Sec. 9. A System of Plane Rectangular Geodetic Coordinates

The origin of coordinates for any point of any zone is taken in this system at the point where the central meridian of a particular zone cuts the equator (Fig. 9a). The central meridian of the zone is considered to be the x-axis. That is why this meridian is sometimes called an axial meridian. The earth's equator, represented as a straight line at right angles to the central meridian, is the y-axis. The x-coordinates are reckoned from the equator to the poles. Those north of the equator are positive, those south of the equator are negative. The y-coordinates measured from the central meridian eastward are regarded as being positive; those measured westward are negative.

The rectangular geodetic coordinates for the point A (Fig. 9b) will be x_a for the x-coordinate and y_a for the y-coordinate. All the

Fig. 9

x-coordinates for the territory occupied by the USSR are positive since it lies in the northern hemisphere. To avoid differences in the signs of y-coordinates it is customary to take the y-coordinate of points on the central meridian as being +500 km rather than zero (Fig. 9c). Moreover, each y-coordinate is preceded by the number of the zone in which the particular point lies. Since any zone always extends less than 1000 km along the y-axis in such a coordinate system all the y-coordinates prove to be positive. The sequence number of the zone preceding the y-coordinate always occupies a place corresponding in the total number to digits showing thousands of kilometres. To give an example, the number 17 487 230 m indicates that the given point lies in the 17-th zone and that its y-coordinate, Y = 487 230 - 500 000 = -12 770 m.

This system of plane rectangular geodetic coordinates has been employed for geodesy since 1928 and in 1932 was made obligatory in this country.

Sec. 10. An Arbitrary System of Rectangular Geodetic Coordinates

I t is common for the position of terrain points on a plan to be determined with respect to a system of rectangular geodetic coor­dinates whose origin is chosen arbitrarily. In such a case the rectan­gular coordinate system is represented by two mutually perpen­dicular straight lines OX and OY (Fig. 10) referred to as coordinate axes. OX is termed the X-axis and OY is called the y-axis. The point O, where the axes cross, is the origin of the coordinates. The position of a point A in this system is determined by the segments Aa₂ = X_a (the x-coordinate) and Aa₁ = Y_a (the y-coordinate), these being parallel to the coordinate axes. The values of the x and y coordinates are accompanied by a plus or a minus sign. In geo­desy it is customary to take the direction of the x-axis to be coincident with that of the meridian through the origin of the coordi­nates. The northward direction of the axis is regarded as positive. The eastward direction of the y-axis is positive; the westward direc­tion is negative. The coordinate axes divide the plane of a drawing into four parts termed quadrants, NE, SE, SW, NW. The signs of the coordinates of points lying in these quadrants are presented in Table 1.

Coordinates	Quadrants
	I NE	II SE	III SW	IV NW
X Y	+ +	- +	- -	+ -

The rectangular coordinate system employed in geodesy is right-handed since the quadrants and the direction of reckoning the angles in the system are clockwise. In contrast, analytical geometry employs a left-handed rectangular coordinate system where, like in trigonometry, the quadrants and direction of reckoning the angles are counterclockwise.

We can see that the signs of the coordinates of the points lying in like quadrants of the right-handed and left-handed systems agree. This makes it possible to use trigonometrical formulae unchanged whichever system is employed for computation.