US2870957A - Compressors - Google Patents

Description

Jan. 27, 1959 I E. A. STALKER 2,870,957

COMPRESSORS Original Filed Dec. 26, 1947 9 3 Sheets-Sheet 1 M 60w 707; LfiZfigii figigl it I I: t; 77

92 i 42 g 44 4 5 46 R IN V EN TOR.

1959 E. A STALKER 2,870,957

' COMPRESSORS Original Filed Dec. 26, 194'? 3 Sheets-Sheet 2 I /d@ w INVENTOR. w. am. 42; 4%

Jan. 27, 1959 Original Filed Dec. 26, 194'? E. A. STALKER COMPRESSORS 3 Sheets-Sheet 3 INVENTOR.

COMPRESSORS Edward A. Stalker, Bay City, Mich.

Original application December 26, 1947, Serial No. 794,018, now Patent No. 2,749,027, dated June 5, 1956. Divided and this application March 11, 1954, Serial No. 415,459

6 Claims. 01. 230-122 with an axial flow stage of another type, to ameliorate the great loss in efliciency at off-design conditions when the compressor has been designed for a high compression ratio.

Other objects will appear from the drawings, specification, and claims.

The above objects are accomplished by the means illustrated in the accompanying drawings in which:

Figure 1 shows a vector diagram for the air approache ing a rotor blade;

Figure 2 shows a vector diagram for the air approaching a rotor blade at a flat angle;

Figure 3 is a chordwise section along the line 3-3 in Fig. 4;

Figure 4 is an axial section through an axial flow compressor according to this invention;

Figure 5 is a fragmentary diagrammatic development of some of the stages of the compressor of Fig. 1 with the blades shown solid although they are hollow in the machine;

Figure 6 is a section along line 66 in Fig. 4;

Figure 7 is a fragmentary development of the last stage of the compressor to show the vector relations;

Figure 8 is a fragmentary development of the last rotor showing the blades in section as they are in the machine; Figure 9 is an alternate rotor construction to that of Fig. 8; t

Figure 10 is an enlarged fragmentary axial section through a part of the last rotor and part of the case of the compressor of Fig. 4;

Figure 11 shows an isolated group of blades and a connecting duct, one blade having an induction slot and the other having a discharge slot;

Figure 12 is a fragmentary axial section through another compressor in which the rotor and stator blades have discharge slots and the other walls have slots for facilitating the entrance of a supersonic flow into the passages between blades; and

Figure 13 is a section along line 13- -13 in Fig. 12.

This application is a division of my application Serial No. 794,018 filed December 26, 1947, now Patent No.

2,749,027. This application is directed chiefly to compressor means incorporating blade sections designed for efficient operation at tip speeds in the neighborhood of sonic speed as well as at subsonic speeds, referred to the speed of sound in the fluid in the compressor upstream from the blades under consideration.

When a multi-stage axial flow compressor is operating at amass flow per revolution less than the optimum or design value with a back pressurethat is relatively low United States Patent 0 the axial velocity in the downstream stages may be as much. as three times the velocity which would prevail at the optimum or design condition. This is so because the upstreamlstages do. a certain amount of compressing at off design conditions and the lack of backpressure permits the flow compressed by the upstream stages to stream at greatly increased velocity through the later stages. This leadsto a great change in the direction of the fluid approaching a later rotor or stator with respect to the direction for the optimum operating condition, reducing the angle of attack of the blades and their compressing ability. t

' For instance Figure 1 shows the vector diagram for a conventional axial flow compressor for a downstream stage when the compressor is operating under optimum condition, that isatabout best efliciency and corresponding pressureratio. In this instance the axial velocity for optimum operation is C equal to a fraction of u' the peripheral velocity. Under this condition the direction of the fluid leaving the stator blade 1 and approaching the rotor blade 2 is the vector 4. Now if the axial velocity is increased to 3 times C the new direction is the vector 6 and the change in the angle of approach is' Act, which is equal to about 30. This is a greater range of angles of attack than a blade can accommodate.

Now consider a case as in Fig. 2 where the leading velocity vector from blade 10 is C directed at the positive, angle B toward the rotor blade 12. The resultant vector is 14. If the axial component of C is increased from C as for Fig. l to 3 C the new resultant velocity vector is 20, whose peripheral component is much larger than that of vector 14. The peripheral component is not magnified as greatly as the axial since the new triangle of which20 is the longer side isnot symmetrical with respect to the triangle 14 Cu. The change in angle of approach to blade 12 is now Aa equal to about 7. This is not only within the range of angles which the blade can accommodate but is also well within the range of angles ofattack for. best efficiency of the blade itself.

