.GENERAL PRINCIPLES 17 



, Instead of s = ^ft 2 , we write s = ^ gt 2 . A body placed on a 

 table exerts pressure by reason of gravity ; a hand that pushes 

 an obstacle exerts pressure, or, rather, effort. It would seem that 

 the idea of force is derived unconsciously from the sensation of 

 muscular effort, whether in the case of traction of pressure, of 

 the extension of a piece of elastic, of the flexion of a stick, in 

 short, of all sorts of deformations. Force and deformation are 

 really cause and effect, and one serves as a measure of the other ; 

 the measurement of forces or dynamometry is founded on the 

 deformation of springs (see Methods, 205). 



The force of gravity exists between the stars in the universe 

 and has received the name of universal attraction or gravitation 

 on the earth. The value of the acceleration g diminishes with 

 altitude, and increases in the opposite direction ; but these 

 variations are of practically no account in the cases we are 

 considering. As for the origin of universal force, there are 

 speculations which favour a theory of electric attraction ; perhaps 

 the attraction called chemical affinity may be referred to the 

 same theory. We shall see elsewhere to what hypothesis the 

 origin of muscular force is attributed ( 345). 



Force is a calculable quantity, a vector ; it possesses sense, 

 direction, and magnitude, besides having a point of application 

 on the body on which it acts. All that has been said on the 

 subject of vectors applies strictly to forces. 



M 

 12. Composition & Resolution of Forces. 



Two forces Fj and F 2 , are composed on the 

 principle of a parallelogram ( 8), and have a 

 resultant R (fig. 29) ; the vectors F l F 2 and 

 R measure the composing and resultant in- 

 tensities. There is an example of that com- 

 position in the tow rope on the bow of a boat, 

 a horse being on either bank and the boat 

 advancing in the direction of the stream. 



The magnitude or intensity of R is easily calculated. In the 



A 

 triangle MCE, CE = F 2 and R 2 = ' + F 2 2 2F X F 2 cos MCE. 



Therefore the angles at C and M are supplementary (making 

 together 180), from which it follows that the positive cosine of one 

 is equal to the negative cosine of the other. 



Thus cos MCE = + cos CMD = + cos F x , F 2 . 

 from which we get finally 



R 2 = F . + F * + 2F!F 2 cos F!, F 2 . 



