VOL. LXXXV.] PHILOSOPHICAL TRANSACTIONS. A']^ 



resistance, and let the sails make one revolution in i seconds : then the velocity 

 will be — feet in a second. 



To find the resistance when the fluid strikes the planes at any angle, set them 

 to that angle, and find the resistance in the very same manner as before. But 

 here we must set 2 of the opposite planes inclined one way and 2 the other, so 

 that the fluid may strike the 2 former on their upper sides, and the 2 latter on 

 their under sides, but both at the same angle. This caution is necessary in order 

 to prevent any alteration in the pressure, and consequently in the friction on the 

 axis in the direction of it ; for the fluid striking the planes obliquely, part of the 

 force will be employed in resisting the motion, and part will act perpendicular to 

 it, or in the direction of the axis, and this latter effect will manifestly be destroyed 

 by the above disposition of the planes, because this force will act upwards against 

 2 of the planes, and downwards against the other 2, and being equal, they will 

 destroy each other's effects. The planes may be set to any angle thus : Take a 

 small quadrant divided into degrees ; let mn (fig. 20) be the outward inclined 

 edge of the plane ; suspend a plumb-line ab so as just to touch it at n, and at n 

 apply the centre of the quadrant, and let the radius passing through 90° coincide 

 with AB, and turn the plane till nm coincides with that degree at which you 

 would have the plane strike the fluid, and the plane stands right for that angle. 



To find the resistance of a solid, we must have 2 such solids equal to each 

 other, and put on at the opposite ends of 2 of the arms, for with one only its 

 centrifugal force will increase the friction against the nut, whereas with 2 op- 

 posite to each other this effect will be destroyed. We must also get 2 thin pieces 

 of lead with the edges feathered off, and of the same weight with the 2 solids. 

 These must first be put on the opposite arms, and a weight w found as before. 

 Then the leads are to be taken off, and the solids put on in their place, with 

 that side to go foremost whose resistance is required, and then find w as in the 



case of the planes ; and the absolute resistance will be ;^ X w on one of the 



solids. 



By this machine we may find the absolute resistance on the planes in a direc- 

 tion perpendicular to that of their motion. For let the lower end of the axis, in- 

 stead of resting on the base of the frame, stand on one end of an horizontal lever, 

 like that in fig. 17, and let it be balanced by a weight in a scale hanging at the same 

 distance on the other side of the fulcrum, when the sails have acquired a uniform 

 motion, with the planes horizontal, or when moving edgeways. Then turn the 

 planes to any angle, and add equal weights to the scales r and t, till the planes 

 have acquired the same uniform velocity as before, and put a weight p into the 

 scale at the other end of the lever, which shall novv just balance it, and p will be 



