Abstract:
A bathtub that has a contoured head support and a contoured neck support formed in the lower portions of the tub. The tub comes in a standard length (in which the knees are drawn up) and a full length size (84 inches long) in which the user lies flat. In both cases, the head is not only supported above the water so drowning is prevented, the head and neck are supported at the proper angle so that all four spinal curves are in proper alignment.

Description:
This invention relates to bath tubs for reclining in and particularly to bath tubs for reclining in having integral head and neck supports. 
     BACKGROUND OF THE INVENTION 
     Bath tubs have evolved over the years from simple wash tubs to elaborate and ornate fixtures. Some tubs include bubble action and other amenities. Despite these improvements, bath tubs still have one main problem: they are not designed to allow a user to lie flat in the tub. The biggest reason for this is to prevent people from drowning. Although prevention of drowning is an important consideration in bath tub design, this restriction causes other problems. Most bath tubs today force the bather into a semi reclined position with the head pressed forward and down over the chest. This is uncomfortable and harmful to the body. Pushing the head forward flattens the cervical curve of the neck. It also similarly distorts the thoracic and lumbar curves and stresses the sacrum. 
     One alternative is simply to sit up in the tub. However, sitting upright is stressful to the lower back. The best position for resting in a tub is to lie with the torso flat in the tub and the knees bent, or better yet, with the legs fully extended. This position offers the best comfort for the head, neck and spine. 
     Simply supporting the neck is not the answer unless full support for the head can be accommodated because it can intensify rather than flatten the four natural curves of the spine, which is just as detrimental as flattening them. 
     Several bath tubs with some type of neck support have been developed. All of these suffer from the problems discussed above in that they do not support the head and back properly, thereby being uncomfortable at best or harmful at worst. Examples of these designs can be found in U. S. Patents as follows: U.S. Pat. No. 3,295,146 teaches a support device for a user. It fits over the side walls of a tub and lays in the plane of the top of the tub. This places the head at a high location within the tub. Although it is safe, it bends the back and neck in an uncomfortable position. U.S. Pat. No. 1,315,643 shows a tub having a contoured wall surface that can act as a head support as well as a seat. Again, the problem here is that the head is supported at a very bad angle, causing stress in the back and neck. U.S. Pat. No. 1,962,076 shows another contour tub. This tub has additional contours for the back and seat. However, these contours are at a bad angle for the back and neck. It does no good to provide support for the neck and back if the support puts the neck and back into an uncomfortable position. Pat. No. 1,546,536 shows another type of tub that has a high neck support. Clearly this type of neck support is not conducive to relaxation. U. S. Pat. No. 2,828,489 and UK patent 2,053,673, show tubs for infants that have head supports. However, these tubs, like those above, the head support is designed to prevent drowning and is not at all conducive to relaxing and eliminating stress points on the head and spine while in a tub. Finally, U.S. Pat. No. 4,734,944 illustrates a popular style of spa that is now available. These spas are large tubs designed for outdoor use. Although they allow reclining, the tubs have seats that provide an angled surface that does not permit a user to fully recline. Again, these spas use large quantities of water and the danger of drowning is high unless the user&#39;s head remains out of the water. 
     SUMMARY OF THE INVENTION 
     The instant invention overcomes these problems. It is a bathtub that has contoured head and neck supports formed directly into the tub. The tub comes in a standard length (60 inches long), in which the knees are drawn up, and a full length size (84 inches long) in which the user lies flat. In both cases, the head is not only supported above the water so drowning is prevented, the head and neck are supported at the proper angle so that all for spinal curves are in proper alignment. To say that lying in this tub is like being in heaven, is an understatement. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a top view of my new full-length tub. 
     FIG. 2 is a cross-sectional view of my new tub taken along the lines 2--2 of FIG. 1. 
     FIG. 3 is a side view of the tub with the enclosure wall in place. 
     FIG. 4 is a top view of a shortened tub, designed to fit in existing tub spaces, showing an optional knee support bar. 
     FIG. 5 is a top view of a shortened tub that includes space for jetting. 
     FIG. 6 is a top view of a double wide tub having side-by-side head supports. 
     FIG. 7 is a cross-sectional detail view of the first embodiment taken at station 7.5 inches, showing the head bowl. 
     FIG. 8 is a cross-sectional detail view of the first embodiment taken at station 12 inches, showing the beginning of the neck support. 
     FIG. 9 is a cross-sectional detail view of the first embodiment taken at station 12.5 inches, showing the curvature of the neck support at this point in the tub. 
     FIG. 10 is a cross-sectional detail view of the first embodiment taken at station 13 inches, showing the curvature of the neck support at this point in the tub. 
     FIG. 11 is a cross-sectional detail view of the first embodiment taken at station 13.5 inches, showing the curvature of the neck support at this point in the tub. 
     FIG. 12 is a top view of my new tub without jetting equipment. 
     FIG. 13 is a perspective view of my new tub showing the head bowl and neck support. 
     FIG. 14 is a detail perspective view of my new tub showing the head bowl and neck support. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to FIG. 1, the preferred embodiment of my new tub 1 is shown. The tub 1 has a rectangular perimeter 2 that forms a slight deck as shown. This deck 2 can be from four to six inches wide. The preferred embodiment has for a four inch deck 2 formed around the tub perimeter. The tub 1 is designed to be placed in a support frame that forms a tub enclosure 3 (see FIG. 3). FIG. 1 shows the tub 1 with jetting equipment 5 (see also FIG. 2). To fit the jetting equipment into the tub enclosure 3, the side distance between walls 6 of the tub 1 must be narrowed as shown by numeral 17. FIG. 12 shows a tub 30 without jetting. In this design, the side walls 6a are straight because they do not have to accommodate the jetting equipment 5. All other features of this tub 30 are the same as the other tubs. 
     A unique feature of this tub 1 is the head and neck support system. FIGS. 13 and 14 show the shapes of the head support 10 and neck support 15 in perspective. The head support 10 is formed from a raised shelf 11, located at the head of the tub 1. In the center of this shelf 11 is a semi-spherical head bowl 12 that is cut into the shelf 11 as shown. The head bowl 12 is designed to hold average sized heads without restraint. At a spaced distance from the shelf 11 is a neck support 15. The neck support 15 is a sculpted portion that has a sloped pair of ridges that form a recessed portion between them. A space 16 is provided between the shelf 11 and the neck support 15 to allow water to drain from the head bowl 12 and shelf 11. The space 16 extends to the side walls 6 of the tub 1. The neck support 15 ridges do not extend to the side walls 6, the space between the ridges and the side walls 6 connects to the space 16, which forms a channel to allow all the water in the head of the tub 1 to drain completely. 
     Referring now to FIGS. 7-11 and 13 and 14, details of the neck support 15 are shown. A complete data sheet, showing the height measurements at half-inch intervals along the length of the tub 30 and one-inch intervals across the width of the tub 30, is attached as an appendix. The height measurements shown in the table are the exact measurement of the tub floor height at any pair of coordinates chosen. The top horizontal axis of the data table shows the width measurements for a 30 inch wide tub. The zero point is the center of the tub 30. The length is for a tub having an interior length of 84 inches. This data table is for a tub 30 with no jetting 5 and straight side walls 6a, such as the tub 30 shown in FIG. 12. The data points indicate the height of the tub surface from flat bottom to the top of the bottom surface of the tub. For example, at point (0,0), where the first number indicates the length (y) coordinate and the second number indicates the width (x) coordinate, the reading is 16 inches. This represents the deck portion of the tub 30, which is at full height of the tub wall. At point (22,0) the reading is 2.75 inches. This is read that at a point 22 inches from the head of the tub 30, at the centerline of the tub, the tub floor is 2.75 inches high. Thus, the tub floor height at all the points indicated is provided. 
