INTRODUCTION.—The purpose of this paper is to treat boundaries geographically. The boundaries of the New England states have been selected as the basis for this study of the geography of boundaries, because New England is compact and important, the boundary features are extremely diversified, and the history accessible and illuminating.

     ADVANTAGES OF SHORE BOUNDARIES.—In general, the shore boundary has numerous advantages; it is the most obvious of boundary lines, it requires no survey to ascertain its position, no monuments are needed to designate its course. The shore boundary has a further great advantage over all others in that it is a physical and ethnic, as well as a political boundary. It thus is the most harmonious of boundaries. In the history of New England no controversy has ever arisen over the sea shore as a boundary.

     It may be said that the shore boundary has a disadvantage because the coast line may change rapidly, as happens along the coast of sandy islands bordering the outer margin of a coastal plain. Near Atlantic City, New Jersey, one estate may lose several acres in a few years, and another gain as much in the same time. Nevertheless, the changes do not cause a transfer of jurisdiction from one government to another, and so do not lead to disputes, as do changes in the course of rivers which serve as boundary lines.

     In times of war, the sea boundary is one of the easiest to defend.

The harbors are like mountain passes; being the only ways of easy access, they make it possible for all the defensive forces to be concentrated at a few points. Macauley emphasizes this advantage in considering countries which are largely bounded by the sea. “Some states have been enabled by their geographical position to defend themselves with advantage against immense forces. The sea has repeatedly protected England against the fury of the whole Continent. The Venetian Government, driven from its possessions on the land, could still bid defiance to the Confederacy of Cambray from the arsenal amid the lagoons.” In the case of a very irregular coastline, like that of Maine, however, where the harbors are over numerous the ease of defense is lessened.

     In times of peace, the modern development of marine transportation causes a country with an ocean boundary to be close neighbors with half the world, and is one of the best means of promoting commercial prosperity. The extent and character of her coastal boundary has done as much as anything else to build up New England’s manufactures and commerce. In short, in spite of the difficulties in the interpretation of the term, shore boundaries possess great advantages and are quite free from the disadvantages which we shall soon see to be common among some other boundary lines.

     RIVER BOUNDARIES. THEIR TYPES.—The position of a river boundary may be determined by any part of a river, such as the middle a bank, the deepest channel, etc. Moreover, in this paper, a sub-class under this head includes boundaries that are determined by reference to a river, for example, “parallel to and three miles north of” a stream. In New England the river boundary takes first place both in length and the number of references made to it in the charters, grants, acts, and agreements.

     No other boundary feature offers so many parts that may be taken to determine the position of boundary lines. New England seems to exhaust the list of possible references, as appears in the following descriptions.

     RIVER. NO PART SPECIFIED.—In some cases where the river is inconspicuous in width no part is specified as the boundary, as is illustrated in a part of the northeastern boundary of Maine (3).³ Here the line goes “Southerly, by the said branch, (the southwest branch of the St. John’s) to the source thereof.” (Treaty of Great Britain 1842). Another example of this is found in the most southern portion of the New York-Connecticut line, where the boundary begins “in the mouth of a brook or a river called Byram’s River, where it falls into

FIG. 1. Location map for points cited in text.

Long Island Sound, and running thence up along said river . . . (12). (Revised Statutes of New York 1881).

     MIDDLE OF VARIOUS PARTS.—The most common part of a river designated for a boundary line is the middle of its course or of the channel. This is the part of the river St. Croix used for a portion of the eastern boundary of the State of Maine. The treaty of 1782 with

     RIVER BANK.—When King Charles II of England in 1664 gave to his brother, the Duke of York, “all the land from the west side of Connecticut River to ye east side of Delaware Bay” he established a precedent that eventually determined George III, a hundred years later, to declare “the Western banks of the river Connecticut” to be the western boundary of New Hampshire (11). Since the Connecticut

river is entirely within the jurisdiction of New Hampshire, that state collects revenue from all factories using the river for power even if they are located on the Vermont shore. It also has the responsibility of building and keeping in repair all the bridges to Vermont. (Letter from the N. H. Secretary of State 1910).

     HIGHEST WATER MARK.—A peculiar local type of river boundary is found along the eastern border of Rhode Island, where the highest water mark is designated as a boundary. The line follows “the highest water mark on the easterly side of Farmer’s or Seven Mile River” (8), and “the highest water mark on the southerly and easterly side of said Ten Mile River” (9). (Decree of U. S. Supreme Court 1861).

