In this paper we study the volume and surface symmetry energy coefficients (c (V ) sym and c (S) sym ) by using the double differences of "experimental" symmetry energies. We assume a sym = c (V ) sym − c (S) sym /A 1/3 and obtain c (V ) sym = 31.26 ± 0.32 MeV and c (S) sym = 52.15 ± 1.12 MeV, or c (V ) sym = 32.10 ± 0.31 MeV and c (S) sym = 58.91 ± 1.08 MeV, depending on the form of the Wigner energy. The uncertainties of these coefficients are smaller than those in the literature. The values of c (V ) sym and κ S/V are unstable for different mass regions if one assumes a sym = c (V ) sym /(1 + κ S/V /A 1/3 ). We notice an odd-even staggering in the double differences of "experimental" symmetry energies under a few situations, and suggest that the pairing interaction might not be properly taken into account in the current mass formulas.The symmetry energy in nuclei is one of the focuses in both astrophysics and nuclear physics because of its very important role in the structure of neutron stars as well as in the dynamical process of nuclear reactions [1][2][3][4][5][6][7][8][9][10][11]. In recent years there have been many parametrizations in different models [11][12][13][14][15][16][17][18][19][20][21][22][23] for the volume coefficient c (V ) sym and the surface coefficient c (S) sym (or the surface-to-volume ratio κ S/V ≡ c (S) sym /c (V ) sym ) in the symmetry energy term.In the literature, two different definitions are used for c (V ) sym and κ S/V . The first is a sym = c (V ) sym (1 − κ S/V /A 1/3 ) (a sym to be defined later). By this definition, c (V ) sym = 30.3-31.8 MeV and κ S/V = 1.43-1.61 in the local-density approximation with different parametrizations [12,14]; c (V ) sym = 30.76 MeV and κ S/V = 1.62 in a mass formula based on the finite-range liquid-drop model [18]; c (V ) sym = 33.0 MeV and κ S/V = 1.98 in a hydrodynamic model [19], and so on. In this paper our results are presented by assuming this definition. Another definition is a sym = c (V ) sym /(1 + κ S/V /A 1/3 ). By this definition, c (V ) sym = 31.1 ± 1.7 MeV and κ S/V = 2.31 ± 0.38 by investigating "experimental" symmetry energies of isobaric nuclei [11]; c (V ) sym = 27-31 MeV and κ S/V = 2.0-2.8 in a modified mass formula [17]; and so on. One sees that the values of c (V ) sym are close to each other while those of κ S/V are quite different for these two definitions. A brief review of recent studies of the surface symmetry energy can

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