     
                                           TABLE 1__________________________________________________________________________Top line of each page shows position from center line of tub in inchesLeft Column shows distance from head of tub (0.0) to foot of tub (88.0)in inchesData in table shows height of tub floor at indicated points in__________________________________________________________________________inches   -18.0  -17.0      -16.0          -15.0              -14.0                  -13.0                      -12.0                          -11.0                              -10.0__________________________________________________________________________0.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0000.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.5   16.000  16.000      16.000          16.000              8.000                  8.000                      8.000                          8.000                              8.0004.0   16.000  16.000      16.000          16.000              7.875                  7.875                      7.875                          7.875                              7.8754.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8135.0   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8135.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8136.0   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8136.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8137.0   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8137.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8138.0   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8138.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8139.0   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.8139.5   16.000  16.000      16.000          16.000              7.813                  7.813                      7.813                          7.813                              7.87510.0   16.000  16.000      16.000          16.000              7.813                  7.719                      7.563                          7.438                              7.25010.5   16.000  16.000      16.000          16.000              6.875                  6.563                      6.500                          6.375                              6.12511.0   16.000  16.000      16.000          16.000              5.625                  5.500                      5.438                          5.250                              5.00011.5   1G.000  16.000      16.000          16.000              4.719                  4.438                      4.344                          4.313                              4.31312.0   16.000  16.000      16.000          16.000              4.219                  4.156                      4.188                          4.125                              4.18812.5   16.000  16.000      16.000          16.000              4.094                  4.063                      4.125                          4.188                              4.37513.0   16.000  16.000      16.000          16.000              4.001                  4.031                      4.063                          4.188                              5.31313.5   16.000  16.000      16.000          16.000              3.948                  4.031                      4.063                          4.188                              6.25014.0   16.000  16.000      16.000          16.000              3.894                  3.975                      4.125                          4.188                              6.81314.5   16.000  16.000      16.000          16.000              3.841                  3.920                      4.313                          5.813                              6.87515.0   16.000  16.000      16.000          16.000              3.787                  3.864                      4.500                          5.750                              6.78115.5   16.000  16.000      16.000          16.000              3.734                  3.808                      4.594                          5.500                              6.34416.0   16.000  16.000      16.000          16.000              3.680                  3.752                      4.625                          5.344                              6.04416.5   16.000  16.000      16.000          16.000              3.627                  3.696                      4.531                          5.125                              5.69617.0   16.000  16.000      16.000          16.000              3.573                  3.640                      4.438                          4.893                              5.34817.5   16.000  16.000      16.000          16.000              3.520                  3.584                      4.375                          4.688                              5.00018.0   16.000  16.000      16.000          16.000              3.466                  3.528                      4.290                          4.520                              4.75018.5   16.000  16.000      16.000          16.000              3.413                  3.473                      4.188                          4.344                              4.50019.0   16.000  16.000      16.000          16.000              3.359                  3.417                      4.063                          4.250                              4.31319.5   16.000  16.000      16.000          16.000              3.306                  3.361                      4.000                          4.063                              4.12520.0   16.000  16.000      16.000          16.000              3.252                  3.305                      3.875                          3.938                              3.87520.5   16.000  16.000      16.000          16.000              3.199                  3.249                      3.750                          3.688                              3.71921.0   16.000  16.000      16.000          16.000              3.145                  3.193                      3.625                          3.625                              3.50021.5   16.000  16.000      16.000          16.000              3.092                  3.137                      3.500                          3.500                              3.25022.0   16.000  16.000      16.000          16.000              3.038                  3.081                      3.375                          3.313                              3.18822.5   16.000  16.000      16.000          16.000              2.985                  3.026                      3.313                          3.188                              3.12523.0   16.000  16.000      16.000          16.000              2.931                  2.970                      3.219                          3.063                              3.00023.5   16.000  16.000      16.000          16.000              2.878                  2.914                      3.125                          3.000                              2.93124.0   16.000  16.000      16.000          16.000              2.824                  2.858                      2.969                          2.875                              2.86324.5   16.000  16.000      16.000          16.000              2.771                  2.802                      2.938                          2.880                              2.79425.0   16.000  16.000      16.000          16.000              2.717                  2.746                      2.813                          2.760                              2.72625.5   16.000  16.000      16.000          16.000              2.664                  2.690                      2.719                          2.669                              2.65726.0   16.000  16.000      16.000          16.000              2.610                  2.634                      2.688                          2.635                              2.58926.5   16.000  16.000      16.000          16.000              2.557                  2.579                      2.617                          2.568                              2.52027.0   16.000  16.000      16.000          16.000              2.503                  2.523                      2.547                          2.501                              2.45127.5   16.000  16.000      16.000          16.000              2.496                  2.467                      2.477                          2.437                              2.38328.0   16.000  16.000      16.000          16.000              2.488                  2.411                      2.406                          2.367                              2.31428.5   16.000  16.000      16.000          16.000              2.481                  2.355                      2.336                          2.303                              2.24629.0   16.000  16.000      16.000          16.000              2.474                  2.299                      2.266                          2.228                              2.17729.5   16.000  16.000      16.000          16.000              2.466                  2.243                      2.195                          2.158                              2.10930.0   16.000  16.000      16.000          16.000              2.459                  2.188                      2.125                          2.089                              2.04030.5   16.000  16.000      16.000          16.000              2.451                  2.128                      2.055                          2.021                              1.97131.0   16.000  16.000      16.000          16.000              2.444                  2.069                      1.984                          1.954                              1.90331.5   16.000  16.000      16.000          16.000              2.437                  2.009                      1.914                          1.880                              1.83432.0   16.000  16.000      16.000          16.000              2.429                  1.950                      1.844                          1.813                              1.76632.5   16.000  16.000      16.000          16.000              2.422                  1.813                      1.750                          1.727                              1.69733.0   16.000  16.000      16.000          16.000              2.415                  1.727                      1.656                          1.638                              1.62833.5   16.000  16.000      16.000          16.000              2.407                  1.642                      1.594                          1.576                              1.56034.0   16.000  16.000      16.000          16.000              2.400                  1.556                      1.500                          1.484                              1.49134.5   16.000  16.000      16.000          16.000              2.392                  1.471                      1.438                          1.424                              1.42335.0   16.000  16.000      16.000          16.000              2.385                  1.385                      1.375                          1.365                              1.35435.5   16.000  16.000      16.000          16.000              2.378                  1.378                      1.367                          1.356                              1.34536.0   16.000  16.000      16.000          16.000              2.370                  1.370                      1.359                          1.348                              1.33736.5   16.000  16.000      16.000          16.000              2.363                  1.363                      1.351                          1.340                              1.32937.0   16.000  16.000      16.000          16.000              2.355                  1.355                      1.344                          1.332                              1.32037.5   16.000  16.000      16.000          16.000              2.348                  1.348                      1.336                          1.324                              1.31238.0   16.000  16.000      16.000          16.000              2.341                  1.341                      1.328                          1.316                              1.30438.5   16.000  16.000      16.000          16.000              2.333                  1.333                      1.321                          1.308                              1.29539.0   16.000  16.000      16.000          16.000              2.326                  1.326                      1.313                          1.300                              1.28739.5   16.000  16.000      16.000          16.000              2.319                  1.319                      1.305                          1.292                              1.27940.0   16.000  16.000      16.000          16.000              2.311                  1.311                      1.298                          1.284                              1.27040.5   16.000  16.000      16.000          16.000              2.304                  1.304                      1.290                          1.276                              1.26241.0   16.000  16.000      16.000          16.000              2.296                  1.296                      1.282                          1.268                              1.25341.5   16.000  16.000      16.000          16.000              2.289                  1.289                      1.274                          1.260                              1.24542.0   16.000  16.000      16.000          16.000              2.282                  1.282                      1.267                          1.252                              1.23742.5   16.000  16.000      16.000          16.000              2.274                  1.274                      1.259                          1.244                              1.22843.0   16.000  16.000      16.000          16.000              2.267                  1.267                      1.251                          1.236                              1.22043.5   16.000  16.000      16.000          16.000              2.259                  1.259                      1.244                          1.228                              1.21244.0   16.000  16.000      16.000          16.000              2.252                  1.252                      1.236                          1.220                              1.20344.5   16.000  16.000      16.000          16.000              2.245                  1.245                      1.228                          1.212                              1.19545.0   16.000  16.000      16.000          16.000              2.237                  1.237                      1.220                          1.203                              1.18745.5   16.000  16.000      16.000          16.000              2.230                  1.230                      1.213                          1.195                              1.17846.0   16.000  16.000      16.000          16.000              2.223                  1.223                      1.205                          1.187                              1.17046.5   16.000  16.000      16.000          16.000              2.215                  1.215                      1.197                          1.179                              1.16147.0   16.000  16.000      16.000          16.000              2.208                  1.208                      1.190                          1.171                              1.15347.5   16.000  16.000      16.000          16.000              2.200                  1.200                      1.182                          1.163                              1.14548.0   16.000  16.000      16.000          16.000              2.193                  1.193                      1.174                          1.155                              1.13648.5   16.000  16.000      16.000          16.000              2.186                  1.186                      1.166                          1.147                              1.12849.0   16.000  16.000      16.000          16.000              2.178                  1.178                      1.159                          1.139                              1.12049.5   16.000  16.000      16.000          16.000              2.171                  1.171                      1.151                          1.131                              1.11150.0   16.000  16.000      16.000          16.000              2.163                  1.163                      1.143                          1.123                              1.10350.5   16.000  16.000      16.000          16.000              2.156                  1.156                      1.136                          1.115                              1.09551.0   16.000  16.000      16.000          16.000              2.149                  1.149                      1.128                          1.107                              1.08651.5   16.000  16.000      16.000          16.000              2.141                  1.141                      1.120                          1.099                              1.07852.0   16.000  16.000      16.000          16.000              2.134                  1.134                      1.112                          1.091                              1.06952.5   16.000  16.000      16.000          16.000              2.127                  1.127                      1.105                          1.083                              1.06153.0   16.000  16.000      16.000          16.000              2.119                  1.119                      