Observations for Determining the Length of a Degree of Latitude in the Provinces of Maryland and Pennsylvania, in North America, by Messieurs Charles Mason and Jeremiah Dixon

XLII. Observations for determining the Length of a Degree of Latitude in the Provinces of Maryland and Pennsylvania, in North America, by Messieurs Charles Mason and Jeremiah Dixon. Read Nov. 24, 1768. In this work, the first thing to be considered was, how to continue a right line: and this was done by setting up marks with the assistance of an equal altitude or transit instrument (for it was contrived so as to serve either purpose at pleasure), made by Mr. John Bird, of the same construction with that described by M. Le Monnier, in the preface to the single volume of the French Histoire Celeste. The cylindrical ends of the cross axis of the telescope were laid in two angles of the supporters, which rose perpendicularly from a horizontal bar, that was fastened firmly to the upper part of the vertical axis. The axis of the telescope was set truly horizontal, by a spirit level hung on its cylindrical ends. The brass frame, which receives the vertical axis, was screwed to a post fixed in the ground, in the direction of the line which was to be continued. When the vertical wire in the telescope was brought to bisect any mark, it was kept in that direction, by confining firmly, between two pushing screws, a horizontal arm that projected from a collar that surrounded the vertical axis; and, to prove that a small shock would not alter its position, a small pressure pressure was applied against one of the supporters, which being removed, it was carefully noted, whether the wire returned again to bisect the mark. At every station (or mark) the telescope was turned two or three times after the mark was fixed in the line, to prove that the said mark was truly set.—In general, the distances between the marks did not exceed a mile, nor were they less than half a one. The telescope magnified about 25 times. Three or four marks were always left standing, and on a little rising ground they would all be seen in a right line, the vertical wire in the telescope bisecting their centers without sensible error. The marks made use of in continuing the lines were concentrical circles of black and white, painted upon both sides of a board 14 inches square. This board moved in mortices made in two posts, which were drove into the ground; and, when the center of the said mark was brought, by means of signals, into the line, it was fastened by wedges to the posts. By means of a plummet, a peg was driven into the ground, and a notch cut in it, under the center of the said mark, in order to secure the line. In the evening, when we left off, a mark was placed before, and two or three left behind us; and in the morning the instrument was again set up in the same place, to prove that the marks were not moved. The tremour of the air (caused by the sun's rays) was often very great; and, to avoid any error that might arise from the fluttering of the marks, we intermitted our operations sometimes for five or six hours in a day, and were often obliged to make use of the morning or evening twilight. In the continuation of the line, a person was left at the mark, behind the instrument, till another mark was set forward, to prove with a plummet that its center was not moved. The vistco cut through the woods, in this work, was about eight or nine yards wide, and, in general, seen about two miles, beautifully terminating to the eye in a point. The zenith distances of the stars, for determining the celestial arc, answering to the interval of the parallels of the northernmost and southernmost points of the lines, were made with an excellent sector of six foot radius, constructed by Mr. John Bird. In the course of the work, for dividing the provinces of Maryland and Pennsylvania, the following lines were traced out, that offered themselves for determining the length of a degree of latitude. In the following fig. let N represent the northernmost point, and A the most southern of the said lines. Beginning at N, a meridian was traced from N to P. = 14 64 8. In this line there were some hills, which were measured horizontally with a level, but the plains were measured with a chain. P C = 2 79 27; C being in the parallel of latitude with P, which was determined by the sector. D C a meridian = 5 2 43, in which are three or four small ascents and descents. The points B D E and M are in a right line. BD = 22 51', and the angle CDM = 86° 32' nearly. Hence, B is south of D = 1 36' = Dg. The line A B = 81 78 31', in which is one gentle rising hill, about half a mile over; all the rest of the line is an entire level or plain. These measurements, expressed in English statute miles and parts of the same, were made with a chain, established from a brass statute yard, which was proved and corrected, in the course of the work, by another statute chain (kept only for that purpose) made from the said brass yard. They were only designed for dividing the provinces of Maryland and Pennsylvania: the same lines were re-measured afterwards with wooden rectangular levels, for the purpose of determining the length of a degree of latitude, as will appear in the sequel of this work. The point C was placed in the parallel of latitude of P, thus. Let N (see Tab. XIII. fig. 2.) represent the north pole of the terrestrial globe; P and R two places lying in the same parallel of latitude RCP; PR an arch of a great circle = 10' joining the said points; and PN, RN two meridians. PN or the complement of the latitude of P being = 50° 16' 42'', the angle NPR or the azimuth of the great circle PR was found by calculation to be 89° 55' 51''. The going of the clock being found by equal altitudes of stars, the times were computed when the same or other stars would pass the azimuth of the line PR; and, at the time computed for any star, the intersection of the cross wires of the transit instrument being brought to cover the star, the telescope was turned down to the horizon, and a land-mark was fixed up at the distance of about half a mile, answering to the intersection of the wires. In like manner, by other stars, several other marks were fixed up, and the mean of all was taken. In this direction the line PR was continued; and though it was at first intended to extend it only to R, to the distance of 10' of a great circle, it was in fact prolonged somewhat further, to S, PS being = 12,312 miles, or 10' 45'' of a great circle. Now PC being = 2,991 miles, or 2' 37'' of a great circle, the angle NPC is = 89° 58' 55''; from whence NPS = 89° 55' 51'' being subtracted, there remains the angle SPC or aPC = 3' 4'', whence aC, or the distance of the parallel PCR at C, south of a, should be 14,1 feet. But it having been made a rule, in dividing the provinces of Pennsylvania and Maryland, to trace out the parallels of latitude by the observations taken with the astronomical sector only, the sector was put up at P and S successively (see fig. 1.) and the zenith distances of the stars Capella & Lyrae, and others, were observed at both places; whence the point S was concluded to be 43 yards or 129 feet = SQ more northerly than P; and thence it was found by calculation, that the parallel of latitude PQ at the point C should be 45½ feet, = aC distant from the great circle PS, and to the south of the same; and the point C was placed accordingly, bp laying off 45½ feet = aC, at right angles, to the line Pa from the point a towards the south. aC found by the sector, being 45½ feet, and found by the azimuth of the line PS being 14,1 feet only, it follows, that had the position of the point C been determined by the latter method, instead of the former, it would have been placed 31.4 feet more to the northward than it was found by the sector; and, in consequence, the length of the degree of latitude would have come out 21 feet longer. But the difference is so small, that it only serves to confirm the exactness of the work, and renders it unnecessary to enter into any consideration, which of the two methods ought to be preferred. The meridians NP, CD, and AM, were found by celestial observations. The method of proceeding was as follows: To find the meridian AM, and the angle that the line AB makes with the said meridian. The equal altitude instrument being set up at the point A, with its vertical axis over the said point, equal altitudes of stars were observed for finding the motion of the clock. The time was next computed when some northern stars would pass the meridian by the clock, at which instant (shown by the clock) the vertical wire in the telescope was brought to bisect the star; and, the vertical axis of the instrument remaining fixed, the telescope was turned down in the same azimuth to the horizon, and a candle placed opposite to the vertical wire, as a point in the meridian. And the time of stars passing an azimuth in the direction of the line AB, for determining the angle BAM, was found by bringing the vertical wire in the telescope to bisect a candle placed (about 1¼ mile from A) in the line AB; the telescope was then elevated to the star, and the time when it passed the said vertical wire taken. The observations for determining the meridian A M, and the angle that the line A B makes with the said meridian, were as follows: | Year | Time per clock | Sum | Half Sum | |------|----------------|-----|----------| | | | | | | Oct. | | | | | 1766 | | | | | | | | | | | | | | Mean 20 35 42 star passed the meridian per clock. 20 33 30 star's apparent right ascension. 2 12 clock too fast for sidereal time. equal altitudes α Cygni. Mean = 20 36 45 star passed per clock. 20 33 30 star's apparent right ascension. 3 15 = clock too fast for sidereal time. 22 20 13 α Ursa major 23 26 β Ursa major passed an azimuth in the direction of the line A B. \[ \text{1766. Time per clock. Sum. Half Sum.} \] \[ \begin{array}{cccc} \text{October.