An experimental determination of the universal constant R// xi ** plus (for the class of fluids n equals 1, d equals 3) concerning the amplitude of the diverging part of the specific heat is reported. For the first time a good accuracy is obtained, which allows the experimental values in 3 binary fluids (R// xi ** plus equals 0. 29 plus or minus 0. 04; 0. 280 plus or minus 0. 011; 0. 255 plus or minus 0. 013) to be favorably compared to the renormalization group result (0. 269 6 plus or minus 0. 000 8) and the high temperature series expansion value (0. 253 plus or minus 0. 001), the renormalization group result giving a better agreement with the experimental results.