1.097                          1.075                              1.05353.5   16.000  16.000      16.000          16.000              2.112                  1.112                      1.089                          1.067                              1.04454.0   16.000  16.000      16.000          16.000              2.104                  1.104                      1.082                          1.059                              1.03654.5   16.000  16.000      16.000          16.000              2.097                  1.097                      1.074                          1.051                              1.02855.0   16.000  16.000      16.000          16.000              2.090                  1.090                      1.066                          1.043                              1.01955.5   16.000  16.000      16.000          16.000              2.082                  1.082                      1.058                          1.035                              1.01156.0   16.000  16.000      16.000          16.000              2.075                  1.075                      1.051                          1.027                              1.00356.5   16.000  16.000      16.000          16.000              2.068                  1.068                      1.043                          1.019                              0.99457.0   16.000  16.000      16.000          16.000              2.060                  1.060                      1.035                          1.011                              0.98657.5   16.000  16.000      16.000          16.000              2.053                  1.053                      1.028                          1.003                              0.97858.0   16.000  16.000      16.000          16.000              2.045                  1.045                      1.020                          0.995                              0.96958.5   16.000  16.000      16.000          16.000              2.038                  1.038                      1.012                          0.987                              0.96159.0   16.000  16.000      16.000          16.000              2.031                  1.031                      1.005                          0.978                              0.95259.5   16.000  16.000      16.000          16.000              2.023                  1.023                      0.997                          0.970                              0.94460.0   16.000  16.000      16.000          16.000              2.016                  1.016                      0.989                          0.962                              0.93660.5   16.000  16.000      16.000          16.000              2.008                  1.008                      0.981                          0.954                              0.92761.0   16.000  16.000      16.000          16.000              2.001                  1.001                      0.974                          0.946                              0.91961.5   16.000  16.000      16.000          16.000              1.994                  0.994                      0.966                          0.938                              0.91162.0   16.000  16.000      16.000          16.000              1.986                  0.986                      0.958                          0.930                              0.90262.5   16.000  16.000      16.000          16.000              1.979                  0.979                      0.951                          0.922                              0.89463.0   16.000  16.000      16.000          16.000              1.972                  0.972                      0.943                          0.914                              0.88663.5   16.000  16.000      16.000          16.000              1.964                  0.964                      0.935                          0.906                              0.87764.0   16.000  16.000      16.000          16.000              1.957                  0.957                      0.927                          0.898                              0.86964.5   16.000  16.000      16.000          16.000              1.949                  0.949                      0.920                          0.890                              0.86065.0   16.000  16.000      16.000          16.000              1.942                  0.942                      0.912                          0.882                              0.85265.5   16.000  16.000      16.000          16.000              1.935                  0.935                      0.904                          0.874                              0.84466.0   16.000  16.000      16.000          16.000              1.927                  0.927                      0.897                          0.866                              0.83566.5   16.000  16.000      16.000          16.000              1.920                  0.920                      0.889                          0.858                              0.82767.0   16.000  16.000      16.000          16.000              1.912                  0.912                      0.881                          0.850                              0.81967.5   16.000  16.000      16.000          16.000              1.905                  0.905                      0.873                          0.842                              0.81068.0   16.000  16.000      16.000          16.000              1.898                  0.898                      0.866                          0.834                              0.80268.5   16.000  16.000      16.000          16.000              1.890                  0.890                      0.858                          0.826                              0.79469.0   16.000  16.000      16.000          16.000              1.883                  0.883                      0.850                          0.818                              0.78569.5   16.000  16.000      16.000          16.000              1.876                  0.876                      0.843                          0.810                              0.77770.0   16.000  16.000      16.000          16.000              1.868                  0.868                      0.835                          0.802                              0.76870.5   16.000  16.000      16.000          16.000              1.861                  0.861                      0.827                          0.794                              0.76071.0   16.000  16.000      16.000          16.000              1.853                  0.853                      0.819                          0.786                              0.75271.5   16.000  16.000      16.000          16.000              1.846                  0.846                      0.812                          0.778                              0.74372.0   16.000  16.000      16.000          16.000              1.839                  0.839                      0.804                          0.770                              0.73572.5   16.000  16.000      16.000          16.000              1.831                  0.831                      0.796                          0.761                              0.72773.0   16.000  16.000      16.000          16.000              1.824                  0.824                      0.789                          0.753                              0.71873.5   16.000  16.000      16.000          16.000              1.816                  0.816                      0.781                          0.745                              0.71074.0   16.000  16.000      16.000          16.000              1.809                  0.809                      0.773                          0.737                              0.70274.5   16.000  16.000      16.000          16.000              1.802                  0.802                      0.766                          0.729                              0.69375.0   16.000  16.000      16.000          16.000              1.794                  0.794                      0.758                          0.721                              0.68575.5   16.000  16.000      16.000          16.000              1.787                  0.787                      0.750                          0.713                              0.67676.0   16.000  16.000      16.000          16.000              1.780                  0.780                      0.742                          0.705                              0.66876.5   16.000  16.000      16.000          16.000              1.772                  0.772                      0.735                          0.697                              0.66077.0   16.000  16.000      16.000          16.000              1.765                  0.765                      0.727                          0.689                              0.65177.5   16.000  16.000      16.000          16.000              1.757                  0.757                      0.719                          0.681                              0.64378.0   16.000  16.000      16.000          16.000              1.750                  0.750                      0.712                          0.673                              0.63578.5   16.000  16.000      16.000          16.000              1.750                  0.764                      0.726                          0.687                              0.64879.0   16.000  16.000      16.000          16.000              1.766                  0.779                      0.739                          0.700                              0.66179.5   16.000  16.000      16.000          16.090              1.781                  0.793                      0.753                          0.714                              0.67580.0   16.000  16.000      16.000          16.000              1.797                  0.807                      0.767                          0.728                              0.68880.5   16.000  16.000      16.000          16.000              1.813                  0.821                      0.781                          0.741                              0.70281.0   16.000  16.000      16.000          16.000              1.828                  0.836                      0.795                          0.755                              0.71581.5   16.000  16.000      16.000          16.000              1.844                  0.850                      0.809                          0.769                              0.72882.0   16.000  16.000      16.000          16.000              1.860                  0.864                      0.823                          0.783                              0.74282.5   16.000  16.000      16.000          16.000              1.875                  0.878                      0.837                          0.796                              0.75583.0   16.000  16.000      16.000          16.000              1.891                  0.893                      0.851                          0.810                              0.76883.5   16.000  16.000      16.000          16.000              1.907                  0.907                      0.865                          0.824                              0.78284.0   16.000  16.000      16.000          16.000              1.907                  1.907                      1.865                          1.823                              1.78284.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00088.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.000__________________________________________________________________________   -9.0  -8.0      -7.0          -6.0              -5.0                  -4.0                      -3.0                          -2.0                              -1.0__________________________________________________________________________0.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0000.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.5   8.000  8.000      8.000          8.000              8.000                  8.000                      8.000                          8.000                              8.0004.0   7.875  7.875      7.875          7.875              7.875                  7.875                      7.875                          7.875                              7.8754.5   7.813  7.813      7.813          7.813              7.813                  7.813                      7.813                          7.813                              7.8135.0   7.813  7.813      7.813          7.813              7.813                  7.813                      7.813                          7.625                              7.2505.5   7.813  7.813      7.813          7.813              7.813                  7.813                      7.813                          7.125                              6.6886.0   7.813  7.813      7.813          7.813              7.813                  7.813                      7.813                          6.563                              6.0006.5   7.813  7.813      7.813          7.813              7.813                  7.813                      7.063                          6.000                              5.3757.0   7.813  7.813      7.813          7.813              7.813                  7.813                      6.625                          5.438                              5.0007.5   7.813  7.813      7.813          7.813              7.813                  7.813                      6.313                          5.125                              4.7508.0   7.813  7.813      7.813          7.813              7.813                  7.813                      5.875                          4.813                              4.5638.5   7.813  7.813      7.813          7.813              7.813                  7.813                      5.500                          4.625                              4.5639.0   7.813  7.813      7.813          7.813              7.563                  6.938                      5.156                          4.500                              4.5429.5   7.563  7.625      7.625          7.625              7.438                  6.438                      4.813                          4.469                              4.52110.0   7.188  7.000      6.938          6.750              6.438                  5.750                      4.563                          4.438                              4.50010.5   6.063  6.000      5.844          5.563              5.438                  4.969                      4.438                          4.406                              4.47911.0   4.938  4.813      4.563          4.438              4.438                  4.375                      4.406                          4.375                              4.45811.5   4.250  4.250      4.263          4.275              4.288                  4.300                      4.313                          4.438                              4.43812.0   4.250  4.250      4.438          4.625              4.813                  4.875                      4.750                          4.500                              4.50012.5   4.875  5.375      5.750          5.938              6.000                  5.938                      5.656                          4.813                              4.62513.0   6.313  6.563      6.875          6.813              6.938                  6.750                      6.313                          5.563                              4.93813.5   7.000  7.250      7.500          7.625              7.500                  7.375                      6.844                          6.125                              5.50014.0   7.375  7.656      7.750          7.813              7.813                  7.625                      7.063                          6.500                              6.00014.5   7.500  7.688      7.750          7.813              7.813                  7.688                      7.125                          6.625                              6.37515.0   7.438  7.563      7.563          7.625              7.563                  7.500                      7.063                          6.625                              6.43815.5   7.125  7.188      7.188          7.344              7.125                  7.125                      6.750                          6.500                              6.25016.0   6.625  6.688      6.750          6.750              6.688                  6.594                      6.375                          6.188                              6.00016.5   6.125  6.156      6.125          6.063              6.125                  6.156                      5.875                          5.688                              5.68817.0   5.625  5.688      5.625          5.563              5.563                  5.625                      5.375                          5.250                              5.37517.5   5.188  5.188      5.125          5.125              5.094                  5.094                      4.906                          4.750                              4.96918.0   4.813  4.813      4.688          4.625              4.625                  4.625                      4.438                          4.406                              4.56318.5   4.500  4.375      4.250          4.313              4.250                  4.250                      4.125                          4.063                              4.18819.0   4.188  4.125      4.000          3.938              3.938                  3.875                      3.750                          3.750                              3.87519.5   3.938  3.875      3.688          3.688              3.688                  