} & h & ' & " \\ \hline 3 \ldots 13 & 19 & 50 & 41 \\ & 21 & 22 & 12 + \\ & 51 & 58 & \\ & 53 & 20 & \frac{1}{2} \\ & 24 & 52 & \\ & 15 & 33 & \\ & 15 & 33 & \frac{1}{2} \\ & 37 & 47 & \frac{1}{2} \\ & 37 & 46 & \frac{1}{2} \\ \end{array} \] \[ \begin{array}{c} \text{Mean} = 20 & 37 & 46 & \frac{1}{2} \\ 20 & 33 & 30 & \\ \end{array} \] \[ \begin{array}{c} \text{Clock too fast. Hence the clock gained of sidereal time the last } 24 \text{ h. } 62" . \end{array} \] \[ \begin{array}{c} 22 & 21 & 16 & \alpha \text{ Ursa major } \\ 22 & 24 & 21 & \beta \text{ Ursa major } \end{array} \] passed an azimuth in the direction of the line A B. The apparent right ascension of \(\alpha\) Ursa major The clock will be too fast, when this star will be on the meridian \[ \begin{array}{c} \alpha \text{ Ursa will be on the meridian per clock } \\ \text{In like manner I find that } \gamma \text{ Ursa major will be on the meridian per clock } \\ \text{And the pole } * \text{ at } \end{array} \] At the instant when the clock shewed \(22^{\text{h}} 53' 30''\), the vertical wire was brought to bisect the star \(\alpha\) Ursa major; and then the vertical axis was made fast (the level shewing the horizontal position of the axis of the telescope and the line of collimation being just), the telescope was then brought down to the horizon, and by means of a candle seen through a small hole in a board, a mark, at the distance of \(21^{\text{h}} 42'\), was placed in a line with the said vertical wire. Vol. LVIII. In like manner, when γ Ursae majoris, and the Pole star passed the meridian, as known by the clock, the vertical wire was brought, at those instants of time, to the said stars, and the telescope turned down to the horizon, in the same manner above mentioned, and the wire bisected the candle, when held to the 1st mark, as near as could be judged. | 1766 | Time per clock | Sum | Half Sum | |------|----------------|-----|----------| | October | h | " | h | " | h | " | h | " | | δ ... 14 | 20 | 21 | 21 | 12 | 15 | 41 | 17 | 35 | | 3 48 | 13 | 47 | 17 | 35 | 38 | 47½ | | 5 20+ | 15 | 14 | 17 | 35+ | 38 | 47½ | \[ \text{equal altitudes of } α \text{ Cygni.} \] \[ 20 38 47\frac{1}{2} \] \[ 33 30 = \text{stars A.R.} \] \[ 5 17\frac{1}{2} \] \[ \text{Clock fast.} \] \[ 23 37 44\frac{1}{2} \] \[ 0 20 49 \] \[ 0 3 36 \] \[ 0 1 48 \] \[ 40 6\frac{1}{2} \] \[ 23 32 \] \[ 3 38\frac{1}{2} \] \[ 1 49+ \] \[ 42 47 \] \[ 25 54 \] \[ 3 38 \] \[ 1 49+ \] \[ 0 1 49- \] \[ 23 56 22 \] \[ 5 27- \] \[ \text{clock too fast.} \] \[ 0 51 30 \] \[ 2 57 10\frac{1}{2} \] \[ \text{the Pole } \neq \text{ will be on the meridian.} \] \[ β \text{ Ursa minor on ditto.} \] \[ 2 3 40 β \text{ Ursa minor passed the line A.B.} \] Cloudy when the Pole star passed the meridian. At 2 57 10\(\frac{1}{2}\) β Ursa minor was bisected by the vertical wire for finding a meridian; and the telescope then turned down to the horizon, and by bringing a candle, at the distance of a mile, to be bisected by the vertical wire, we there placed a mark. After these observations, the clock was wound up, in doing which it was stopped about 23''. | Year | Time per clock | Sum | Half Sum | |------|---------------|-----|----------| | 1766 | October | | | | h | h | h | h | h | h | |-----|-----|-----|-----|-----|-----| | 19 | 52 | 14+ | 21 | 23 | 47 | | 53 | 22½| 25 | 10 | 18 | 42½| | 54 | 55½| 26 | 28 | 18 | 42+ | | 41 | 18 | 42½| 20 | 39 | 21+| | 18 | 42½| 39 | 21+| 39 | 21 | \[ \text{equal altitudes } \alpha \text{ Cygni.} \] \[ 20 \quad 39 \quad 21+ \] \[ 33 \quad 30 \] \[ 5 \quad 51+ \quad \text{clock too fast.} \] \[ 22 \quad 31 \quad 56 \quad \delta \text{ Ursa minor passed the line A B.} \] \[ 2 \quad 4 \quad 18 \quad \beta \text{ Ursa minor passed ditto.} \] | h | h | h | h | h | h | |-----|-----|-----|-----|-----|-----| | 20 | 0 | 17 | 21 | 17 | 24 | | 1 | 41 | 18 | 5½ | 20 | 32½| | 3 | 8 | 20 | 16 | 20 | 33 | | 40 | 16 | 16½| 20 | 33 | 30 | \[ \text{equal altitudes } \alpha \text{ Cygni.} \] \[ 20 \quad 40 \quad 16+ \] \[ 20 \quad 33 \quad 30 \] \[ 6 \quad 46+ \quad \text{clock too fast.} \] \[ 22 \quad 23 \quad 46 \quad \alpha \text{ Ursa major passed the line A B.} \] \[ 22 \quad 26 \quad 45½ \quad \beta \text{ Ursa major passed ditto.} \] \[ 22 \quad 32 \quad 45 \quad \delta \text{ Ursa minor passed ditto.} \] | Time per clock | Sum | Half Sum | |---------------|-----|----------| | October | | | | 23 41 16 | 0 | 6 37 | | 43 51½ | 22 46 | 6 37½ | | 46 51 | 25 22 | 6 38 | Mean = 0 3 19 * passed the meridian per clock. *’s apparent A R. 6 57— the clock too fast. Hence by the going of the clock, in the interval between α Cygni and α Andromeda passing the meridian. At { 0 53 0 } the Pole * will be on the meridian. At { 2 58 41 } β Ursa minor will be on ditto. At { 0 53 0 } by the clock, the vertical wire was brought to the Pole * as usual; and, by means of a candle at the distance of a mile, a mark was placed, which fell, as near as could be judged, on the mark placed the 14th instant. At { 2 5 10 } β Ursa minor passed the line A.B. At { 2 58 41 } the wire was brought to β Ursa minor for finding a meridian as before; and, by means of a candle at the distance of a mile, a mark was placed, which fell 3 inches east of that placed the 14th. N. B. In this last observation the axis of the telescope was turned end for end; that is, the telescope itself was turned upside down. This proved the ends of the cylinder to be good. In the evening, by means of a candle placed behind a board, with a small hole in it over the mark placed the 13th instant, the line was extended to the marks at a mile distance, and there a mark placed, which fell \( \frac{1}{4} \) of an inch east of the mark placed the 14th instant. From the whole, there are six observations, all within the space of about 3 inches, at the distance of a mile: The mean was taken as a point in the meridian, north of the point A. At this meridian point \( m \), we laid off the line \( mp \), at right angles to the meridian \( A, m, M \), and, by a candle being placed at \( o \), in the right line \( AB \) (about \( \frac{1}{2} \) miles from \( A \)), another candle was advanced along the line \( mp \), till the vertical wire in the telescope bisected both candles: Under the candle, at the intersection of \( mp \), with \( AB \), viz. at \( p \), a mark was placed in the ground. The ground between \( m \) and \( p \), being made smooth (it was level as a floor by nature) the distance \( mp \), was mea- sured twice, and found to be 5 chains, 14 feet, and \( \frac{1}{4} \) of an inch. With this same chain the distance \( mA \) was measured = 80 chains exactly. --- For the Angle BAM, by celestial measure. | AR of the meridian when \( \alpha \) Ursa major passed an azimuth in the direction of the line \( AB \) | \( 22^\circ 16' 53.8'' \) by observations made October 12. | | --- | --- | | \( 22^\circ 16' 55.1'' \) D° on the | \( 13' \) | | \( 22^\circ 16' 54.7'' \) D° on the | \( 16' \) | Mean = \( 22^\circ 16' 54.5'' \) \( \alpha \) Ursa major \( = 334^\circ 13' 38'' \) \( = 162^\circ 16' 54'' \) Angle at the Pole = \( 171^\circ 56' 44'' \) AR's of the meridian when β Ursa minor passed the direction of the line A.B. | Direction | AR (h, m, s) | |-----------|--------------| | | 1h 58m 7s.8s by observations made October 14. | | | 1h 58m 14s.2s Dº on the . . . . . . 15. | | | 1h 58m 7s.1s Dº on the . . . . . . 16. | Mean of the first and last = 1h 58m 7s.5 = 29º 31' 52" AR of β Ursa minor = .............. 222º 53' 30" Angle of the Pole .......... = 166º 38' 22" Now having the distance of the *s from the Pole, the angles at the Pole, and the latitude of the point A, per spherics, we find the star's azimuth from the north = the angle BAM. And for the said Angle by terrestrial measurement. As AM : Rad :: p m : Tangent Angle p A m. = the Angle BAM. = 3º 43' 40" Angle per α Ursa major .......... = 3º 43' 25" Dº per β Ursa minor ............... = 3º 43' 25" Mean .................................................. 3º 43' 30" = Angle BAM. In the same manner as the point m, in the meridian from A was found, points in the meridian, north of P and N, were also found; and having two points given, with them a right line was extended as follows; first N.P. in a line with N e.—At N the equal altitude instrument was set up, and the vertical wire in the telescope was brought to bisect the mark at e; and there the vertical axis made fast. The spirit level shewing the axis of the telescope to be horizontal. The vertical axis being well secured, the telescope part is taken off the supporters, and turned to point to the southward (carefully taking off, and putting it on the supporters so as not to move the axis); then on the farthest rising ground that could be seen, another mark was placed at l, in a right line with the vertical wire. A mark being left at N, the instrument is taken, and set up three or four feet south of the mark l, and having brought the vertical wire in the telescope in a right line with the marks at l, and N, the vertical axis is then made fast as before, the telescope immediately turned, and a third mark placed to the southward; and so the operation was continued. In the same manner the lines P S, C D, A B, and A E were traced out; and, to prove that by this method a right line may be extended, we shall here give the result of continuing the lines A B and A E. A and D being two points between which a right line was to be drawn. The point n was known to be nearly in the line A D. At A and n marks were placed, and 3 or 4 feet north of n (which was \( \frac{1}{4} \) of a mile from A), the instrument was set up; then, in the same manner as above, the vertical wire in the telescope was brought in a line with A and n, and the vertical axis made fast; the telescope was then turned to point to the northward, and a third mark placed, &c. &c. In this manner the line A n was continued to B. Having continued the line to B, it fell 22 51', west of the point D: we then returned and laid off eastward off-sets from the line A B, at every fifth mile from A, proportional to the distance from A, and at the end of every off-set placed a post, in order to form the line A D. Off-sets were measured very correct at \( \left\{ \begin{array}{l} \text{about } 10\frac{1}{2} \text{ miles . . . . = ab.} \\ \text{the } 10^{th} \text{ mile . . . . = fc.} \\ \text{about the } 9^{th} \text{ d° . . . . = bd.