70 tECTonE vii» 



distance from each other, so that two equal weights may be attached to their 

 extremities, the depression of the first weight below either pulley, will be to 

 its distance from the pulley, in tlie same proportion as half of the weight to 

 either of the other weights ; and if, instead of having a weight attached to it, 

 one end of the thread be fixed to a firm obstacle, the effect will be precisely 

 the same. A machine of this kind is sometimes called a swig, perhaps by 

 corruption from swing. (Plate IV. Fig. 61.) 



If all the weights are unequal, we must draw a triangle, of which the three 

 sides are in the same proportions as the weights ; and we may determine the 

 directions of the threads, by placing such a triangle, with the side, representing 

 the middle weight, in a vertical position. 



A force may also be applied obliquely to a wheel and axis. Supposing a 

 rope to be coiled obli(}uely round the axis, it will require, in order to preserve 

 the equilibrium, a force as much greater than would be sufficient, if it were 

 simply applied in the direction of the motion, as the length of any part of 

 the rope uncoiled is greater than the perpendicular distance of its extremity 

 from the axis. So that when the rope becomes very oblique, a great force is 

 required in order to counteract a much smaller one acting perpendicidarly. 

 This remark may be in some measure illustrated by considering the method 

 used by joiners and stonecutters for keeping a saw straight: two ropes or 

 braces are twisted together by means of a pin or lever passing between them, 

 and serve each other in place of an axis, round which they are coiled obliquely, 

 so that they act with great force, when they are sufficiently tight, and not too 

 much twisted. (Plate IV. Fig. 62.) . 



It appears from the laws which have already been laid down, respecting the 

 motions of bodies on inclined surfaces, that a weight, acting vertically, will 

 hold in equilibrium another weight, resting on an inclined plane, without 

 friction, when the first is to the second as the height of the plane to its ob- 

 lique length. The pressure on the plane is in this case to the weight resting 

 on it, as the horizontal length of the plane is to its oblique length. This 

 pressure rnay be measured experimentally, by substituting for the resistance 

 of the plane, that of a thread perpendicular to it. (Plate IV. Fig. 63.) 



