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The definition of north and east are pretty straight forward to grasp but only becomes difficult when used interchangably with x-y coordinates which have varying definitions for the direction of the axes. In Mathematics y was always vertical and x was always horizontal so logically I would assume that "up" == "northing" == "y" and "along" == "easting" == "x".
Why is this not the case in GIS?
There are many different conventions. It might help to first consider X-Y-Z, not necessarily as having any implied geographical directions, but simply as being the 1st, 2nd, 3rd ordinates or axes in a cartesian system. As a bonus, let's also address B, a directional measure.
In mathematics, a so-called right-handed system is used:
In geomatics, a so-called left-handed system is sometimes used.
As far as surveyors in USA and Canada are concerned:
Notice that the, northing-easting-elevation ordering, is compatible with the traditional latitude-longitude-altitude ordering used in navigation.
As for South African surveyors (via Andre's answer, but i may need to be corrected about terminology):
In other geomatics cases, (what i call) a hybrid system is used.
For Hawaiian and Phillipino surveyors:
In GIS, we usually follow the UTM convention, as do UK surveyors:
The usual coordinate orientation of X to the East and Y to the North works well in Central Europe and Asia, where both have positive values.
South Africans do it the other way round, calculating X from the equator southwards and Y westwards to get a right-hand coordinate system.:
http://www.ngi.gov.za/index.php/technical-information/geodesy-and-gps/datum-s-and-coordinate-systems
The Krovak projection used in Czech Republic and Slovakia also uses a South-West-orientated coordinate system, based on an imaginary point in Finland (for a reason I don't quite understand):
Talking about Northing and Easting for X and Y cartesian coordinate system is somehow abusive. Most of the projected coordinate systems do not have both X and Y axes parallel to the parallels and meridians. Some times it will be approximately the case, but some times you can't even define a direction (for instance, take an polar Azimuthal projection).
Based on the examples from @user31467 and @Robert Buckley, X and Y are "inverted" in the case of transverse projections (so that the Y axis follows the axis of the cylinder)
I realize this thread is WAY old, but I would like to offer another opinion that may shed some light on why northings,eastings are used in favor of x,y.
First, x,y is a rectangular system, Cartesian coordinates, and are ORDERED PAIR (x,y or x then y. X (being "a cross", actually goes across the page as the east west axis), Y as the north south axis. Y increases in the NE and NW quadrants, decreases in the SE & SW. X increases in the NE and SE quadrants, decreases in the NW & SW.
Northings and Eastings are just x and y reversed, meaning that they aren't an ordered pair...they are actually (y,x).
so why would we do this? Well, I would imagine it has a lot to do with surveyors and having to convert between rectangular coordinates and polar coordinates (r,θ) or (distance, angle). Remember that it is a rectangular coordinate system, therefore it is a RIGHT TRIANGLE, we can use Sin,Cos,Tan to find length of sides between coordinates, with the line between the two points being the hypotenuse, and one side being change in Y, the other change in X. so what side is adjacent and which opposite...well since in surveying lines are based off of bearings measured from north or south axis as zero always to east or west axis being the 90's (bearings never are greater than 90 degrees), the change in Y or the northing is always the adjacent side of the reference angle (the bearing angle). For instance a bearing of North 40 degrees East is measured from the North being zero, toward the east 40 degrees. Same for a South 40 degrees East bearing, measured from the south axis as zero toward the east 40 degrees.
But that doesn't explain why Northing, then easting or Y first then X. Well, if we continue on, converting from polar coordinates (distance, angle) to rectangular coordinates always gives us relative coordinates, not ABSOLUTE. In other words it gives us deltas or change in X, change in Y rather than absolute coordinate values. This is important, but not nearly as important as the understanding of bearing definition as compared to the Unit Circle in mathematics. Polar coordinates with (distance, angle) are based off of the Unit Circle in trigonometry. In the unit circle in trigonometry, 0 degrees is DUE EAST and increases in a counter clockwise manner. Example, due north would be 90, due west would be 180, due south 270 degrees. You know this if you are familiar with autocad. BUT...bearing angles are based off of North or South being zero and increasing clockwise or counterclockwise to the east or west. Many older calculators had functions of converting from polar to rectangular coordinates, but are based off of math and science using the unit circle from trig. Therefore, when using Sin of the angle multiplied by the distance of the line (sin θ multiplied by the hypotenuse length) results in the change in X rather than the change in Y. You must understand that the angle that the unit circle refers to is the complimentary angle to the bearing angle referenced (at least for northeast) With the single button function a surveyor in the field could convert polar to rectangular or vice versa rather than doing separate calculations using sin, then cosine. Since calculators give the rectangular coordinate conversion as Y, then X, I would imagine many mistakes were made with applying the change in Y to the X coordinate and so on. It was probably easier for the surveyors to start using (Northings, Eastings) rather than ordered pairs to decrease the number of mistakes made by not remembering to put the Y value first then the X value in the calculator.
That's my opinion, based upon absolutely nothing more than seeing my own students making mistakes with their calculators and getting confused with X,Y and N,E.