It is thus shown that deflecting the air'toward the oncoming rotor blades reduces the range of approach angles or angles of attack which the blade must accommodate when the compressor is operating at a pressure and speed substantially below optimum conditions provided the deflection through the angle B is accompanied by a rise in velocity.

The angle B for the vector representing the entering vector for a rotor (or stator) is positive when the vector has a peripheral component directed toward the concave face of the blade of the succeeding stage. Thus in Fig. 2, B is positive. Also in Fig. 3, B is positive since the vector 32 approaching the stator attacks the concave side of theblade 86..

The range of approach angles which can be accommc.

dated by the downstream stages can also be extended toa considerable extent by making the noses of the blades successively thicker in successive stages in the downstream direction. Thus in Fig. 3 the nose 30 is substantialy semicircular so that the relative flow wi l be able to flow about the nose without burbling when the approach vectors vary from vector 32 to vector 34 disposed angularly with respect to each other by the angle 8 (delta).

To further encourage the flow the nose is provided with the slots 36 and 38 (Figs. 3, 4, and 8) through which a flow may be inducted to control the boundary layer.

Since the fluid is compressed in successive stages the temperature rises along the compressor axis. Conse quently the velocity of sound in the fluid increases in magnitude so that the velocity of the fluid relative to the blades can be increased withoutprecipitating a com pressibility'shock. Inother Words the local velocity on theblade surfaces can be higher on the downstream bladeswithoutreaching the critical Mach number of one.

Thickening the nose of the blades makes possible a wider range of angles 6 (see Fig. 3) but increases the local velocity on the nose. However by taking advantage of the rise of temperaturefrom stage to stage, the noses of theblades of successive stages may be thickenedwithout the local Mach number exceeding the critical value.

Figs. 4-to 8 show a compressor incorporating the'foregoing features.

--In Fig. 4 the compressor is indicated generally by 4i comprised of the case 42 the rotor stages 41-46 and the stators 5156.- (See also Fig. 5.) Fluid enters the inlet 60 and is pumped through the annular or main flow passage 62 to the exit passage 64.

At the upstream end (Fig. 4) the stator 51 deflects the incoming air by means of the stator blades 66 in the direction of rotation 67 .of rotor stage 41 comprising blades-68 and hub 69. The next stator 52 also deflects the fluid in the direction of rotation of rotor stage 42, but to a'less extent, by blades 70. At the third stage the stator 53 deflects the fluid substantially axially toward the rotor 43. This stage is comprised of blades 74 and 76. The blades of each rotor are mounted on a hub similar to hub 69. The hubs and blades are adapted for rotation by shaft means '77 comprising shafts 79 and 81 fixed together.

In the succeeding stages of Fig. 4 the stator blades deflect the flow with increasing peripheral velocity components against the direction of motion of the rotor blades.

blades of the fourth stage are 78- and 80 and the blades 'ofthe fifth stage are 82 and 84. It is to be noted that in each of these stator stages (see Fig. and in the sixth stator stage the stator blades are curved to give the flow a progressively greater peripheral component in successive downstream stages.

The stator blades 86 for instance in the sixth stage have tail portions directed substantially in the peripheral direction.

In Fig. 7 the velocity vector 90 leaving the blades 86 when combined with the peripheral velocity vector u of the rotor gives the velocity vector 92 acting relative to the rotor 46. The vector 90 makes the positive angle B with the axial direction and hence even for a great increase inaxial velocity through the compressor the direction of 92 relative to the blades 94 of rotor 46 will change only a small amount in direction.

The rotor blades 94, Fig. 8 may be hollow and as shown in Figs. 4 and 11 each has its interior in communication by means of individual ducts 96 with the hollow blades 76 of the third stage. Since the fluid pressure is greater in the sixth stage than in the third stage fluid will enter the blades 94 through slot 95 and be discharged through the discharge slots 93 in blades 76. Thus the flow is induced to follow the curved portion of blade 94 making it possible to discharge the flow from the stage with a velocity direction closely perpendicular to the plane of rotation. The slots may also be omitted as shown in Fig. 5 with some small loss in effectiveness.