} \end{array} \right. \) and at the 3 points, b, c, d, three marks were placed. At b the instrument was set up, to see if the 3 marks were placed in a right line; when it appeared they were not exactly so; but, on moving the middle one \( \frac{1}{2} \) an inch east, they then made a right line. In this direction we continued the lines b, c, d, to A, which fell 2 feet 2 inches west of the point A, at q. The distance A q being so small a quantity (gradually rising) in ten miles, we thought it would be superfluous to change the direction, and therefore returned to the point b, and extended the line northward, proceeding in the same manner as before. Having continued the line to E, it fell 16 feet 9 inches east of the point D. Hence the off-sets from this line to the true line A D, are as shewn by the Table B. And as we passed by the off-set posts made from A B, we measured the distance of this line A E from the said off-set posts, which were as given in the Table D. ### Table B | Miles from point A | Off-sets in Feet Inches | |-------------------|-------------------------| | 0 | 2 2 | | 5 | 1 0 | | 10 | 0 2.2 | | 15 | 1 4 | | 20 | 2 6 | | 25 | 3 8 | | 30 | 4 10 | | 35 | 5 11 | | 40 | 7 1 | | 45 | 8 3 | | 50 | 9 5 | | 55 | 10 6 | | 60 | 11 8 | | 65 | 12 10 | | 70 | 14 0 | | 75 | 15 2 | | 80 | 16 4 | | 82 | 16 9 | To the eastward. ### Table D | Miles from point A | Off-sets in Feet Inches | |-------------------|-------------------------| | 0 | 2 2 | | 5 | 0 10 | | 10 | 0 0 | | 15 | 0 4 | | 20 | 4 8 | | 25 | 7 4 | | 30 | 8 3 | | 35 | 7 6 | | 40 | 8 5 | | 45 | 9 6 | | 50 | 10 11 | | 55 | 11 1 | | 60 | 10 6 | | 65 | 11 7 | | 70 | 12 11 | | 75 | 15 7 | | 80 | 16 7 | | 82 | 16 9 | Eastward. The distance of the off-set posts, west from the line AE. From these Tables we have the difference of the results of the two lines AB and AE; that is, the off-set posts from the line AB, which form the true line AD: And the off-set posts from the line (AE) traced last, that also form the said line AD, will be distant from each other, at every fifth mile, as follows: Miles This is a sufficient proof that the line A B is the arch of a great circle; but, as a farther confirmation that no error could arise, we observed at different points in the line the right ascensions of the meridian when the star δ Ursæ minoris passed an azimuth corresponding to the direction of the line, being in the upper part of its circle. The method of proceeding was in the same manner, as described before, for finding the angle BAM. OBSERVATIONS for determining the right Ascensions of the Meridian, when δ Ursæ Minoris passed the Line A B. June 25, 1764, we began at the point A, to trace the line A B; and the weather being so cloudy prevented our making any one observation till July 10, though we attended every night. By this time we had continued the line 20 miles from A. 1764. Time per watch. July. h " h " δ... 10 15 49 0 17 5 10 55 0 17 12 17 16 2 8 18 3 equal altitudes of Antares. Hence the * passed the meridian per watch at A R of Antares - - - - - - - - - - - - - - Watch too fast for sidereal time - - - - - - - - - - - - - - VOL. LVIII. P p 20 Miles from A. 1764. Time per watch. July. \[ \begin{array}{cccc} \delta & \ldots & 10 & 19 \\ & & 29 & 26 \\ & & 34 & 18 \\ & & 40 & 21 \\ \end{array} \] \[ \begin{array}{cccc} \alpha & \ldots & 20 & 15 \\ & & 21 & 40 \\ & & 26 & 30 \\ \end{array} \] equal alt. α Aquilæ. Hence * passed at . . . 19 57 58 Right ascen. of α Aquilæ 19 39 18 Watch too fast . . . . 0 18 40 22 44 45 δ Ursæ minoris passed an azimuth in the direction of the line A B. — 18 44 watch too fast when the * passed the line. 22 26 = the right ascension of the meridian, when δ Ursæ minoris passed the line A B. --- 27 18 10 45 19 45 4 \[ \begin{array}{cccc} 11 & 54 & 46 & 10 \\ 12 & 56 & 47 & 11 \\ \end{array} \] equal altitude α Lyrae. Hence * passed at . . . 18 59 0 Right ascension = . . . 18 28 58 Watch too fast . . . . 0 30 2 43 Miles from A. \[ \begin{array}{cccc} 20 & 33 & 58 & 21 \\ 35 & 33 & 32 & 23 \\ 37 & 3 & 33 & 58 \\ \end{array} \] equal alt. α Cygni. Hence * passed at . . . 21 3 58 Right ascension . . . 20 33 25 Watch too fast , . . . 0 30 33 22 57 36 δ Ursæ minoris passed the direction of the line A B. — 31 1 watch too fast at this time. 22 26 35 = the right ascension of the meridian when δ Ursæ minoris passed the line A B. 1764. Time per clock. July. \[ \begin{array}{cccc} 30 & 18 & 32 & 40 \\ & 33 & 42 & \ldots \\ & 34 & 55 & 1 4 59 \\ \end{array} \] equal alt. of \( \alpha \) Lyrae. Hence \( \ast \) passed at . . . 19 18 51 Right ascension . . . 18 28 58 Watch too fast . . . 0 49 58 46 Miles from A. \[ \begin{array}{cccc} 20 & 56 & 12 & 21 49 13 \\ & 57 & 56 & 50 52 \\ & 59 & 36 & 52 26 \\ \end{array} \] equal alt. of \( \alpha \) Cygni. Hence passed at . . . 21 24 23 \( \ast \)'s right ascension . . . 20 33 25 Watch too fast . . . 0 50 58 23 18 25 \( \delta \) Ursae minoris passed the direction of the line A B. — 51 57 Watch too fast. 22 26 28 = the right ascension of the meridian when \( \delta \) Ursae minoris passed the line A B. August. \[ \begin{array}{cccc} 17 & 18 & 47 & 25 \\ & 48 & 24 & 37 \\ & 49 & 33 & 38 \\ \end{array} \] equal alt. of \( \alpha \) Lyrae. Hence \( \ast \) passed at . . . 19 12 42 its right ascension . . . 18 28 58 Watch too fast . . . 0 43 44 II Miles from A. \[ \begin{array}{cccc} 20 & 42 & 45 & 21 50 48 \\ & 44 & 8 & 52 12 \\ & 45 & 30 & 53 30 \\ \end{array} \] equal alt. \( \alpha \) Cygni. Hence \( \ast \) passed at . . . 21 18 9 its right ascension . . . 20 33 25 Watch too fast . . . 0 44 44 23 12 48 \( \delta \) Ursae minoris passed the direction of the line A B. — 45 39 = watch too fast. 22 27 9 = the right ascension of the meridian, when \( \delta \) Ursae minoris passed the direction of the line A B. PP 2 1764. Time per watch. August. \[ \begin{array}{cccc} \text{equal altitudes} & \alpha \text{ Lyrae.} \\ \text{Right ascension of} & \alpha \text{ Lyrae} \\ \text{Watch too fast} \\ \end{array} \] Here we were 80 miles from A. \[ \begin{array}{cccc} \text{equal alt.} & \alpha \text{ Cygni.} \\ \text{Hence passed at} \\ \text{*’s right ascension} \\ \text{Watch too fast} \\ \end{array} \] 23 25 55 δ Ursae minoris passed the direction of the line A B. — 59 21 watch too fast. 22 26 34 = the right ascension of the meridian when δ Ursae minoris passed the line A B. Most of these equal altitudes were observed per Mr. Dixon, I judging the time by the watch, which had only the hour and minute hands; therefore the seconds must not be expected as from a good clock, nor does the problem require it, as the star δ Ursae minoris changed its azimuth very slowly.—The passage of the star δ Ursae minoris over the line A B was in general taken by myself. The AR of meridian when δ Ursae minoris passed A B. by observations made on the 15th and 16th of October, 1766, at the point A. Whether the small effects of the aberration and nutation of the star δ Ursae minoris, at the different times, will add to or diminish from the correspondence of these numbers, I have not determined; the above being sufficient for the purpose intended: for if the direction of the line had been changed any quantity of note, it would have caused a much greater difference in the right ascensions of the meridians, when the star passed the line, than any we here find, The following are observations for determining the celestial arch between the points A and N.—Those marked with dots and *, thus, ...*... were made by Mr. Dixon. 1766. We set up the sector at the point A, in the middle of a west line, drawn between Cape Hinlopen and Chesopeak Bay, and made the following observations. N.B. Each revolution of the micrometer = 52" **PLANE OF THE SECTOR EAST.** | *'s names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zen. distances | |-----------|-----------------------------|--------------------------|------------------------------------------|------------------------| | γ Andromedæ | 2 45— { 5 31— 6 10 } | o 31,3 2 44 28,7 North. | | β Persei | 1 35— { 7 8 7 14 } | o 6,0 1 34 54,0 N. | | δ D° | 8 35— { 7 32+ 9 13+ } | i 25,0 8 33 35,0 N. | | Capella | 7 15+ { 4 39— } | i 21,3 7 16 21,3 N. | | β Aurigæ | 6 25+ { 3 24— 2 22½ } | i 3,2 6 26 3,2 N. | | Castor | 6 5— { 1 10 } | o 9,5 6 4 50,5 South; | | #’s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------------|-----------------------------|--------------------------|-------------------------------------------|--------------------------| | 1766. October | | | | | | 24 | 9 Cloudy | | | | | 3 | 10 | | | | | α Lyrae | o 5+ | { 3 26½ 2 19,0 0 7 19,0 North. } | | | | γ Cygni | i 5− | { 4 42 6 6− 1 7,7 1 3 52,3 N. } | | | | α D° | 6 o− | { 5 41 5 46− 0 4,7 5 59 55,3 N. } | | | | γ Andromedæ | 2 45− | { 7 12 7 42 0 30,0 2 44 30,0 N. } | | | | β Persei | i 35− | { 8 15½ 8 22 0 6,5 1 34 53,5 N. } | | | | δ D° | 8 35− | { 5 51½ 7 33 1 25,5 8 33 34,5 N. } | | | | Capella | 7 15+ | { 6 48½ 5 20½ 1 20,0 7 16 20,0 N. } | | | | β Aurigæ | 6 25+ | { 3 29½ 2 17½ 1 4,0 6 26 4,0 N. } | | | | Castor | 6 5− | { 15 25 15 15½ 0 9,5 6 4 50,5 N. } | | | | h | 11 α Lyrae | { 8 26 5 41+ 2 20,7 0 7 20,7 N. } | | | | | | { 5 44− 3 37− 1 51,0 6 6 51,0 N. } | | | | δ Cygni | 6 5+ | { 3 37 5 1 8,0 1 3 52,0 N. } | | | | γ D° | i 5+ | { 3 37 5 1 8,0 1 3 52,0 N. } | | | | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------------|-----------------------------|---------------------------|------------------------------------------|--------------------------| | 1766. October | | | | | | b II α Cygni | 6 o+ | {4 32} | {5:5} | {5:5 North} | | γ Andromedæ | 2 45— | {6 14—} | {29:3} | {30:7 N.} | | β Persei | 1 35— | {7 42—} | {4:3} | {55:7 N.} | | δ D° | 8 35— | {5 38½} | {23:0} | {37:0 N.} | | Capella | 7 15+ | {8 51} | {20:3} | {20:3 N.} | | β Auriga | 6 25+ | {7 23—} | {4:0} | {4:0 N.} | | Castor | 6 5— | {4 31} | {10:5} | {49:5 South} | | O | | | | | | 12 | | | | | | α Lyrae | 0 5+ | {5 29—} | {2 22:0} | {7 22:0} | | δ Cygni | 6 5+ | {4 31½} | {51:0} | {6 51:0} | | γ D° | 1 5— | {6 26} | {9:0} | {3 51:0} | | α D° | 6 0+ | {13 8} | {3:5} | {3:5} | | γ Andromedæ | 2 45— | {2 37½} | {32:4} | {24 27:6} | | β Persei | 1 35— | {3 46} | {5:0} | {34 55:0} | | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-------------------|----------------------------|--------------------------|-------------------------------------------|--------------------------| | 1766. October | | | | | | ο | 12 | 8 35— | { 1 43 | 1 27,0 | | | | | { 3 26 | 8 33 | | | | | { 0 28 | 33,0 | | Capella | 7 15+ | | { 4 50 | 1 22,0 | | | | | { 7 16 | 22,0 | | β Aurigae | 6 25+ | | { 1 33+ | 1 45,0 | | | | | { 6 26 | 4,0 | | Caftor | 6 5— | | { 15 37½ | 0 8,0 | | | | | { 15 29½ | 6 4 | | | | | | 52,0 | TURNED THE SECTOR PLANE WEST. | * | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |--------------------|-----------------------------|---------------------------|-------------------------------------------|--------------------------| | η Andromedæ | 2 45— | { 6 2+ | 0 24,8 | 2 44 | | | | { 5 29½ | | 35,2 | | β Persei | 1 35+ | { 5 43 | 0 0,7 | 1 35 | | | | { 5 44— | | 0,7 | | δ D° | 8 35— | { 6 2½ | 1 22,5 | 8 33 | | | | { 4 24 | | 37,5 | | Capella | 7 15+ | { 7 4½ | 1 27,5 | 7 16 | | | | { 8 40 | | 27,5 | | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------------|-----------------------------|--------------------------|-------------------------------------------|--------------------------| | **1766. October** | | | | | | δ Lyrae | 0 5+ | {14 12 | 2 21,0 | 0 7 21,0 | | α Cygni | 6 0 | {16 49 | 0 0,0 | 6 0 0,0 | | γ Andromedae | 2 45— | {13 16 | 0 0,0 | 6 0 0,0 | | β Persei | 1 35+ | {2 46 | 0 24,0 | 2 44 36,0 | | δ D° | 8 35— | {2 22 | 0 0,6 | 1 35 0,6 | | Capella | 7 15+ | {3 27+ | 1 19,6 | 8 33 40,4 | | β Aurigae | 6 25+ | {3 36 | 1 29,7 | 7 16 29,7 | | Castor | 6 5— | {7 17 | 0 12,0 | 6 4 48,0 | | δ Lyrae | 0 5+ | {3 33 | 2 22,7 | 2 7 22,7 | | α Cygni | 6 5+ | {6 20— | 1 58,0 | 6 6 58,0 | | γ D° | 1 5— | {6 18 | 1 58,0 | 6 6 58,0 | | α D° | 6 0+ | {8 32 | 1 58,0 | 6 6 58,0 | | Andromedae | 2 45— | {7 4 | 1 58,0 | 6 6 58,0 | | β Persei | 1 35+ | {5 43— | 1 58,0 | 6 6 58,0 | | Year | Month | Star's Name | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zen. distances | |------|-------|-------------|-----------------------------|--------------------------|------------------------------------------|------------------------| | 1766 | October | δ Persei | 8° 35' | {8° 2' 6° 24'} | 1° 22.0" 8° 33' 38" | | | | | Capella | 7° 15' | {7° 21½' 9° 5'} | 1° 27.5" 7° 16' 27.5" | | | | | ε Aurigae | 6° 25' | {9° 25' 10° 44½'} | 1° 11.8" 6° 26' 11.8" | | | | | Castor | 6° 5' | {12° 45' 13° 6'} | 0° 12.7" 6° 4' 47.3" | | | 1766 | April | α Lyrae | 0° 5' | {4° 48' 7° 35'} | 2° 22.7" 0° 7' 22.7" | | | | | δ Cygni | 6° 5' | {4° 32' 0° 25'} | 1° 55.2" 6° 6' 55.2" | | | | | γ D° | 1° 5' | {1° 25' 0° 8½'} | 1° 4.5" 1° 3' 55.5" | | | | | α D° | 6° 0' | {0° 9' 4° 3½'} | 0° 0.5" 6° 0' 0.5" | | | | | γ Andromedae | 2° 45' | {4° 31½' 4° 3½'} | 0° 28.0" 2° 44' 32.0" | | | | | β Persei | 1° 35' | {3° 25' 4° 4'} | 0° 0.0" 1° 35' 0.0" | | | | | δ D° | 8° 35' | {4° 24½' 4° 4'} | 1° 23.5" 8° 33' 36.5" | | | | | Capella | 7° 15' | {1° 20' 3° 5'} | 1° 29.3" 7° 16' 29.3" | | | | | β Aurigae | 6° 25' | {5° 29½' 6° 48'} | 1° 10.5" 6° 26' 10.5" | | | | | Castor | 6° 5' | {8° 5' 8° 15½'} | 0° 10.5" 6° 4' 49.5" | | | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------|-----------------------------|--------------------------|------------------------------------------|--------------------------| | α Lyrae | 0 5+ | { 5 18— 2 23.3 0 7 23.3 } | | | | γ Cygni | 1 5— | { 8 1½ 6 41½ 1 4.0 1 3 56.0 } | | | | α D° | 6 c— | { 6 48½ 6 48 } | 0 0.5 5 59 59.5 | | | Capella | 7 15+ | { 8 43 10 26½ } | 1 27.5 7 16 27.5 | | | β Auriga | 6 25+ | { 10 39— 12 6 } | 1 11.3 6 26 11.3 | | | Castor | 6 5— | { 12 14— 12 25+ } | 0 11.6 6 4 48.4 | | --- | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------|-----------------------------|--------------------------|------------------------------------------|--------------------------| | α Lyrae | 0 5+ | { 6 49 9 38+ } | 2 25.3 0 7 25.3 | | | δ Cygni | 6 5+ | { 7 45— 10 8 } | 1 59.3 6 6 59.3 | | | γ D° | 1 5— | { 5 15 4 3 } | 1 4.0 1 3 56.0 | | | α D° | 6 0+ | { 16 47— 16 49 } | 0 2.3 6 0 2.3 | | THE RESULT OF THESE Star's zenith distance at the point A. | | α Lyrae | δ Cygni | γ Cygni | α Cygni | γ Androm. | |----------|---------|---------|---------|---------|-----------| | D. | | | | | | | Oct. | 1766 | 1866 | 1866 | 1866 | 1866 | | | 10 | 11 | 12 | 10 | 11 | | | 7 19,0 | 7 20,7 | 7 22,0 | 7 19,0 | 7 20,7 | | | 6 6 51,0| 6 6 51,0| 6 6 51,0| 6 6 51,0| 6 6 51,0 | | | 3 52,3 | 3 52,0 | 3 51,0 | 3 51,0 | 3 51,0 | | | 5,5 | 5,5 | 3,5 | 3,5 | 3,5 | | | 24 28,7 | 24 30,0 | 24 27,6 | 24 29,25 | 24 29,25 | | | 24 30,0 | 24 30,7 | 24 27,6 | 24 29,25 | 24 29,25 | | | 24 27,6 | 24 27,6 | 24 27,6 | 24 29,25 | 24 29,25 | Mean 11 11 0 7 20,57 6 6 51,0 1 3 51,7 6 0 4,50 2 44 29,25 Aberration - 17,17 - 18,49 - 17,33 - 17,75 - 4,08 Nutation + 6,12 + 4,14 + 2,92 + 2,25 + 7,53 Precefs. Oct. 0,0 0,0 0,0 0,0 0,0 11, 1764. + 0,12 + 6,11 + 1,06 + 6,0 + 2,75 Mean zen. dist. 0 7 9,70 6 6 42,85 1 3 38,42 5 59 55,0 2 44 20,39 PLANE OF THE October. | | | | | | | |----------|---------|---------|---------|---------|-----------| | D. | | | | | | | Oct. | 14 | 15 | 16 | 17 | 18 | | | 0 7 21,0| 0 7 22,7| 0 7 22,7| 0 7 23,3| 0 7 23,3 | | | 6 6 58,0| 6 6 58,0| 6 6 58,0| 6 6 59,3| 6 6 59,3 | | | 3 54,7 | 3 55,5 | 3 56,0 | 3 56,0 | 3 56,0 | | | 0,0 | 0,0 | 0,0 | 0,0 | 0,0 | | | 24 35,2 | 24 36,0 | 24 35,5 | 24 35,5 | 24 35,5 | | | 24 36,0 | 24 35,5 | 24 35,5 | 24 35,5 | 24 35,5 | | | 24 35,5 | 24 35,5 | 24 35,5 | 24 35,5 | 24 35,5 | Mean - 0 7 22,42 6 6 58,65 1 3 55,55 6 0 0,70 2 44 35,57 Aberration - 16,74 - 18,31 - 17,40 - 17,93 - 4,79 Nutation + 6,12 + 4,14 + 2,92 + 2,25 + 7,53 Precefs. - 0,03 - 0,14 - 0,18 - 0,19 - 0,19 Refract. + 0,12 + 6,11 + 1,06 + 6,0 + 2,75 Mean zen. dist. 0 7 11,89 6 6 50,45 1 3 41,95 5 59 50,83 2 44 25,84 Oct. 11, 1766. 0 7 9,70 6 6 42,85 1 3 38,42 5 59 55,0 2 44 20,39 Mean zen. dist. 0 7 10,79 6 6 46,65 1 3 40,18 5 59 52,92 2 44 23,10 at the point A. OBSERVATIONS, AS FOLLOWS: SECTOR EAST. | Year | Month | Day | Hour | Minute | Second | |------|-------|-----|------|--------|---------| | 1766 | Oct. | 8 | 34 | 54.0 | 0 | | | | 10 | 34 | 53.5 | 0 | | | | 11 | 34 | 55.7 | 0 | | | | 12 | 34 | 55.0 | 0 | | Beta Persei | Delta Persei | Capella | Beta Aurigae | Castor | |-------------|--------------|---------|--------------|--------| | 8 34 54.0 | 8 33 35.0 | 8 7 16 21.3 | 8 6 26 3.2 | 8 6 4 50.5 | | 8 34 53.5 | 8 33 34.5 | 10 7 16 20.0 | 10 6 26 4.0 | 10 6 4 50.5 | | 8 34 55.7 | 11 7 16 20.3 | 11 6 26 4.0 | 11 6 4 49.5 | | | 8 34 55.0 | 12 7 16 22.0 | 12 6 26 4.0 | 12 6 4 52.0 | | | 8 34 54.55 | 8 33 34.17 | 7 16 20.90 | 6 26 3.80 | 6 4 50.62 | | 1.09 | 2.0 | 5.48 | 6.55 | 3.52 | | 8.27 | 8.40 | 7.85 | 7.15 | 4.70 | | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | 1.58 | 8.55 | 7.26 | 6.43 | 6.08 | | 8 34 46.77 | 8 33 36.32 | 7 16 25.79 | 6 26 9.63 | 6 4 57.88 | SECTOR WEST. | Year | Month | Day | Hour | Minute | Second | |------|-------|-----|------|--------|---------| | 1766 | Oct. | 13 | 35 | 0.7 | 13 | | | | 14 | 35 | 0.6 | 14 | | | | 15 | 35 | 0.0 | 15 | | | | 16 | 35 | 0.0 | 16 | | Beta Persei | Delta Persei | Capella | Beta Aurigae | Castor | |-------------|--------------|---------|--------------|--------| | 8 33 37.5 | 13 7 16 27.5 | 14 6 26 11.5 | 14 6 4 48.0 | | 8 33 40.4 | 14 16 29.7 | 14 6 26 11.8 | 15 4 47.3 | | 8 33 38.0 | 15 16 27.5 | 15 26 11.8 | 15 4 47.3 | | 8 33 36.5 | 16 16 29.3 | 16 26 10.5 | 16 4 49.5 | | 8 33 36.5 | 17 16 27.5 | 17 26 11.3 | 17 4 48.4 | | 8 33 38.10 | 7 16 28.30 | 6 26 11.28 | 6 4 48.30 | | 1.79 | 1.20 | 4.98 | 6.28 | 3.75 | | 8.27 | 8.46 | 7.85 | 7.15 | 4.70 | | 0.16 | 0.74 | 0.07 | 0.02 | 0.10 | | 1.58 | 8.55 | 7.26 | 6.43 | 6.08 | | 8 34 51.69 | 8 33 39.31 | 7 16 32.62 | 6 26 16.76 | 6 4 55.23 | | 8 34 46.77 | 8 33 36.32 | 7 16 25.79 | 6 26 9.63 | 6 4 57.88 | | 8 34 49.23 | 8 33 37.84 | 7 16 29.20 | 6 26 13.20 | 6 4 56.56 | 1766. December. Set up the sector at the point N, in the forks of the river Brandywine, in Pennsylvania, and made the following observations. | Star's Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |--------------|----------------------------|--------------------------|------------------------------------------|--------------------------| | γ Andromedæ | 15+ | {5 20½} | 0 54,8 | 1 15 54,8 North | | β Persei | 5+ | {4 46½} | 1 20,3 | 0 6 20,3 N | | δ D° | 7 5+ | {4 8} | 0 2,0 | 7 5 2,0 N | | Capella | 5 50— | {5 35} | 2 18,0 | 5 47 42,0 N | Cloudy. | Star's Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |--------------|----------------------------|--------------------------|------------------------------------------|--------------------------| | γ Andromedæ | 15+ | {7 32} | 0 55 0 | 1 15 55,0 N | | β Persei | 5+ | {8 3} | 1 21,7 | 0 6 21,7 N | | δ D° | 7 5+ | {6 27} | 0 3,0 | 7 5 3,0 N | | Capella | 5 50— | {4 46½} | 2 19 0 | 5 47 41,0 N | | β Aurigæ | 4 55+ | {9 20½} | 2 27 0 | 4 57 27,0 N | | Castor | 7 35— | {9 14½} | 1 23,5 | 7 33 36,5 South | | **Name** | Nearst point on the factor. | Points on the micrometer. | Diff. between the points on the micrometer. | Apparent zenith distances. | |----------|-----------------------------|---------------------------|--------------------------------------------|---------------------------| | δ | 16 γ Andromedae | 15+ | 9°37' - 8°33' | 1°15' 55"7 North | | β Persei | 0 | 5+ | 7°45'51" - 6°16'41" | 1°21'0 0°6 21"0 | | δ Dο | 7 | 5+ | 5°21'12" - 5°19'21" | 0°20'7 5°5 2"0 | | Capella | 5 | 50- | 7°11' - 9°46' | 2°18'7 5°47 41"3 | | β Aurigae| 4 | 55+ | 9°39' - 6°47'41" | 2°27'7 4°57 27"7 | | Cator | 7 | 35- | 6°34'2" - 5°5" | 1°21'8 7°33 38"2 | | ε Lyrae | 1 | 20+ | 5°44' - 7°42' | 1°42'0 1°21 42"0 South | | Cloudy | | | | | | ε Lyrae | 1 | 20+ | 5°11' - 7°1' | 1°43'5 1°21 43"5 | | β Persei | 0 | 5+ | 8°42'5" - 7°14'4" | 1°20'2 0°6 20"3 | | Capella | 7 | 5+ | 7°0' - 5°42'5" | 0°37'7 5°3'7 | | β Aurigae| 4 | 55+ | 5°15' - 4°45' | 1°16'0 5°47 44"0 | | Cator | 7 | 35- | 4°45' - 3°16' | 1°21'3 7°33 38"7 | | *'s Names | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |-----------|-----------------------------|--------------------------|------------------------------------------|--------------------------| | h | 20 Cloudy. | | | | | o ...*... | 21 α Lyrae ................. | 1 20+ {3 2 5 0} | 1 41,7 | 1 21 41,7 | TURNED THE SECTOR PLANE WEST. | o | 21 β Persei ............... | 0 5+ {6 4+ 7 42} | 1 29,7 | 0 6 29,7 | | | | | | | | | 3 D° ...................... | 7 5+ {7 50 8 8} | 0 10,3 | 7 5 10,3 | | Capella | 5 45+ {4 5 7 25½} | 2 56,8 | 5 47 56,8 | | | | 5 50- {4 5 1 33½} | 2 7,2 | 5 47 52,8 | | | β Aurigae | 4 55+ {7 0 9 51} | 2 35,3 | 4 57 35,3 | | | Castor | 7 35- {10 0+ 11 38+} | 1 30 | 7 33 30,0 | | D | 22 Cloudy. | | | | | | 23 D° | | | | | | 24 α Lyrae | 1 20+ {6 44 5 0} | 1 36,0 | 1 21 36,0 | | | γ Andromedae | 1 15+ {4 41 6 1½} | 1 4,8 | 1 16 4,8 | | | β Persei | 0 5+ {4 16½ 6 3} | 1 30,2 | 0 6 30,2 | | | 3 D° | 7 5+ {6 16½ 6 27} | 0 10,5 | 7 5 10,5 | | | Date | Star Name | Nearest point on the sector | Points on the micrometer | Diff. between the points on the micrometer | Apparent zenith distances | |------------|---------------|-----------------------------|--------------------------|-------------------------------------------|--------------------------| | 1766 Decemb | Capella | 5° 50' | {9° 19', 6° 47', 6° 2'} | 2° 7', 5° 47', 5° 23' | | | | β Aurigae | 4° 55' | {9° 1', 6° 31'} | 2° 35', 4° 57', 3° 50' | | | | Castor | 7° 35' | {8° 16½', 1° 29½'} | 1° 29', 7° 33', 3° 8' | | | 24 | Cloudy | | | | | | 26 | D° | | | | | | 27 | α Lyrae | 1° 20' | {5° 13', 3° 22'} | 1° 35', 1° 21', 3° 5' | | | | γ Andromedæ | 1° 15' | {8° 19', 9° 31'} | 1° 4', 1° 16', 4° | | | | β Persei | 0° 5' | {9° 17½', 11° 3'} | 1° 29', 0° 6', 2° 9' | | | | δ | 7° 5' | {12° 16', 12° 26'} | 0° 9', 7° 5', 9° 7' | | | | Capella | 5° 50' | {6° 32', 4° 7'} | 2° 9', 5° 47', 5° 1' | | | 28 | γ Andromedæ | 1° 15' | {4° 14', 5° 26'} | 1° 3', 1° 16', 3° 7' | | | | β Persei | 0° 5' | {2° 42½', 4° 27'} | 1° 28', 0° 6', 2° 8' | | | | β Aurigæ | 4° 55' | {8° 14', 11° 13'} | 2° 35', 4° 57', 3° 56' | | Vol. LVIII. ### PLANE OF THE #### 1766. **December.** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 13 | 15 54°8 | 13 06°20 | | | 15 | 15 55°0 | 15 06°21 | | | 16 | 15 55°7 | 16 06°21 | | | 17 | 21 42°0 | | | | 19 | 21 43°5 | | | | 21 | 21 41°7 | | | **Mean Zen. dist. Oct. 11, 1766** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 21 | 40°78 | 15 33°95 | 06 08°7 | ### PLANE OF THE #### 1766. **December.** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 24 | 21 36°0 | 24 16 4°8 | 24 06 30°2 | | 27 | 21 35°3 | 27 16 4°0 | 27 06 29°5 | | | | | | **Mean Zen. dist. Oct. 11, 1766** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 21 | 32°03 | 15 42°44 | 06 8°78 | **True mean Zen. dist. Oct. 11, 1766, at the point N.** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 21 | 36°42 | 15 38°19 | 06 4°87 | **D° at the point A.** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 7 | 10°79 | 24 23°10 | 34 49°23 | **Difference** | Date | α Lyrae | γ Andromeda | β Persei | |------|---------|-------------|----------| | | | | | | 28 | 47°21 | 28 44°91 | 28 44°40 | | | | | | | | | | | **Mean** \[ = 28 44°99 \] = the true celestial arch between the points N and A. ### SECTOR EAST. | δ Persei | Capella | β Aurigae | Castor | |----------|---------|-----------|--------| | 13 7 5 2,0 | 13 5 47 42,0 | ... | ... | | 15 5 3,0 | 15 47 41,0 | 15 4 57 27,0 | 15 7 33 36,5 | | 16 5 2,0 | 16 47 41,3 | 16 57 27,7 | 16 7 33 38,2 | | 19 5 3,7 | 19 47 44,0 | 19 57 27,3 | 19 33 38,7 | | 7 5 2,67 | 5 47 42,08 | 4 57 27,33 | 7 33 37,80 | | --- | --- | --- | --- | | 8,61 | 3,20 | 0,60 | 3,78 | | 8,26 | 7,52 | 6,75 | 4,20 | | 2,26 | 0,95 | 0,29 | 1,25 | | + 7,08 | + 5,80 | + 4,95 | + 7,55 | | 7 4 50,62 | 5 47 36,21 | 4 57 24,64 | 7 33 44,52 | ### SECTOR WEST. | 21 7 5 10,3 | 21 5 47 52,8 | 21 4 57 35,3 | 21 7 33 30,0 | | 24 7 5 10,5 | 24 5 47 52,3 | 24 57 35,0 | 24 33 30,8 | | 27 5 9,7 | 27 47 51,0 | ... | ... | | 7 5 10,17 | 5 47 52,03 | 4 57 35,30 | 7 33 30,40 | | --- | --- | --- | --- | | 9,37 | 4,24 | 1,60 | 3,52 | | 8,26 | 7,52 | 6,75 | 4,20 | | 2,56 | 1,09 | 0,32 | 1,36 | | + 7,08 | + 5,80 | + 4,95 | + 7,55 | | 7 4 57,06 | 5 47 44,98 | 4 57 31,58 | 7 33 37,27 | | 7 4 50,62 | 5 47 36,21 | 4 57 24,64 | 7 33 44,52 | | 7 4 53,84 | 5 47 40,60 | 4 57 28,11 | 7 33 40,90 | | 8 33 37,82 | 7 16 29,20 | 6 26 13,20 | 6 4 56,56 | | 1 28 43,98 | 1 28 48,60 | 1 28 45,09 | 1 28 44,34 | This being a little wide of the rest is left out. R r e The following are Observations made at the Points N, and near P, in the Year 1764: But the Length of Time between these, and those made at A, being near three Years—probably the Set made at N, in December 1766, may be best to be used in determining the Length of a Degree of Latitude. ### STAR'S ZENITH DISTANCES. #### SECTOR IN THE TENT, PLANE EAST. | 1764 | γ Andromedæ | β Persei | α Persei | δ Persei | |------|-------------|----------|----------|---------| | | o' | " | o' | " | o' | " | o' | " | | January | 17 | 1 15 | 0,0 | 0 5 40,0 | . . . . . | 7 4 29,5 | | | 19 | . . . . . | 0 5 39,6 | . . . . . | 7 4 31,0 | | | 20 | 1 15 | 2,2 | 0 5 39,0 | 9 3 47,0 | 7 4 30,2 | | | 21 | 1 15 | 1,3 | 0 5 37,5 | 9 3 49,7 | 7 4 30,8 | | | 22 | 1 15 | 1,2 | 0 5 38,0 | . . . . . | 7 4 31,0 | Mean, January | 20 | 1 15 | 1,2 | 0 5 38,8 | 9 3 48,3 | 7 4 30,5 | Aberration declin. | — | 10,0 | — | 9,1 | — | 11,4 | — | 10,4 | Deviation D° | — | 3,3 | — | 5,7 | — | 6,2 | — | 6,7 | Precefs. fr. 1 Jan. 1764 | — | 1,0 | — | 0,8 | — | 0,7 | — | 0,7 | Refraction | + | 1,4 | + | 0,1 | + | 10,5 | + | 8,3 | Observatory S° of Tent | + | 0,3 | + | 0,3 | + | 0,3 | + | 0,3 | Mean zen. dist. 1 Jan. 1764 | 1 14 48,6 | 0 5 23,6 | 9 3 40,8 | 7 4 21,3 | #### SECTOR IN THE OBSERVATORY, PLANE WEST. | January | 26 | 1 15 | 4,7 | 0 5 41,7 | . . . . . | 7 4 32,8 | | | 27 | 1 15 | 5,7 | 0 5 41,0 | 9 3 57,0 | . . . . . | | | 28 | 1 15 | 4,5 | 0 5 44,0 | 9 3 57,5 | 7 4 33,0 | | | 29 | 1 15 | 5,5 | 0 5 44,0 | 9 3 55,3 | 7 4 32,7 | Mean, January | 27½ | 1 15 | 5,1 | 0 5 42,7 | 9 3 56,6 | 7 4 32,8 | Aberration in Declin. | — | 9,0 | — | 8,6 | — | 11,1 | — | 10,3 | Deviation D° | — | 3,3 | — | 5,7 | — | 6,2 | — | 6,7 | Precefs. from 1 Jan. 1764 | — | 1,3 | — | 1,1 | — | 1,0 | — | 0,9 | Refraction | + | 1,4 | + | 0,1 | + | 10,5 | + | 8,3 | Mean zen. dist. 1 Jan. 1764 | 1 14 52,9 | 0 5 27,4 | 9 3 48,8 | 7 4 23,2 | D° Plane East | 1 14 48,6 | 0 5 23,6 | 9 3 40,8 | 7 4 21,3 | True zen. dist. at the point | 1 14 50,8 | 0 5 25,5 | 9 3 44,8 | 7 4 22,2 | N, 1 Jan. 1764 | + | 49,45 | 40,56 | . . . . . | + | 34,61 | Reduced to Oct. 11, 1766 | 1 15 40,25 | 0 6 6,06 | . . . . . | 7 4 56,81 | **PLANE WEST** | Capella | β Aurigae | Castor | α Lyrae | |---------|-----------|--------|---------| | 1764 | | | | | January | Feb. | Jan. | | | February| | Feb. | | Mean zen. dist. 1 Jan. 1764 **PLANE EAST** February Mean zen. dist. 1 Jan. 1764 True zen. dist. at the point N. 1 Jan. 1764 Precels. to Oct. 11, 1766 Stars Zenith Distances observed at a Point 7 chains 91 links North of P. **PLANE EAST** | Capella | α Lyrae | δ Cygni | γ Cygni | α Cygni | |---------|---------|---------|---------|---------| | May | | | | | | 1764 | | | | | | 7 | 6° 29'8" | 6° 19'10"5" | 13° 4'50" | 6° 3" | | 8 | 6° 28'3" | 7° 9'10"0" | Ab. + | 14'9" | | 9 | 6° 29'0" | 9° 10'5" | Dev. + | 8'74" | | 13 | 6° 30'0" | 11° 9'0" | Prec. - | 3'05" | | | 12° 10'0" | Ref. + | 5'6" | | | 13° 7'7" | | | | Mean of the 1st fett | Mean of the above | 4° 43' 0"4" | |-------------------|-------------| Aberration | Ab. + | 16'5" | | Nutation | 7'6" | | Precels. fr. | 4'5" | | Refract. | 5'5" | True zen. dist. 1 Jan. 1764 | 6° 23'9" | 1° 8'50"2" | 22° 4'50" | 9'5" | 22° 0'12" | 57'75" | |-----------|------------|-----------|------|-----------|--------| | Ab. + | 13'2" | | | | | | Nut. + | 8'74" | | | | | | Prec. - | 3'25" | | | | | | Refr. + | 5'6" | | | | | Mean | 4° 50' 33'8" | 0° 12' 40'6" | |--------------|--------------| True zen. dist. 1 Jan. 1764, from the mean of all the five observations. | 4° 50' 33'15" | 0° 12' 40'60" | |---------------|---------------| May α Lyrae | 19° 1'9" | 4'3" | | 23° 9'3"8" | | | 25° 9'3'7" | | Mean of the 2d fett | 22° 1'9" | 4'3" | |-----------|-----| Aberration | 9'5" | | Nutation | 9'4" | | Precels. | 1'1" | | Refraction | 1'2" | Mean | 1° 8'47'7" | | Mean above | 8° 50'2" | | Mean of all the observations | 1° 8'49'0" | True zen. dist. 1 Jan. 1764, from the mean of all the observations. | 4° 43' 25'0" | |---------------| Star's Zenith Distances observed at a Point 7 chains 91 links North of P. **PLANE WEST.** | Year | Month | Day | Hour | Minute | Second | |------|-------|-----|------|--------|--------| | 1764 | May | 28 | 6 | 32,7 | 27 | | | June | 1 | 32,3 | 28 | | | | | 5 | 31,7 | June | | | Star | Capella | α Lyrae | δ Cygni | γ Cygni | α Cygni | |------|---------|---------|---------|---------|---------| | | 28 6 o 32,7 | 1 08 59,0 | 4 50 14,8 | 0 12 52,6 | 4 48 4,3 | | | 1 o 32,3 | 8 59,5 | 4 50 51,0 | 12 51,0 | 43 4,2 | | | 5 o 31,7 | June | 3 58,0 | 50 15,0 | 12 51,0 | 43 4,0 | | | | | 4 59,8 | 50 15,3 | 12 51,0 | 43 7,5 | | | | | 8 58,2 | 50 16,8 | 12 50,3 | 43 5,4 | | | | | 8 57,3 | 50 16,3 | 12 49,8 | 43 6,5 | | | | | 8 57,3 | 50 18,0 | 12 50,0 | 43 7,8 | | | | | | | 12 49,0 | 43 8,0 | | | | | | | 12 48,0 | 43 8,3 | Mean | Aberration | Nutation | Precefs. from 1 Jan. 1764 | Refraction | |------------|----------|---------------------------|------------| | + 1,4 | - 9,0 | - 2,2 | + 7,0 | | | | | | | | | | | Mean zen.diff | 1 Jan. 1764 at a point 7 cha. 91 lin. | |---------------------------------------| | 6 o 29,4 | 1 8 45,0 | 4 50 37,24 | 0 12 35,7 | 4 43 26,9 | D° Plane East | 0 23,9 | 1 8 49,0 | 4 50 33,15 | 0 12 40,60 | 4 43 25,0 | True zen.diff | 1 Jan. 1764 at a point 7 cha. 91 lin. North of P | |-------------------------------------------------| | 6 o 26,60 | 1 8 47,00 | 4 50 35,19 | 0 12 38,20 | 4 43 25,95 | Precefs. to 11 Oct. 1766 | + 14,56 | - 7,03 | + 23,03 | - 30,75 | + 34,59 | True zen.diff | 1 Oct. 1766 | |-------------| | 6 o 41,16 | 1 8 39,97 | 4 50 58,22 | 0 12 7,45 | 4 44 0,54 | D° at the point A | 7 16 29,20 | + 7 10,79 | 6 6 46,65 | 1 3 40,18 | 5 59 52,92 | Difference | 1 15 48,04 | 1 15 50,76 | 1 15 48,43 | 1 15 47,63 | 1 15 52,38 | Arches by different Stars Mean | 1 15 49,45 | = the celestial arch between the point 7 cha. 91 lin. N. of P and the point A | Remarks on re-measuring the Lines with two rectangular Levels, or measuring Frames. The levels used in this work were, each, 20 feet in length, and 4 feet in height. They were made of pine, an inch thick, and in form of a rectangle; the breadth of the bottom board was $7\frac{1}{2}$ inches, that of the top = 3 inches, of the ends = $4\frac{1}{2}$ inches, and the bottom and top were strengthened with boards firmly fixed to them at right angles. The joints were secured with plates of iron, and the ends were plated with brass. The plumb lines used in setting them level, were = 3 feet and 2 inches in length, and hung in the middle of the levels, being secured in a tube from the wind, in the manner of carpenters levels; wherefore we called these by the same name. When the plumb-line bisected a point at the bottom, the ends were perpendicular. Where the ground was not horizontal, or there were logs, &c. to pass over, one end of the level was raised by a winch and pully. The level being set, a short staff was drove into the ground (very near and opposite the plumb-line), in the top of which moved a thin plate of iron, about 12 inches long; at the ends of which were points, which were directed to the intersections of lines, drawn on the board that covered the plumb-line. By bringing the points in a line with one of the said intersections, if the level was by accident moved, it might be discovered, and brought again to its place. A level being thus marked, the end of the other was brought in contact with it, and marked in the same manner, before the first was moved; the first was then taken up, and set before the last. And so the operation was continued. Mr. Dixon attended one plumb-line and staff, and I the other. The measure was carried on in a straight line, and in the proper direction, by pointing the levels to the farthest part of the vista that could be seen; this was readily and accurately done, on account of their lengths. The levels were frequently compared with the brass standard, of 5 feet, provided for that purpose, and the difference was noted between 8 times the brass standard, and the length of the two levels taken together; as may be seen in the 3d and 4th columns of the following table. This difference serves for reducing the measure taken with the levels, to what it would have been if it had been taken with the brass standard itself; see column 6th. For facilitating this comparison