     RIVER BOUNDARIES. DETERMINED BY REFERENCE.—This type of line might well be considered under another head since it runs over the land at some distance from the river to which it is related. But as its direction, position, and contour are supposedly determined, by a river, it seems best to discuss it here.

     The most striking example of this class of river boundaries is the eastern two-fifths of the Massachusetts-New Hampshire line (13). This was described in a declaration of the King in 1740 “as a similar curve line pursuing the course of the Merrimac River, at three miles distance on the north side thereof, beginning at the Atlantic Ocean and ending at a point due north of Pawtucket Falls.”

     The only other example in New England of a boundary determined by reference to a river is between New York on the one hand and Connecticut, Massachusetts and a portion of Vermont on the other. The Connecticut portion of this line (14) was first described as “parallel to the Hudson and twenty miles distant from it, until the bounds of Massachusetts were reached.” Later it was observed that if its course followed the constant, though slight bends in the river “it would be of such an irregular and ‘zig-zag’ character, as to make it quite unsuited for a permanent boundary between two states.” So it was agreed that the line should be a straight line, with a general direction the same as that of the Hudson River, and twenty miles distant from it.

     As actually run the line deserves to be classed with mathematical boundaries; and in its relation to the topography of the district it is

almost a crest line, and a divide. At the time it was run, it coincided with the ethnic boundary between the Dutch and English colonies. So it has the peculiar distinction of coming under six distinct classes of boundary lines. The same characteristics hold throughout most of the northern extension of the New England-New York boundary to Poultney River.

     The early coincidence of the ethnic, physical and political boundaries in this region was not accidental. The Indians sold grants of land along the Hudson, above the gorge, to the Dutch and described the eastern boundary as a line parallel to the Hudson and half a day’s walk distant. This is practically the crest of the highlands. The Dutch settled their grant and came under the jurisdiction of New Amsterdam which is now New York. So it would seem that topography was the controlling factor in fixing the position of the line.

     In Massachusetts the precedent established by Connecticut and New York was followed, for the, line is here straight, with termini twenty miles from the Hudson River, so that it follows the general course of the river (15). A nearly similar relation holds in the Vermont section of the line (16).

     ADVANTAGES OF RIVER B0UNDARIES.—The most obvious advantage of a river boundary is that it can be easily described in a treaty and indicated on a map. Moreover, its position is so unmistakable, that no survey is needed to identify it. Again, except where interrupted by falls and rapids so that it can be used for power, a river seldom leads to industrial controversies between the sections which it bounds. Also in times of war the river boundary has to a certain degree the same advantages as a coast with its harbors and a mountain range with its passes. The fording places and bridges like the harbors and passes are but places for the concentration of forces, while the other parts may serve as lines of protection. The New England states have never had occasion to test this use of the river boundary.

     All the disputes over river boundaries in New England have resulted from the inadequate wording of treaties, as in the cases where the St. Croix river is mentioned without stating which of the several rivers of that name is meant, or from hostility to accepting a certain river as a boundary because it did not include the right area, which happened when New Hampshire refused to accept the Connecticut as her western boundary. There has been no controversy over the position of the line when once a river was accepted.

     DISADVANTAGES OF RIVER B0UNDARIES.—Of the disadvantages of the river boundary probably the greatest results from the inconstancy of rivers. The part specified in a treaty is liable to change, be it

the middle of the river, the main channel, the deepest channel, one of the banks, or highest or lowest water mark, and with a change may come controversies and inconveniences. This is especially true of rivers meandering in broad flood plains, for such are likely to change their course and transfer much land and possibly people from one jurisdiction to another. The lower Rio Grande has often played such a part and by transferring people from the United States to Mexico or the reverse has well demonstrated the inconveniences of river boundaries. Since New England has been recently glaciated, it has few rivers of this type, and none of these now serve as boundaries.

     Rivers with falls, which are valuable commercially, are often sources of disputes if they serve as boundary lines, especially between nations. The Niagara is most famous. In 1910 the water power of the Niagara and other rivers between the Great Lakes led to a treaty between the United States and Great Britain which establishes an international commission to investigate any question arising in respect to the boundary.

