This paper looks at the process of establishing the historic administrative district areas and county areas as Japan established itself as a single nation and the transitional changes that led to today's prefectures, and the perspective for future wide-area administrative districts in Japan.

Japan's historic administrative district areas and county areas comprised a regional administration system, established by the ancient Japanese state under the Ritsuryo legal code, based on the regional systems of China and Korea.

The old maps from these times show the process of change from administrative districts to territorial divisions that identify regions, that occurred in the early modern period of feudal society, after the historic administrative district areas and county areas that formed the administrative districts of ancient Japan became superficial in medieval times.

These maps also show that, with the further progression into the Meiji Restoration period, prefectures were established in the place of feudal domains, although these prefectural districts were established in line with the historic administrative district areas and county areas that formed the regions of early modern feudal society. The process through which counties became regional administrative districts possessing juridical personality, and then subsequently returned to geographical naming that identified regions after acquiring the role of administrative regions is also shown.

In addition, these maps show the meandering process through which the prefectural districts, in other words the wide-area administrative districts that followed the establishment of prefectures in the place of feudal domains, were established, and they can also be applied to the analyses of proposals for the far-sighted yet un-realized further merging of prefectural districts.

The ancient Japanese administrative district areas and county areas that underwent these transitional changes maintained regions that were coherent in terms of geography and climate and still exist today as cultural and historical regions.

Meanwhile, the municipalities that comprise the basic local authorities that are closest to today's residents were expanded during the mergers of municipalities from the Meiji to the Showa period and subsequent mergers in the Heisei period, and inverse phenomena, namely the creation of cities with wider areas than prefectures, also occurred. However, many instances where the old county districts have literally become cities in their own right give testimony to the geographical coherence of the old county districts.

In view of these prefectures, which comprise the new wide-area administrative districts, and the current status of the expanded municipalities, the objective of this study is to introduce proposals for wide-area provinces that will form the next new wide-area administrative districts, and to form a perspective for future wide-area administrative districts in Japan.

The China maps published in Japan during the Edo Period were the republications of the maps made in China. However, at the end of the Edo Period the China maps which reprinted the ones made in the Western countries were published in Japan.

One of them was “Map of Daishin Itto Zu” on which German origin and Shibata's manuscripts were written in. While trying to find the origin of the map, the author reached the conclusion that the common belief of previous research was a mistake. A new fact came out. The origin of “Map of Daishin Itto Zu” was a copy of a Chinese version of “Map of the Chinese Empire” attached to the book “The Middle Kingdom”, （first edition, 1847, NY）. “Map of the Chinese Empire” was the result of modern China drawings edited by Samuel W. Williams, an evangelist, who lived in China for 40 years.

Ginkou Kishida who got acquainted with Samuel W. Williams through J.C. Hepburn, valued “Map of the Chinese Empire” and bought the printing blocks of Shibata's “Map of Daishin Itto Zu”.

After correcting some mistakes he published “Map of Daishin Itto Zu” and then adding some place names related to Taiwan troops in 1874, he published “支那全図（Map of the Entire China）”.

Also in 1894 when the relation of China and Japan got worse because of war, the city maps of Shanghai and Beijing were inserted and the revised “清国輿地全図（Map of Qing Dynasty）” was published.

“Map of Daishin Itto Zu” was a revolutionary one but after “亜細亜東部輿地図（Map of East Asia）” was published in 1875 and “亜細亜全図（Map of the entire Asia）” was published in 1884, its role was over. It was these ten years that “The Middle Kingdom” by Samuel W. Williams was revalued and in 2005 it was translated into Chinese for the first time.

The author is looking forward to finding the Chinese version of “Map of Daishin Itto Zu” in the near future.

This paper proposes 3 series of map projections for world map with interruption over ±180° of longitude. Root-mean-square error of area and angle, which is L₂ of Kamiya （2012）, or simply noted L in this paper, is minimized in the proposed projections. The objective function L depends on one parameter w_S（0 ≤ w_S ≤ 1）, which is a weight for area error.

Proposed projections are polynomials of longitude and latitude under the condition that poles shall be a point. If 360° of angle at pole corresponds to θ° on a map, angle defect of pole is defined as 360−θ. This paper proposes 3 series of global optimal projections： with 0° of angle defect of pole, named whole pole； without constraint condition for angle defect of pole, named free pole；with 180° of angle defect of pole, named half pole. Order of the polynomials is 13 for whole pole and 11 for others.

Proposed projection by w_S＝0.S are named “Global optimal projection SW” for whole pole, i.e. “Global optimal projection 5W” for w_S＝0.5, “Global optimal projection SF” for free pole, and “Global optimal projection SH” for half pole.

Value of L, weighted root-mean-square-error, is much smaller in proposed projections than in conventional projections except almost conformal condition or almost equal area condition. Therefore, the global optimal projections are excellent projection as mean of minimizing both area and angle error.

Though value of L is slightly larger in whole pole than in free/half pole, distortion around the poles is smaller in whole pole than in free/half pole. If distortions of Arctic/Antarctic area （for example 80° or higher latitude） are important, whole pole shall be selected. Otherwise, free pole or half pole shall be selected.

Global optimal projections reduce near origin region almost isotropically under the conformal-like condition. They also stretch the region in the northsouth direction almost equivalently under equal-arealike condition. Parallel lines are concave to the pole, but less concave or sometimes convex to the pole near central meridian.

Aspect ratio of map shall be around 1.5 for minimizing distortion, though many map projections adopt 2.0. Necking at poles like Eisenlohr projection is important to decrease angular distortion.

Technical information about global optimal projections will be disclosed at http://www.gsi.go.jp/cais/geoinfo-index.html.