The last set of stators 100 (Fig. 4) takes out the peripheral component of velocity relative to the case 42 and directs the discharge of fluid axially along the passage 64.

As an alternate form the rotor may be formed as in Fig. 9. Here the blade is made in two parts, the fore part 102 and the aft part 104 spaced from the fore part to provide the slot 1%. The flow through the slot provides a jet to control the boundary layer on the convex angle B, the variation 6 (Fig. 3) is kept small and consequently the blades 94 (Figs. 4 and 5) may be thin at the nose and particularly eflicient for high velocities of flow.

As shown in Figs. 4 and 10, particularly the latter, the case 42 diverges from the wall 110 of the rotor 46 so that each passage 112 between'blades 94 is expanding in cross sectional area until the locality of the blade curvature is reached where the passage area is preferably made to contract slightly so that the flow about the curve is in a favorable pressure gradient. This facilitates an eflicient flow about the curve but is not essential.

There is also another advantage in the divergence of the hub and case walls. The increasefin the cross sectional areas of the rotor passages in the downstream direction slows down the velocity of flow before the flow is turned by the blade. Hence the appearance of compressibility shock Waves is delayed. That is, the peripheral tip speed of the blades can be higher before the shock wave appears in the passages between blades. This means that substantially greater pressure ratios can be obtained from a rotor.

The first shock waves appear at the leading edge of a blade but the critical shock wave which limits the mass flow through the rotor occurs in the passage downstream from the nose of'the blade.

-If the passages between blades begin to diverge radially opposite the blade noses, the radial expansion can compensate for the peripheral contraction due to the blade thickness. Hence there need not be a throat along the passages between blades or at least the throat may be placed far downstream from the inlet of each rotor passage. 'Thus as shown in Figs. 5 and 8 the maximum thickness may be in the neighborhood of mid chord or even further rearward. In this connection the blades: may have substantially parallel sides as shown by blades 102 in Fig. 9.

The opposite sides of the blade sections such as blades 86 (Fig. 5) are substantially parallel along a substantial length between the nose portion and the aft portion.

By making the last stage with thin blades and relatively sharp noses it can operate with, very high fluid velocities without generating shock waves at the nose or in the passage. However in some applications the velocity may become supersonic in the last stage if the back pressure is reduced sufliciently when the rate of rotation of the rotor is near the optimum speed for the compressor as a whole. For this reason the type of rotor shown in the last stage is very advantageous since it can operate even at a supersonic velocity as has been disclosed in my application Serial No. 624,013 filed October 23, 1945 entitled Compressors, now Patent No. 2,648,493. Furthermore for a high performance compressor the last stage is preferably made to have a supersonic velocity of approach of the air at the optimum condition of operation. For such a compressor it is important that the angular range of the approach vector should be small to obtain the proper shock waves at the nose of the blades and within the rotor or stator passages. These are provided by this invention.

If the blade has a tip speed relative to the case equal to the speed of sound in the fluid then the fluid speed relative to the blade exceeds. the speed of sound because the axial. component adds vectorially to the peripheral component of velocity.

In an axial flow compressor if the pressure rise is great between inlet and exit for the design condition,

' then the machine will be much less eihcient at a lower portionof the blade and induces the flow in the passage 108, between blades 102 to follow the blade surface.

The stators as shownin Fig. 4 are also interconnected by duets such as 169 to provide for flows of fluid through the blade slots. Thisconstruet ion is similarto that shown inmy U. 8. Patent No. 2,44,8 35 issuedMarch Zl, 1944. By providing the stator which gives a large positive delivery, that is at a lower value of the mass of fluid delivered per revolution. The greater the pressure rise, the greater the drop inefficiency at an ofi-design dclivery.

The compressor of this invention using the type 0 rotor 46 is provided to assuage this undesirable condition and places the axial flow compressor on a more favorby walls on four sides.

able footing with respect to other compressors, such as for instance the centrifugal compressor, than heretofore existed. P

Figure 12 shows an alternate structure for the last rotor and the stator ahead of it The balance of the compressor ahead of this statorwould have a structure similar to that of Figs. 4 and 5.

