referring to fig1 there is shown an athletic shoe 10 including an upper portion 12 and the two - part sole 14 of the present invention , including an upper or mid - sole 16 and an out - sole 18 having a treaded bottom surface 20 . a portion of the out - sole 18 is broken away to reveal the bottom surface 22 of the mid - sole 16 and a groove 24 located therein for the removeable attachment of the out - sole 18 to the mid - sole 16 . as clearly shown in fig1 the overall outline of the mid - sole 16 and the out - sole 18 are identical to form a compound sole 14 . the mid - sole 16 element of the shoe sole 14 of the present invention is preferably constructed of a low density polyurethane foam material having a hardness factor as measured on the shore a scale ( which is analogous to the rockwell hardness scale for metals ) of about 60 - 80 . at this degree of hardness , the mid - sole 16 advantageously is lightweight , flexible and durable . alternatively , the mid - sole 16 can be constructed from rubber or from a nonfoam polyurethane resin . the out - sole 18 is preferably constructed from a polyurethane resin having a shore a hardness of about 70 - 90 . at this degree of hardness , the out - sole 18 exhibits excellent qualities of durability and abrasive resistance . although other polyurethane materials are possible , one specific example is polyurethane system no . 20 manufactured by poly - west , inc . of covina , calif . fig2 , and 4 illustrate the detailed construction of out - sole 18 and mid - sole 16 of the present invention . although these elements are described in conjunction with a diamond shaped ridge , other ridge configurations are also possible , as will be explained below in more detail in connection with fig5 , and 7 . referring initially to fig2 the out - sole 18 is shown having a raised ridge 26 integrally formed on its planar upper surface 28 . the ridge 26 is located near the perimeter of the out - sole 18 and extends continuously thereabout . the continuity of this ridge 26 advantageously prevents dirt and other foreign elements from entering and becomming lodged in between the mid - sole 16 and the out - sole 18 . fig3 illustrates the interengagement between the out - sole 18 and the mid - sole 16 . as shown in this cross sectional view , the mid - sole 16 is essentially u - shaped , being attached at its sides 30 to the upper portion 12 of the athletic shoe 10 by means of stitching or adhesives ( not shown ). preferably , the lower portion of the mid - sole 16 , with the exception of the groove 24 , is of a solid construction ; although the central portion of the upper surface of the mid - sole 16 can be relieved , as shown in the dotted line 32 in fig3 in order to reduce the weight of the mid - sole . as shown in fig2 and 3 , the out - sole 18 of the present invention is essentially planar , except for the diamond - shaped ridge 26 which mates into the groove 24 on the mid - sole 16 . the out - sole 18 is firmly attached to the mid - sole 16 by means of the tight interengagement between the undercut portion of the ridge and the projecting edges of the opening of the groove , both indicated generally at 34 in fig3 . because of the snug fit of the ridge 26 within the groove 24 , there are no cavities in the interface between the out - sole 18 and the mid - sole 16 which could permit vertical movement of one with respect to the other . furthermore , the continuous nature of the ridge 26 and the groove 24 also serves to prevent longitudinal and transverse movement of the out - sole 18 with respect to the mid - sole 16 . this construction in the present invention produces a uniform shoe sole 14 which provides the same amount of security and traction as the one piece , integral shoe soles of the prior art , and additionally provides better durability . fig4 illustrates the detailed construction of the matching groove 24 and ridge 26 , which are diamond - shaped in cross section . the narrow opening 36 of the groove 24 is formed by two opposing , projecting edges 38 . the width of this groove opening 36 is just slightly larger than the width a of the base 40 of the ridge 26 . the ridge 26 on the out - sole 18 is characterized by a sharp leading edge 44 which is formed by the sloping upper sides 42 of the ridge 26 , each side 42 having a length b of about one quarter inch . the ridge 26 is further characterized by a wide , pointed midsection 46 and a narrower base 40 or neck where the ridge 26 is connected to the top surface 28 of the out - sole 18 . a broad undercut portion 34 of the ridge is formed between the midsection 46 and the base 40 and provides , in connection with the projecting edges 38 of the opening 36 of the groove 24 , a secure attachment of the out - sole 18 to the mid - sole 16 . this undercut 34 is determined by the relative widths of the base 40 and midsection 46 of the ridge . preferably , the width a of the base 40 is about one eighth of an inch while the width c of the midsection 46 , which of course is the widest portion of the ridge , is about one quarter inch . this construction of the shoe sole 14 of the present invention permits the ridge 26 on the out - sole 18 to be quickly and easily snapped into and out of the groove 24 in the mid - sole 16 . in attaching the out - sole 18 , the leading edge 44 of the ridge 26 initially permits easy insertion of the ridge 26 into the groove 24 . the sloping upper sides 42 of the ridge 26 then bear against the projecting edges 38 of the groove 24 to spread apart and widen the opening 36 thereof , permitting passage of the midsection 46 into the groove 24 . furthermore , the flexibility of the midsection 46 and particularly the projecting edges 38 of the groove 24 , permit the ridge 26 to be snapped