Electro-optical Kerr effect data have been obtained for 6CB, 6CHBT, 6PCH and 6BOBT at temperatures above the nematic-isotropic transition temperature. All the compounds had a positive Kerr constant which increased with decreasing of temperature. The second order phase transition temperatures, T*, were determined for these compounds. The linear dependence of (T - T*)<sup>-1</sup> on the Kerr constant is found to be relatively in good agreement with the predications of the Landau-De Gennes model. The replacement of aromatic ring by a flexible cyclohexyl group and or by a bulkier bicyclooctane has a marked effect on the birefringence. Hexyl 4-(4-isothiocyanato-phenyl) bicycle [2,2,2] octane, 6BOBT, with the highest transition temperature had the lowest Kerr constant. In contrast, hexyl cyanobiphenyl,6CB, showed the largest Kerr constant (6<i>BOBT</i> → 6<i>CHBT</i> ≈ 6<i>PCH</i> → 6<i>CB</i>). The effect of the rigid core and polar head group of the liquid crystals was investigated.