Scales Math

Scales, MATHEMATICAL. It is obviously impossible to draw a map upon paper which shall be the same size as the country indicated, and the same holds with regard to architectural plans, etc. It is therefore usual to settle upon a convenient size for the map, and then reduce all the actual linear measurements in the same ratio, that ratio being so chosen that the whole can be fitted into the size of the map. The drawing is then said to be made to scale, and this is indicated by stating the "representative fraction" or ratio which the scale bears to the original, for example, 1 : 63360, or by noting the equivalent fact that it is a scale of 1 inch to the mile. This scale would only need a foot-rule divided in the usual way into inches and convenient fractions, but a scale of, say, 1 inch to 25 miles could be constructed in the following way to show a distance of 50 miles. Since 25 miles is indicated by 1 inch, 50 miles will need 2 inches; draw, therefore, a line 2 inches long and divide it into 5 parts, the points of division being numbered from 0 to 50, and each division representing ten miles. One division is subdivided into 10 parts representing single miles, this may be either the first division (from 0 to 10), or another 10-mile division drawn on the left of zero.