











may say 



.thout dotormining tho 

 t > take it on 



nearly, tliat in, seven 

 i.f a hundred of ono grain. 



. :i avoinln; 



: by 7'35, wo Bholl havo tho number of 

 ii we shall call tho ihjiiamical 

 .ml \M i^'M is equal. Tho divinion gives 

 .u-lj- I"!" t: thus we learn how we may 



pass fr or from pounds to these 



: may bo summed u\> in tho following table : 

 785 Grains make nearly oue Dynamical Unit. 

 892 Dyiunnii:il I one Pound. 



111! Pounds iniiko one Ilmidrou-weiyht. 

 20 Hundreds make ouo Tuu. 



- A\ lion a single force is up]>li<il 



to any point of a body, if tho latter be free, motion will 



ensue, and tho question belongs to . If it bo not free, 



but fastened in any way to fixed objects, tho force will bo 



communicated through its substance to tho p .port or 



connection, which will resist, and by resisting cause the body to 



sustain strain. For example, suppose a beam of wood is fixed 



at one point, round which, as on a pivot, it can turn in any 



direction, and that a force is . it at soino other point. 



iear that this foroo will pull tho beam round towards 



> far as it can go, that is. until the- line of direction of 



tho force pa i point. Then this point will 



[uilibriiun will bo produced. Tho case thus becomes 



ono of two forces namely, that applied and tho resistance pro-. 



dncod ; and wo see thus that a single force can never in 



bo tho subject of study, without involving tho consideration of 



: TCCS which it calls into existence. A. statical problem 



must bo concerned about at least two forces. 



If two forces bo applied to a point in the same direction, we 

 assume in Mechanics, as a self-evident truth, tho result of 

 experience, that their joint effect is tho same as that which 

 would be produced by a single force equal to their sum. If two 

 men of unequal strength pull on a rope against another man 

 stronger than cither, who succeeds in balancing their united 

 strength, wo say, without hesitation, that his force is equal to 

 tho sum of those put forth by the two. When two forces thus 

 act separately at a point, tho single force to which their joint 

 power is equal is called tho "resultant" of those forces. We 

 therefore say, if two forces act on a point in tho sa'mo direction, 

 their resultant is tho sum of these forces. . If three act on it, 

 since two of them are equivalent to ono equal to their sum, this 

 one with tho third must bo equivalent to a single force equal to 

 tho sum of tho throe. And so on, as to more than three, wo 

 may lay it down as a general rule that - 



The resultant of any number of forces acting on a point in 

 ..<e direction, is a single force equal to the sum of tho 

 separate forces. 



When two forces act in opposite directions on a point, for tho 

 same reason as in the former case. tha,t tho resultant 



is the difference of tho two. And this Ic *ds us to the most 

 general case that can occur of such forces namely, that in 

 which any number of them are applied to a body along the 

 "me, some in ono direction and others in tho opposite 

 direction. To determine tho resultant of all, it is evident that 

 it is sufficient to talro tho separate resultants of tho opposing 

 sets, then tako tho difference of tl: nit this 



difference will bo tho required resultant of oil, and its direction 

 that of th'o greater of tho two separate resultants. Hence tho 

 following rule : 



If any number of for >d to a body along the snme 



line, their resultant is {'. ;ims of those 



which act in tho opposite direction, and its direction, is the same 

 as that of the greater sum. 



For example, if fifteen men pnll on a rope against cloven, 

 and drag them a] !, tho resultant of the tv.< 



forco* applied to the rope along it* length i* the 



(1 power* of the fifteen and of the Uvoa, 



Htrength of each man, uud t* 



that in which the fifteen poll. 



o now that two force* only are employed, and that 



'. opporiU direction*; what will t>e th 



result? They will balance, or bo in equilibrium. Now it i some- 



body to which two rach force* are applied 



ana condition as if no force had 



.", strictly . Mune 



11 so far c- ,* it concerned, bat not otherwise. 



.he same condition an to procure or utrain. Th* 

 .t one moment ia lying stretched on the ground, i* 

 not in the name < 'von in a few minute* before, when 



two strong men wore pulling at opposite end* of it with balanced 

 strength. In the latter caw it U trained along it* whol-j 

 length every thread on the stretch, ready to map. It* condi- 

 tion is very different on the two occasions different in every 

 circumstance, except that of there being no motion. So, sJno, 

 if two equal and opposite pressure* are applied to a round ball, 

 it will bo an equilibrium, bat tho condition of its tubttanre will 

 be changed. 'us will be pressed toward* one another 



; and, if it be made of soft or elastic material, it* form 

 will be altered by tho fattening effect of the opposing forces. 

 And this is trne, whatever bo the magnitude of the baJL It 

 may bo as small as we please, even so small as an atom, or 

 what is called a " material particle," and yet there will be this 

 internal compression or straining. Thus we see that even the 

 " material particle," acted on by two equal and opposite forces, 

 cannot be said to be in the same condition before and after their 

 application. 



The case of equal and opposite forces presents some other 

 points of interest, which may well occupy your attention in this 

 lesson. Suppose, for example, two men pull against each other 

 with equal strength at the opposite ends of a rope. What will 

 bo tho strain on the rope? What will be its amount, eon^ 

 that both are pulling? Most persons at first incline to f -.: 

 it is strained by the united strength of both, or by double the 

 strength of either man. Such is not the case; the strain is 

 only equal to the strength of one of tho men. What is tho 

 reason of this ? A moment's reflection makes it c-. 

 Suppose one man only to pull ; the rope follows him, and thero 

 is no strain on it. But tho instant the other seizes his end and 

 pulls, strain begins, caused by bis resistance. If ho gives a 

 strong pull, it is great; if a weak, it is slight. But, to f 

 in another way, suppose the first man leads, pulling with all hi* 

 might, while the other, holding on with less strength, is dragged 

 after. Tho rope is strained in this case also. By how much ? 

 By the less of the two forces. The stronger pnll V> 

 divided into two parts, ono putting both tho rope a- 

 second man in motion, and the other balancing the latter' 

 It is this second portion which strains tho rope, and TT. 

 equal to the strength of the hinder man, while the other, which 

 causes motion, is the difference of the two pnlla or f' 

 pose, lastly, that the two pulls become equal, their dif:' 

 becomes nothing, motion ceases, and the men como to a stand- 

 still. But the strain remains, as before, equal to the ' 

 force, which, being equal to that of the leading man, we can 

 say it is equal to either of tho forces. 



Let us next suppose that for one of the men an iro: 

 fastened on a wall, is substituted, to which ono end of t' 

 is attached. So long as the rope hangs loosely from t!i 

 there is no strain on it. Let the other man now pull at ' 

 end, the rope at once is strained, evidently not by tho wall, but 

 by the man's pull. The wall puts forth no more effort to 

 it than it did before; but simply resists the force commuii 

 to : t through tho rope. It is, in fact, a case of a force n; 

 to the wall through the rope, every point of which may bo con- 

 sidered a point of its application. 



Again, tako two equal weights attached to the end-> 

 cord which passes over a pulley. The strain on tho cord which 

 hangs down at either side is evidently equal to the weight on 

 that side ; and, since tho weights arc equal, the etruins on both 

 sides, and therefore all through the cord, are equal to that 



> bullocks raise water from a pond in a large bucket by 

 a ropo which posses over a pulley, as tho bucket ascend* two 

 forces c.ro tuv. ropo The stronger ; 



