Asada Gōryū

(b. Kizuki, Bungo Province, Japan, 10 March 1734; d. Osaka, Japan, 25 June 1799)

astronomy.

Asada was instrumental in turning Japanese astronomy and calendrical science away from the traditional Chinese style and toward Western models. His given name was Yasuaki but he is better known by his pen name Gōryū. He was the fourth son of Ayabe Yasumasa a Confucian scholar-administrator of the Kizuki fief government.

Asada taught himself medicine and astronomy. Because Japanese books written on the basis of the Chinese Shou-shih calendrical system (promulgated in 1281) were abundant and popular in his youth, his first steps in the study of astronomy must have been to read some of these works. He may also have had direct access to some Chinese writings of the seventeenth- and early eighteenth-century Jesuit missionaries.

Asada placed great weight upon empirical verification, and every time he came across a new theory, he determined its value by observation. The earliest record of an observation by him is that of a lunar eclipse in 1757.

A year before the current official ephemeris caused a crisis of confidence in the official techniques by miscalculating a solar eclipse in 1763, Asada had already pointed out the systematic error and had shown the results of his calculations to his friends. When the day arrived, the eclipse coincided exactly with his calculations. It is apparent that his capacity as a student of astronomy was far superior to that of the official astronomers of the shogunate. Because the position of official astronomer was hereditary, it often happened that the incumbent lacked the ability required to produce a sound revision of the calendar. Such untalented officials did no more than concentrate on preserving their sinecures. Within this hereditary bureaucracy conservatism naturally prevailed, and the spirit of free inquiry was stifled; innovations were dangerous. But in the eighteenth century astronomical knowledge was diffused by various means to private scholars, who then openly criticized the failure of the official ephemeris. Asada was most prominent among those amateur astronomers.

Asada was financially dependent upon his father until 1767; the freedom from money worries left him free to devote himself to the study of astronomy and medicine. In that year, however, he was appointed a physician of the fief government, and since he was ever on the move accompanying his feudal lord to Edo (Tokyo) or Osaka, he found it impossible to pursue his favorite study. He repeatedly implored his lord to excuse him front service, but in vain. He made up his mind at last to desert his fief and in 1772 went to Osaka, where he resumed the study of astronomy, making his living by practicing medicine. It was during his residence in Osaka that he changed his surname from Ayabe to Asada, because normal relations with his fief could no longer be openly maintained.

Osaka was the right choice for his residence, for the city was the focus of nationwide commercial activities; and the wealthy Osaka merchants, whose financial power often surpassed that of the fief governments, could afford expensive imported books and could support instrument-making and astronomical observation. Such was the case of the wealthy merchant Hazama Shigetomi (1756–1816), one of Asada’s most able pupils.

Asada and his school introduced modern instruments and observational methods into Japan. Traditional fieldwork was limited largely to solstitial observations of gnomon shadows, eclipses, and occultations. It was customary to make regular observations during the few years preceding an anticipated calendar reform; beyond this, only occasional checks were made. Earlier astronomers had done little more than make minor amendments to the Shou-shih calendar.

Long before, the shogun Tokugawa Yoshimune (1684–1751) had intended to carry out observations with new instruments, but even at the time of the Hōryaku calendar reform in 1755, astronomers employed instruments of the traditional Chinese type, such as the gnomon. Japanese observations up to this period had been much inferior to those of Kou Shouching in thirteenth-century China; the data could be used only to check a calendar, not to make significant improvements.

Now the Asada school began to gather more reliable data. Asada himself initiated techniques for precise observation. He ground lenses and made a telescope, which he used to observe the movements of Jupiter’s satellites. Hazama showed the greatest talent of his time for inventing and improving instruments; expending his wealth freely, he also sponsored the training of talented instrument-makers and conducted systematic observations with the assistance of his employees.

