US3289997A - Mine prop and shoe arrangement - Google Patents

Description

6, 1966 F. BEULKER ETAL 3,289,997

MINE PROP AND SHOE ARRANGEMENT Filed May 5, 1965 2 Sheets-Sheet 1 IN VENTOR Franz Beulker Huniberf Bqck BY Manfred Flot r Dec. 6, 1966 F. BEULKER ETAL 3,289,997

MINE PROP AND SHOE ARRANGEMENT Filed May 5,. 1965 2 Sheets-Sheet 2 INVENTOP Franz Bea/ker- Kuniberz Becker BY Manfred Fl'zer United States Patent M 40,52 8 Claims. c1. 248357) This invention relates in general to mine roof prop and support shoe arrangements, and more particularly to mine prop and shoe arrangement wherein the shoe member which functions as a base support for a columnar mine prop, is releasably connected with the prop and can be positioned relative to the prop within limits along one or more selected paths.

Essentially, the prop and shoe arrangement of the invention provides a foot element which is fixedly connected to the bottom end of the prop, and which has a curved socket surface, a post element having a curved end surface disposed in operative slidable engagement with the curved socket surface of the foot element to permit limited articulate relative movement between said foot and post elements, the shoe member fixedly connected to the post element, and means operatively connecting said foot and post elements for limited relative articulate movement in a selected path for positioning the shoe member relative to the mine prop in a corresponding path.

Although such post element to foot element connecting means which permits relative articulate movement along a single selected path, will in many mine applications be useful, the invention in its preferred embodiment further provides a connecting means which permits limited relative articulate movement of the post and foot in each of new selected paths for positioning the shoe relative to the prop in corresponding paths, and thus provides an additional degree of freedom in the relative movement capability of the shoe and prop.

In general, any suitable contours can be provided on the surfaces of the foot and post elements which will permit slidable surface movement therebetween when said elements are articulated. However, in accordance with a preferred embodiment of the invention, the foot element is provided with a concavely curved, and preferably hemispherical surface, with the post element being provided with a similar, but convexly curved hemispherical surface, so that when said post and foot elements articulate, their respective surfaces cooperate with one another in the manner of a ball and socket joint.

It is advantageous to use such mating curved surfaces in the post and foot elements because of their load bearing area, which serves for transferring the roof support load exerted by the prop column to the shoe member for distribution over a relatively larger mine floor bearing area.

As will be apparent to those skilled in the art, the contacting surface arrangement in the foot and post elements can be reversed, with the convex loading bearing surface being provided on the foot, and the concave surface being on the post.

While for purposes of clarity and simplification, the contacting curved surfaces of the post and foot elements are described herein as hemispherical, it is intended that their designation as such includes other types of curved surfaces, such as elipsoids, paraboloids, as well as other surfaces of revolution in general, which are generated by lines rotated about a generating axis. As will be appreciated by the artisan, such other curved surfaces can be readily substituted for theoretically hemispherical surfaces to accomplish the objects of the instant invention.

Patented Dec. 6, 1966 In accordance with the invention, the means for operatively connecting the foot and post elements for limited articulate movement includes means defining a passage extending through the post, a pin member extending through said passage, and a collar member disposed in spaced-apart surrounding relation to said post. The collar member is operatively connected in fixed relation to the foot element and is also operatively, but releasably, connected to the end portions of the pin member which extends through the post. This spaced-apart collar and post arrangement limits the relative articulate movement of the foot and post elements, by reason of the fact that at limit positions of articulation, a portion of the collar bears in abutment against the post, thereby preventing further articulate movement.

The passage through the post is bounded in relation to the size and shape of the pin member extending therethrough in order to limit the relative articulate movement of the foot and post in a path corresponding to the limited transverse displacement capability of said pin within the passage, whereas the collar limits the relative articulate movement in a path corresponding to rotation of the prop about the longitudinal axis of the pin member. This limited articulate movement capability can be provided in accordance with the invention by creating the passage through the post with a flattened bi-conical boundary surface which is flattened approximately parallel to the generating axis of the curved end surface on the post.