     Lord Curzon⁷ points out that rivers as the creation of nature, in contradistinction to the creation of man, are natural boundaries; but in relation to the natural habits of man, rivers are not the natural divisions, because people of the same race are apt to reside on both banks. This relation of rivers to people, in the early history of New England, nearly established a new state under the title of “New Connecticut,” in the valley of the Connecticut river, north of the Massachusetts line. Settlers on one side of the river had closer social bonds with those on the other side, than they had with the colonists over the divide at their backs, and so they desired close political union with them. Outside influence prevented the consummation of this inclination.

     A similar relation between rivers and people was responsible for moving the northern limit of New England from the St. Lawrence river, as it was previous to the cession of Canada from France to Great Britain in 1763, southward to a divide.

     3. LAKE BOUNDARIES.—The northern two-thirds of the New York-Vermont boundary is the most conspicuous example of a lake boundary in New England (17).

     Here, in Lake Champlain the line follows the deepest channel between certain islands. The longest and probably the most important lake boundary in the world, that of the United States and Canada in the Great Lakes, with the exception of part of Lake Superior, follows the middle course of the lakes. This seems to be the just position of such a boundary. Conditions in Lake Champlain rendered such a position inadvisable for numerous islands would have been thereby divided between the adjacent states.

     SOUND BOUNDARY.—The southern boundary of Connecticut is a line through Long Island Sound, (23-31-32). For years Connecticut acknowledged that New York owned “all the islands specifically named in her boundary statute” . . . but she denied “that the general dividing line between the States is farther north than the middle line of the Sound.”⁸ Thus it seemed at one time that the middle line of the Sound would become the boundary, but in 1880 commissioners made the Sound line a series of mathematical lines and their report was ratified. These lines practically follow the middle of the Sound but since no part of the Sound is referred to as a controlling factor in determining the character, position, or direction of this line, they are left for consideration under mathematical boundaries.

     BAY BOUNDARIES.—The southern portion of the international boundary between Maine and New Brunswick is a bay boundary (19). In the treaty with Great Britain of 1872, Article II refers to this boundary in these words “a line to be drawn along the middle of the River St. Croix, from its mouth in the bay of Fundy, to its source,” and further on, “comprehending all islands . . . lying between lines to be drawn due east from the points, where the aforesaid boundaries . . . shall respectively touch the Bay of Fundy, and the Atlantic Ocean; excepting such islands as now are, or heretofore have been, within the limits of the said Province of Nova Scotia.”⁹

     The first reference gives merely the starting point, the first part of the second would make the boundary a parallel, and the last part nullifies the first by making it a tortuous line in the bay, winding seaward among the islands. A Board of Commissioners awarded three of these islands to the United States and all the rest to Great Britain. As the line is today then, it has no more specific position as far as its description goes, than a line of separation among islands.

     Actually the line is carefully marked by means of white buoys. The need of nice designation is prominently felt here because of the excellent lobster grounds throughout the bay, and the diversity of the laws of Maine and New Brunswick that control the taking of lobsters. Maine protects the young throughout the year by prescribing a minimum length, and New Brunswick aims to conserve the supply by establishing a closed season of seven months, and a minimum length, less than that of Maine, during the open season. This condition offers an opportunity to the fishermen on both sides for increasing their profits, by stealthily ignoring the position of the line.

     The southern part of the Rhode Island-Connecticut boundary is a bay boundary (20). It follows the midline of Little Narragansett Bay for several miles. The bay is an open lagoon in a glacial outwash plain into which .a river empties. It seems to have been taken to be a part of the river, for the charter of Charles II of 1663, describes Rhode Island as extending to the west, “to the middle or channel of a river there. . . .” with no specific mention of the bay boundary.

     The Southern portion of the Maine-New Hampshire line is a bay boundary (22). His Majesty’s commissioners reported, in 1735, “That the dividing line shall pass up through the mouth of Piscataqua Harbor, and up the middle of the river,” and, “that the dividing line shall part the Isle of Sholes, and run through the middle of the harbor, between the islands, to the sea on the southerly side. . . .

     DIVIDE BOUNDARIES.—In New England, for over eighty years, a boundary determined by a divide was the cause of disputes. Historically, this line was first described by a proclamation issued by Great Britain, in 1763, following the Peace of Paris of that year. The line was to cross the St. Lawrence and Lake Champlain in the 45th degree of north latitude, “and thence to proceed along the highlands which divide the rivers that empty themselves into the St. Lawrence from those which fall into the sea.”³

     This precedent led Great Britain, in the treaty of 1782, in describing the limits of the United States, to declare this part of the boundary to be “From the northwest angle of Nova Scotia . . . along the highlands which divide those rivers that empty themselves into the river St. Lawrence from those which fall into the Atlantic Ocean, to the northwestern-most head of Connecticut River. . . .