Only a few of Asada’s treatises exist. One of them, Jikkenroku (“Records Based on Observations,” 1786), gives the essentials of his calendar; taking the winter solstice of 1781 as the temporal origin and Osaka as the standard station, he gives the fundamental constants and his method for determining the positions of the sun and the moon, and calculating solar and lunar eclipses. He adopted the method described in the first volume of the Chinese Li-hsiang k’ao-ch’eng (“Compendium of Calendrical Science,” 1713)—essentially Tychonian in content—which was his chief means of studying Western astronomy. The constants employed for calculation were mostly new ones that Asada had worked out from his own data.

In the spring of 1793 he made a considerable correction in the constant for the distance between the sun and the earth, and corrected other constants affected by it. That the corrected constant is almost identical with that given in the partly Keplerian sequel to the Li-hsiang k’ao-ch’eng (hou p’ien, compiled in 1737) shows that Asada had access to the sequel about this time, when he came across the theory of the elliptic orbit and became aware of the gross error in the constant for the distance of the sun given in the first volume. It seems, remarkably enough, that Asada retained the old theory concerning the mode of the motions of the sun and the moon while he made radical corrections in the important constants, evidently for the purpose of testing their adaptability. From the time that Asada obtained the sequel to the Li-hsiang k’ao-ch’eng, through the efforts of Hazama, he and his best pupils occupied themselves with studying the theory of the elliptic orbit.

The sequel employs Kepler’s first and second laws without reference to the heliocentric system. Dynamics, as an approach, is absent, and the name of Newton is associated only with observational data, most of which are J. D. Cassini’s. The arrangement of the treatise is to a great extent that dictated by traditional Chinese calendar-making practice. Within this framework it was unnecessary to relate Kepler’s laws to heliocentric coordinates. Lack of interest in planetary motion in traditional calendar-making seems to have made adoption of the third law unnecessary.

Asada’s pupils attributed two major innovations to him—cyclic variation of astronomical parameters and independent discovery of Kepler’s third law.

He mistakenly claimed the discovery of the Antarctic continent by means of lunar eclipse observations. After repeated observations of the shadow of the earth projected on the surface of the moon, Asada came to believe that the parts of the shadow corresponding to the South Pole and the Asian continent are somewhat more upthrust than the other parts of the shadow, and identified part of the shadow outline with the Antarctic continent, which appeared on a world map newly imported from the West.

Asada, after settling down in Osaka, was busily engaged for twenty years in making observations and in educating his pupils. Consequently, his influence increased and led to the formation of an important school of calendrical scientists. For this reason, when the shogunate proposed to revise the current Japanese calendar by use of the new theories of Western astronomy and found that its own official astronomers were not equal to the task, it turned to him. Instead of accepting the appointment himself, Asada recommended his best pupils, Takahashi Yoshitoki (1764–1804) and Hazama. Takahashi, since he belonged to the Samurai class (although he was only a minor official), was appointed an official astronomer; Hazama became a consultant or assistant.

When Asada deserted his fief and hid in Osaka, his feudal lord, to whom his whereabouts was known, was generous enough not to charge him with the crime of desertion, and even permitted him to communicate with his relatives at home, because he was eager for him to succeed in his pursuit of learning. This made it possible for Asada to receive a gift of some money each year from his eldest brother and thus to study astronomy without being destitute. Asada was so grateful to his former master for this that when he became a well-known scholar and was offered a high position by other feudal lords—and even by the shogunate—he always refused, saying that he could not turn his back on his former lord.

In Asada’s later years a limited number of Japanese pioneers, the rangakusha (scholars of Dutch learning), undertook the prodigious and almost completely unaided labor of translating Dutch scientific works into Japanese. In the 1770’s a notable expansion of the study of the Dutch language and of science led to a movement for the translation of Dutch scientific works—or retranslation of Dutch translations of European works. This task was begun by two groups, the official interpreters at Nagasaki, who alone were authorized access to foreign books, and the physicians of Edo.