of the levels with the brass standard, pieces of brass were fixed into the bottom boards of the levels, on each of which was drawn a faint line. And one tenth of an inch at the end of the brass standard being divided into ten parts or hundredths of an inch, the difference between eight times the brass standard, and the two levels joined together, was with the help of a magnifying glass of a short focus, determined to great accuracy. Moreover, the brass standard being liable to alter with the changes of heat and cold, a further correction becomes necessary on that account, in order order to reduce the measures to the temperature of 62° of Fahrenheit's thermometer, which is the term to which the former operations of this kind have been reduced. For this purpose, the rate of expansion of brass is taken from Mr. Smeaton's experiments, made with a pyrometer of his invention (see Philos. Trans. Vol. XLVIII. Part II.) which is $\frac{1}{100}$th of an inch upon a length of one foot for a variation of 180° of Fahrenheit's thermometer; whence the expansion answering to four times the length of the brass standard, or 20 feet, or the length of one level, would be $\frac{4}{100}$th of an inch for the same difference of the thermometer; and $\frac{25}{100}$th of an inch for 1° of the same thermometer. Therefore, in order to find the correction of column 7th, the constant quantity .00258 was multiplied by the difference of 62, and the degree of the height of the thermometer; and that product, again multiplied by the number of levels measured, gave the correction required in inches and decimal parts of an inch; which was additive or subtractive, according as the thermometer was higher or lower than 62 degrees. In the following Process, the 1 and 2 Columns contain the time of the day, M signifying morning, A afternoon. 3 - - - - the height of the thermometer at D°. 4 - - - - the quantity, in hundredth parts of an inch, that the two levels, taken together, were more or less than eight times the brass standard, or 40 feet. 5 - - - - the number of levels measured between the times, that the levels themselves were measured with the brass standard. 6 - - - - the corrections, or quantity in inches, to be added to, or subtracted from, the number of levels measured each day, arising from the levels being more or less than the brass standard. 7 - - - - the correction, or quantity arising from the thermometer in inches. Began, at the point N, to re-measure the lines with two rectangular levels, 20 feet each in length. | Year | Month | Day | Hour | Minute | Temperature | Correction | |------|-------|-----|------|--------|-------------|------------| | 1768 | February | 6 | 23 | 10 | M 52 +.12 | 203 +12.18 - 4.97 | | | | | | 3 | A 53 +.12 | | | | | | | | The breadth of Brandwine the 1st time | 8.18 + 0.49 = 8.47 | | | | | | | D° a 2d, where we crossed 12.20 + 0.73 | | Vol. LVIII. | Date | Time | Temperature | Description | |------|------|-------------|-------------| | Feb 1768 | 9 AM | M 32 +,23 | | | | 4 PM | A 42 +,21 | | | Feb 24 | 9 AM | M 54 +,08 | | | | 1 PM | A 44 +,12 | | | | 5 PM | 39 +,32 | | | Feb 25 | 9 AM | M 40 +,12 | | | | 4 PM | A 45 +,11 | | | Feb 27 | | | Rain | | Feb 28 | 8 AM | M 40 +,08 | | | | 8 PM | 80 + 3,20 | Rain in the afternoon | | Mar 1 | 9 AM | M 32 +,23 | | | | 4 PM | A 42 +,21 | | | Mar 2 | 8 AM | M 32 +,20 | | | | 1 PM | A 51 +,10 | | | | 5 PM | 48 +,115 | | | Mar 3 | 8 AM | M 40 +,185 | | | | 2 PM | A 48 +,125 | | | | 5 PM | 43 +,145 | | | Mar 4 | 8 AM | M 31 +,19 | | | | 2 PM | A 38 +,16 | | | | 5 PM | 30 +,185 | | | Mar 5 | 8 AM | M 27 +,18 | | | | 1 PM | A 41 +,12 | | | | 5 PM | 29 +,165 | | | Mar 6 | 8 AM | M 28 +,155 | | | | 2 PM | A 38 +,09 | | | | 5 PM | 36 +,105 | | | Mar 7 | 8 AM | M 36 +,103 | | | | 1 PM | A 52 -,037 | | | | 5 PM | 45 +,06 | | | Mar 8 | 8 AM | M 36 +,103 | | | | 1 PM | A 52 -,037 | | | | 5 PM | 45 +,06 | | Very dry winds with frost. Here subtract 4 inches, for going round the corner of a barn. This reached the point P. Hence NP = 3914.45 levels + 199.02 inches = 178,40 inches = 78290.72 feet. Began at the Point C. | Date | Time | M | 60 | 137.15 | 2.74 | 0.71 | Rain | |------|------|---|----|--------|------|------|------| | | 12 | 9 | 52 | +0.07 | 108 | +2.16| 1.95 | | | | A | 58 | +0.01 | 156 | +3.51| 2.61 | | | | 5½| 53 | +0.08 | | | | Began where we left off, on the 12th instant, to measure as before. | Date | Time | M | 34 | 132 | +5.94 | 8.51 | |------|------|---|----|-----|-------|------| | | 2 | A | 40 | +0.09 | 144 | +6.12| 8.91 | | | | | 36 | +0.08 | | | | | Date | Time | M | 36 | 264 | +7.65 | 15.66 | |------|------|---|----|-----|-------|-------| | | 2 | A | 42 | +0.03 | 156 | +4.06| 9.45 | | | | 5½| 35 | +0.073| | | | This reached the point D. Hence CD = 1330.50 levels + 41.63 inches = 64.95 inches = 26608.06 feet. From D to g = 1 chain, and 36 links found before; = 89.76 feet. Sent to Philadelphia, about 40 miles distant, for tents, &c. Began at the point B, to measure the line A.B. | Date | Time | M | 49 | 132 | -5.28 | 4.42 | |------|------|---|----|-----|-------|------| | | 25 | | | | | | | | 26 | Noon | 57 | -0.05 | 211.05 | +1.58 | -6.53 | | | | 6 | A | 43 | +0.065| | | S f 2 | Date | Time | Temperature | Description | |------|------|-------------|-------------| | March 28 | 8 M | +19 | Compared two thermometers; they agreed within one division. | | 2 A | +09 | 264 | +13,2 -12,60 | | 5½ | +11 | 264 | +13,2 -12,60 | | 8 30 | 8½ M | +14 | 288 | +11,95 -9,28 | | 2½ A | +025 | 288 | +11,95 -9,28 | | 6½ | +10 | 192 | +5,95 -4,46 | | 4 31 | 8½ M | +15 | 204 | +12,85 -4,21 | | 2 A | +105 | 204 | +12,85 -4,21 | | 6½ | +17 | 192 | +13,15 -2,97 | | April 1 | 8 M | +195 | 324 | +31,10 -13,79 | | 2 A | +19 | 324 | +31,10 -13,79 | | 6 | +19 | 204 | +19,38 -9,73 | | 2 9 | 40 | +18 | 228 | +18,24 -11,17 | | 2½ A | +14 | 228 | +18,24 -11,17 | | 6½ | +15 | 168 | +12,18 -8,88 | | 3 | | | | | | 4 9½ M | +04 | 312 | +12,48 -14,08 | | 3 A | +12 | 312 | +12,48 -14,08 | | 6 | +13 | 192 | +12,00 -9,16 | | 5 | | | | | | 6 8½ M | +14 | 228 | +15,39 -10,58 | | 3 A | +13 | 228 | +15,39 -10,58 | | 6½ | +13 | 204 | +13,26 -10,70 | | Crossed Bohemia river obliquely = 33,875 + 2,21 -10,70 | | 7 | | | | | | 8 11 M | +23 | 396 | +38,02 -24,01 | Snow in the evening. Snow all day, and frost at night. | Date | Time | Temperature | Description | |------|------|-------------|-------------| | April 9th | M 44 | +165 | | | April 9th | A 57 | CO 192 | +7.96 -5.69 | | April 9th | 6 | 51 | +0.02 204 | +1.02 -4.21 | | April 10th | M 59 | -0.17 | | | April 10th | A 66 | -0.16 | -12.81 +0.37 | | April 10th | 6½ | 59 | -0.10 | -14.82 +0.29 | | April 12th | M 47 | -0.02 | | | April 12th | A 70 | -0.14 | -13.92 -3.14 | | April 12th | 6 | 60 | -0.03 | -6.63 +1.21 | | April 13th | M 64 | -0.08 | | | April 13th | A 76 | -0.105 | -11.16 +4.95 | | April 13th | 6 | 64 | -0.07 | -6.86 +3.22 | | April 14th | M 53 | -0.02 | | | April 14th | A 53 | OO | -1.98 -9.19 | | April 15th | M 45 | +1.18 | | | April 15th | 264 | +23.76 -11.57 | | April 16th | M 46 | +2.20 | | | April 16th | A 56 | +2.05 | +39.99 -11.23 | | April 17th | M 52 | +1.11½ | | | April 17th | Noon 67 | -0.02 | +6.20 -1.70 | | April 17th | A 58 | -0.01 | -1.44 +0.24 | | April 19th | M 53 | +0.01 | | | April 19th | A 74 | -0.075 | -9.50 +2.23 | | April 19th | after 3h aft. | 132 | | | April 20th | M 57 | +0.025 | | | April 20th | A 78 | -0.065 | -3.12 +4.43 | | April 20th | 6½ | 61 | -0.02 | -4.54 +4.18 | Rain in the afternoon: this day we passed through water, two feet deep, for half a mile. | Date | Time | Temperature | Notes | |------|------|-------------|-------| | April 1768 | 21 | M 52 +0.06 | Left off in a swamp of water 18 inches deep. | | | 22 | A 75 +0.02 | Rain day and night. | | | 23 | aft. 1/2 A | Rain till 11 AM. | | | 24 | | Swamps so full of water we could not proceed. | | | 25 | | | | | 26 | | | | | 27 | M 73 00 | | | | 5 1/2 | A 72 -0.35 | | | | 28 | M 54 -0.03 | | | | 6 | A 61 1/2 -0.02 | | | | 29 | M 60 +0.19 | | | | 7 | A 76 +0.11 | | | | 6 | 73 +0.11 | | | May | 1 | M 54 +0.05 | | | | 2 | M 54 +0.09 | | | | 3 | M 61 +0.15 | | | | 3 | A 82 +0.02 | | | | 6 1/2 | 75 1/2 +0.075 | | | | 4 | M 79 +0.15 | Thunderstorm all the morning; passed the main branch of Choptank. | This day we found the dist. between the 42d and 43d mile posts 3 levels and 6 feet more than usual between 2 mile posts. | Date | Time | M | A | Temperature | Dew Point | Humidity | |------|------|---|---|-------------|-----------|----------| | May 24 | 5 | M | 70½ | +1.15 | 264 | +8.97 | +10.93 | | | 2 | A | 86 | +1.02 | 132 | +3.63 | +5.79 | | | 5½ | 72 | +0.09 | | | | | | May 25 | 6 | 9½ | M | 66 | +1.14 | 324 | | | | | 4 | A | 63 | +1.55 | | | | | | | aft. 4h A | | | | | | | | May 26 | 7 | 8 | M | 60 | +1.85 | 408 | +25.5 | +5.26 | | | 3 | A | 74 | +0.65 | | | | | | May 27 | 9 | 7½ | M | 63 | +0.3 | 528 | -8.69 | +16.35 | | | 4½ | A | 85 | -0.95 | | | | | | May 28 | 10 | 8½ | M | 61 | +0.05 | 372 | +1.49 | +2.40 | | | 7 | A | 68 | +0.01 | | | | | | May 29 | 11 | 9½ | M | 70 | +1.11 | 528 | +22.44 | +12.26 | | | 6½ | A | 72 | +0.06 | | | | | | May 30 | 12 | 7 | M | 54½ | +2.23 | 264 | +17.16 | -0.68 | | | 2 | A | 67 | +0.03 | 276 | +3.03 | +3.92 | | May 31 | 13 | 8½ | M | 68 | +1.10 | 300 | +7.33 | +9.71 | | | 3 | A | 75 | -0.25 | | | | | | | aft. 3h A | | | | | | | | June 1 | 14 | 10½ | M | 66 | +1.45 | 264 | +18.74 | +5.45 | | | 3 | A | 74½ | +1.14 | | | | | | June 2 | 15 | 7½ | M | 57 | +1.19 | 384 | +22.44 | +9.53 | | | 3½ | A | 81 | -0.02 | | | | | | | aft. 3½ h A | | | | | | | | June 3 | 17 | 8½ | M | 66 | +1.12 | 384 | +4.75 | +19.75 | | | 3 | A | 87 | -0.85 | | | | | | | aft. 3h A | | | | | | | Rain in the night and morning. Rain last night. | Date | Time | Temperature | Notes | |------|------|-------------|-------| | May 1768 | 18 | 8½ M 67 +,085 | Passed through Marshy Hope, water 4 or 5 feet deep. | | | 1 A 90 +,14 | 144 + 8,13 + 6,13 | | 24 | 19 | 9½ M 69 +,15 | | | | 3 A 86 +,075 | 264 + 14,78 + 10,55 | | 20 | 8 | M 69 +,17 | Great dew for 4 mornings past. | | | 3 A 93 +,04 | 276 | | | aft. 3½ A 168 + 23,31 + 21,76 | | 21 | 9 | M 73 +,08 | Great dew. | | | 4 A 86 —,01 | 360 + 6,30 + 16,25 | | 22 | | | Rain. | | 23 | | | Rain. | | 24 | 7 | M 50 +,35 | | | | 3 A 75 +,21 | 480 | | | aft. 3½ A 180 + 92,40 + 0,85 | | 25 | 9½ M 59 +,28 | | | | 4 A 56 +,34 | 396 + 61,38 — 4,59 | | | | | Passed through water part of the day. | | 26 | 9½ M 58 +,38 | | | | 5½ A 53 +,36 | 528 + 97,68 — 8,85 | | | | | Rain last night and part this day, the levels continually wet. | | 27 | 8 | M 65 +,18 | Dry weather. | | | 3½ A 79 +,14 | 396 | | | aft. 3½ A 264 + 52,80 + 17,02 | | 28 | | | | | 