     It will be observed from the map (Fig. 1) that there is a main

divide and a subdivide in this section of the country. One truly divides all the rivers flowing into the Atlantic from those emptying into the St. Lawrence; the other separates the basins of the St. Croix, Penobscot, Kennebec, etc., from those of St. John, Chaudiere, St. Francis, Yamaska, etc. But the St. John is an Atlantic river and so ought not to be grouped with the St. Lawrence rivers. However, Great Britain reasoned that as in the treaty the St. Lawrence bay was not considered a part of the Atlantic ocean, so the Bay of Fundy, into which the St. John empties, should not be so considered. Hence the St. John is not an Atlantic flowing river. So the highlands to the south were those referred to according to the contention of Great Britain. She was so persistent in this view, apparently for strategic reasons, that compromise finally resulted, concerning which, Webster, who represented the United States, declared the underlying principle to be “that the arrangement shall be for the mutual convenience and advantage of both parties, if the terms can be made fair, and equal, and honorable to both.”

     As a result the divide boundary was cut down to one fourth the length it would have had, had the “American line” been adopted. As it is today, the boundary extends from the source of the southwest branch of the St. John’s “in the highlands at the Metjarmette portage; thence down along the said highlands which divide the waters which empty themselves into the river St. Lawrence, from these which fall into the Atlantic Ocean, to the head of Hall’s stream”¹⁵ (25).

     The geographic lesson taught by such an outcome seems to be that in a little known country even a divide boundary designated with careful specifications, can be brought into dispute, if the incentive is great enough.

     As has been stated above, the line which forms the western boundary of Connecticut, Massachusetts and a portion of Vermont, (14-15-16), practically follows a divide which is nearly at the crest of the Taconic Mountains. Along the southern course, it is the divide between the Hudson basin and that of the Housatonic; and in the northern part, it is a subdivide between the Hudson and its tributaries, especially the Hoosic. But since this boundary was not defined as a divide boundary, it will not be considered here as such.

     CREST BOUNDARY.—A crest boundary may be defined as one that follows the highest parts or summits of a range of hills or mountains. It does not necessarily coincide with the divide, for any considerable distance, and may not even approximate it. Land forms are so variant

in degree of resistance that some rivers, by headward erosion, or otherwise, may have carved their valleys far beyond the general crest line, while others are just approaching it. So the crest line is often very discontinuous. Such is the relation between the divide and crest line in the Andes, where is located the disputed Argentina-Chile boundary; also, in the northward extension of the Rockies, where the Alaska-Canada line was first described as following the summit of the mountains situated parallel with the coast.

     As far as specific reference to a crest line goes, New England furnishes no example in her boundaries. But in following a line parallel with and twenty miles east of the Hudson, sections of the eastern New York boundary approximate closely the crest line of the Taconic Mountains, as has already been noticed.

     Crest lines, like divides, form lines of separation far from the scenes of people’s usual activities, and thus are well adapted to serve as boundaries. But because they are seldom continuous and at best difficult to ascertain, they are less desirable than are divides. Lord Curzon¹⁶ in referring to the Alaska-Canada line, questions “the practicability or meaning of a line that scaled inaccessible peaks and was lost amid ice and eternal snow.”

     PARALLELS.—The shape of the earth is such that lines can be precisely located on its surface in relation to its daily motion. One set of lines so determined are east-west lines or parallels. They are more extensively used as boundary lines in the United States than are any other mathematical lines.

     In fact, with the exception of Maine, New Jersey, and Ohio, there is no state in the Union that does not include at least part of one parallel in its boundary. Even in Maine part of the boundary was originally described as a “due east line” but was nullified later; and Ohio, in her constitution, defined the northern boundary as an “east and west line” but that was also made void. One cause for the extensive use of parallels in United States seems to be the comparative ease with which they can be described by diplomats in relation to sections sparsely inhabited, and little known. Another cause that probably had some influence., is the north and south direction of the coast line and the habit of making one set of boundary lines at right angles to the coast line. Still another cause is the early movement of settlement from east to west.

