MECHANICS. 



[Lesson V. 



In calculating the action of any compound system of levers, it does not affect the 

 principles of calculation if some of the levers are of the first kind, and some of any 

 other. The rule is, to " multiply the weight on any lever by its distance from the 

 fulcrum, and multiply the power by its distance from the same point ; if the products 

 are equal, then the weight and power will balance each other." If we wish to calculate 

 the effect of the system given in Fig. 17, we must multiply the length of the long arm 

 by the power, and multiply the short arm by the weight or resistance offered. 



QUESTIONS. 



ttb. T. What is a compound lever ? 



P. It is a lever composed of several 

 simple levers connected together, so as to 

 act one upon the other. 



57. T. How can the force of a com- 

 pound lever be regulated ? 



P. Very easily ; because, as each lever 

 acts with a power equal to the pressure on 

 it of the next lever between it and the 

 power, the force may be increased or de- 

 creased by the kind of levers employed, 

 and their number. 



58. T. How can you determine the 

 advantages of a compound lever formed of 

 any number of levers ? 



P. We must, first of all, call the arms 

 of the various levers next to the power, 

 arms of power ; and those next to the 

 weight, arms of weight; then we shall have 

 prepared the way. Now, if the length of 

 the arms of power and the power itself be 

 successively multiplied together, we shall 

 obtain a product equal to the continued 

 product of the arms of weight and the 

 weight, when the power and weight are in 

 equilibrium. 



59. T. What do you mean by the 

 power of a machine ? 



P. It is the number which represents 

 the proportion of the weight to the equili- 

 brating power of any machine. Thus, if 

 one pound sustains a weight of six pounds, 

 the power of the machine is six. Again, 

 if a power of three pounds supports a 

 weight of eighteen pounds, the power of 

 the machine is six, because 3 is contained 

 in 18 only six times. 



60. T. There is one important thing 

 that we should consider in all our experi- 

 ments with respect to the lever the weight 

 of the lever itself. Can you tell me if this 

 makes any great difference in its effect? 



P. If the centre of gravity of the lever 

 be in the vertical line through the axis, its 

 weight will only increase the pressure on 

 the axis by its own amount, without 

 causing any other effect. 



61. T. Suppose that the centre of gra- 

 vity of the lever be on the same side of 

 the axis as the weight, what will be the 

 effect then? 



P. It will oppose the effect of the 

 power ; and, therefore, a certain amount of 

 power must be allowed for its support. 



62. T. How can this amount of power 

 be estimated ? 



P. By common calculation. First, 

 you find the moment of the weight of the 

 lever collected at its centre of gravity, 

 which is done by multiplying that weight 

 by the distance from the centre of gravity 

 to the fulcrum ; therefore, we know that 

 the moment of that part of the power 

 which supports it, because it must be 

 equal to it. Now we have only to find 

 out how much of the power, multiplied by 

 double the distance from its centre of 

 gravity to the fulcrum, will be equal to the 

 weight of the lever multiplied by the 

 distance from the fulcrum to the centre of 

 gravity. 



63. T. Suppose that the centre of gra- 

 vity of the lever be at a different side of 

 the axis from the weight, what will be the 

 effect then ? 



P. The weight of the lever will assist 

 the power in sustaining the weight. 



64. T. How can you determine the 

 amount of the weight thus sustained ? 



P. Find out how much of the weight, 

 multiplied by the distance from the weight 

 to the fulcrum, is equal to the weight of 

 the lever multiplied by the distance from 

 the centre of gravity to the fulcrum. 



