g(x)=10.6*((x-25)/-25)*((x-50)/-50)*((x-75)/-75)*((x-100)/-100)*((x-125)/-125)*((x-150)/-150)*((x-175)/-175)*((x-200)/-200)\
 + 16*((x)/25)*((x-50)/(25-50))*((x-75)/(25-75))*((x-100)/(25-100))*((x-125)/(25-125))*((x-150)/(25-150))*((x-175)/(25-175))*((x-200)/(25-200))\
 + 45*(x/50)*((x-25)/(50-25))*((x-75)/(50-75))*((x-100)/(50-100))*((x-125)/(50-125))*((x-150)/(50-150))*((x-175)/(50-175))*((x-200)/(50-200))\
 + 83.5*(x/75)*((x-25)/(75-25))*((x-50)/(75-50))*((x-100)/(75-100))*((x-125)/(75-125))*((x-150)/(75-150))*((x-175)/(75-175))*((x-200)/(75-200))\
 + 52.8*(x/100)*((x-25)/(100-25))*((x-50)/(100-50))*((x-75)/(100-75))*((x-125)/(100-125))*((x-150)/(100-150))*((x-175)/(100-175))*((x-200)/(100-200))\
 + 19.9*(x/125)*((x-25)/(125-25))*((x-50)/(125-50))*((x-75)/(125-75))*((x-100)/(125-100))*((x-150)/(125-150))*((x-175)/(125-175))*((x-200)/(125-200))\
 + 10.8*(x/150)*((x-25)/(150-25))*((x-50)/(150-50))*((x-75)/(150-75))*((x-100)/(150-100))*((x-125)/(150-125))*((x-175)/(150-175))*((x-200)/(150-200))\
 + 8.25*(x/175)*((x-25)/(175-25))*((x-50)/(175-50))*((x-75)/(175-75))*((x-100)/(175-100))*((x-125)/(175-125))*((x-150)/(175-150))*((x-200)/(175-200))\
 + 4.7*(x/200)*((x-25)/(200-25))*((x-50)/(200-50))*((x-75)/(200-75))*((x-100)/(200-100))*((x-125)/(200-125))*((x-150)/(200-150))*((x-175)/(200-175))

set xlabel "E (MeV)"
set ylabel "Cross Section (mb)"
set title "Numerical Interpolation of Experimental results for a Briet-Wigner Neutron scattering problem"
plot [x=0:200] [0:120] 63890/((x - 78)*(x-78) + 55*55/4) title "Breit-Wigner Function", "interdata.txt" using 1:2 title "Experimental Results", g(x) title "Langrange Interpolation",  "nevillesdata.txt" every :::0::0 using 1:2 title "Neville's 8th degree polynomial", "nevillesdata.txt" every :::1::1 using 1:2 title "Nevilles Interpolation using ploynomials of degree three"