referring now to the drawings and in particular to fig1 there is shown a simple diagram of a vertically moored platform ( vmp ) indicated generally by the numeral 10 having a jacket leg 12 into which is inserted , through the bottom , a riser pipe 26 which is in effect a continuation of a pipe or casing 38 which is anchored below the mudline after passing through conductor casing 36 . the bottom anchor of the riser pipe is such that it can support the tension which will be required to hold the vertically moored platform in position on the sea surface . at the point 22 there is a horizontal bearing for transmitting lateral or horizontal forces , and at point 14 there is a vertical bearing for transmission of axial forces . there are flexure zones 24 and 28 within the length of the riser pipe near the platform and the mudline , respectively . the portion 26a between the flexure point is substantially straight but non - vertical , while the riser pipe is vertical in the earth and is vertical inside the platform leg . thus bending is concentrated where the curvature is shown just below the platform leg and just above the well template 32 which rests on the mud surface 34 . the object of the terminator is not only to anchor the riser pipe at the platform but also to design the anchor mechanism so as to properly provide the necessary curvature shown in fig1 without stressing the pipe or terminator and other tubular members , that may be inside the riser , more than a selected maximum . fig2 illustrates a typical prior art design of a terminator , which is joined at its two ends 42a and 42b , to riser pipes extending upwardly and downwardly . the terminator is designated generally by the numeral 40 and has a cylindrical portion 40d of selected length and diameter which tapers off through appropriate conical pipes 40e going down to the riser pipe , and various sections 40c , 40b , 40a , etc . going upwardly to the riser pipe . as shown on the drawing , the inner diameter and outer diameter vary throughout the length of the terminator , while one is constant the other varies and vice versa , or both vary simultaneously depending upon the most convenient way to design and construct the device . there is no precise dimension for the overall length of the terminator . it can have the two ends of equal length or have a longer portion in one direction , length l1 , and a shorter portion of length l2 in the other direction . the reason that this is preferred is that in the end which is joined to pipe inside a containig pipe or sleeve , the amount of deflection that can be permitted is less than the other long end l1 , where the pipe is in the water and has no lateral constraint . if the design were symmertical about the anchor point 43 , then the deflection would be symmetrical on each side of the point , and the design of the terminator would be symmetrical also . the mathematics for determining lateral deflection of a vertically suspended pipe are well known . the system can be described by the following beam column differential equation : ## equ1 ## where : by applying the kwown boundary conditions of a system , the differential equation can be solved such as to satisfy all required conditions . such required conditions can include stress level , lateral deflection limits , or structural section size and / or configuration . referring now to fig3 there is shown in schematic outline a construction of a novel multiterminator having a terminator indicated generally by the numeral 58 and a termination extension generally indicated by numeral 64 . terminator 58 has a short leg 59 and a long leg 60 . the long leg is directed downwardly and joins a length of riser pipe 26 . the mid section , which is preferably not in the center of the terminator is held in horizontal bearing 54 . this bearing 54 provides a lateral restraint for the terminator 58 . if bearing 54 is modified as shown in fig6 it can also provide for axial force transmission . as previously indicated , the lengths of the short and long ends 59a and 60a preferably are not equal and may roughly be defined in a ratio of approximately 1 : 2 . the overall length can vary depending on the size and dimensions of the pipes , etc ., and the tension required . the terminator 58 is provided with horizontal support at the lower bearing 54 which will be discussed in connection with fig6 . the length of the terminator extension is indicated by the numeral 62 and is a portion of the assembly reaching from the point of bearing 54 of the terminator 58 to the point 66 , above the second horizontal bearing 56 . the length of the terminator 58 is indicated by 58a . a suitable horizontal bearing is shown in u . s . pat . no . 4 , 130 , 995 entitled &# 34 ; vmp riser horizontal bearing &# 34 ; issued on dec . 