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Origin, Distribution and Role of the Kaito Phenomenon in the Settlement of Japan (Part two of two)

著者 Kikuchi Ichiro, Kakiuchi George  H.

journal or

publication title

奈良教育大学紀要. 人文・社会科学

volume 21

number 1

page range 83‑92

year 1972‑11‑15

URL http://hdl.handle.net/10105/2815

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83

Origin, Distribution and Role of the Kaito Phenomenon in the Settlement of Japan*

(Part two of two)

Ichiro Kikuchi

Department of Geography, Nara University of Education

George H. Kakiuchi

Department of Geography, University of Washington

Some Thoughts on the Origin of the Kaito

In the evolution of the kaito phenomenon to the form of settlement, it is generally believed that it originated as a small unit of land set apart for reclamation by an individual {kojin-kaito). Then as other similar units came to be established nearby, there formed the neighborhood kaito (rinpo-kaito). Finally, the rinpo-kaito or the dozoku-kaito expanded into a larger settlement, the buraku-kaito. Three reasons have been proposed to justify this evolutionary process. The first is that within the area of some kaito buraku there still can be observed the rinpo-kaito

and the kojin-kaito. Secondly, there are buraku-kaito today which have names of

individuals or occupations preceding the term kaito. Thirdly, even in those buraku which are not called kaito, there are rinpo-kaito and kojin-kaito."

One interpretation of the evolutionary process states that as the land set apart in some way for reclamation was being developed, a small shed-like temporary structure (jtaya) (|33g) came to be built. Such examples can still be found in the

Kumano area of Wakayama prefecture and elsewhere. Eventually the taya was

replaced by a permanent residence. The unit of cultivated land, the residence,

and associated forestland formed the kojin-kaito. This unit may have been sur-

rounded by some kind of simple enclosure, but more likely was set apart in some way by boundary markers of some kind." The foregoing description seems to fit the kakitsu (or kakiuchi) mentioned in the Manyoshu.

Next as other lands were cleared in adjacent areas and more houses were built,

centered on the first house, the settlement or the community took on more

significance. This then became the rinpo-kaito or the buraku-kaito. Once the

name kaito came to focus on a small settlement, then it came to be associated with

certain communal ownership, such as the forestlands and grasslands, and group

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activities. Still later, branch or new settlements seem to have been established from the older kaito buraku as there are settlements referred to as de-gaito (f±iM F*3) ("branch" kaito). Such cases are not uncommon in the Nara basin."

In the attempts to get at the original form and characteristics of the kaito, the

isolated Kumano mountain area of Wakayama prefecture appears to be one of the

more promising regions for study. In fact, a fairly detailed study of the kaito

has been made of Chikano and Tomisato-mura. In both of these villages, many of

the kaito are found on the less desirable agricultural land such as the river

terraces and the foot of the mountains." The location of the kaito on the less

desirable lands seems to be a common characteristic seen in other regions of

Japan and is an interesting observation for speculation.

One of the aims was to try to determine the original size of the kojin-kaito. In Chikano-mura, of the fourteen kaito units, only two (Naka-kaito had seven houses and Baba-kaito Gil^Sf*!) had four houses) had more than one house. In Tomisato- mura ((§Mt^)> fourout often had two or more houses. Assuming these kaito units are close to the original size, then it is seen that the sizes were relatively small.

In Chikano-mura (fiUfcf), the cultivated area of each unit ranged from about four tan to eight tan. In addition each usually had a limited acreage of additional grassland and mountain forestland. In Tomisato-mura the smallest unit had about

five tan and the largest about two cho (1 cAo=2.45acres). The average was about

one cho. Again in addition to the cultivated lands, each kaito had some forestland.

Part of the reason for the difference in acreage was undoubtedly due to the nature

of the topography and productivity of the land. Reflecting these differences in

quality of the land, the size of the original kojin-kaito probably ranged from

four to ten tan of cultivated land and had in addition some grasslands and

forestlands. It is presumed these acreages were sufficient to support one family in those days.

