ADDENDA.] 



MECHANICAL PHILOSOPHY. DYNAMICS. 



733 



ADDENDA. 



[!N the foregoing pages the student has had a full ex- 

 position of the theory of various mechanical arrange- 

 ments, technically termed "powers." It has been 

 thought desirable, however, to give further illustrations 

 of the most commonly used machines ; and accordingly 



i such will be found in the annexed plate, respecting 

 which the following observations may be made. 



Figs. 1, 2, 3, represent the three orders of levers in 

 their proper succession ; the numerals on each lever 



1 and on the weights, and powers of application of force, 

 will materially assist the student in understanding Pro- 

 positions XXIII. and XXIV., as they show the position 

 in which two unequal weights must be placed to neutralise 



I each other's effect. The game observations apply to 

 Fig. 4, which illustrates the bent le<>v,r. Figs. 6 and 6 

 are equally extended illustrations of the balance already 

 described under the head of Levers. Figs. 7 to 10 illustrate 

 various arrangements of the pulley ; and Figs. 11, 12, 

 and 13, refer to the affinity between the inclined plane 

 and the screw. The following is a special description of 

 each figure. 



Fig. 1 . A lever of the first order. A, C, the lever ; 

 D, the fulcrum ; W, the weight ; P, the "power;" A, 



B, distance of weight from fulcrum ; B, C, distance of 

 " iwer" from fulcrum. In this cut, a "power" of one 

 pound balances a weight of twelve pounds. 



r ig. 2. A lever of the second order. A, B, the lever ; 



C, a cord (runs over pulley D), to which is attached the 

 power, P, balancing the weight, W ; E is the fulcrum. 



Fig. 3. A lever of the third order. Here the letters 

 have the same signification as in Fig. 2, except that F is 

 the point at which the power in applied. 



Fig. 4. The bent lever. A, B, the lever ; C, tho 

 axis ; D, a pulley over which runs a cord, E, supporting 

 the power P, which thus balances the weight, W. 



Fit;. 5 is an application of the form of lever as a 

 balance, described at page 721. 



Fig. 6. The Roman balance. A, B, is the lever ; C, 

 the fulcrum ; a, k, an arm and ring by means of which 

 the lever is suspended. The article to be weighed is 

 suspended from the arm e by the hook /. If the lever 

 be inverted, it is then suspended by 6, d, as already ex- 

 plained at page 724. 



Fig. 7 is a simple pulley, A ; over it is stretched the 

 cord B B, to which the "power" and weight P W, in 

 this case equal, are attached. In Fig. 8, the power P is 

 represented by a hand drawing upward the weight W, 

 suspended to the pulley A, B. In Fig. 9, the power P 

 balances the weight W, after the cord has been suc- 

 cessively passed over pulleys A, B, C. The cord, how- 

 ever, is not continuous.* Fig. 10 is a further illustration 

 of the system of pulleys described at page 730. A, D, 

 and B, (', are two sets of pulleys, the lesser pair being 

 smaller than the former. They are suspended at X; the 

 cord stretches necessarily from the power P in the direc- 

 tion e, k, o, u, terminating at s, and balances the weight W. 



Fig. 11 illustrates the inclined plane, of which A, B, 

 is the base ; C, D, the inclination ; E, a descending 

 weight ; and F, G, tho altitude. The theory of the 

 inclined plane has been explained at page 731. 



Fig. 12 shows an inclined plane, A, B, C, which if 

 wrapped round a cylinder, as in Fig. 13, produces a screw 

 whose threads are respectively a, 6, e, d. G is the end 

 of the plane, forming the terminal of the thread. ED.] 



CHAPTER III. 

 DYNAMICS. 



I 



INTRODUCTION. Every body, or material particle, is 

 necessarily in a state of either rest or motion. A body 

 strictly at rest is regarded as acted upon either by no 

 force at all, or else by forces which oppose and neutralise 

 one another. Investigations respecting forces which, 

 acting upon a body or upon a system of bodies, thus 

 keep the whole at rest, belong to tho first division of 

 lanical Philosophy Statics. In this branch of the 

 subject, we investigate the result of the several applied 

 forces, which is pressure or tension, but no movement. In 

 rtie second division, now to be treated of, the result of 

 the applied forces, motion, falls under review : there may 

 be pressure as well, but it is the motion or change of 

 place of the body acted upon, that is the exclusive sub- 

 ject of Dynamics. 



" Of physical causes we know little or nothing : we 

 observe motion or pressure, and we infer force that is, 

 some cause for the phenomena : but it is with the effects 

 or phenomena alone that our observations and reasonings 

 are concerned. 



Ignorant, however, as we are of the essence of force, 

 we cannot be under any doubt that it is the same in 

 kind, when operating in the production of motion, as 

 when operating in the production of pressure ; for 

 whfiii-vcr, ii the latter case, the resistance or obstacle is 

 removed, motion necessarily ensues. But there is one 

 consideration inseparably connected with that of motion, 

 which has no place in statics : it is the consideration of 

 time, an element which necessarily enters into the very 

 idea of motion. 



Nor can we conceive of a force which transmits its 

 influence to a distant body as tho force of magnetism, 

 or the force of gravity as doing so independently of 

 timo. It is inconceivable that some interval does not 

 elnpso, however minute, between the cause and the 

 pffi-ct : the transmission of a force through space must 

 ma A few vcnrs ago, the following question was 



proposed to the author of the present treatise : A beam 

 or bar uniformly strong that is, resisting fracture in 

 every part alike is immovably fixed at one extremity, 

 from which it hangs vertically ; to the other, or lower 

 extremity, is then attached a weight indefinitely great : 

 where will the beam break ? The condition is, that the 

 beam has no tendency to break at one place more than 

 at another, and yet the weight suspended to it is to be 

 immeasurably great. The answer is, that time being 

 required to transmit the force through the particles of 

 the beam, the fracture takes place at the lowest part, 

 the falling weight bringing with it only the lamina of 

 material in immediate contact with it. 



As the dynamical effect of force is motion, and as 



| motion implies space passed through, and the time of 



passage, it is clear that, as in all physical inquiries, 



measuring causes by their effects, the measure of force 



must in some way be compounded of space and time. 



The simplest kind of motion is uniform motion, or 

 that in which the moving body passes through equal 

 spaces in equal intervals of time ; and the simplest path 

 the moving body can describe, is a straight path. We 

 can fully examine motion of this kind without any refer- 

 ence to force at all ; we can take the motion as we find 

 it, without any inquiry as to its origination ; and ascer- 

 tain all we wish to know respecting it. In fact, a body 

 so moving is not, during the motion, acted upon by any 

 force at all. Conceive an isolated body at rest, all other 

 bodies and forces in nature being removed : it is plain 

 that that body will remain at rest, for there is nothing 

 to disturb its condition. In like manner, conceive such 

 isolated body to be moving uniformly in a straight line : 

 it roust continue to move uniformly, for there is nothing 

 to disturb its condition : to suppose a force to act upon 

 it at any point of its path, and yet for tho uniform 

 onward motion to remain tho same, would be to suppose 

 Sec Fig. 129, ante, p. 729. 