29 | | | | | 30 | | | | This reach'd to the North side of the river Nanticoke, near to the 7th mile post; here we left a mark. 24 June 2 Passed over the river Nanticoke, and began at the 6th mile post from the point A. | Time | M | A | Distance | |------|-----|-----|----------| | 8 | 84 | +075| | | 2½ | 74 | +08 | | | aft. 2½h | A | 228 | +20,59 | | | | | +23,15 | | Time | M | A | Distance | |------|-----|-----|----------| | 3 | 76 | +155| | | 3 | 85 | +02 | | | aft. 3h | A | 264 | +29,04 | | | | | +31,50 | | Time | M | A | Distance | |------|-----|-----|----------| | 4 | 64 | +213| | | 1 | 82 | oo | | | | | | 398,875 | | | | | +21,15 | | | | | +11,32 | At the point A. Began at the 6th mile post, and measured Northward through the swamp of Nanticoke. | Time | M | A | Distance | |------|-----|-----|----------| | 7½ | 67 | +12 | | | 2 | 77 | +055| | | | | | 230 | | | | | +10,12 | Crosses the river to the mark left the 31st of May. This finished the line A B. Hence AB = 21696.47 levels + 892.34 inches + 94.51 inches = 434011.64 feet. The breadth of the rivers was found by measuring a base, and taking angles with a Hadley's quadrant. Note. The reckoning was kept by stretching a rope in the line to be measured (in general) = 12 levels, which was often proved: and it was almost impossible that an error could arise; as we always began the rope with the same level, and ended it with the other; the rope not being removed till the last level was set. The person that stretched the rope, sometimes Mr. Dixon, and sometimes myself, kept the account of the number of ropes measured: though the mile posts in the lines AB and DC were sufficient for that purpose, as the lines had been so often measured before. In the line NP there were no mile posts, but two or three intermediate marks, which we found to agree in a general law with the levels. Supposing the levels exactly = 20 feet each; then in the line NP a mile per chain measure = a mile and 9.44 feet by the levels; and in the line CD a mile per chain measure = a mile and 9.86 feet by the levels. Vol. LVIII. In the line AB, what the levels make more than the chain, between the mile posts is as follows. | Miles from the point | Diff. in feet | |----------------------|--------------| | A. | | | 81 | 14½ | | 80 | 74 | | 78 | 30½ | | 76 | 40 | | 75 | 25 | | 72 | 39 | | 70 | 16 | | 66 | 38 | | 65 | 14 | | 63 | 37 | | 61 | 14½ | | 60 | 36 | | 59 | 14 | | 58 | 35 | | 57 | 14½ | | 56 | 34 | | 55 | 14½ | | 54 | 33 | | 53 | 14 | | 52 | 32 | | 51 | 13 | | 50 | 12 | | 49 | 11 | | 48 | 10 | | 47 | 9½ | | 45 | 9 | | 44 | 8 | | 43 | 7 | | Miles from the point | Diff. in feet | |----------------------|--------------| | A. | | | 43 | 14½ | | 42 | 74 | | 40 | 30½ | | 39 | 40 | | 38 | 25 | | 37 | 39 | | 36 | 16 | | 35 | 38 | | 34 | 14 | | 33 | 37 | | 32 | 14½ | | 31 | 36 | | 30 | 14 | | 29 | 35 | | 28 | 14½ | | 27 | 34 | | 26 | 14 | | 25 | 33 | | 24 | 13 | | 23 | 32 | | 22 | 12 | | 21 | 12½ | | 20 | 11½ | | 19 | 11 | | 18 | 10½ | | 17 | 10 | | 16 | 9½ | | 15 | 9 | | 14 | 8 | | 13 | 7½ | | 12 | 8 | | 11 | 7 | | 10 | 6 | | 9 | 6 | | 8 | 5 | | 7 | 5 | | 6 | 4 | | 5 | 4 | | 4 | 3 | | 3 | 3 | | 2 | 2 | | 1 | 2 | | 0 | 1½ | We took notice of these differences as we measured from B' to A, always finding the miles greater by the chain measure, by the quantity above, which shows that the chain was continually extending itself by use; as we had direct proof of, being obliged to contract it every day, and re-adjust it to its proper length by means of the standard chain. To find the Latitude of the Point N. | Star | Declination | |---------------|-------------| | δ Persei | 7° 4' 22.2" | | Capella | 5° 47' 32.3" | | β Aurigae | 4° 57' 26.3" | | Castor | 7° 33' 23.1" | | α Lyrae | 1° 21' 44.2" | Stars decl. by Dr. Bradley. | Latitude by different stars | 39° 56' 17.8" | 56° 20' 7" | 56° 17' 9" | 56° 19' 9" | 56° 18' 2" | |-----------------------------|--------------|------------|------------|------------|------------| | | 20.7 | 17.9 | 19.9 | 18.2 | | | Mean | 39° 56' 18.9" | | | | | | Arch between N and A | 1° 28' 44.9" | | | | | The latitude of the point N. The latitude of the point A. The mean latitude. Cha. Mason. Jere. Dixon. The Length of a Degree of Latitude in the Province of Maryland and Pennsylvania, deduced from the foregoing Operations; by the Astronomer Royal. The difference of latitude of the points N and A, or the amplitude of the celestial arch, answering to the distance between the parallels of latitude passing through N and A, has been found by the sector, page 306, to be 1° 28' 45", 0. The terrestrial measure of the distance of the said parallels is next to be found. This is composed of the sum of the lines NP, CD, Dg, and AR, the last mentioned line being the reduction of AB to a meridian line passing through A; therefore BR expresses a parallel of latitude passing through B. Let BT be an arch of a great circle drawn perpendicular to the meridian line, AR produced; The triangle BAT, on account of the smallness of its sides with respect to the radius of the earth, and the smallness of the angle BAT = 3° 43' 30" may be taken for a plane rectilinear triangle, in what follows, without any sensible error, as will appear to any one who makes the trial. Therefore it will be, by proportion, as radius is to the cosine of the angle BAT = 3° 43' 30" so is AB = 434011.6 English feet, to AT = 433094.6 English feet. But this is to be lessened by the small quantity RT, or the distance of the parallel circle BR from the great circle. \( B_t \), which is to a third proportional to the diameter of the earth and the line \( BR \), as the tangent of the latitude of the point \( B_t \) to the radius. Whence \( R_t = 15.8 \) feet which subtracted from \( A_t \) just found \( = \) \[ \begin{align*} 433094.6 \text{ leaves} & \quad AR = 433078.8 \text{ feet} \\ \text{To which add} & \quad NP = 78200.7 \\ \text{as found before} & \quad CD = 26608.0 \\ & \quad Dg = 89.7 \end{align*} \] The sum is \( = 538067 \) feet \( = \) an arch of meridian intercepted between the parallels of latitude passing through the points \( N \) and \( A \), answering to the celestial arch \( 1^\circ 28' 45'' \). Then say, as \( 1^\circ 28' 45'' \); is to \( 1^\circ : : \) so is \( 538067 \) feet, to \( 363763 \) English feet, which is the length of a degree of latitude in the provinces of Pennsylvania and Maryland. The latitude of the Northernmost point \( N \), was determined from the zenith distances of several stars, see page \( 323 = 39^\circ 56' 19'' \) and the latitude of the Southernmost point \( A = 38^\circ 27' 34'' \). Therefore the mean latitude expressed in degrees and minutes is \( = 39^\circ 12' \). To reduce this measure of a degree to the measure of the Paris toise, it must be premised, that the measure of the French foot was found upon a very accurate comparison, made by Mr. Graham, of the toise of the Royal Academy of Sciences at Paris, with the Royal Society's brass standard, to be to the English foot, as \( 114 \) to \( 107 \). See Philosophical Transact, Vol. XLII, p. 185. Therefore say as \( 114 : \) is to \( 107 : : \) so is \( 363763 \) the measure of the degree in English feet, to \( 341427 \) the measure of the degree in French feet, which divided by \( 6 \), the number of feet in a toise, gives the length of the degree \( = 56904 \frac{1}{2} \) Paris toises, in the latitude \( 39^\circ 12' \) North. Such is the length of a degree in this latitude, supposing the five feet brass standard made use of in this measure to have been exactly adjusted to the length of the Royal Society's brass standard. It was really adjusted by Mr. Bird, by his accurate brass scale of equal parts, which he makes such excellent use of in dividing astronomical instruments, and which is just \( \frac{1}{1000} \)th part of an inch shorter than the Royal Society's brass standard upon a length of three feet. If one would take notice of so small a difference, the length of a degree just found must be lessened by \( \frac{1}{1000} \)th part, or by ten feet, in order to reduce it to the measure of the Royal Society's standard. Since I am treating of such niceties, may it be allowed me to add, that the five feet brass standard having been again compared with Mr. Bird's scale, since its return from North America, appeared both to myself and Mr. Bird to be just \( \frac{1}{1000} \)th part of an inch shorter than the scale, upon that side on which the hundredths of an inch are placed at one end, and \( \frac{2}{1000} \)ths of an inch shorter than the scale upon the opposite side? which diminution of its length is undoubtedly owing to the small wearing or battering which it has met with in the frequent use that was made of it. But the divided side of the rod having been that which was made use of in measuring the levels, is what is to be regarded in the present case. If one would allow for the wearing of the rod, one may suppose it to have suffered a gradual diminution; and then one must take a mean between its first length, which was the same with Mr. Bird's scale, and its present length, which is \( \frac{1}{1000} \)th of an inch shorter; as one may suppose it a medium to have been \( \frac{1}{1000} \)th part of an inch shorter than A MAP of that Part of AMERICA where a Degree of LATITUDE was measured for the Royal Society by Cha. Mason & Jere Dixon. J. Mynde sculp. than Mr. Bird's scale; on which account the length of the degree should be further diminished by $\frac{1}{360}$th part, or 3 feet, which added to 10 feet, the correction required on account of the difference of Mr. Bird's scale and the Royal Society's standard, gives 13 feet to be subtracted from the length of the degree calculated above. The whole correction will perhaps be thought scarce deserving of notice, especially as an error of only $1''$ in the celestial measure would produce an error of no less than 67 feet in the length of the degree. Moreover it is probable that the length of a degree has been already taken 10 or 20 feet too short, by placing the point C too far to the Southward; which would about balance the small correction in question. Therefore, all things being considered, the length of the degree may be stated as given above, viz. = 363763 English feet or 56904$\frac{1}{2}$ Paris toises. It must, however, be observed, that the accuracy of this reduction into Paris toises depends upon a supposition that the length of the French toise, which is of iron, was laid off by the gentlemen of the Royal Academy of Sciences, upon the brass rod sent over to them for that purpose by Mr. Graham (which was afterwards returned to him); in a room where the heat of the air answered