It is difficult to generalize about the original size of the kojin-kaito from only the

examples found in the Kumano area, especially as a great number of them are

located in narrow valleys, and therefore topographic factors may have influenced

the size. Thus, although it is rather difficult today to find other examples, a

few more can be given. In Okawase CfcllliS), Ai-mura (H^if) of Arima-gun (^iffUS) in Hyogo prefecture, the Okamoto-kaito (pSj^fill*}) had about one cho and nine tan of paddy fields." In Takashima-gun CjBJilSIS) of Shiga prefecture, the sizes of the

kojin-kaito averaged about one cho. However there are some which are small as

one tan.1" The koaza of Kakiuchi in Fuke-mura (HH^^) of Kami-gun in Kochi

prefecture had about one chb of cultivated land, and again Aza Kakigauchi (ffji-SrF'i) of Iwa-mura (SW in the same gun had one cho of paddy field."1

Records written during the Middle Ages have given clues also to the size of the original kojin-kaito. For example, the records of Nitta-gun (0fE3§(5) in Gunma

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Origin, Distribution and Role of the Kaito Phenomenon

in the Settlement of Japan (Kikuchi. Kakiuchi) 85

prefecture show, in the cases where a person's name is attached to the term

kakiuchi, the smallest kaito had an area of seven tan and the largest one had an acreage of four cho and three tan."' Going back slightly farther into history, the literary records of the Heian (^pg?) period (794-1192) indicate the average kaito was about one cho.1" In general, then, it seems that the average size of the kojin-katio was about one cho or some-what smaller.

Some further interesting points have been ascertained from the records of the

Middle Ages and earlier. For instance, the names of the kojin-kaito had many

prefixes, but the most common ones were associated with direction, topographical

features, names of trees, names of the lords of manors, or the names of the

cultivators. These kaito were comprised usually of paddy fields, dry-field croplands

and wastelands, and they may or may not have any dwellings on them. When

the kojin-kaito were sold or bought, transactions were carried out without changing

the names or composition of the individual kaito. However, there were cases

where kaito units were abolished or where just the dry-field croplands were left

and continued to be called kaito. There were also instances where the income

from a kojin-kaito had been donated (kishiri)^^). Also, according to the records,

many of the kaito were established on the wastelands, giving credence to the

belief that the cultivator might have been given special privileges such as tax

exemptions or reduced taxes to encourage the expansion of cultivated land into the less desirable agricultural lands.1"

At this point, a brief review of the system of land ownership in rural Japan

during the early periods of history may help understand the role, origin and

evolution of the kaito phenomenon.

Prior to the Taika <ckit) Reform (645A.D.), the "be" (^5) or "tomo" (#) or occupational guilds had been the basic units of society, each with a chieftain wielding absolute control over the peoples and owning all their resources of land

and labor.1" Farming was done on a communal basis. However, evidence of

private ownership of land began to appear when individual farmers began to

reclaim land for themselves. In time the powers in control were to encourage land reclamation as the society and economy expanded and population numbers continued

to increase. By the beginning of the eighth century, private ownership and

reclamation of agricultural land had become important enough so that the central government began to issue rules and regulations. For example, during the Gensho

(7ClE) period (715-24), records show that a system known as the sanze isshin

konden OE-fff-å Jf'ilES) 'was in existence. Under this system if a farmer cleared a piece of land for cropping, it belonged to his family for three generations. Then sometime during the following Shomu (JMlSi) period (724-49), perpetual ownership was established. Although for a short time during the next Shotoku (f?FMD period

(764-70), reclamation for developing new farm lands was prohibited, in the

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following Konin Qtfcfc.) period (770-81), reclamation was once again allowed by

individuals. Written evidence seems to indicate the term kaito came into use

sometime during the eighth century, associated in some way with the newly

cleared lands.1" It seems too the kaito of this time was a special kind of landholding possessed by a pioneer farmer (kusawake) who received certain special rights. It

is believed the kaito in the aforementioned context was closely related to the

myoden (^EH), which was also a form of private landholding in existence from

the middle of the Heian through the Muromachi (3IHX) periods.1" The general consensus of opinion is that the kaito throughout the areas of Japan in which they

are found came to be established as reclamation of new lands for cultivation was encouraged.

The kojin-kaito probably came into being from the early efforts of the kusawake.

