306 
ON THE MATHEMATICAL THEORY OF STREAM-LINES. 
partially to neutralize each other. Suppose, for example, that at a certain point (which 
may be denoted by A), at or near the bow of the ship, there is a disturbance producing 
a wave-ridge. This first ridge is followed by a series of other wave-ridges, at distances 
apart depending on the period and virtual depth of the original disturbance, and di- 
verging at an angle depending on the ratio borne by the speed of the waves to the speed 
of the ship. 
Mr. Froude remarks, as an observed fact, that the second wave-ridge of the series is 
that which appears to carry away the most energy. This wave-ridge is in contact with 
the side of the vessel at a point which we may call B, at a distance astern of A depending 
on the dimensions and position of the waves. Suppose, now, that the surface of the 
vessel is so shaped that the disturbance impressed by it on the water has a tendency to 
produce a wave-trough at B ; this disturbance will, to a certain extent, neutralize, by 
interference, the disturbance originating at A; that is, to use Mr. Froude’s words, the 
wave-troughs originating at B will “swallow” the second and following ridges of the 
series of waves originating at A, leaving unaltered the first wave-ridge only of that series 
— thus diminishing the quantity of energy which is carried away by diverging waves. 
It is obvious that the greatest effect of the interference of two given series of waves can 
be realized at one particular speed of the ship only, because of the influence of the 
speed of the ship on the positions of the waves ; and this may account for the dimi- 
nutions of the rate of increase of resistance with speed w'hich occur at certain particular 
velocities of a given vessel. As regards this and many other questions of the resistance 
of vessels and of the motions which they impress on the water, a great advancement 
of knowledge is to be expected from the publication in detail of the results of the expe- 
riments on which Mr. Froude has long been engaged. 
