Academician of the Soviet Union Langdsberg (Jlaimcoepr) introduced a dielectric constant ellipsoid in this book "Optics". He condsidered that the total values of the dieleotric oonstants in crystals can be represented by a dielectric constant ellipsoid. The three semi-axes of this ellipsoid are respectively of lengths &1} ea, e3, i. e. the principle oomponents of the dieleotric constant tensor, and the length of any radius veotor of this ellipsoid is equal to the dielectric constant in that direction. In other words, Langd-sberg's dielectric constant ellipsoid corresponds to the dielectric constant tensor. It is pointed out in this paper that the dieleotric constant tensor corresponds to Fresnel's ellipsoid rather than Langdsberg <3 dielectric constant ellipsoid. This correspondence relation is unique. Dielectric constant tensor is a symmetrical second rank tensor, its six independent components are just equal to the six coefficients of Fresnel's ellipsoid equation respectively. Mathmatical derivation indicates that the length of any radius vector of Langdsberg's ellipsoid in not equal to the dielectric constant in that direction. Conversely, the surface whose length of radius vector in a given direotion is equal to the dielectric constant in that direction, is an ovaloid of six degrees. Besides, in this paper, confusing terms, such as dielectric constant ellipsoid, dielectric ellipsoid Fresnel's ellipsoid and index ellipsoid, and their respective corresponding tensors are clearly defined.