The “Sokuchi-Genzu” owned by the General Library of the University of Tokyo is the “Shita-zu”, which are namely the manuscripts of the first real surveyed maps by Inoh Tadataka(1745-1818). It is composed of 93 sheets which are 1 large scale(1:36000), 36 medium scale (1:216000) and 56 small scale(1:432000).

On the each Sokuchi-Genzu, the surveyed points are plotted by pin holes and the surveyed lines are drawn by tying them. Furthermore, the place names and the astronomical observed points are recorded. On the medium scale Sokuchi-Genzu, the survey results during several days are plotted and the distances of directions of south-north and east-west between the end points of each survey line were measured on the correspondent large scale map mapsheet and were scaled down one sixth. The drawn areas on some of medium scale Sokuchi-Genzu corespond to the contents of some of Shita-zu owned by Inoh Tadataka Memorial Museum, which are the manuscripts of the Large scale maps.

On the other hand, the map sheet line of directions of south-north and east-west are drawn on the small scale Sokuchi-Genzu. These lines coincide with the map frameworks of the Large scale maps. The length of each framework lines and the distances between the cross points of each survey line and framework lines were scaled down one twelfth by using the reduce measure from the large scale map sheets.

These distances recorded on both scale SokuchiGenzu are expressed by the Japnese measuring system, namely “Shaku-Sun-Bu-Rin”=“30.3cm-3.03cm-3.03mm-0.303mm”. The numerical values under Rin are described by the multiple figures of 1/12. These were read by using the reduce measure on the large scale．

Since Ohtani Ryokichi's voluminous “INOH Tadataka” (1917), it has been commonly accepted that the small scale map were reduced from the medium scale map by reduction in half. However, as the framework of small scale Sokuchi-Genzu corresponds to that of the large scale map, it is said that the small scale maps were prepared from the

large scale mapsby scaling down one twelfth.. The medium scale maps were prepared by reduction from also the large scale maps, so that the medium scale maps and the small scale maps were prepared separately.

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Inoh’s map is the first scientifically surveyed map of Japan. Inoh Tadataka (1745-1818) started his nationwide survey over ten times from 1800 and the maps of his results were compiled and submitted to Tokugawa Shogunate Government in 1821 three years after his death.

His motive of the nationwide survey was to get the latitude distance. He drew the map of Japan based on the latitude distance obtained by his survey. His method of survey was traversing, intersection and astronomical observing. We can know his method briefly from the explanation record left by Watanabe Shin who was one of his best pupils. Afterward Ohtani Ryokichi wrote the voluminous work in 1917 about Inoh’s achievements based on Watanabe’s record, Inoh’s maps and his existent survey instruments, and Hoyanagi Mutsumi compiled famous work in 1974 about the scientific technology of Inoh’s survey and mapping.

These two classical studies on Inoh’s achievements, namely INOH TADATAKA written by Ohtani Ryokichi and A NEW APPRECIATION OF THE SCIENTIFIC ACHIEVEMENT OF INÔ-TADATAKA WHO ESTABLISHED A LANDMARK IN THE HISTORY OF LANDSURVEY AND CARTOGRAPHY OF JAPAN edited by Hoyanagi Mutsumi, have variously influenced and been commonly accepted on the studies of Inoh’s survey and maps since then,

Although Inoh’s original maps submitted to Tokugawa Shogunate Government were burnt out in 1873, some duplicates are existing still now. Taking the opportunity of two hundred years anniversary from the commencement of Inoh’s survey, some new Inoh’s maps were found out and bibliographical studies on Inoh’s maps have much progressed. However, scientific cartographical studies have not so much progressed yet.

As for the scientific cartographical themes, the four subjects such as 1) Latitude distance, 2) Inoh’s survey method, 3) Map projection and 4) Mapping process are discussed. Concerning these subjects, the author introduces the commonly accepted views, which are based on the two classical studies of Ohtani and Hoyanagi, and introduces newly reconsidered theories by Nogami Michio. Nogami denied the commonly accepted views and emphasized that the numerical value of latitude by astronomical observing is most fundamental survey framework and traversing corresponds to the detail mapping. The author evaluates his new theories.

