INTRODUCTION TO MECHANICS. xxv 



nected with the pulley. But a moveable pulley affords mechanical as- 

 sistance (Jig. 30). The hand which sustains the cask by means of the 

 cord D E going; over the moveable pulley, does it more easily than it 

 it held the cask suspended to a cord without a pulley ; for the fixed 

 hook H, to which one end of the cord is fastened, bearing one half of 

 the weight of the cask, the hand has only the other half to sustain. 

 Now it is evident, that the hook affords the same assistance in 

 raising- as in sustaining the cask, so that the hand will have only one half 

 of the weight to raise. But observe that the velocity of the hand must be 

 '"- 30 double that of the cask ; for in order to raise the latter 

 one inch, the hand must draw the two strings (or rather 

 the two parts D and E into which the string is divided by 

 the pulley) one inch each ; the whole string being 

 shortened two inches, while the cask is raised only one. 

 Thus the advantage of a moveable pulley consists in 

 dividing the difficulty ; twice the length of string it is 

 true must be drawn, but only half the strengh is required 

 which would be necessary to raise the weight without such 

 assistance ; so that the difficulty is overcome in the same 

 manner as it would be by dividing the weight into two 

 equal parts, and raising them successively. The pulley, 

 therefore, acts on the same principle as the lever, the de- 

 ficiency of strength of the power being compensated by 

 its superior velocity ; and it is on this principle that all 

 mechanical power is founded. In the fixed pulley (Jig. 

 29) the line A C may be considered as a lever, and B the 

 fulcrum ; then the two arms A B and B C being equal, the lever will 

 afford no aid as a mechanical power ; since the power must be equal to 

 the weight in order to balance it, and superior to the weight in order to 

 raise it. In the moveable pulley (fig. 30) you must consider the point 

 A as the fulcrum ; A B or half the diameter of the pulley as the shortest 

 arm ; and A C or the whole diameter as the longest arm. It may, 

 perhaps, be objected to pulleys that a longer time is required to raise a 

 weight with their aid than without it : that is true, for it is a fundamental 

 law in mechanics, that what is gained in power is lost in time : this 

 Fie 31 applies not only to the pulley but to the lever and all the 

 other mechanical powers. It would be wrong, however, to 

 suppose that the loss was equivalent to the gain, and that 

 we derived no advantage from the mechanical powers ; for 

 since we are incapable of augmenting our strength, that 

 science is of wonderful utility which enables us to reduce the 

 resistance or weight of any body to the level of our strength. 

 This we accomplish, by dividing the resistance of a body 

 into parts which we can successively overcome ; and if it 

 require a sacrifice of time to attain this end, you must be 

 sensible how very advantageously it is exchanged for power. 

 The greater the number of pulleys connected by a string, 

 the more easily the weight is raised, as the difficulty is 

 divided amongst the number of strings, or rather of parts 

 into which the string is divided by the pulleys. Several 

 pulleys thus connected form what is called a system, or 

 tackle of pulleys (fig. 31). You may have seen them sus- 

 pended from cranes to raise goods into warehouses, and in 

 ships to draw up the sails. Here both the advantages of 

 an increase of power and a change of direction are united j 