The next step could have been the evolution of the dozoku-kaito, where a number

of families branched off from the honke. This dozoku-kaito may very well have

included the houses and families of the slaves (geniri) (~FA) an<3 the farm workers (sakuotoko) (fpJEj). Baba-kaito of Chikano-mura and O-gaito, Kuwabara-kaito, and Shintani-kaito of Tomisato-mura would be of this type. Many others can be cited

in the various parts of Japan. The so-called kaichi found in Yoshida-gum (llfEHilO

of Fukui prefecture are usually comprised of a consanguinal group and would be

included in the dozoku-kaito. Also, it is known in parts of Yoro-gun (§i^iif|$) in Gifu prefecture for the people to call families with the same surname as Mr. So-

and-So's kaito. In Takashima-gun of Shiga prefecture, the honke refers to the

bunke as its kaito lineage (kaito-suji). Examples of dozoku-kaito are quite numerous in the Kinki district and connote not only areal units but also very strong local socio-economic organizations. Lastly, to establish a linkage between the kojin-kaito and the dozoku-kaito, it is reported in Kato-gun in Hyogo prefecture and in Sennan- gun in Osaka prefecture the local kaito groups have deified the original kusawake by dedicating a shrine to that person and holding annual festivals.1"

Just as the dozoku-kaito evolved from the kojin-kaito, it can be assumed the

rinpo-kaito, comprised of a few households of unrelated families, evolved in the

same way. An example of this type is Naka-kaito of Chikano-mura, which had

only one household until the beginning of the Meiji (Win) period but now

has seven unrelated households. Also Oaza Tsubara of Nishi Katsuragi-mura in

Sennan-gun (jjlfH) (Osaka prefecture) is divided into seven parts, and although four of them have personal names attached, today they are all rinpo-kaito. There are numerous other examples, where it can be presumed the so-called neighborhood kaito evolved from the kojin-kaito. However, it must not be assumed all rinpo- kaito or others comprised of more than one household originated in this way, for as in the cases in the development of new paddy fields (shinderi) (§fE3) of the Kinsei (ffittt) period (1600-1867), many are thought to have been developed by a number

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Origin, Distribution and Role of the Kaito Phenomenon

in the Settlement of Japan (Kikuchi. Kakiuchi) 87

of households under the leadership of powerful families or by groups of cooperating families. For example, in Kawadaka (?BJ^) of Takino-machi (?§H?HX) in Kato-gun (jRiKitB) (Hyogo prefecture), there is a kaito called Goken-gachi (iff#*?å ), which is composed of twenty households and is a local grouping similar to a kumi. It is said the settlement was established by five persons, Isaemon (IfrSilifPI), Shinbei (§f

£M), Yoshichi (#-fc), Kyubei (%.gM), and Gorobei (SSI^ffi), and it is for this reason the settlement came to be named Goken-gachi (five-house gachi).1"

Then, going one evolutionary step forward, it is assumed the aforementioned two

could have expanded into the buraku-kaito, which were often equivalent to the

kumi in size and function. Apart from kaito communities there are those which

are only place names and those where a settlement collectively became a buraku- kaito by the amalgamation of a number of smaller kaito units.1" Many such examples are found in the Nara basin.

The most often-cited buraku-kaito and the best examples are found in the Nara basin. These buraku-kaito were rectangular in shape and evidently were surrounded by moats (Fig.4). Some settlements still have retained the moats (footnote 2). It

has been claimed the rectangular shape of the moat-surrounded settlements was

copied after the walled villages of North China.1" It has also been argued that the

shape was due to the implementation of the rectangular-patterned jori system of

land division after the 7th century, and that the existence of the moats was for the defense of the settlement.ll' Still another argument is that the moats came to be as an adjustment to the local physical environment, namely as an innovation to overcome the wet conditions. The argument states that: (1) the dirt from the

moat was used to raise the land of the settlement proper, (2) the moats were

used for drainage during the wet seasons and for irrigation during the dry seasons, and (3) the moats were used for the storage of water to fight fires in the village.1"

It is interesting to note that in respect to the distribution of the kaito settlements intheNara basin a good number of them are found in the lower-lying areas of the basin (Fig. 3). One viewpoint explains this particular distribution by associating

it with a period of time, namely, the Japanese Middle Ages, when much of the

better lands had already been reclaimed and also the society had reached the level, in terms of technology and social organization, where the more difficult to reclaim lands, such as swampy and low-lying areas, could be brought under cultivation.1"

It is to be noted that with the beginning of early Japanese feudalism (late Heian

and Kamakura periods) in the Middle Ages, the shoen (manorial) system of land

ownership became increasingly important, with men of power and prestige, both

at the Imperial Court and in the provinces, in control of the land, replacing the Imperial handen-shuju (EffilKfiD system. Under the handen-shuju, all cultivated land had theoretically been allotted to the farmers according to size of the family and was periodically redistributed. But by the tenth century it had already begun