26 , 1978 . sleeve 50 forms an inner opening through the jacket leg 12 through which the riser pipe enters up into the drilling and producing portions of the platform . the top of the short leg 59 goes to a short length 26 &# 39 ; of the riser pipe which is connected to a &# 34 ; short &# 34 ; terminator 63 that has a double - ended , substantially symmetrical , tapered section 64 , which is provided with horizontal bearing 56 inside sleeve 50 . riser pipe section 26 &# 39 ; and short terminator 63 and terminator end 58 form what can be called a terminator extension 62 . that portion of fig3 indicated by sections 60a and 62 can be called a &# 34 ; multiterminator &# 34 ;. the upper end 66 of the terminator extension is roughly set at the point where there is little or no bending moment in the pipe 26 &# 34 ;. the riser pipe 26 &# 34 ; then goes upwardly through a vertical bearing 57 , which permits sliding contact of very small amounts which occur as the curvature of the pipe 26 varies . however , since the motion of the pipe 26 &# 34 ; through the vertical bearing 56 is very small , the construction can be simple friction contact . a suitable vertical bearing 57 can be such as shown in u . s . pat . no . 4 , 127 , 005 entitled &# 34 ; riser / jacket vertical bearing assembly for vertically moored platform &# 34 ; issued nov . 28 , 1978 . referring to fig4 and 5 , fig4 shows the lower end of the riser pipe as it is anchored to the conductor pipe 70 , which is anchored in the earth 71 . the principal terminator 58 with legs 60 and 59 , are the same as illustrated in fig3 and the section of riser pipe 26 &# 39 ; and also the second terminator 64 and horizontal bearings 56 and 54 are all as shown in fig3 except that at the lower end of the pipe , the terminator is inverted with respect to the upper end of the anchoring at the vmp . fig5 is similar except that it is now in the same direction of installation as in fig3 with the long leg 60 of the principal terminator pointed downwardly into the water , while the short end is connected through a section of riser pipe 26a and the short terminator 63 and the pipe 26b going up through the vertical bearing 57 . the curved line 76 which passes through the center 86 of the lower horizontal bearing 54 and also through the center 88 of the upper horizontal bearing 56 would illustrate in an exaggerated fashion , the curvature of the structure of fig5 when there is a deflection , for example , of the vmp to the left . the lower portion 75 of the curve is deflected to the right of the upper portion 76 of the curve as the jacket tends to move to the left . the terminator rotates , i . e ., angularly deflects inside bearing 54 . again , the upper terminator 64 angularly deflects a small amount in its bearing 56 in a reverse direction with decreasing amplitude over the amplitude in the section between the two terminators . thus the curvature would be greatest at the lower end 75 , less on the top 77 of the lower 58 terminator and lower still 78 above the smaller terminator 64 . the arrow 80 is shown as the direction of the force being applied by the platform to the riser pipe through the horizontal bearing 54 . the lower portion of the riser pipe is anchored in the earth and the earth provides a restraining force 82 . there is also a restraining force 89 applied above the lower terminator by a horizontal force applied at the upper bearing 56 . any type of bearing support 54 may be used between the upper terminator 63 and the platform leg , as previously mentioned , so long as it provides for a bending in any vertical plane through the leg of the jacket of the vmp . it is also necessary to provide a tension in the riser pipe below the lower bearing 54 . a bearing of the type shown in fig6 provides for transmission of both vertical and horizontal forces . the direction of portion 75 of the line 79 in fig5 makes an angle 81 with the axis of sleeve 72 . the direction of the line 79 above the lower bearing 54 makes an angle 83 . the lower terminator 58 mid section angularly deflects about point 86 to be tangent to this curve . angle 83 is smaller than 81 . again , the upper terminator 63 will rotate about point 88 to be tangent to the line 79 at 88 . there will be a smaller deflection 78 of the pipe above the upper terminator . thus , by providing the multiple terminators ( there could be a third and fourth one above the top terminator 63 , now shown ), each in its own rotary bearing 54 , 56 , a much greater deflection angle 81 can be provided without increasing the stress in the riser pipe . bearing 54 of fig3 can be a fixture such as shown in fig6 . this indicates a fixture 90 surrounding the pipe 58b which is the cylindrical center portion of the terminator 58 . this fixture indicated generally by the numeral 90 , has two rings , an upper ring 92 , and a lower ring 94 . point 86 represents the center of the spherical portions . the horizontal bearing centerline 54a will pass through that center 86 . the bearing elements are essentially an outer steel base ring 96 and an inner steel ring 98 supported by ring 92 . ring 98 is attached to ring 92 and its outer surface is spherical . the inner surface of the outer portion 96 which is attached to the sleeve 50 is also spherical and the center shell portion 100 is a resilient elastomeric compliant material , which is bonded to the spherical surfaces of the portions 98 and 96 . thus the two surfaces 98 and 96 have limited movement to rotate about the center 86 with respect to each other , while the inner material 100 moves in a shearing action , so that a substantially frictionless rotation is possible over a limited angle . the lower spherical bearing has an inner ring 98a and an outer ring 96a , with a corresponding intermediate portion 100a . this is an alternate means to provide the thrust transmission means required to maintain the tension in the riser pipe , but still permits the rotational feature controlled by the horizontal