This survey is the second part of the history of science of Song and Yuan dynasties and will covers the period from Jin to Yuan. Following the first part, we look at the calendrical astronomy, mathematics and medicine. In this survey we again follow Yabuuchi's work on the history of science of Song and Yuan period and Du Shiran's work on the history of science of China. We start from the sciences and mathematics of Jin which inherited those of Northern Song and see how they influenced the whole China including Yuan and Southern Song. As a conclusion the tendency to practical usages in the Southern Song as well as the suppression of Han people in Yuan prevented developments of theoretical sciences in Yuan and Ming later.