ON PRESSURE AND EQUILIBRIUM. 53 



tions which help to support the moveable block, each of them bearing a 

 weight equivalent to the force which is applied at the end of the thread. 

 In the common ship's blocks, the pullies or shieves are equal in magni- 

 tude, and placed side by side ; here their number cannot conveniently 

 exceed two or three, without causing an obliquity in the block, when the 

 force is applied to the rope. Mr. Smeaton,* for this reason, invented a 

 system of pullies, arranged in two rows in each block, one larger, and the 

 other smaller : the force being applied in the middle, the rope passes on the 

 larger pullies till it arrives at the last, then returns through the whole of 

 the smaller series to the opposite side, and comes back again on the larger, 

 to be finally attached in the middle. (Plate IV. Fig. 54... 56.) 



If the diameters of all the pullies in both blocks be taken in the ratio of 

 the number of portions of the thread intervening between them and the 

 fixed extremity, their angular velocity will be equal, each of them turning 

 on its axis in the same time. They may therefore be fixed to a single axis 

 in each block ; and in this case the axis being longer, there will be less 

 accidental friction from its want of steadiness, and even the necessary fric- 

 tion may, perhaps, be somewhat diminished. (Plate IV. Fig. 57.) 



If one end of a thread supporting a moveable pulley be fixed, and the 

 other attached to another moveable pulley, and the threads of this pulley 

 be similarly arranged, the weight will be counterpoised by a ppwer which 

 is found by halving it as many times as there are moveable pullies ; for it 

 is obvious that each of these pullies doubles the effect of the power. 

 (Plate IV. Fig. 58.) 



There are also other arrangements, by which the effect of pullies may be 

 increased or diversified : for instance, where one end of each rope is attached 

 to the weight to be moved ; or where two of the pullies are connected by a 

 rope passing over a third ; but these methods are of little practical utility. 

 (Plate IV. Fig. 59, 60.) 



We have hitherto supposed the ropes passing over the pullies to be either 

 perfectly or very nearly parallel to each other ; but when their directions 

 are oblique the forces applied to them require to be modified accordingly. 

 Thus, if two threads be attached to a weight, and passed over two pullies 

 fixed at a 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 the 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 deter- 

 mine 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 obliquely round the axis, it will require, in order to pre- 

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

 * Ph.Tr. 1752, xlvii. 404. 



