Placing the Post Mark’d West

Features appear in each issue of Pennsylvania Heritage showcasing a variety of subjects from various periods and geographic locations in Pennsylvania.

After eighty years of contention, in 1763  the proprietors of Maryland and Pennsylvania em­ployed Charles Mason and Jeremiah Dixon to settle the boundaries between their provinces “for all times forever hereafter.” Mason and Dixon were astronomers associated with the Royal Observatory in England and were well versed in the mathematical and other skills needed for this complicated project. The most critical step in the task which would occupy them for the next four years was selecting the starting point for the east-west line which would mark the northern boundary of Maryland and beyond to the western extent of the survey.

This line, which Mason and Dixon called the “Western Line,” but ever since known as the Mason and Dixon Line, was the most extensive phase of their work and was destined in future decades to take on special significance as the dispute between North and South grew heated. But the issue in 1763 was how to divide the land and its bounty in a way the pro­prietors would accept. It is one of history’s ironies that this thorny issue was finally resolved, after numerous attempts and much litigation involving several generations of Calverts and Penns, only about a decade before the revolution which would strip these great land owners of their New World colonies.

According to the agreement which served as the basis of Mason and Dixon’s work, the Western Line was to be drawn due east and west, fifteen miles south of the most southern point of Philadelphia. Among other things, Mason and Dixon were to establish the latitude of the southern edge of Philadelphia, measure the prescribed distance southward and run the Western Line. Location of the starting point of the Western Line was vital, considering that the Western Line would eventually mark 196 miles of boundary. Each foot that the starting point was too far north or south would place nearly twenty-four acres in the wrong province.

When the Western Line was resurveyed one hundred and forty years later, W. C. Hodgkins, the engineer in charge, calculated that Mason and Dixon’s starting point was a little more than four hundred feet too far south, with adverse conse­quences for the Province of Maryland. To see how this may have happened, and to appreciate the care with which Mason and Dixon labored, it might be well to review the work which led to placing the “Post Mark’d West,” as it is so often called in Mason and Dixon’s Journal.

A series of agreements from 1732 to 1760 between the proprietors of Pennsylvania and Maryland, and ratified by the Lord Chancellor of London, laid the groundwork for the employment of Mason and Dixon to put a “final and perpetual end forever to all disputes and differences between the parties” regarding the extent of their provinces. On December 5, 1763, twenty-one days after arriving from England, the two surveyors ordered a shelter built to serve as an observatory near the point which had been established as the “South Point of the City of Philadelphia.” Following several cloudy days, Mason and Dixon began their star obser­vations on December 19.

Since their objective was to fix the latitude of the southern edge of Philadelphia, they employed a “zenith sector,” an in­strument enabling them to measure the angle between a point in the sky directly over their observatory and the star they were observing. At the exact moment when the star was on their meridian, or directly north or south of their position, the zenith angle was noted with all the precision that their sector would allow. This zenith angle, combined with the star’s decli­nation – the known angular distance that the star was north or south of the equator-was used to establish the latitude of the observatory.

The observations continued over several nights with the plane of the sector (the flat side with the scale) facing east. On December 28, the sector was turned so that the plane faced west and observations continued until January 4, 1764. Averaging the results of the two sets of observations helped compensate for tiny inaccuracies in the sector’s scale.

Mason and Dixon made numerous observations on eight stars and selected five of them for latitude purposes. They took the declinations of these stars from tables “per Dr. Bradley,” a former director of the Royal Observatory, and they made the corrections usually applied to star observations to allow for irregularities of motion and the physics of light transmission. Finally, they allowed for the short distance which their observatory stood north of the southern point of Philadelphia, concluding that this critical point was at 39° 56′ 29.1″ north latitude. In his report of the resurvey work done in 1900-02, Hodgkins commented that the current charts gave the latitude of this point (as nearly as it could be identified) as 39° 56′ 26.6″, a discrepancy of just 2.5 seconds.

