584 Proceedings of Royal Society of Edinburgh. 
[sefs. 
the forcive is infinitely small; and therefore, by end of §41, the 
depression is that hydrostatically due to the forcive pressure. This, 
at 0 = 0°, is equal to 
i 
1 - e 
D9 
2 C 
9’5 .c . 
§ 63. The interpretation of the curves of fig. 17 for points 
between those corresponding to integral values of j is exceedingly 
interesting. We shall be led by it into an investigation of the 
disturbance produced by the motion of a single forcive, expressed 
>>y 
n = 
gel) 
(94); 
but this must be left for a future communication, when it will be 
taken up as a preliminary to sea ship-waves. 
§ 64. The plan of solving by aid of periodic functions the 
two-dimensional ship-wave problem for infinitely deep water, 
adopted in the present communication, was given in Part IV. 
of a series of papers on Stationary Waves in Flowing Water, 
published in the Philosophical Magazine , October 1886 to January 
1887, with analytical methods suited for water of finite depths. 
The annulment of sinusoidal waves in front of the source of 
disturbance (a bar across the bottom of the canal), by the super- 
position of a train of free sinusoidal waves which double the 
sinusoidal waves in the rear, was illustrated (December 1886) by 
a diagram on a scale too small to show the residual disturbance 
of the water in front, described in § 53 above, and represented 
in figs. 18, 19, 20. 
In conclusion, I desire to thank Mr J. de Graaff Hunter for 
his interested and zealous co-operation with me in all the work of 
the present communication, and for the great labour he has given 
in the calculation of results, and their representation by diagrams. 