The interpreters concentrated on introducing the core of genuine Western science—particularly of elementary astronomy, navigation, and geography—but this material did not have much interest for practical astronomers, except when directly applicable to traditional calendar-making. Men like Asada wanted observational data and astronomical constants. For this reason the writings of the Jesuit missionaries in China, although cosmologically obsolete, were much more useful to him. He himself had found no time to learn the Dutch language.

In studying medicine, as in studying astronomy, Asada collected and read the very best literature. He also dissected dogs and cats, and thus became acquainted with internal organs. From Asada’s expounding of Western-style astronomy, some people conclude that his medical art was copied from some Dutch school of medicine. This is entirely wrong. At the time that Asada taught himself there were a few Japanese physicians who taught a type of very elementary Western-style surgery, but there was no proper literature for students. As for the European style of internal treatment, no one in Japan knew about it, and naturally there was nothing written on it. Asada could have had no access to what knowledge was available. Thus, his style of medicine was not Western, but the positivistic and clinical koihō (ancient medical learning) school that flourished during the mideighteenth century in Japan.

In Osaka, Asada practiced medicine, but it was only a means to make his living. All his energy had been devoted to the study of astronomy, but now his research was temporarily completed. When, in addition, Takahashi and Hazama, on whom his mantle had fallen, accomplished the task of revising the official calendar in 1797 and Asada himself was rewarded by the shogunate, he could say, “I have found men who will develop my astronomy. I have henceforth to devote myself to the study of medicine.”

His health failed about the beginning of 1798 and he suffered a stroke, of which he died in the summer of the following year.

In praise of Asada, his distinguished pupil Takahashi stated in his Zōshū shōchō hō (“Variations of Astronomical Parameters,” rev. and enl., 1798):

Laboring over Chinese and Western works, Asada Gōryū at Osaka discovered the shōchō law. Although Western astronomy is most advanced, we have not heard of its mentioning this law, known only in our country. Therefore I have said that although we are unable to boast about our achievements in comparison with those of the Westerners, my country should be proud of this man and his discovery.

This is perhaps the only notable originality to be found in the entire history of Japanese astronomy; it therefore merits critical examination.

In adopting the idea of shōchō (hsiao-ch’ang in Chinese, the secular diminution of tropical-year length), astronomers at the time of the Shou-shih and Jōkvō (promulgated in 1685) calendars were required only to account for the ancient records and modern data of Chinese solstitial observations by a single formula. While it is true that neither the Jesuits nor the Chinese had incorporated the concept of hsiao-ch’ang into their calendars during the Ming and Ch’ing periods, the Jesuit compilation Ch’ung-chen li-shu (“Ch’ung-chen Reign Period Treatise on Calendrical Science,” 1635) pointed out three possible causes of variation in tropical-year length: (1) rotation of the center of the solar orbit in reference to the earth (perhaps referring to the progressive motion of the solar perigee); (2) variation of the eccentricity of the solar orbit; (3) variable precession (trepidation). Numerical values were not given, however, because such a minute parameter was not determinable within a single lifetime.

Classical Western data, such as those listed in the Almagest of Ptolemy, became available to Asada through the Jesuit treatises. He dared endeavor to synthesize Western and Chinese astronomy and to give a numerical explanation, by means of a single principle, of all the observational data available to him—old and new, Eastern and Western.

It seems that Asada did not fully comprehend the epicyclic system, based on that of Tycho Brahe, which appeared in the Jesuit works. In Western astronomy, only observed data and numerical parameters interested him. These he could utilize for his purely traditional approach, that of obtaining an algebraic representation that corresponded as closely as possible to the observed phenomena.

