The contours represent lines on the ground that are horizontal and whose meanderings follow the surface, just as the edge of a flood would follow the irregularities of the hills about it.  Those lines that contours stand for are just as level as the water’s edge of a lake, but horizontally they wander back and forth to just as great a degree.

The line marked 880, at the penitentiary, passes through on that particular piece of ground every point that is 880 feet above sea level.  Should the Missouri River rise in flood to 880 feet, the penitentiary would be on an island, the edge of which is marked by the 880 contour.

Contours show several things; among them the height of the ground they cross.  Usually the contour has labeled on it in figures the height above some starting point, called the DATUM PLANE—­generally sea level.  If, with a surveying instrument, you put in on a piece of ground a lot of stakes, each one of which is exactly the same height above sea level—­that is, run a line of levels—­then make a map showing the locution of the stakes, a line drawn on the map through all the stake positions is a contour and shows the position of all points of that particular height.

On any given map all contours are equally spaced in a vertical direction, and the map shows the location of a great number of points at certain fixed levels.  If you know the vertical interval between any two adjacent contours, you know the vertical interval for all the contours on that map, for these intervals on a given map are all the same.

With reference to a point through which no contour passes, we can only say that the point in question is not higher than the next contour up the hill, nor lower than the next one down the hill.  For the purposes of any problem, it is usual to assume that the ground slopes evenly between the two adjacent contours and that the vertical height of the point above the lower contour is proportional to its horizontal distance from the contour, as compared to the whole distance between the two contours.  For instance, on the map, find the height of point A. The horizontal measurements are as shown on the map.  The vertical distance between the contours is 20 feet.  A is about one-quarter of the distance between the 800 and the 820 contours, and we assume its height to be one-quarter of 20 feet (5 feet) higher than 800 feet.  So the height of A is 805 feet.

The vertical interval is usually indicated in the corner of the map by the letters “V.  I.”  For instance:  V. I.=20 feet.

On maps of very small pieces of ground, the V. I. is usually small—­perhaps as small as 1 foot; on maps of large areas on a small scale it may be very great—­even 1,000 feet.

Contours also show SLOPES.  It has already been explained that from any contour to the next one above it the ground rises a fixed number of feet, according to the vertical interval of that map.  From the scale of distances on the map the horizontal distance between any two contours can be found.  For example:  On the map the horizontal distance between D and E is 90 yards, or 270 feet.  The vertical distance is 20 feet the V. I. of the map.  The slope then is 20/270 = 1/13.5 = 7-1/2% = 4-1/2 deg., in all of which different ways the slope can be expressed,