shape shown in Fig. 2, the
the above mathematical expressions.
components must be made of a glass having an
In Fig. 2 a compound prism including com 60 index of about N3=1.69. With this arrangement
ponents 20 and 2| is made up so that the angle
N3 sin A=N1 sin B which equals
of incidence D is 45°. The incident ray 22 strikes
N1Ng
a multilayer material located between the com
ponents 20 and 2| to give a transmitted ray 24
1/N12‘i'N22 '
and a re?ected ray 23. The entrance surface 25 65
With six interfaces as shown in Fig. 1 the total
and the exit surfaces 26 and 21 are all at 45° to
re?ectance R52 is over 99% for light of one wave
the multilayer material.
length polarized (in azimuth s) perpendicular
In Fig. 3 the components 30 and 3| are of a
to the plane of incidence and if this wavelength
lower index of refraction so that the angle of
incidence is E and the incident ray 32 and the 70 is selected in the green it is over 95% throughout
the visible spectrum. From four interfaces the
re?ected and transmitted rays 33 and 34 pass
re?ectance would be about 95.2% in the green
respectively through the entrance and exit faces
35, 36 and 31 perpendicularly, when these faces
are at an angle E to the interlayer.
In.‘ Fig. 4 the interlayer 40 is cemented be
I
I
and slightly less for the whole spectrum. Also,
for a 1° shift in the angle of incidence, to allow
75 for convergence or divergence of the incident
~
I
--
~
I
Search. R00
2,408,781
5
beam, the re?ectivity of light polarized parallel
to the plane of incidence (i. e. azimuth 9) would
rise from zero only to about |/z%, again assum
ing six interfaces. The tolerances for any other
particular arrangement can be similarly com- -
puted.
where G is the thickness of the layer
In Fig. 3 a prism material is selected to have
an index of refraction Na equal to that of the
low index interfering layer, 1. e. equal to Na. If
Ni=2.4 and Na=Na=L5 the angle A should be
=gggg-N1 sin a(2G tan 5)
but N1 sin a=Nz sin 3 and therefore
such that sin A equals
A-2GNI
2 cos B (l-sinI ?)
i
w/N1’+Nl’
=2GN; cos 5
Thus A equals 65° 40' approximately. In Fig. 3
Therefore
this angle is marked E to distinguish from the
angle of incidence in Fig. 1.
A
In Fig. 4 the index of refraction of the piano
G=4N, cos B
fllm layers binding the interfering multilayer may
be neglected when computing the correct angle of 20 But from the relationship for Brewster's angle,
we know that
incidence. The angle of incidence on this outer
__N1
tan B-w;
layer is the same as if the light were striking the
face of the multilayers directly. From the equa
tion
25
it is seen that to
sin give
A the Brewsterian relation
and therefore the thickness G must equal
Ml Nf'i'" N1'
4N1'
In Fig. 5, the layers 50 are ?rst coated on
within the multilayer the angle of incidence is in
dependent of whether the high or low index layer 30 prisms 5i and then are cemented together by a
cement 52 having an index of refraction N4. If
comes ?rst and if both N1 and N: are greater
the layer 52 is made thin enough, such an ar
than
rangement is satisfactory for most purposes. On .,
{2'
the other hand, if the layer 52 has an apprecia
this angle of incidence becomes imaginary. Of
ble thickness, this particular beam splitter is use
course when a layer of medium index is between 35 ful only in collimated light where the offset of
one of lower index and one of higher index, its
the re?ected beams does not interfere with the
thickness must be equivalent to a half wave
optical quality of the system in which the beam
length rather than a quarter wavelength to give
splitter is used.
In Fig. 6 a thin supporting layer 60 having a
addititive interference.