Copernicus appears in the Ch’ung-chen li’shu, not as an advocate of heliocentrism but as an observational astronomer and the inventor of the eighth sphere of trepidation. He is said in that work to have believed that the ancient tropical year was longer than that of the Middle Ages, which in turn was shorter than the contemporary constant. Asada, perhaps struck by this passage, formulated a modified conception in which the length of the ancient tropical year tended to decrease until it reached a minimum in the Middle Ages and to grow longer afterward, varying in a precession cycle of 25,400 years. The minimum was not associated with the solar perigee, but was arbitrarily chosen in order to fit the recorded data. He also presumed that the only perpetual constant was the length of the anomalistic (sidereal) year. Other basic parameters, such as the length of the synodic, nodical, and anomalistic months, were assumed to be subject to variation in a precession cycle. This idea seems to have originated in the Chinese T’ung-t’ien calendar (1199) of the Sung period. In the West, the first systematic study of the variation of basic astronomical parameters was carried out by Laplace on the basis of the perturbation theory. Although superficially similar, Asada’s approach was by no means comparable with Laplace’s well-founded theoretical considerations.

Although the mathematical derivation is quite complicated, the length of the tropical year, T, in Asada’s formula is essentially expressed in terms of the equations

T = 365.250469717756 - 1.038645 × 10^-5t,

where t is years elapsed since the epoch of 720 b.c. (this equation is valid up to a. d. 133), and

T = 365.2416204385 + 0.0435370 × 10^-5t,

where t is years elapsed since the epoch of a.d. 133 (this equation is valid up to a. d. 11981).

These two equations together cover only half of the precession cycle since 720 b.c. In the other half of the cycle, t is expressed in the dotted line of Figure 1. Applying this formula to historical observations, we see in Figure 2 the extent to which it reconciles the data. After a. d. 133, the year of the epoch, the formulas of Simon Newcomb, Asada, and the Shou-shih calendar roughly coincide. Before the epoch, Asada’s formula appears as a parabola of deep curvature, which comprehends the Greek observations as well as the ancient Chinese records. It is apparent

that what Asada really intended to do was account for the newly acquired Western data. His basic goal, that of “saving the ancient records” by numerical manipulation, differs not at all from that of the traditional approach. His consideration of the precession cycle was theoretical decoration.

In spite of resistance from the conservative hereditary official astronomers, Asada’s pupils finally succeeded in applying Asada’s variation term to the Kansei calendar promulgated in 1798. In the same year, Takahashi wrote the Zōshū shōchō hō in order to provide a theoretical foundation for his teacher’s method. Takahashi had attained a mastery of the theory of spherical geometry and epicycles. Furthermore, rejecting the authority of Tycho, he revived the old idea of trepidation as contained in the Ch’ung-chen li-shu, in which trepidation was somewhat vaguely mentioned in order to contrast it with Tycho’s more accurate view. Unlike Alphonsine trepidation, which had a 7,000-year cycle, however, Takahashi’s cycle of trepidation had the same period as the cycle of precession.

The falsity of Asada’s variation concept soon became apparent. In the 1830’s it was realized that observations did not agree with the Kansei calendar; removal of Asada’s variation factors gave better agreement. Asada’s idea was doomed. In the next calendar reform, that of Tenpo (1843), it was entirely neglected.

During the Tokugawa period (seventeenth to early nineteenth centuries) Japanese astronomers were continually preoccupied by the contrast between Chinese and Western astronomy. While they generally followed Chinese astronomy in the first half of the period, Western astronomy became dominant during the latter half. During the period of transition there appeared mental attitudes like those of Asada, who tended to syncretize and synthesize Chinese and Western astronomy. His originality proved to be rather anachronistic, however, in view of the rapid contemporary development of Western astronomy.

His pupils claimed for Asada the honor of having independently discovered the relationship between the distances of planets from the sun and the periods of their revolution (in other words, Kepler’s third law), although he did not publish it. Ōtani Ryōkichi maintained, however, that the law was first known in Japan in 1800, after Asada’s death, when his pupils obtained the Dutch translation of J. J. L. de Lalande’s Astronomic. Kepler’s third law had, as a matter of fact, been described in the Tenmon kanki (“Astronomical Collection,” 1782), one of Shizuki Tadao’s draft translations of the Dutch version of John Keill’s Introductiones ad veram astronomiam. One suspects that Asada somehow had the chance to become acquainted with Shizuki’s works.

