436 Proceedings of Royal Society of Edinburgh. [sess. 
Royal Society paper, on the same subject, and under the same title 
(June 20, 1904). That second paper contained a first instalment 
of the “calculations and graphic representations ” promised in the 
old first ; the present paper contains, in figs. 35, 36, 37, 38, a 
further instalment of such illustrations. 
§ 158. Throughout my work, §§ 96-157, I have had most valuable 
assistance from Mr George Green, not only in the very long and 
laborious calculations and drawings, which have been wholly made 
by him, but also in many interesting and difficult questions which 
occurred in the fundamental mathematics of the subject. 
We hope to apply before long the method of § 128 to calculate, 
by aid of the formula f dq\]/(x - vq , z,t- q ), the initiation and con- 
*'0 
tinued growth of Canal Ship-waves, due to the sudden com- 
mencement and continued application of a moving, steady 
surface-pressure, xf/(x, 1, 0). We hope also to apply (139) of the 
present paper to the fulfilment of my old promise (§ 30, June 20, 
1904, R.S.E.) to deal with the beautifully varying procession seen 
circling outwards from the place of a stone thrown into deep water. 
( Issued separately November 17 , 1906 .) 