40
The re?ectivity R2 of X interfaces can be com
low index of refraction (about 1.5 say) is coated
with a quarter wavelength layer ii (the quarter
puted from the formula
wavelength being computed at the proper angle
R =tanh
tanh-lr]
of incidence as discussed above). Methods of
where r is the ratio of re?ected to incident am
plitude at each surface and the hyperbolic tan
coating such layers are described in Nadeau and
45 Hilborn application 358,512, ?led September 26,
gents are obtained from any suitable tables. This
formula holds where all the layers have a thick
ness such that the re?ectivities interfere additive
ly. If the components have an index lower or
1940. The resulting ?lm is then cut into sections
as shown by the broken lines 82 and a pile of lay
ers is made as shown in Fig. '7. These layers are
cemented together; the cemented layer is not
of incidence a is re?ected toward L at an angle a
rality of quarter wavelength layers 8| interleaved
higher than both of the layers, the layers imme 50 shown and may have an index equal to N: so as
to be ineffective optically. This pile is then ce
diately adjacent to the components should have
mented between materials 63 such as prisms hav
a thickness equivalent to a half wavelength but
ing an index of refraction N: which may be equal
the rest of the interlayers are equivalent to a
to N: as discussed in connection with Fig. 3 or
quarter wavelength as above.
. '
The formula used above for actual thickness 55 may be of any particular value required to give
the desired angle of incidence as in Fig. 2. In
can be computed trigonometrically from Fig. 8.
Fig. 7 the multilayer material consists of a plu
The incident ray reaching the point H at an angle
with relatively thick layers 60 and is hence most
and refracted toward J at an'angle p. The re
'
fracted ray is re?ected from J to K also at an 60 useful in a collimated beam.
angle ,6 and is then refracted at an angle a. This
Mathematical analysis is all apparent from the ?gure. The line KL is
This analysis is included purely for mathema
drawn perpendicular to the re?ected ray so that
ticians as an explanation of the theory involved
the angle at L is 90°. The optical path differ
ence which determines the interference between 65 in the reflection of light from multilayer ?lms.
It demonstrates, however, a phenomenon practi
the ray ‘ID from H and the ray ‘II from K equals
HJ-i-JK-HL, since the line IQ: represents the
wave front. Of course, the distances HJ and JK
cally unique in nature. The desired re?ectivity
(of light vibrating perpendicular to the plane of
incidence) varies with wavelength according to
must be multiplied by Na since optical distance is
the important factor and similarly the distance 70 an oscillating function between 0 and 100%
throughout the spectrum, but just before this
I-H.» must be multiplied by N1. Therefore, to give
function enters the visible spectrum it rises to a
constructive interference which requires that the
value greater than 95%, it remains there until it
ray 10 and ‘H be a half wave out of phase (the
passes through the visible range. and then it re
other half wave being provided .by the known
change of phase at one interface) ,
78 verts to its oscillating form. This e?iciency of
n
e
2,403,731
8
Therefore,
the invention throughout the visible spectrum is
obviously most fortunate.
Pn=Pn+ ('" 1) “App-1
Consider a light beam of wavelength x incident
upon a series of 11. parallel non-scattering iso
which may be‘ expanded to its individual terms
and added, and in general any value may be spe
tropic layers forming n interfaces, the top layer
being thick (e. g. the prism discussed above) and
the top surface of the top layer hence not being
involved in this analysis. The indices of the lay
ci?cally calculated. When the layers consist of
two substances alternating Tn=—-Tn—l and if the
70 value for each layer is odd
Rn=tanh [n tanh-lrn-il
which is easy to calculate with tanh tables. In
ers and of the bounding media are represented by
No to Nn as shown in Fig. 9, the incident beam
striking surface n ?rst and at an angle an. The
cidentally, if the lc’s are even and n is even Rn is
subsequent angles are of course such that
zero, but if n is odd Rn equals m.
N» sin Gm=Nn-1 sin (1n-—1=N0 sin do
In the speci?c zinc sul?de, magnesium ?uoride
case
discussed above with angles of 30° and 60°
The phase change T introduced by the double 15
in the two media, the re?ected amplitude :- is .5
traversal of any layer (the top thin layer n-l.