For example, assuming that the mine prop when it is supported by the shoe member resting on a horizontal floor is to be made capable of limited articulate movement relative to a given horizontal line passing through the longitudinal axis of the prop, i.e. the prop is to be swung through a given angle in a plane perpendicular to the horizontal floor bearing surface of the shoe and parallel to the given horizontal line, the pin member is connected to the collar so as to be horizontal and perpendicular to the plane of proper articulation, with the clearance space between the post and collar being such that when the foot pivots With the prop about the longitudinal axis of the pin member, the collar abuts against the post when the selected limit articulation of the prop relative to the shoe has been reached.

In such case, where it is desired to provide a second limited prop to shoe articulation capability in a plane perpendicular to the plane of articulate movement about the pin axis, the bi-conical oval, slot-like passage is made flattened in a plane parallel to the second plane of articulate motion, with the effective apex angles of said biconical passage defining the articulation limits in this plane of movement.

Thus, considering the articulate movement of the prop relative to the shoe about the longitudinal axis of the pin as fore and aft articulate movement, and the limited movement established by the slot and pin configuration as lateral articulate movement, it can be readily noted that the collar to post clearance establishes the fore and aft movement limits, whereas the slot passage and pin arrangement establishes the lateral movement limits.

As can be appreciated by the artisan, the articulate movement limitations imposed by the collar and post, and by the pin and post passage can be interchanged as desired, and furthermore, it is assumed that the movement limitation imposed by the collar is greater than that imposed by the pin and post passage. In applications of the invention wherein a greater lateral prop swing capability is desired than is permitted by the collar in the fore and aft prop swing plane, appropriate lateral portions of the collar can be cut away and the pin member can be supported at its end portions by suitably extended lugs aflixed to the collar.

In the automatic winning of coal by means, for example, of a coal planer carried on a conveyor or by any automatic winning system, economic success ultimately depends substantially upon setting props and recovering them with the necessary speed. In coal mining operations of this type, an automatically advancing prop system is most frequently used to meet this requirement. Such prop advancing systems are usually hydraulically operated.

An automatic prop advancing system of this type must necessarily meet a number of minimum requirements. For example, the props must be removably fastened to the frame or rack, or at least to their associated shoes. The method used for fastening the shoe to the prop must provide for a certain amount of articulation, which is expediently greater in a selected vertical plane than in another vertical plane perpendicular thereto.

The greater pivoting action is desired in the plane parallel to the direction of advancement of the propping system. At the same time, the elongated prop shoes must be fastened to the prop in a non-rotating manner relative to the longitudinal axis of the prop, so that they will not turn sideways as the props and shoes are advanced. Additionally, for various reasons, for adaptation to the unevenness of the mine floor, a certain articulation capability between the props and their associated shoes, as in dipping and striking, is indispensable. This invention is directed to mining prop with a removably fastened shoe, in which the shoe has a ball post member aflixed thereto which engages into a matching cup shaped recess in a foot member which is aflixed to the bottom end of the prop.

The prop and hoe arrangement of the instant invention features a novel releasable fastening means for operatively connecting the foot to the post, this connecting means providing an annular collar member which is fastened releasably to the foot of the prop, and which envelopes the post with a selected clearance and which is attached to a cross bolt pin which passes through the post, a clearance space being provided between said pin and the collar body and/or pin and post, to permit a certain pivoting action in one plane, preferably the vertical plane passing through the longitudinal axis of the bolt. In the vertical plane perpendicular thereto, i.e. and also perpendicular to the longitudinal axis of the pin, a certain limited articulation capability is also provided, the pin serving as the pivoting axis.

Furthermore, it is advantageous for the interlocking parts of the foot on the prop and the shoe to be secured in their normal Working position in relation to one another by holding members which can be driven out in order to release the connection by driving them in the same direction as that in which they were driven in to make the connection. For example, radially disposed drift pins can be driven through portions of the collar ring surrounding the foot, and above the foot, so that portions of their length overreach the edge of the prop foot. Instead of being surrounded by a ring, the prop foot can also be surrounded by a plurality of lug members distributed about the periphery of the foot and afiixed thereto, with the holding pins being driven through said lugs to connect the collar member to the foot. The radial holes in the lug members through which the pins engage can have a substantially larger diameter than the ends themselves. The free space remaining between such holes and the pins can be filled by one or more half bushings placed in tandem lengthwise with respect to the pin, said half or split bushings being capable of being driven out of the hole in the direction toward the longitudinal axis of the prop in order to free the holding pin and release the connection. The other half portion of the space between the hole and the pin, preferably the lower half, can be filled with another split bushing.