In Fig. 12 the slots 140 and 142 are located in peripheral Walls, that is the shroud ring 143 and the hub wall 110respectively. That is the rotor blades 144 of the last rotor are encircled by the shroud ring and its leading edge formsfthe slot 140 with the case wall 42. 3

Air for the case or outer wall slot 140 is bled from the passage 64 via the annular duct 150 formed in the case. The air is at a higher pressure in than in the passage at the leading edge of blade 144 and hence can flow at a higher velocity from the slot 140 than the velocity of the local main flow.

Air is also supplied from duct 150 to the slot 152 positioned in the rotor passage 62 a substantial distance inward from the leading edge of blade 144.

Air is also supplied to the slot 142 and slot 156 from passage 64 via the annular ducts 160 and 162. Air also enters the hollow interior of blade 144 via 162 to serve the slot 164.

The discharge slots 170 and 172 of stator blade 174 are also served with air from duct 150. As shown in Fig. 13 this blade has. a well rounded nose 176 and the discharge slots located near the ends of the nose contour.

The passages 112 in the rotor between the blades in Fig. 12 are similar to those in Fig. 8 and are bounded The walls 110 of the hub of the rotor and the shroud ring 143 bound the passage on radially opposite sides while the adjacent blades bound the other two opposite sides. All of the walls may have slots therein but preferably only hub and case walls and one blade have slots. Theslots in opposite walls within the passages are preferably not directly opposite each other. I

The blades discussed herein are to be considered thin blades if their maximum thickness is less than 15 percent of the blade section chord length.

In the preferred forms of the blades the chordwise length of the blade, that is the dimension along the direction of flow is preferably not more than twice the span. edges extending in the same general radial direction.

Axial flow compressors have blade structures whose main flow passages extend in the general axial direction from an inlet at the front to an exit at the rear to discharge fluid in the general axial direction.

It is to be noted that the blades of the downstream rotor blades have blade sections of fair or streamline.

. r 6 v tion of the blade section. Preferably the fore portioii of the blades as determined by the tangents 180 are set more along the plane of rotation than along the axis of rotation, that is more nearly parallel to the rotation plane than to the rotation axis. In Fig. 7 for instance the nose portion of blade 94 is set parallel to vector 92.

Also each following blade 94 preferably has the normal projection of its leading edge on the adjacent leading blade forward ofthe mid chord point thereof and ahead ofthe maximum thickness thereof.

The portion of the case opposite the high speed blades 144, Fig. 12, preferably deviates outwardly with respect to the axis of rotation. It should not converge to any great degree toward this axis so as to preclude the presence of a substantial component of the centrifugal pressure in the fluid acting upstream in the vicinity of the case. Alarge. component of pressure would reduce the mass flow of fluid per unit of time and lead to improper angles of attack of the blades and a reducedetficiency. The portion of the inner surface of the case opposite the axially central portions of the tips of said blades should be about parallel to the axis of rotation or preferably diverge outwardly.

While I haveillustrated a specific form of this invention it is to be understood that I do not intend to limit myself to this exact form but intend to claim my invention broadly as indicated by the appended claims.

I claim:

1. In combination in an axial flow compressor, a case having an inlet and an exit,.a plurality of axial flow stators supported within said case and spaced axially therealong, a plurality of axial flow rotor stages alternated with said stators and cooperating to direct a flow of said fluid at increasing pressure from said inlet to The blades also have free leading and trailing said exit, each said rotor stage comprising a hub surface and a plurality of axial flow blades carried thereon peripherally spaced thereabout with a plurality of rotor axial flow passages between said blades, each said passage having an exit facing downstream chiefly in the general axial direction to discharge fluid rearward substantially in the general axial direction, one of said rotor stages having blades of streamline blade section having a maximum thickness ordinate at about mid chord and having itsmean camber line curved chiefly in the rear half thereof, said section having a tapered foreportion extending forward from said ordinate and a tapered aft portion extending rearward therefrom, said portions having a convex upper streamline contour extending rearward from substantially the leading edge over said aft portion, and means to rotate at least one of said rotor stages such that the fluid speed relative to the blades thereof is less than the speed of sound in said fluid upstream adjacent thereto and to rotate another said rotor stage having blades formed with said streamline blade sections at blade tip speeds relative to said fluid at or above the speed of sound in said fluid upstream adjacent to the last said blades, to extend the range of operation of said compressor at high efllciency.

crease rearwardly in the radial direction but this is not w essential for increasing the range of mass flow per revolution with sustained high efliciency. The blade sections disclosed provide for eificient operation in the neighborhood of the velocity of sound in the fluid upstream from the rotor blades. These sections are relatively thin and have their maximum thickness preferably at about midchord. Preferably they are also chiefly cambered in the rear half of the chord length.

