SECTION VIII. 

 MECHANICAL PHILOSOPHY. 



CHAPTER I. 

 STATICS. 



MECHANICAL PHILOSOPHY is that branch of Natural 

 Philosophy which investigates the laws that govern the 

 action of force on matter. By the application of the 

 purely mathematical sciences to a few general results, 

 suggested by experiment and universal experience, we 

 demonstrate these laws in their highest degree of generali- 

 sation, and under all the various conditions, in which 

 force can produce an effect on matter. 



Matter may exist in three states the solid, liquid, 



and aeriform. Force is that which either produces, or 



tends to produce, the motion of matter. Force may 



therefore be considered in relation to its effects on these 



onditions of matter. 



When forces produce the rest or equilibrium of the 

 body, or system of bodies to which they are applied, we 

 have the three following distinct subjects : 



1. STATICS, the rest, or equilibrium of solid bolies 

 under the influence of forces. 



2. HYDROSTATICS, the rest, or equilibrium of fluid 

 bodies under the influence of forces. 



3. AEROSTATICS, the rest, or equilibrium of aeriform 

 bodies under the influence of forces. 



When motion is the result of the application of 

 forces to these conditions of matter, we have then these 

 three subjects : 



1. DVNAMICS, the motion of solid bodies produced by 

 the influence of forces. 



2. HYDRODYNAMICS, the motion of fluid bodies pro- 

 duced by the influence of forces. 



3. AERODYNAMICS, or PNEUMATICS, the motion of 

 rm bodies produced by the influence of forces. 



That branch of mechanical philosophy which treats of 

 the rest, or equilibrium of solid bodies, when under the 

 action of any forces, is called Statics. Statics is de- 

 rived from a Greek word, oranrij', the science of weight. 



MATERIAL PARTICLE. The smallest portion into 

 which any solid body can be conceived to be divided by 

 any means whatever, we call a Material Particle. This 

 material particle is an abstract mental conception, alto- 

 gether independent of any theories of the ultimate 

 division of matter, anil does nut therefore correspond 

 with the "atom" of the properties of matter. Tho 

 material particle is a more geometrical point, which wo 

 conceive destitute of every property save one that of 

 ; sot in motion, or brought to rest under the influ- 

 ence of forces which are supposed to act upon it. It is 

 conceived to be destitute of form or sensible magnitude. 



RIGID BODY. A rigid body is a collection or 

 assemblage of a number of material particles, held to- 

 gether in an invariable form, by forces of such intensity, 

 that no conceivable force is supposed to be capable of 

 altering the form of the body, or disturbing the position 

 of any of its particles. 



TJiis rigid body is also a mental abstraction, having 

 no representative in nature. No material solid, with 

 whicli we are acquainted, is perfectly rigid, though the 

 unknown molecular forces, which hold the particles of 

 most solid bodies together, are so great, that for many 

 practical purposes we may regard them, within certain 

 limits, as rigid. The various solid bodies which occur 

 in nature, though differing from one another by many 



VOL. I. 



properties, seem to possess one property in common 

 that of being able to transmit any forces applied to any 

 one of their particles, unimpaired in their intensity, 

 through all the particles of their substance, which are in 

 the same straight line with the direction of the applica- 

 tion of the force. Experiment shows that most solid 

 bodies possess this property more or less ; it is this 

 which distinguishes, in a great measure, solids from 

 fluids, any force applied to a particle of a fluid being 

 conveyed through every particle throughout its substance 

 in every direction. 



This property, which natural solid bodies possess more 

 or less, we shall assume our rigid body to possess per- 

 fectly ; and this will enable us to enunciate a principle 

 upon which the whole science of Statics may be said to 

 depend. 



PRINCIPLE OF THE TRANSMISSION OF 

 FORCE. When a force, acting in combination with 

 others, holds a rigid body in equilibrium, the equilibrium 

 of the body will not be disturbed if we transfer the point 

 of application of the force to any other point whatever 

 in the line in which the force is acting. 



Upon this one assumption, suggested by nature and 

 experiment, together with the abstract idea of the nature 

 of force as capable of producing motion, and the idea 

 already denned of a rigid body, the whole science of 

 Statics can be built up without any further reference to 

 nature or experiment. We must bear in mind, however, 

 when wo apply the conclusions to which the science of 

 Statics leads us, that these conclusions will only hold 

 true, for the solid bodies of nature, so far as they possess 

 the properties of perfect rigidity, and the perfect trans- 

 mission of force. Within these limits we may apply our 

 science to the action of forces on natural bodies with 

 accuracy. 



STATICS AN ABSTRACT SCIENCE. Statics is an 

 abstract mathematical science, and many of its results 

 cannot be directly confirmed by experiment. Thus, one of 

 the simplest propositions, which we shall hereafter prove, 

 is, that if two weights, P and Q (Fig. 1) bo suspended 

 from the extremities of a rigid rod, A B, resting on tho 

 sharp edge of a support at F, the weights P and Q will 

 balance one another, and the rod A B will be in a state 

 of equilibrium, provided A F be as many inches in length 

 as Q is ounces in weight, and F B as many inches in 

 length as P is ounces in weight. This proposition cannot 

 Fig. l. 



bo proved by experiment, since it is only true on the 

 supposition that A B is destitute of weight, and no bar r 



