economic politics, between individual interest and public interest

According with A. Smith “by pursuing his own interest individual frequently promotes that of society more effectually than when he really intends to promote it.” But what is the passing way from individual interest to public interest? If there is such a way then there is a strong base for economic policy. We intent to analyse the modality of passing from individual interest to group interest and forward to public interest. But, what is the nature of public interest?