The results of an ab initio investigation of the Jones birefringence (JB) of noble gases (He, Ne, Ar, Kr) and of a few linear molecules-both centrosymmetric (H-2,N-2,C2H2) and dipolar (CO)-carried out employing coupled cluster response techniques and rather extended correlation-consistent basis sets are presented. The relationships existing between the appropriate linear, quadratic, and cubic frequency-dependent response functions and the tensors introduced in the theoretical derivation of the anisotropy by Graham and Raab in 1983 [Proc. R. Soc. London, Ser. A, 390, 73 (1983)] are introduced. The magnitude of the effect is determined and comparison is made with that of the Cotton-Mouton effect (CME), which, together with the Kerr effect, is closely related to Jones birefringence and superimposed to it in actual measurements, and of electric field gradient induced birefringence (EFGB). CME yields anisotropies of the refractive index approximate to100 to approximate to3500 larger than those predicted for JB in the eight systems studied, whereas EFGB and JB are shown to be of comparable strength. (C) 2003 American Institute of Physics.