The extremities of the pin member extending through the post and connected through the collar ring, can be sel. cured by means of elastic drift pins passed through appropriate holes in their opposite end portions.

In accordance with another embodiment of the invention, the foot element is provided with a plurality of affixed lug members, and the collar member is provided with a corresponding plurality of affixed yoke members, with said collar member being fastened releasably in fixed relation to the foot element by means of a plurality of pin members disposed through holes provided in said yoke members and extending in operative engagement into corresponding holes provided in said lug members.

It i therefore, an object of this invention to provide a mine prop and shoe arrangement wherein the mine prop is releasably connected with the shoe.

Another object of the invention is to provide a mine prop and shoe arrangement as aforesaid, wherein the mine prop can be articulately positioned in one or more selected paths relative to the shoe.

A further object of the invention is to provide a mine prop and shoe arrangement as aforesaid having simple and releasable fastening means for operatively connecting the mine prop with its associated shoe.

Another and further object of the invention is to provide a mine prop and shoe arrangement as aforesaid wherein the mine prop can be articulately positioned relative to the shoe within selected limits in each of two paths.

A still further object of the invention is to provide a mine prop and shoe arrangement as aforesaid wherein rotation of the shoe relative to the longitudinal axis of the prop is substantially precluded.

Other and further objects and advantages of the invention will become apparent from the following detailed description and accompanying drawings in which:

FIG. 1 is a side elevation view, partly in section of a mine prop and shoe arrangement according to a preferred embodiment of the invention.

FIG. 2 is plan view of the shoe and prop foot connection means of FIG. "1.

FIG. 3 is sectional view taken along the line 33 of FIG. 1.

FIG. 4 is a side elevation view, partly in section, of a mine prop and shoe arrangement according to another embodiment of the invention.

FIG. 5 is a plan view, partly in section, of the mine prop and shoe arrangement of FIG. 4 taken along the line 55 therein.

Referring now to FIGS. 1 and 2 which show a mine prop and shoe arrangement A wherein the shoe member 10 is constructed in the manner of a skid, and is provided with upturned forward and rear lip portions 11 and 11 respectively, which adapt said shoe member to travel slidably along a mine fioor (not shown) when the prop and shoe ararngement A is displaced toward or away from a mine face (not shown) together with the entire mine roof propping frame (not shown).

A hemispherical-ended post 12 which transfers the load forces exerted by a mine prop 13 into the shoe 10 extends upward therefrom at approximately a midpoint position between the forward and rear lips 11 and 11'. In the preferred embodiment shown, the hemispherical post 12 is manufactured separately and is fastened fixedly to the shoe 10 by passing the bottom shank portion 18 of said post 12 into a hole 19 provided in shoe 10, and welding said shank 18 to the boundary surface of the hole 19.

For purposes of simplification, only one prop 1-3 is shown, since it will be readily understood by those skilled in the art that the other props (not shown) in the same propping frame (not shown) as the prop 13 can be similarly equipped with the shoe arrangement A. The prop 13 can be connected by means of a lug 14 and a bar 15 to such other props in the propping frame (not shown).

The bottom end of the column-like prop 13 is operatively connected in fixed relation to a foot member 16,

such as by welding, bolting, etc. The foot 16 is pro vided with a recessed concave, curved surface 17 which is preferably hemispherical, and similar to the hemispherical surface S on the post 12, so that when the surfaces 17 and S are disposed in operative slidable engagement as shown for transferring the load forces exerted by said prop 13 to the shoe via the foot 16 and post 12, said surfaces 17 and S cooperate in the manner of a ball and socket joint. This particular arrangement of the surfaces 17 and S permits limited articulate movement of the prop 13 and foot 16 relative to the post 12 and shoe 10.

In order to couple the shoe 10 and prop 13 to one another so as to retain a selected pivoting capability, and yet prevent the unintentional separation of said shoe 10 and prop 13, a collar member C having a ring 21) and annular sleeve 21 welded to the bottom side of said ring 20 is provided. The central opening of said ring 20 and sleeve 21 is of such dimensions as to admit the hemispherical surface S portion of the post 12 therethrough for operative engagement with the surface 17 on the foot 16.