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to collapse, and by the twelfth century the system had lost its effectiveness completely. The development of the shden, too, seemed to have been an outgrowth of, or least was first associated with, the reclamation of new lands, especially paddy lands, and in this respect the historical timing of the establishment of the shoen and the kaito, although not identical, seem closely related (see footnote for further clarification).1"

Not all kaito phenomena can be explained as parts of the evolutionary process

from the kojin-kaito through to the buraku-kaito. Thus another path must be

taken to account for the remaining types. The most plausible explanation seems

to be that some are remnants of the kojin-kaito, which originally consisted of the yashiki, cultivated lands, forestlands, and in certain cases wastelands.

It is thought the establishment of the yashiki as one kind of kaito phenomena came fairly early in the process of change. Just as in the cases where the focus came to be placed on the buraku, so, too, in the cases of the "yashiki"-kaito the focus came to be on the dwellings and the land associated with it or the yashiki.

Evidence for the latter assumptions is seen on the plains area of Minami Kawachi (ffiMF*3) in Osaka prefecture, where the local people speak of certain former sites of yashiki as kaito-chi (jtaF*3it6) {kaito land). More direct evidence is found in the northern mountains of the same area where the yashiki is actually called kaichi.

The same is true in Shiriuchi near the city of Hachinoe (A^) in Aomori prefecture, except the term used is kakuchi, and in parts of Tokushima prefecture on Shikoku the yashiki is called kakiuchi.'" Many of these yashiki are surrounded by rows of trees or hedges, and the question which rises in my mind is whether the term

kakiuchi may not have evolved as a descriptive word, unrelated to the kaito

phenomenon.

Studies of the records of the Middle Ages reveal the yashiki-kaito to have existed by that time. For example, the local village records of the Koyasan fief often cited

the kaito to consist of a house and lot, and a person's name was attached to

the term. The average size of such a yashiki was about 200 tsubo (j5p) (1 tsubo equals 3-95 square yards).117 The records of the settlement of Yamato-Wakatsuki C^nSfil) in the Nara basin, written during Tokuji (@f£) period (1306-07), indicate a similar situation, but the area of the yashiki averaged about 300 tsubo.1"

From the yashiki-kaito, there could have been further fragmentation, for cases exist where only certain parts of the yashiki are called kaito, such as the house itself (in the case of yago), the open yard in the front or back of the house, the small garden, the cemetery, etc. Some examples can be given. The open yard in front of

the house is called kaido in the area of Mikkabi-machi of Inasa-gun (Shizuoka

prefecture), kairo in the northern part of Sado Island, and kaito in the Ikeda area of Osaka prefecture, whereas from Echigo to the Tohoku district, the backyard is

referred to as kakuchi. Then, too, in the Ikeda area and in the Tajima ({M,l§)

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Origin, Distribution and Role of the Kaito Phenomenon 89 in the Settlement of Japan (Kikuchi. Kakiuchi)

region, the dry-field croplands within the yashiki are called kaito or kaichi.

Lastly, in Shimadachi-machi (J§3£fflT) of Higashi Chikuma-gun in Nagano prefecture, the burial plot in a corner of the yashiki is called kaito.ll'

On the other hand, cases are found where cultivated plots of land appear to be

remnants of the kojin-kaito. In much of Nagano prefecture, it is reported the

immediate area around the yashiki is called keido-bata {keido dry-field cropland),

and in Yomura of Higashi Muro-gun in Wakayama prefecture the large dry-field

cropland in front of the yashiki is called kaito-batake. The same is true in

Takashima-gun of Shiga prefecture. There are even cases where the narrow path

leading to the rice nursery (nawashiro) (iSfti) is called kaito-michi {kaito path).

Finally, there are units of cultivated land or of wasteland which are called kaito

but never seemed to have had any dwellings on them. Many such cases can be

observed in the northern mountains of Hyogo prefecture and in an area from the

mountains of Aichi prefecture through the Akashi (^5) mountains into Chiisagata-

gun in Nagano prefecture and thence into the mountains of Gunma prefecture.

