Yes, a company can make public issue of equity shares if partly paid shares are not fully paid as equity shares are that part of share capital of company which is not been included in the preference shares. The condition which has to be considered for this is that at any time after 2 years of expiray from the date of starting of company or after 1 year of shares allotment, public company shares the issues within the authorised area, and directors must decide to offer shares to existing holder of equity shares in proportion to capital which has been paid up on the holder's shares at the time of further issue.