The collar member C is operatively connected to the post 12 by means of a cross bolt pin member 22 shown as tubular in construction, and which passes through a passage 23 extending completely through the post 12. The passage 23 is defined by a flattened, bi-conical boundary surface which is flattened approximately par-allel to the generating axis Y of the hemispherical surface S, and which is also the longitudinal axis of the post 12. This bi-conical flattened and flared shape of the passage 23 is more clearly apparent as shown in FIG. 3, :as is the cooperating relation between the pin member 22 and said passage 23 which limits the relative articulation of the prop 13 and its foot member 16 with respect to the post 12 and shoe 10 in the plane of section 3-3, i.e., the plane normal to the bottom surface plane B of the shoe 10 and which passes through the longitudinal axis Z of the pin member 22.

The pin 22 can thus perform both tilting movements in this plane 33 relative to the post 12, as well as rotation about its longitudinal axis Z. The extremities of the tubular pin 22 pass through mating holes D in the sleeve 21 of collar member C and are secured to said sleeve 21, and hence to the collar C by means of elastic drift pins 24 which are driven into corresponding transverse drift holes in the pin 22 located on the opposite end portions thereof which are outside of the sleeve 21. These drift pins 24 can be conveniently driven into their respective holes on pin 22 with light hammer blows and can be likewise driven out whenever the arrangement A is to be disassembled.

Three lugs 25 are disposed on the top side of ring 20 at intervals around the periphery of the foot member 16, said lugs 25 being extended above the periphery of the foot member '16. The lugs 25 have radial holes 26 having diameters which are substantially larger than those of the elastic drift pins 27. In these holes 26, the lower portion of the clearance between each drift pin 27 is filled by a half bushing 28, which is actually a cylindrical semi-circular longitudinally split bushing 28, and above the pin 27, two semi-circular rings 29 are disposed radially in tandem. In any case, an elastic drift pin 27 of this sort is held perfectly fast by the split bushings 28 and semi-circular rings 29 in the hole 26 in each of the lugs 25. When this pin '27 assumes the position illustrated in 'FIGS. 1 and 2, its inwardly facing free end overlaps the foot member 16 of the prop 13. As FIG. 2 illustrates, the prop foot member 16 and hence the prop 13 is positively coupled to the ring 20 by the plurality of radially disposed drift pins 27 supported by the ring 20 of the collar member C and disposed in operative engagement with the foot member 16.

Whenever an elastic drift pin 27 is to be removed, the split rings 29 can be driven out by driving them radially inward, thus freeing them successively. When the split rings 29 are removed, the pin 27 can be pulled out. After one or two of such pins 27 have been removed, the prop 13 and its affixed foot member 16 can be easily lifted off from the post 12.

FIGS. 4 and 5 exemplify another embodiment of the invention in the form of a prop and shoe arrangement A, wherein the same basic prop 13, post 12 and shoe 10 arrangement is provided, but a somewhat diiferent collar member C is used in combination with a modified foot member 31.

The ring 20 of the collar member C is similar to that used in the case of the collar member C, except that a second annular ring 30 is aflixed, such as by welding, to the top side of ring 20 so as to laterally surround the foot member 31. The ring 30 has three yoke members E aflixed to it, each yoke member E having a radially disposed opening 32 into which corresponding matching lugs 33 projecting radially from the foot 31 and aflixed thereto engage, and said yoke E is provided with a pair of affixed lugs 34 disposed to define said radial opening 32 and on each side of the foot lug 33. Each of the lugs 34 is provided with tangentially directed holes 35 extending through said lugs 34 to receive an elastic drift pin 36. After the prop 13 and its aflixed foot member 31 have been placed against the ring 20, the elastic drift pins 36 are driven in tangentially, so that their free extremities overlap the radial lug projections 33 of the foot member 31. The pins 36 thus positively secure the connection between the prop 13 and ring 20, by reason of the operative engagement of said pins 36 with the foot member 31 which in turn is articulately coupled to the shoe member 10 in the manner already described.

To disassemble the prop and shoe arrangement A, it is only necessary to drive the pins 36 out of their respective holes 35, such as by light hammer blows oriented lengthwise along the pins 36, and to lift up the prop 13 and foot member 31. T 0 remove the collar member C from the post 12, the drift pins 24 are removed and the pin member 22 is withdrawn from the passage 23 so as to permit the collar member C to be lifted off from the post 12.

