ON SHIP WA VES. 481 



The full mathematical theory of ship waves has 

 been exceedingly attractive in one sense, and in 

 another sense it has been somewhat repulsive 

 because of its great difficulty, for mathematicians 

 who have been engaged in hydrodynamical 

 problems. Following out that principle of Stokes, 

 which was further developed and generalised by 

 Lord Rayleigh, we can see how to work out this 

 theory in a thorough manner. In fact I can now 

 put before you a model [model shown] constructed 

 from calculations which I have actually made, by 

 following out the lines of theory that I have 

 indicated. I find that the whole pattern of waves 

 is comprised between two straight lines drawn 

 from the bow of the ship and inclined to the wake 

 on its two sides at equal angles of 19 28'. It is 

 seen in Fig. 48 that two such lines, drawn from 

 the bow or front shoulders of the ship, include the 

 whole wave-pattern. There is some disturbance 

 in the water abreast of the ship, before coming to 

 these two lines. Theoretically there is a disturbance 

 to an infinite distance ahead and in every direction ; 

 but the amount of that disturbance practically is 



VOL. in. I I 