completely into place within the groove 24 when a force is exerted on the bottom surface 20 of the out - sole 18 in a direction normal to the plane thereof . the ease of insertion and removal and the security of the attachment of the out - sole 18 to the mid - sole 16 is related to the amount of undercut 34 on the ridge 26 . that is , the greater or deeper the undercut 34 , the more secure the attachment . however , at the same time it is more difficult to insert the midsection 46 of the ridge 26 within the groove 24 because of the correspondingly narrow groove opening 36 . on the other hand , the smaller the amount of the undercut 34 , the easier it is to insert the ridge 26 within the groove 24 , but the attachment is less secure . the amount of undercut 34 can be measured by comparing the width a of the base 40 to the width c of the midsection 46 . it has been found that a ratio of a to c of about one third to two thirds produces the optimum in ridge construction for both easy insertion and removal and secure attachment . this range of a / c ratios applies as well as to the ridges of fig5 - 7 , although other ratios are possible which will produce satisfactory results . it should also be pointed out that the width a of the base 40 is sufficient to prevent the ridge 26 from wobbling during insertion within the groove 24 . furthermore , once the ridge 26 is completely within the groove 24 at one point , the edges 38 of the groove 24 at adjacent points flex open to facilitate the complete attachment of the out - sole 18 to the mid - sole 16 . the same is true in reverse when the out - sole 18 is being removed from the mid - sole 16 . fig5 illustrates an alternate ridge / groove construction which is essentially round . the rounded ridge 48 is connected to the out - sole 18 by means of a short , narrow neck 50 , which also provides an undercut portion for securely attaching the out - sole 18 to the mid - sole 16 . fig6 illustrates a diamond shaped ridge 58 similar to that shown in fig4 except that it is connected to the out - sole 18 by means of a longer neck 60 . this longer neck 60 permits the ridge 58 to be more securely retained in the mid - sole 16 because it provides for a higher undercut portion 62 . that is , the attachment shown in fig6 is very secure since the projecting edges 64 of the groove opening are thicker , stronger , and less resilient , and therefore require a greater withdrawal force than the ridge of fig4 in order to detach the out - sole 18 . on the other hand , the ridge 26 of fig4 requires a lesser insertion force than that of fig6 . furthermore , the stronger edges 64 are able to withstand many more in and out cycles of the ridge 58 without experiencing wear or erosion which could undermine the retentiveness of the ridge 58 within the mid - sole 16 . fig7 illustrates a mushroom shape ridge 66 . besides being connected to the out - sole 18 by means of a long neck 68 , similar to that of the ridge 58 of fig6 this mushroom shaped ridge 66 is characterized by a blunt leading edge 60 , sloping upper surfaces 72 , a rectangular mid section 74 , and a horizontal upper surface 76 on the under cut portion 78 . the ridge 66 also exhibits good retentiveness in the mid - sole 16 because of the thick under cut portion 78 provided by the long neck 68 , and particularly because of the flat upper surface 76 on the under cut portion 78 . furthermore , this retentiveness is enhanced by the thick , rectangular mid section 74 which provides rigidity , great durability to withstand many in and out cycles . the blunt leading edge 70 advantageously reduces the overall height of the ridge / groove combination , reducing the weight of the shoe sole of the present invention and permitting it to more closely approximate the thickness of a single element sole . at the same time , the leading edge 70 facilitates insertion of the ridge 66 since it is narrower than the groove opening , as shown in fig7 . thus , in sports where excellent retention of the out - sole by the mid - sole is required , the ridge configurations of fig5 , and 7 are preferable since they are provided with large under cut portions . on the other hand , in sports where less retention is desired , and perhaps more ease of insertion and removal , the ridge of fig3 and 5 is advantageous . fig8 illustrates an alternate out - sole 52 having a noncontinuous ridge 54 . the ridge 54 is discontinuous at the heel portion where a pair of short longitudinal ridges 56 are located . this redge 54 orientation permits the out - sole 52 of fig8 to compensate for any shrinkage experienced by the out - sole or mid - sole during the casting process . since this shrinkage usually occurs in a longitudinal direction , the short ridges 56 permit the out - sole 52 to be attached to the mid - sole even though the overall length of the larger , main ridge 54 does not perfectly match that of the mid - sole . the mid - sole is also provided with matching parallel grooves ( not shown ). the cross sectional shape of the ridge of fig8 can be those of fig4 through 7 , or other equivalent cross sections . thus , in conclusion , the shoe sole of the present invention provides a removable out - sole which can be quickly and inexpensively replaced by means of a simple snap fit interengagement between a ridge on the fresh out - sole and a groove on the mid - sole . besides providing a simple means for the repair and replacement of one tread , the shoe sole of the present invention permits ready interchangeability in tread patterns and out - sole colors . furthermore , the ridge can be cycled into and out of the groove many times without damage to either the mid - sole or the out - sole , thereby permitting reusability of the out - sole of the present invention .