MECHANICS. 



necessaiy that means should be con- 

 trived of modifying them so as to suit 

 them to our wants. It may so happen 

 that we have at our command a natural 

 force of variable intensity, when it is 

 necessary to apply to the work which 

 we design to execute one of a perfectly 

 uniform intensity. We are, therefore, 

 compelled to contrive some means by 

 which, in transmitting the force from the 

 natural mechanical agent, whatever it 

 be, to the working point, it may be so 

 modified as to be rendered uniform in 

 its action. Again, the natural force may 

 act constantly in one direction, as for 

 example, a running stream, or a perpen- 

 dicular fall of water, or a current of air, 

 when it may be required that the force 

 on the working point should be alternate 

 or reciprocating, as for example, that 

 which is necessary to work the piston 

 of a common pump. In such cases, 

 therefore, some apparatus must be inter- 

 posed between the natural agent and 

 the working point, which is capable of 

 converting the one species of motion 

 into the other. Such a contrivance is 

 called a machine, and the natural force 

 which it is designed to modify is called 

 its first mover; lhat part of the machine 

 at which the required modification is 

 produced, being generally called the 

 working point. 



In that part of Mechanics which is 

 confined to the consideration of the na- 

 ture and principles of machinery, there 

 are two objects intimately related each 

 to the other, and each of which strongly 

 demands our attention ; first, the natural 

 mechanical agents or first movers ; se- 

 condly, machines, or the means whereby 

 these powers are modified and rendered 

 applicable to our purposes. We propose 

 in this first treatise to confine the 

 attention of the reader to the explana- 

 tion of the nature and laws of those 

 powers in nature which furnish first 

 movers, and to the properties of motion 

 and force in general. In conformity 

 with this method, we shall devote the 

 second treatise to the elements of ma- 

 chinery. 



CHAPTER II. On the composition and 

 resolution of Motion and Force. 



(5.) IF two equal forces act upon the 

 same point of a body, in directions im- 

 mediately opposite, they will keep that 

 body at rest. Such forces, then, are the 

 most simple example of equilibrium, and 

 the truth of this principle is self-evident. 



Thus, if to a point P two threads be at- 

 tached, and that two wheels C D, turn- 

 ing on fixed centres, and having grooves 

 on their edges, be so placed that when 

 the strings are passed over them the 

 parts P C and P D shall be in the same 

 straight line, equal weights A and B 

 suspended from the strings will draw 

 the point P equally in the opposite 

 directions P C and P D, and they will 

 thus evidently neutralise each other, and 

 the body P will be in equilibrium. 



(6.) But now let us suppose that the 

 weight B is greater than the weight A. 

 In that case the point P will be drawn 

 in the direction P D with a greater force 

 than that which draws it in the opposite 

 direction P C, and it will evidently have 

 a tendency to move in the direction P D. 

 But what tendency ? To what amount, 

 or, in other words, with what force is P 

 pulled in the direction PD? This is 

 easily determined. Suppose that the 

 weight B is divided into two parts, one 

 of which is equal to A ; the other part 

 will be evidently equal to the difference 

 of the weights A and B, or to the excess 

 of the weight B above the weight A. 

 Call this excess E, and let the apparatus 

 assume the form/g-. 2. Now, it appears 



by (5.), that the weight A acting in the 

 direction P C, exactly balances the 

 weight A acting in the direction P D ; 

 so that the combined effect of these 

 weights is nothing. The consequence 

 is, that the point P is pulled in the 

 direction P D only by the force E, or 

 the excess of the greater weight B 

 above the lesser weight A. 

 Hence we may, in general, infer, that 