3.625                      3.500                          3.500                              3.56320.0   3.750  3.625      3.500          3.500              3.438                  3.406                      3.375                          3.313                              3.37520.5   3.563  3.438      3.313          3.250              3.250                  3.250                      3.188                          3.188                              3.18821.0   3.375  3.250      3.125          3.125              3.063                  3.031                      3.000                          3.000                              3.03121.5   3.188  3.063      3.000          2.938              2.938                  2.875                      2.844                          2.938                              2.87522.0   3.063  2.938      2.875          2.813              2.813                  2.750                      2.750                          2.750                              2.75022.5   2.875  2.813      2.750          2.625              2.625                  2.625                      2.625                          2.625                              2.62523.0   2.813  2.688      2.625          2.563              2.563                  2.500                      2.500                          2.500                              2.50023.5   2.751  2.631      2.571          2.510              2.510                  2.450                      2.449                          2.449                              2.44824.0   2.690  2.575      2.516          2.458              2.457                  2.399                      2.398                          2.398                              2.39724.5   2.629  2.518      2.463          2.406              2.405                  2.349                      2.348                          2.346                              2.34525.0   2.568  2.462      2.408          2.354              2.352                  2.299                      2.297                          2.295                              2.29325.5   2.507  2.405      2.354          2.302              2.300                  2.248                      2.246                          2.244                              2.24226.0   2.445  2.349      2.299          2.250              2.247                  2.198                      2.195                          2.193                              2.19026.5   2.384  2.293      2.245          2.198              2.195                  2.148                      2.145                          2.141                              2.13827.0   2.323  2.236      2.191          2.146              2.142                  2.097                      2.094                          2.090                              2.08727.5   2.262  2.180      2.137          2.094              2.090                  2.047                      2.043                          2.039                              2.03528.0   2.201  2.123      2.082          2.042              2.037                  1.997                      1.992                          1.988                              1.98428.5   2.139  2.067      2.028          1.990              1.985                  1.946                      1.941                          1.937                              1.93229.0   2.078  2.010      1.974          1.938              1.932                  1.896                      1.891                          1.885                              1.88029.5   2.017  1.954      1.920          1.885              1.880                  1.845                      1.840                          1.834                              1.82930.0   1.956  1.898      1.865          1.833              1.827                  1.795                      1.789                          1.783                              1.77730.5   1.895  1.841      1.811          1.781              1.775                  1.745                      1.738                          1.732                              1.72531.0   1.833  1.785      1.757          1.729              1.722                  1.694                      1.688                          1.681                              1.67431.5   1.772  1.728      1.703          1.677              1.670                  1.644                      1.637                          1.629                              1.62232.0   1.711  1.672      1.648          1.625              1.617                  1.594                      1.586                          1.578                              1.57032.5   1.650  1.615      1.594          1.573              1.565                  1.543                      1.535                          1.527                              1.51933.0   1.589  1.559      1.540          1.521              1.512                  1.493                      1.484                          1.476                              1.46733.5   1.527  1.503      1.486          1.469              1.460                  1.443                      1.434                          1.424                              1.41534.0   1.466  1.446      1.431          1.417              1.407                  1.392                      1.383                          1.373                              1.36434.5   1.405  1.390      1.377          1.365              1.355                  1.342                      1.332                          1.322                              1.31235.0   1.344  1.333      1.323          1.313              1.302                  1.292                      1.281                          1.271                              1.26035.5   1.335  1.324      1.313          1.303              1.292                  1.281                      1.271                          1.260                              1.24936.0   1.326  1.315      1.304          1.293              1.282                  1.271                      1.260                          1.249                              1.23836.5   1.317  1.306      1.295          1.283              1.272                  1.261                      1.249                          1.238                              1.22637.0   1.309  1.297      1.285          1.274              1.262                  1.250                      1.239                          1.227                              1.21537.5   1.300  1.288      1.276          1.264              1.252                  1.240                      1.228                          1.216                              1.20438.0   1.291  1.279      1.267          1.254              1.242                  1.230                      1.217                          1.205                              1.19338.5   1.283  1.270      1.257          1.245              1.232                  1.219                      1.207                          1.194                              1.18139.0   1.274  1.261      1.248          1.235              1.222                  1.209                      1.196                          1.183                              1.17039.5   1.265  1.252      1.239          1.225              1.212                  1.199                      1.185                          1.172                              1.15940.0   1.257  1.243      1.229          1.216              1.202                  1.188                      1.175                          1.161                              1.14740.5   1.248  1.234      1.220          1.206              1.192                  1.178                      1.164                          1.150                              1.13641.0   1.239  1.225      1.211          1.196              1.182                  1.168                      1.153                          1.139                              1.12541.5   1.230  1.216      1.201          1.187              1.172                  1.157                      1.143                          1.128                              1.11342.0   1.222  1.207      1.192          1.177              1.162                  1.147                      1.132                          1.117                              1.10242.5   1.213  1.198      1.183          1.167              1.152                  1.137                      1.121                          1.106                              1.09143.0   1.204  1.189      1.173          1.158              1.142                  1.126                      1.111                          1.095                              1.08043.5   1.196  1.180      1.164          1.148              1.132                  1.116                      1.100                          1.084                              1.06844.0   1.187  1.171      1.155          1.138              1.122                  1.106                      1.089                          1.073                              1.05744.5   1.178  1.162      1.145          1.129              1.112                  1.095                      1.079                          1.062                              1.04645.0   1.170  1.153      1.136          1.119              1.102                  1.085                      1.068                          1.051                              1.03445.5   1.161  1.144      1.126          1.109              1.092                  1.075                      1.058                          1.040                              1.02346.0   1.152  1.135      1.117          1.100              1.082                  1.064                      1.047                          1.029                              1.01246.5   1.144  1.126      1.108          1.090              1.072                  1.054                      1.036                          1.018                              1.00047.0   1.135  1.117      1.098          1.080              1.062                  1.044                      1.026                          1.007                              0.98947.5   1.126  1.108      1.089          1.071              1.052                  1.033                      1.015                          0.996                              0.97848.0   1.118  1.099      1.080          1.061              1.042                  1.023                      1.004                          0.985                              0.96748.5   1.109  1.090      1.070          1.051              1.032                  1.013                      0.994                          0.974                              0.95549.0   1.100  1.081      1.061          1.042              1.022                  1.003                      0.983                          0.963                              0.94449.5   1.091  1.072      1.052          1.032              1.012                  0.992                      0.972                          0.952                              0.93350.0   1.083  1.063      1.042          1.022              1.002                  0.982                      0.962                          0.942                              0.92150.5   1.074  1.054      1.033          1.013              0.992                  0.972                      0.951                          0.931                              0.91051.0   1.065  1.045      1.024          1.003              0.982                  0.961                      0.940                          0.920                              0.89951.5   1.057  1.036      1.014          0.993              0.972                  0.951                      0.930                          0.909                              0.88752.0   1.048  1.027      1.005          0.984              0.962                  0.941                      0.919                          0.898                              0.87652.5   1.039  1.018      0.996          0.974              0.952                  0.930                      0.908                          0.887                              0.86553.0   1.031  1.008      0.986          0.964              0.942                  0.920                      0.898                          0.876                              0.85453.5   1.022  0.999      0.977          0.955              0.932                  0.910                      0.887                          0.865                              0.84254.0   1.013  0.990      0.968          0.945              0.922                  0.899                      0.877                          0.854                              0.83154.5   1.005  0.981      0.958          0.935              0.912                  0.889                      0.866                          0.843                              0.82055.0   0.996  0.972      0.949          0.926              0.902                  0.879                      0.855                          0.832                              0.80855.5   0.987  0.963      0.940          0.916              0.892                  0.868                      0.845                          0.821                              0.79756.0   0.978  0.954      0.930          0.906              0.882                  0.858                      0.834                          0.810                              0.78656.5   0.970  0.945      0.921          0.897              0.872                  0.848                      0.823                          0.799                              0.77457.0   0.961  0.936      0.912          0.887              0.862                  0.837                      0.813                          0.788                              0.76357.5   0.952  0.927      0.902          0.877              0.852                  0.827                      0.802                          0.777                              0.75258.0   0.944  0.918      0.893          0.868              0.842                  0.817                      0.791                          0.766                              0.74158.5   0.935  0.909      0.884          0.858              0.832                  0.806                      0.781                          0.755                              0.72959.0   0.926  0.900      0.874          0.848              0.822                  0.796                      0.770                          0.744                              0.71859.5   0.918  0.891      0.865          0.839              0.812                  0.786                      0.759                          0.733                              0.70760.0   0.909  0.882      0.856          0.829              0.802                  0.775                      0.749                          0.722                              0.69560.5   0.900  0.873      0.846          0.819              0.792                  0.765                      0.738                          0.711                              0.68461.0   0.892  0.864      0.837          0.810              0.782                  0.755                      0.727                          0.700                              0.67361.5   0.883  0.855      0.828          0.800              0.772                  0.744                      0.717                          0.689                              0.66162.0   0.874  0.846      0.818          0.790              0.762                  0.734                      0.706                          0.678                              0.65062.5   0.866  0.837      0.809          0.781              0.752                  0.724                      0.695                          0.667                              0.63963.0   0.857  0.828      0.800          0.771              0.742                  0.714                      0.685                          0.656                              0.62863.5   0.848  0.819      0.790          0.761              0.732                  0.703                      0.674                          0.645                              0.61664.0   0.839  0.810      0.781          0.752              0.722                  0.693                      0.664                          0.634                              0.60564.5   0.831  0.801      0.771          0.742              0.712                  0.683                      0.653                          0.623                              0.59465.0   0.822  0.792      0.762          0.732              0.702                  0.672                      0.642                          0.612                              0.58265.5   0.813  0.783      0.753          0.722              0.692                  0.662                      0.632                          0.601                              0.57166.0   0.805  0.774      0.743          0.713              0.682                  0.652                      0.621                          0.590                              0.56066.5   0.796  0.765      0.734          0.703              0.672                  0.641                      0.610                          0.579                              0.54867.0   0.787  0.756      0.725          0.693              0.662                  0.631                      0.600                          0.568                              0.53767.5   0.779  0.747      0.715          0.684              0.652                  0.621                      0.589                          0.557                              0.52668.0   0.770  0.738      0.706          0.674              0.642                  0.610                      0.578                          0.546                              0.51468.5   0.761  0.729      0.697          0.664              0.632                  0.600                      0.568                          0.535                              0.50369.0   0.753  0.720      0.687          0.655              0.622                  0.590                      