     In New England the international representative of this type of boundary is in Vermont (26). In the Treaty of 1842 with Great

Britain, this was referred to as “the old boundary surveyed and marked by Valentine and Collins, previously to the year 1774, as the 45th degree of north latitude. . . .” This boundary was first described when England acquired Canada from France in 1763 by the Peace of Paris. It was then that the claim of Massachusetts to the north bank of the St. Lawrence river was disallowed by England and Massachusetts was limited by a line “that was to cross the St. Lawrence and Lake Champlain in the 45th degree of north latitude, and thence to proceed along the highlands. . . .”¹⁷

     In making this change Great Britain was apparently prompted by a desire to bring her newly acquired sections of ethnic homogeneity, (Quebec, New Brunswick and Nova Scotia) into closer physical or geographic union. When the desire was felt, the maps of the region were inadequate to suggest to British diplomats any physical features that might serve the purpose of a boundary, and the region had been little explored. Hence for convenience and exactness the parallel seems to have been adopted.

     The greater parts of the northern and southern boundaries of Massachusetts (27 and 28) are described in the original grants, in terms that would seem to mean parallels, and attempts were made to locate them as such, but inadequate geographic knowledge prevented this. In a decision promulgated by the Lords of Trade in March, 1740, the western part of the northern boundary of Massachusetts was described as beginning at a point “three miles due north of Pawtucket Falls, and thence due west to His Majesty’s other governments.”¹⁸ Thus three fourths of the northern boundary of Massachusetts was defined as the parallel passing through a point three miles due north of Pawtucket Falls on the Merrimac. Richard Hazen attempted to mark this line in 1741, under instruction from Governor Belcher, and allowed for a westerly variation of the needle of 10 degrees. This variation was later found to be too large.

     Another error was made in the line, for a constant variation of 10 degrees was used, whereas it should have been constantly decreased from east to west, the total decrease being about one degree. Hence the line curves to the north, favoring Massachusetts. Nevertheless, the line as run was accepted and is still the boundary.

     The other Massachusetts boundary that was first interpreted to be a parallel (28-29) was defined in a grant from the council of Plymouth of 1628 in these terms: “all . . . landes . . . lyeing within the space of Three Englishe Myles on the South Parte of the said River called Charles River, or of any or every Parte thereof . . . lyeing within the Lymitts aforesaid, North and South, in Latitude

and Breadth, and in Length and Longitude . . . from the Atlantic . . . ocean . . . to the South Sea.”¹⁹

     Commissioners from Massachusetts and Rhode Island in 1710 discarded the due west line, for some reason not apparent, and adopted one that was to start from a point “3 English miles distant southward from the southernmost part of the river called Charles River,” and run, “so it may (at Connecticut River) be two and one half miles to the southward of a due west line.” This brought about a series of controversies over this section of the line (29), that lasted for nearly two hundred years and in which were involved two appeals to the Supreme Court of the United States. Gannett pronounces this prolonged dispute “in some respects the most remarkable boundary case with which this country has had to do.”²⁰

     The reason for this seems geographic. The country over which the line was to run was comparatively level and relatively inviting for settlement, and although distant from the coast line, was much frequented by colonists passing between the Massachusetts Bay settlements and those of Long Island Sound and Narragansett Bay. Thus it was early known and settled, long before an attempt was made to fix the boundary line formally. As early as 1642 a stake was set up on the plain at Wrentham to mark the commencement of the line but the westward extension was not designated. Each colony granted to settlers sections which were presumed to be within its jurisdiction. But since the definition referred the line to no topographic feature, except the point of departure, it could not be ascertained exactly except by skilled geodesists. Thus is illustrated one of the disadvantages of the mathematical line as a boundary. Nevertheless a line of jurisdiction was early established, but this only approximated the defined line of the grant. This gave the colonies, and later the states, many grounds for dispute, and so followed a long controversy. The jurisdictional boundary, a very irregular line, was finally adopted in 1881 and is still extant. It is treated under parallels because its progenitor was a parallel, and a parallel determined its general direction, position, and extent.

     The other portion of the parallel which is a part of the southern boundary of Massachusetts, is that separating it from Connecticut (28). This underwent a similar history, and reached a termination similar to the Rhode Island section. As it is today, it is made up of sections of parallels, other mathematical lines (town boundaries), and short topographic lines. It however approximates the parallel originally

described as that of a point three miles south of the southernmost part of the Charles River.

