Before Han times it was believed that the pole star was in the center of the sky, so it was called Jixing (Summit star). Zu Geng(-zhi) found out with the help of the sighting tube that the point in the sky which really does not move was a little more than 1 degree away from the summit star. In the Xining reign-period (1068–1077) I accepted the order of the emperor to take charge of the Bureau of the Calendar. I then tried to find the true pole by means of the tube. On the very first night I noticed that the star which could be seen through the tube moved after a while outside the field of view. I realized, therefore, that the tube was too small, so I increased the size of the tube by stages. After three months' trials I adjusted it so that the star would go round and round within the field of view without disappearing. In this way I found that the pole star was distant from the true pole somewhat more than 3 degrees. We used to make the diagrams of the field, plotting the positions of the star from the time when it entered the field of view, observing after nightfall, at midnight, and early in the morning before dawn. Two hundred of such diagrams showed that the 'pole star' was really a circumpolar star. And this I stated in my detailed report to the emperor.