0.557                          0.524                              0.49269.5   0.744  0.711      0.678          0.645              0.612                  0.579                      0.546                          0.513                              0.48170.0   0.735  0.702      0.669          0.635              0.602                  0.569                      0.536                          0.503                              0.46970.5   0.726  0.693      0.659          0.626              0.592                  0.559                      0.525                          0.492                              0.45871.0   0.718  0.684      0.650          0.616              0.582                  0.548                      0.514                          0.481                              0.44771.5   0.709  0.675      0.641          0.606              0.572                  0.538                      0.504                          0.470                              0.43572.0   0.700  0.666      0.631          0.597              0.562                  0.528                      0.493                          0.459                              0.42472.5   0.692  0.657      0.622          0.587              0.552                  0.517                      0.483                          0.448                              0.41373.0   0.683  0.648      0.613          0.577              0.542                  0.507                      0.472                          0.437                              0.40173.5   0.674  0.639      0.603          0.568              0.532                  0.497                      0.461                          0.426                              0.39074.0   0.666  0.630      0.594          0.558              0.522                  0.486                      0.451                          0.415                              0.37974.5   0.657  0.621      0.585          0.548              0.512                  0.476                      0.440                          0.404                              0.36875.0   0.648  0.612      0.575          0.539              0.502                  0.466                      0.429                          0.393                              0.35675.5   0.640  0.603      0.566          0.529              0.492                  0.455                      0.419                          0.382                              0.34576.0   0.631  0.594      0.557          0.519              0.482                  0.445                      0.408                          0.371                              0.33476.5   0.622  0.585      0.547          0.510              0.472                  0.435                      0.397                          0.360                              0.32277.0   0.614  0.576      0.538          0.500              0.462                  0.424                      0.387                          0.349                              0.31177.5   0.605  0.567      0.529          0.490              0.452                  0.414                      0.376                          0.338                              0.30078.0   0.596  0.558      0.519          0.481              0.442                  0.404                      0.365                          0.327                              0.28878.5   0.609  0.570      0.532          0.493              0.454                  0.415                      0.377                          0.338                              0.29979.0   0.622  0.583      0.544          0.505              0.466                  0.427                      0.388                          0.349                              0.31079.5   0.635  0.596      0.557          0.517              0.478                  0.439                      0.399                          0.360                              0.32180.0   0.649  0.609      0.569          0.530              0.490                  0.450                      0.411                          0.371                              0.33180.5   0.662  0.622      0.582          0.542              0.502                  0.462                      0.422                          0.382                              0.34281.0   0.675  0.634      0.594          0.554              0.514                  0.474                      0.433                          0.393                              0.35381.5   0.688  0.647      0.607          0.566              0.526                  0.485                      0.445                          0.404                              0.36482.0   0.701  0.660      0.619          0.578              0.538                  0.497                      0.456                          0.415                              0.37482.5   0.714  0.673      0.632          0.591              0.550                  0.508                      0.467                          0.426                              0.38583.0   0.727  0.686      0.644          0.603              0.562                  0.520                      0.479                          0.437                              0.39683.5   0.740  0.699      0.657          0.615              0.573                  0.532                      0.490                          0.448                              0.40784.0   1.740  1.698      1.657          1.615              0.573                  1.532                      1.490                          1.448                              1.40784.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00088.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.000__________________________________________________________________________   0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0__________________________________________________________________________0.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0000.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.5   8.000  8.000      8.000          8.000              8.000                  8.000                      8.000                          8.000                              8.0004.0   7.875  7.875      7.875          7.875              7.875                  7.875                      7.875                          7.875                              7.8754.5   7.813  7.813      7.813          7.813              7.813                  7.813                      7.813                          7.813                              7.8135.0   7.125  7.250      7.625          7.813              7.813                  7.813                      7.813                          7.813                              7.8135.5   6.625  6.688      7.125          7.813              7.813                  7.813                      7.813                          7.813                              7.8136.0   5.983  6.000      6.563          7.813              7.813                  7.813                      7.813                          7.813                              7.8136.5   5.375  5.375      6.000          7.063              7.813                  7.813                      7.813                          7.813                              7.8137.0   4.750  5.000      5.438          6.625              7.813                  7.813                      7.813                          7.813                              7.8137.5   4.500  4.750      5.125          6.313              7.813                  7.813                      7.813                          7.813                              7.8138.0   4.500  4.563      4.813          5.875              7.813                  7.813                      7.813                          7.813                              7.8138.5   4.438  4.563      4.625          5.500              7.813                  7.813                      7.813                          7.813                              7.8139.0   4.438  4.542      4.500          5.156              6.938                  7.563                      7.813                          7.813                              7.8139.5   4.438  4.521      4.469          4.813              6.438                  7.438                      7.625                          7.625                              7.62510.0   4.438  4.500      4.438          4.563              5.750                  6.438                      6.750                          6.938                              7.00010.5   4.438  4.479      4.406          4.438              4.969                  5.438                      5.563                          5.844                              6.00011.0   4.375  4.458      4.375          4.406              4.375                  4.438                      4.438                          4.563                              4.81311.5   4.375  4.438      4.438          4.313              4.300                  4.288                      4.275                          4.263                              4.25012.0   4.438  4.500      4.500          4.750              4.875                  4.813                      4.625                          4.438                              4.25012.5   4.438  4.625      4.813          5.656              5.938                  6.000                      5.938                          5.750                              5.37513.0   4.469  4.938      5.563          6.313              6.750                  6.938                      6.813                          6.875                              6.56313.5   5.250  5.500      6.125          6.844              7.375                  7.500                      7.625                          7.500                              7.25014.0   5.875  6.000      6.500          7.063              7.625                  7.813                      7.813                          7.750                              7.65614.5   6.063  6.375      6.625          7.125              7.688                  7.813                      7.813                          7.750                              7.68815.0   6.125  6.438      6.625          7.063              7.500                  7.563                      7.625                          7.563                              7.56315.5   6.188  6.250      6.500          6.750              7.125                  7.125                      7.344                          7.188                              7.18816.0   6.000  6.000      6.188          6.375              6.594                  6.688                      6.750                          6.750                              6.68816.5   5.656  5.688      5.688          5.875              6.156                  6.125                      6.063                          6.125                              6.15617.0   5.313  5.375      5.250          5.375              5.625                  5.563                      5.563                          5.625                              5.68817.5   4.938  4.969      4.750          4.906              5.094                  5.094                      5.125                          5.125                              5.18818.0   4.500  4.563      4.406          4.438              4.625                  4.625                      4.625                          4.688                              4.81318.5   4.250  4.188      4.063          4.125              4.250                  4.250                      4.313                          4.250                              4.37519.0   3.906  3.875      3.750          3.750              3.875                  3.938                      3.938                          4.000                              4.12519.5   3.625  3.563      3.500          3.500              3.625                  3.688                      3.688                          3.688                              3.87520.0   3.375  3.375      3.313          3.375              3.406                  3.438                      3.500                          3.500                              3.62520.5   3.188  3.188      3.188          3.188              3.250                  3.250                      3.250                          3.313                              3.43821.0   3.063  3.031      3.000          3.000              3.031                  3.063                      3.125                          3.125                              3.25021.5   2.938  2.875      2.938          2.844              2.875                  2.938                      2.938                          3.000                              3.06322.0   2.750  2.750      2.750          2.750              2.750                  2.813                      2.813                          2.875                              2.93822.5   2.656  2.625      2.625          2.625              2.625                  2.625                      2.625                          2.750                              2.81323.0   2.563  2.500      2.500          2.500              2.500                  2.563                      2.563                          2.625                              2.68823.5   2.438  2.448      2.449          2.449              2.450                  2.510                      2.510                          2.571                              2.63124.0   2.375  2.397      2.398          2.398              2.399                  2.457                      2.458                          2.516                              2.57524.5   2.250  2.345      2.346          2.348              2.349                  2.405                      2.406                          2.462                              2.51825.0   2.188  2.293      2.295          2.297              2.299                  2.352                      2.354                          2.408                              2.46225.5   2.125  2.242      2.244          2.246              2.248                  2.300                      2.302                          2.354                              2.40526.0   2.063  2.190      2.193          2.195              2.198                  2.247                      2.250                          2.299                              2.34926.5   2.031  2.138      2.141          2.145              2.148                  2.195                      2.198                          2.245                              2.29327.0   2.000  2.087      2.090          2.094              2.097                  2.142                      2.146                          2.191                              2.23627.5   2.000  2.035      2.039          2.043              2.047                  2.090                      2.094                          2.137                              2.18028.0   1.938  1.984      1.988          1.992              1.997                  2.037                      2.042                          2.082                              2.12328.5   1.938  1.932      1.937          1.941              1.946                  1.985                      1.990                          2.028                              2.06729.0   1.813  1.880      1.885          1.891              1.896                  1.932                      1.938                          1.974                              2.01029.5   1.750  1.829      1.834          1.840              1.845                  1.880                      1.885                          1.920                              1.95430.0   1.688  1.777      1.783          1.789              1.795                  1.827                      1.833                          1.865                              1.89830.5   1.656  1.725      1.732          1.738              1.745                  1.775                      1.781                          1.811                              1.84131.0   1.625  1.674      1.681          1.688              1.694                  1.722                      1.729                          1.757                              1.78531.5   1.500  1.622      1.629          1.637              1.644                  1.670                      1.677                          1.703                              1.72832.0   1.469  1.570      1.578          1.586              1.594                  1.617                      1.625                          1.648                              1.67232.5   1.469  1.519      1.527          1.535              1.543                  1.565                      1.573                          1.594                              1.61533.0   1.438  1.467      1.476          1.484              1.493                  1.512                      1.521                          1.540                              1.55933.5   1.375  1.415      1.424          1.434              1.443                  1.460                      1.469                          1.486                              1.50334.0   1.313  1.364      1.373          1.383              1.392                  1.407                      1.417                          1.431                              1.44634.5   1.281  1.312      1.322          1.332              1.342                  1.355                      1.365                          1.377                              1.39035.0   1.250  1.260      1.271          1.281              1.292                  1.302                      1.313                          1.323                              1.33335.5   1.238  1.249      1.260          1.271              1.281                  1.292                      1.303                          1.313                              1.32436.0   1.227  1.238      1.249          1.260              1.271                  1.282                      1.293                          1.304                              1.31536.5   1.215  1.226      1.238          1.249              1.261                  1.272                      