INDEXED 



the 



LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SC 



[SIXTH SERIES 



JANUAR F 190 



I. Initiation of Deep- Sea Waves of Three Clt 



a Single Displacement ; (2) from a Group aj l !Egual and 

 Similar Displacements ; (3) by a Periodically Varying 

 Surface-Pressure *. (Continued from Phil. Mag.^ Jan. 

 1906.) By Lord Kelvin. 



(1) Disturbance due to an Initiational Form more convenient 

 than that of §§ 3—31 of Previous Papers on Waves. 

 §§ 96-113.' 



§ 96. HHHE investigations of §§ 5-31, including the 

 _l_ u front and rear " of infinitely long free pro- 

 cessions of waves in deep water, are all founded on initiational 

 disturbances, according to the first of two typical forms 

 described in § § 3, 4. In this form the initial disturbance is 

 everywhere elevation or everywhere depression, and its 

 amount, at great distances from the origin varies inversely 

 as the square root of the distance p, from a horizontal line at 

 a small height It above the water-surface in the middle of the 

 disturbance. In the present paper a new form of type- 

 disturbance is derived indifferently from either the first or 

 the second, of the forms of §§ 3, 4 : from the first, by double 

 differentiation with reference to tune, t ; from the second, by 

 single differentiation with reference to space, x. 



§ 97 (being a repetition of §§ 1, 2, slightly modified with 

 respect to notation). Consider a frictionless incompressible 



* From the Proc. Boy. Soc. Edin. vol. xxvi. Commimicated by the 

 Author. 



Phil. Mao. S. 6. Vol. 13. No. 73. Jan. 1907. B 