Inoh’s maps are divided to “The large-scale map (“Daizu” 1:36000)”, “The medium- scale map (“Chuuzu” 1:216000)” and “The small-scale map (“Shouzu” 1:432000)”. According to Inoh’s mapping process, a draft map (“Shitazu”) is plotted from his survey data for every one day surveyed area at first. Every “Shitazu” is connected each other to one sheet of “Daizu” and the manuscript maps are prepared. He reproduced Inoh’s maps from these manuscript maps by using needle plotting method. Therefore, we can recognize existing of needle plot hole of surveying data on Inoh’s maps prepared by Inoh Tadataka and his group.

The existent Inoh’s maps are divided to complete maps prepared after the complete of his nationwide survey and intermediate maps prepared after every stage of his survey. Furthermore, besides Inoh’s maps prepared by him and his group themselves, various duplicate maps have been prepared until present time. Duplicate maps vary from faithfully copied to transformed. Especially, Japanese Army, Navy and Ministry of Interior copied Inoh’s maps in the early Meiji period. These copied maps were used for preparing the modern Japanese National Maps.

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伊能忠敬は間縄で測った測線距離を方位によって南北成分と東西成分に分解し，成分ごとに加算して，折れ線となる導線の節点の座標値を次々に求めた．座標値は大図縮尺（1/36,000）の値が用いられ，緯度差1度=28.2里は101.52寸となる．星測点では導線測量による南北座標値は星測緯度の座標値で補正された．補正率（補正量／南北距離）によって，星測点付近の導線の南北・東西位置も滑らかになるように補正された．このようにして得られた座標値をそのまま正距直交座標系の紙面にプロットして大図の導線が描かれた．中図（1/216,000）では6で除した座標値を得て，同じように正距直交座標系の平面にプロットされた．

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 Inoh Tadataka (1745-1818) drew the first Map of Japan based on a scientific survey. The maps forming Inoh's Map are classified into large-scale map (Daizu 1/36000), medium-scale map (Chuuzu 1/216000), and small-scale map (Shouzu 1/432000). Each map forming Inoh's Map was drawn from manuscript maps called Shita-ezu (1/36000), Yosezu (1/36000), Chuuzu-shitazu (1/216000), and Shouzu-shitazu (1/432000). Shita-ezu is a draft map plotted from the results of a survey carried out over one day. Yosezu is a manuscript map created by combining several Shita-ezu. Chuuzu-shitazu is a manuscript map reduced to one-sixth scale from Yosezu. Shouzu-shitazu is a manuscript map reduced to one twelfth from Daizu, which is compiled from a number of Yosezu. Concerning the mapping process used to draft Inoh's Map, a theory of Ohtani, R. (1917) has been most fundamental and influential in studies of Inoh's Map. According to this theory, Shita-ezu was plotted from the results of a daily survey and Yosezu was compiled from several Shita-ezu. Furthermore, he states that for the Tsukitehon, a Daizu manuscript was compiled from several Yosezu, and then Yosezu were graphically reduced and compiled to create Chuuzu, which in turn was reduced to Shouzu. On the other hand, recently, Nogami, M. (2021, 2022) rejected Ohtani's theory and concluded that Inoh's Map was drawn by calculating the coordinates of survey points, and map reduction was also based on calculations. In this study, it is concluded that the process of drawing Inoh's Map is divided into two flows. One is the reduction process from Yosezu to Chuuzu, the other is the reduction process from Yosezu to Daizu and from Daizu to Shouzu. The terminal survey points on Shita-ezu were plotted by calculating coordinates, which means the east-west/south-north component distance on a map. However, the survey points between the terminal survey points were then plotted graphically on Yosezu. It is added that the plotted areas of each Yosezu and each Chuuzu-shitazu correspond. Therefore, after Yosezu was drawn by combining Shita-ezu, Chuuzu-shitazu were drawn sequentially by reducing Yosezu. Regarding Shouzu-shitazu, it is clarified that the framework of the plotted area of Shouzu-shitazu is the same as that of Daizu. Consequently, Shouzu-shitazu were drawn by reducing to one twelfth the area of the same framework as Daizu after the frameworks of Daizu were decided.

