Maximum Effect of Machines, 277 



2vwdiD 3w 2 dw = 0; 



whence 2 v = 3 w, and w = f v. Substituting this value in 

 equations (11), (i), we obtain 



or 



also 



that is, *fte work done is a maximum when the agent moves with one 

 third part of the greatest velocity of which he is capable, and when 

 the weight or load is of the greatest which hz is able to put in mo- 

 tion during the whole time he is supposed to act. 



395. Having thus considered the maximum effect of living 

 agents, we shall proceed to the subject of machines, and shall 

 take the case of a wheel and axle, as almost all other machines 

 may be reduced to this. 



The powers by which a machine is put in motion, and by 

 which that motion is kept up, are called first movers, or moving 

 powers, or more familiarly, mechanical agents ; and when various 

 moving powers are applied to the same machine, the resultant 

 of them, or the equivalent force, is called the moving force. 



The first movers of machinery, are, the force of men and that 

 of other animals, the force of steam, the force of wind, the force 

 of moving water, the weight of water, the reaction of water, the 

 descent of a weight, the elasticity of a spring, &c. If a machine 

 be driven by two powers acting in two different directions, we 

 must then find their resultant, and consider the machine as driv- 

 en by the resulting force. 



The powers which oppose the production of motion in a ma- 

 chine, and its continuance, are called resistances ; and the resul- 

 tant of all the resisting forces is called the resistance. 



The work to be performed is, in general, the principal resist- 

 ance to be overcome 5 but, in addition to this, we must consider 



