Maternal Effect as a Cause of the Difference between the Reciprocal Crosses in Drosophila Pseudoöbscura.

intuition that in cases of quadratic friction the theory shows an increase of damping effect when the elevation of the wave increases. This is a new feature in the theory of wave propagation; it is introduced by the non-linear character of our wave equarion. The Determination of k (Volume Factor).-The coefficient Cf iS supposed to be given by the physical conditions of the channel. The value of k will then depend entirely on the average elevation of the wave. An infinite number of waves other than the ones here investigated may exist in a channel, depending on the initial elevations and speeds. It is, however, probable that if we start with a local swelling initially at rest it will propagate and deform as the wave of same average height investigated above. The origin of time to be chosen depends on the height of the wave front as shown by equation (9). The average height or volume determines the coefficient k to be used for the corresponding theoretical curve. The type of initial condition here mentioned may be roughly identified with conditions arising from a sudden input of water at a given point of a river or a channel and propagating as a flood wave. 4. Conclusion.-An exact solution of the equation of propagation of waves with quadratic damping has been found. It shows that high amplitude waves are more quickly damped and how this damping effect depends on both the volume of the wave and the friction coefficient of the channel. The solution may be interpreted physically as representing certain types of flood waves.