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The General Library of the University of Tokyo owns the manuscript maps named "Sokuchi-Genzu", which were drawn for the first surveyed map of Japan by Inoh Tadataka (1745-1818). "Sokuchi-Genzu" is based on 93 sheets of the "Shitazu", the manuscript maps. The scales of "Sokuchi-Genzu" are classified into large(1:36000), medium(1:216000) and small(1:432000), which correspond to the scales of Inoh’s Map of Japan. On the "Sokuchi-Genzu" the results of Inoh's survey are plotted by needle points. The "Sokuchi-Genzu" is very important material for the research of Inoh's Map.

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１　江戸時代の料紙と料紙の選択

　享保年間（1716～1736）に京都に流通した紙を網羅的に掲載した『新撰紙鑑』（木村青竹著、安永6年［1777］刊）には、品質上に18に分類された400種以上の紙名が紹介される。また、文政9年（1826）に大坂にて収集された『大日本諸国名産紙集』（オランダ国立民族学博物館所蔵）には、西日本産のものを中心に約130種の紙が綴じ込まれる。これらの記述や遺品により、江戸時代中後期（18～19世紀）には、需要の拡大、製作技術の発展を背景に、全国各地で多量、多様な紙が作られたことを知ることができる。

　これら多様な紙は、機能性や、政治性（御用紙）、社会性（儀式など）により使い分けられた。文書・記録類のみならず絵図・地図類においても、元禄国絵図や越中国の和算家・測量家の石黒信由（1760～1837）作製の測量図の例にみるように、地図の性格により料紙の使い分けがみられる。

２　伊能図の料紙の先行研究、調査の方法と結果

　伊能図の料紙については、渡辺慎（尾形慶助、1786～1836）述編『伊能東河先生流量地

』（1824）、大谷亮吉著『伊能忠敬』（1917）に伊能図の種類別に使用された料紙名と裏打紙についての言及がある。これらを整理すれば以下のようになり、作図の段階、地図の性格により料紙が使い分けられたことを窺うことができる。 ① 小区域下図　西ノ内紙、裏打なし ② 寄図　西ノ内紙、裏打なし ③ 扣図　美濃紙（礬水引）／唐紙＊、裏打あり／なし ④ 官府上呈本・副本　唐紙／間似合紙、唐紙は裏打あり ＊③扣図の唐紙は大谷（1917）のみ指摘

　この点を踏まえ、以下2点を課題とし、伊能図の原本料紙調査を実施した。

ア　渡辺・大谷の指摘の検証と当該料紙の品質・形状上の特徴を明らかにすること

イ　伊能測量隊以外の第三者により製作された写本の料紙を明らかにすること

　調査は、主として以下の項目を対象とした。一紙の法量及び厚さの計測、簀目・糸目の見え方、簀目の太さ（本数／1寸）、糸目の平均長の計測、肉眼と透過光下における100倍光学顕微鏡による原料、塡料、斑、繊維束、樹皮片、非繊維物質の観察、である。

　今次の調査結果と、前述の『新撰紙鑑』の記載内容や、『大日本諸国名産紙集』の料紙調査報告とを比較し、（1）竹紙、（2）美濃紙、（3）美濃紙（小判）・大半紙、（4）典具帖紙、（5）西ノ内紙、（6）杉原紙、（7）半紙と、7種に料紙名を比定した。

　調査対象の伊能図は、『大日本沿海輿地全図』を幕府に上呈した文政4年（1821）前後にて時代を区分し、地図の性格（官府上呈本、伊能家扣図、同下図、同麁絵図、伊能隊以外の第三者写本）を記し、針突法による製作の有無、当初からの裏打の有無と併せ、調査した。