     The method of defining a boundary by giving its latitude in degrees as was done with the parallel of 45° in northern Vermont, is very common in the West. Another means, however, has been employed in separating North and South Dakota. The dividing line agreed upon when they were admitted as states was the “seventh standard parallel” from the base of the fifth principal meridian. The “standard parallels” are those which have been carefully laid out by government geodesists in certain parts of the country, as standards for local surveys of boundaries of smaller divisions. “This line is about four miles south of the parallel 40 degrees from the Equator, and was chosen in preference to the geographic parallel because it was the boundary line between farms, sections, townships, and to a considerable extent, counties.”²¹

     A peculiar method of referring to parallels is found in the Treaty with Great Britain in 1782 in defining the limits of the United States. The line was defined to the Mississippi River, “thence by a line to be drawn along the middle of the said river Mississippi until it shall intersect the northernmost part of the thirty-first degree of north latitude.”²² The same method was employed in the Revised Statute of New York of 1881, relative to the southern boundary of that state. The act reads: “then south along said meridian line to a monument in the beginning of the forty-third degree of north latitude . . . then east along the line . . . in the same parallel of latitude.”²³ The parallel meant here is the forty-second. It was so run and marked.

     In both cases the idea of a parallel of latitude seems to be a band about the earth parallel to the equator and one degree wide, with the “begining” nearest the equator.

     The advantages and disadvantages of parallels as boundaries are nearly identical with those of other mathematical lines, so they will be numerated later in relation to the larger class.

     MERIDIANS.—In the United States among mathematical boundaries, meridians are second only to parallels in extensiveness of use. Meridians as boundaries are illustrated in New England by the northern half of the eastern boundary of Maine (30), and the greater part of the Rhode Island-Connecticut boundary (38).

     “STRAIGHT LINE” BOUNDARIES.—The “straight line” as used in a boundary definition means the line of intersection between the earth’s surface and a plain which contains the termini of the line and the center of the earth, and which unlike a meridian or parallel, does not depend upon the movement of the earth for its direction. Although called “straight” this line is usually very irregular, due to the irregularities of the surface over which it runs. And if the surface were an ideal plain, the line would not be straight because it would be on the surface of a nearly spherical body, the earth. It would really be the arc of a great circle.

     After all, the limit of jurisdiction is a plane. The aerial extension may not be commonly conceived until aeroplanes and balloons become much more numerous, but the subterranean extension is of great importance in mining regions. So a boundary is really a plane. It was so acknowledged in a description of a boundary monument to be used on the U. S.-Mexico line as given in a report of the Commissioners. It reads; “These rings will be placed, one at the top of shaft, the others twelve inches below, and will be carefully located in the plane of the boundary.”

     Under this conception the straight line boundary becomes a part of a plane which contains the given termini and the center of the earth. It is the intersection of this plane and the earth’s surface nevertheless that monuments mark; so that is the important thing, as far as the present use of the boundary outside of mining regions is concerned.

     An example of the “straight line” boundary in New England is the northern portion of the Maine-Quebec line (35), which is a portion of the compromise line between Canada and the United States. In the treaty with Great Britain of 1842, it is described as running from the outlet of Lake Pokenagarnook; “thence southwesterly, in a straight line, to a point on the northwest branch of the river St. John, which point shall be ten miles distant from the main branch of the St. John, in a straight line, and in the nearest direction.” In this case drainage features are used to determine the position of the termini, with another straight line as an auxiliary.

     The next section of the compromise line to the south is also a straight line (36). From the southern terminus of the line just described, it runs, “in a straight line, in a course about south, eight

degrees west, to the point where the parallel of latitude 46 degrees 25 minutes north intersects the southwest branch of the St. John’s.” Such a reference to a point could be made only in a region that had been carefully mapped and such a point could not be actually located without the aid of skillful geodesists. The line has numerous monuments to show its course.

     The longest straight line boundary in New England is the central part of the Connecticut-Long Island line (31). The ratified report of the commissioners in 1880 gave this part as running from the end of a true southeast course three and a quarter statute miles from Byram Point, “thence in a straight line (the arc of a great circle) northeasterly to a point four statute miles due south of New London Light House; . . .”²⁶ This line is eighty-two statute miles long. With a few short segments of loxodromic curves at either end it determines the respective jurisdictions of New York and Connecticut over the waters and islands of Long Island Sound.

