@staticmethod
def p3_hs(h, s):
    """function p3_hs = p3_hs(h, s)

        Supplementary Release on Backward Equations () , p h s for Region 3, Equations as a function of h and s for the Region Boundaries, and an Equation sat , T hs for Region 4 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam 2004

        Section 3 Backward functions p(h, s), T(h, s), and v(h, s) for Region 3
        """
    if s < 4.41202148223476:
        Ii = [0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8,
            10, 10, 14, 18, 20, 22, 22, 24, 28, 28, 32, 32]
        Ji = [0, 1, 5, 0, 3, 4, 8, 14, 6, 16, 0, 2, 3, 0, 1, 4, 5, 28, 28, 
            24, 1, 32, 36, 22, 28, 36, 16, 28, 36, 16, 36, 10, 28]
        ni = [7.70889828326934, -26.0835009128688, 267.416218930389, 
            17.2221089496844, -293.54233214597, 614.135601882478, -
            61056.2757725674, -65127225.1118219, 73591.9313521937, -
            11664650591.4191, 35.5267086434461, -596.144543825955, -
            475.842430145708, 69.6781965359503, 335.674250377312, 
            25052.6809130882, 146997.380630766, 5.38069315091534e+19, 
            1.43619827291346e+21, 3.64985866165994e+19, -2547.41561156775, 
            2.40120197096563e+27, -3.93847464679496e+29, 
            1.47073407024852e+24, -4.26391250432059e+31, 
            1.94509340621077e+38, 6.66212132114896e+23, 
            7.06777016552858e+33, 1.75563621975576e+41, 
            1.08408607429124e+28, 7.30872705175151e+43, 1.5914584739887e+24,
            3.77121605943324e+40]
        Sigma = s / 4.4
        eta = h / 2300
        Pi = 0
        for i in range(0, 33):
            Pi = Pi + ni[i] * (eta - 1.01) ** Ii[i] * (Sigma - 0.75) ** Ji[i]
        p3_hs = Pi * 99
    else:
        Ii = [-12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -8, -6, -6, 
            -6, -6, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -1, 0, 2, 2, 5,
            6, 8, 10, 14, 14]
        Ji = [2, 10, 12, 14, 20, 2, 10, 14, 18, 2, 8, 2, 6, 7, 8, 10, 4, 5,
            8, 1, 3, 5, 6, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 3, 7]
        ni = [1.25244360717979e-13, -0.0126599322553713, 5.06878030140626, 
            31.7847171154202, -391041.161399932, -9.75733406392044e-11, -
            18.6312419488279, 510.973543414101, 373847.005822362, 
            2.99804024666572e-08, 20.0544393820342, -4.98030487662829e-06, 
            -10.230180636003, 55.2819126990325, -206.211367510878, -
            7940.12232324823, 7.82248472028153, -58.6544326902468, 
            3550.73647696481, -0.000115303107290162, -1.75092403171802, 
            257.98168774816, -727.048374179467, 0.000121644822609198, 
            0.0393137871762692, 0.00704181005909296, -82.910820069811, -
            0.26517881813125, 13.7531682453991, -52.2394090753046, 
            2405.56298941048, -22736.1631268929, 89074.6343932567, -
            23923456.5822486, 5687958081.29714]
        Sigma = s / 5.3
        eta = h / 2800
        Pi = 0
        for i in range(0, 35):
            Pi = Pi + ni[i] * (eta - 0.681) ** Ii[i] * (Sigma - 0.792) ** Ji[i]
        p3_hs = 16.6 / Pi
    return p3_hs
