CHAMBERS'S INFORMATION FOR THE PEOPLE. 



Fig. 4- 



upon it ; but if it is already in motion in one 

 direction, and a force then comes to act upon it 

 in another direction, it is not so clear what course 

 it will take. To determine the path or line in 

 which a body will move when thus acted upon by 

 more forces than one, is one of the fundamental 

 problems of the science of mechanics. It is 

 usually treated under the title of the 



Composition and Resolution of Motion. 



Let the ball, B, be moving along the line AC 

 with a velocity that would carry it from B to C in 



two seconds, and 

 when at B let it 

 receive a blow that 

 would carry it from 

 B to E in the same 

 time ; the question 

 is : How will the 

 ballnowmove? This 

 is best understood 

 by supposing it placed, not on a plane surface, but 

 in a groove in the upper side of a movable bar 

 lying on a table. The ball being then set rolling 

 at the same rate as before along a groove in the 

 bar AC, let the bar be made at the same time to 

 slide across the table, keeping parallel to itself, 

 and carrying the ball along with it, so as to arrive 

 at the position ED in two seconds. The common 

 motion of the bar and the ball will not in any way 

 interfere with the motion of the ball in the groove, 

 any more than the common motion of a ship and 

 a man on board of it interferes with the man 

 in walking across the deck. The ball will be at 

 the end of the groove at the end of the two 

 seconds, just as if the bar had been at rest ; it 

 will, therefore, as a result of the two movements, 

 be found at the point D. 



If the position of the ball on the table is observed 

 at the intermediate points, it will be found to 

 describe a straight line from B to D ; for since 

 we have supposed both motions uniform, the bar 

 will, at the end of the first second, be in the posi- 

 tion gf, midway between BC and ED, and the 

 ball will at the same instant be half-way from g to 

 fj at k ; and it can be proved that k is in a straight 

 line between B and D. The same could be shewn 

 as to any intermediate stage. When both motions 

 are not uniform, the body moves in a curve, as 

 will be seen in speaking of projectiles. 



The movable groove is introduced to make the 

 effect of two movements conjoined more readily 

 conceived ; to shew palpably, as it were, that a 

 body may be moving in two directions at one and 

 the same time. But if it receive the second 

 impulse by a blow while rolling freely on the table, 

 it will still arrive at D by the same path. 



In any case, then, when two impulses act upon 

 a body, if we draw two straight lines, AB and AC, 

 in the directions of the two impulses, and make 

 the lengths AD and AE in proportion to the 



velocities that the 

 forces would give 

 to the body if act- 

 ing separately ; then 

 if we draw EF and 

 DF parallel to AD 

 and AE, and join 

 AF, this line, which 

 is called the diag- 

 onal, gives the direction that the body will move 



198 



Fig- 5- 



in, and also its velocity, 

 represents both the 

 velocities and the im- 

 pulsive forces that 

 produce them, and 

 is called the paral- 

 lelogram of -veloci- 

 ties, or the parallelo- 

 gram of forces. AD 



A figure thus formed 



Fig. 6. 



and AE are called the components, and AF the 

 resultant. 



In figs. 4 and 5, the forces are represented as 

 acting at right angles to one another ; but the 

 angle may vary, as in figs. 6 and 7, and the 

 learner should observe the effect on the resultants 

 as he draws paral- 

 lelograms with angles 

 still narrower or still 

 wider. 



We arrive at a 

 similar result if, in- 

 stead of motions, we 

 consider a set of 



Fig- 7- 



forces acting against one another so as to prevent 

 motion. When forces thus balance one another, 

 they are said to be in equilibrium; and the in- 

 vestigation of such cases forms the part of 

 Mechanics called Statics (from a Greek word 

 signifying 'to stand '), while the consideration of 

 force producing motion belongs to Dynamics 

 (from the Greek word for ' power ') 



Two strings fastened to the ring R, and drawn 

 in opposite directions 



by equal forces, F and F R F' 



F', will keep the ring 

 at rest, and the forces Fig. 8. 



are then in equilib- 

 rium. Now, it is evident that for one of the two 

 forces we could substitute two other forces, as in 

 fig. 9, pulling in the directions R/, R/', which, if 



Fig. 9. 



properly adjusted, would still keep the ring at rest 

 The effect of the two new forces, /and /', is thus 

 equal to the effect of the one force, F', and the 

 force F' is said to be resolved or decomposed into 

 the two, /and/'. 



If the two new forces are equal, it is self-evident 

 that they must pull at equal angles to the direc- 

 tion of the original force ; if they are unequal, that 

 the greater must be more nearly in that direction 

 than the other, as is represented in the figure. 

 The exact proportion of the two to each other and 

 to the one original force, may be determined thus : 

 Supposing that F' was a force of six pounds, set 

 off a length of six parts from R to a, and then 

 draw ab, ac parallel to R/ and Rf. We have 

 then a parallelogram of forces. Re represents the 

 magnitude of the force / Rl> that of the force /', 

 and Ra is the resultant, and represents the 

 amount of their combined effect in the direction 

 of RF'. The truth of this may be proved both 

 by mathematical demonstration and by actual 



