STEAM NAVIGATION. 



changed by any motion imparted to L ; the radial arms are connected at 

 the other end with a centre, round which they are capable of revolving, 

 Now, since the points ABC, &c., which are the pivots on which the paddle- 1 

 boards turn, are moved in the circumference of a circle, of which the centre 

 is o, they are always at the same distance from that point, consequently they 

 will continually vary their distance from the other centre P. Thus, when 

 a paddle-board arrives at that point of its revolution at which the centre 



Fig. 14. 



round which it revolves lies precisely between it and the centre o, its 

 distance from the former centre is less than in any other position. As it 

 departs from that point, its distance from that centre gradually increases 

 until it arrives at the opposite point of its revolution, where the centre o 

 is exactly between it and the former centre ; then the distance of the 

 paddle-board from the former centre is greatest. This constant change of 

 distance between each paddle-board and the centre p is accommodated by 

 the variation of the angle between the radial arm L and the short paddle- 

 board arm K : as the paddle-board approaches the centre P, this gradually 

 diminishes ; and as the distance of the paddle-board increases, the angle is 

 likewise augmented. This change in the magnitude of the angle, which 

 thus accommodates the varying position of the paddle-board with respect 

 to the centre P, will be observed in the figure. The paddle-board D is 

 nearest to P ; and it will be observed that the angle contained between L 

 and K is there very acute ; at E the angle between L and K increases, 

 154 



