The fame number of stars were taken with each sector; but the large one from the length of its radius, being at least three times as accurate as the small one, the latitude by the large one, was multiplied by three, and the latitude by the fmall one added to that product, and the fum divided by four, the quotient 30° 21′ 39′′.5 was taken for the true latitude of the observatory.

This being the highest point to which we could afcend the river, and the country fo covered with water, that it was impoffible with our few remaining broken down pack horfes to convey our apparatus by land to the fource of the river: we therefore had to determine the geographical pofition of its fource by a traverfe; the courfes of which are as follows: viz. begin. ning at the obfervatory A, (Plate VIII.) where a hewn poft was fet up and furrounded by a large mound of earth, from thence N. 10° 1' W. 4435.6 perches, thence S. 85° 14' W. 115.6 perches, thence north 44.8 perches at the end of which a hewn poft was fet up, and furrounded by a mound of earth B.-Thefe courfes when tabled will ftand as below.

The last mentioned mound of earth was thrown up on the margin of the Okefonoke fwamp, and as near to it as any permanent mark could be placed on account of the water.

From Plate VIII. upon which the above traverse is laid down, it may be feen that the river St. Mary's is formed by the water draining out of the Okefonoke swamp along feveral marfhes, or fmall fwamps, which join into one, and form, or conftitute the main branch or body of the river. The principal, or largeft of thofe fwamps, or drains, is the most casterly one, and in which the current is the most visible. This marfh, or drain is croffed by the last course of the traverse, which terminates at the mound B. From this mound north-easterly into the swamp, the water has but little, if any perceptible current. The fource of the river is therefore in an indeterminate

determinate space; and no specific point could be fixed on, as the swamp is at all times almost impenetrable, and at this season of the year abfolutely fo without immenfe labour, and expence. It was therefore agreed that the termination of a line, fuppofed to be drawn N. 45°, E. 640 perches from the mound B, fhould be taken as a point to, or near which, a line should be drawn from the mouth of Flint river; which line when drawn, should be final, and confidered as the permanent boundary between the United States and His Catholic Majefty, provided it passed not less, than one mile north of the mound B: but if upon experiment, it should be found to pass within lefs than one mile north of the faid mound, it should then be corrected to carry it to that distance. To obtain as near as poffible the course of the faid line, with the distance between the points to be joined, the following materials deduced from our previous operations were used. The longitudes made ufe of are from meafurements, compounded with the eclipfes of the 1ft fatellite of Jupiter.

The longitude of the oblervatory near the mouth of Flint river by the eclipfes of the 1ft fatellite of 4 is 5h 39′ 19′′ weft from Greenwich. The longitude of our ftation on Thompson's Creek, by a mean of five good obfervations is 6 4′ 48′′ weft from Greenwich. From Thompson's Creek to the Flint river observatory, the distance is 371.21 miles, which in the parallel of 31° is equal to 24′ 57′′ in time, which deducted from the longitude at Thomson's Creek, will leave 5" 39' 51" for the longitude of the obfervatory near the mouth of Flint river; which difagrees with the longitude by obfervation 32" in time. Measurements when accurately executed, in a known parallel of latitude, are generally preferable to obfervations for distances, not exceeding 100 miles: yet in this cafe, the measurement is not entitled to that weight, being done in hafte, with a common chain, through thickets, fwamps, and ponds, where pins of more than ordinary lengths had to be made use of, which involved an unfurmountable fource of error: but not in fo confiderable a degree as to justify its rejection. It was therefore concluded, that if to twice the longitude of the obfervatory near the mouth of Flint river, the longitude by measurement from Thompfon's Creek be added, and the fum divided by three, the quotient 5h 39′ 30" would be the longitude of the obfervatory near the mouth of Flint river, as correctly as it could be had from our materials: But the mouth of Flint river was found by mealurement to be 260 perches, equal in time to 3" 3 weft from the obfervatory; which added to the above determination, the decimal .3 being rejected, as unimportant, when errors much larger are unavoidable, will give 5h 39' 33" for the longitude of the mouth of Flint river.--The latitude has already been fettled at 30° 42′ 42".8.

The longitude of the obfervatory at A, up the St. Mary's by obfervation is 5 29. The longitude of the obfervatory at Point Peter by four good obfervations is 5h 26' 34": the difference of longitude by obfervation is 2' 26"-The difference of longitude between the obfervatories, by a traverse taken for that purpofe, was 37.45 miles which is equal to 2' 32". The traverse being made under very unfavourable circumstances, and confifted of an uncommon number of courfes, owing to the fwamps, and ponds, (with which the country abounds), being full of water, and im

paffable

paffable: the mean 2' 29" was therefore taken for the difference of longitude, which added to 5 26′ 34′′ the longitude of Point Peter will give 5h 29' 3" for the longitude of the obfervatory at A.-The difference of latitude between A, and the mound B, has been fhewn to be 4403.2 perehes, and the difference of longitude 886.4 perches weft: thence to the end of the line fuppofed to be drawn N. 45 E. 640 perches from the mound B, the difference of latitude will be 452.5 perches; which added to the difference of latitude between A, and B, will give 4855.7 perches, or 13' 8".5 nearly, which added to 30° 21′ 39.5 the latitude of A, will give 30° 34′ 48′′ for the latitude of the termination of the line fupposed to be drawn from B.-From the observatory at A, to the mound B, the difference of longitude by measurement has been ftated at 886.4 perches weft, from thence to the termination of the line fuppofed to be drawn from B, the difference of longitude is 452.5 perches eaft, which deducted from the wefting, will leave 433.9 perches weft, which is equal to about 6" in time, and when added to 5h 29′ 3′′ the longitude at A will give 5h 29′ 9′′ for the longitude of the termination of the line fuppofed to be drawn as above; which deducted from the longitude of the mouth of Flint river, will leave 10′ 24′′ for the difference of longitude between the points.

There are now given

The latitude of the mouth of Flint river =
The latitude of the termination of the line supposed
to be drawn from B

supposed?

The difference of longitude between the mouth

}=0

30° 42′ 42′′.8

= 30 34 48

of Flint river, and the termination of the line oh to' 24" = 2° 36' fuppofed to be drawn from B

To find the course, and diftance between the given points, that is, between the mouth of Flint river, and the termination of the line fupposed to be drawn from B, which is done as follows:

In the fpherical triangle DEF, let DE represent the co. latitude of the mouth of Flint river = 59° 17' 17".2. FE the co. latitude of the termination of the line fuppofed to be drawn from B = 59° 25′ 12′′, and the included angle DEF 2° 36', being the difference of longitude between the given points.

For