52 MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



towards the maximum breadth, having an intennediate point of contrary flexure. 

 Delineations of this form, and tables of comparative resistances, are given in 

 Paxtm. 



I have given, at the end of the fii-st part of this paper, some illustrations of 

 the subject, drawn from facts and observations in practical experience, which 

 have either been communicated to me or recorded by myself The navigation of 

 shallow rivers, lakes, seas, and canals, affords many illustrations of the principles 

 I have developed. The canals of HoUand and the rivers of America, as weU as 

 those of our own country, are navigated on a practical system, which is fuUy ex- 

 plained by the interference of the wave, — and the improvements of which those 

 species of navigation may be capable, can only be effected in conformity with the 

 knowledge of these laws that has now been obtained. By the propagation of 

 waves, and propelling vessels upon those waves, there is a prospect opened iip of 

 attaining velocities upon the surface of the water, that have been hitherto held to 

 be impracticable. The length, however, to which this communication had pre- 

 viously extended compelled me to shorten this part of the paper, and I have been 

 contented rather to shew the applicability of the principles to practical improve- 

 ment than to carry out this application. 



Such are the results of that portion of the investigations I have undertaken, 

 which has been completed ; and I feel it to be my duty thus publicly to aclcnow- 

 ledge, that if any benefit shall be conferred, either upon theoretical hydrodynamics 

 or the practical arts connected with it, by these inquiries, it is not to myself alone 

 that they owe theu- value. To so large and extensive a series of experiments my 

 own exertions and my o^vn pecuniary resources would have proved inadequate, 

 had I not been placed in circumstances pecuMarly fortunate. Two scientific 

 friends, Alexander Gordon and Andrew Crawford, Esqrs. afforded me invalu- 

 able and long continued assistance, and to their labom-s and those of Dr George 

 Glover, Mr Wilkinson, and Mr Muir, with about a dozen of hu-ed assistants, the 

 experiments owe much of their extent and acciu-acy. To the Committees of 

 Management of the Edinburgh and Glasgow Canal Companies, who have permit- 

 ted the use of their public works, and of their servants, and of their moving 

 power, and of then- vessels, and defrayed a large expenditure of money, and to 

 Robert Ellis, Esq. W. S., through whose influence principally these privileges were 

 obtained, under the enlightened conviction, that, from the improvement of that 

 science with the applications of which they are so nearly connected, these mercan- 

 tile companies would be the fu-st to derive important benefit ; to them and to him, 

 for his devotion to the interests of science, and for the unwearied kindness, and 

 judgment and skiU with wliich he has assisted me in this undertaking, I consider 

 it my privilege to offer my thanks, as the means of accomplishing a task which 

 might otherwise have proved to be impracticable. To J. W. Smith, Esq. of Phila- 