The fore portion of each rotor blade is preferably set in the rotors at a small pitch angle. This angle is to be measured between the tangent 180 (Fig. 8 to the mean camber line 182 at the leading edge or nose per- 2. In combination in an axial flow compressor, a case having an inlet and an exit, a plurality of axial flow stators supported within said case and spaced axially therealong, a plurality of axial flow rotor stages alternated with said stators and cooperating to direct a flow of said fluid at increasing pressure from said inlet to said exit, each said rotor stage comprising a hub surface and a plurality of axial flow blades carried thereon peripherally spaced thereabout with a plurality of rotor flow passages between said blades, each said passage having an exit facing downstream chiefly in the general axial direction to discharge fluid rearward substantially in the general axial direction, one of said rotor stages having blades of streamline blade section having a maximum thickness ordinate at about mid chord having its mean camber line curved chiefly in the rear half thereof, said section having a tapered fore portion extending forward from said-ordinate and .a tapered aft portion extending rearward therefrom, said portions havinga :convex upper streamline contour extending rearward-from the leading edge over said aft ,portion, said aft portion of each last saidblade section being directed. more nearly parallel to the axis of rotation of-said rotors than to the direction of said fore portionat the nose thereof, and means to rotate at least .one of said rotor stages such ,that the fluid speed'relative to-the blades th'ereofds less than the speed of sound in said fluidu'pstream adjacentthereto and to rotate another saidrotor: stage having blades formed with said-streamline blade sectionsat blade tip speeds relative to said fluid at or "abov'ethespeed of soundin said fluid upstream adjacentto the last'saidblades, 'to'extend therange -of-oper-ation-ofrsaid compressor at high efficiency.

,3. In combination inant-axial flowrcompressor for impelling a'flow of elastic fluid therethrough, a case, a rotor having a hub, said hub defining an annular-"flow passage with said case for the flow of said fluid-therethrough, and a plurality of peripherally-spaced axial flow blades carried on said hub dividing said annular =p-assage into a plurality of rotor axial flowpassagesibetween said blades, each said passage having an 'exit fa'cing downstream chiefly in the general axialdirection to discharge fluid rearward substantially -in the general axial direction, said rotor being positioned in said case for rotation about an axis, each said blade having.ta blade section of streamline form and having a curved mean camber linewith the greatest curvature in "the rear ha'lf thereof, said annular passage :havingas great alflow'cross sectional area at the exit-side of said rotoras the inlet side thereof, each said rotor passage increasing 'in cross sectional area rearward with the'exit cross sectional area greater than the inlet cross sectional arcathere'o'f, each following blade having the normal projection=of its leading edge on the adjacent leading blade substantially forward chordwise of the mid-chord pointof-saidradja'cent leading blade, said rotor blades each having blade sections each with maximum thickness thereof lying rearward of the point of normal projection thereon of the leading edge of the adjacent following blade and closely adjacent to said mid-chordpoint, and means to rotate said blades with a tip speed relative :to said fluid -at=or above the speed of sound in said fluid upstream adjacent to said blades to increase the'rangc of operation at high efiiciency during the norm-a1 optimum condition of 'operation of said compressor corresponding to fluid pressures at substantially maximum values thereof at substantially the maximum normal rate of rotation of said rotor.

4. In combination in an axial flow compressor, a case having an inlet and an exit, a plurality of axial'flow stators supported within said caseand spaced axially therealong, a plurality of axial flow "rotor stages positioned in said case and alternated with said stators and cooperating to direct a flow of said fluid at increasingpressure from said inlet to said exit, each said'rotor stage' comprising a plurality of axial flow blades peripherally spaced with a plurality of rotor. axial flow passages between said blades, each said passage having an' exit facing downstream chiefly in the general axial direction to discharge fluid rearward substantially in the general axial direction, each said rotor passage increasing in cross sectional area rearward therealong with the exit cross sectional area greater than the inlet cross sectional area, one