As can be seen more readily in FIG. 3, the sleeve 21 of the collar member C is disposed approximately concentric with the longitudinal axis of symmetry Y of the post 12, said sleeve 21 having an inside diameter which is greater than the outside diameter of the post 12 to pro vide a selected radial clearance therebetween. This clearance, which is preferably circumferentially uniform, establishes the maximum amplitude of the tilt angle capability of the prop 13 and foot 16 relative to the post 12 and shoe 10 in the plane of articulate movement XX. The maximum amplitude of prop 13 to shoe 10 tilt angle capability in the plane 3-3 is established by the clearance between the bi-conical passage 23 and the pin member 22, this maximum tilt amplitude in ment XX. The maximum amplitude of prop 13 to shoe 10 tilt angle capability in the plane 33 is established by the sleeve 21 is less than that permitted by the passage 23 in plane 3-3, it will be necessary to cut away peripheral portions from the sleeve 21, so as to permit the realization of the full tilt capability afforded by the passage 23. In such cases where portions of the periphery of the sleeve 21 adjacent to the ends of the pin 22 are cut away, the pin 22 can be supported at its end portions by lugs (not shown) extending outward from the ring 20, so as to provide support for the pin 22 which is equivalent to that support provided by the holes in the sleeve 21, but at a greater radial distance.

Since the primary difference between the prop and shoe arrangements A and A lies in the manner in which their collar members C and C respectively, are connected in fixed relation to the corresponding foot members 16 and 31, the same tilt angle limitations apply for both arrangements A and A.

Among the other novel features of the prop and shoe arrangements A and A according to the instant invention, the invention also provides a novel fastening device arrangement for supporting a cylindrical pin 27 in an oversize bore 26. This fastening device uses a longitudinally split bushing 28 disposed through the bore 26 and in abutting contact with corresponding semicylindrical portions of said bore 26 and said pin 27, and a plurality of semi-circular split rings 29 disposed within said bore 26, said split rings 29 being in abutting contact with corresponding remaining semi-cylindrical portions of said bore 26 and said pin 27. These split rings 29 cooperate with the split bushing 28 to encompass the pin 27 and support same in fixed relation to the bore 26.

What is claimed is:

1. A mine prop and shoe arrangement which comprises a first element operatively connectable in fixed relation to a mine prop, said first element having a concavely curved surface, a second element having a convexly curved surface disposed in operative slidable engagement with the concavely curved surface of said first element to permit limited articulate movement of said second element relative to said first element, a shoe member fixedly connected to said second element, and means operatively connecting said first and second elements for a limited relative articulate movement in each of two selected paths for positioning said shoe member relative to the mine prop in corresponding paths, said connecting means including a means defining a passage extending through said second element, a pin member extending through said passage means, and a collar member operatively connected in fixed relation to said first element, said collar member being operatively connected to the end portions of said pin member, and being disposed in spaced-apart relation to said second element to limit the relative articulate movement of said first and second elements in one of said selected paths, and said passage being bounded in relation to said pin member to limit the relative articulate movement of said first and second elements in the other of said selected paths.

2. The mine prop and shoe arrangement according to claim 1 wherein the convexly surved surface on said second element is a surface of revolution, and wherein the passage extending through said second element is defined by a flattened bi-conical boundary surface, said boundary surface being flattened approximately parallel to the generating axis of said convexly curved surface of revolution of said second element.

3. The mine prop and shoe arrangement according to claim 1 including a drift pin disposed in operative engagement with each end portion of said pin member to operatively connect same to said collar member.

4. The mine prop and shoe arrangement according to claim 1 including means for releasably fastening said collar member in fixed relation to said first element.

5. The mine prop and shoe arrangement according to claim 4 wherein the means for releasably fastening said collar member in fixed relation to said first element includes a plurality of radially disposed drift pins supported by said collar member and disposed in operative engagement with said first element.

6. The mine prop and shoe arrangement according to claim 4 wherein said first element is provided with a plurality of protruding affixed lug members and wherein the means for releasably fastening said collar member in fixed relation to said first element includes a plurality of drift pins supported by said collar member and disposed in operative engagement with said lug members on said first element.

