“Not only at Peking, but in this capital also (Nanking) there is a College of Chinese Mathematicians, and this one certainly is more distinguished by the vastness of its buildings than by the skill of its professors.  They have little talent and less learning, and do nothing beyond the preparation of the almanacs on the rules of calculation made by the ancients; and when it chances that events do not agree with their calculation they assert that what they had calculated was the regular course of things, but that the aberrant conduct of the stars was a prognostic from heaven of something going to happen on the earth.  This something they make out according to their fancy, and so spread a veil over their own blunders.  These gentlemen did not much trust Father Matteo, fearing, no doubt, lest he should put them to shame; but when at last they were freed from this apprehension they came and amicably visited the Father in hope of learning something from him.  And when he went to return their visit he saw something that really was new and beyond his expectation.

“There is a high hill at one side of the city, but still within the walls.  On the top of the hill there is an ample terrace, capitally adapted for astronomical observation, and surrounded by magnificent buildings which form the residence of the Professors....  On this terrace are to be seen astronomical instruments of cast-metal, well worthy of inspection whether for size or for beauty; and we certainly have never seen or read of anything in Europe like them.  For nearly 250 years they have stood thus exposed to the rain, the snow, and all other atmospheric inclemencies, and yet they have lost absolutely nothing of their original lustre.  And lest I should be accused of raising expectations which I do not justify, I will do my best in a digression, probably not unwelcome, to bring them before the eyes of my readers.

“The larger of these instruments were four in number.  First we inspected a great globe [A], graduated with meridians and parallels; we estimated that three men would hardly be able to embrace its girth....  A second instrument was a great sphere [B], not less in diameter than that measure of the outstretched arms which is commonly called a geometric pace.  It had a horizon and poles; instead of circles it was provided with certain double hoops (armillae), the void space between the pair serving the purpose of the circles of our spheres.  All these were divided into 365 degrees and some odd minutes.  There was no globe to represent the earth in the centre, but there was a certain tube, bored like a gun-barrel, which could readily be turned about and fixed to any azimuth or any altitude so as to observe any particular star through the tube, just as we do with our vane-sights;[8]—­not at all a despicable device!  The third machine was a gnomon [C], the height of which was twice the diameter of the former instrument, erected on a very large and long slab of marble, on the northern side of the