METHOD OF COMPILING THE MAP. 93 
The compilation was begun at the eastern portion—the valley of the Mississippi. Here the 
surveys of the United States lands furnish a great amount of accurate material, but as they do 
not generally depend upon astronomical determinations, it is necessary to seek elsewhere for 
the means of fixing them in correct geographical position. I have, perhaps, attached more 
than the usual value to these surveys, and feel that it is needful, in order to sustain the accu- 
racy of the compilation, to give my reasons for so doing.* 
The first operation of land surveying, according to the principles adopted in the United 
States General Land Office, is to mark out and carefully measure a principal meridian. A 
principal base line is then established and measured along a parallel of latitude. Sometimes 
this line is run first. ‘‘Standard parallels are established at stated intervals, to provide for or 
counteract the error that otherwise would result from the convergency of the meridians."' 
Some of these lines are measured several times; and the numerous checks which the system 
presents in the subsequent subdivision makes the measurements between any two meridians or 
parallels very reliable. "The error in the difference of longitude between any two points near 
the same parallel, or in the difference of latitude near the same meridian, as determined by the 
Land Office plots, will not probably exceed one minute of arc in a distance of 500 miles.T Any 
slight deviation which may be made in the establishment of the meridian will not materially affect 
such differences of longitude; but it will affect the relative longitude of points along the meri- 
dian. It wil be seen hereafter that there is reason to think that errors of deviation from 
the true meridian have been made in running the land survey meridians. 
The first step made in compiling the Land Office maps was to fix upon the geographical 
— of the different p meridians. 
The fourth principal meridian runs north from the mouth of the Illinois river through Illinois 
and Wisconsin, and, according to the land surveys, is about 134 miles east of the mouth of the 
Minnesota river. This point, as determined by Mr. Colhoun, of Major Long’s expedition, in 
xd Captain a T. E., in his map of 1843-44 ; Major Emory, T. E., in his map of military reconnaissance, in 1846 ; 
Captain Stansbury, T. E., Eo a MEME 1849; and Lieut. Bryan, T. E., on his map of 
route from Fort Leavenworth to the Big Timbers, 1855 ; all used Mr. Nicollet’s gitude of Fort Leay- 
enworth, though the connexions by Land Office surveys, with aie hien ai toes Taide, bial — them the 
Sica ی یی‎ Lieutenant Beckwith; ره‎ Beckie: Railroad Roper, weh, d 4to edition, page 125, states that 
principal meridians to be perpendicular to the parallels, and consequently parallel to each other. 
When the plat is made from the surveys, from one principal meridian, the projection known as the Flamsteed can be 
constructed directly upon it—all that is necessary being to lay off, in the parallels, the lengths of degrees, and to draw the 
meridians through these points. The meridians will be curved lines, the curvature increasing with the distance from the 
principal meridian. The map can then be readily reduced to any other projection by the ordinary method of ruling corre, 
prem lines on each projection. 
The Flamsteed projection is one of the simplest and best for persons desirous of constructing maps where there are few 
facilities. All that is necessary is to know the lengths of a degree of the meridian. The lengths of the parallels will be 
(assuming the earth as a sphere) proportional to the cosines of the latitude. The parallels are all drawn as parallel straight 
lines, at the distance of a degree or part of a degree from each other. The middle meridian of the map is perpendicular 
to them. The lengths of degrees, or parts of degrees, are then marked off, from the middle meridian each way, on the 
parallels. Lines drawn through the points thus fixed give the other meridians, which are all curved lines, crossing the 
parallels obliquely, the angle decreasing as the distance from the middle meridian is increased. Where the distance from 
the middle meridian does not exceed 4°, this simple projection will be found sufficiently accurate for nearly all purposes. 