1.283                          1.295                              1.30637.0   1.203  1.215      1.227          1.239              1.250                  1.262                      1.274                          1.285                              1.29737.5   1.192  1.204      1.216          1.228              1.240                  1.252                      1.264                          1.276                              1.28838.0   1.180  1.193      1.205          1.217              1.230                  1.242                      1.254                          1.267                              1.27938.5   1.169  1.181      1.194          1.207              1.219                  1.232                      1.245                          1.257                              1.27039.0   1.157  1.170      1.183          1.196              1.209                  1.222                      1.235                          1.248                              1.26139.5   1.145  1.159      1.172          1.185              1.199                  1.212                      1.225                          1.239                              1.25240.0   1.134  1.147      1.161          1.175              1.188                  1.202                      1.216                          1.229                              1.24340.5   1.122  1.136      1.150          1.164              1.178                  1.192                      1.206                          1.220                              1.23441.0   1.110  1.125      1.139          1.153              1.168                  1.182                      1.196                          1.211                              1.22541.5   1.099  1.113      1.128          1.143              1.157                  1.172                      1.187                          1.201                              1.21642.0   1.087  1.102      1.117          1.132              1.147                  1.162                      1.177                          1.192                              1.20742.5   1.076  1.091      1.106          1.121              1.137                  1.152                      1.167                          1.183                              1.19843.0   1.064  1.080      1.095          1.111              1.126                  1.142                      1.158                          1.173                              1.18943.5   1.052  1.068      1.084          1.100              1.116                  1.132                      1.148                          1.164                              1.18044.0   1.041  1.057      1.073          1.089              1.106                  1.122                      1.138                          1.155                              1.17144.5   1.029  1.046      1.062          1.079              1.095                  1.112                      1.129                          1.145                              1.16245.0   1.017  1.034      1.051          1.068              1.085                  1.102                      1.119                          1.136                              1.15345.5   1.006  1.023      1.040          1.058              1.075                  1.092                      1.109                          1.126                              1.14446.0   0.944  1.012      1.029          1.047              1.064                  1.082                      1.110                          1.117                              1.13546.5   0.983  1.000      1.018          1.036              1.054                  1.072                      1.090                          1.108                              1.12647.0   0.971  0.989      1.007          1.026              1.044                  1.062                      1.080                          1.098                              1.11747.5   0.959  0.978      0.996          1.015              1.033                  1.052                      1.071                          1.089                              1.10848.0   0.948  0.967      0.985          1.004              1.023                  1.042                      1.061                          1.080                              1.09948.5   0.936  0.955      0.974          0.994              1.013                  1.032                      1.051                          1.070                              1.09049.0   0.924  0.944      0.963          0.983              1.003                  1.022                      1.042                          1.061                              1.08149.5   0.913  0.933      0.952          0.972              0.992                  1.012                      1.032                          1.052                              1.07250.0   0.901  0.921      0.942          0.962              0.982                  1.002                      1.022                          1.042                              1.06350.5   0.890  0.910      0.931          0.951              0.972                  0.992                      1.013                          1.033                              1.05451.0   0.878  0.899      0.920          0.940              0.961                  0.982                      1.003                          1.024                              1.04551.5   0.866  0.887      0.909          0.930              0.951                  0.972                      0.993                          1.014                              1.03652.0   0.855  0.876      0.898          0.919              0.941                  0.962                      0.984                          1.005                              1.02752.5   0.843  0.865      0.887          0.908              0.930                  0.952                      0.974                          0.996                              1.01853.0   0.831  0.854      0.876          0.898              0.920                  0.942                      0.964                          0.986                              1.00853.5   0.820  0.842      0.865          0.887              0.910                  0.932                      0.955                          0.977                              0.99954.0   0.808  0.831      0.854          0.877              0.899                  0.922                      0.945                          0.968                              0.99054.5   0.798  0.820      0.843          0.866              0.889                  0.912                      0.935                          0.958                              0.98155.0   0.785  0.808      0.832          0.855              0.879                  0.902                      0.926                          0.949                              0.97255.5   0.773  0.797      0.821          0.845              0.868                  0.892                      0.916                          0.940                              0.96356.0   0.762  0.786      0.810          0.834              0.858                  0.882                      0.906                          0.930                              0.95456.5   0.750  0.774      0.799          0.823              0.848                  0.872                      0.897                          0.921                              0.94557.0   0.738  0.763      0.788          0.813              0.837                  0.862                      0.887                          0.912                              0.93657.5   0.727  0.752      0.777          0.802              0.827                  0.852                      0.877                          0.902                              0.92758.0   0.715  0.741      0.766          0.791              0.817                  0.842                      0.868                          0.893                              0.91858.5   0.703  0.729      0.755          0.781              0.806                  0.832                      0.858                          0.884                              0.90959.0   0.692  0.718      0.744          0.770              0.796                  0.822                      0.848                          0.874                              0.90059.5   0.680  0.707      0.733          0.759              0.786                  0.812                      0.839                          0.865                              0.89160.0   0.669  0.695      0.722          0.749              0.775                  0.802                      0.829                          0.856                              0.88260.5   0.657  0.684      0.711          0.738              0.765                  0.792                      0.819                          0.846                              0.87361.0   0.645  0.673      0.700          0.727              0.755                  0.782                      0.801                          0.837                              0.86461.5   0.634  0.661      0.689          0.717              0.744                  0.772                      0.800                          0.828                              0.85562.0   0.622  0.650      0.678          0.706              0.734                  0.762                      0.790                          0.818                              0.84662.5   0.610  0.639      0.667          0.695              0.724                  0.752                      0.781                          0.809                              0.83763.0   0.599  0.628      0.656          0.685              0.714                  0.742                      0.771                          0.800                              0.82863.5   0.587  0.616      0.645          0.674              0.703                  0.732                      0.761                          0.790                              0.81964.0   0.576  0.605      0.634          0.664              0.693                  0.722                      0.752                          0.781                              0.81064.5   0.564  0.594      0.623          0.653              0.683                  0.712                      0.742                          0.771                              0.80165.0   0.552  0.582      0.612          0.642              0.672                  0.702                      0.732                          0.762                              0.79265.5   0.541  0.571      0.601          0.632              0.662                  0.692                      0.722                          0.753                              0.78366.0   0.529  0.560      0.590          0.621              0.652                  0.682                      0.713                          0.743                              0.77466.5   0.517  0.548      0.579          0.610              0.641                  0.672                      0.703                          0.734                              0.76567.0   0.506  0.537      0.568          0.600              0.631                  0.662                      0.693                          0.725                              0.75667.5   0.494  0.526      0.557          0.589              0.621                  0.652                      0.684                          0.715                              0.74768.0   0.483  0.514      0.546          0.578              0.610                  0.642                      0.674                          0.706                              0.73868.5   0.471  0.503      0.535          0.568              0.600                  0.632                      0.664                          0.697                              0.72969.0   0.459  0.492      0.524          0.557              0.590                  0.622                      0.655                          0.687                              0.72069.5   0.448  0.481      0.513          0.546              0.579                  0.612                      0.645                          0.678                              0.71170.0   0.436  0.469      0.503          0.536              0.569                  0.602                      0.635                          0.669                              0.70270.5   0.424  0.458      0.492          0.525              0.559                  0.592                      0.626                          0.659                              0.69371.0   0.413  0.447      0.481          0.514              0.548                  0.582                      0.616                          0.650                              0.68471.5   0.401  0.435      0.470          0.504              0.538                  0.572                      0.606                          0.641                              0.67572.0   0.390  0.424      0.459          0.493              0.528                  0.562                      0.597                          0.631                              0.66672.5   0.378  0.413      0.448          0.483              0.517                  0.552                      0.587                          0.622                              0.65773.0   0.366  0.401      0.437          0.472              0.507                  0.542                      0.577                          0.613                              0.64873.5   0.355  0.390      0.426          0.461              0.497                  0.532                      0.568                          0.603                              0.63974.0   0.343  0.379      0.415          0.451              0.486                  0.522                      0.558                          0.594                              0.63074.5   0.331  0.368      0.404          0.440              0.476                  0.512                      0.548                          0.585                              0.62175.0   0.320  0.356      0.393          0.429              0.466                  0.502                      0.539                          0.575                              0.61275.5   0.308  0.345      0.382          0.419              0.455                  0.492                      0.529                          0.566                              0.60376.0   0.297  0.334      0.371          0.408              0.445                  0.482                      0.519                          0.557                              0.59476.5   0.285  0.322      0.360          0.397              0.435                  0.472                      0.510                          0.547                              0.58577.0   0.273  0.311      0.349          0.387              0.424                  0.462                      0.500                          0.538                              0.57677.5   0.262  0.300      0.338          0.376              0.414                  0.452                      0.490                          0.529                              0.56778.0   0.250  0.288      0.327          0.365              0.404                  0.442                      0.481                          0.519                              0.55878.5   0.260  0.299      0.338          0.377              0.415                  0.454                      0.493                          0.532                              0.57079.0   0.271  0.310      0.349          0.388              0.427                  0.466                      0.505                          0.544                              0.58379.5   0.281  0.321      0.360          0.399              0.439                  0.478                      0.517                          0.557                              0.59680.0   0.292  0.331      0.371          0.411              0.450                  0.490                      0.530                          0.569                              0.60980.5   0.302  0.342      0.382          0.422              0.462                  0.502                      0.542                          0.582                              0.62281.0   0.313  0.353      0.393          0.433              0.474                  0.514                      0.554                          0.594                              0.63481.5   0.323  0.364      0.404          0.445              0.485                  0.526                      0.566                          0.607                              0.64782.0   0.334  0.374      0.415          0.456              0.497                  0.538                      0.578                          0.619                              0.66082.5   0.344  0.385      0.426          0.467              0.508                  0.550                      0.591                          0.632                              0.67383.0   0.355  0.396      0.437          0.479              0.520                  0.562                      0.603                          0.644                              0.68683.5   0.365  0.407      0.448          0.490              0.532                  0.573                      0.615                          0.657                              0.69984.0   1.365  1.407      1.448          0.490              1.532                  1.573                      1.615                          1.657                              1.69884.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00088.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.000__________________________________________________________________________   9.0 10.0      11.0          12.0              13.0                  14.0                      15.0                          16.0                              17.0__________________________________________________________________________0.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0000.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0001.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0002.