1084 Proceedings of Royal Society of Edinburgh. [sess. 
large maximum at if/= ±35° 16'; but not to infinity; and so 
arrive mathematically at an expression for the very high waves 
seen on the two bounding lines of the wave-disturbance, inclined 
at 19° 28' to the mid-wake. But it is interesting to remember 
that we see in reality a considerable number of white-capped waves 
(would-be infinities) before the well-known large glassy waves 
which form so interesting a feature of the wave-disturbances. 
§§ 80-95 of the present paper are merely a working out of the 
simple problem of purely gravitational waves with no surface- 
tension on the principle given by Rayleigh* in 1883 for the much 
more complex problem of capillary waves in front, in which 
surface-tension is the chief constituent of the forcive, and waves 
in the rear, in which the chief constituent of the forcive is 
gravitational. 
In all the work arithmetical, algebraic, graphic of §§ 32-95 
above, I have had much valuable assistance from Mr J. de Graaff 
Hunter ; who has just now been appointed to a post in the 
National Physical Laboratory. 
*Proc. Lond. Math. Soc., xv. pp. 69-78, 1883 ; reprinted in Lord Rayleigh’s 
Scientific Papers , vol. ii. pp. 258-267. 
( Issued separately December 11, 1905.) 
