120 MEETING OP THE BRITISH ASSOCIATION 



served that the motion of a vessel through a fluid communicates to 

 its particles motion in the form of waves. These waves are formed 

 by the anterior accumulation of the fluid which the vessel pushes 

 before it ; they propagate themselves in the same direction with the 

 motion of the vessel, and with a velocity nearly uniform. Their 

 form is determinate ; their length nearly constant, and their velocity 

 nearly uniform. From the formation of these waves, the resistance 

 is very different from the amount on the supposition of quiescence 

 in the fluid. 



The velocity of the wave is that acquired by falling through a 

 space equal to half the depth of the fluid. In water about four 

 inches deep, the velocity of the water is about three feet a second ; 

 in a depth of seven inches, the velocity is about four feet a second ; 

 at a depth of thirteen inches, the velocity of the wave is five feet a 

 second ; at forty inches, ten feet a second ; and at sixty-six inches, 

 more than eight miles an hour. 



The resistance of the fluid was found, by a long train of experi- 

 ments, to be intimately connected with the formation of the waves, 

 in such a manner that the resistance was greater than in the ratio 

 of the squares of the velocities, or less than in that ratio, according 

 as the velocity of the wave was greater or less than that of the 

 vessel. It was thus found that the generation of waves at the 

 prow of the vessel impeded its velocity, so long as its motion was 

 less rapid than that of the wave ; when, on the other hand, a suffi- 

 cient power was obtained to make the vessel move faster than the 

 waves, the heaping up of water at the prow ceased, the waves fell 

 back towards the middle of the vessel, and, bearing it up upon their 

 summits, carried it on with diminished immersion and resistance. 

 From the law of the wave the following practical conclusions are 

 to be drawn. 1. That in every canal there are two most service- 

 able rates ; one below the wave, up to about two-thirds of its velo- 

 city, and another immediately beyond the velocity of the wave. 2. 

 That all velocities a little slower than that of the wave, are in some 

 cases impossible, in others impracticable, and in all unprofitable. 

 3. That in shallow rivers and canals depth is an element of much 

 greater importance than breadth. 4. That banks nearly vertical 

 are, for all velocities, more economical of power, and more durable, 

 then wide surfaces and long slopes. 5. That very high velocities 

 are to be attained in shallow water with greater economy of power, 

 by getting over the wave. 



Professor Powell read Observations for determining the Refrac- 

 tive Indices for the Standard Rays of the Polar Spectrum in vari- 

 ous Media ; a subject to which he has for years directed his atten- 

 tion. 



Sir David Brewster read a paper on a singular development of po- 

 larising structure in the crystalline lens of the eyes of animals, 

 after death. The inquiries which form the subject of this paper were 

 made by comparing the changes which take place in the polarising 

 structure of the crystalline lenses of animals in old age with those 