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.0003.5   8.000  8.000      8.000          8.000              8.000                  8.000                      16.000                          16.000                              16.0004.0   7.875  7.875      7.875          7.875              7.875                  7.875                      16.000                          16.000                              16.0004.5   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0005.0   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0005.5   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0006.0   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0006.5   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0007.0   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0007.5   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0008.0   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0008.5   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0009.0   7.813  7.813      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.0009.5   7.563  7.875      7.813          7.813              7.813                  7.813                      16.000                          16.000                              16.00010.0   7.188  7.250      7.438          7.563              7.719                  7.813                      16.000                          16.000                              16.00010.5   6.063  6.125      6.375          6.500              6.563                  6.875                      16.000                          16.000                              16.00011.0   4.938  5.000      5.250          5.438              5.500                  5.625                      16.000                          16.000                              16.00011.5   4.250  4.313      4.313          4.344              4.438                  4.719                      16.000                          16.000                              16.00012.0   4.250  4.188      4.125          4.188              4.156                  4.219                      16.000                          16.000                              16.00012.5   4.875  4.375      4.188          4.125              4.063                  4.094                      16.000                          16.000                              16.00013.0   6.313  5.313      4.438          4.063              4.031                  4.001                      16.000                          16.000                              16.00013.5   7.000  6.250      5.125          4.063              4.031                  3.948                      16.000                          16.000                              16.00014.0   7.375  6.813      5.563          4.125              3.975                  3.894                      16.000                          16.000                              16.00014.5   7.500  6.875      5.813          4.313              3.920                  3.841                      16.000                          16.000                              16.00015.0   7.438  6.781      5.750          4.500              3.864                  3.787                      16.000                          16.000                              16.00015.5   7.125  6.344      5.500          4.594              3.808                  3.734                      16.000                          16.000                              16.00016.0   6.625  6.044      5.344          4.625              3.752                  3.680                      16.000                          16.000                              16.00016.5   6.125  5.696      5.125          4.531              3.696                  3.627                      16.000                          16.000                              16.00017.0   5.625  5.348      4.893          4.438              3.640                  3.573                      16.000                          16.000                              16.00017.5   5.188  5.000      4.688          4.375              3.584                  3.520                      16.000                          16.000                              16.00018.0   4.813  4.750      4.520          4.290              3.528                  3.466                      16.000                          16.000                              16.00018.5   4.500  4.500      4.344          4.188              3.473                  3.413                      16.000                          16.000                              16.00019.0   4.188  4.313      4.250          4.063              3.417                  3.359                      16.000                          16.000                              16.00019.5   3.938  4.125      4.063          4.000              3.361                  3.306                      16.000                          16.000                              16.00020.0   3.750  3.875      3.938          3.875              3.305                  3.252                      16.000                          16.000                              16.00020.5   3.563  3.719      3.688          3.750              3.249                  3.199                      16.000                          16.000                              16.00021.0   3.375  3.500      3.625          3.625              3.193                  3.145                      16.000                          16.000                              16.00021.5   3.188  3.250      3.500          3.500              3.137                  3.092                      16.000                          16.000                              16.00022.0   3.063  3.188      3.313          3.375              3.081                  3.038                      16.000                          16.000                              16.00022.5   2.875  3.125      3.188          3.313              3.026                  3.985                      16.000                          16.000                              16.00023.0   2.813  3.000      3.063          3.219              2.970                  2.931                      16.000                          16.000                              16.00023.5   2.751  2.931      3.000          3.125              2.914                  2.878                      16.000                          16.000                              16.00024.0   2.690  2.863      2.875          2.969              2.858                  2.824                      16.000                          16.000                              16.00024.5   2.629  2.794      2.880          2.938              2.802                  2.771                      16.000                          16.000                              16.00025.0   2.568  2.726      2.760          2.813              2.746                  2.717                      16.000                          16.000                              16.00025.5   2.507  2.657      2.669          2.719              2.690                  2.664                      16.000                          16.000                              16.00026.0   2.445  2.589      2.635          2.688              2.634                  2.610                      16.000                          16.000                              16.00026.5   2.384  2.520      2.568          2.617              2.579                  2.557                      16.000                          16.000                              16.00027.0   2.323  2.451      2.501          2.547              2.523                  2.503                      16.000                          16.000                              16.00027.5   2.262  2.383      2.437          2.477              2.467                  2.496                      16.000                          16.000                              16.00028.0   2.201  2.314      2.367          2.406              2.411                  2.488                      16.000                          16.000                              16.00028.5   2.139  2.246      2.303          2.336              2.355                  2.481                      16.000                          16.000                              16.00029.0   2.078  2.177      2.228          2.266              2.299                  2.474                      16.000                          16.000                              16.00029.5   2.017  2.109      2.158          2.195              2.243                  2.466                      16.000                          16.000                              16.00030.0   1.956  2.040      2.089          2.125              2.188                  2.459                      16.000                          16.000                              16.00030.5   1.895  1.971      2.021          2.055              2.128                  2.451                      16.000                          16.000                              16.00031.0   1.833  1.903      1.954          1.984              2.069                  2.444                      16.000                          16.000                              16.00031.5   1.772  1.834      1.880          1.914              2.009                  2.437                      16.000                          16.000                              16.00032.0   1.711  1.766      1.813          1.844              1.950                  2.429                      16.000                          16.000                              16.00032.5   1.650  1.697      1.727          1.750              1.813                  2.422                      16.000                          16.000                              16.00033.0   1.589  1.628      1.638          1.656              1.727                  2.415                      16.000                          16.000                              16.00033.5   1.527  1.560      1.576          1.594              1.642                  2.407                      16.000                          16.000                              16.00034.0   1.466  1.491      1.484          1.500              1.556                  2.400                      16.000                          16.000                              16.00034.5   1.405  1.423      1.424          1.438              1.471                  2.392                      16.000                          16.000                              16.00035.0   1.344  1.354      1.365          1.375              1.385                  2.385                      16.000                          16.000                              16.00035.5   1.335  1.345      1.356          1.367              1.378                  2.378                      16.000                          16.000                              16.00036.0   1.326  1.337      1.348          1.359              1.370                  2.370                      16.000                          16.000                              16.00036.5   1.317  1.329      1.340          1.351              1.363                  2.363                      16.000                          16.000                              16.00037.0   1.309  1.320      1.332          1.344              1.355                  2.355                      16.000                          16.000                              16.00037.5   1.300  1.312      1.324          1.336              1.348                  2.348                      16.000                          16.000                              16.00038.0   1.291  1.304      1.316          1.328              1.341                  2.341                      16.000                          16.000                              16.00038.5   1.283  1.295      1.308          1.321              1.333                  2.333                      16.000                          16.000                              16.00039.0   1.274  1.287      1.300          1.313              1.326                  2.326                      16.000                          16.000                              16.00039.5   1.265  1.279      1.292          1.305              1.319                  2.319                      16.000                          16.000                              16.00040.0   1.257  1.270      1.284          1.298              1.311                  2.311                      16.000                          16.000                              16.00040.5   1.248  1.262      1.276          1.290              1.304                  2.304                      16.000                          16.000                              16.00041.0   1.239  1.253      1.268          1.282              1.296                  2.296                      16.000                          16.000                              16.00041.5   1.230  1.245      1.260          1.274              1.289                  2.289                      16.000                          16.000                              16.00042.0   1.222  1.237      1.252          1.267              1.282                  2.282                      16.000                          16.000                              16.00042.5   1.213  1.228      1.244          1.259              1.274                  2.274                      16.000                          16.000                              16.00043.0   1.204  1.220      1.236          1.251              1.267                  2.267                      16.000                          16.000                              16.00043.5   1.196  1.212      1.228          1.244              1.259                  2.259                      16.000                          16.000                              16.00044.0   1.187  1.203      1.220          1.236              1.252                  2.252                      16.000                          16.000                              16.00044.5   1.178  1.195      1.212          1.228              1.245                  2.245                      16.000                          16.000                              16.00045.0   1.170  1.187      1.203          1.220              1.237                  2.237                      16.000                          16.000                              16.00045.5   1.161  1.178      1.195          1.213              1.230                  2.230                      16.000                          16.000                              16.00046.0   1.152  1.170      1.187          1.205              1.223                  2.223                      16.000                          16.000                              16.00046.5   1.144  1.161      1.179          1.197              1.215                  2.215                      16.000                          16.000                              16.00047.0   1.135  1.153      1.171          1.190              1.208                  2.208                      16.000                          16.000                              16.00047.5   1.126  1.145      1.163          1.182              1.200                  2.200                      16.000                          16.000                              16.00048.0   1.118  1.136      1.155          1.174              1.193                  2.193                      16.000                          16.000                              16.00048.5   1.109  1.128      1.147          1.166              1.186                  2.186                      16.000                          16.000                              16.00049.0   1.100  1.120      1.139          1.159              1.178                  2.178                      16.000                          16.000                              16.00049.5   1.091  1.111      1.131          1.151              1.171                  2.171                      16.000                          16.000                              16.00050.0   1.083  1.103      1.123          1.143              1.163                  2.163                      16.000                          16.000                              16.00050.5   1.074  1.095      1.115          1.136              1.156                  2.156                      16.000                          16.000                              16.00051.0   1.065  1.086      1.107          1.128              1.149                  2.149                      16.000                          16.000                              16.00051.5   1.057  1.078      1.099          1.120              1.141                  2.141                      16.000                          16.000                              16.00052.0   1.048  1.069      1.091          1.112              1.134                  2.134                      16.000                          16.000                              16.00052.5   1.039  1.061      1.083          1.105              1.127                  2.127                      16.000                          16.000                              16.00053.0   1.031  1.053      1.075          1.097              1.119                  2.119                      16.000                          16.000                              16.00053.5   1.022  1.044      1.067          1.089              1.112                  2.112                      16.000                          16.000                              16.00054.0   1.013  1.036      1.059          1.082              1.104                  2.104                      16.000                          16.000                              16.00054.5   1.005  1.028      1.051          1.074              1.097                  2.097                      16.000                          16.000                              16.00055.0   0.996  1.019      1.043          1.066              1.090                  2.090                      16.000                          16.000                              16.00055.5   0.987  1.011      1.035          