３　伊能図の料紙の種類と選択

　前項で記した課題に対し、以下の結論が導かれた。

ア　渡辺・大谷の指摘は概ね首肯されたが、次のとおり新たな知見があった。①一部の下図に（5）西ノ内紙の代用として（6）杉原紙が用いられていたこと。③扣図には（2）美濃紙のみならず、やや小ぶりな（3）美濃紙（小判）・大半紙類が用いられていたこと。④官府上呈本は、（1）唐紙（竹紙）の事例のみであったこと。

イ　第三者による写本は、（3）美濃紙（小判）・大半紙、（4）典具帖の2種のみが用いられていたこと。

　このように、伊能図の料紙は機能性による料紙の使い分けがみられ、加えて上呈図の料紙選択は政治性・社会性が加味されことが知られる。料紙の紙質は、伊能図の作製主体、作製段階、製作目的を示す一要素に位置づけられよう。

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Whatever is called "arithmetic" in our present system of school education is "yozan" (western arithmetic). This dates back to 1872, when it took the place of "wazan" (Japanese arithmetic) which is quite peculiar to our country. The present thesis is intended as a brief inquiry into the process of the pervasion of yozan in our school system. Yozan came to be known in Japan as early as the first half of 18th century, in close connection with the coming of the western knowledges of astronomy, tactics and so on. But it was mainly via China through the Chinese translations. The visit of American warships in 1853 was really an epoch-making event in the history of yozan in Japan. Yozan, which had been considered only as useful against the crisis of the domestic economy, came to be regarded as "necessary" for surmounting the diplomatic crisis. It is only then that the systematic teaching of yozan began in our country. It was launched out at the Nagasaki Naval Academy (1855-59), where yozan was regarded as the most important basic knowledge for all military sciences. In Hanko (educational institution for the military class), there had been a tendency toward neglecting arithmetic, even wazan. But as the problem of national defense became urgent after the visit of the American warships, yozan began to be taught at some Hanko. To most Terakoya (private school for the lower class), however, yozan gave no great influence worth mentioning, except a few where it was taught in compliance with the pupils' request. Though yozan had thus given quite a limited influence on our school education, it was decided in 1872 in the code entitled "Gakusei" that only yozan should be taught as "arithmetic" at every school in Japan. The aim of Gakusei was, first of all, the rapid growth of Japan into one of the advanced countries. In this sense, it seems natural that we have accepted yozan as our only "arithmetic", following other advanced countries. But it shouldn't be regarded only as a matter of imitation. The largest motive of our having accepted yozan lay in the then urgent desire for the increase of our defensive power which is eloquently expressed in the active attitude of the Nagasaki Naval Academy toward the introduction of tactics. Preference of yozan to wazan came in fact more from the need of national defense than from any academic comparison between them. In other words, the western knowledge which was indispensable in our national defense couldn't be learned efficiently without western methods of calculation and description. "The western arithmetic for learning the western knowledge" this was what made us prefer yozan to our old wazan.

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１．はじめに

　本報告では、伊能忠敬とも昵懇であった和算家・会田安明(1747-1817)が残した天文学に関する小品『天文簡要論』(1802年頃)を紹介する。本史料には、伊能が第3回測量までの間に測定したデータに基づき、会田に直接提供されたと考えられる情報や測量データが随所に盛り込まれている。20年余に及ぶ伊能の測量事業のほぼ初期に該当する年代に記され、伊能の同時代人による証言を留める史料として『天文簡要論』は貴重である。この観点から、『天文簡要論』が伊能忠敬について言及する内容を中心に紹介する。

２．『天文簡要論』が記す伊能忠敬由来の情報について

　本報告で紹介をする会田の『天文簡要論』は、天文暦学の基本的概念や歴史、雑録的な内容を上下2冊にまとめた写本である。日本学士院、東北大学附属図書館狩野文庫、山形大学小白川図書館佐久間文庫に所蔵が確認される。『天文簡要論』の上冊では過去の天文暦学者たちが残した成果の問題点を指摘、解説し、下冊ではそれらを乗り越えた最新の知見が披露される。伊能忠敬に関する記載は、最新の知見を示す事例として下冊に登場する。以下、その概要を掲出する。

