Introduction . . 5
China in World Astronomy . . 7
Contents of this Book . . 9
Principles of the Translation . . 11
Conventions . . 14

1 Astronomical Reform and Occupation Politics . . 19
Cultural . . 21
Political . . 23
Bureaucratic . . 26
Personal . . 28
Technical . . 30
Conclusions . . 33

2 Orientation . . 35
The Social Organization of Astronomy . . 35
Astronomical Reforms . . 38
The Politics of Astronomical Reform . . 56
Observatories . . 60
Mathematical Tools . . 61
Metrology . . 67
Celestial Motions . . 97
Eclipses . . 106
Stars . . 113
Precision and Accuracy . . 115
The Enigma of Delta-T . . 116
Comparisons with Europe and Islam . . 119
Conclusion . . 131

3 The Project: Origins and Process . . 133
Origins . . 133
The Process . . 146

4 The Astronomers . . 151
Liu Ping-chung . . 153
Wang Hsun . . 156
Kuo Shou-ching . . 158
Chang I . . 160
Hsu Heng . . 161
Chang Wen-ch'ien . . 163
Yang Kung-i . . 164
Ch'en Ting . . 168
Specialists . . 169
Conclusion . . 169

5 The Observatory and its Instruments . . 171
The Observatory . . 171
Predecessors of the Yuan Project . . 176
The Instruments of the Reform Project . . 179
Ming Instruments . . 211
Influence on the System from the West . . 218
Conclusion . . 225

6 The Records . . 227
The Standard Histories and their Treatises . . 227
Astronomical Treatises . . 230
Transmission and Publication . . 234
Studies . .238
Conclusion . . 246

7 Evaluation of the Season-Granting System . . 249
Introduction by the Compilers of the Yuan History . . 249

Evaluation of the Season-Granting System, Part 1 . . 254
1. Determination of Ch'i from Observation . . 254
2. Year Surplus and Annual Difference . . 271
3. Angular Extensions of the Lunar Lodges along the Celestial Perimeter . . 291
4. Tread of the Sun . . 296
5. Expansion and Contraction of the Solar Motion . . 297
6. Slackening and Hastening of the Lunar Motion . . 300
7. Crossing Cycle of the White Way . . 304
8. Day and Night Marks . . 309

8 Evaluation of the Season-Granting System, Part 2 . . 311 
9. Eclipses . . 311
10. Corrected Conjunctions . . 367
11. Disuse of Accumulated Years and Day Divisor . . 370 

9 Canon of the Season-Granting System, Part 1 . . 389 
1. Pacing the Ch'i and Lunations . . 389
2. Pacing the Putting Forth and Gathering In . . 399
3. Pacing the Tread of the Sun . . 408
4. Pacing the Travel of the Moon . . 452

10 Canon of the Season-Granting System, Part 2 . . 487
5. Pacing the Centered Star . . 487
6. Pacing Crossing Coincidences . . 497
7. Pacing the Five Stars . . 516

11 Conclusion . . 551
The Problem of Evaluation . . 551
Accuracy of the Season-granting system . . 557
A Final Word . . 559

Appendix A The Instruments of Kuo Shou-ching . . 561
The Simplified Instrument . . 561
The Celestial Globe . . 566
The Upward-facing Instrument . . 567
The Lamp Water Clock for the Palace of Supernal Brightness . . 567 
The Direction-determining Table . . 567
The Template and Gnomon . . 569
The Shadow Aligner . . 570
The Observing Table . . 571

Appendix B The Account of Conduct of Kuo Shou-ching . . 573 
Biography . . 573
Water Control . . 574
New Astronomical Instruments. . . 574
The Polar Altitude Survey . . 577
Predecessors of the Reform . . 579
Topics of Research . . 582
New Methods . . 586
Documents of the Reform . . 588
Water Control, Continued . . 590
Biography, Continued . . 590
Character . . 591
Kuo's Uniqueness . . 594

Appendix C Technical Terms . . 597
Named Results, English . . 597
Constants, English . . 604
Named Results, Chinese . . 606
Constants, Chinese . . 613

Acknowledgements . . 616

Bibliography . . 617
East Asian Sources before 1900 . . 617
Secondary Sources . . 623

Index-Glossary . . 651