and 0 respectively for light vibrating perpendicu
say) as discussed in connection with Fig. 8 is equal
to
Y
where G is the thickness of the layer. For con
lar and parallel respectively to the plane of in
cidence. For six layers therefore (6 interfaces,
the top layer being the prism)
20
Rs=tanh 6 tanh-1.5
=.9972
structive interference T must equal 1r (or a mul
Since re?ectivity is the square of the amplitude
tiple thereof) ; this simpli?cation of the analysis
R2e=.9944 for light vibrating perpendicularly and
will be introduced at the proper time. Also, due
‘to the phase shift difference between re?ection 25 0 for light vibrating parallel to the plane of in
cidence.
at a dense-rare interface and at the interface
Now to ?nd the effect of different wavelengths,
from the other side to give rare-dense conditions,
assume that T1.=1r for M, i. e., that the above
any quantity representing phase change will be
computations were made for some standard
positive or negative depending on which way the
30 wavelength in. Thus we already know that for
beam strikes any surface in question.
)\==}\o, T=1r and Rs (perpendicular) =.9972 and for
Let Tn be a symbol representing amplitude and
)\=1/2)\o, T=21r and Rs (perpendicular) =0. In
phase change of a ray re?ected from interface n
fact R6=.9972 for )\=)\o, 1/3M, 1/5)“) etc. and equals
and let Rn be a similar symbol of the total wave
zero for )\=1/2)\o, 1AM, etc. There are other wave
re?ected from the n interfaces, numbers 1 to n.
Then by simply adding amplitudes for the mul 35 length values for which Rs equals zero and the
exact values can only be calculated by elaborat
tiple re?ections, the total for n interfaces is
ing the original equation for Rn+1. The actual
calculations are laborious, but for anyone inter
_rn+Rn—-leiT'_l
' ')_1+n.Rn-1e"T-1
It will be noticed that for the last interface (num
ber l), R1=r1. All of the amplitudes are meas
ured in the bounding medium n in the above
expression. Complexities introduced by absorp
ested in them, (1) the general equation and (2)
40 the simpli?ed equation for six layers of the same
45
tion in each ‘layer are not here considered. From
Fresnel’s laws it is known that Tn for light vi
Sin (a1|+an—l)
and for light vibrating parallel to the plane of
logarithmically.
‘
General Equation l
brating perpendicular to the plane of incidence
= —sin (as-11H)
optical thickness and alternate layers of the same
material are given below.
Figure 10 shows a graph of the second equation,
the wavelength scale being given as a ratio, 1. e.,
‘II
50
'II
‘
R?=zriem+ 2 Tirkne:(o,-n+m+ _ . _
i=1
r>k>j=1
all divided by
incidence
___tan (an-am)
'
tan (a»+a..-1)
55
It happens that when the thickness of the lay
I ers is such that T=k1r where k is an integer, the
equation for re?ectivity can be conveniently con
verted to one. involving hyperbolic tangents and 60
tables of these functions can then be used in cal
culating a particular value. When T=k1r,
65
Let
.
and
R,.=tanh P.
‘V
r,,=tanh p,
70
then
It will be noted in Fig. 10, that if the standard
wavelength is M=510 millimicrons (i. e., if the op
Search R0‘
2,403,731
10
the layers and components forming at least four
tical thickness of each layer is one quarter of 510
millimicrons at the angle at which light travels
through that layer) the value of R28 remains
above 97% for the visible spectrum, and when
interfaces and the entrance and exit faces of the -
prism being oriented to transmit light striking
the interfaces between the layers at Brewster’s
angle.
this is integrated against the visibility curve
would be about 99%.
Having thus described various embodiments of
my invention, I wish to point out that it is not
6. A prism according to claim 5 in which the
components have an index of refraction N: and
the entrance and exit faces of the prism are each
at angle A to the layers where
limited to these structures but is of the scope
10
of the appended claims.
sin A=
What I claim and desire to secure by Letters
Patent of the United States is:
7. A prism according to claim 5 in which the
1. A multilayer material for polarizing light of
alternate layers are zinc sul?de and the inter
wavelength 7\ comprising a plurality of thin trans
parent layers each of which is of uniform thick 15 vening layers are a ?uoride.