of said rotor stages being a high speed rotor having bladesof streamline blade section having a maximum thickness ordinate and; having a mean camber line curved chiefly in the rear half thereof, eachylast said section having a tapered fore portion extending forward from said ordinate and a tapered aft portion extending rearward therefrom, saidportions having a convex upper streamline contour extending rearward from substantially' the leadinged'ge over said aft portion, said blade sections of said high speed rotor stage having smaller 8' maximum thicknesses than the corresponding sections of another said rotor expressed as fractions of the corresponding chord lengths, and means to rotate at least one ofsaidrotor stages such that the fluid speed relative to the blades thereof is less than the speed of sound in said fluid upstreamadjacent thereto and to rotate *said high speed rotor stage at blade tip speeds relative to adjacent said fluid at or above the speed of sound in said fluid upstream adjacent the last said blades, to extend the range of operation of said compressor at high efliciency during the normal optimum condition of operation of said compressor corresponding to fluid pressures at substantially maximum values thereof at substantially the maximum normal rate of rotation of said rotor.

5. In combination in an axial flow compressor for impelling a flow of elastic fluid therethrough, "a case, 'a plurality of axial flow-stators supported within said case and spaced axially therealong, -a plurality-of axial flow rotor stages positioned in said case and alternated with said stators and cooperating therewith to direct a flow of said fluid at increasing pressure from said inlet to'said exit, each said rotor stage comprising a plurality of axial flow blades peripherally spaced with a plurality of axial flow passages between said blades, each said passage having an exit facing downstream chiefly in the general axial direction to discharge fluid rearward substantially in the general axial direction, each said rotor passage increasing in cross sectional area rearward therealong with the exit greater than the inlet cross sectional area, said plurality of rotor stages including a downstream rotor having blades of streamline blade'section with a maximum thickness ordinate at about mid'chord and a mean camber line curved chiefly in the rearhalfthereof, each said section having a tapered fore portion extending forward from said ordinate and a tapered aft portion extending rearward therefrom, said portions having a convex upper streamline contour extending rearward from substantially the leading edge over said aft portion, and means to rotate said downstream rotor stage at blade tip speeds relative to said fluid of sonic or greater than sonic speed in said fluid adjacent said blades during the normal condition of operation of said compressor corresponding to fluid pressures of substantially maximum values at substantially the maximum normal rate of rotation of said downstream rotor stage.

6. In combination in an axial flow compressor, a case having an inlet and an exit, a plurality of axial flow stators supported within said case and spaced axially therealong, a plurality of axial flow rotor stages alternated with said stators and cooperating to direct a flow of said fluid at increasing pressure from said inlet to said exit, each said rotor stage comprising a hub and a plurality of axial flow blades carried thereon peripherally spaced thereabout with a plurality of rotor flow passages between said blades, each said passage having an exit facing downstream in the general axial direction to discharge fluid rearward substantially in the general axial direction, each said rotor passage having at least the aft portion thereof increasing in cross sectional area downstream therealong with an exit cross sectional area greater than the inlet cross sectional area thereof, at least one of said rotor stages being a high speed rotor having blades of high speed blade section whose maxium thickness ordi nate is at about the mid-point of the chord of said section, this last said section having a tapered fore portion extending forward from said ordinate and a tapered aft portion extending rearward therefrom, said portions having a convex upper streamline contour extending rearward from substantially the leading edge over said aft portion, and shaft means to rotate at least one of said rotor stages such that the fluid speed relativeto-the blades thereof is less than the speed of sound in, said fluid upstream adjacent thereto, and a stator positioned upstream adjacent said high speed rotor stage for directing fluid against the direction of rotation of said 9 high speed rotor stage and cooperating with said shaft means to rotate said high speed rotor stage at blade tip speeds relative to said fluid at or above the speed of sound in said fluid upstream adjacent said blades of said high speed rotor stage, to extend the range of operation 5 of said compressor at high efiiciency.

References Cited in the file of this patent UNITED STATES PATENTS Ponomareff Oct. 29, 1940 10 Whittle June 12, 1945 UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,870,957 January 27, 1959 I v Edward A. Stalker It is hereby certified that error appears in the printed specification of the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 2, line 24, for Au, read Aoc column 6, line 73, for chord having read chord and having-.

Signed and sealed this 1st day of December 1959.

[SEAL] Attest:

KARL H. AXLINE, ROBERT C. WATSON, Attesting Ofiioer. Commissioner of Patents.

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