The scattering function was determined for four samples of atactic oligo- and poly(alpha -methylstyrene)s (a-P alpha MS), each with the fraction of racemic diads f(r) = 0.72, in the range of weight-average molecular weight M-w from 1.27 x 10(3) to 6.46 x 10(4) in cyclohexane at 30.5 degreesC (O) in the range of the magnitude k of the scattering vector smaller than 1 li-l by the use of a point-focusing small-angle X-ray scattering (SAXS) camera. The Kratky function F-s as a function of k increases monotonically with increasing k for M-w less than or similar to 0.5 x 10(3) and exhibits a plateau in the range of 0.15 Angstrom (-1) less than or similar to k less than or similar to 0.3 A(-1) for M-w greater than or similar to 5 x 10(3). For k less than or similar to 0.5 Angstrom (-1), all the experimental data may be well explained by the corresponding helical wormlike (HW) chain theory. For k greater than or similar to 0.5 Angstrom (-1), however, agreement between theory and experiment is only qualitative. A comparison is made of the present SAXS data for a-P alpha MS with the previous data for atactic polystyrene with f(r) = 0.59, atactic poly(methyl methacrylate) (a-PMMA) with f(r) = 0.79, isotactic PMMA with f(r) - 0.01, and syndiotactic (s-) PMMA with f(r) = 0.92. It is then found that the HW theory may give a good explanation of the difference in the behavior of F-s for k less than or similar to 0.3 A(-1) between the four polymers except s-PMMA, for which the. HW model parameters have not been determined.