to 62 of Fahrenheit's thermometer, or 15 of Reaumur's, or nearly so, which is probable enough, but is a point that does not appear to have been ascertained. For, on account of the difference of expansion of brass and iron; 2 rods made of those metals, however accurately they may be made of equal lengths at first, will only agree together afterwards in the same temperature of the air in which they were originally adjusted together. It is fortunate that the uncertainty in the present case is but small, since 20° difference of Fahrenheit's thermometer or 10° of Reaumur's produces, according to Mr. Smeaton's experiments, a difference of the expansions of brass and iron of only $\frac{1}{360}$th part, which would cause an error of only 27 English feet or about 4 Paris toises in the length of the degree. It is however to be wished, that the proportion of lengths of the French and English measures might be again ascertained by another careful experiment, in which the temperature of the air, as shewn by the thermometer, might be noted at the time. [See the Map of the Country, where the foregoing Observations were made, Tab. XIV] POSTSCRIPT, BY THE ASTRONOMER ROYAL. HAVING, some time ago, acquainted M. De la Lande, of the Royal Academy of Sciences at Paris, by letter, of this measure of a degree of latitude in North America, and at the same time expressed my doubts about the certainty of reducing it to French measure, from the proportion of the English to the French foot found by Mr. Graham; principally because no notice had been taken of the height of the thermometer at Paris, when the length of the French iron toise was laid off upon the brass rod sent thither by Mr. Graham, whence the proportion of the two measures was afterwards determined by him; and having also mentioned my opinion of the expediency of making another experiment of the proportion of the two measures, in which every necessary circumstance should be noted; and that I might probably request the favour of M. De la Lande to take the trouble to cause a French toise to be made for me, and to see it exactly adjusted to their standard, and then sent to me; he has been pleased to lend me two toises, toises, which he says are exactly adjusted to the standard of the toise used by Messrs. De la Condamine and Bouguer in the measure of the degrees of latitude at Peru, in order to their being compared with the English measure. This comparison has been made by Mr. Bird, with his usual accuracy, while I was present, and also examined the same, since my account of the length of the degree of latitude aforegoing was printed; and the result is, that the longest of the two toises (for there is a small difference between them), and which has since been marked with the letter A, is equal to 76,738 inches by Mr. Bird's brass scale of equal parts, and the shortest toise, which is marked B, is = 76,735 inches by the same scale; the height of Fahrenheit's thermometer in the room being 61 degrees. The mean of the lengths of the two toises is therefore = 76,736.5 inches by Mr. Bird's scale. But Mr. Bird's scale is \(\frac{1}{1000}\)th of an inch upon 3 feet shorter than the Royal Society's brass standard, and consequently \(\frac{2}{1000}\)th too short for the same upon 76,736.5 inches; therefore \(\frac{2}{1000}\)th of an inch must be subtracted from 76,736.5; which leaves 76,734.4 for the length of the Paris toise in measures of the Royal Society's brass standard, in the temperature of 61° of Fahrenheit's thermometer. In the temperature of 62° it will be a little shorter; or it may be taken = 76,734 inches in measures of the Royal Society's brass standard. This is \(\frac{2}{1000}\)th or about \(\frac{1}{42}\)d of an inch longer than was determined by Mr. Graham's experiment. Hence it appears, that I was mistaken in supposing, in p. 325, that the uncertainty about the true proportion of the English and French measures was but small, since the error in the former determination now appears to have been \(\frac{4}{197}\)th of the whole, or equivalent to what might have been produced by a difference of 84° of Fahrenheit's thermometer. Whence it arose I cannot pretend to say, neither is it very material to enquire; but the fact is plain, and fully justifies the propriety of repeating the experiment. I shall now state the length of the degree, measured by Messieurs Mason and Dixon, first in English feet, according to the Royal Society's standard, and then reduced to the French measure by the proportion just established. From 363763 English feet, the length of the degree found by the 5 feet brass standard, see p. 324, I subtract 10 feet for the difference between Mr. Bird's scale and the Royal Society's standard, and 3 feet for the wearing of the brass rod; and there remain 363750 feet, according to the Royal Society's standard, for the length of the degree. But to this it seems proper to add 21 feet, in order to correct the position of the point C, determined by the sector, which cannot be so certain as that inferred from the azimuth of the line PS. See p. 279. Therefore the true length of the degree, according to the Royal Society's brass standard, in the temperature of 62° of Fahrenheit's thermometer, is 363771 feet, or 68,8960 English statute miles. To reduce this to the measure of the Paris toise, by the proportion above established, say as 76,734 is to 72, so is 363771 to 341328 French feet, or 56888 Paris toises, of the standard of that used in the measure of the degrees of the meridian at Peru. The method made use of by Mr. Bird, in finding the length of the toises by his scale, was as follows, which may serve as a direction for the like purpose on any future occasion. Two brass pins were drove into a strong deal board 4 inches thick, and longer than the toise; and two brass cheeks were made very square, and the ends brought upon the pins. The toise was then put in between the cheeks, one of which was made to slide so as to be easily brought into contact with the end of the toise, and the other end at the same time touching the other cheek, the moveable cheek was screwed fast; and thus the toise was exactly contained between the cheeks without any shake, and it is evident that the interval between the cheeks was exactly equal to the length of the toise. In order to measure this interval, the toise being taken away, very fine lines were drawn with a fine point, at the end of each cheek, upon the brass pins which were in the same plain with the board: then the cheeks were removed, and fine points made at the outer extremity of each line, and this distance being taken between the fine points of a beam compass, was transferred to the scale, and thus the length of the toise was found in measures of the scale, which is divided by a vernier to thousandths of an inch. The toises and brass scale had been left together in the same room, and near one another all the night before, and till the very time of making the comparison of the toises with the scale, in order to be sure that they were all affected with the same degree of heat. As it may be agreeable to the reader to see the result of the principal measures of degrees of latitude, that have been taken with later instruments and proper accuracy, brought together into one view, the following table is here added. | Length of a degree in Paris toises | Mean latitude | Names of the observers | Years in which the degrees were measured | |-----------------------------------|---------------|------------------------|------------------------------------------| | 57422 | 66° 20' N | M. de Maupertuis, &c. | 1736 and 1737 | | 57074 | 49° 23' N | M. de Maupertuis, &c. and M. Cassini | 1739 and 1740 | | 57091 | 47° 40' N | P. Liefgang | 1768 | | 57028 | 45° 0' N | M. Cassini | 1739 and 1740 | | 57069 | 44° 44' N | P. Beccaria. | 1768 | | 56979 | 43° 0' N | Le Pere Boscowich and Le Maire | 1752 | | 56888 | 39° 12' N | Meff. Mason and Dixon | 1764 to 1768 | | 56750 | 0° 0' N | M. Bouguer and M. de la Condamine | 1736 to 1743 | | 57037 | 33° 18' S | Abbé de La Caille | 1752 | If this degree be compared with the degree measured at the equator = 56750 toises, in the hypothesis of the earth's being an oblate spheroid, the ratio of the equatorial to the polar diameter will come out as 494 to 493. But, if it be compared with the degree measured in Laplandy, in the latitude 66° 20', = 57419 toises (I have subtracted 3 toises, because the toise used in Laplandy was \(\frac{1}{2}\) th or \(\frac{1}{3}\) th of a line less than the toise used in Peru, see M. De la Lande's Astronomy, Article 2107), the ratio of the diameters will be as 142 to 141. The great difference of these results is a fresh proof of what has appeared from the comparison of the measures of the several degrees taken before, either that the figures of the meridians are not accurately elliptical, or that the inequalities of the Earth's surface have a considerable effect in deflecting the plumb-line from its true situation, or both. I had indeed supposed that any deflections of the plumb-line were not to be feared with respect to this particular measure of a degree, at the end of my Introduction to Messieurs Mason and Dixon's account of the same, by arguing arguing, perhaps too far, from the level disposition of the country through which the degree passes. But the Honourable Mr. Henry Cavendish has since considered this matter more minutely; and having mathematically investigated several rules for finding the attraction of the inequalities of the Earth, has, upon probable suppositions of the distance and height of the Allegany mountains from the degree measured, and the depth and declivity of the Atlantic ocean, computed what alteration might be produced in the length of the degree, from the attraction of the said hills, and the defect of attraction of the Atlantic; and finds the degree may have been diminished by 60 or 100 toises from these causes. He has also found, by similar calculations, that the degrees measured in Italy, and at the Cape of Good Hope, may be very sensibly affected by the attraction of hills, and defect of the attraction of the Mediterranean Sea and Indian Ocean. The rules, which I used in calculating the ratio of the equatorial diameter to the polar axis, from the North American degree, compared with those measured in Peru and Laplandy, are those given by Mr. John Robertson, Librarian to the Royal Society, in his Elements of Navigation, p. 597, as deduced by him from Dr. Letherland's Geometrical Analysis of the problem, which he has also given to the public in the same place, together with some other problems depending upon it, which were necessary to complete the subject.