THE LEVER AND WHEELWORK. 



249 



rium, and thereby enables it to sustain the weight. It is necessary to attend 

 to this distinction, to remove the difficulty which may arise from the paradox 

 of a small power sustaining a great weight. 



In a lever of the first kind, the fulcrum F, fig. 1, or axis, sustains the united 

 forces of the power and weight. 



In a lever of the second kind, if the power be supposed to act over a wheel, 

 R, fig. 2, the fulcrum F sustains a pressure equal to the difference between the 

 power and weight, and the axis of the wheel R sustains a pressure equal to 

 twice the power ; so that the total pressures on F and R are equivalent to the 

 united forces of the power and weight. 



In a lever of the third kind similar observations are applicable. The wheel 

 R, fig. 3, sustains a pressure equal to twice the power, and the fulcrum F sus- 

 tains a pressure equal to the difference between the power and weight. 



These facts may be experimentally established by attaching a string to the 

 lever immediately over the fulcrum, and suspending the lever by that string from 

 the arm of a balance. The counterpoising weight, when the fulcrum is re- 

 moved, will, in the first case, be equal to the sum of the weight and power, and 

 in the last two cases equal to their difference. 



We have hitherto omitted the consideration of the effect of the weight of the 

 lever itself. If the centre of gravity of the lever be in the vertical line through 

 the axis, the weight of the instrument will have no other effect than to increase 

 the pressure on the axis by its own amount. But if the centre of gravity be 

 on the same side of the axis with the weight, as at G, it will oppose the effect 

 of the power, a certain part of which must therefore be allowed to support it. 

 To ascertain what part of the power is thus expended, it is to be considered 

 that the moment of the weight of the lever collected at G, is found by multi- 

 plying that weight by the distance G F. The moment of that part of the power 

 which supports this must be equal to it ; therefore, it is only necessary to find 

 how much of the power multiplied by P F will be equal to the weight of the 

 lever multiplied by G F. This is a question in common arithmetic. 



If the centre of gravity of the lever be at a different side of the axis from the 

 weight, as at G', the weight of the instrument will co-operate with the power 

 in sustaining the weight W. To determine what portion of the weight W is 

 thus sustained by the weight of the lever, it is only necessary to find how 

 much of W, multiplied by the distance W F, is equal to the weight of the lever 

 multiplied by G' F. 



In these cases, the pressure on the fulcrum, as already estimated, will always 

 be increased by the weight of the lever. 



The sense in which a small power is said to sustain a great weight, and the 

 manner of accomplishing this, being explained, we shall now consider how the 

 power is applied in moving the weight. Let P W, fig. 4, be the places of the 



Fig. 4. 



power and weight, and F that of the fulcrum, and let the power be depressed 

 to P' while the weight is raised to W. The space P P' evidently bears the 

 same proportion to W W, as the arm P F to W F. Thus, if P F be ten times 

 W F, P P' will be ten times W W. A power of one pound at P, being moved 

 from P to P', will carry a weight of ten pounds from W to W. But in this 

 case it ought not to be said that a lesser weight moves a greater, for it is not 



