AND OTHER WATER WAVES 349 



make an angle with the ship's course, and the 

 transverse series which lie across her course, travel- 

 ling in the same direction. Leaving out of account 

 the first two or three diverging bow-waves, every 

 wave of this series has a front concave to the 

 direction of advance. The transverse series have 

 fronts convex to the direction of their advance. 

 They are flatter than the diverging waves, and 

 therefore less conspicuous if the water be ruffled. 

 This whole system of waves is bounded on the 

 right and left by two imaginary straight lines, each 

 making an angle of 19^ with the ship's course. 

 A similar dual series of waves originates from the 

 stern. The pattern of waves originating from the 

 bow or from the stern, as deduced mathematically, 

 satisfies all that is usually visible at sea. 



Being anxious to see ship-waves undisturbed 

 by the waves of swell or wind, I decided to make 

 observations on the placid waters of Swiss lakes. 

 I began on the Thunersee during the fine summer 

 weather of 1904, and continued the observations 

 at Montreux, on the Lake of Geneva, in the spring 

 of 1905. On still mornings the surface of the 

 Thunersee was frequently as smooth as plate -glass, 

 without any ruffle or darkening by even the gentlest 

 breeze. 



Under these conditions I found that the thwart 



