public class Potential 
{
        double rr;             //The ring width    
        double rx;
        double ry;
        double Pota;
        double E, K, m, num, den, den1,t1,t2,t3,t4;

public Potential(double pot_A, double ring_radius, double ring_x, double ring_y)
        {
        Pota = pot_A;
        rr = ring_radius;
        rx = ring_x;
        ry = ring_y;

//compute argument "m"  to elliptic integrals E and K
       num = 4. * rr * java.lang.Math.abs(rx);
       den = rr * rr + rx * rx + ry * ry + 2.*rr*java.lang.Math.abs(rx);
       m = num/den;

//  Elliptic integrals
  E = 1.+0.46302*(1.-m)+0.10778*((1.-m) * (1.-m))+  java.lang.Math.log(1./(1.-m))*(0.24527*(1.-m)+0.04125*((1.-m) * (1.-m)));
  K = 1.3863+0.11197*(1.-m)+0.07253*((1.-m) * (1.-m))+ java.lang.Math.log(1./(1.-m))*(0.5+0.12135*(1.-m)+0.02887*((1.-m) * (1.-m)));

// Potential

//  note this scale for Pota apparently missing a factor of "a", the radius of the ring,
//   but this is deliberate to make the resultant quantity dimensionless

//   Pota = (rx/(Math.PI * Math.sqrt(den)))*(((2.-m)*K-2.*E)/m) ;
//  This is the potential given in equations 4.2 and 6.1 of Force Memo #4 and #6 sans current and mhu naught
     Pota = (rr/(Math.PI * Math.sqrt(den)))*(((2.-m)*K-2.*E)/m) ;

//System.out.println("rr " + rr + " rx " + rx + " ry " + ry + " pota " + Pota);
    }
}