The horizontal scale at the top of the illustration shows points where velocity measurements were made through holes in the ice. Velocities at different depths are indicated by the curves in the lower half of the chart, each curve being plotted to the right of a vertical zero line which corresponds with some hole in the ice. Lines are drawn in the upper portion of the chart showing different points in the stream where velocities are the same

is frozen. The velocity curves end abruptly at the bottom of the stream. It will be seen by reading velocities horizontally from the different zero lines from which the curves are plotted that the velocities are considerably greater in the center of the stream than they are near the banks or the bottom. This is natural, as the friction of the earth bottom and sides, as well as the friction of the ice at the top, causes the water to be retarded and the velocity lessened. In the upper portion of the illustration lines are drawn through all those points in the stream cross-section which have the same velocities. The lines are similar to the well-known isothermal lines on a weather map show-

GRAPHIC METHODS

ing where the temperatures are the same. From these hnes it can be seen instantly that the highest velocity is at the center of the stream, as far away as possible from retarding influences. Velocities gradually grow less as the sides, the bottom, or the ice at the top are approached.