There is another possible interpretation. Prior to Asada’s time. Chinese and Japanese observations of planetary motions were infrequent and imprecise. Even if neither the Keplerian planetary theory nor adequate observational data were available to him, he was fully acquainted with the first two volumes of the Li-lisiang k’ao-ch’eng, in which values for the relative sizes of planetary orbits are mentioned. These are close to the modern values, as they are calculated by trigonometry in the post-Copernican fashion. Thus, Asada might have tried a blind search for some numerical relationship between these values and the planets’ revolution periods, and finally reached Kepler’s third law independently.

Asada was not geometry-oriented, as were Western astronomers, but he was accustomed to the traditional algebraic approach and was fascinated by numerical manipulation. It would have been impossible for him to recognize the potential importance of Kepler’s third law, which led to the discovery of Newton’s inverse-square law and the establishment of modern mechanics.

Although Asada missed the meaning of his alleged discovery, it is interesting that his pupils believed that Asada had suggested a crude analogy between a balance and the solar system in a pseudomechanistic interpretation of Kepler’s third law. Hazama elaborated it in his own fashion, as follows:

If we express a weight in a balance as the area of a square, the side of which is x, the relationship between arm length a and weight x² is ax² = constant. A similar relationship holds between length l and frequency v of a pendulum: lv² = constant.

The radius of planetary orbit r seems to correspond to balance arm length a, which in turn corresponds to pendulum length l. The velocity of the planet u is taken to correspond to the frequency of the pendulum v. An analogous relationship between r and u thus should hold in the planetary domain: ru² = constant. Substituting 2r/T (T = period of revolution) for r in the above equation, r³/T² = constant is obtained. In this way, we arrive at Kepler’s third law.

The argument is, of course, quite misleading, but at a time when modern mechanics was not well understood, this crude analogy between planetary motion and simple mechanical laws gave an explanation satisfactory to Hazama’s contemporaries.

BIBLIOGRAPHY

1. Original Works. Asada has left unusually few works. Almost all of his ideas appear in his pupils’ writings and compilations. Notable among his own works are Jichūhō (“The Method of the Jichū Calendar” [1786]), MS preserved in Mukyūkai Library; Shōchō hō (“Variation of Astronomical Parameters” [1788]), MS preserved in Tohoku University Library; Gekkei o moue nisshoku o osu hō (“A Method to Predict Solar Eclipses by Means of Observing the Moon’s Shadow” [n.d.]), MS preserved in the Sonkeikaku Library; Gosei kyochi no kihō (“Remarkable Law of Planetary Distance” [n.d.]), MS preserved in the Sonkeikaku Library; and Takahashi Yoshitoki, Zōshū shōchō hō (“Variation of Astronomical Parameters,” enl. and rev.[1798]), MS preserved in the Tokyo Astronomical Observatory.

II. Secondary Litrature. Works on Asada in English are Shigeru Nakayama, “Cyclic Variation of Astronomical Parameters and the Revival of Trepidation in Japan,” in Japanese Studies in the Historv of Science, no. 3 (1964), 68–80, and Outline History of Japanese Astrononn (Cambridge, Mass., in press); and Ryōkichi Ōtani, Tadataka Inō (Tokyo, 1932).

A work on Asada in Japanese is Nishimura Tachū (one of Asada’s four major pupils), “Asada sensei gyōjōki” (“Achievements of Master Asada”) in Nomura Jun et al., eds., Nishimura Tachū jiseki (“Achievements of Nishimura Tachū” [Toyama, 1934]). Watanabe Toshio is now preparing a comprehensive hiography of Asada.

Shigeru Nakayama