     The straight line boundary is illustrated outside New England by portions of the U. S.-Mexico line. California is separated from Lower California by “a straight line drawn from the middle of Rio Gila, where it unites with the Colorado, to a point on the coast of the Pacific Ocean distant one marine league due south of the south-westernmost point of the port of San Diego.”²⁷

     Such a line was used in the Gadsden Purchase of 1853, with short stretches of parallels and meridians. It follows roughly the southern divide the Gila River and so fixes a large part of the United States-Mexico boundary. The reason why the mathematical approximate of this divide should have been used instead of the topographic feature is not clear. The topography is everywhere pronounced making the divide conspicuous. Thus it would have required only a hasty reconnaissance to locate the line and only a few monuments to mark it. As it was, an extended and costly survey had to be made and many monuments erected, some with difficulty and hazard on precipitous slopes.

     A rectangular relation is found between the straight line and the divide in the northern part of the Wisconsin-Michigan boundary. A similar relation holds between a straight line and the divide between the Hudson Bay and Gulf drainage in a part of the Minnesota-South Dakota line.

     The New York-New Jersey boundary is “a direct or straight line.” Before the District of Columbia ceded a portion of its area to Virginia, it was practically a square, bounded by four ten-mile “direct”

lines. The longest “straight line” boundary on the earth is that which constitutes the greater part of the eastern limit of California.

     LOXODROME BOUNDARIES.—The loxodrome boundary is a curve that cuts all meridians at the same angle and is oblique to parallels, or it may be defined as a line of constant bearing. It will be observed that this line is unlike the “straight line” in that it cannot be contained in a plane.

     In early times, when surveyors had meagre and uncertain knowledge concerning the magnetic variation of the compass, they often allowed for too much or too little variation in fixing boundaries, determined by parallels of latitude. The resulting line was a loxodrome, providing correction was made for the differences of variation in different places. Thus, if the latter provision had been made in running the parallel of northern Massachusetts, since the primary variation was too great, the line would have been a loxodrome. As it is the line is very nearly one.

     The mathematical portion of the Maine-New Hampshire boundary (37) is a loxodrome as expressed in the report of a board of commissioners in 1737. From the “furthest head” of the Newhichawack River, the line was to “run north two degrees west till 120 miles were finished . . . or until it meets with His Majesty’s other governments.”²⁸ A portion of this line was “spotted and measured” in 1741, a continuance in 1767, and the remainder in 1789.

     It was claimed by Massachusetts, with seeming justice, that the first surveyor did not make due allowance for the variation of the compass. It is probable the other two did not correct for annual change in the variation. All three let topographic features influence mildly the position of the line, according to their convenience. So it will be seen the marked line only approximates the loxodrome described in the early papers.

     Other examples of the loxodromic boundary in New England, are found in short portions of the Connecticut-New York line in the Sound. Here they are referred to as “a true southeast course” (23), “east three-quarters north, sailing course” (32), etc. Other varieties of expression for the loxodrome are “a line to be run north 45 degrees east” till it intersects a specified river, as in the description of the Virginia-Kentucky boundary; and “from Goat Island northwest to the 35th degree parallel,” as in that of the North Carolina-South Carolina line.

     The loxodrome is not used nearly so often as a boundary as are the other mathematical lines mentioned above. When it is used in documents the engineers in the field, either through ignorance

or for mutual convenience are likely to convert it into a straight line, or a broken line made up of a series of straight lines which approximate the true curve.

     ARCS OF SMALL CIRCLES.—This class of mathematical boundaries has no representative in the boundaries of the New England States, but is considered here to round out the class, and because it is an interesting member of the group. As a boundary line a small circle may be defined as a circular arc of small radius, which has for its center a natural or artificial object.

     The only state boundary in the Union that includes a circular line is that of Delaware-Pennsylvania. It is described as “an arc of a circle, having for its center the steeple of the old court-house at New Castle, Delaware, and a radius of twelve miles.”²⁹ This circular boundary of a state was evolved from a county line which was described in a conveying deed as “the town of New Castle and a twelve-mile circle around the same.”³⁰ Later Delaware was formed by the union of three counties, one of which was New Castle.