Most of these kaito are dry-field croplands located on the less desirable tablelands along the foothills and on river terraces. The size of the individual units is about one cho. These cases would represent those types which never reached the stage of the kojin-kaito. Many of them, especially in the isolated areas, were probably set apart for future reclamation and were for a long time used as grassland or other

non-crop purposes. This might be surmised from the situation in Tsukui-gun of

Kanagawa prefecture, where there are numerous such kaito place names along the

transition zone between the mountains and the present dry-field croplands.120 Many of the aforementioned may have been developed as supplementary plots to the main farm, because in many cases of the kaito of Gunma prefecture, the documents from the Middle Ages list them as dezukuri-wake (fiSfFt)^?) or just dezukuri (going outto cultivate).121 These then would not have dwellings planned for them from the beginning.

Thus taking one path of evolution, the kojin-kaito which came to focus on the

yashiki expanded into the dozoku-kaito or rinpo-kaito and then into the buraku-kaito.

Taking another path the kojin-kaito became fragmented and the term kaito came to be applied to certain parts of it. The variety of forms and meanings, then, found today in various parts of Japan are relics resulting from these two processes.

Summary

Studies on the kaito indicate the phenomenon came into existence quite early in the history of Japan. The earliest documentary evidence discovered so far appears in the kiinokuni-zaiden-gungi-ge (lE^B^ffliil^IPP) written in 854.12J Its origin appa- rently coincides with a period of time when private ownership of land was beginning

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to be permitted and the reclamation of hitherto undeveloped lands was being encouraged. Although some scholars feel the kaito may have preceded the mydden, in the aforementioned respect it was similar to the mydden. However, in contrast to the latter, the areal distribution of the kaito phenomena generally seems to be associated with the less desirable agricultural areas, whereas the mydden are found in the plains and basin areas. Further study on this difference in areal distribution

might prove to be significant in the analysis of these two seemingly similar

phenomena, especially as the two are found within the same general areal extent of the distribution of the jdri system.123

The kaito as local place names and very small socio-economic grouping were and are most numerous in the Kinki district, especially in and around the Nara basin.

It was the rectangular moat-surrounded kaito settlements in the basin which first attracted attention as a rural settlement type. One of the question which needs to be investigated is how strongly the communal functions and characteristics have been retained in the small kaito settlements and communities.

Footnotes

95 Naoye, "Kaito no kenkyu," op. cit., p.19.

96 Many of the kaito place names, which are preceded by names of certain kinds of

trees, may have been taken from the kind of trees used as boundary markers. Ibid., p.31.

97 Wakamori, "Kaito," op. cit., pp. 20-30; "Kaito," Kyodo-shi jiten (M±&M$§) (Dictionary of Regional History) (Tokyo: Asakura shoten, 1955), pp. 87-88.

98 It might be noted that in a great many cases, the name of the kaito became surnames of the family or families living there, such as Tsutsumi of Tsutsumi-kaito, Yumiba

of Yumiba- kaito, Kuwahara, Shintani, etc. It can be presumed that the people of

the kaito took the names of the kaito at the time of the Meiji Restoration, when

commoners were allowed to take on surnames. Oftentimes, the name of the kaito

became the yago, such as Ushiro-kaito and Se-kaito of Chikano-mura. Also, they

have become names of koaza, such as Kami-kaito, Naka-kaito and Baba kaito of

Chikano-mura. Naoye, "Kaito no kenkyu," op. cit,. pp. 19-23.

99 Taoka, op. cit., p.24.

100 Adachi, "Omi Takashima-gun ni okeru kaito kenkyu," op. cit., pp. 188-122.

101 Naoye, "Kaito no kenkyu," op. cit., p. 23.

102 Gomi Norio, "Chusei joshu no kaito," op. cit., p.33.

103 Isshi, "Kaito-ko," op. cit., pp. 65-66.

104 Chiba, "Kaito ni tsuite," op. cit., pp. 29-30.

105 R. K. Reischauer, Early Japanese History (Princeton, 1937), pp. 1-20.

106 Nakayama, op. cit., p.14.

107 The myoden (;gE3) (name paddy field) referred to newly reclaimed rice fields during

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Origin, Distribution and Role of the Kaito Phenomenon

in the Settlement of Japan (Kikuchi. Kakiuchi) 91

the periods from the Heian (784-1185) through the Muromachi (1392-1490). The person

who reclaimed the land was entitled to its use and also named the land after his

own name. From the eighth century on, edicts and regulations issued by the

government indicated an increasing concern for the opening up of new lands on the

frontiers to alleviate the needs of the increasing population, probably the myoden came into being to encourage reclamation and to distinguish them from the govern- ment paddy fields, the koden (£15).