The precise latitude value of the south point of Philadelphia was not needed in determining the position of a point 15 miles due south. That is, the absolute latitude value was immaterial and only the measurements of the zenith angles of the stars were critical to this phase of the survey. But the agreement did call for establishing the latitude of this point and the precision of Mason and Dixon’s astronomical work is evidenced by the close agreement between their calculations and later deter­minations.

Because a due south line beginning at their Philadelphia observatory would cross the Delaware River into New Jersey, Mason and Dixon moved to a site near “the house of Mr. John Harlands,” about 31 miles to the west. They used a quadrant (similar to a modern sextant) to find a spot on nearly the same parallel of latitude as the southern point of Philadelphia. After selecting a location in Harland’s garden, on January 14 they began a series of star sightings to find the zenith angles of the same stars they had observed in Philadelphia. (In keeping with Mason and Dixon’s Journal, the name Harlan is spelled Harland throughout this article.)

Interruptions due to snow, rain and cloudy weather extend­ed this phase of their work to February 28. The next day they computed zenith angles for the eight stars they bad observed previously. Upon comparison, the new angles differed from the former by 8.6 to 12.7 seconds of arc. Computing a mean of the differences, weighted to consider the number of times each star was observed, they concluded that the mean difference was 10.5 seconds. They also computed the latitude at Harland’s garden, using the measurements for the same five stars they had used in Philadelphia. On comparing latitudes, they found a difference of 10.2 seconds, or .3 second less than the difference in the zenith angles computed from all eight stars. They decided to accept 10.5 seconds as the true dif­ference because “the mean of the results from eight stars must be prefer’ d to that of five.” This decision regarding .3 second of angular measurement became a factor in computing the distance that the observatory near John Harland’s house was south of the southern point of Philadelphia and saved Maryland over 700 acres along its northern border.

Mason and Dixon were now ready to measure to a point 15 miles due south, less an allowance for the 10.5 seconds. Because the figure of the earth was not then thoroughly understood, and no previous attempts had been made to measure accurately the linear distance equivalent to a degree of latitude in the vicinity of Philadelphia, Mason and Dixon used “Norwood’s measure” of 69.5 miles as the length of a degree. With 3,600 seconds in a degree, this length gives a distance for 10.5 seconds of 1,070.3 feet, or 356.8 yards. On this basis, Mason and Dixon calculated that their new obser­vatory was about 357 yards south of the southern edge of Philadelphia, but they were careful to note that, “if we find the Arch in the Heavens not to agree to Mr. Norwood’s measure, 69.5 to a Degree we shall account for the 10.5″ ac­cordingly.” That is, after measuring 15 miles due south and finding the zenith angle corresponding to that measure, they planned to recompute the linear distance equivalent to an angle of 10.5 seconds. When this was done in mid-June 1764, Mason and Dixon corrected the allowance for 10.5 seconds to 350.24 yards on the basis that one degree was equal to 68.223 miles, a finding that was about as much less than the correct value (68.98 miles) as “Mr. Norwood’s measure” was too great.

When Mason and Dixon were ready to start measuring to the south, they needed a star observation to determine the proper direction. Not until March 16 did cloud conditions permit an observation to prove the direction of the meridian and allow them to start cutting a clear line through the forest. On April 2 they began measuring from their observatory in Harland’s garden. Their principal measuring device was a surveyor’s chain, consisting of one hundred links, each link being a length of heavy wire with a loop at each end. The chain was sixty-six feet long and fitted with handles so that it could be pulled tight. This length was widely used for surveying because it was convenient to handle and because it related easily to other measures. Since the chain consisted of one hun­dred links, each link was 7.92 inches from the inside of the loop at one end to the outside of the loop at the other end; one mile was equivalent to eighty chains.

To obtain horizontal equivalents for slopes, Mason and Dixon used long wooden pieces called “levels.” These were held horizontally, probably with one end touching the ground at the uphill end. The upper end of another level was then placed, with the aid of a plumb bob, immediately beneath the downhill end of the first level. On the first few slopes they used levels twenty-two feet in length (one-third of a chain), but these proved to be too cumbersome so they changed to levels 16.5 feet in length. This length, still known as a rod, is much easier to use and also relates well to other measures. Each rod is one-fourth of a chain in length.

