An equation is derived which correlates the unperturbed dimensions $_o$ of polypeptides in the helix-coil transition region with the helical content by using a simple model of a polypeptide chain which is a chain connected by repeating units, although the unit is composed of -CO-NH-CHR-, but it behaves as if it were a ball. This is based on the fact that the repeating unit has a plane structure. The changing trend of the expansion factor $\alpha$ in the transition region is connected with the helical content $f_H$. The mean-square end-to-end distances $$ and the intrinsic viscosities $[\eta]$ ofpolypeptides are calculated from the unperturbed dimensions and the $\alpha$ factors. The above caluclated results concerning $_o$ and $[\eta]$ are compared with others`` theoretical and experimental results. From the comparision, we concluded that our theory explains better the chain dimensional behavior of polypeptides in the helixcoil transition region than others, and agrees well with the experimental results.