7. The mine prop and shoe arrangement according to claim 4 wherein said first element is provided with a plurality of aflixed lug members, and wherein said collar member is provided with a corresponding plurality of affixed yoke members, and wherein the means for releasably fastening said collar member in fixed relation to said first element includes a plurality of pin members disposed through said yoke members in operative engagement with said lug members to releasably fasten said collar member in fixed relation to said first element.

8. A fastening device for supporting a cylindrical pin in fixed relation to oversize bore, which comprises a longitudinally split bushing disposed through the bore, said split bushing being in abutting contact with corresponding semi-cylindrical portions of said bore and said pin, and a plurality of semi-circular split rings disposed within said bore, said split rings being in abutting contact with corresponding remaining semi-cylindrical portions of said bore and said pin and cooperating with said split bushing to encompass said pin and support same in fixed relation to the bore.

References Cited by the Examiner UNITED STATES PATENTS 852,872 5/1907 Collins 248-40 1,653,126 12/1927 Schwerin 254-10l 1,820,727 8/1931 Bayles 52112 1,869,984 8/1932 Sklarek 28789 2,885,181 5/1959 McCully et al 25486 FOREIGN PATENTS I 693,899 9/1964 Canada. 1,201,150 7/1959 France.

OTHER REFERENCES German application, 1,027,157, 4-1958. German application, 1,085,120, 7-1960. German application, 1,091,509, 10-1960.

CLAUDE A. LE ROY, Primary Examiner.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,289,997 December 6, 1966 Franz Beulker et al.

It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 6, line 57, beginning with "ment X-X" strike out all to and including "sage 23.", in line 63, and insert instead plane 3-3 being preferably less than that in the plane X-X. Otherwise, if the tilt angle limit established by the sleeve 21 is less than that permitted by the passage 23 in plane 3-3, it will be necessary to cut away peripheral portions from the sleeve 21, so as to permit the realization of the full tilt capability afforded by the passage 23.

Signed and sealed this 19th day of September 1967.

(SEAL) Attest:

EDWARD J. BRENNER Commissioner of Patents ERNEST W. SWIDER Attesting Officer

Claims (1)

1. A MINE PROP AND SHOE ARRANGEMENT WHICH COMPRISES A FIRST ELEMENT OPERATIVELY CONNECTABLE IN FIXED RELATION TO A MINE PROP, SAID FIRST ELEMENT HAVING A CONCAVELY CURVED SURFACE, A SECOND ELEMENT HAVING CONVEXLY CURVED SURFACE DISPOSED IN OPERATIVE SLIDABLE ENGAGEMENT WITH THE CONCAVELY CURVED SURFACE OF SAID FIRST ELEMENT TO PERMIT LIMITED ARTICULATE MOVEMENT OF SAID SECOND ELEMENT RELATIVE TO SAID FIRST ELEMENT, AND MEANS FIXEDLY CONNECTED TO SAID SECOND ELEMENT, AND MEANS OPERATIVELY CONNECTING SAID FIRST AND SECOND ELEMENTS FOR A LIMITED RELATIVE ARTICULATE MOVEMENT IN EACH OF TWO SELECTED PATHS FOR POSITIONING SAID SHOE MEMBER RELATIVE TO THE MINE PROP IN CORRESPONDING PATHS, SAID CONNECTING MEANS INCLUDING A MEANS DEFINING A PASSAGE EXTENDING THROUGH SAID SECOND ELEMENT, A PIN MEMBER EXTENDING THROUGH SAID PASSAGE MEANS, AND A COLLAR MEMBER OPERATIVELY CONNECTED IN FIXED RELATION TO SAID FIRST ELEMENT, SAID COLLAR MEMBER BEING OPERATIVELY CONNECTED TO THE END PORTIONS OF SAID PIN MEMBER, AND BEING DISPOSED IN SPACED-APART RELATION TO SAID SECOND ELEMENT TO LIMIT THE RELATIVE ARTICULATE MOVEMENT OF SAID FIRST AND SECOND ELEMENTS IN ONE OF SAID SELECTED PATHS, AND SAID PASSAGE BEING BOUNDED IN RELATION TO SAID PIN MEMBER TO LIMIT THE RELATIVE ARTICULATE MOVEMENT OF SAID FIRST AND SECOND ELEMENTS IN THE OTHER OF SAID SELECTED PATHS.

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