ELEMENTARY PRINCIPLES OP MECHANICS. 



421 





to the ground with that velocity; thus incurring an almost certain injury 

 to avoid one remotely contingent. 



The force, momentum, or quantity of motion in a body is measured 

 by the velocity, multiplied into the quantity of matter. A cannon-ball, 

 for example, may be rolled so gently against a man's leg, as not even to 

 bruise it; but if it be projected by means of gunpowder, it may mow 

 down a dense column of men, or penetrate the most solid substance. 

 If a man be running, and strike against another who is standing, a 

 certain shock is received by both ; but if both be running in opposite 

 directions with the same velocity, the shock will be doubled. 



The subject of the direction of forces applies to most cases of mus- 

 cular movement. Where only one force acts upon a body, the body 

 proceeds in the direction in which the force is exerted, as in the case 

 of a bullet fired from a gun ; but if two or more forces act upon it at 

 the same time, the direction of its motion will be a middle course be- 

 tween the direction of the separate forces. This course is called the 

 resulting direction, that is, resulting from the 

 composition of the forces. Let us suppose two Fig. 171. 



forces a T and b T in Fig. 171, acting upon 

 the body T, which may be regarded as the ten- 

 don of a muscle, and the two forces as the 

 power developed by muscular fibres holding 

 the same situation; the result will be the same, 

 whether they act together or in succession. 

 For example, if the force a T is sufficient to 

 draw T to a, and immediately afterwards the 

 force b T be exerted upon it, the tendon will 

 be at c, the place towards which it would be 

 drawn by the simultaneous action of the two Composition of Forces. 

 forces or fibres. If, therefore, we complete 



the figure, by drawing a c equal and parallel to T b, and c b equal and 

 parallel to a T, we have the parallelogram of forces, as it is called, of 

 which the diagonal shows the resultant of the forces, 

 and the course of the body on which they act. In 

 the case, assumed in Fig. 171, the forces are equal. 

 If not, the parallelogram may result as in Fig. 173; 

 in which T c will, again, be the resultant of the 

 forces a T and T b, or we may have the arrangement 

 in Fig. 172. 



By these parallelograms, we are enabled, also, to 

 resolve the resultant into its component forces. 

 Suppose, for example, we desire to know the quan- 

 tity of force in the resultant, T c, Fig. 171, which is 

 capable of acting in the directions T a and T b; it 

 is only necessary to draw, from the point c, c a 

 parallel to T b, and c b parallel to T a ; and the lines Composition of Forces. 

 T a and T b, cut off by these, will be the forces into 

 which it may be resolved. The same applies to Figs. 172 and 173, and 

 to every other of the kind. 



Friction is the resistance necessary to be overcome in making one 