1.058              1.082                  2.082                      16.000                          16.000                              16.00056.0   0.978  1.003      1.027          1.051              1.075                  2.075                      16.000                          16.000                              16.00056.5   0.970  0.994      1.019          1.043              1.068                  2.068                      16.000                          16.000                              16.00057.0   0.961  0.986      1.011          1.035              1.060                  2.060                      16.000                          16.000                              16.00057.5   0.952  0.978      1.003          1.028              1.053                  2.053                      16.000                          16.000                              16.00058.0   0.944  0.969      0.995          1.020              1.045                  2.045                      16.000                          16.000                              16.00058.5   0.935  0.961      0.987          1.012              1.038                  2.038                      16.000                          16.000                              16.00059.0   0.926  0.952      0.978          1.005              1.031                  2.031                      16.000                          16.000                              16.00059.5   0.918  0.944      0.970          0.997              1.023                  2.023                      16.000                          16.000                              16.00060.0   0.909  0.936      0.962          0.989              1.016                  2.016                      16.000                          16.000                              16.00060.5   0.900  0.927      0.954          0.981              1.008                  2.008                      16.000                          16.000                              16.00061.0   0.892  0.919      0.946          0.974              1.001                  2.001                      16.000                          16.000                              16.00061.5   0.883  0.911      0.938          0.966              0.994                  1.994                      16.000                          16.000                              16.00062.0   0.874  0.902      0.930          0.958              0.986                  1.986                      16.000                          16.000                              16.00062.5   0.866  0.894      0.922          0.951              0.979                  1.979                      16.000                          16.000                              16.00063.0   0.857  0.886      0.914          0.943              0.972                  1.972                      16.000                          16.000                              16.00063.5   0.848  0.877      0.906          0.935              0.964                  1.964                      16.000                          16.000                              16.00064.0   0.839  0.869      0.898          0.927              0.957                  1.957                      16.000                          16.000                              16.00064.5   0.831  0.860      0.890          0.920              0.949                  1.949                      16.000                          16.000                              16.00065.0   0.822  0.852      0.882          0.912              0.942                  1.942                      16.000                          16.000                              16.00065.5   0.813  0.844      0.874          0.904              0.935                  1.935                      16.000                          16.000                              16.00066.0   0.805  0.835      0.866          0.897              0.927                  1.927                      16.000                          16.000                              16.00066.5   0.796  0.827      0.858          0.889              0.920                  1.920                      16.000                          16.000                              16.00067.0   0.787  0.819      0.850          0.881              0.912                  1.912                      16.000                          16.000                              16.00067.5   0.779  0.810      0.842          0.873              0.905                  1.905                      16.000                          16.000                              16.00068.0   0.770  0.802      0.834          0.866              0.898                  1.898                      16.000                          16.000                              16.00068.5   0.761  0.794      0.826          0.858              0.890                  1.890                      16.000                          16.000                              16.00069.0   0.753  0.785      0.818          0.850              0.883                  1.883                      16.000                          16.000                              16.00069.5   0.744  0.777      0.810          0.843              0.876                  1.876                      16.000                          16.000                              16.00070.0   0.735  0.768      0.802          0.835              0.868                  1.868                      16.000                          16.000                              16.00070.5   0.726  0.760      0.794          0.827              0.861                  1.861                      16.000                          16.000                              16.00071.0   0.718  0.752      0.786          0.819              0.853                  1.853                      16.000                          16.000                              16.00071.5   0.709  0.743      0.778          0.812              0.846                  1.846                      16.000                          16.000                              16.00072.0   0.700  0.735      0.770          0.804              0.839                  1.839                      16.000                          16.000                              16.00072.5   0.692  0.727      0.761          0.796              0.831                  1.831                      16.000                          16.000                              16.00073.0   0.683  0.718      0.753          0.789              0.824                  1.824                      16.000                          16.000                              16.00073.5   0.674  0.710      0.745          0.781              0.816                  1.816                      16.000                          16.000                              16.00074.0   0.666  0.702      0.737          0.773              0.809                  1.809                      16.000                          16.000                              16.00074.5   0.657  0.693      0.729          0.766              0.802                  1.802                      16.000                          16.000                              16.00075.0   0.648  0.685      0.721          0.758              0.794                  1.794                      16.000                          16.000                              16.00075.5   0.640  0.676      0.713          0.750              0.787                  1.787                      16.000                          16.000                              16.00076.0   0.631  0.668      0.705          0.742              0.780                  1.780                      16.000                          16.000                              16.00076.5   0.622  0.660      0.697          0.735              0.772                  1.772                      16.000                          16.000                              16.00077.0   0.614  0.651      0.689          0.727              0.765                  1.765                      16.000                          16.000                              16.00077.5   0.605  0.643      0.681          0.719              0.757                  1.757                      16.000                          16.000                              16.00078.0   0.596  0.635      0.673          0.712              0.750                  1.750                      16.000                          16.000                              16.00078.5   0.609  0.648      0.687          0.726              0.764                  1.750                      16.000                          16.000                              16.00079.0   0.622  0.661      0.700          0.739              0.779                  1.766                      16.000                          16.000                              16.00079.5   0.635  0.675      0.714          0.753              0.793                  1.781                      16.000                          16.000                              16.00080.0   0.649  0.688      0.728          0.767              0.807                  1.797                      16.000                          16.000                              16.00080.5   0.662  0.702      0.741          0.781              0.821                  1.813                      16.000                          16.000                              16.00081.0   0.675  0.715      0.755          0.795              0.836                  1.828                      16.000                          16.000                              16.00081.5   0.688  0.728      0.769          0.809              0.850                  1.844                      16.000                          16.000                              16.00082.0   0.701  0.742      0.783          0.823              0.864                  1.860                      16.000                          16.000                              16.00082.5   0.714  0.755      0.796          0.837              0.878                  1.875                      16.000                          16.000                              16.00083.0   0.727  0.768      0.810          0.851              0.893                  1.891                      16.000                          16.000                              16.00083.5   0.740  0.782      0.824          0.865              0.907                  1.907                      16.000                          16.000                              16.00084.0   1.740  1.782      1.823          1.865              1.907                  1.907                      16.000                          16.000                              16.00084.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00085.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00086.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00087.5   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.00088.0   16.000  16.000      16.000          16.000              16.000                  16.000                      16.000                          16.000                              16.000__________________________________________________________________________   18.0__________________________________________________________________________0.0   16.0000.5   16.0001.0   16.0001.5   16.0002.0   16.0002.5   16.0003.0   16.0003.5   16.0004.0   16.0004.5   16.0005.0   16.0005.5   16.0006.0   16.0006.5   16.0007.0   16.0007.5   16.0008.0   16.0008.5   16.0009.0   16.0009.5   16.00010.0   16.00010.5   16.00011.0   16.00011.5   16.00012.0   16.00012.5   16.00013.0   16.00013.5   16.00014.0   16.00014.5   16.00015.0   16.00015.5   16.00016.0   16.00016.5   16.00017.0   16.00017.5   16.00018.0   16.00018.5   16.00019.0   16.00019.5   16.00020.0   16.00020.5   16.00021.0   16.00021.5   16.00022.0   16.00022.5   16.00023.0   16.00023.5   16.00024.0   16.00024.5   16.00025.0   16.00025.5   16.00026.0   16.00026.5   16.00027.0   16.00027.5   16.00028.0   16.00028.5   16.00029.0   16.00029.5   16.00030.0   16.00030.5   16.00031.0   16.00031.5   16.00032.0   16.00032.5   16.00033.0   16.00033.5   16.00034.0   16.00034.5   16.00035.0   16.00035.5   16.00036.0   16.00036.5   16.00037.0   16.00037.5   16.00038.0   16.00038.5   16.00039.0   16.00039.5   16.00040.0   16.00040.5   16.00041.0   16.00041.5   16.00042.0   16.00042.5   16.00043.0   16.00043.5   16.00044.0   16.00044.5   16.00045.0   16.00045.5   16.00046.0   16.00046.5   16.00047.0   16.00047.5   16.00048.0   16.00048.5   16.00049.0   16.00049.5   16.00050.0   16.00050.5   16.00051.0   16.00051.5   16.00052.0   16.00052.5   16.00053.0   16.00053.5   16.00054.0   16.00054.5   16.00055.0   16.00055.5   16.00056.0   16.00056.5   16.00057.0   16.00057.5   16.00058.0   16.00058.5   16.00059.0   16.00059.5   16.00060.0   16.00060.5   16.00061.0   16.00061.5   16.00062.0   16.00062.5   16.00063.0   16.00063.5   16.00064.0   16.00064.5   16.00065.0   16.00065.5   16.00066.0   16.00066.5   16.00067.0   16.00067.5   16.00068.0   16.00068.5   16.00069.0   16.00069.5   16.00070.0   16.00070.5   16.00071.0   16.00071.5   16.00072.0   16.00072.5   16.00073.0   16.00073.5   16.00074.0   16.00074.5   16.00075.0   16.00075.5   16.00076.0   16.00076.5   16.00077.0   16.00077.5   16.00078.0   16.00078.5   16.00079.0   16.00079.5   16.00080.0   16.00080.5   16.00081.0   16.00081.5   16.00082.0   16.00082.5   16.00083.0   16.00083.5   16.00084.0   16.00084.5   16.00085.0   16.00085.5   16.00086.0   16.00086.5   16.00087.0   16.00087.5   16.00088.0   16.000__________________________________________________________________________ 
    
     FIG. 7 is a graphical representation of the cross-section described at 7.5 inches from the head of the tub. This section shows the lower edge of the head bowl 12 and the shelf 11. FIGS. 8-11 are graphical representations of the neck support 15 taken at the positions indicated. 
     FIGS. 3 and 14 show that the neck support 15 slopes from the peak of the support down toward the foot of the tub 1. This slope provides proper back support and is designed to keep the vertebrae in proper alignment while reclining in the tub 1. This system allows a user to fully stretch out and relax the back and legs while ensuring that the user is protected from slipping under the water and drowning. Moreover, as discussed above the combination of the head support 10 and neck support 15 works to maintain a comfortable position that does not cause neck stiffness. This is the key advantage of this design over the prior art discussed above. All of those designs had some type of head support. However, none of them have a head support 10 and neck support 15 that cradles the head and neck in the proper position to eliminate stiffness in the neck over time. 
     As discussed above, it is necessary to have a head support to keep a bather&#39;s face out of the water. It is also necessary to maintain the anatomically correct relationships in the natural curves of the spine. We know that pushing the head forward flattens the cervical curve of the neck, distorts the thoracic and lumbar curves and stresses the sacrum. Cervical supports without corresponding accommodation for the head&#39;s posterior mass can intensify, rather than flatten, the four natural curves of the spine. That is just as detrimental as flattening the curves. The instant design balances the relationship between the curve of the neck and the opposing cure of the head. Without the appropriate scoop for the head, the head is thrust forward, which creates misalignments throughout the skeleton and the soft tissues of the head, neck and torso all the way down to the sacrum and coccyx. Thrusting the head forward flattens the natural curve of the neck and presses it uncomfortably against the shelf. Thus, the sculpted neck support 15 is added. The neck support 15 is designed to work in conjunction with the head bowl 12 so that the neck is supported and the posterior shape of the head is also properly supported and positioned to create the ideal alignment for maximum comfort. 
     By using a head support 10 and neck support 15 that maintain proper alignment of the spine, and using the buoyancy of the water, the torso can almost float freely. Freed of it normal compression, the spine lengthens and the torso widens, producing a natural state of relaxation and comfort. 
     Referring now to FIGS. 4-6, the head support 10 and neck support 15 as described above, need not be restricted to full size tubs of 84 inch length. They can be also installed in a standard length 60 inch tub. See FIG. 4. Here, an optional knee support 20 can be installed to provide additional comfort because the shorter length does not allow the bather to fully recline in the tub. FIG. 5 shows the shorter length tub with jetting 5 and the knee support 20. 
     Finally, custom tubs that use the head support 10 and neck support 15 combination in other configurations can be manufactured. FIG. 6 shows a double wide tub 40 that has a parallel set of head and neck supports 15. Construction of the head 10 and neck supports 15 for this tub 40 uses the same techniques and basic forms as for the single tubs 1 and 30. The only material difference is the width of the tub 40. The pair of head and neck supports are shown adjacent in the drawings. However, the supports can be reversed so that one support is at the head of the tub 40 on one side and at the foot of the tub 40 on the other. 
     The present disclosure should not be construed in any limited sense other than that limited by the scope of the claims having regard to the teachings herein and the prior art being apparent with the preferred form of the invention disclosed herein and which reveals details of structure of a preferred form necessary for a better understanding of the invention and may be subject to change by skilled persons within the scope of the invention without departing from the concept thereof.