bearings 54 . the bearing rings 98a , 96a , and 100a are supported on ring 94 . the center of the spherical surfaces 98a , 96a is at point 86 . while the success of the bearing , such as the one illustrated in fig6 is important to the success of the entire anchoring system , including the terminator and the terminator extension ; and while the design shown in fig6 may be preferred , other designs can , of course , be used provided they meet all of the motion and stress requirements , and utilize flexibility of the terminator extension previously described . the upper bearing 56 of fig5 which supports the upper terminator 63 , is not required to take thrust . therefore , bearing 56 may simply be the horizontal bearing portion 92 of the bearing assembly shown in fig6 . this would include the ring 92 , the two spherical rings 98 and 96 and the compliant shell 100 . ring 98 has an outer surface which is spherical , centered at point 86 . ring 96 has an inner surface which is spherical , also centered at point 86 . point 86 is on the axis of the terminator and sleeve 50 . it also lies on the central horizontal plane 54a through the rings 98 , 96 . the spherical surfaces of the rings 98 and 96 are spaced apart a selected distance , and this space is filled with a selected elastomeric material , which is preferably bonded to both spherical surfaces . the two portions of the bearing assembly lateral bearing 92 and thrust bearing 94 are mounted on a rigid internal pipe 58b , which comprises the cylindrical midsection of the principal terminator 58 . the tubular members 91 , shown by dashed lines , represent one of a plurality of casings which may lie in the annulus between the innermost casing or conductor pipe 93 . these are all substantially co - axial pipes , and form another reason for limiting the maximum stress and deflection at all points along the riser pipe . we have shown in fig3 and 5 a complete set of bearings for the multiterminator or terminator extension of this invention . in fig6 we have shown the thrust bearing 94 as a part of an assembly with one of the lateral bearings 92 . however , it is equally possible to apply the thrust bearing widely spaced from the lateral bearings . with the thrust bearing widely spaced from the lateral bearings , a lateral bearing is required which has a combination of rotary and sliding motion . such a bearing is illustrated in fig5 of u . s . pat . no . 4 , 130 , 995 which has a portion 48 which combines an outer cylindrical surface 82 with an inner spherical surface 56 . we have described a multiterminator which is an improvement in the anchoring mechanism by which a riser pipe is attached in a vertical manner inside a jacket leg of a vertically moored platform or other floating structure . the same construction can also be utilized at the lower anchorage of the riser pipe with the earth . by the use of the terminator and terminator extension ( multiterminator ), it is possible to maintain a greater total angular deflection of the pipe without providing any greater maximum value of stress in the pipe at any point . the required length and weight of the prior art terminator and of the multiterminator of our invention were calculated using known tension beam equations for the following design conditions of an offshore location . diameter of sleeve 50 in jacket leg through which riser passes -- 45 inches diameter of piles or conductor pipes 70 in sea floor through which riser extends -- 40 inches the following table shows the results of our calculations comparing the length and weight of our multiterminator ( as indicated in fig3 ) and the prior art terminator ( as indicated in fig2 ) in which the outer fiber stress from the combined effects of axial tension and bending moment is equal to the maximum allowable value along the entire length of the terminator assembly . ______________________________________length length weight weight ( prior art ( multi - ( prior art ( multi - terminator ) terminator ) terminator ) terminator ) ______________________________________upper 176 ft . 106 ft . 83 , 300 lbs 42 , 700 lbsassemblylower 176 ft . 127 ft 6 in 127 , 000 lbs 90 , 800 lbsassembly______________________________________ this reduction in overall length and total weight is most important . for example , these terminators will have to be manufactured at specially equipped fabrication centers and shipped and installed as a unit . the reduction in length and weight of multiterminators using our invention makes the offshore installation much more practical and in some cases permits installations which might otherwise be prohibited because of the size of terminator required under the prior art system . while we have described this invention as related to the vertically moored platform , for which it is admirably suited , it can also be used with other types of floating structure . while the invention has been described with a certain degree of particularity , it is manifest that many changes may be made in the details of construction and the arrangement of components without departing from the spirit and scope of this disclosure . it is understood that the invention is not limited to the exemplified embodiments set forth herein but is to be limited only by the scope of the attached claim or claims , including the full range of equivalency to which each element thereof is entitled .