310 MR. P. W. BARLOW ON THE LAWS WHICH GOVERN 



invented, which have, however, been so complicated in their construction, and 

 attended with so much friction and liability to get out of order, that they have not 

 hitherto, been brought into general use. The method employed in the wheel above 

 alluded to is certainly the most simple that has appeared : it is, however, attended 

 with a considerable liability to derangement, and consequent expense in repair, 

 which materially lessens its value. 



As my object in the present paper is in some measure to make a comparison of 

 the action of this with that of the common wheel, I have added a short description 

 of its construction. It is represented in fig. 1. where a a, a a, &c., are paddles, which 

 turn upon spindles having a bearing in the frame-work c, c, c, &c., of the wheel, 

 which is of a polygonal figure, having as many sides as it is required to have 

 paddles. The inside frame or polygon is alone attached to the shaft of the engine, 

 which does not continue beyond the side of the vessel, and the outer one has an 

 independent bearing on a centre attached to the paddle-box, so that it receives its 

 motion entirely from the rim or angles of the polygon : by this means the space 

 between the wheels is left quite free. A is a part of the shaft or centre upon which 

 the outer polygon of the wheel revolves, projected in an inclined direction to the 

 middle between the sides, but of course to a point considerably eccentric with the 

 wheel. Each paddle has a crank h attached to it at an angle of about 70°, and rods 

 «?, c?, &c., connect the extremities of the cranks, with a moveable boss which revolves 

 upon the fixed point A. 



It will thus be seen, that in consequence of the point A being situated out of the 

 centre, the paddles will assume different positions during the revolution of the wheel, 

 which positions can be so arranged as to differ very little from the vertical while 

 passing the lower part of the revolution, or that part where the action of the paddle 

 takes place. 



Description of the Experiments. 

 In making the experiments above referred to, the time chosen was generally as 

 nearly as possible that of high water, when there is but little tide ; but the effect of 

 this, whatever it may be, was always eliminated by the following equations : 

 Let t = time in seconds in performing the mile against the tide. 

 t! = the time with the tide. 

 V = velocity in miles per hour of the boat, 

 v' = velocity of the tide water. 

 n = number of seconds in an hour. 



Then y = v -f t/. 



Therefore ^^-^jf = v, the velocity independently of the tide. 