108 Chiba "Kaito ni tsuite," op. cit., p. 33.

109 Nishioka, "Kaichi," op. cit., p.60,

110 Naoye, "Kaito no kenkyu," op. cit., pp. 24-25.

111 Ogawa, op. cit., pp. 1-26-

112 Makino, op. cit., No.l, pp. 180-202.

113 Muramatsu Shigeki, "Iwayuru kango-shuraku ni tsuite, Yamato heiya o chushin ni

shite mitaru (I^WSSljg^igitge^T-AWI^t«bt h- lz Z) (On the So-called

Moat-surrounded Settlements, Viewed with the Focus on the Yamato Basin)." Jinbun kenkyu (Aj£5Jf%), I (Dec. 1950), pp. 4-7.

114 Makino, op. cit., "Sankyo narabi ni ".

115 One of the more interesting problems for the future would be to try to see if there

really is a relationship between the kaito, shoen, and the myOden. It is known

that the myoden or myo came into being during the latter part of the Heian period

and increased in number during the Kamakura period. In terms of time, the

kaito and myoden are similar. The evolution of the kaito can be likened to the

evolution of the myoden, That is, just as the shoya (££il) on the myoden became

the shotaku (££%) (mansion) of the shoen, the taya (EHM) (temporary living quarters or a small hut used for resting and storing of farm implements) on the kaito became

the yashiki. The kaito in this sense could be thought of as a small-scale shoen.

One scholar has stated that the kaito or kakitsu perhaps was the forerunner of the

shoen. But this raises the question that if the kaito was the forerunner of the

shoen, why is it the two are differentiated. Others have claimed the kaito was a

type of mydden. Another has called attention to the general relationship between

the kaito and myo in that records show many myo names to which are added the

term kaito-myO. No one, as yet, has claimed the two are the same. Many feel,

however, the two had interesting similarities. Two of the more important ones, in

addition to the similarity in time, are that both were associated with the development of new lands and appeared to have special privileges attached to the reclaimed land.

Nakayama, "Kaito-ko," op. cit., pp. 14-24; Yonekura, op. cit.; Watanabe, op. cit., pp.

59-64.

116 Chiba, "Kaito ni tsuite," op. cit., p.31 117 Yonekura, op. cit.

118 Watanabe, op. cit., pp. 53-59.

119 Isshi, "Kaito-ko," op. cit., p.68.

120 Naoye, "Kaito no kenkyu," op. cit., p.26.

121 Gomi, op. cit., p.33.

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122 Takeuchi Rizo (fJftSH). Heian ibun i^-^MSO (Literary Records of the Heian Period) Tokyo-do, 1947), I, p.96.

123 One plausible explanation given to account for the difference in areal distribution is that the implementation of the jori system on the plains area was much more strict and affected the earlier settlements, and, as a result, many of the kaito settlements disappeared, were reduced in number or at least altered in form, assuming that the kaito phenomenon preceded the establishment of the jori system of land division.

In the mountainous or isolated areas, it appears that the system was not strongly enforced and therefore many more kaito place names were retained. Isshi, "Kaito- ko," op. cit., pp.65-66. Certain evidences seem to point to the above explanation.

Historical records and maps of Gamo (?|ffi) and Echi-gun (§5?li|5) in Shiga prefecture show that kaito koaza names are much more numerous in the uplands and in areas susceptible to flooding. These areas coincide with areas where the jori system was not enforced. In Aichi prefecure the kaito or kaitsu names are far more numerous in the more hilly and mountainous areas than in the lowland paddy field areas near the city of Nagoya. Chiba, "Kaito ni tsuite," op- cit., p.34.

(1972fp5^30H SS)

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Keywords: continuous time random walk, Brownian motion, collision time, skew Young tableaux, tandem queue.. AMS 2000 Subject Classification: Primary:

Kilbas; Conditions of the existence of a classical solution of a Cauchy type problem for the diffusion equation with the Riemann-Liouville partial derivative, Differential Equations,

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

Applications of msets in Logic Programming languages is found to over- come “computational inefficiency” inherent in otherwise situation, especially in solving a sweep of