     The work of running the line was done years after its definition, and was attended by many surveying difficulties. Such a line in order to be recognized has a unique disadvantage as a boundary, in that it requires an almost continuous visible indication of its course.

     The circular boundary is used in the United States very sparingly for town boundaries. Some of the old Hanse towns of Germany were bounded by circular lines.

     The study of the mathematical boundaries of New England has shown that, in general, they can be easily expressed in treaties, even in reference to a country that is little known. This explains why they are so common in the United States, Canada, Africa, and Australia. Mathematical boundaries can also be easily identified on a map; they can be definitely located on the ground; and, unlike some river boundaries, their courses can be precisely marked by monuments.

     Their one great drawback, and this is vital, is that unless they are carefully related to the topography, they are almost certain to create political divisions in ethnic, physical, industrial, and perhaps religious units, and this may be a basis for strife. Hence the mathematical boundary, especially if it is international, is liable to undergo changes until it becomes more harmonious with the surroundings. This may be one reason why there are so few boundaries of this type in Europe and Asia.

     BOUNDARY MARKS.—Some of the marks by which the courses of the early boundary lines of New England were indicated were indeed crude and inadequate. Yet some of these are still extant as the only authoritative marks. The loxodrome boundary of the Maine-New Hampshire line illustrates the matter. A part of the record reads: “thence same course two hundred twenty-five rods across a bay of said lake; thence same course two hundred six rods across a peninsula of the same; thence same course . . . across the north bay of said lake, to a cedar post marked “N.” “M.” . . . thence same course one hundred sixty-two rods to a spruce . . . thence to a perpendicular precipice; thence same course . . . to a beaver pond; thence same course . . . to a yellow birch on the highlands.”³¹

     It will be easily seen how forest fires, clearings by man, and destruction by natural agencies would soon make such a record nearly worthless. It was such a description of a boundary line that made Rufus Choate exclaim, “I would as soon think of setting forth the boundaries between sovereign states as beginning at a blue jay on the bough of a pine tree, thence easterly to a dandelion gone to seed, thence due south to three hundred foxes with firebrands tied between their tails.”³²

     CONDITIONS NEAR BOUNDARIES.—The effect of a special geographic feature such as a boundary may be clearly seen in the people who live near it, especially if the line is undetermined, ill-defined or disputed. This is well illustrated in the history of the Sound boundary between Connecticut and New York. Before the definite establishment of this line, many of the islands in the Sound were used as convenient resorts by persons wishing to engage in illegal trades or practices, since an arrest under authority of either state might be met by a claim of jurisdiction of the other. The following citations of illegal proceedings in relation to this region are abridged from the New Haven Historical Society Papers, Vol. III.

     On one occasion, a party of prize fighters and spectators from New York landed on one of the questionable islands to have an encounter. A company of Connecticut militia was levied, rushed to the scene of combat, and captured the whole party. The counsel of the prize fighters took exception to the jurisdiction of the Connecticut courts on the ground that the acts complained of were committed in New York, and the cases were never brought to trial.

     A case of piracy occurred on a schooner lying a distance from shore in the Sound. The offender was seized, tried and convicted, but the Supreme Court of the United States arrested the sentence of death, because it was doubtful whether the spot where the schooner lay, was or was not within the jurisdiction of New York. A second trial resulted in the pirate’s discharge, because the jury were of the opinion that the act was done outside the jurisdiction of the court which tried him.

     Thefts and assaults occurred on the many steamers and other crafts plying the Sound, and it was always questionable in what jurisdiction they were to be deemed committed,

     The notorious pirate, Captain Kidd, used a small group of the Sound Islands as his haunt because of their inviting position in relation to the unsettled boundary.

     Previous to 1853 the boundaries of Massachusetts included a small district in the southwestern corner, called Boston Corner, that was separated by rugged highlands from the rest of the state. For obvious reasons, this became a resort for desperadoes. This condition finally brought about its transfer to the neighboring state of New York.

     The more usual activities of people near boundary lines, take the form of evasion of taxes and license laws, illegal voting, and the like. To facilitate the evasion of laws hotels are often built along the line. Experience with this condition led the United States commissioners of the U. S.-Mexico Boundary Commission to recommend that a reservation of not less than fifty feet be declared by the United States to extend along the entire length of the boundary on the American side, and that the Republic of Mexico be asked to declare a like reservation on the Mexican side, and that the erection of buildings on either side, within these limits be prohibited.