On flat ground, Mason and Dixon recorded their measure­ments in chains and links. On the slopes, they recorded their measurements in levels. The levels were converted to chains by dividing by four, and the total distance measured was finally expressed in miles, chains and links. By April 12, Mason and Dixon had measured a horizontal distance of slightly less than 15 miles. They added 357 yards for the distance the observa­tory in Harland’s garden was too far south, and concluded that a tree in the southern fence line of a field belonging to “Mr. Bryan,” was 15 miles, 2 chains and 93 links south of the southern edge of Philadelphia. They then moved back 2.52 chains to a suitable location for an observatory, at what they believed was nearly the proper distance south of Philadelphia.

Moving their equipment to Bryan’s field, they made new star observations as weather permitted. On May 14 they began to remeasure the distance along their north-south line to verify their previous measurements. They found one 5.29-mile sec­tion of the line with a discrepancy of several chains, so this sec­tion was measured a third time, with the last two measurements differing by just a few feet and being seven chains less than first thought. If they had not made this remeasurement, the Maryland-Pennsylvania boundary might have been placed seven chains farther north; nearly 11,000 acres now in Pennsylvania would be in Maryland. Another section of 2.33 miles showed a discrepancy of thirty-five feet, so this was also measured a third time. After discarding the measurements believed to be in error, Mason and Dixon had two lengths for each of five sections of the line that differed by only a few feet. For each section of the line they averaged the two measurements and calculated the total distance between the observatory location in Harland’s garden and the tree on the south edge of Bryan’s field to be about 14.75 miles. They added 357 yards for the distance that Harland’s garden was south of the parallel of Philadelphia, producing a total distance of about 14.94 miles, including an allowance of 71 links for slopes not measured with the levels. Again they noted that the 357-yard distance would be adjusted, if necessary, after they made new star observations, but they thought that any change would be very small.

Until June 11, they were occupied with star sights and calculating zenith angles for the new observatory location in Bryan’s field. Numerous observations were made on five stars from this position, but only two of the stars, Cappella and Vega, were the same as the stars used previously. The dif­ferences between the zenith angles measured in Harland’s garden and Bryan’s field were 12′ 54.3″ for Cappella and 12′ 57.2″ for Vega. Mason and Dixon averaged these values and used 12′ 55.8″ as the zenith angle corresponding to the measured distance of 1,176 chains 17 links between the two observatories. Setting 12′ 55.8″ equal to this value gives a distance of 68.223 miles for one degree and 10.5 seconds becomes 350.24 yards, as described earlier. Converting all of the measurements and calculations thus far to yards gives the following:
 

Southern Edge of Philadelphia to Observatory in Harland’s Garden 350.24 yards
Observatory in Harland’s Garden to Observatory in Bryan’s Field (1,176.17 chains) 25,875.74 yards
Observatory in Bryan’s Field to Tree in Fence Line (2.52 chains) 55.44 yards
Total 26,281.42 yards

Since 15 miles contains 26,400 yards, the tree was evidently 118.58 yards north of the proper point. This distance plus the 55.44 yards from the observatory to the tree amounts to 7.91 chains, which Mason and Dixon measured south from the observatory in Bryan’s field and there, still in Mr. Bryan’s plantation, on June 12, 1764, set the famous “Post Mark’d West.”

Thus, the placement of the Post Mark’d West 15 miles south of Philadelphia was determined by measurements over the ground, except for the northernmost 350.24 yards which was calculated from the relationship between the zenith angles of the stars and the measured distance between the observatories. The methods employed by Mason and Dixon were appropriate to the problem and demonstrated a sophisticated knowledge of astronomy. Their measurements were carried out with as much accuracy as the precision of the instruments and the skills of the surveyors and the chainmen would allow. The errors which crept in were of the sort that still trouble surveyors, particularly keeping an accurate count on the chains and levels, as well as errors in the chain measurements produced by differing tension, temperature variation, lack of accurate standardization and wear. Weather conditions and terrain were difficult and the results must be viewed as remarkably accurate for the day.