　(1)伊能の測量術について

　｢地球大小論｣という項目で会田は、伊能忠敬による測量の目的、緯度１^°の距離(28.2里)、測量の技法の概要について言及する。伊能の測量法を示した史料としては従来、渡辺慎『東河先生流量地

』が知られていたが、会田の叙述は簡単ながら、これと類似の内容を含んでおり、伊能の測量事業の初期の技法の一端をうかがうことができる。

　(2)北極星の高度と太陽の南中高度の測定について

「予カ勾陣大星ノ測量」「十七日夜勾陣大星ノ一測量」「同十七日立表測量」の項目において会田は、伊能宅において北極星の高度と太陽の南中高度を測定したことを記す(1798年12月23日のこと)。伊能宅に設置されていた天文観測器具を会田は自ら操作しており、『寛政暦書』に描かれている同様の器具類の実際の用法を知る上での参考となる情報が記されている。 　　

　(3)山形城下での観測データ

　｢羽州山形測量｣の項目において、第3次測量の際に伊能隊が通過した山形城下での天文観測記録を会田は記録に留めている。この記録の中に、どの恒星を観測したのかが略記されている。

　(4)山岳の標高に関するデータ

　「諸国山高測量」の項目で、会田は12箇所の山岳(月山、赤城山、磐梯山、岩木山、鳥海山、他)の標高を記している。伊能から会田に提供されたデータは象限儀で計測した山頂を見通した際の仰角であった。これらの数値は、伊能が測量した山岳に関わるデータを集成した史料『山島方位記』（現存67 冊）には記載されていないものである。会田はこれら仰角のデータと、伊能測量隊が作成した地図上での２地点間の距離、そして三角比を用いて標高(正確には標高差)を算出している。この計算を行うために、会田は伊能図に実際に物差しを当てて長さを測っていたことが記されている。

　(5)垂揺球儀の概要について

　｢垂揺球儀｣の項目において、伊能が計時のために用いた振り子時計「垂揺球儀」の概説をまとめる。会田は、この時計の発明者として間重富と高橋至時の2名を挙げている。

３．おわりに

　『天文簡要論』下冊から明らかになった事柄は以下のようになる。

・会田が伊能宅で天文観測を体験していたこと。

・伊能が第3 回測量旅行中に測定したデータ類を、会田は提供されていたこと。さらに伊能図も実見していたことがうかがえる。

・提供されたデータの中には、山頂を見通した仰角の測定値が含まれており、これらは既存の史料には確認できないものである。

・垂揺球儀の概要を記していること。

　伊能忠敬の同時代人が伊能の動向について書き残した史料は、書簡を中心として数多く残されている。しかし、間重富や高橋至時のように非常に近い関係にあった数人の天文暦学者を例外として、伊能の測量や天文観測の実態を的確な知識に基づいて記録をした史料は思いの外少ない。その観点から、会田安明の『天文簡要論』下冊は小篇でありながら、伊能の天文暦学、測量の実践に関する情報を現在に残す史料として位置づけられる。

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　　In order to realize technological history of the French type silk-reeling process in modern Japan, we carefully examined 68 academic documents and technical books for raw silk production which published from the Meiji era, the Taisho era to the Showa era. As a result of analyzing geometrical structure and technological parameters such as distance between hook and surface of reeling basin, distance between hooks, number of crossing, length of crossing, angle of getting uncrossed threads, it was found that transition of technique for the French type silk-reeling cross and process can be classified into three period: the European technology introduced period, the adaption period and the Japanese technology established period. Furthermore, we analyzed experimental data in “Tomoyori Souchi Shiken” published by Mr. Mitani to know influences of technological parameters on the quality and productivity of raw silk. We installed density of crossing as a new parameter to realize the phenomenon of the French type silk-reeling cross. As a result, it seems that the French type silk-reeling cross includes a complexity of geometrical structure and a nonlinearity of each technological parameters. This situation might have been difficult to optimize the process conditions in the era. It turned out that factors of the technological transitions were attributable to adaptation of Japanese silk mills to the introduced Western style technology, quality of raw material cocoon and changes of the global market structure and needs.

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