18 REPORT 1869. 



Naval Architects ' for 1864 (the substance of which is repeated in a treatise 

 on ' Shipbuilding : Theoretical and Practical '), states that the processes 

 amongst the particles of water through -which resistance to the ship's motion 

 may be caused indirectly may bo thus enumerated : — 



1. The distortion of the particles of water. 



2. The production of currents. 



3. The production of waves. 



4. The production of frictional eddies. 



The first cause he regards as having no appreciable effect on actual ships, 

 although possibly sensible in small models. Of the second cause (the pro- 

 duction of currents), Professor llankine remarks that it " never acts upon a 

 weU-designed ship ; for such a ship is so formed that the particles of water 

 glide over her surface throughout its whole length, and are left behind her 

 with no more motion than such as is unavoidably impressed upon them 

 through adhesion and stiffness ; and hence the failure of the earlier theories 

 of the resistance of ships, which were founded on experiments made with 

 flat plates, wedges, and blocks of unfair shapes." 



Mr. llankine then gives a detailed account of the waves which accompany 

 a vessel driven at a speed greater than the limit to which she is properly 

 adapted, showing that they diverge from the course of the vessel at an angle 

 depending on the proportion in which their speed of advance is less than her 

 speed, and thus carry off energy, which is lost ; and he proceeds to state : 

 " The conclusion to be drawn from these principles is, that for each vessel 

 there is a certain limit of speed, below which the resistance due to the pro- 

 duction of waves is insensible ; and that as soon as that limit is exceeded, 

 that resistance begins to act, and increases at a veiy rapid rate with the ex- 

 cess of speed Through the discoveries of Mr. Scott EusseU, a vessel can 



be designed in which this kind of resistance shall be insensible up to a given 

 limit of speed; and therefore the resistance due to waves has no sensible 

 action on a well-formed ship." These remarks of course apply only to 

 waves formed by the ship, and not to sea-waves which she may have to 

 encounter. 



" The resistance due to frictional eddies thus remains alone to be considered. 

 That resistance is a combination of the direct and indirect effects of the ad- 

 hesion between the skin of the ship and the particles of water which glide 

 over it ; which adhesion, together with the stiffness of the water, occasions 

 the production of a Vast niimbcr of small whirls or eddies in the layer of 

 water immediately adjoining the ship's surface." Instead of assuming that 

 the frictional resistance is simply proportional to the actual immersed surface, 

 Mr. llankine uses what he calls the avgmented surface, which is obtained by 

 multiplying each infinitesimal element of the surface bj" the cube of the ratio 

 which the velocity of gliding of the water over that portion bears to the speed 

 of the ship, and summing them. Let s be the actiial surface, and q the velo- 

 city-ratio of gliding ; then the augmented surface is^^^ (7s ; and if, further, 

 V be the speed, g gravity, iv the heaviness of -^-ater, and / the coefficient of 

 friction, then 



Eddy-resistance =V^/— j^^ ds. 



w 

 Taking the cubic foot as the unit, ;j- does not differ much from unity for 



sea-water, and the formula thus reduces to ^^ ff q^ ds. 



It is, of course, impossible to ealculatey^'^ ds in detail for every sliip; and 