Looking back 140 years, Hodgkins expressed surprise that Mason and Dixon found a difference in latitude of 13′ 11.5″ between the southern edge of Philadelphia and the Post Mark’d West, since “15 miles in that latitude are actually equal to 13′ 2. 7″.” It seemed strange to him that their measured interval was (according to his charts) 404 feet more than 15 miles and their arc was 8.8 seconds too great, “especially as they based their computations upon a length of a degree of latitude equal to 69.5 miles, about 1,000 yards greater than the true value.”

Of course, Hodgkins knew more about the figure of the earth than did Mason and Dixon, having as he did the benefit of very accurate triangulations carried out by the U.S. Coast and Geodetic Survey. But he was wrong in stating that they based their computations on one degree being equal to 69.5 miles as they had abandoned Norwood’s measure and used 68.223 miles as shown above. The 68.223 value eventually proved to be about the same amount too low as 69.5 miles is too great. But there was no way they could notice the discrepancy which Hodgkins questioned since using one degree as equal to their value of 68.223 miles, 13′ 11.5″ is equal to 14.9996 miles, or as close to 15 miles as could possibly be ex­pected. Their instruments and their field work may have been slightly less than perfect, but their mathematics cannot be faulted.

When measurements around the Newcastle circle (a 12-mile radius around the town in Delaware having been exempted by former agreements from the Pennsylvania-Maryland dispute) were checked by J. D. Graham in 1849, he found “striking discrepancies between some of our measured distances and those of Messrs. Mason and Dixon.” Graham’s results were determined by very careful chaining with improved equipment and he noted in connection with Mason and Dixon’s work that “their measured distances are found to be affected by many errors, incident always to measurements of great extent with the chain.” He also stated about Mason and Dixon’s work that “the fifteen miles south of the parallel of the most southern limits of the city of Philadelphia was, after measure­ment with the chain, corrected by very accurate observations for the corresponding difference of latitude.” This was not the case because, as described earlier, what was corrected was a small part of the distance (357 yards corrected to 350.24 yards) and the basis for this correction was the distance measured over the ground.

Graham provided a table comparing eleven of bis measure­ments, about a mile in length, with measurements over the same ground by Mason and Dixon. Three of these measurements show differences of eighty feet or more, which most likely resulted from an error by Mason and Dixon in counting the chains. The other eight show differences in feet as follows (a + sign indicates that Graham’s measure was the larger): +32.5, +30, -22.5, +3, +5.3, +20, +2, + 15.2. In seven of the eight measurements, Graham’s result was the larger, clearly indicating a tendency for Mason and Dixon to undervalue their distance measurements as a result of their technique, problems with the “levels,” an inaccurate chain or all three. Hodgkins’ resurvey work in 1902-03 also found many cases where the actual distance between mile posts was greater than one mile. Since Mason and Dixon measured each section of the 15 miles at least twice, it is unlikely that there was a mis­count of the chains in the final result.

The conclusion that follows is that the excess of about 400 feet cited above most likely occurred because Mason and Dixon’s chain was slightly longer than 66 feet and because of slight errors in marking the point where the chain lengths end­ed. There are 1,200 chains in 15 miles, which means that an error of 400 feet would result if the chain were 66 feet, 4 inches in length. It seems unlikely that this great a deviation would have gone unnoticed, since the journal reports that the chain was checked five times during the measurement of the 15 miles and was corrected on the one occasion when it was found to be too long.

But how the chain was checked is not clear, and they cer­tainly did not have the facilities for doing so with great ac­curacy. It is possible that the average link length was too long by a few hundredths of an inch. If so, this equipment problem, and not any carelessness on the part of Mason and Dixon, is what cost Maryland some 9,500 acres. Their painstaking ef­forts and meticulous attention to detail not only resolved a dif­ficult and long-standing problem, but provided a timeless model of the application of the principles of science.

 

Charles D. Leach is a professor of education and vice presi­dent for administration at Clarion State College. He is a former commander of the 876th Engineer Battalion of the Pennsylvania National Guard and was previously employed as director of development and research at Indiana University of Pennsylvania.