8. A prism according to claim 5 in which the
ness and forms a refracting interface with the
alternate layers have an index of refraction about
adjacent layers, the alternating and intervening
2.4 and the intervening layers have an index less
layers having different indices of refraction N1
than 1.55.
and N: respectively, the alternate layers each
20
9. A prism according to claim 5 in which the‘
havingathickness
alternate layers have an index N1 about 2.4, the
intervening layers have an index N2 between 1.35
WN1=+N2=
and 1.50, and the components have an index N:
liNlz
about 1.7.
and the intervening layers each having a thick
10. A compound prism for polarizing light over
25
ness
the visible spectrum, said prism having two trans
parent components, one entrance and two exit
faces, and sandwiched between the two compo
’
4N,I
nents a plurality of thin transparent layers each
which causes constructive optical interference to
light re?ected at Brewster’s angle and which 30 of which is of uniform thickness and forms a re
fracting interface with the adjacent layers or
hence causes increased re?ectivity at said angle.
components, alternate layers having one index
2. A multilayer material according to claim 1
of refraction N1 and the intervening layers hav
having at least four interfaces spaced to give said
constructive optical interference and hence to 35 ing a different index of refraction N2, said alter
nate layers each having a thickness approximat
increase the ratio of reflected t0 transmitted light
gm
at Brewster’s angle.
ing
~
3. A multilayer material according to claim 1
14O‘/N1'+N—T
having six interfaces spaced to give said construc
N,2
tive optical interference at Brewster’s angle.
40 millimicrons and said intervening layers each
4. A multilayer material according to claim 1
having a thickness approximating
in which the thicknesses are determined precisely
with respect to the indices of refraction for green
light.
5. A compound prism for beam splitting and 45 millimicrons, the layers and components forming
at least four interfaces and the entrance and exit
x
3).
faces of the prism ‘being oriented to transmit light
a t° '2
striking the interface between the layers at Brew
polarizing light over a wave length range of
said prism having two transparent components, 50 ' ster’s angle.
‘ 11. A prism according to claim 10 in which the
one entrance and two exit faces, and sandwiched
components have an index of refraction N: and
the entrance and exit faces of the prism are each
at an angle A to the layers where
between the two components a plurality of thin
transparent layers each of which is of uniform
thickness and forms a retracting interface with
the adjacent layers or components, alternate 55
layers having one index of refraction N1 and the
intervening layer having a different index of re
N1N3
A = —————
N3w/N1—’+'N¢'
12. A prism according to claim 10 in which the
components have an index of refraction N: where
fraction N2, said alternate layers each having a
thickness approximating
60
and said intervening layers each having a thick
ness approximating
.
Sm
N1N1
Na] N1__z+
N2:
is approximately .7 and the components are 45
degree prisms with the layers between their hi’
potenuse faces.
65
STEPHEN M. MAcNEIILE.
'
Certi?cate of Correction
Patent No. 2,403,731.
July 9, 1946.
STEPHEN M. MACNEILLE
It is hereby certi?ed that errors appear in the printed speci?cation of the above
numbered patent requiring correction as follows: Column 1, lines 33 and 34, for
_ “acting” read actual; column 5, line 15, for “65°” read 63°; column 8, lines 55 and 56,
for that portion of the equation reading
""
~em,-a,+a,+e-a.>+
.
ei(0i"0b+'l"9n)+
read
and that the said Letters Patent should be read with these corrections therein that
the same may conform to the record of the case in the Patent O'?ice.
Signed and sealed this 8th day of October, A. D. 1946.
[m]
LESLIE FRAZER,
First Assistant Gammiaeioner of Patents.
Certi?cate of Correction
Patent No. 2,403,731.
_
July 9, 1946.
STEPHEN M. MACNEILLE
It is hereby certi?ed that errors appear in the printed speci?cation of the above
numbered patent requiring correction as follows: Column 1, lines 33 and 34, for
“acting” read actual; column 5, line 15, for “65°” read 63°; column 8, lines 55 and 56,
for that portion of the equation reading
and that the said Letters Patent should be read with these corrections therein that
the same may conform to the record of the case in the Patent Of?ce.
Signed and sealed this 8th day of October, A. D. 1946.
[cm]
LESLIE FRAZER,
First Assistant Commissioner of Patents.
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